Subgroups — C₆₇×#61071 #30740322

Order 17152.

2876 conjugacy classes of subgroups.

The subgroup lattice has 1446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3484	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×SD₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3280	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3275	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3272	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3266	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3265	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3264	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3154	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#450×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	C₂×2₋¹⁺⁴×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
28	#577×C₆₇	—	2	8	no	—
29	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
31	C₂×AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
32	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
35	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
37	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, 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×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	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	D₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
50	#548×C₆₇	C₂²	1	2	yes	complemented
51	#547×C₆₇	—	2	2	no	—
52	#547×C₆₇	C₂²	1	2	yes	complemented
53	#546×C₆₇	—	2	1	no	—
54	#546×C₆₇	—	2	1	no	—
55	#546×C₆₇	—	2	2	no	—
56	#546×C₆₇	C₂²	1	2	yes	—
57	#546×C₆₇	C₂²	1	2	yes	complemented
58	#546×C₆₇	C₂²	1	2	yes	complemented
59	D₄²×C₆₇	—	2	1	no	—
60	D₄²×C₆₇	—	2	1	no	—
61	D₄²×C₆₇	C₂²	1	2	yes	—
62	D₄²×C₆₇	C₂²	1	2	yes	complemented
63	#537×C₆₇	—	2	1	no	—
64	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#536×C₆₇	—	2	1	no	—
66	#536×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
73	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
74	C₂×C₂²⋊Q₈×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	#497×C₆₇	C₂²	1	2	yes	complemented
79	#496×C₆₇	C₂²	1	2	yes	complemented
80	#495×C₆₇	C₂²	1	2	yes	complemented
81	#492×C₆₇	C₂²	1	2	yes	complemented
82	#470×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	#467×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	#461×C₆₇	C₂²	1	2	yes	complemented
95	#461×C₆₇	C₂²	1	2	yes	complemented
96	#460×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	2	yes	complemented
104	#450×C₆₇	C₂²	1	2	yes	complemented
105	#450×C₆₇	C₂²	1	2	yes	complemented
106	#450×C₆₇	C₂²	1	2	yes	complemented
107	#450×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#449×C₆₇	C₂²	1	2	yes	complemented
109	#449×C₆₇	C₂²	1	2	yes	complemented
110	#449×C₆₇	C₂²	1	2	yes	complemented
111	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#448×C₆₇	C₂²	1	2	yes	complemented
114	#448×C₆₇	C₂²	1	2	yes	complemented
115	#448×C₆₇	C₂²	1	1	yes	characteristic, 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	#419×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	2₋¹⁺⁴×C₆₇	—	2	4	no	—
139	2₋¹⁺⁴×C₆₇	—	4	2	no	—
140	H(5,𝔽₂)×C₆₇	—	2	4	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	2	no	—
145	C₂×#41×C₆₇	—	2	1	no	—
146	C₂×#41×C₆₇	—	2	1	no	—
147	C₂×#41×C₆₇	—	2	4	no	—
148	C₂×#41×C₆₇	—	4	2	no	—
149	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×#41×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
156	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
157	C₂²×Q₈×C₆₇	—	2	1	no	—
158	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₂²×Q₈×C₆₇	C₂³	1	2	yes	complemented
161	C₂²×D₄×C₆₇	—	2	4	no	—
162	C₂²×D₄×C₆₇	—	2	1	no	—
163	C₂²×D₄×C₆₇	—	2	2	no	—
164	C₂²×D₄×C₆₇	—	2	1	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	2	yes	—
173	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
174	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
175	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂³×C₄×C₆₇	—	2	1	no	—
178	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
179	#137×C₆₇	—	2	8	no	—
180	#137×C₆₇	—	2	4	no	—
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	4	no	—
187	AGL(1,ℤ/8)×C₆₇	D₄	1	8	yes	complemented
188	#135×C₆₇	—	2	4	no	—
189	#135×C₆₇	—	2	8	no	—
190	#135×C₆₇	—	4	2	no	—
191	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
192	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
193	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
194	C₂×SD₁₆×C₆₇	—	2	4	no	—
195	C₂×SD₁₆×C₆₇	—	2	8	no	—
196	C₂×SD₁₆×C₆₇	—	2	8	no	—
197	C₂×SD₁₆×C₆₇	—	4	2	no	—
198	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
199	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
200	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
201	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
202	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
203	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
204	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
205	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
206	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
207	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
208	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
209	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
210	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
211	C₂×D₈×C₆₇	—	2	8	no	—
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	1	yes	characteristic, complemented
217	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
218	#131×C₆₇	—	2	4	no	—
219	C₂×M₁₆×C₆₇	—	2	4	no	—
220	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
221	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
224	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
225	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
226	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
228	C₄⋊Q₈×C₆₇	—	2	2	no	—
229	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
230	#127×C₆₇	—	2	1	no	—
231	#127×C₆₇	C₂³	1	2	yes	—
232	#124×C₆₇	—	2	1	no	—
233	#124×C₆₇	—	2	2	no	—
234	#124×C₆₇	C₂³	1	2	yes	—
235	#124×C₆₇	C₂³	1	2	yes	complemented
236	#123×C₆₇	—	2	1	no	—
237	#123×C₆₇	—	2	2	no	—
238	#123×C₆₇	—	2	2	no	—
239	#123×C₆₇	—	2	2	no	—
240	#123×C₆₇	—	2	2	no	—
241	#123×C₆₇	—	2	2	no	—
242	#123×C₆₇	—	2	2	no	—
243	#123×C₆₇	D₄	1	2	yes	—
244	C₂²⋊Q₈×C₆₇	—	2	1	no	—
245	C₂²⋊Q₈×C₆₇	—	2	1	no	—
246	C₂²⋊Q₈×C₆₇	—	2	1	no	—
247	C₂²⋊Q₈×C₆₇	—	2	1	no	—
248	C₂²⋊Q₈×C₆₇	—	2	2	no	—
249	C₂²⋊Q₈×C₆₇	—	2	1	no	—
250	C₂²⋊Q₈×C₆₇	—	2	2	no	—
251	C₂²⋊Q₈×C₆₇	—	2	2	no	—
252	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
253	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
254	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
257	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
258	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	complemented
259	#121×C₆₇	—	2	1	no	—
260	#121×C₆₇	—	2	2	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	1	no	—
266	#121×C₆₇	—	2	1	no	—
267	#121×C₆₇	—	2	2	no	—
268	#121×C₆₇	—	2	2	no	—
269	#121×C₆₇	—	2	2	no	—
270	#121×C₆₇	D₄	1	1	yes	characteristic
271	#121×C₆₇	D₄	1	1	yes	characteristic
272	#121×C₆₇	C₂³	1	2	yes	—
273	#121×C₆₇	C₂³	1	2	yes	—
274	#121×C₆₇	C₂³	1	1	yes	characteristic
275	#121×C₆₇	C₂³	1	1	yes	characteristic
276	#121×C₆₇	C₂³	1	2	yes	complemented
277	#120×C₆₇	—	2	1	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	D₄	1	2	yes	—
288	C₄×Q₈×C₆₇	C₂³	1	2	yes	complemented
289	C₄×D₄×C₆₇	—	2	2	no	—
290	C₄×D₄×C₆₇	—	2	1	no	—
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	2	no	—
295	C₄×D₄×C₆₇	—	2	2	no	—
296	C₄×D₄×C₆₇	C₂³	1	2	yes	—
297	C₄×D₄×C₆₇	C₂³	1	2	yes	—
298	C₄×D₄×C₆₇	C₂³	1	2	yes	—
299	C₄×D₄×C₆₇	C₂³	1	2	yes	—
300	C₄×D₄×C₆₇	C₂³	1	2	yes	complemented
301	#117×C₆₇	—	2	1	no	—
302	#117×C₆₇	C₂³	1	1	yes	characteristic
303	#117×C₆₇	C₂³	1	1	yes	characteristic
304	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
305	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
306	C₂×C₄⋊C₄×C₆₇	—	2	2	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	2	yes	complemented
320	#103×C₆₇	C₂³	1	2	yes	complemented
321	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
322	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
323	#103×C₆₇	C₂³	1	2	yes	complemented
324	#102×C₆₇	C₂³	1	2	yes	—
325	#102×C₆₇	C₂³	1	2	yes	—
326	#102×C₆₇	C₂³	1	2	yes	—
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
329	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
330	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
331	#102×C₆₇	C₂³	1	2	yes	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	1	no	—
343	C₂⁴×C₆₇	—	2	2	no	—
344	C₂⁴×C₆₇	—	2	2	no	—
345	C₂⁴×C₆₇	—	2	1	no	—
346	C₂⁴×C₆₇	—	2	2	no	—
347	C₂⁴×C₆₇	—	4	4	no	—
348	C₂⁴×C₆₇	—	8	2	no	—
349	C₂⁴×C₆₇	—	8	2	no	—
350	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
351	#41×C₆₇	—	2	2	no	—
352	#41×C₆₇	—	2	2	no	—
353	#41×C₆₇	—	2	2	no	—
354	#41×C₆₇	—	2	2	no	—
355	#41×C₆₇	—	2	4	no	—
356	#41×C₆₇	—	2	4	no	—
357	#41×C₆₇	—	2	2	no	—
358	#41×C₆₇	—	2	2	no	—
359	#41×C₆₇	—	2	2	no	—
360	#41×C₆₇	—	2	2	no	—
361	#41×C₆₇	—	2	2	no	—
362	#41×C₆₇	—	4	4	no	—
363	#41×C₆₇	—	4	1	no	—
364	#41×C₆₇	—	4	1	no	—
365	#41×C₆₇	—	4	2	no	—
366	#41×C₆₇	—	4	2	no	—
367	#41×C₆₇	—	4	4	no	—
368	#41×C₆₇	—	4	4	no	—
369	#41×C₆₇	—	4	8	no	—
370	#41×C₆₇	—	4	4	no	—
371	#41×C₆₇	C₂×D₄	1	4	yes	complemented
372	C₂×Q₈×C₆₇	—	2	1	no	—
373	C₂×Q₈×C₆₇	—	2	2	no	—
374	C₂×Q₈×C₆₇	—	2	1	no	—
375	C₂×Q₈×C₆₇	—	2	2	no	—
376	C₂×Q₈×C₆₇	—	2	4	no	—
377	C₂×Q₈×C₆₇	—	2	2	no	—
378	C₂×Q₈×C₆₇	—	2	2	no	—
379	C₂×Q₈×C₆₇	—	4	1	no	—
380	C₂×Q₈×C₆₇	—	4	2	no	—
381	C₂×Q₈×C₆₇	—	4	4	no	—
382	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
383	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
385	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×D₄×C₆₇	—	2	1	no	—
388	C₂×D₄×C₆₇	—	2	2	no	—
389	C₂×D₄×C₆₇	—	2	4	no	—
390	C₂×D₄×C₆₇	—	2	4	no	—
391	C₂×D₄×C₆₇	—	2	4	no	—
392	C₂×D₄×C₆₇	—	2	1	no	—
393	C₂×D₄×C₆₇	—	2	1	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	1	no	—
398	C₂×D₄×C₆₇	—	2	1	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	2	no	—
408	C₂×D₄×C₆₇	—	2	1	no	—
409	C₂×D₄×C₆₇	—	2	1	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	—	4	2	no	—
415	C₂×D₄×C₆₇	—	4	2	no	—
416	C₂×D₄×C₆₇	—	4	1	no	—
417	C₂×D₄×C₆₇	—	4	2	no	—
418	C₂×D₄×C₆₇	—	4	4	no	—
419	C₂×D₄×C₆₇	—	4	4	no	—
420	C₂×D₄×C₆₇	—	4	4	no	—
421	C₂×D₄×C₆₇	—	4	4	no	—
422	C₂×D₄×C₆₇	—	4	4	no	—
423	C₂×D₄×C₆₇	—	4	8	no	—
424	C₂×D₄×C₆₇	—	8	4	no	—
425	C₂×D₄×C₆₇	—	8	4	no	—
426	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
427	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
428	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
429	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
430	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
431	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
432	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
433	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
435	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₆₇	—	2	1	no	—
437	C₂²×C₄×C₆₇	—	2	2	no	—
438	C₂²×C₄×C₆₇	—	2	2	no	—
439	C₂²×C₄×C₆₇	—	2	1	no	—
440	C₂²×C₄×C₆₇	—	2	2	no	—
441	C₂²×C₄×C₆₇	—	2	1	no	—
442	C₂²×C₄×C₆₇	—	2	1	no	—
443	C₂²×C₄×C₆₇	—	2	2	no	—
444	C₂²×C₄×C₆₇	—	2	2	no	—
445	C₂²×C₄×C₆₇	—	2	1	no	—
446	C₂²×C₄×C₆₇	—	2	1	no	—
447	C₂²×C₄×C₆₇	—	2	1	no	—
448	C₂²×C₄×C₆₇	—	2	1	no	—
449	C₂²×C₄×C₆₇	—	2	2	no	—
450	C₂²×C₄×C₆₇	—	2	2	no	—
451	C₂²×C₄×C₆₇	—	2	2	no	—
452	C₂²×C₄×C₆₇	—	4	4	no	—
453	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
454	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
455	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
456	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
457	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
460	Q₁₆×C₆₇	—	2	2	no	—
461	Q₁₆×C₆₇	—	2	4	no	—
462	Q₁₆×C₆₇	—	4	1	no	—
463	SD₁₆×C₆₇	—	2	2	no	—
464	SD₁₆×C₆₇	—	2	4	no	—
465	SD₁₆×C₆₇	—	2	4	no	—
466	SD₁₆×C₆₇	—	2	4	no	—
467	SD₁₆×C₆₇	—	2	4	no	—
468	SD₁₆×C₆₇	—	2	2	no	—
469	SD₁₆×C₆₇	—	2	4	no	—
470	SD₁₆×C₆₇	—	2	4	no	—
471	SD₁₆×C₆₇	—	4	2	no	—
472	SD₁₆×C₆₇	—	4	2	no	—
473	SD₁₆×C₆₇	—	4	1	no	—
474	SD₁₆×C₆₇	—	4	1	no	—
475	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
476	D₈×C₆₇	—	2	4	no	—
477	D₈×C₆₇	—	2	4	no	—
478	D₈×C₆₇	—	2	2	no	—
479	D₈×C₆₇	—	2	4	no	—
480	D₈×C₆₇	—	4	1	no	—
481	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
482	M₁₆×C₆₇	—	2	2	no	—
483	M₁₆×C₆₇	—	2	4	no	—
484	M₁₆×C₆₇	—	2	4	no	—
485	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
486	C₂×C₈×C₆₇	—	2	2	no	—
487	C₂×C₈×C₆₇	—	2	2	no	—
488	C₂×C₈×C₆₇	—	2	4	no	—
489	C₂×C₈×C₆₇	—	2	4	no	—
490	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
492	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
493	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
494	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
495	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
496	C₄⋊C₄×C₆₇	—	2	2	no	—
497	C₄⋊C₄×C₆₇	—	2	1	no	—
498	C₄⋊C₄×C₆₇	—	2	2	no	—
499	C₄⋊C₄×C₆₇	—	2	2	no	—
500	C₄⋊C₄×C₆₇	—	2	2	no	—
501	C₄⋊C₄×C₆₇	—	2	2	no	—
502	C₄⋊C₄×C₆₇	—	2	1	no	—
503	C₄⋊C₄×C₆₇	—	2	1	no	—
504	C₄⋊C₄×C₆₇	—	2	2	no	—
505	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
506	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
507	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
508	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
509	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
510	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
511	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
512	C₂²⋊C₄×C₆₇	—	2	1	no	—
513	C₂²⋊C₄×C₆₇	—	2	1	no	—
514	C₂²⋊C₄×C₆₇	—	2	1	no	—
515	C₂²⋊C₄×C₆₇	—	2	2	no	—
516	C₂²⋊C₄×C₆₇	—	2	2	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	1	no	—
528	C₂²⋊C₄×C₆₇	—	2	1	no	—
529	C₂²⋊C₄×C₆₇	—	2	2	no	—
530	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
531	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
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	C₄²×C₆₇	—	2	2	no	—
536	C₄²×C₆₇	—	2	1	no	—
537	C₄²×C₆₇	C₂⁴	1	2	yes	—
538	C₂³×C₆₇	—	2	2	no	—
539	C₂³×C₆₇	—	2	2	no	—
540	C₂³×C₆₇	—	2	1	no	—
541	C₂³×C₆₇	—	2	2	no	—
542	C₂³×C₆₇	—	2	4	no	—
543	C₂³×C₆₇	—	2	1	no	—
544	C₂³×C₆₇	—	2	2	no	—
545	C₂³×C₆₇	—	2	1	no	—
546	C₂³×C₆₇	—	4	1	no	—
547	C₂³×C₆₇	—	4	2	no	—
548	C₂³×C₆₇	—	4	4	no	—
549	C₂³×C₆₇	—	4	4	no	—
550	C₂³×C₆₇	—	4	4	no	—
551	C₂³×C₆₇	—	4	4	no	—
552	C₂³×C₆₇	—	4	2	no	—
553	C₂³×C₆₇	—	4	4	no	—
554	C₂³×C₆₇	—	4	2	no	—
555	C₂³×C₆₇	—	8	1	no	—
556	C₂³×C₆₇	—	8	1	no	—
557	C₂³×C₆₇	—	8	1	no	—
558	C₂³×C₆₇	—	8	2	no	—
559	C₂³×C₆₇	—	8	1	no	—
560	C₂³×C₆₇	—	8	1	no	—
561	C₂³×C₆₇	—	8	2	no	—
562	C₂³×C₆₇	—	8	2	no	—
563	C₂³×C₆₇	—	8	2	no	—
564	C₂³×C₆₇	—	8	16	no	—
565	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
566	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
567	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
568	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
569	Q₈×C₆₇	—	2	2	no	—
570	Q₈×C₆₇	—	2	1	no	—
571	Q₈×C₆₇	—	2	1	no	—
572	Q₈×C₆₇	—	2	2	no	—
573	Q₈×C₆₇	—	2	1	no	—
574	Q₈×C₆₇	—	2	2	no	—
575	Q₈×C₆₇	—	2	1	no	—
576	Q₈×C₆₇	—	2	1	no	—
577	Q₈×C₆₇	—	4	4	no	—
578	Q₈×C₆₇	—	4	2	no	—
579	Q₈×C₆₇	—	4	2	no	—
580	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
581	D₄×C₆₇	—	2	4	no	—
582	D₄×C₆₇	—	2	4	no	—
583	D₄×C₆₇	—	2	4	no	—
584	D₄×C₆₇	—	2	4	no	—
585	D₄×C₆₇	—	2	2	no	—
586	D₄×C₆₇	—	2	1	no	—
587	D₄×C₆₇	—	2	2	no	—
588	D₄×C₆₇	—	2	1	no	—
589	D₄×C₆₇	—	2	2	no	—
590	D₄×C₆₇	—	2	1	no	—
591	D₄×C₆₇	—	2	1	no	—
592	D₄×C₆₇	—	2	1	no	—
593	D₄×C₆₇	—	2	2	no	—
594	D₄×C₆₇	—	4	2	no	—
595	D₄×C₆₇	—	4	4	no	—
596	D₄×C₆₇	—	4	4	no	—
597	D₄×C₆₇	—	4	4	no	—
598	D₄×C₆₇	—	4	2	no	—
599	D₄×C₆₇	—	4	2	no	—
600	D₄×C₆₇	—	4	4	no	—
601	D₄×C₆₇	—	4	2	no	—
602	D₄×C₆₇	—	4	4	no	—
603	D₄×C₆₇	—	4	2	no	—
604	D₄×C₆₇	—	4	2	no	—
605	D₄×C₆₇	—	4	2	no	—
606	D₄×C₆₇	—	4	2	no	—
607	D₄×C₆₇	—	4	2	no	—
608	D₄×C₆₇	—	8	2	no	—
609	D₄×C₆₇	—	8	2	no	—
610	D₄×C₆₇	—	8	2	no	—
611	D₄×C₆₇	—	8	2	no	—
612	D₄×C₆₇	—	8	2	no	—
613	D₄×C₆₇	C₂²×D₄	1	2	yes	—
614	D₄×C₆₇	C₂²×D₄	1	4	yes	—
615	C₂×C₄×C₆₇	—	2	2	no	—
616	C₂×C₄×C₆₇	—	2	1	no	—
617	C₂×C₄×C₆₇	—	2	2	no	—
618	C₂×C₄×C₆₇	—	2	2	no	—
619	C₂×C₄×C₆₇	—	2	4	no	—
620	C₂×C₄×C₆₇	—	2	1	no	—
621	C₂×C₄×C₆₇	—	2	2	no	—
622	C₂×C₄×C₆₇	—	2	1	no	—
623	C₂×C₄×C₆₇	—	2	1	no	—
624	C₂×C₄×C₆₇	—	2	1	no	—
625	C₂×C₄×C₆₇	—	2	2	no	—
626	C₂×C₄×C₆₇	—	2	1	no	—
627	C₂×C₄×C₆₇	—	2	1	no	—
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	1	no	—
632	C₂×C₄×C₆₇	—	4	2	no	—
633	C₂×C₄×C₆₇	—	4	2	no	—
634	C₂×C₄×C₆₇	—	4	2	no	—
635	C₂×C₄×C₆₇	—	4	4	no	—
636	C₂×C₄×C₆₇	—	4	4	no	—
637	C₂×C₄×C₆₇	—	4	4	no	—
638	C₂×C₄×C₆₇	—	4	2	no	—
639	C₂×C₄×C₆₇	—	4	2	no	—
640	C₂×C₄×C₆₇	—	4	2	no	—
641	C₂×C₄×C₆₇	—	8	2	no	—
642	C₂×C₄×C₆₇	—	8	2	no	—
643	C₂×C₄×C₆₇	—	8	2	no	—
644	C₂×C₄×C₆₇	—	8	1	no	—
645	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
646	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
647	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
648	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
649	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
650	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
651	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
652	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
653	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
654	C₈×C₆₇	—	2	1	no	—
655	C₈×C₆₇	—	2	2	no	—
656	C₈×C₆₇	—	2	1	no	—
657	C₈×C₆₇	—	2	1	no	—
658	C₈×C₆₇	—	2	1	no	—
659	C₈×C₆₇	C₂²×D₄	1	4	yes	—
660	C₂²×C₆₇	—	2	1	no	—
661	C₂²×C₆₇	—	2	1	no	—
662	C₂²×C₆₇	—	2	1	no	—
663	C₂²×C₆₇	—	2	1	no	—
664	C₂²×C₆₇	—	2	1	no	—
665	C₂²×C₆₇	—	2	2	no	—
666	C₂²×C₆₇	—	2	1	no	—
667	C₂²×C₆₇	—	2	2	no	—
668	C₂²×C₆₇	—	2	2	no	—
669	C₂²×C₆₇	—	2	4	no	—
670	C₂²×C₆₇	—	2	2	no	—
671	C₂²×C₆₇	—	2	1	no	—
672	C₂²×C₆₇	—	4	4	no	—
673	C₂²×C₆₇	—	4	1	no	—
674	C₂²×C₆₇	—	4	2	no	—
675	C₂²×C₆₇	—	4	2	no	—
676	C₂²×C₆₇	—	4	1	no	—
677	C₂²×C₆₇	—	4	1	no	—
678	C₂²×C₆₇	—	4	2	no	—
679	C₂²×C₆₇	—	4	1	no	—
680	C₂²×C₆₇	—	4	1	no	—
681	C₂²×C₆₇	—	4	1	no	—
682	C₂²×C₆₇	—	4	2	no	—
683	C₂²×C₆₇	—	4	1	no	—
684	C₂²×C₆₇	—	4	2	no	—
685	C₂²×C₆₇	—	4	1	no	—
686	C₂²×C₆₇	—	8	4	no	—
687	C₂²×C₆₇	—	8	4	no	—
688	C₂²×C₆₇	—	8	8	no	—
689	C₂²×C₆₇	—	8	4	no	—
690	C₂²×C₆₇	—	8	8	no	—
691	C₂²×C₆₇	—	16	4	no	—
692	C₂²×C₆₇	D₄²	1	2	yes	—
693	C₂²×C₆₇	#577	1	2	yes	complemented
694	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
695	C₄×C₆₇	—	2	2	no	—
696	C₄×C₆₇	—	2	1	no	—
697	C₄×C₆₇	—	2	1	no	—
698	C₄×C₆₇	—	2	2	no	—
699	C₄×C₆₇	—	2	2	no	—
700	C₄×C₆₇	—	2	2	no	—
701	C₄×C₆₇	—	4	1	no	—
702	C₄×C₆₇	—	4	2	no	—
703	C₄×C₆₇	—	4	1	no	—
704	C₄×C₆₇	—	4	1	no	—
705	C₄×C₆₇	—	4	2	no	—
706	C₄×C₆₇	—	4	1	no	—
707	C₄×C₆₇	D₄²	1	2	yes	—
708	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
709	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
710	#61071	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
711	C₂×C₆₇	—	2	2	no	—
712	C₂×C₆₇	—	2	2	no	—
713	C₂×C₆₇	—	4	1	no	—
714	C₂×C₆₇	—	4	2	no	—
715	C₂×C₆₇	—	4	2	no	—
716	C₂×C₆₇	—	4	4	no	—
717	C₂×C₆₇	—	8	1	no	—
718	C₂×C₆₇	—	8	2	no	—
719	C₂×C₆₇	—	8	1	no	—
720	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
721	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
722	C₂×C₆₇	#3585	1	1	yes	characteristic
723	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
724	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
725	#3489	C₂×C₆₇	1	1	yes	characteristic, complemented
726	#3484	C₂×C₆₇	1	1	yes	characteristic, complemented
727	D₄×SD₁₆	C₂×C₆₇	1	2	yes	complemented
728	#3280	C₂×C₆₇	1	2	yes	complemented
729	#3275	C₂×C₆₇	1	2	yes	complemented
730	#3272	C₂×C₆₇	1	2	yes	complemented
731	#3267	C₂×C₆₇	1	2	yes	complemented
732	#3266	C₂×C₆₇	1	2	yes	complemented
733	#3265	C₂×C₆₇	1	2	yes	complemented
734	#3264	C₂×C₆₇	1	2	yes	complemented
735	#3154	C₂×C₆₇	1	1	yes	characteristic, complemented
736	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
737	#3056	C₂×C₆₇	1	1	yes	characteristic, complemented
738	#3045	C₂×C₆₇	1	1	yes	characteristic, complemented
739	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
740	#3012	C₂×C₆₇	1	1	yes	characteristic, complemented
741	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
742	#3002	C₂×C₆₇	1	1	yes	characteristic, complemented
743	C₂×#450	C₂×C₆₇	1	1	yes	characteristic, complemented
744	#2946	C₂×C₆₇	1	1	yes	characteristic, complemented
745	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
746	C₆₇	#61071	1	1	yes	characteristic, direct product factor, Sylow
747	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
749	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
750	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
751	#577	—	2	8	no	—
752	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
753	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
754	C₂×AGL(1,ℤ/8)	—	2	8	no	—
755	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
756	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
757	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
758	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
759	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
761	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
762	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
764	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
765	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
767	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
768	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
769	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
770	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
771	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
772	D₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
773	#548	C₂²×C₆₇	1	2	yes	complemented
774	#547	—	2	2	no	—
775	#547	C₂²×C₆₇	1	2	yes	complemented
776	#546	—	2	1	no	—
777	#546	—	2	1	no	—
778	#546	—	2	2	no	—
779	#546	C₂²×C₆₇	1	2	yes	—
780	#546	C₂²×C₆₇	1	2	yes	complemented
781	#546	C₂²×C₆₇	1	2	yes	complemented
782	D₄²	—	2	1	no	—
783	D₄²	—	2	1	no	—
784	D₄²	C₂²×C₆₇	1	2	yes	—
785	D₄²	C₂²×C₆₇	1	2	yes	complemented
786	#537	—	2	1	no	—
787	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
788	#536	—	2	1	no	—
789	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
790	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
791	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
792	#534	—	2	2	no	—
793	#525	—	2	1	no	—
794	#525	C₂²×C₆₇	1	1	yes	characteristic
795	#525	C₂²×C₆₇	1	1	yes	characteristic
796	C₂×C₂²⋊Q₈	—	2	1	no	—
797	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
798	C₂×#120	—	2	2	no	—
799	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
800	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
801	#497	C₂²×C₆₇	1	2	yes	complemented
802	#496	C₂²×C₆₇	1	2	yes	complemented
803	#495	C₂²×C₆₇	1	2	yes	complemented
804	#492	C₂²×C₆₇	1	2	yes	complemented
805	#470	C₂²×C₆₇	1	2	yes	complemented
806	#469	C₂²×C₆₇	1	2	yes	complemented
807	#468	C₂²×C₆₇	1	2	yes	complemented
808	#468	C₂²×C₆₇	1	2	yes	complemented
809	#467	C₂²×C₆₇	1	2	yes	complemented
810	#466	C₂²×C₆₇	1	2	yes	complemented
811	#465	C₂²×C₆₇	1	2	yes	complemented
812	#465	C₂²×C₆₇	1	2	yes	complemented
813	#464	C₂²×C₆₇	1	2	yes	complemented
814	#463	C₂²×C₆₇	1	2	yes	complemented
815	#463	C₂²×C₆₇	1	2	yes	complemented
816	#463	C₂²×C₆₇	1	2	yes	complemented
817	#461	C₂²×C₆₇	1	2	yes	complemented
818	#461	C₂²×C₆₇	1	2	yes	complemented
819	#460	C₂²×C₆₇	1	2	yes	complemented
820	#459	C₂²×C₆₇	1	2	yes	complemented
821	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
822	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
823	#452	C₂²×C₆₇	1	2	yes	complemented
824	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
825	#450	C₂²×C₆₇	1	2	yes	complemented
826	#450	C₂²×C₆₇	1	2	yes	complemented
827	#450	C₂²×C₆₇	1	2	yes	complemented
828	#450	C₂²×C₆₇	1	2	yes	complemented
829	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
830	#450	C₂²×C₆₇	1	2	yes	complemented
831	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
832	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
833	#449	C₂²×C₆₇	1	2	yes	complemented
834	#449	C₂²×C₆₇	1	2	yes	complemented
835	#449	C₂²×C₆₇	1	2	yes	complemented
836	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
837	#448	C₂²×C₆₇	1	2	yes	complemented
838	#448	C₂²×C₆₇	1	2	yes	complemented
839	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
840	#447	C₂²×C₆₇	1	2	yes	complemented
841	#442	C₂²×C₆₇	1	2	yes	complemented
842	#440	C₂²×C₆₇	1	2	yes	complemented
843	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
844	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
845	#436	C₂²×C₆₇	1	2	yes	complemented
846	#435	C₂²×C₆₇	1	2	yes	complemented
847	#435	C₂²×C₆₇	1	2	yes	complemented
848	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
849	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
850	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
851	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
852	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
853	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
854	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
855	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
856	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
857	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
858	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
859	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
860	C₂⁵	—	2	1	no	—
861	2₋¹⁺⁴	—	2	4	no	—
862	2₋¹⁺⁴	—	4	2	no	—
863	H(5,𝔽₂)	—	2	4	no	—
864	H(5,𝔽₂)	—	4	2	no	—
865	C₂×#41	—	2	1	no	—
866	C₂×#41	—	2	1	no	—
867	C₂×#41	—	2	2	no	—
868	C₂×#41	—	2	1	no	—
869	C₂×#41	—	2	1	no	—
870	C₂×#41	—	2	4	no	—
871	C₂×#41	—	4	2	no	—
872	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
873	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
874	C₂×#41	C₂³×C₆₇	1	2	yes	—
875	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
876	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
877	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
878	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
879	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
880	C₂²×Q₈	—	2	1	no	—
881	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
882	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
883	C₂²×Q₈	C₂³×C₆₇	1	2	yes	complemented
884	C₂²×D₄	—	2	4	no	—
885	C₂²×D₄	—	2	1	no	—
886	C₂²×D₄	—	2	2	no	—
887	C₂²×D₄	—	2	1	no	—
888	C₂²×D₄	—	2	2	no	—
889	C₂²×D₄	—	2	2	no	—
890	C₂²×D₄	—	2	1	no	—
891	C₂²×D₄	—	2	1	no	—
892	C₂²×D₄	—	2	1	no	—
893	C₂²×D₄	—	4	2	no	—
894	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
895	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
896	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
897	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
898	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
899	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
900	C₂³×C₄	—	2	1	no	—
901	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
902	#137	—	2	8	no	—
903	#137	—	2	4	no	—
904	AGL(1,ℤ/8)	—	2	4	no	—
905	AGL(1,ℤ/8)	—	2	4	no	—
906	AGL(1,ℤ/8)	—	2	8	no	—
907	AGL(1,ℤ/8)	—	2	8	no	—
908	AGL(1,ℤ/8)	—	2	8	no	—
909	AGL(1,ℤ/8)	—	2	4	no	—
910	AGL(1,ℤ/8)	D₄×C₆₇	1	8	yes	complemented
911	#135	—	2	4	no	—
912	#135	—	2	8	no	—
913	#135	—	4	2	no	—
914	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
915	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
916	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
917	C₂×SD₁₆	—	2	4	no	—
918	C₂×SD₁₆	—	2	8	no	—
919	C₂×SD₁₆	—	2	8	no	—
920	C₂×SD₁₆	—	4	2	no	—
921	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
922	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
923	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
924	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
925	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
926	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
927	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
928	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
929	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
930	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
931	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
932	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
933	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
934	C₂×D₈	—	2	8	no	—
935	C₂×D₈	C₂³×C₆₇	1	2	yes	—
936	C₂×D₈	C₂³×C₆₇	1	2	yes	—
937	C₂×D₈	C₂³×C₆₇	1	2	yes	—
938	C₂×D₈	C₂³×C₆₇	1	2	yes	—
939	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
940	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
941	#131	—	2	4	no	—
942	C₂×M₁₆	—	2	4	no	—
943	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
944	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
945	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
946	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
947	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
948	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
949	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
950	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
951	C₄⋊Q₈	—	2	2	no	—
952	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
953	#127	—	2	1	no	—
954	#127	C₂³×C₆₇	1	2	yes	—
955	#124	—	2	1	no	—
956	#124	—	2	2	no	—
957	#124	C₂³×C₆₇	1	2	yes	—
958	#124	C₂³×C₆₇	1	2	yes	complemented
959	#123	—	2	1	no	—
960	#123	—	2	2	no	—
961	#123	—	2	2	no	—
962	#123	—	2	2	no	—
963	#123	—	2	2	no	—
964	#123	—	2	2	no	—
965	#123	—	2	2	no	—
966	#123	D₄×C₆₇	1	2	yes	—
967	C₂²⋊Q₈	—	2	1	no	—
968	C₂²⋊Q₈	—	2	1	no	—
969	C₂²⋊Q₈	—	2	1	no	—
970	C₂²⋊Q₈	—	2	1	no	—
971	C₂²⋊Q₈	—	2	2	no	—
972	C₂²⋊Q₈	—	2	1	no	—
973	C₂²⋊Q₈	—	2	2	no	—
974	C₂²⋊Q₈	—	2	2	no	—
975	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
976	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
977	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
978	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
979	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
980	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
981	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	complemented
982	#121	—	2	1	no	—
983	#121	—	2	2	no	—
984	#121	—	2	2	no	—
985	#121	—	2	2	no	—
986	#121	—	2	2	no	—
987	#121	—	2	2	no	—
988	#121	—	2	1	no	—
989	#121	—	2	1	no	—
990	#121	—	2	2	no	—
991	#121	—	2	2	no	—
992	#121	—	2	2	no	—
993	#121	D₄×C₆₇	1	1	yes	characteristic
994	#121	D₄×C₆₇	1	1	yes	characteristic
995	#121	C₂³×C₆₇	1	1	yes	characteristic
996	#121	C₂³×C₆₇	1	1	yes	characteristic
997	#121	C₂³×C₆₇	1	2	yes	—
998	#121	C₂³×C₆₇	1	2	yes	—
999	#121	C₂³×C₆₇	1	2	yes	complemented
1000	#120	—	2	1	no	—
1001	#120	—	2	2	no	—
1002	#120	—	2	2	no	—
1003	#120	—	2	2	no	—
1004	#120	—	2	2	no	—
1005	#120	—	2	2	no	—
1006	#120	—	2	2	no	—
1007	#120	—	2	2	no	—
1008	#120	—	2	2	no	—
1009	#120	—	2	2	no	—
1010	#120	D₄×C₆₇	1	2	yes	—
1011	C₄×Q₈	C₂³×C₆₇	1	2	yes	complemented
1012	C₄×D₄	—	2	2	no	—
1013	C₄×D₄	—	2	1	no	—
1014	C₄×D₄	—	2	1	no	—
1015	C₄×D₄	—	2	1	no	—
1016	C₄×D₄	—	2	1	no	—
1017	C₄×D₄	—	2	2	no	—
1018	C₄×D₄	—	2	2	no	—
1019	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1020	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1021	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1022	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1023	C₄×D₄	C₂³×C₆₇	1	2	yes	complemented
1024	#117	—	2	1	no	—
1025	#117	C₂³×C₆₇	1	1	yes	characteristic
1026	#117	C₂³×C₆₇	1	1	yes	characteristic
1027	C₂×C₄⋊C₄	—	2	1	no	—
1028	C₂×C₄⋊C₄	—	2	1	no	—
1029	C₂×C₄⋊C₄	—	2	2	no	—
1030	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	—	2	1	no	—
1032	C₂×C₂²⋊C₄	—	2	2	no	—
1033	C₂×C₂²⋊C₄	—	2	2	no	—
1034	C₂×C₂²⋊C₄	—	2	2	no	—
1035	C₂×C₂²⋊C₄	—	2	2	no	—
1036	#107	C₂³×C₆₇	1	2	yes	complemented
1037	#106	C₂³×C₆₇	1	2	yes	complemented
1038	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1039	C₄⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1040	#103	C₂³×C₆₇	1	1	yes	characteristic, complemented
1041	#103	C₂³×C₆₇	1	1	yes	characteristic, complemented
1042	#103	C₂³×C₆₇	1	1	yes	characteristic, complemented
1043	#103	C₂³×C₆₇	1	1	yes	characteristic, complemented
1044	#103	C₂³×C₆₇	1	2	yes	complemented
1045	#103	C₂³×C₆₇	1	2	yes	complemented
1046	#103	C₂³×C₆₇	1	2	yes	complemented
1047	#102	C₂³×C₆₇	1	2	yes	—
1048	#102	C₂³×C₆₇	1	2	yes	—
1049	#102	C₂³×C₆₇	1	2	yes	—
1050	#102	C₂³×C₆₇	1	2	yes	—
1051	#102	C₂³×C₆₇	1	1	yes	characteristic, complemented
1052	#102	C₂³×C₆₇	1	1	yes	characteristic, complemented
1053	#102	C₂³×C₆₇	1	1	yes	characteristic, complemented
1054	#102	C₂³×C₆₇	1	1	yes	characteristic, complemented
1055	#102	C₂³×C₆₇	1	2	yes	complemented
1056	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1057	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1058	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1059	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1060	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1061	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	complemented
1062	#97	C₂³×C₆₇	1	2	yes	complemented
1063	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
1064	C₂⁴	—	2	1	no	—
1065	C₂⁴	—	2	1	no	—
1066	C₂⁴	—	2	2	no	—
1067	C₂⁴	—	2	2	no	—
1068	C₂⁴	—	2	1	no	—
1069	C₂⁴	—	2	2	no	—
1070	C₂⁴	—	4	4	no	—
1071	C₂⁴	—	8	2	no	—
1072	C₂⁴	—	8	2	no	—
1073	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1074	#41	—	2	2	no	—
1075	#41	—	2	2	no	—
1076	#41	—	2	2	no	—
1077	#41	—	2	2	no	—
1078	#41	—	2	4	no	—
1079	#41	—	2	4	no	—
1080	#41	—	2	2	no	—
1081	#41	—	2	2	no	—
1082	#41	—	2	2	no	—
1083	#41	—	2	2	no	—
1084	#41	—	2	2	no	—
1085	#41	—	4	4	no	—
1086	#41	—	4	1	no	—
1087	#41	—	4	1	no	—
1088	#41	—	4	2	no	—
1089	#41	—	4	2	no	—
1090	#41	—	4	4	no	—
1091	#41	—	4	4	no	—
1092	#41	—	4	8	no	—
1093	#41	—	4	4	no	—
1094	#41	C₂×D₄×C₆₇	1	4	yes	complemented
1095	C₂×Q₈	—	2	1	no	—
1096	C₂×Q₈	—	2	2	no	—
1097	C₂×Q₈	—	2	1	no	—
1098	C₂×Q₈	—	2	2	no	—
1099	C₂×Q₈	—	2	4	no	—
1100	C₂×Q₈	—	2	2	no	—
1101	C₂×Q₈	—	2	2	no	—
1102	C₂×Q₈	—	4	1	no	—
1103	C₂×Q₈	—	4	2	no	—
1104	C₂×Q₈	—	4	4	no	—
1105	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1106	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1107	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1108	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1109	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1110	C₂×D₄	—	2	1	no	—
1111	C₂×D₄	—	2	2	no	—
1112	C₂×D₄	—	2	4	no	—
1113	C₂×D₄	—	2	4	no	—
1114	C₂×D₄	—	2	4	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	2	1	no	—
1117	C₂×D₄	—	2	1	no	—
1118	C₂×D₄	—	2	2	no	—
1119	C₂×D₄	—	2	2	no	—
1120	C₂×D₄	—	2	1	no	—
1121	C₂×D₄	—	2	1	no	—
1122	C₂×D₄	—	2	1	no	—
1123	C₂×D₄	—	2	2	no	—
1124	C₂×D₄	—	2	2	no	—
1125	C₂×D₄	—	2	2	no	—
1126	C₂×D₄	—	2	1	no	—
1127	C₂×D₄	—	2	2	no	—
1128	C₂×D₄	—	2	2	no	—
1129	C₂×D₄	—	2	2	no	—
1130	C₂×D₄	—	2	2	no	—
1131	C₂×D₄	—	2	1	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	—	4	2	no	—
1138	C₂×D₄	—	4	2	no	—
1139	C₂×D₄	—	4	1	no	—
1140	C₂×D₄	—	4	2	no	—
1141	C₂×D₄	—	4	4	no	—
1142	C₂×D₄	—	4	4	no	—
1143	C₂×D₄	—	4	4	no	—
1144	C₂×D₄	—	4	4	no	—
1145	C₂×D₄	—	4	4	no	—
1146	C₂×D₄	—	4	8	no	—
1147	C₂×D₄	—	8	4	no	—
1148	C₂×D₄	—	8	4	no	—
1149	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1150	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1151	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1152	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
1153	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1154	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1155	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1156	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1157	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1158	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1159	C₂²×C₄	—	2	1	no	—
1160	C₂²×C₄	—	2	2	no	—
1161	C₂²×C₄	—	2	2	no	—
1162	C₂²×C₄	—	2	1	no	—
1163	C₂²×C₄	—	2	2	no	—
1164	C₂²×C₄	—	2	1	no	—
1165	C₂²×C₄	—	2	1	no	—
1166	C₂²×C₄	—	2	2	no	—
1167	C₂²×C₄	—	2	2	no	—
1168	C₂²×C₄	—	2	1	no	—
1169	C₂²×C₄	—	2	1	no	—
1170	C₂²×C₄	—	2	1	no	—
1171	C₂²×C₄	—	2	1	no	—
1172	C₂²×C₄	—	2	2	no	—
1173	C₂²×C₄	—	2	2	no	—
1174	C₂²×C₄	—	2	2	no	—
1175	C₂²×C₄	—	4	4	no	—
1176	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1177	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1178	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1179	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1180	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1181	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1182	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1183	Q₁₆	—	2	2	no	—
1184	Q₁₆	—	2	4	no	—
1185	Q₁₆	—	4	1	no	—
1186	SD₁₆	—	2	2	no	—
1187	SD₁₆	—	2	4	no	—
1188	SD₁₆	—	2	4	no	—
1189	SD₁₆	—	2	4	no	—
1190	SD₁₆	—	2	4	no	—
1191	SD₁₆	—	2	2	no	—
1192	SD₁₆	—	2	4	no	—
1193	SD₁₆	—	2	4	no	—
1194	SD₁₆	—	4	2	no	—
1195	SD₁₆	—	4	2	no	—
1196	SD₁₆	—	4	1	no	—
1197	SD₁₆	—	4	1	no	—
1198	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
1199	D₈	—	2	4	no	—
1200	D₈	—	2	4	no	—
1201	D₈	—	2	2	no	—
1202	D₈	—	2	4	no	—
1203	D₈	—	4	1	no	—
1204	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
1205	M₁₆	—	2	2	no	—
1206	M₁₆	—	2	4	no	—
1207	M₁₆	—	2	4	no	—
1208	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1209	C₂×C₈	—	2	2	no	—
1210	C₂×C₈	—	2	2	no	—
1211	C₂×C₈	—	2	4	no	—
1212	C₂×C₈	—	2	4	no	—
1213	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1214	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1215	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1216	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1217	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1218	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1219	C₄⋊C₄	—	2	2	no	—
1220	C₄⋊C₄	—	2	1	no	—
1221	C₄⋊C₄	—	2	2	no	—
1222	C₄⋊C₄	—	2	2	no	—
1223	C₄⋊C₄	—	2	2	no	—
1224	C₄⋊C₄	—	2	2	no	—
1225	C₄⋊C₄	—	2	1	no	—
1226	C₄⋊C₄	—	2	1	no	—
1227	C₄⋊C₄	—	2	2	no	—
1228	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1229	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1230	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1231	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1232	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1233	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1234	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1235	C₂²⋊C₄	—	2	1	no	—
1236	C₂²⋊C₄	—	2	1	no	—
1237	C₂²⋊C₄	—	2	1	no	—
1238	C₂²⋊C₄	—	2	2	no	—
1239	C₂²⋊C₄	—	2	2	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	2	no	—
1245	C₂²⋊C₄	—	2	2	no	—
1246	C₂²⋊C₄	—	2	2	no	—
1247	C₂²⋊C₄	—	2	2	no	—
1248	C₂²⋊C₄	—	2	2	no	—
1249	C₂²⋊C₄	—	2	2	no	—
1250	C₂²⋊C₄	—	2	1	no	—
1251	C₂²⋊C₄	—	2	1	no	—
1252	C₂²⋊C₄	—	2	2	no	—
1253	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1254	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1255	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1256	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1257	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1258	C₄²	—	2	2	no	—
1259	C₄²	—	2	1	no	—
1260	C₄²	C₂⁴×C₆₇	1	2	yes	—
1261	C₂³	—	2	2	no	—
1262	C₂³	—	2	2	no	—
1263	C₂³	—	2	1	no	—
1264	C₂³	—	2	2	no	—
1265	C₂³	—	2	4	no	—
1266	C₂³	—	2	1	no	—
1267	C₂³	—	2	2	no	—
1268	C₂³	—	2	1	no	—
1269	C₂³	—	4	1	no	—
1270	C₂³	—	4	2	no	—
1271	C₂³	—	4	4	no	—
1272	C₂³	—	4	4	no	—
1273	C₂³	—	4	4	no	—
1274	C₂³	—	4	4	no	—
1275	C₂³	—	4	2	no	—
1276	C₂³	—	4	4	no	—
1277	C₂³	—	4	2	no	—
1278	C₂³	—	8	1	no	—
1279	C₂³	—	8	1	no	—
1280	C₂³	—	8	1	no	—
1281	C₂³	—	8	1	no	—
1282	C₂³	—	8	2	no	—
1283	C₂³	—	8	2	no	—
1284	C₂³	—	8	1	no	—
1285	C₂³	—	8	2	no	—
1286	C₂³	—	8	2	no	—
1287	C₂³	—	8	16	no	—
1288	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1289	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1290	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1291	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1292	Q₈	—	2	2	no	—
1293	Q₈	—	2	1	no	—
1294	Q₈	—	2	1	no	—
1295	Q₈	—	2	2	no	—
1296	Q₈	—	2	1	no	—
1297	Q₈	—	2	2	no	—
1298	Q₈	—	2	1	no	—
1299	Q₈	—	2	1	no	—
1300	Q₈	—	4	4	no	—
1301	Q₈	—	4	2	no	—
1302	Q₈	—	4	2	no	—
1303	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1304	D₄	—	2	4	no	—
1305	D₄	—	2	4	no	—
1306	D₄	—	2	4	no	—
1307	D₄	—	2	4	no	—
1308	D₄	—	2	2	no	—
1309	D₄	—	2	1	no	—
1310	D₄	—	2	2	no	—
1311	D₄	—	2	1	no	—
1312	D₄	—	2	2	no	—
1313	D₄	—	2	1	no	—
1314	D₄	—	2	1	no	—
1315	D₄	—	2	1	no	—
1316	D₄	—	2	2	no	—
1317	D₄	—	4	2	no	—
1318	D₄	—	4	4	no	—
1319	D₄	—	4	4	no	—
1320	D₄	—	4	4	no	—
1321	D₄	—	4	2	no	—
1322	D₄	—	4	2	no	—
1323	D₄	—	4	4	no	—
1324	D₄	—	4	2	no	—
1325	D₄	—	4	4	no	—
1326	D₄	—	4	2	no	—
1327	D₄	—	4	2	no	—
1328	D₄	—	4	2	no	—
1329	D₄	—	4	2	no	—
1330	D₄	—	4	2	no	—
1331	D₄	—	8	2	no	—
1332	D₄	—	8	2	no	—
1333	D₄	—	8	2	no	—
1334	D₄	—	8	2	no	—
1335	D₄	—	8	2	no	—
1336	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1337	D₄	C₂²×D₄×C₆₇	1	4	yes	—
1338	C₂×C₄	—	2	2	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	2	no	—
1341	C₂×C₄	—	2	2	no	—
1342	C₂×C₄	—	2	4	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	2	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	2	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	2	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	2	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	4	2	no	—
1356	C₂×C₄	—	4	2	no	—
1357	C₂×C₄	—	4	2	no	—
1358	C₂×C₄	—	4	4	no	—
1359	C₂×C₄	—	4	4	no	—
1360	C₂×C₄	—	4	4	no	—
1361	C₂×C₄	—	4	2	no	—
1362	C₂×C₄	—	4	2	no	—
1363	C₂×C₄	—	4	2	no	—
1364	C₂×C₄	—	8	2	no	—
1365	C₂×C₄	—	8	2	no	—
1366	C₂×C₄	—	8	2	no	—
1367	C₂×C₄	—	8	1	no	—
1368	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1369	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1370	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1371	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1372	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1373	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1374	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1375	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1376	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1377	C₈	—	2	1	no	—
1378	C₈	—	2	2	no	—
1379	C₈	—	2	1	no	—
1380	C₈	—	2	1	no	—
1381	C₈	—	2	1	no	—
1382	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1383	C₂²	—	2	1	no	—
1384	C₂²	—	2	1	no	—
1385	C₂²	—	2	1	no	—
1386	C₂²	—	2	1	no	—
1387	C₂²	—	2	2	no	—
1388	C₂²	—	2	1	no	—
1389	C₂²	—	2	1	no	—
1390	C₂²	—	2	2	no	—
1391	C₂²	—	2	1	no	—
1392	C₂²	—	2	2	no	—
1393	C₂²	—	2	2	no	—
1394	C₂²	—	2	4	no	—
1395	C₂²	—	4	4	no	—
1396	C₂²	—	4	2	no	—
1397	C₂²	—	4	1	no	—
1398	C₂²	—	4	1	no	—
1399	C₂²	—	4	2	no	—
1400	C₂²	—	4	1	no	—
1401	C₂²	—	4	2	no	—
1402	C₂²	—	4	1	no	—
1403	C₂²	—	4	1	no	—
1404	C₂²	—	4	2	no	—
1405	C₂²	—	4	1	no	—
1406	C₂²	—	4	1	no	—
1407	C₂²	—	4	1	no	—
1408	C₂²	—	4	2	no	—
1409	C₂²	—	8	4	no	—
1410	C₂²	—	8	8	no	—
1411	C₂²	—	8	4	no	—
1412	C₂²	—	8	4	no	—
1413	C₂²	—	8	8	no	—
1414	C₂²	—	16	4	no	—
1415	C₂²	D₄²×C₆₇	1	2	yes	—
1416	C₂²	#577×C₆₇	1	2	yes	complemented
1417	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1418	C₄	—	2	2	no	—
1419	C₄	—	2	2	no	—
1420	C₄	—	2	1	no	—
1421	C₄	—	2	1	no	—
1422	C₄	—	2	2	no	—
1423	C₄	—	2	2	no	—
1424	C₄	—	4	1	no	—
1425	C₄	—	4	1	no	—
1426	C₄	—	4	2	no	—
1427	C₄	—	4	1	no	—
1428	C₄	—	4	1	no	—
1429	C₄	—	4	2	no	—
1430	C₄	D₄²×C₆₇	1	2	yes	—
1431	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1432	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1433	C₂	—	2	2	no	—
1434	C₂	—	2	2	no	—
1435	C₂	—	4	1	no	—
1436	C₂	—	4	2	no	—
1437	C₂	—	4	4	no	—
1438	C₂	—	4	2	no	—
1439	C₂	—	8	2	no	—
1440	C₂	—	8	1	no	—
1441	C₂	—	8	1	no	—
1442	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1443	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
1444	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×#577×C₆₇	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
3. C₆₇×#3489	C₂	semidirect
4. C₆₇×#3484	C₂	semidirect
5. D₄×SD₁₆×C₆₇	C₂	semidirect
6. C₆₇×#3280	C₂	semidirect
7. C₆₇×#3275	C₂	semidirect
8. C₆₇×#3272	C₂	semidirect
9. C₆₇×#3267	C₂	semidirect
10. C₆₇×#3266	C₂	semidirect
11. C₆₇×#3265	C₂	semidirect
12. C₆₇×#3264	C₂	semidirect
13. C₆₇×#3154	C₂	semidirect
14. C₆₇×#3062	C₂	semidirect
15. C₆₇×#3056	C₂	semidirect
16. C₆₇×#3045	C₂	semidirect
17. C₆₇×#3042	C₂	semidirect
18. C₆₇×#3012	C₂	semidirect
19. C₆₇×#3010	C₂	semidirect
20. C₆₇×#3002	C₂	semidirect
21. C₂×#450×C₆₇	C₂	semidirect
22. C₆₇×#2946	C₂	semidirect
23. C₆₇×#2933	C₂	semidirect
24. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
25. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
26. C₂²×#41×C₆₇	C₂²	semidirect
29. C₂×#137×C₆₇	C₂²	semidirect
30. C₂×#137×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×SD₁₆×C₆₇	C₂²	semidirect
44. C₂²×SD₁₆×C₆₇	C₂²	semidirect
45. C₂²×SD₁₆×C₆₇	C₂²	semidirect
46. C₂²×D₈×C₆₇	C₂²	semidirect
47. C₂×#131×C₆₇	C₂²	semidirect
48. C₂²×M₁₆×C₆₇	C₂²	semidirect
49. D₄×Q₈×C₆₇	C₂²	semidirect
50. #548×C₆₇	C₂²	semidirect
52. #547×C₆₇	C₂²	semidirect
57. #546×C₆₇	C₂²	semidirect
58. #546×C₆₇	C₂²	semidirect
62. D₄²×C₆₇	C₂²	semidirect
64. #537×C₆₇	C₂²	semidirect
66. #536×C₆₇	C₂²	semidirect
67. #535×C₆₇	C₂²	semidirect
68. #535×C₆₇	C₂²	semidirect
74. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
76. #520×C₆₇	C₂²	semidirect
77. #518×C₆₇	C₂²	semidirect
78. #497×C₆₇	C₂²	semidirect
79. #496×C₆₇	C₂²	semidirect
80. #495×C₆₇	C₂²	semidirect
81. #492×C₆₇	C₂²	semidirect
82. #470×C₆₇	C₂²	semidirect
83. #469×C₆₇	C₂²	semidirect
84. #468×C₆₇	C₂²	semidirect
85. #468×C₆₇	C₂²	semidirect
86. #467×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. #461×C₆₇	C₂²	semidirect
95. #461×C₆₇	C₂²	semidirect
96. #460×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. #450×C₆₇	C₂²	semidirect
105. #450×C₆₇	C₂²	semidirect
106. #450×C₆₇	C₂²	semidirect
107. #450×C₆₇	C₂²	semidirect
108. #449×C₆₇	C₂²	semidirect
109. #449×C₆₇	C₂²	semidirect
110. #449×C₆₇	C₂²	semidirect
111. #449×C₆₇	C₂²	semidirect
112. #449×C₆₇	C₂²	semidirect
113. #448×C₆₇	C₂²	semidirect
114. #448×C₆₇	C₂²	semidirect
115. #448×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. #419×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
156. C₂×#41×C₆₇	C₂³	semidirect
160. C₂²×Q₈×C₆₇	C₂³	semidirect
187. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
191. C₂×Q₁₆×C₆₇	C₂³	semidirect
192. C₂×Q₁₆×C₆₇	C₂³	semidirect
193. C₂×Q₁₆×C₆₇	C₂³	semidirect
206. C₂×SD₁₆×C₆₇	C₂³	semidirect
207. C₂×SD₁₆×C₆₇	C₂³	semidirect
208. C₂×SD₁₆×C₆₇	C₂³	semidirect
209. C₂×SD₁₆×C₆₇	C₂³	semidirect
210. C₂×SD₁₆×C₆₇	C₂³	semidirect
216. C₂×D₈×C₆₇	C₂³	semidirect
217. C₂×D₈×C₆₇	C₂³	semidirect
223. C₂×M₁₆×C₆₇	C₂³	semidirect
227. C₂²×C₈×C₆₇	C₂³	semidirect
229. C₄⋊Q₈×C₆₇	C₂³	semidirect
235. #124×C₆₇	C₂³	semidirect
258. C₂²⋊Q₈×C₆₇	C₂³	semidirect
276. #121×C₆₇	C₂³	semidirect
288. C₄×Q₈×C₆₇	C₂³	semidirect
300. 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
322. #103×C₆₇	C₂³	semidirect
323. #103×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
371. #41×C₆₇	C₂×D₄	semidirect
475. SD₁₆×C₆₇	C₂×D₄	semidirect
481. D₈×C₆₇	C₂×D₄	semidirect
485. M₁₆×C₆₇	C₂×D₄	semidirect
693. C₂²×C₆₇	#577	semidirect
710. #61071	C₆₇	direct (N × H)
723. C₂×#577	C₂×C₆₇	semidirect
724. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
725. #3489	C₂×C₆₇	semidirect
726. #3484	C₂×C₆₇	semidirect
727. D₄×SD₁₆	C₂×C₆₇	semidirect
728. #3280	C₂×C₆₇	semidirect
729. #3275	C₂×C₆₇	semidirect
730. #3272	C₂×C₆₇	semidirect
731. #3267	C₂×C₆₇	semidirect
732. #3266	C₂×C₆₇	semidirect
733. #3265	C₂×C₆₇	semidirect
734. #3264	C₂×C₆₇	semidirect
735. #3154	C₂×C₆₇	semidirect
736. #3062	C₂×C₆₇	semidirect
737. #3056	C₂×C₆₇	semidirect
738. #3045	C₂×C₆₇	semidirect
739. #3042	C₂×C₆₇	semidirect
740. #3012	C₂×C₆₇	semidirect
741. #3010	C₂×C₆₇	semidirect
742. #3002	C₂×C₆₇	semidirect
743. C₂×#450	C₂×C₆₇	semidirect
744. #2946	C₂×C₆₇	semidirect
745. #2933	C₂×C₆₇	semidirect
746. C₆₇	#61071	direct (N × H)
747. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
748. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
749. C₂²×#41	C₂²×C₆₇	semidirect
752. C₂×#137	C₂²×C₆₇	semidirect
753. C₂×#137	C₂²×C₆₇	semidirect
757. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
758. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
759. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
760. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
761. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
762. C₂×#135	C₂²×C₆₇	semidirect
763. C₂×#135	C₂²×C₆₇	semidirect
764. C₂×#135	C₂²×C₆₇	semidirect
765. C₂²×SD₁₆	C₂²×C₆₇	semidirect
766. C₂²×SD₁₆	C₂²×C₆₇	semidirect
767. C₂²×SD₁₆	C₂²×C₆₇	semidirect
768. C₂²×SD₁₆	C₂²×C₆₇	semidirect
769. C₂²×D₈	C₂²×C₆₇	semidirect
770. C₂×#131	C₂²×C₆₇	semidirect
771. C₂²×M₁₆	C₂²×C₆₇	semidirect
772. D₄×Q₈	C₂²×C₆₇	semidirect
773. #548	C₂²×C₆₇	semidirect
775. #547	C₂²×C₆₇	semidirect
780. #546	C₂²×C₆₇	semidirect
781. #546	C₂²×C₆₇	semidirect
785. D₄²	C₂²×C₆₇	semidirect
787. #537	C₂²×C₆₇	semidirect
789. #536	C₂²×C₆₇	semidirect
790. #535	C₂²×C₆₇	semidirect
791. #535	C₂²×C₆₇	semidirect
797. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
799. #520	C₂²×C₆₇	semidirect
800. #518	C₂²×C₆₇	semidirect
801. #497	C₂²×C₆₇	semidirect
802. #496	C₂²×C₆₇	semidirect
803. #495	C₂²×C₆₇	semidirect
804. #492	C₂²×C₆₇	semidirect
805. #470	C₂²×C₆₇	semidirect
806. #469	C₂²×C₆₇	semidirect
807. #468	C₂²×C₆₇	semidirect
808. #468	C₂²×C₆₇	semidirect
809. #467	C₂²×C₆₇	semidirect
810. #466	C₂²×C₆₇	semidirect
811. #465	C₂²×C₆₇	semidirect
812. #465	C₂²×C₆₇	semidirect
813. #464	C₂²×C₆₇	semidirect
814. #463	C₂²×C₆₇	semidirect
815. #463	C₂²×C₆₇	semidirect
816. #463	C₂²×C₆₇	semidirect
817. #461	C₂²×C₆₇	semidirect
818. #461	C₂²×C₆₇	semidirect
819. #460	C₂²×C₆₇	semidirect
820. #459	C₂²×C₆₇	semidirect
821. #452	C₂²×C₆₇	semidirect
822. #452	C₂²×C₆₇	semidirect
823. #452	C₂²×C₆₇	semidirect
824. #451	C₂²×C₆₇	semidirect
825. #450	C₂²×C₆₇	semidirect
826. #450	C₂²×C₆₇	semidirect
827. #450	C₂²×C₆₇	semidirect
828. #450	C₂²×C₆₇	semidirect
829. #450	C₂²×C₆₇	semidirect
830. #450	C₂²×C₆₇	semidirect
831. #449	C₂²×C₆₇	semidirect
832. #449	C₂²×C₆₇	semidirect
833. #449	C₂²×C₆₇	semidirect
834. #449	C₂²×C₆₇	semidirect
835. #449	C₂²×C₆₇	semidirect
836. #448	C₂²×C₆₇	semidirect
837. #448	C₂²×C₆₇	semidirect
838. #448	C₂²×C₆₇	semidirect
839. #447	C₂²×C₆₇	semidirect
840. #447	C₂²×C₆₇	semidirect
841. #442	C₂²×C₆₇	semidirect
842. #440	C₂²×C₆₇	semidirect
843. C₄×SD₁₆	C₂²×C₆₇	semidirect
844. C₄×D₈	C₂²×C₆₇	semidirect
845. #436	C₂²×C₆₇	semidirect
846. #435	C₂²×C₆₇	semidirect
847. #435	C₂²×C₆₇	semidirect
848. C₈×D₄	C₂²×C₆₇	semidirect
849. #428	C₂²×C₆₇	semidirect
850. #424	C₂²×C₆₇	semidirect
851. #419	C₂²×C₆₇	semidirect
852. #417	C₂²×C₆₇	semidirect
853. #416	C₂²×C₆₇	semidirect
854. #416	C₂²×C₆₇	semidirect
855. C₂×#102	C₂²×C₆₇	semidirect
856. C₂×#102	C₂²×C₆₇	semidirect
857. #408	C₂²×C₆₇	semidirect
858. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
859. #405	C₂²×C₆₇	semidirect
879. C₂×#41	C₂³×C₆₇	semidirect
883. C₂²×Q₈	C₂³×C₆₇	semidirect
910. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
914. C₂×Q₁₆	C₂³×C₆₇	semidirect
915. C₂×Q₁₆	C₂³×C₆₇	semidirect
916. C₂×Q₁₆	C₂³×C₆₇	semidirect
929. C₂×SD₁₆	C₂³×C₆₇	semidirect
930. C₂×SD₁₆	C₂³×C₆₇	semidirect
931. C₂×SD₁₆	C₂³×C₆₇	semidirect
932. C₂×SD₁₆	C₂³×C₆₇	semidirect
933. C₂×SD₁₆	C₂³×C₆₇	semidirect
939. C₂×D₈	C₂³×C₆₇	semidirect
940. C₂×D₈	C₂³×C₆₇	semidirect
946. C₂×M₁₆	C₂³×C₆₇	semidirect
950. C₂²×C₈	C₂³×C₆₇	semidirect
952. C₄⋊Q₈	C₂³×C₆₇	semidirect
958. #124	C₂³×C₆₇	semidirect
981. C₂²⋊Q₈	C₂³×C₆₇	semidirect
999. #121	C₂³×C₆₇	semidirect
1011. C₄×Q₈	C₂³×C₆₇	semidirect
1023. C₄×D₄	C₂³×C₆₇	semidirect
1036. #107	C₂³×C₆₇	semidirect
1037. #106	C₂³×C₆₇	semidirect
1038. C₄⋊C₈	C₂³×C₆₇	semidirect
1039. C₄⋊C₈	C₂³×C₆₇	semidirect
1040. #103	C₂³×C₆₇	semidirect
1041. #103	C₂³×C₆₇	semidirect
1042. #103	C₂³×C₆₇	semidirect
1043. #103	C₂³×C₆₇	semidirect
1044. #103	C₂³×C₆₇	semidirect
1045. #103	C₂³×C₆₇	semidirect
1046. #103	C₂³×C₆₇	semidirect
1051. #102	C₂³×C₆₇	semidirect
1052. #102	C₂³×C₆₇	semidirect
1053. #102	C₂³×C₆₇	semidirect
1054. #102	C₂³×C₆₇	semidirect
1055. #102	C₂³×C₆₇	semidirect
1060. C₂²⋊C₈	C₂³×C₆₇	semidirect
1061. C₂²⋊C₈	C₂³×C₆₇	semidirect
1062. #97	C₂³×C₆₇	semidirect
1063. C₄×C₈	C₂³×C₆₇	semidirect
1094. #41	C₂×D₄×C₆₇	semidirect
1198. SD₁₆	C₂×D₄×C₆₇	semidirect
1204. D₈	C₂×D₄×C₆₇	semidirect
1208. M₁₆	C₂×D₄×C₆₇	semidirect
1416. C₂²	#577×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#3489	2
C₆₇×#3484	2
D₄×SD₁₆×C₆₇	2
C₆₇×#3280	2
C₆₇×#3275	2
C₆₇×#3272	2
C₆₇×#3267	2
C₆₇×#3266	2
C₆₇×#3265	2
C₆₇×#3264	2
C₆₇×#3154	2
C₆₇×#3062	2
C₆₇×#3056	2
C₆₇×#3045	2
C₆₇×#3042	2
C₆₇×#3012	2
C₆₇×#3010	2
C₆₇×#3002	2
C₂×#450×C₆₇	2
C₆₇×#2946	2
C₆₇×#2933	2
#61071	67

Subgroups — C67×#61071 #30740322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61071 #30740322