Subgroups — C₆₇×#61072 #30740323

Order 17152.

2944 conjugacy classes of subgroups.

The subgroup lattice has 1476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#576×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3282	C₂	1	2	yes	maximal, complemented
6	D₄×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3273	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3268	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3265	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3264	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3264	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#447×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#576×C₆₇	—	2	8	no	—
29	C₂×AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
30	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
34	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
38	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
39	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
42	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
43	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
44	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
47	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#550×C₆₇	C₂²	1	2	yes	complemented
50	#548×C₆₇	C₂²	1	2	yes	complemented
51	#546×C₆₇	—	2	2	no	—
52	#546×C₆₇	—	2	1	no	—
53	#546×C₆₇	—	2	1	no	—
54	#546×C₆₇	C₂²	1	2	yes	complemented
55	#546×C₆₇	C₂²	1	2	yes	complemented
56	#546×C₆₇	C₂²	1	2	yes	complemented
57	D₄²×C₆₇	—	2	1	no	—
58	D₄²×C₆₇	—	2	1	no	—
59	D₄²×C₆₇	—	2	2	no	—
60	D₄²×C₆₇	C₂²	1	2	yes	complemented
61	D₄²×C₆₇	C₂²	1	2	yes	complemented
62	D₄²×C₆₇	C₂²	1	2	yes	complemented
63	#537×C₆₇	—	2	1	no	—
64	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#535×C₆₇	—	2	1	no	—
66	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#534×C₆₇	—	2	2	no	—
70	#525×C₆₇	—	2	1	no	—
71	#525×C₆₇	C₂²	1	1	yes	characteristic
72	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	C₂×#121×C₆₇	—	2	1	no	—
74	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₂×#120×C₆₇	—	2	2	no	—
76	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#518×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#496×C₆₇	C₂²	1	2	yes	complemented
79	#496×C₆₇	C₂²	1	2	yes	complemented
80	#495×C₆₇	C₂²	1	2	yes	complemented
81	#493×C₆₇	C₂²	1	2	yes	complemented
82	#469×C₆₇	C₂²	1	2	yes	complemented
83	#469×C₆₇	C₂²	1	2	yes	complemented
84	#468×C₆₇	C₂²	1	2	yes	complemented
85	#468×C₆₇	C₂²	1	2	yes	complemented
86	#466×C₆₇	C₂²	1	2	yes	complemented
87	#466×C₆₇	C₂²	1	2	yes	complemented
88	#465×C₆₇	C₂²	1	2	yes	complemented
89	#465×C₆₇	C₂²	1	2	yes	complemented
90	#464×C₆₇	C₂²	1	2	yes	complemented
91	#463×C₆₇	C₂²	1	2	yes	complemented
92	#463×C₆₇	C₂²	1	2	yes	complemented
93	#463×C₆₇	C₂²	1	2	yes	complemented
94	#460×C₆₇	C₂²	1	2	yes	complemented
95	#459×C₆₇	C₂²	1	2	yes	complemented
96	#459×C₆₇	C₂²	1	2	yes	complemented
97	#459×C₆₇	C₂²	1	2	yes	complemented
98	#452×C₆₇	C₂²	1	2	yes	complemented
99	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#451×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#450×C₆₇	C₂²	1	2	yes	complemented
103	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#449×C₆₇	C₂²	1	2	yes	complemented
105	#449×C₆₇	C₂²	1	2	yes	complemented
106	#449×C₆₇	C₂²	1	2	yes	complemented
107	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#448×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#447×C₆₇	C₂²	1	2	yes	complemented
111	#447×C₆₇	C₂²	1	2	yes	complemented
112	#447×C₆₇	C₂²	1	2	yes	complemented
113	#447×C₆₇	C₂²	1	2	yes	complemented
114	#447×C₆₇	C₂²	1	2	yes	complemented
115	#447×C₆₇	C₂²	1	2	yes	complemented
116	#447×C₆₇	C₂²	1	2	yes	complemented
117	#447×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#442×C₆₇	C₂²	1	2	yes	complemented
119	#440×C₆₇	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
121	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
122	#436×C₆₇	C₂²	1	2	yes	complemented
123	#435×C₆₇	C₂²	1	2	yes	complemented
124	#435×C₆₇	C₂²	1	2	yes	complemented
125	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₂⁵×C₆₇	—	2	1	no	—
138	H(5,𝔽₂)×C₆₇	—	2	4	no	—
139	H(5,𝔽₂)×C₆₇	—	2	4	no	—
140	H(5,𝔽₂)×C₆₇	—	4	2	no	—
141	H(5,𝔽₂)×C₆₇	—	4	2	no	—
142	C₂×#41×C₆₇	—	2	1	no	—
143	C₂×#41×C₆₇	—	2	1	no	—
144	C₂×#41×C₆₇	—	2	1	no	—
145	C₂×#41×C₆₇	—	2	1	no	—
146	C₂×#41×C₆₇	—	2	4	no	—
147	C₂×#41×C₆₇	—	4	2	no	—
148	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×#41×C₆₇	C₂³	1	2	yes	—
151	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
156	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
157	C₂²×D₄×C₆₇	—	2	4	no	—
158	C₂²×D₄×C₆₇	—	2	1	no	—
159	C₂²×D₄×C₆₇	—	2	1	no	—
160	C₂²×D₄×C₆₇	—	2	2	no	—
161	C₂²×D₄×C₆₇	—	2	1	no	—
162	C₂²×D₄×C₆₇	—	2	1	no	—
163	C₂²×D₄×C₆₇	—	2	2	no	—
164	C₂²×D₄×C₆₇	—	2	2	no	—
165	C₂²×D₄×C₆₇	—	2	2	no	—
166	C₂²×D₄×C₆₇	—	2	2	no	—
167	C₂²×D₄×C₆₇	—	2	1	no	—
168	C₂²×D₄×C₆₇	—	2	1	no	—
169	C₂²×D₄×C₆₇	—	2	1	no	—
170	C₂²×D₄×C₆₇	—	4	2	no	—
171	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
175	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
176	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
177	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂²×D₄×C₆₇	C₂³	1	2	yes	complemented
179	C₂³×C₄×C₆₇	—	2	1	no	—
180	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
181	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
182	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
183	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
184	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
185	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
186	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
187	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
188	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
189	AGL(1,ℤ/8)×C₆₇	D₄	1	8	yes	complemented
190	#135×C₆₇	—	2	4	no	—
191	#135×C₆₇	—	2	8	no	—
192	#135×C₆₇	—	4	2	no	—
193	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
194	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
195	C₂×SD₁₆×C₆₇	—	2	8	no	—
196	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
197	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
198	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
199	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
200	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
201	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
202	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
203	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
204	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
205	C₂×D₈×C₆₇	—	2	4	no	—
206	C₂×D₈×C₆₇	—	2	8	no	—
207	C₂×D₈×C₆₇	—	2	8	no	—
208	C₂×D₈×C₆₇	—	4	2	no	—
209	C₂×D₈×C₆₇	C₂³	1	2	yes	—
210	C₂×D₈×C₆₇	C₂³	1	2	yes	—
211	C₂×D₈×C₆₇	C₂³	1	2	yes	—
212	C₂×D₈×C₆₇	C₂³	1	2	yes	—
213	C₂×D₈×C₆₇	C₂³	1	2	yes	—
214	C₂×D₈×C₆₇	C₂³	1	2	yes	—
215	C₂×D₈×C₆₇	C₂³	1	2	yes	—
216	C₂×D₈×C₆₇	C₂³	1	2	yes	—
217	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
218	C₂×D₈×C₆₇	C₂³	1	2	yes	complemented
219	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
220	#131×C₆₇	—	2	4	no	—
221	C₂×M₁₆×C₆₇	—	2	4	no	—
222	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
223	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
226	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
227	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
230	#127×C₆₇	—	2	2	no	—
231	#127×C₆₇	—	2	1	no	—
232	#127×C₆₇	C₂³	1	2	yes	—
233	#127×C₆₇	C₂³	1	2	yes	complemented
234	#124×C₆₇	—	2	1	no	—
235	#124×C₆₇	—	2	2	no	—
236	#124×C₆₇	C₂³	1	2	yes	—
237	#124×C₆₇	C₂³	1	2	yes	complemented
238	#123×C₆₇	—	2	1	no	—
239	#123×C₆₇	—	2	2	no	—
240	#123×C₆₇	—	2	2	no	—
241	#123×C₆₇	—	2	2	no	—
242	#123×C₆₇	D₄	1	2	yes	—
243	C₂²⋊Q₈×C₆₇	—	2	1	no	—
244	C₂²⋊Q₈×C₆₇	—	2	2	no	—
245	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
246	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
247	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
248	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
249	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
250	#121×C₆₇	—	2	1	no	—
251	#121×C₆₇	—	2	2	no	—
252	#121×C₆₇	—	2	2	no	—
253	#121×C₆₇	—	2	1	no	—
254	#121×C₆₇	—	2	1	no	—
255	#121×C₆₇	—	2	1	no	—
256	#121×C₆₇	—	2	1	no	—
257	#121×C₆₇	—	2	2	no	—
258	#121×C₆₇	—	2	2	no	—
259	#121×C₆₇	—	2	1	no	—
260	#121×C₆₇	—	2	1	no	—
261	#121×C₆₇	—	2	2	no	—
262	#121×C₆₇	—	2	2	no	—
263	#121×C₆₇	—	2	2	no	—
264	#121×C₆₇	—	2	2	no	—
265	#121×C₆₇	—	2	2	no	—
266	#121×C₆₇	—	2	2	no	—
267	#121×C₆₇	D₄	1	1	yes	characteristic
268	#121×C₆₇	D₄	1	1	yes	characteristic
269	#121×C₆₇	C₂³	1	1	yes	characteristic
270	#121×C₆₇	C₂³	1	1	yes	characteristic
271	#121×C₆₇	C₂³	1	2	yes	—
272	#121×C₆₇	C₂³	1	2	yes	—
273	#121×C₆₇	C₂³	1	2	yes	—
274	#121×C₆₇	C₂³	1	2	yes	—
275	#121×C₆₇	C₂³	1	2	yes	complemented
276	#120×C₆₇	—	2	1	no	—
277	#120×C₆₇	—	2	2	no	—
278	#120×C₆₇	—	2	2	no	—
279	#120×C₆₇	—	2	2	no	—
280	#120×C₆₇	—	2	2	no	—
281	#120×C₆₇	—	2	2	no	—
282	#120×C₆₇	—	2	2	no	—
283	#120×C₆₇	—	2	2	no	—
284	#120×C₆₇	—	2	2	no	—
285	#120×C₆₇	—	2	2	no	—
286	#120×C₆₇	—	2	2	no	—
287	#120×C₆₇	—	2	2	no	—
288	#120×C₆₇	—	2	2	no	—
289	#120×C₆₇	D₄	1	2	yes	—
290	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
291	C₄×D₄×C₆₇	—	2	1	no	—
292	C₄×D₄×C₆₇	—	2	1	no	—
293	C₄×D₄×C₆₇	—	2	1	no	—
294	C₄×D₄×C₆₇	—	2	1	no	—
295	C₄×D₄×C₆₇	—	2	2	no	—
296	C₄×D₄×C₆₇	—	2	2	no	—
297	C₄×D₄×C₆₇	—	2	2	no	—
298	C₄×D₄×C₆₇	C₂³	1	2	yes	—
299	C₄×D₄×C₆₇	C₂³	1	2	yes	—
300	C₄×D₄×C₆₇	C₂³	1	2	yes	—
301	C₄×D₄×C₆₇	C₂³	1	2	yes	—
302	C₄×D₄×C₆₇	C₂³	1	2	yes	complemented
303	#117×C₆₇	—	2	1	no	—
304	#117×C₆₇	C₂³	1	1	yes	characteristic
305	#117×C₆₇	C₂³	1	1	yes	characteristic
306	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
307	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
309	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
310	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
311	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
312	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
313	#107×C₆₇	C₂³	1	2	yes	complemented
314	#106×C₆₇	C₂³	1	2	yes	complemented
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
316	C₄⋊C₈×C₆₇	C₂³	1	2	yes	complemented
317	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
318	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
319	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
320	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
321	#103×C₆₇	C₂³	1	2	yes	complemented
322	#102×C₆₇	C₂³	1	2	yes	—
323	#102×C₆₇	C₂³	1	2	yes	—
324	#102×C₆₇	C₂³	1	2	yes	—
325	#102×C₆₇	C₂³	1	2	yes	—
326	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
327	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
328	#102×C₆₇	C₂³	1	2	yes	complemented
329	#102×C₆₇	C₂³	1	2	yes	complemented
330	#102×C₆₇	C₂³	1	2	yes	complemented
331	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
332	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
333	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
338	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	complemented
339	#97×C₆₇	C₂³	1	2	yes	complemented
340	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
341	C₂⁴×C₆₇	—	2	1	no	—
342	C₂⁴×C₆₇	—	2	2	no	—
343	C₂⁴×C₆₇	—	2	2	no	—
344	C₂⁴×C₆₇	—	2	1	no	—
345	C₂⁴×C₆₇	—	2	1	no	—
346	C₂⁴×C₆₇	—	2	2	no	—
347	C₂⁴×C₆₇	—	2	1	no	—
348	C₂⁴×C₆₇	—	2	2	no	—
349	C₂⁴×C₆₇	—	4	4	no	—
350	C₂⁴×C₆₇	—	8	2	no	—
351	C₂⁴×C₆₇	—	8	2	no	—
352	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
353	#41×C₆₇	—	2	2	no	—
354	#41×C₆₇	—	2	2	no	—
355	#41×C₆₇	—	2	2	no	—
356	#41×C₆₇	—	2	4	no	—
357	#41×C₆₇	—	2	2	no	—
358	#41×C₆₇	—	2	4	no	—
359	#41×C₆₇	—	2	2	no	—
360	#41×C₆₇	—	2	2	no	—
361	#41×C₆₇	—	2	2	no	—
362	#41×C₆₇	—	2	2	no	—
363	#41×C₆₇	—	2	2	no	—
364	#41×C₆₇	—	4	4	no	—
365	#41×C₆₇	—	4	1	no	—
366	#41×C₆₇	—	4	1	no	—
367	#41×C₆₇	—	4	2	no	—
368	#41×C₆₇	—	4	2	no	—
369	#41×C₆₇	—	4	4	no	—
370	#41×C₆₇	—	4	4	no	—
371	#41×C₆₇	—	4	4	no	—
372	#41×C₆₇	C₂×D₄	1	4	yes	complemented
373	C₂×Q₈×C₆₇	—	2	1	no	—
374	C₂×Q₈×C₆₇	—	2	2	no	—
375	C₂×Q₈×C₆₇	—	4	1	no	—
376	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂×D₄×C₆₇	—	2	1	no	—
381	C₂×D₄×C₆₇	—	2	2	no	—
382	C₂×D₄×C₆₇	—	2	4	no	—
383	C₂×D₄×C₆₇	—	2	4	no	—
384	C₂×D₄×C₆₇	—	2	4	no	—
385	C₂×D₄×C₆₇	—	2	4	no	—
386	C₂×D₄×C₆₇	—	2	1	no	—
387	C₂×D₄×C₆₇	—	2	1	no	—
388	C₂×D₄×C₆₇	—	2	2	no	—
389	C₂×D₄×C₆₇	—	2	1	no	—
390	C₂×D₄×C₆₇	—	2	2	no	—
391	C₂×D₄×C₆₇	—	2	1	no	—
392	C₂×D₄×C₆₇	—	2	1	no	—
393	C₂×D₄×C₆₇	—	2	2	no	—
394	C₂×D₄×C₆₇	—	2	1	no	—
395	C₂×D₄×C₆₇	—	2	2	no	—
396	C₂×D₄×C₆₇	—	2	2	no	—
397	C₂×D₄×C₆₇	—	2	2	no	—
398	C₂×D₄×C₆₇	—	2	2	no	—
399	C₂×D₄×C₆₇	—	2	1	no	—
400	C₂×D₄×C₆₇	—	2	2	no	—
401	C₂×D₄×C₆₇	—	2	2	no	—
402	C₂×D₄×C₆₇	—	2	2	no	—
403	C₂×D₄×C₆₇	—	2	1	no	—
404	C₂×D₄×C₆₇	—	2	2	no	—
405	C₂×D₄×C₆₇	—	2	2	no	—
406	C₂×D₄×C₆₇	—	2	2	no	—
407	C₂×D₄×C₆₇	—	2	1	no	—
408	C₂×D₄×C₆₇	—	2	1	no	—
409	C₂×D₄×C₆₇	—	2	2	no	—
410	C₂×D₄×C₆₇	—	2	2	no	—
411	C₂×D₄×C₆₇	—	2	2	no	—
412	C₂×D₄×C₆₇	—	2	2	no	—
413	C₂×D₄×C₆₇	—	2	2	no	—
414	C₂×D₄×C₆₇	—	2	2	no	—
415	C₂×D₄×C₆₇	—	2	2	no	—
416	C₂×D₄×C₆₇	—	4	2	no	—
417	C₂×D₄×C₆₇	—	4	2	no	—
418	C₂×D₄×C₆₇	—	4	1	no	—
419	C₂×D₄×C₆₇	—	4	2	no	—
420	C₂×D₄×C₆₇	—	4	2	no	—
421	C₂×D₄×C₆₇	—	4	4	no	—
422	C₂×D₄×C₆₇	—	4	4	no	—
423	C₂×D₄×C₆₇	—	4	4	no	—
424	C₂×D₄×C₆₇	—	4	4	no	—
425	C₂×D₄×C₆₇	—	4	8	no	—
426	C₂×D₄×C₆₇	—	4	4	no	—
427	C₂×D₄×C₆₇	—	4	4	no	—
428	C₂×D₄×C₆₇	—	4	8	no	—
429	C₂×D₄×C₆₇	—	8	4	no	—
430	C₂×D₄×C₆₇	—	8	4	no	—
431	C₂×D₄×C₆₇	—	8	2	no	—
432	C₂×D₄×C₆₇	—	8	4	no	—
433	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
435	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
436	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
437	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
438	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
439	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
440	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
443	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₆₇	—	2	1	no	—
445	C₂²×C₄×C₆₇	—	2	2	no	—
446	C₂²×C₄×C₆₇	—	2	2	no	—
447	C₂²×C₄×C₆₇	—	2	1	no	—
448	C₂²×C₄×C₆₇	—	2	1	no	—
449	C₂²×C₄×C₆₇	—	2	1	no	—
450	C₂²×C₄×C₆₇	—	2	2	no	—
451	C₂²×C₄×C₆₇	—	2	1	no	—
452	C₂²×C₄×C₆₇	—	2	1	no	—
453	C₂²×C₄×C₆₇	—	2	2	no	—
454	C₂²×C₄×C₆₇	—	2	1	no	—
455	C₂²×C₄×C₆₇	—	2	2	no	—
456	C₂²×C₄×C₆₇	—	2	2	no	—
457	C₂²×C₄×C₆₇	—	2	2	no	—
458	C₂²×C₄×C₆₇	—	4	4	no	—
459	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
460	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
461	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
462	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
465	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
466	Q₁₆×C₆₇	—	2	2	no	—
467	Q₁₆×C₆₇	—	4	1	no	—
468	SD₁₆×C₆₇	—	2	4	no	—
469	SD₁₆×C₆₇	—	2	2	no	—
470	SD₁₆×C₆₇	—	2	4	no	—
471	SD₁₆×C₆₇	—	2	2	no	—
472	SD₁₆×C₆₇	—	2	4	no	—
473	SD₁₆×C₆₇	—	2	4	no	—
474	SD₁₆×C₆₇	—	4	1	no	—
475	SD₁₆×C₆₇	—	4	1	no	—
476	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
477	D₈×C₆₇	—	2	4	no	—
478	D₈×C₆₇	—	2	2	no	—
479	D₈×C₆₇	—	2	4	no	—
480	D₈×C₆₇	—	2	4	no	—
481	D₈×C₆₇	—	2	4	no	—
482	D₈×C₆₇	—	2	4	no	—
483	D₈×C₆₇	—	2	4	no	—
484	D₈×C₆₇	—	4	2	no	—
485	D₈×C₆₇	—	4	2	no	—
486	D₈×C₆₇	—	4	1	no	—
487	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
488	M₁₆×C₆₇	—	2	2	no	—
489	M₁₆×C₆₇	—	2	4	no	—
490	M₁₆×C₆₇	—	2	4	no	—
491	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
492	C₂×C₈×C₆₇	—	2	2	no	—
493	C₂×C₈×C₆₇	—	2	2	no	—
494	C₂×C₈×C₆₇	—	2	4	no	—
495	C₂×C₈×C₆₇	—	2	4	no	—
496	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
497	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
498	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
499	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
500	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
501	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
502	C₄⋊C₄×C₆₇	—	2	1	no	—
503	C₄⋊C₄×C₆₇	—	2	2	no	—
504	C₄⋊C₄×C₆₇	—	2	2	no	—
505	C₄⋊C₄×C₆₇	—	2	1	no	—
506	C₄⋊C₄×C₆₇	—	2	1	no	—
507	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
508	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
509	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
510	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
511	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
512	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
513	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
514	C₂²⋊C₄×C₆₇	—	2	1	no	—
515	C₂²⋊C₄×C₆₇	—	2	1	no	—
516	C₂²⋊C₄×C₆₇	—	2	1	no	—
517	C₂²⋊C₄×C₆₇	—	2	2	no	—
518	C₂²⋊C₄×C₆₇	—	2	2	no	—
519	C₂²⋊C₄×C₆₇	—	2	2	no	—
520	C₂²⋊C₄×C₆₇	—	2	2	no	—
521	C₂²⋊C₄×C₆₇	—	2	2	no	—
522	C₂²⋊C₄×C₆₇	—	2	2	no	—
523	C₂²⋊C₄×C₆₇	—	2	2	no	—
524	C₂²⋊C₄×C₆₇	—	2	2	no	—
525	C₂²⋊C₄×C₆₇	—	2	2	no	—
526	C₂²⋊C₄×C₆₇	—	2	2	no	—
527	C₂²⋊C₄×C₆₇	—	2	2	no	—
528	C₂²⋊C₄×C₆₇	—	2	1	no	—
529	C₂²⋊C₄×C₆₇	—	2	1	no	—
530	C₂²⋊C₄×C₆₇	—	2	2	no	—
531	C₂²⋊C₄×C₆₇	—	2	2	no	—
532	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
533	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
534	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
535	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
536	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
537	C₄²×C₆₇	—	2	2	no	—
538	C₄²×C₆₇	—	2	1	no	—
539	C₄²×C₆₇	C₂⁴	1	2	yes	—
540	C₂³×C₆₇	—	2	2	no	—
541	C₂³×C₆₇	—	2	2	no	—
542	C₂³×C₆₇	—	2	1	no	—
543	C₂³×C₆₇	—	2	2	no	—
544	C₂³×C₆₇	—	2	4	no	—
545	C₂³×C₆₇	—	2	2	no	—
546	C₂³×C₆₇	—	2	2	no	—
547	C₂³×C₆₇	—	2	1	no	—
548	C₂³×C₆₇	—	2	1	no	—
549	C₂³×C₆₇	—	4	1	no	—
550	C₂³×C₆₇	—	4	2	no	—
551	C₂³×C₆₇	—	4	4	no	—
552	C₂³×C₆₇	—	4	4	no	—
553	C₂³×C₆₇	—	4	4	no	—
554	C₂³×C₆₇	—	4	4	no	—
555	C₂³×C₆₇	—	4	4	no	—
556	C₂³×C₆₇	—	4	2	no	—
557	C₂³×C₆₇	—	4	2	no	—
558	C₂³×C₆₇	—	4	4	no	—
559	C₂³×C₆₇	—	4	2	no	—
560	C₂³×C₆₇	—	8	1	no	—
561	C₂³×C₆₇	—	8	1	no	—
562	C₂³×C₆₇	—	8	2	no	—
563	C₂³×C₆₇	—	8	1	no	—
564	C₂³×C₆₇	—	8	1	no	—
565	C₂³×C₆₇	—	8	1	no	—
566	C₂³×C₆₇	—	8	2	no	—
567	C₂³×C₆₇	—	8	1	no	—
568	C₂³×C₆₇	—	8	2	no	—
569	C₂³×C₆₇	—	8	2	no	—
570	C₂³×C₆₇	—	8	2	no	—
571	C₂³×C₆₇	—	8	1	no	—
572	C₂³×C₆₇	—	8	2	no	—
573	C₂³×C₆₇	—	8	16	no	—
574	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
575	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
576	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
577	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
578	Q₈×C₆₇	—	2	2	no	—
579	Q₈×C₆₇	—	2	1	no	—
580	Q₈×C₆₇	—	2	1	no	—
581	Q₈×C₆₇	—	2	1	no	—
582	Q₈×C₆₇	—	2	1	no	—
583	Q₈×C₆₇	—	2	1	no	—
584	Q₈×C₆₇	—	4	2	no	—
585	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
586	D₄×C₆₇	—	2	4	no	—
587	D₄×C₆₇	—	2	4	no	—
588	D₄×C₆₇	—	2	4	no	—
589	D₄×C₆₇	—	2	4	no	—
590	D₄×C₆₇	—	2	2	no	—
591	D₄×C₆₇	—	2	1	no	—
592	D₄×C₆₇	—	2	2	no	—
593	D₄×C₆₇	—	2	1	no	—
594	D₄×C₆₇	—	2	2	no	—
595	D₄×C₆₇	—	2	2	no	—
596	D₄×C₆₇	—	2	1	no	—
597	D₄×C₆₇	—	2	2	no	—
598	D₄×C₆₇	—	2	2	no	—
599	D₄×C₆₇	—	2	1	no	—
600	D₄×C₆₇	—	2	1	no	—
601	D₄×C₆₇	—	4	2	no	—
602	D₄×C₆₇	—	4	4	no	—
603	D₄×C₆₇	—	4	4	no	—
604	D₄×C₆₇	—	4	4	no	—
605	D₄×C₆₇	—	4	4	no	—
606	D₄×C₆₇	—	4	2	no	—
607	D₄×C₆₇	—	4	4	no	—
608	D₄×C₆₇	—	4	2	no	—
609	D₄×C₆₇	—	4	4	no	—
610	D₄×C₆₇	—	4	2	no	—
611	D₄×C₆₇	—	4	2	no	—
612	D₄×C₆₇	—	4	2	no	—
613	D₄×C₆₇	—	4	2	no	—
614	D₄×C₆₇	—	4	2	no	—
615	D₄×C₆₇	—	4	4	no	—
616	D₄×C₆₇	—	4	2	no	—
617	D₄×C₆₇	—	4	2	no	—
618	D₄×C₆₇	—	8	2	no	—
619	D₄×C₆₇	—	8	2	no	—
620	D₄×C₆₇	—	8	2	no	—
621	D₄×C₆₇	—	8	2	no	—
622	D₄×C₆₇	—	8	2	no	—
623	D₄×C₆₇	—	8	2	no	—
624	D₄×C₆₇	—	8	2	no	—
625	D₄×C₆₇	—	8	2	no	—
626	D₄×C₆₇	C₂²×D₄	1	2	yes	—
627	D₄×C₆₇	C₂²×D₄	1	4	yes	—
628	C₂×C₄×C₆₇	—	2	2	no	—
629	C₂×C₄×C₆₇	—	2	1	no	—
630	C₂×C₄×C₆₇	—	2	2	no	—
631	C₂×C₄×C₆₇	—	2	2	no	—
632	C₂×C₄×C₆₇	—	2	4	no	—
633	C₂×C₄×C₆₇	—	2	1	no	—
634	C₂×C₄×C₆₇	—	2	2	no	—
635	C₂×C₄×C₆₇	—	2	1	no	—
636	C₂×C₄×C₆₇	—	2	1	no	—
637	C₂×C₄×C₆₇	—	2	1	no	—
638	C₂×C₄×C₆₇	—	2	2	no	—
639	C₂×C₄×C₆₇	—	2	1	no	—
640	C₂×C₄×C₆₇	—	2	1	no	—
641	C₂×C₄×C₆₇	—	2	2	no	—
642	C₂×C₄×C₆₇	—	2	1	no	—
643	C₂×C₄×C₆₇	—	2	1	no	—
644	C₂×C₄×C₆₇	—	4	2	no	—
645	C₂×C₄×C₆₇	—	4	4	no	—
646	C₂×C₄×C₆₇	—	4	2	no	—
647	C₂×C₄×C₆₇	—	4	2	no	—
648	C₂×C₄×C₆₇	—	4	4	no	—
649	C₂×C₄×C₆₇	—	4	2	no	—
650	C₂×C₄×C₆₇	—	4	2	no	—
651	C₂×C₄×C₆₇	—	8	2	no	—
652	C₂×C₄×C₆₇	—	8	2	no	—
653	C₂×C₄×C₆₇	—	8	2	no	—
654	C₂×C₄×C₆₇	—	8	1	no	—
655	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
656	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
657	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
658	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
659	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
660	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
661	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
662	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
663	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
664	C₈×C₆₇	—	2	1	no	—
665	C₈×C₆₇	—	2	1	no	—
666	C₈×C₆₇	—	2	2	no	—
667	C₈×C₆₇	—	2	1	no	—
668	C₈×C₆₇	—	2	1	no	—
669	C₈×C₆₇	C₂²×D₄	1	4	yes	—
670	C₂²×C₆₇	—	2	1	no	—
671	C₂²×C₆₇	—	2	1	no	—
672	C₂²×C₆₇	—	2	1	no	—
673	C₂²×C₆₇	—	2	1	no	—
674	C₂²×C₆₇	—	2	1	no	—
675	C₂²×C₆₇	—	2	2	no	—
676	C₂²×C₆₇	—	2	1	no	—
677	C₂²×C₆₇	—	2	2	no	—
678	C₂²×C₆₇	—	2	2	no	—
679	C₂²×C₆₇	—	2	4	no	—
680	C₂²×C₆₇	—	2	2	no	—
681	C₂²×C₆₇	—	2	1	no	—
682	C₂²×C₆₇	—	4	4	no	—
683	C₂²×C₆₇	—	4	2	no	—
684	C₂²×C₆₇	—	4	1	no	—
685	C₂²×C₆₇	—	4	1	no	—
686	C₂²×C₆₇	—	4	2	no	—
687	C₂²×C₆₇	—	4	1	no	—
688	C₂²×C₆₇	—	4	2	no	—
689	C₂²×C₆₇	—	4	1	no	—
690	C₂²×C₆₇	—	4	2	no	—
691	C₂²×C₆₇	—	4	1	no	—
692	C₂²×C₆₇	—	4	2	no	—
693	C₂²×C₆₇	—	4	1	no	—
694	C₂²×C₆₇	—	4	2	no	—
695	C₂²×C₆₇	—	4	1	no	—
696	C₂²×C₆₇	—	4	2	no	—
697	C₂²×C₆₇	—	4	1	no	—
698	C₂²×C₆₇	—	4	2	no	—
699	C₂²×C₆₇	—	8	4	no	—
700	C₂²×C₆₇	—	8	4	no	—
701	C₂²×C₆₇	—	8	8	no	—
702	C₂²×C₆₇	—	8	4	no	—
703	C₂²×C₆₇	—	8	8	no	—
704	C₂²×C₆₇	—	16	2	no	—
705	C₂²×C₆₇	—	16	4	no	—
706	C₂²×C₆₇	—	16	4	no	—
707	C₂²×C₆₇	D₄²	1	2	yes	—
708	C₂²×C₆₇	#576	1	2	yes	complemented
709	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
710	C₄×C₆₇	—	2	2	no	—
711	C₄×C₆₇	—	2	1	no	—
712	C₄×C₆₇	—	2	1	no	—
713	C₄×C₆₇	—	2	2	no	—
714	C₄×C₆₇	—	2	2	no	—
715	C₄×C₆₇	—	2	2	no	—
716	C₄×C₆₇	—	4	1	no	—
717	C₄×C₆₇	—	4	1	no	—
718	C₄×C₆₇	—	4	1	no	—
719	C₄×C₆₇	—	4	1	no	—
720	C₄×C₆₇	—	4	2	no	—
721	C₄×C₆₇	D₄²	1	2	yes	—
722	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
723	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
724	#61072	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
725	C₂×C₆₇	—	2	2	no	—
726	C₂×C₆₇	—	2	2	no	—
727	C₂×C₆₇	—	4	1	no	—
728	C₂×C₆₇	—	4	2	no	—
729	C₂×C₆₇	—	4	4	no	—
730	C₂×C₆₇	—	4	2	no	—
731	C₂×C₆₇	—	8	1	no	—
732	C₂×C₆₇	—	8	2	no	—
733	C₂×C₆₇	—	8	1	no	—
734	C₂×C₆₇	—	8	2	no	—
735	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
736	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
737	C₂×C₆₇	#3585	1	1	yes	characteristic
738	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
739	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
740	#3488	C₂×C₆₇	1	1	yes	characteristic, complemented
741	#3484	C₂×C₆₇	1	1	yes	characteristic, complemented
742	#3282	C₂×C₆₇	1	2	yes	complemented
743	D₄×D₈	C₂×C₆₇	1	2	yes	complemented
744	#3274	C₂×C₆₇	1	2	yes	complemented
745	#3273	C₂×C₆₇	1	2	yes	complemented
746	#3268	C₂×C₆₇	1	2	yes	complemented
747	#3265	C₂×C₆₇	1	2	yes	complemented
748	#3264	C₂×C₆₇	1	2	yes	complemented
749	#3264	C₂×C₆₇	1	2	yes	complemented
750	#3155	C₂×C₆₇	1	1	yes	characteristic, complemented
751	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
752	#3055	C₂×C₆₇	1	1	yes	characteristic, complemented
753	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
754	#3041	C₂×C₆₇	1	1	yes	characteristic, complemented
755	#3012	C₂×C₆₇	1	1	yes	characteristic, complemented
756	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
757	#3002	C₂×C₆₇	1	1	yes	characteristic, complemented
758	C₂×#447	C₂×C₆₇	1	1	yes	characteristic, complemented
759	#2946	C₂×C₆₇	1	1	yes	characteristic, complemented
760	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
761	C₆₇	#61072	1	1	yes	characteristic, direct product factor, Sylow
762	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
764	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
765	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	#576	—	2	8	no	—
767	C₂×AGL(1,ℤ/8)	—	2	8	no	—
768	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
769	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
770	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
771	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
772	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
773	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
774	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
775	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
776	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
777	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
778	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
779	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
780	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
781	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
782	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
783	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
785	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
786	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
787	#550	C₂²×C₆₇	1	2	yes	complemented
788	#548	C₂²×C₆₇	1	2	yes	complemented
789	#546	—	2	2	no	—
790	#546	—	2	1	no	—
791	#546	—	2	1	no	—
792	#546	C₂²×C₆₇	1	2	yes	complemented
793	#546	C₂²×C₆₇	1	2	yes	complemented
794	#546	C₂²×C₆₇	1	2	yes	complemented
795	D₄²	—	2	1	no	—
796	D₄²	—	2	1	no	—
797	D₄²	—	2	2	no	—
798	D₄²	C₂²×C₆₇	1	2	yes	complemented
799	D₄²	C₂²×C₆₇	1	2	yes	complemented
800	D₄²	C₂²×C₆₇	1	2	yes	complemented
801	#537	—	2	1	no	—
802	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
803	#535	—	2	1	no	—
804	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
805	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
806	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
807	#534	—	2	2	no	—
808	#525	—	2	1	no	—
809	#525	C₂²×C₆₇	1	1	yes	characteristic
810	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
811	C₂×#121	—	2	1	no	—
812	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
813	C₂×#120	—	2	2	no	—
814	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
815	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
816	#496	C₂²×C₆₇	1	2	yes	complemented
817	#496	C₂²×C₆₇	1	2	yes	complemented
818	#495	C₂²×C₆₇	1	2	yes	complemented
819	#493	C₂²×C₆₇	1	2	yes	complemented
820	#469	C₂²×C₆₇	1	2	yes	complemented
821	#469	C₂²×C₆₇	1	2	yes	complemented
822	#468	C₂²×C₆₇	1	2	yes	complemented
823	#468	C₂²×C₆₇	1	2	yes	complemented
824	#466	C₂²×C₆₇	1	2	yes	complemented
825	#466	C₂²×C₆₇	1	2	yes	complemented
826	#465	C₂²×C₆₇	1	2	yes	complemented
827	#465	C₂²×C₆₇	1	2	yes	complemented
828	#464	C₂²×C₆₇	1	2	yes	complemented
829	#463	C₂²×C₆₇	1	2	yes	complemented
830	#463	C₂²×C₆₇	1	2	yes	complemented
831	#463	C₂²×C₆₇	1	2	yes	complemented
832	#460	C₂²×C₆₇	1	2	yes	complemented
833	#459	C₂²×C₆₇	1	2	yes	complemented
834	#459	C₂²×C₆₇	1	2	yes	complemented
835	#459	C₂²×C₆₇	1	2	yes	complemented
836	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
837	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
838	#452	C₂²×C₆₇	1	2	yes	complemented
839	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
840	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
841	#450	C₂²×C₆₇	1	2	yes	complemented
842	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
843	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
844	#449	C₂²×C₆₇	1	2	yes	complemented
845	#449	C₂²×C₆₇	1	2	yes	complemented
846	#449	C₂²×C₆₇	1	2	yes	complemented
847	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
848	#447	C₂²×C₆₇	1	2	yes	complemented
849	#447	C₂²×C₆₇	1	2	yes	complemented
850	#447	C₂²×C₆₇	1	2	yes	complemented
851	#447	C₂²×C₆₇	1	2	yes	complemented
852	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
853	#447	C₂²×C₆₇	1	2	yes	complemented
854	#447	C₂²×C₆₇	1	2	yes	complemented
855	#447	C₂²×C₆₇	1	2	yes	complemented
856	#442	C₂²×C₆₇	1	2	yes	complemented
857	#440	C₂²×C₆₇	1	2	yes	complemented
858	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
859	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
860	#436	C₂²×C₆₇	1	2	yes	complemented
861	#435	C₂²×C₆₇	1	2	yes	complemented
862	#435	C₂²×C₆₇	1	2	yes	complemented
863	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
864	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
865	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
866	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
867	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
868	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
869	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
870	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
871	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
872	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
873	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
874	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
875	C₂⁵	—	2	1	no	—
876	H(5,𝔽₂)	—	2	4	no	—
877	H(5,𝔽₂)	—	2	4	no	—
878	H(5,𝔽₂)	—	4	2	no	—
879	H(5,𝔽₂)	—	4	2	no	—
880	C₂×#41	—	2	1	no	—
881	C₂×#41	—	2	1	no	—
882	C₂×#41	—	2	1	no	—
883	C₂×#41	—	2	1	no	—
884	C₂×#41	—	2	4	no	—
885	C₂×#41	—	4	2	no	—
886	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
887	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
888	C₂×#41	C₂³×C₆₇	1	2	yes	—
889	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
890	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
891	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
892	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
893	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
894	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
895	C₂²×D₄	—	2	4	no	—
896	C₂²×D₄	—	2	1	no	—
897	C₂²×D₄	—	2	1	no	—
898	C₂²×D₄	—	2	2	no	—
899	C₂²×D₄	—	2	1	no	—
900	C₂²×D₄	—	2	1	no	—
901	C₂²×D₄	—	2	2	no	—
902	C₂²×D₄	—	2	2	no	—
903	C₂²×D₄	—	2	2	no	—
904	C₂²×D₄	—	2	2	no	—
905	C₂²×D₄	—	2	1	no	—
906	C₂²×D₄	—	2	1	no	—
907	C₂²×D₄	—	2	1	no	—
908	C₂²×D₄	—	4	2	no	—
909	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
910	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
911	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
912	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
913	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
914	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
915	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
916	C₂²×D₄	C₂³×C₆₇	1	2	yes	complemented
917	C₂³×C₄	—	2	1	no	—
918	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
919	AGL(1,ℤ/8)	—	2	4	no	—
920	AGL(1,ℤ/8)	—	2	4	no	—
921	AGL(1,ℤ/8)	—	2	8	no	—
922	AGL(1,ℤ/8)	—	2	8	no	—
923	AGL(1,ℤ/8)	—	2	8	no	—
924	AGL(1,ℤ/8)	—	2	8	no	—
925	AGL(1,ℤ/8)	—	2	4	no	—
926	AGL(1,ℤ/8)	—	2	4	no	—
927	AGL(1,ℤ/8)	D₄×C₆₇	1	8	yes	complemented
928	#135	—	2	4	no	—
929	#135	—	2	8	no	—
930	#135	—	4	2	no	—
931	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
932	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
933	C₂×SD₁₆	—	2	8	no	—
934	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
935	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
936	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
937	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
938	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
939	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
940	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
941	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
942	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
943	C₂×D₈	—	2	4	no	—
944	C₂×D₈	—	2	8	no	—
945	C₂×D₈	—	2	8	no	—
946	C₂×D₈	—	4	2	no	—
947	C₂×D₈	C₂³×C₆₇	1	2	yes	—
948	C₂×D₈	C₂³×C₆₇	1	2	yes	—
949	C₂×D₈	C₂³×C₆₇	1	2	yes	—
950	C₂×D₈	C₂³×C₆₇	1	2	yes	—
951	C₂×D₈	C₂³×C₆₇	1	2	yes	—
952	C₂×D₈	C₂³×C₆₇	1	2	yes	—
953	C₂×D₈	C₂³×C₆₇	1	2	yes	—
954	C₂×D₈	C₂³×C₆₇	1	2	yes	—
955	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
956	C₂×D₈	C₂³×C₆₇	1	2	yes	complemented
957	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
958	#131	—	2	4	no	—
959	C₂×M₁₆	—	2	4	no	—
960	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
961	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
962	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
963	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
964	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
965	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
966	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
967	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
968	#127	—	2	2	no	—
969	#127	—	2	1	no	—
970	#127	C₂³×C₆₇	1	2	yes	—
971	#127	C₂³×C₆₇	1	2	yes	complemented
972	#124	—	2	1	no	—
973	#124	—	2	2	no	—
974	#124	C₂³×C₆₇	1	2	yes	—
975	#124	C₂³×C₆₇	1	2	yes	complemented
976	#123	—	2	1	no	—
977	#123	—	2	2	no	—
978	#123	—	2	2	no	—
979	#123	—	2	2	no	—
980	#123	D₄×C₆₇	1	2	yes	—
981	C₂²⋊Q₈	—	2	1	no	—
982	C₂²⋊Q₈	—	2	2	no	—
983	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
984	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
985	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
986	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
987	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
988	#121	—	2	1	no	—
989	#121	—	2	2	no	—
990	#121	—	2	2	no	—
991	#121	—	2	1	no	—
992	#121	—	2	1	no	—
993	#121	—	2	1	no	—
994	#121	—	2	1	no	—
995	#121	—	2	2	no	—
996	#121	—	2	2	no	—
997	#121	—	2	1	no	—
998	#121	—	2	1	no	—
999	#121	—	2	2	no	—
1000	#121	—	2	2	no	—
1001	#121	—	2	2	no	—
1002	#121	—	2	2	no	—
1003	#121	—	2	2	no	—
1004	#121	—	2	2	no	—
1005	#121	D₄×C₆₇	1	1	yes	characteristic
1006	#121	D₄×C₆₇	1	1	yes	characteristic
1007	#121	C₂³×C₆₇	1	2	yes	—
1008	#121	C₂³×C₆₇	1	2	yes	—
1009	#121	C₂³×C₆₇	1	1	yes	characteristic
1010	#121	C₂³×C₆₇	1	1	yes	characteristic
1011	#121	C₂³×C₆₇	1	2	yes	—
1012	#121	C₂³×C₆₇	1	2	yes	—
1013	#121	C₂³×C₆₇	1	2	yes	complemented
1014	#120	—	2	1	no	—
1015	#120	—	2	2	no	—
1016	#120	—	2	2	no	—
1017	#120	—	2	2	no	—
1018	#120	—	2	2	no	—
1019	#120	—	2	2	no	—
1020	#120	—	2	2	no	—
1021	#120	—	2	2	no	—
1022	#120	—	2	2	no	—
1023	#120	—	2	2	no	—
1024	#120	—	2	2	no	—
1025	#120	—	2	2	no	—
1026	#120	—	2	2	no	—
1027	#120	D₄×C₆₇	1	2	yes	—
1028	C₄×Q₈	C₂³×C₆₇	1	2	yes	complemented
1029	C₄×D₄	—	2	1	no	—
1030	C₄×D₄	—	2	1	no	—
1031	C₄×D₄	—	2	1	no	—
1032	C₄×D₄	—	2	1	no	—
1033	C₄×D₄	—	2	2	no	—
1034	C₄×D₄	—	2	2	no	—
1035	C₄×D₄	—	2	2	no	—
1036	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1037	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1038	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1039	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1040	C₄×D₄	C₂³×C₆₇	1	2	yes	complemented
1041	#117	—	2	1	no	—
1042	#117	C₂³×C₆₇	1	1	yes	characteristic
1043	#117	C₂³×C₆₇	1	1	yes	characteristic
1044	C₂×C₄⋊C₄	—	2	1	no	—
1045	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	—	2	1	no	—
1047	C₂×C₂²⋊C₄	—	2	2	no	—
1048	C₂×C₂²⋊C₄	—	2	2	no	—
1049	C₂×C₂²⋊C₄	—	2	2	no	—
1050	C₂×C₂²⋊C₄	—	2	2	no	—
1051	#107	C₂³×C₆₇	1	2	yes	complemented
1052	#106	C₂³×C₆₇	1	2	yes	complemented
1053	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1054	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1055	#103	C₂³×C₆₇	1	1	yes	characteristic, complemented
1056	#103	C₂³×C₆₇	1	1	yes	characteristic, complemented
1057	#103	C₂³×C₆₇	1	1	yes	characteristic, complemented
1058	#103	C₂³×C₆₇	1	1	yes	characteristic, complemented
1059	#103	C₂³×C₆₇	1	2	yes	complemented
1060	#102	C₂³×C₆₇	1	2	yes	—
1061	#102	C₂³×C₆₇	1	2	yes	—
1062	#102	C₂³×C₆₇	1	2	yes	—
1063	#102	C₂³×C₆₇	1	2	yes	—
1064	#102	C₂³×C₆₇	1	1	yes	characteristic, complemented
1065	#102	C₂³×C₆₇	1	1	yes	characteristic, complemented
1066	#102	C₂³×C₆₇	1	1	yes	characteristic, complemented
1067	#102	C₂³×C₆₇	1	1	yes	characteristic, complemented
1068	#102	C₂³×C₆₇	1	2	yes	complemented
1069	#102	C₂³×C₆₇	1	2	yes	complemented
1070	#102	C₂³×C₆₇	1	2	yes	complemented
1071	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1072	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1073	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1074	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1075	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1076	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1077	#97	C₂³×C₆₇	1	2	yes	complemented
1078	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
1079	C₂⁴	—	2	1	no	—
1080	C₂⁴	—	2	2	no	—
1081	C₂⁴	—	2	2	no	—
1082	C₂⁴	—	2	1	no	—
1083	C₂⁴	—	2	1	no	—
1084	C₂⁴	—	2	2	no	—
1085	C₂⁴	—	2	1	no	—
1086	C₂⁴	—	2	2	no	—
1087	C₂⁴	—	4	4	no	—
1088	C₂⁴	—	8	2	no	—
1089	C₂⁴	—	8	2	no	—
1090	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1091	#41	—	2	2	no	—
1092	#41	—	2	2	no	—
1093	#41	—	2	2	no	—
1094	#41	—	2	4	no	—
1095	#41	—	2	2	no	—
1096	#41	—	2	4	no	—
1097	#41	—	2	2	no	—
1098	#41	—	2	2	no	—
1099	#41	—	2	2	no	—
1100	#41	—	2	2	no	—
1101	#41	—	2	2	no	—
1102	#41	—	4	4	no	—
1103	#41	—	4	1	no	—
1104	#41	—	4	1	no	—
1105	#41	—	4	2	no	—
1106	#41	—	4	2	no	—
1107	#41	—	4	4	no	—
1108	#41	—	4	4	no	—
1109	#41	—	4	4	no	—
1110	#41	C₂×D₄×C₆₇	1	4	yes	complemented
1111	C₂×Q₈	—	2	1	no	—
1112	C₂×Q₈	—	2	2	no	—
1113	C₂×Q₈	—	4	1	no	—
1114	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1115	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1116	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1117	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1118	C₂×D₄	—	2	1	no	—
1119	C₂×D₄	—	2	2	no	—
1120	C₂×D₄	—	2	4	no	—
1121	C₂×D₄	—	2	4	no	—
1122	C₂×D₄	—	2	4	no	—
1123	C₂×D₄	—	2	4	no	—
1124	C₂×D₄	—	2	1	no	—
1125	C₂×D₄	—	2	1	no	—
1126	C₂×D₄	—	2	2	no	—
1127	C₂×D₄	—	2	1	no	—
1128	C₂×D₄	—	2	2	no	—
1129	C₂×D₄	—	2	1	no	—
1130	C₂×D₄	—	2	1	no	—
1131	C₂×D₄	—	2	2	no	—
1132	C₂×D₄	—	2	1	no	—
1133	C₂×D₄	—	2	2	no	—
1134	C₂×D₄	—	2	2	no	—
1135	C₂×D₄	—	2	2	no	—
1136	C₂×D₄	—	2	2	no	—
1137	C₂×D₄	—	2	1	no	—
1138	C₂×D₄	—	2	2	no	—
1139	C₂×D₄	—	2	2	no	—
1140	C₂×D₄	—	2	2	no	—
1141	C₂×D₄	—	2	1	no	—
1142	C₂×D₄	—	2	2	no	—
1143	C₂×D₄	—	2	2	no	—
1144	C₂×D₄	—	2	2	no	—
1145	C₂×D₄	—	2	1	no	—
1146	C₂×D₄	—	2	1	no	—
1147	C₂×D₄	—	2	2	no	—
1148	C₂×D₄	—	2	2	no	—
1149	C₂×D₄	—	2	2	no	—
1150	C₂×D₄	—	2	2	no	—
1151	C₂×D₄	—	2	2	no	—
1152	C₂×D₄	—	2	2	no	—
1153	C₂×D₄	—	2	2	no	—
1154	C₂×D₄	—	4	2	no	—
1155	C₂×D₄	—	4	2	no	—
1156	C₂×D₄	—	4	1	no	—
1157	C₂×D₄	—	4	2	no	—
1158	C₂×D₄	—	4	2	no	—
1159	C₂×D₄	—	4	4	no	—
1160	C₂×D₄	—	4	4	no	—
1161	C₂×D₄	—	4	4	no	—
1162	C₂×D₄	—	4	4	no	—
1163	C₂×D₄	—	4	8	no	—
1164	C₂×D₄	—	4	4	no	—
1165	C₂×D₄	—	4	4	no	—
1166	C₂×D₄	—	4	8	no	—
1167	C₂×D₄	—	8	4	no	—
1168	C₂×D₄	—	8	4	no	—
1169	C₂×D₄	—	8	2	no	—
1170	C₂×D₄	—	8	4	no	—
1171	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1172	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1173	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1174	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1175	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
1176	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1177	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1178	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1179	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1180	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1181	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1182	C₂²×C₄	—	2	1	no	—
1183	C₂²×C₄	—	2	2	no	—
1184	C₂²×C₄	—	2	2	no	—
1185	C₂²×C₄	—	2	1	no	—
1186	C₂²×C₄	—	2	1	no	—
1187	C₂²×C₄	—	2	1	no	—
1188	C₂²×C₄	—	2	2	no	—
1189	C₂²×C₄	—	2	1	no	—
1190	C₂²×C₄	—	2	1	no	—
1191	C₂²×C₄	—	2	2	no	—
1192	C₂²×C₄	—	2	1	no	—
1193	C₂²×C₄	—	2	2	no	—
1194	C₂²×C₄	—	2	2	no	—
1195	C₂²×C₄	—	2	2	no	—
1196	C₂²×C₄	—	4	4	no	—
1197	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1198	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1199	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1200	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1201	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1202	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1203	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1204	Q₁₆	—	2	2	no	—
1205	Q₁₆	—	4	1	no	—
1206	SD₁₆	—	2	4	no	—
1207	SD₁₆	—	2	2	no	—
1208	SD₁₆	—	2	4	no	—
1209	SD₁₆	—	2	2	no	—
1210	SD₁₆	—	2	4	no	—
1211	SD₁₆	—	2	4	no	—
1212	SD₁₆	—	4	1	no	—
1213	SD₁₆	—	4	1	no	—
1214	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
1215	D₈	—	2	4	no	—
1216	D₈	—	2	2	no	—
1217	D₈	—	2	4	no	—
1218	D₈	—	2	4	no	—
1219	D₈	—	2	4	no	—
1220	D₈	—	2	4	no	—
1221	D₈	—	2	4	no	—
1222	D₈	—	4	2	no	—
1223	D₈	—	4	2	no	—
1224	D₈	—	4	1	no	—
1225	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
1226	M₁₆	—	2	2	no	—
1227	M₁₆	—	2	4	no	—
1228	M₁₆	—	2	4	no	—
1229	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1230	C₂×C₈	—	2	2	no	—
1231	C₂×C₈	—	2	2	no	—
1232	C₂×C₈	—	2	4	no	—
1233	C₂×C₈	—	2	4	no	—
1234	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1235	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1236	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1237	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1238	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1239	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1240	C₄⋊C₄	—	2	1	no	—
1241	C₄⋊C₄	—	2	2	no	—
1242	C₄⋊C₄	—	2	2	no	—
1243	C₄⋊C₄	—	2	1	no	—
1244	C₄⋊C₄	—	2	1	no	—
1245	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1246	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1247	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1248	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1249	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1250	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1251	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1252	C₂²⋊C₄	—	2	1	no	—
1253	C₂²⋊C₄	—	2	1	no	—
1254	C₂²⋊C₄	—	2	1	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	2	2	no	—
1257	C₂²⋊C₄	—	2	2	no	—
1258	C₂²⋊C₄	—	2	2	no	—
1259	C₂²⋊C₄	—	2	2	no	—
1260	C₂²⋊C₄	—	2	2	no	—
1261	C₂²⋊C₄	—	2	2	no	—
1262	C₂²⋊C₄	—	2	2	no	—
1263	C₂²⋊C₄	—	2	2	no	—
1264	C₂²⋊C₄	—	2	2	no	—
1265	C₂²⋊C₄	—	2	2	no	—
1266	C₂²⋊C₄	—	2	1	no	—
1267	C₂²⋊C₄	—	2	1	no	—
1268	C₂²⋊C₄	—	2	2	no	—
1269	C₂²⋊C₄	—	2	2	no	—
1270	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1271	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1272	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1273	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1274	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1275	C₄²	—	2	2	no	—
1276	C₄²	—	2	1	no	—
1277	C₄²	C₂⁴×C₆₇	1	2	yes	—
1278	C₂³	—	2	2	no	—
1279	C₂³	—	2	2	no	—
1280	C₂³	—	2	1	no	—
1281	C₂³	—	2	2	no	—
1282	C₂³	—	2	4	no	—
1283	C₂³	—	2	2	no	—
1284	C₂³	—	2	2	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	4	1	no	—
1288	C₂³	—	4	2	no	—
1289	C₂³	—	4	4	no	—
1290	C₂³	—	4	4	no	—
1291	C₂³	—	4	4	no	—
1292	C₂³	—	4	4	no	—
1293	C₂³	—	4	4	no	—
1294	C₂³	—	4	2	no	—
1295	C₂³	—	4	2	no	—
1296	C₂³	—	4	4	no	—
1297	C₂³	—	4	2	no	—
1298	C₂³	—	8	1	no	—
1299	C₂³	—	8	1	no	—
1300	C₂³	—	8	1	no	—
1301	C₂³	—	8	2	no	—
1302	C₂³	—	8	1	no	—
1303	C₂³	—	8	2	no	—
1304	C₂³	—	8	1	no	—
1305	C₂³	—	8	1	no	—
1306	C₂³	—	8	2	no	—
1307	C₂³	—	8	2	no	—
1308	C₂³	—	8	2	no	—
1309	C₂³	—	8	1	no	—
1310	C₂³	—	8	2	no	—
1311	C₂³	—	8	16	no	—
1312	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1313	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1314	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1315	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1316	Q₈	—	2	2	no	—
1317	Q₈	—	2	1	no	—
1318	Q₈	—	2	1	no	—
1319	Q₈	—	2	1	no	—
1320	Q₈	—	2	1	no	—
1321	Q₈	—	2	1	no	—
1322	Q₈	—	4	2	no	—
1323	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1324	D₄	—	2	4	no	—
1325	D₄	—	2	4	no	—
1326	D₄	—	2	4	no	—
1327	D₄	—	2	4	no	—
1328	D₄	—	2	2	no	—
1329	D₄	—	2	1	no	—
1330	D₄	—	2	2	no	—
1331	D₄	—	2	1	no	—
1332	D₄	—	2	2	no	—
1333	D₄	—	2	2	no	—
1334	D₄	—	2	1	no	—
1335	D₄	—	2	2	no	—
1336	D₄	—	2	2	no	—
1337	D₄	—	2	1	no	—
1338	D₄	—	2	1	no	—
1339	D₄	—	4	2	no	—
1340	D₄	—	4	4	no	—
1341	D₄	—	4	4	no	—
1342	D₄	—	4	4	no	—
1343	D₄	—	4	4	no	—
1344	D₄	—	4	2	no	—
1345	D₄	—	4	4	no	—
1346	D₄	—	4	2	no	—
1347	D₄	—	4	4	no	—
1348	D₄	—	4	2	no	—
1349	D₄	—	4	2	no	—
1350	D₄	—	4	2	no	—
1351	D₄	—	4	2	no	—
1352	D₄	—	4	2	no	—
1353	D₄	—	4	4	no	—
1354	D₄	—	4	2	no	—
1355	D₄	—	4	2	no	—
1356	D₄	—	8	2	no	—
1357	D₄	—	8	2	no	—
1358	D₄	—	8	2	no	—
1359	D₄	—	8	2	no	—
1360	D₄	—	8	2	no	—
1361	D₄	—	8	2	no	—
1362	D₄	—	8	2	no	—
1363	D₄	—	8	2	no	—
1364	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1365	D₄	C₂²×D₄×C₆₇	1	4	yes	—
1366	C₂×C₄	—	2	2	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	2	no	—
1369	C₂×C₄	—	2	2	no	—
1370	C₂×C₄	—	2	4	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	2	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	2	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	2	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	4	2	no	—
1383	C₂×C₄	—	4	4	no	—
1384	C₂×C₄	—	4	2	no	—
1385	C₂×C₄	—	4	2	no	—
1386	C₂×C₄	—	4	4	no	—
1387	C₂×C₄	—	4	2	no	—
1388	C₂×C₄	—	4	2	no	—
1389	C₂×C₄	—	8	2	no	—
1390	C₂×C₄	—	8	2	no	—
1391	C₂×C₄	—	8	2	no	—
1392	C₂×C₄	—	8	1	no	—
1393	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1394	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1395	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1396	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1397	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1398	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1399	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1400	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1401	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1402	C₈	—	2	1	no	—
1403	C₈	—	2	1	no	—
1404	C₈	—	2	2	no	—
1405	C₈	—	2	1	no	—
1406	C₈	—	2	1	no	—
1407	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1408	C₂²	—	2	1	no	—
1409	C₂²	—	2	1	no	—
1410	C₂²	—	2	1	no	—
1411	C₂²	—	2	1	no	—
1412	C₂²	—	2	2	no	—
1413	C₂²	—	2	1	no	—
1414	C₂²	—	2	1	no	—
1415	C₂²	—	2	2	no	—
1416	C₂²	—	2	1	no	—
1417	C₂²	—	2	2	no	—
1418	C₂²	—	2	2	no	—
1419	C₂²	—	2	4	no	—
1420	C₂²	—	4	4	no	—
1421	C₂²	—	4	1	no	—
1422	C₂²	—	4	2	no	—
1423	C₂²	—	4	2	no	—
1424	C₂²	—	4	1	no	—
1425	C₂²	—	4	1	no	—
1426	C₂²	—	4	2	no	—
1427	C₂²	—	4	1	no	—
1428	C₂²	—	4	2	no	—
1429	C₂²	—	4	1	no	—
1430	C₂²	—	4	2	no	—
1431	C₂²	—	4	1	no	—
1432	C₂²	—	4	2	no	—
1433	C₂²	—	4	1	no	—
1434	C₂²	—	4	2	no	—
1435	C₂²	—	4	1	no	—
1436	C₂²	—	4	2	no	—
1437	C₂²	—	8	4	no	—
1438	C₂²	—	8	8	no	—
1439	C₂²	—	8	4	no	—
1440	C₂²	—	8	4	no	—
1441	C₂²	—	8	8	no	—
1442	C₂²	—	16	2	no	—
1443	C₂²	—	16	4	no	—
1444	C₂²	—	16	4	no	—
1445	C₂²	D₄²×C₆₇	1	2	yes	—
1446	C₂²	#576×C₆₇	1	2	yes	complemented
1447	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1448	C₄	—	2	2	no	—
1449	C₄	—	2	2	no	—
1450	C₄	—	2	1	no	—
1451	C₄	—	2	1	no	—
1452	C₄	—	2	2	no	—
1453	C₄	—	2	2	no	—
1454	C₄	—	4	1	no	—
1455	C₄	—	4	2	no	—
1456	C₄	—	4	1	no	—
1457	C₄	—	4	1	no	—
1458	C₄	—	4	1	no	—
1459	C₄	D₄²×C₆₇	1	2	yes	—
1460	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1461	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1462	C₂	—	2	2	no	—
1463	C₂	—	2	2	no	—
1464	C₂	—	4	1	no	—
1465	C₂	—	4	2	no	—
1466	C₂	—	4	4	no	—
1467	C₂	—	4	2	no	—
1468	C₂	—	8	2	no	—
1469	C₂	—	8	1	no	—
1470	C₂	—	8	1	no	—
1471	C₂	—	8	2	no	—
1472	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1473	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1474	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #525×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#576×C₆₇	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
3. C₆₇×#3488	C₂	semidirect
4. C₆₇×#3484	C₂	semidirect
5. C₆₇×#3282	C₂	semidirect
6. D₄×D₈×C₆₇	C₂	semidirect
7. C₆₇×#3274	C₂	semidirect
8. C₆₇×#3273	C₂	semidirect
9. C₆₇×#3268	C₂	semidirect
10. C₆₇×#3265	C₂	semidirect
11. C₆₇×#3264	C₂	semidirect
12. C₆₇×#3264	C₂	semidirect
13. C₆₇×#3155	C₂	semidirect
14. C₆₇×#3062	C₂	semidirect
15. C₆₇×#3055	C₂	semidirect
16. C₆₇×#3045	C₂	semidirect
17. C₆₇×#3041	C₂	semidirect
18. C₆₇×#3012	C₂	semidirect
19. C₆₇×#3008	C₂	semidirect
20. C₆₇×#3002	C₂	semidirect
21. C₂×#447×C₆₇	C₂	semidirect
22. C₆₇×#2946	C₂	semidirect
23. C₆₇×#2933	C₂	semidirect
24. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
25. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
26. C₂²×#41×C₆₇	C₂²	semidirect
27. C₂³×D₄×C₆₇	C₂²	semidirect
31. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
32. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
36. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
37. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
38. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
39. C₂×#135×C₆₇	C₂²	semidirect
40. C₂×#135×C₆₇	C₂²	semidirect
41. C₂×#135×C₆₇	C₂²	semidirect
42. C₂²×SD₁₆×C₆₇	C₂²	semidirect
43. C₂²×D₈×C₆₇	C₂²	semidirect
44. C₂²×D₈×C₆₇	C₂²	semidirect
45. C₂²×D₈×C₆₇	C₂²	semidirect
46. C₂²×D₈×C₆₇	C₂²	semidirect
47. C₂×#131×C₆₇	C₂²	semidirect
48. C₂²×M₁₆×C₆₇	C₂²	semidirect
49. #550×C₆₇	C₂²	semidirect
50. #548×C₆₇	C₂²	semidirect
54. #546×C₆₇	C₂²	semidirect
55. #546×C₆₇	C₂²	semidirect
56. #546×C₆₇	C₂²	semidirect
60. D₄²×C₆₇	C₂²	semidirect
61. D₄²×C₆₇	C₂²	semidirect
62. D₄²×C₆₇	C₂²	semidirect
64. #537×C₆₇	C₂²	semidirect
66. #535×C₆₇	C₂²	semidirect
67. #535×C₆₇	C₂²	semidirect
68. #535×C₆₇	C₂²	semidirect
72. #525×C₆₇	C₂²	semidirect
74. C₂×#121×C₆₇	C₂²	semidirect
76. #520×C₆₇	C₂²	semidirect
77. #518×C₆₇	C₂²	semidirect
78. #496×C₆₇	C₂²	semidirect
79. #496×C₆₇	C₂²	semidirect
80. #495×C₆₇	C₂²	semidirect
81. #493×C₆₇	C₂²	semidirect
82. #469×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #466×C₆₇	C₂²	semidirect
87. #466×C₆₇	C₂²	semidirect
88. #465×C₆₇	C₂²	semidirect
89. #465×C₆₇	C₂²	semidirect
90. #464×C₆₇	C₂²	semidirect
91. #463×C₆₇	C₂²	semidirect
92. #463×C₆₇	C₂²	semidirect
93. #463×C₆₇	C₂²	semidirect
94. #460×C₆₇	C₂²	semidirect
95. #459×C₆₇	C₂²	semidirect
96. #459×C₆₇	C₂²	semidirect
97. #459×C₆₇	C₂²	semidirect
98. #452×C₆₇	C₂²	semidirect
99. #452×C₆₇	C₂²	semidirect
100. #452×C₆₇	C₂²	semidirect
101. #451×C₆₇	C₂²	semidirect
102. #450×C₆₇	C₂²	semidirect
103. #450×C₆₇	C₂²	semidirect
104. #449×C₆₇	C₂²	semidirect
105. #449×C₆₇	C₂²	semidirect
106. #449×C₆₇	C₂²	semidirect
107. #449×C₆₇	C₂²	semidirect
108. #449×C₆₇	C₂²	semidirect
109. #448×C₆₇	C₂²	semidirect
110. #447×C₆₇	C₂²	semidirect
111. #447×C₆₇	C₂²	semidirect
112. #447×C₆₇	C₂²	semidirect
113. #447×C₆₇	C₂²	semidirect
114. #447×C₆₇	C₂²	semidirect
115. #447×C₆₇	C₂²	semidirect
116. #447×C₆₇	C₂²	semidirect
117. #447×C₆₇	C₂²	semidirect
118. #442×C₆₇	C₂²	semidirect
119. #440×C₆₇	C₂²	semidirect
120. C₄×SD₁₆×C₆₇	C₂²	semidirect
121. C₄×D₈×C₆₇	C₂²	semidirect
122. #436×C₆₇	C₂²	semidirect
123. #435×C₆₇	C₂²	semidirect
124. #435×C₆₇	C₂²	semidirect
125. C₈×D₄×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. #424×C₆₇	C₂²	semidirect
128. #418×C₆₇	C₂²	semidirect
129. #417×C₆₇	C₂²	semidirect
130. #416×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
132. C₂×#102×C₆₇	C₂²	semidirect
133. C₂×#102×C₆₇	C₂²	semidirect
134. #408×C₆₇	C₂²	semidirect
135. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
136. #405×C₆₇	C₂²	semidirect
155. C₂×#41×C₆₇	C₂³	semidirect
178. C₂²×D₄×C₆₇	C₂³	semidirect
189. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
193. C₂×Q₁₆×C₆₇	C₂³	semidirect
194. C₂×Q₁₆×C₆₇	C₂³	semidirect
200. C₂×SD₁₆×C₆₇	C₂³	semidirect
201. C₂×SD₁₆×C₆₇	C₂³	semidirect
202. C₂×SD₁₆×C₆₇	C₂³	semidirect
203. C₂×SD₁₆×C₆₇	C₂³	semidirect
204. C₂×SD₁₆×C₆₇	C₂³	semidirect
217. C₂×D₈×C₆₇	C₂³	semidirect
218. C₂×D₈×C₆₇	C₂³	semidirect
219. C₂×D₈×C₆₇	C₂³	semidirect
225. C₂×M₁₆×C₆₇	C₂³	semidirect
229. C₂²×C₈×C₆₇	C₂³	semidirect
233. #127×C₆₇	C₂³	semidirect
237. #124×C₆₇	C₂³	semidirect
249. C₂²⋊Q₈×C₆₇	C₂³	semidirect
275. #121×C₆₇	C₂³	semidirect
290. C₄×Q₈×C₆₇	C₂³	semidirect
302. C₄×D₄×C₆₇	C₂³	semidirect
313. #107×C₆₇	C₂³	semidirect
314. #106×C₆₇	C₂³	semidirect
315. C₄⋊C₈×C₆₇	C₂³	semidirect
316. C₄⋊C₈×C₆₇	C₂³	semidirect
317. #103×C₆₇	C₂³	semidirect
318. #103×C₆₇	C₂³	semidirect
319. #103×C₆₇	C₂³	semidirect
320. #103×C₆₇	C₂³	semidirect
321. #103×C₆₇	C₂³	semidirect
326. #102×C₆₇	C₂³	semidirect
327. #102×C₆₇	C₂³	semidirect
328. #102×C₆₇	C₂³	semidirect
329. #102×C₆₇	C₂³	semidirect
330. #102×C₆₇	C₂³	semidirect
331. #102×C₆₇	C₂³	semidirect
332. #102×C₆₇	C₂³	semidirect
337. C₂²⋊C₈×C₆₇	C₂³	semidirect
338. C₂²⋊C₈×C₆₇	C₂³	semidirect
339. #97×C₆₇	C₂³	semidirect
340. C₄×C₈×C₆₇	C₂³	semidirect
372. #41×C₆₇	C₂×D₄	semidirect
437. C₂×D₄×C₆₇	C₂×D₄	semidirect
476. SD₁₆×C₆₇	C₂×D₄	semidirect
487. D₈×C₆₇	C₂×D₄	semidirect
491. M₁₆×C₆₇	C₂×D₄	semidirect
708. C₂²×C₆₇	#576	semidirect
724. #61072	C₆₇	direct (N × H)
738. C₂×#576	C₂×C₆₇	semidirect
739. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
740. #3488	C₂×C₆₇	semidirect
741. #3484	C₂×C₆₇	semidirect
742. #3282	C₂×C₆₇	semidirect
743. D₄×D₈	C₂×C₆₇	semidirect
744. #3274	C₂×C₆₇	semidirect
745. #3273	C₂×C₆₇	semidirect
746. #3268	C₂×C₆₇	semidirect
747. #3265	C₂×C₆₇	semidirect
748. #3264	C₂×C₆₇	semidirect
749. #3264	C₂×C₆₇	semidirect
750. #3155	C₂×C₆₇	semidirect
751. #3062	C₂×C₆₇	semidirect
752. #3055	C₂×C₆₇	semidirect
753. #3045	C₂×C₆₇	semidirect
754. #3041	C₂×C₆₇	semidirect
755. #3012	C₂×C₆₇	semidirect
756. #3008	C₂×C₆₇	semidirect
757. #3002	C₂×C₆₇	semidirect
758. C₂×#447	C₂×C₆₇	semidirect
759. #2946	C₂×C₆₇	semidirect
760. #2933	C₂×C₆₇	semidirect
761. C₆₇	#61072	direct (N × H)
762. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
763. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
764. C₂²×#41	C₂²×C₆₇	semidirect
765. C₂³×D₄	C₂²×C₆₇	semidirect
769. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
770. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
771. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
772. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
773. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
774. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
775. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
776. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
777. C₂×#135	C₂²×C₆₇	semidirect
778. C₂×#135	C₂²×C₆₇	semidirect
779. C₂×#135	C₂²×C₆₇	semidirect
780. C₂²×SD₁₆	C₂²×C₆₇	semidirect
781. C₂²×D₈	C₂²×C₆₇	semidirect
782. C₂²×D₈	C₂²×C₆₇	semidirect
783. C₂²×D₈	C₂²×C₆₇	semidirect
784. C₂²×D₈	C₂²×C₆₇	semidirect
785. C₂×#131	C₂²×C₆₇	semidirect
786. C₂²×M₁₆	C₂²×C₆₇	semidirect
787. #550	C₂²×C₆₇	semidirect
788. #548	C₂²×C₆₇	semidirect
792. #546	C₂²×C₆₇	semidirect
793. #546	C₂²×C₆₇	semidirect
794. #546	C₂²×C₆₇	semidirect
798. D₄²	C₂²×C₆₇	semidirect
799. D₄²	C₂²×C₆₇	semidirect
800. D₄²	C₂²×C₆₇	semidirect
802. #537	C₂²×C₆₇	semidirect
804. #535	C₂²×C₆₇	semidirect
805. #535	C₂²×C₆₇	semidirect
806. #535	C₂²×C₆₇	semidirect
810. #525	C₂²×C₆₇	semidirect
812. C₂×#121	C₂²×C₆₇	semidirect
814. #520	C₂²×C₆₇	semidirect
815. #518	C₂²×C₆₇	semidirect
816. #496	C₂²×C₆₇	semidirect
817. #496	C₂²×C₆₇	semidirect
818. #495	C₂²×C₆₇	semidirect
819. #493	C₂²×C₆₇	semidirect
820. #469	C₂²×C₆₇	semidirect
821. #469	C₂²×C₆₇	semidirect
822. #468	C₂²×C₆₇	semidirect
823. #468	C₂²×C₆₇	semidirect
824. #466	C₂²×C₆₇	semidirect
825. #466	C₂²×C₆₇	semidirect
826. #465	C₂²×C₆₇	semidirect
827. #465	C₂²×C₆₇	semidirect
828. #464	C₂²×C₆₇	semidirect
829. #463	C₂²×C₆₇	semidirect
830. #463	C₂²×C₆₇	semidirect
831. #463	C₂²×C₆₇	semidirect
832. #460	C₂²×C₆₇	semidirect
833. #459	C₂²×C₆₇	semidirect
834. #459	C₂²×C₆₇	semidirect
835. #459	C₂²×C₆₇	semidirect
836. #452	C₂²×C₆₇	semidirect
837. #452	C₂²×C₆₇	semidirect
838. #452	C₂²×C₆₇	semidirect
839. #451	C₂²×C₆₇	semidirect
840. #450	C₂²×C₆₇	semidirect
841. #450	C₂²×C₆₇	semidirect
842. #449	C₂²×C₆₇	semidirect
843. #449	C₂²×C₆₇	semidirect
844. #449	C₂²×C₆₇	semidirect
845. #449	C₂²×C₆₇	semidirect
846. #449	C₂²×C₆₇	semidirect
847. #448	C₂²×C₆₇	semidirect
848. #447	C₂²×C₆₇	semidirect
849. #447	C₂²×C₆₇	semidirect
850. #447	C₂²×C₆₇	semidirect
851. #447	C₂²×C₆₇	semidirect
852. #447	C₂²×C₆₇	semidirect
853. #447	C₂²×C₆₇	semidirect
854. #447	C₂²×C₆₇	semidirect
855. #447	C₂²×C₆₇	semidirect
856. #442	C₂²×C₆₇	semidirect
857. #440	C₂²×C₆₇	semidirect
858. C₄×SD₁₆	C₂²×C₆₇	semidirect
859. C₄×D₈	C₂²×C₆₇	semidirect
860. #436	C₂²×C₆₇	semidirect
861. #435	C₂²×C₆₇	semidirect
862. #435	C₂²×C₆₇	semidirect
863. C₈×D₄	C₂²×C₆₇	semidirect
864. #428	C₂²×C₆₇	semidirect
865. #424	C₂²×C₆₇	semidirect
866. #418	C₂²×C₆₇	semidirect
867. #417	C₂²×C₆₇	semidirect
868. #416	C₂²×C₆₇	semidirect
869. #416	C₂²×C₆₇	semidirect
870. C₂×#102	C₂²×C₆₇	semidirect
871. C₂×#102	C₂²×C₆₇	semidirect
872. #408	C₂²×C₆₇	semidirect
873. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
874. #405	C₂²×C₆₇	semidirect
893. C₂×#41	C₂³×C₆₇	semidirect
916. C₂²×D₄	C₂³×C₆₇	semidirect
927. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
931. C₂×Q₁₆	C₂³×C₆₇	semidirect
932. C₂×Q₁₆	C₂³×C₆₇	semidirect
938. C₂×SD₁₆	C₂³×C₆₇	semidirect
939. C₂×SD₁₆	C₂³×C₆₇	semidirect
940. C₂×SD₁₆	C₂³×C₆₇	semidirect
941. C₂×SD₁₆	C₂³×C₆₇	semidirect
942. C₂×SD₁₆	C₂³×C₆₇	semidirect
955. C₂×D₈	C₂³×C₆₇	semidirect
956. C₂×D₈	C₂³×C₆₇	semidirect
957. C₂×D₈	C₂³×C₆₇	semidirect
963. C₂×M₁₆	C₂³×C₆₇	semidirect
967. C₂²×C₈	C₂³×C₆₇	semidirect
971. #127	C₂³×C₆₇	semidirect
975. #124	C₂³×C₆₇	semidirect
987. C₂²⋊Q₈	C₂³×C₆₇	semidirect
1013. #121	C₂³×C₆₇	semidirect
1028. C₄×Q₈	C₂³×C₆₇	semidirect
1040. C₄×D₄	C₂³×C₆₇	semidirect
1051. #107	C₂³×C₆₇	semidirect
1052. #106	C₂³×C₆₇	semidirect
1053. C₄⋊C₈	C₂³×C₆₇	semidirect
1054. C₄⋊C₈	C₂³×C₆₇	semidirect
1055. #103	C₂³×C₆₇	semidirect
1056. #103	C₂³×C₆₇	semidirect
1057. #103	C₂³×C₆₇	semidirect
1058. #103	C₂³×C₆₇	semidirect
1059. #103	C₂³×C₆₇	semidirect
1064. #102	C₂³×C₆₇	semidirect
1065. #102	C₂³×C₆₇	semidirect
1066. #102	C₂³×C₆₇	semidirect
1067. #102	C₂³×C₆₇	semidirect
1068. #102	C₂³×C₆₇	semidirect
1069. #102	C₂³×C₆₇	semidirect
1070. #102	C₂³×C₆₇	semidirect
1075. C₂²⋊C₈	C₂³×C₆₇	semidirect
1076. C₂²⋊C₈	C₂³×C₆₇	semidirect
1077. #97	C₂³×C₆₇	semidirect
1078. C₄×C₈	C₂³×C₆₇	semidirect
1110. #41	C₂×D₄×C₆₇	semidirect
1175. C₂×D₄	C₂×D₄×C₆₇	semidirect
1214. SD₁₆	C₂×D₄×C₆₇	semidirect
1225. D₈	C₂×D₄×C₆₇	semidirect
1229. M₁₆	C₂×D₄×C₆₇	semidirect
1446. C₂²	#576×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#576×C₆₇	2
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#3488	2
C₆₇×#3484	2
C₆₇×#3282	2
D₄×D₈×C₆₇	2
C₆₇×#3274	2
C₆₇×#3273	2
C₆₇×#3268	2
C₆₇×#3265	2
C₆₇×#3264	2
C₆₇×#3155	2
C₆₇×#3062	2
C₆₇×#3055	2
C₆₇×#3045	2
C₆₇×#3041	2
C₆₇×#3012	2
C₆₇×#3008	2
C₆₇×#3002	2
C₂×#447×C₆₇	2
C₆₇×#2946	2
C₆₇×#2933	2
#61072	67

Subgroups — C67×#61072 #30740323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61072 #30740323