Subgroups — C₆₇×#61074 #30740325

Order 17152.

2774 conjugacy classes of subgroups.

The subgroup lattice has 1434 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	C₂×#575×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3284	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×#3269	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3268	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3267	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×#3063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3046	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×#3009	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#449×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
25	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#576×C₆₇	—	2	8	no	—
29	#575×C₆₇	—	2	8	no	—
30	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
32	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
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	2	yes	complemented
38	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
43	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
46	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, 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	#547×C₆₇	—	2	1	no	—
52	#547×C₆₇	—	2	1	no	—
53	#547×C₆₇	C₂²	1	2	yes	complemented
54	#547×C₆₇	C₂²	1	2	yes	complemented
55	#546×C₆₇	—	2	2	no	—
56	#546×C₆₇	—	2	1	no	—
57	#546×C₆₇	—	2	1	no	—
58	#546×C₆₇	C₂²	1	2	yes	complemented
59	#546×C₆₇	C₂²	1	2	yes	complemented
60	#546×C₆₇	C₂²	1	2	yes	complemented
61	D₄²×C₆₇	—	2	2	no	—
62	D₄²×C₆₇	C₂²	1	2	yes	complemented
63	#537×C₆₇	—	2	1	no	—
64	#537×C₆₇	C₂²	1	1	yes	characteristic
65	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#535×C₆₇	—	2	1	no	—
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×#123×C₆₇	—	2	2	no	—
74	C₂×#121×C₆₇	—	2	1	no	—
75	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
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	#462×C₆₇	C₂²	1	2	yes	complemented
95	#461×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	2	yes	complemented
100	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#452×C₆₇	C₂²	1	2	yes	complemented
102	#452×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#451×C₆₇	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
111	#449×C₆₇	C₂²	1	2	yes	complemented
112	#449×C₆₇	C₂²	1	2	yes	complemented
113	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#449×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	#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×#103×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	H(5,𝔽₂)×C₆₇	—	2	4	no	—
138	H(5,𝔽₂)×C₆₇	—	2	4	no	—
139	H(5,𝔽₂)×C₆₇	—	4	2	no	—
140	H(5,𝔽₂)×C₆₇	—	4	2	no	—
141	C₂×#41×C₆₇	—	2	1	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	1	no	—
147	C₂×#41×C₆₇	—	2	4	no	—
148	C₂×#41×C₆₇	—	2	4	no	—
149	C₂×#41×C₆₇	—	4	2	no	—
150	C₂×#41×C₆₇	—	4	2	no	—
151	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×#41×C₆₇	C₂³	1	2	yes	—
154	C₂×#41×C₆₇	C₂³	1	2	yes	—
155	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×#41×C₆₇	C₂³	1	2	yes	—
157	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×#41×C₆₇	C₂³	1	2	yes	—
159	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
161	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×D₄×C₆₇	—	2	1	no	—
164	C₂²×D₄×C₆₇	—	2	1	no	—
165	C₂²×D₄×C₆₇	—	2	1	no	—
166	C₂²×D₄×C₆₇	—	2	1	no	—
167	C₂²×D₄×C₆₇	—	2	2	no	—
168	C₂²×D₄×C₆₇	—	2	2	no	—
169	C₂²×D₄×C₆₇	—	2	1	no	—
170	C₂²×D₄×C₆₇	—	2	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	1	yes	characteristic
174	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
175	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂³×C₄×C₆₇	—	2	1	no	—
177	C₂³×C₄×C₆₇	—	2	1	no	—
178	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
179	#137×C₆₇	—	2	4	no	—
180	#137×C₆₇	—	2	8	no	—
181	#137×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	—	2	8	no	—
191	#135×C₆₇	—	2	8	no	—
192	#135×C₆₇	—	4	2	no	—
193	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
195	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
196	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
197	C₂×SD₁₆×C₆₇	—	4	2	no	—
198	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
200	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
205	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
207	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
208	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
209	C₂×D₈×C₆₇	—	2	4	no	—
210	C₂×D₈×C₆₇	—	2	8	no	—
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	1	yes	characteristic
215	C₂×D₈×C₆₇	C₂³	1	2	yes	—
216	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×D₈×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
222	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
223	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
225	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
226	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₄⋊Q₈×C₆₇	—	2	1	no	—
229	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
230	#127×C₆₇	—	2	2	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	—
236	#123×C₆₇	—	2	2	no	—
237	#123×C₆₇	—	2	1	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	—	2	2	no	—
244	#123×C₆₇	—	2	2	no	—
245	#123×C₆₇	—	2	2	no	—
246	#123×C₆₇	D₄	1	2	yes	—
247	C₂²⋊Q₈×C₆₇	—	2	1	no	—
248	C₂²⋊Q₈×C₆₇	—	2	1	no	—
249	C₂²⋊Q₈×C₆₇	—	2	1	no	—
250	C₂²⋊Q₈×C₆₇	—	2	2	no	—
251	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
252	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
253	C₂²⋊Q₈×C₆₇	C₂³	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	2	yes	—
257	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
258	#121×C₆₇	—	2	1	no	—
259	#121×C₆₇	—	2	2	no	—
260	#121×C₆₇	—	2	2	no	—
261	#121×C₆₇	—	2	2	no	—
262	#121×C₆₇	—	2	2	no	—
263	#121×C₆₇	—	2	1	no	—
264	#121×C₆₇	—	2	1	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	—	2	2	no	—
271	#121×C₆₇	—	2	2	no	—
272	#121×C₆₇	—	2	2	no	—
273	#121×C₆₇	D₄	1	1	yes	characteristic
274	#121×C₆₇	D₄	1	1	yes	characteristic
275	#121×C₆₇	C₂³	1	1	yes	characteristic
276	#121×C₆₇	C₂³	1	2	yes	—
277	#121×C₆₇	C₂³	1	1	yes	characteristic
278	#121×C₆₇	C₂³	1	2	yes	—
279	#121×C₆₇	C₂³	1	2	yes	—
280	#120×C₆₇	—	2	1	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	—
289	C₄×D₄×C₆₇	—	2	1	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	2	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	—
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	2	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	—
314	#106×C₆₇	C₂³	1	2	yes	—
315	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
316	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
317	#103×C₆₇	C₂³	1	1	yes	characteristic
318	#103×C₆₇	C₂³	1	1	yes	characteristic
319	#103×C₆₇	C₂³	1	2	yes	—
320	#103×C₆₇	C₂³	1	2	yes	—
321	#103×C₆₇	C₂³	1	1	yes	characteristic
322	#103×C₆₇	C₂³	1	1	yes	characteristic
323	#103×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
327	#102×C₆₇	C₂³	1	1	yes	characteristic
328	#102×C₆₇	C₂³	1	1	yes	characteristic
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	#102×C₆₇	C₂³	1	1	yes	characteristic
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	—
338	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
347	#41×C₆₇	—	2	2	no	—
348	#41×C₆₇	—	2	2	no	—
349	#41×C₆₇	—	2	2	no	—
350	#41×C₆₇	—	2	2	no	—
351	#41×C₆₇	—	2	4	no	—
352	#41×C₆₇	—	2	4	no	—
353	#41×C₆₇	—	2	2	no	—
354	#41×C₆₇	—	2	4	no	—
355	#41×C₆₇	—	2	4	no	—
356	#41×C₆₇	—	2	2	no	—
357	#41×C₆₇	—	2	2	no	—
358	#41×C₆₇	—	2	2	no	—
359	#41×C₆₇	—	2	2	no	—
360	#41×C₆₇	—	4	4	no	—
361	#41×C₆₇	—	4	2	no	—
362	#41×C₆₇	—	4	1	no	—
363	#41×C₆₇	—	4	2	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	4	no	—
370	#41×C₆₇	—	4	4	no	—
371	#41×C₆₇	—	4	4	no	—
372	#41×C₆₇	C₂×D₄	1	4	yes	—
373	C₂×Q₈×C₆₇	—	2	1	no	—
374	C₂×Q₈×C₆₇	—	2	1	no	—
375	C₂×Q₈×C₆₇	—	2	2	no	—
376	C₂×Q₈×C₆₇	—	2	2	no	—
377	C₂×Q₈×C₆₇	—	2	2	no	—
378	C₂×Q₈×C₆₇	—	4	1	no	—
379	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
380	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
381	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
382	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×D₄×C₆₇	—	2	1	no	—
385	C₂×D₄×C₆₇	—	2	4	no	—
386	C₂×D₄×C₆₇	—	2	4	no	—
387	C₂×D₄×C₆₇	—	2	2	no	—
388	C₂×D₄×C₆₇	—	2	2	no	—
389	C₂×D₄×C₆₇	—	2	1	no	—
390	C₂×D₄×C₆₇	—	2	1	no	—
391	C₂×D₄×C₆₇	—	2	2	no	—
392	C₂×D₄×C₆₇	—	2	2	no	—
393	C₂×D₄×C₆₇	—	2	1	no	—
394	C₂×D₄×C₆₇	—	2	2	no	—
395	C₂×D₄×C₆₇	—	2	2	no	—
396	C₂×D₄×C₆₇	—	2	1	no	—
397	C₂×D₄×C₆₇	—	2	1	no	—
398	C₂×D₄×C₆₇	—	2	1	no	—
399	C₂×D₄×C₆₇	—	2	2	no	—
400	C₂×D₄×C₆₇	—	2	2	no	—
401	C₂×D₄×C₆₇	—	2	1	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	1	no	—
406	C₂×D₄×C₆₇	—	2	2	no	—
407	C₂×D₄×C₆₇	—	2	2	no	—
408	C₂×D₄×C₆₇	—	2	2	no	—
409	C₂×D₄×C₆₇	—	2	2	no	—
410	C₂×D₄×C₆₇	—	2	2	no	—
411	C₂×D₄×C₆₇	—	4	1	no	—
412	C₂×D₄×C₆₇	—	4	2	no	—
413	C₂×D₄×C₆₇	—	4	2	no	—
414	C₂×D₄×C₆₇	—	4	4	no	—
415	C₂×D₄×C₆₇	—	4	8	no	—
416	C₂×D₄×C₆₇	—	4	4	no	—
417	C₂×D₄×C₆₇	—	4	4	no	—
418	C₂×D₄×C₆₇	—	4	8	no	—
419	C₂×D₄×C₆₇	—	4	4	no	—
420	C₂×D₄×C₆₇	—	8	4	no	—
421	C₂×D₄×C₆₇	—	8	2	no	—
422	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
423	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
424	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
425	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
426	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	complemented
427	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
428	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
429	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
430	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
431	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₆₇	—	2	1	no	—
433	C₂²×C₄×C₆₇	—	2	2	no	—
434	C₂²×C₄×C₆₇	—	2	2	no	—
435	C₂²×C₄×C₆₇	—	2	1	no	—
436	C₂²×C₄×C₆₇	—	2	1	no	—
437	C₂²×C₄×C₆₇	—	2	1	no	—
438	C₂²×C₄×C₆₇	—	2	1	no	—
439	C₂²×C₄×C₆₇	—	2	2	no	—
440	C₂²×C₄×C₆₇	—	2	2	no	—
441	C₂²×C₄×C₆₇	—	2	2	no	—
442	C₂²×C₄×C₆₇	—	2	1	no	—
443	C₂²×C₄×C₆₇	—	2	2	no	—
444	C₂²×C₄×C₆₇	—	2	1	no	—
445	C₂²×C₄×C₆₇	—	2	1	no	—
446	C₂²×C₄×C₆₇	—	2	2	no	—
447	C₂²×C₄×C₆₇	—	2	2	no	—
448	C₂²×C₄×C₆₇	—	2	2	no	—
449	C₂²×C₄×C₆₇	—	4	4	no	—
450	C₂²×C₄×C₆₇	—	4	4	no	—
451	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
452	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
453	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
454	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
457	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
458	Q₁₆×C₆₇	—	2	2	no	—
459	Q₁₆×C₆₇	—	2	4	no	—
460	Q₁₆×C₆₇	—	2	4	no	—
461	Q₁₆×C₆₇	—	4	1	no	—
462	SD₁₆×C₆₇	—	2	2	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	—	4	2	no	—
469	SD₁₆×C₆₇	—	4	2	no	—
470	SD₁₆×C₆₇	—	4	1	no	—
471	SD₁₆×C₆₇	—	4	1	no	—
472	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
473	D₈×C₆₇	—	2	4	no	—
474	D₈×C₆₇	—	2	2	no	—
475	D₈×C₆₇	—	2	4	no	—
476	D₈×C₆₇	—	2	4	no	—
477	D₈×C₆₇	—	2	4	no	—
478	D₈×C₆₇	—	4	1	no	—
479	D₈×C₆₇	C₂×D₄	1	8	yes	complemented
480	M₁₆×C₆₇	—	2	2	no	—
481	M₁₆×C₆₇	—	2	4	no	—
482	M₁₆×C₆₇	—	2	4	no	—
483	M₁₆×C₆₇	C₂×D₄	1	4	yes	complemented
484	C₂×C₈×C₆₇	—	2	2	no	—
485	C₂×C₈×C₆₇	—	2	2	no	—
486	C₂×C₈×C₆₇	—	2	4	no	—
487	C₂×C₈×C₆₇	—	2	4	no	—
488	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
489	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
494	C₄⋊C₄×C₆₇	—	2	1	no	—
495	C₄⋊C₄×C₆₇	—	2	1	no	—
496	C₄⋊C₄×C₆₇	—	2	1	no	—
497	C₄⋊C₄×C₆₇	—	2	2	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	2	no	—
503	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
504	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
505	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
506	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
507	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
509	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
510	C₂²⋊C₄×C₆₇	—	2	1	no	—
511	C₂²⋊C₄×C₆₇	—	2	2	no	—
512	C₂²⋊C₄×C₆₇	—	2	2	no	—
513	C₂²⋊C₄×C₆₇	—	2	2	no	—
514	C₂²⋊C₄×C₆₇	—	2	1	no	—
515	C₂²⋊C₄×C₆₇	—	2	1	no	—
516	C₂²⋊C₄×C₆₇	—	2	2	no	—
517	C₂²⋊C₄×C₆₇	—	2	1	no	—
518	C₂²⋊C₄×C₆₇	—	2	1	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	C₂×D₄	1	2	yes	—
529	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
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	C₄²×C₆₇	—	2	2	no	—
534	C₄²×C₆₇	—	2	1	no	—
535	C₄²×C₆₇	C₂⁴	1	2	yes	—
536	C₂³×C₆₇	—	2	2	no	—
537	C₂³×C₆₇	—	2	1	no	—
538	C₂³×C₆₇	—	2	2	no	—
539	C₂³×C₆₇	—	2	4	no	—
540	C₂³×C₆₇	—	2	1	no	—
541	C₂³×C₆₇	—	2	2	no	—
542	C₂³×C₆₇	—	2	1	no	—
543	C₂³×C₆₇	—	4	1	no	—
544	C₂³×C₆₇	—	4	1	no	—
545	C₂³×C₆₇	—	4	2	no	—
546	C₂³×C₆₇	—	4	4	no	—
547	C₂³×C₆₇	—	4	4	no	—
548	C₂³×C₆₇	—	4	2	no	—
549	C₂³×C₆₇	—	4	2	no	—
550	C₂³×C₆₇	—	8	1	no	—
551	C₂³×C₆₇	—	8	1	no	—
552	C₂³×C₆₇	—	8	1	no	—
553	C₂³×C₆₇	—	8	1	no	—
554	C₂³×C₆₇	—	8	2	no	—
555	C₂³×C₆₇	—	8	1	no	—
556	C₂³×C₆₇	—	8	2	no	—
557	C₂³×C₆₇	—	8	2	no	—
558	C₂³×C₆₇	—	8	2	no	—
559	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
560	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
561	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
562	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
563	Q₈×C₆₇	—	2	2	no	—
564	Q₈×C₆₇	—	2	1	no	—
565	Q₈×C₆₇	—	2	1	no	—
566	Q₈×C₆₇	—	2	1	no	—
567	Q₈×C₆₇	—	2	2	no	—
568	Q₈×C₆₇	—	2	2	no	—
569	Q₈×C₆₇	—	2	1	no	—
570	Q₈×C₆₇	—	2	1	no	—
571	Q₈×C₆₇	—	4	2	no	—
572	Q₈×C₆₇	—	4	2	no	—
573	Q₈×C₆₇	C₂²×D₄	1	2	yes	—
574	D₄×C₆₇	—	2	4	no	—
575	D₄×C₆₇	—	2	4	no	—
576	D₄×C₆₇	—	2	4	no	—
577	D₄×C₆₇	—	2	2	no	—
578	D₄×C₆₇	—	2	2	no	—
579	D₄×C₆₇	—	2	1	no	—
580	D₄×C₆₇	—	2	1	no	—
581	D₄×C₆₇	—	2	2	no	—
582	D₄×C₆₇	—	2	1	no	—
583	D₄×C₆₇	—	2	1	no	—
584	D₄×C₆₇	—	2	1	no	—
585	D₄×C₆₇	—	2	2	no	—
586	D₄×C₆₇	—	4	2	no	—
587	D₄×C₆₇	—	4	2	no	—
588	D₄×C₆₇	—	4	4	no	—
589	D₄×C₆₇	—	4	4	no	—
590	D₄×C₆₇	—	4	2	no	—
591	D₄×C₆₇	—	4	4	no	—
592	D₄×C₆₇	—	4	2	no	—
593	D₄×C₆₇	—	4	4	no	—
594	D₄×C₆₇	—	4	4	no	—
595	D₄×C₆₇	—	4	2	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	2	no	—
601	D₄×C₆₇	—	8	2	no	—
602	D₄×C₆₇	—	8	2	no	—
603	D₄×C₆₇	—	8	1	no	—
604	D₄×C₆₇	—	8	1	no	—
605	D₄×C₆₇	—	8	2	no	—
606	D₄×C₆₇	—	8	2	no	—
607	D₄×C₆₇	C₂²×D₄	1	4	yes	—
608	D₄×C₆₇	C₂²×D₄	1	2	yes	—
609	C₂×C₄×C₆₇	—	2	2	no	—
610	C₂×C₄×C₆₇	—	2	1	no	—
611	C₂×C₄×C₆₇	—	2	2	no	—
612	C₂×C₄×C₆₇	—	2	2	no	—
613	C₂×C₄×C₆₇	—	2	4	no	—
614	C₂×C₄×C₆₇	—	2	1	no	—
615	C₂×C₄×C₆₇	—	2	2	no	—
616	C₂×C₄×C₆₇	—	2	1	no	—
617	C₂×C₄×C₆₇	—	2	1	no	—
618	C₂×C₄×C₆₇	—	2	1	no	—
619	C₂×C₄×C₆₇	—	2	2	no	—
620	C₂×C₄×C₆₇	—	2	1	no	—
621	C₂×C₄×C₆₇	—	2	1	no	—
622	C₂×C₄×C₆₇	—	2	2	no	—
623	C₂×C₄×C₆₇	—	2	1	no	—
624	C₂×C₄×C₆₇	—	2	2	no	—
625	C₂×C₄×C₆₇	—	2	1	no	—
626	C₂×C₄×C₆₇	—	4	2	no	—
627	C₂×C₄×C₆₇	—	4	4	no	—
628	C₂×C₄×C₆₇	—	4	2	no	—
629	C₂×C₄×C₆₇	—	4	2	no	—
630	C₂×C₄×C₆₇	—	4	4	no	—
631	C₂×C₄×C₆₇	—	4	4	no	—
632	C₂×C₄×C₆₇	—	4	4	no	—
633	C₂×C₄×C₆₇	—	4	2	no	—
634	C₂×C₄×C₆₇	—	4	2	no	—
635	C₂×C₄×C₆₇	—	4	2	no	—
636	C₂×C₄×C₆₇	—	8	2	no	—
637	C₂×C₄×C₆₇	—	8	2	no	—
638	C₂×C₄×C₆₇	—	8	2	no	—
639	C₂×C₄×C₆₇	—	8	1	no	—
640	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
641	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
642	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
643	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
645	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
647	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
648	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
649	C₈×C₆₇	—	2	1	no	—
650	C₈×C₆₇	—	2	1	no	—
651	C₈×C₆₇	—	2	2	no	—
652	C₈×C₆₇	—	2	1	no	—
653	C₈×C₆₇	—	2	1	no	—
654	C₈×C₆₇	C₂²×D₄	1	4	yes	—
655	C₂²×C₆₇	—	2	1	no	—
656	C₂²×C₆₇	—	2	1	no	—
657	C₂²×C₆₇	—	2	1	no	—
658	C₂²×C₆₇	—	2	2	no	—
659	C₂²×C₆₇	—	2	1	no	—
660	C₂²×C₆₇	—	2	1	no	—
661	C₂²×C₆₇	—	2	2	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	2	no	—
667	C₂²×C₆₇	—	2	4	no	—
668	C₂²×C₆₇	—	4	2	no	—
669	C₂²×C₆₇	—	4	1	no	—
670	C₂²×C₆₇	—	4	1	no	—
671	C₂²×C₆₇	—	4	2	no	—
672	C₂²×C₆₇	—	4	1	no	—
673	C₂²×C₆₇	—	4	2	no	—
674	C₂²×C₆₇	—	4	1	no	—
675	C₂²×C₆₇	—	4	2	no	—
676	C₂²×C₆₇	—	4	1	no	—
677	C₂²×C₆₇	—	4	1	no	—
678	C₂²×C₆₇	—	4	1	no	—
679	C₂²×C₆₇	—	4	2	no	—
680	C₂²×C₆₇	—	4	1	no	—
681	C₂²×C₆₇	—	8	2	no	—
682	C₂²×C₆₇	—	8	4	no	—
683	C₂²×C₆₇	—	8	4	no	—
684	C₂²×C₆₇	—	16	2	no	—
685	C₂²×C₆₇	—	16	4	no	—
686	C₂²×C₆₇	—	16	4	no	—
687	C₂²×C₆₇	D₄²	1	2	yes	—
688	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
689	C₄×C₆₇	—	2	2	no	—
690	C₄×C₆₇	—	2	2	no	—
691	C₄×C₆₇	—	2	1	no	—
692	C₄×C₆₇	—	2	1	no	—
693	C₄×C₆₇	—	2	2	no	—
694	C₄×C₆₇	—	2	2	no	—
695	C₄×C₆₇	—	4	1	no	—
696	C₄×C₆₇	—	4	2	no	—
697	C₄×C₆₇	—	4	1	no	—
698	C₄×C₆₇	—	4	1	no	—
699	C₄×C₆₇	—	4	1	no	—
700	C₄×C₆₇	—	4	2	no	—
701	C₄×C₆₇	D₄²	1	2	yes	—
702	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
703	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
704	#61074	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
705	C₂×C₆₇	—	2	2	no	—
706	C₂×C₆₇	—	4	1	no	—
707	C₂×C₆₇	—	4	1	no	—
708	C₂×C₆₇	—	4	2	no	—
709	C₂×C₆₇	—	4	4	no	—
710	C₂×C₆₇	—	4	2	no	—
711	C₂×C₆₇	—	8	1	no	—
712	C₂×C₆₇	—	8	2	no	—
713	C₂×C₆₇	—	8	1	no	—
714	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
715	C₂×C₆₇	#3584	1	1	yes	characteristic
716	C₂×C₆₇	#3585	1	1	yes	characteristic
717	C₂×#576	C₂×C₆₇	1	1	yes	characteristic, complemented
718	C₂×#575	C₂×C₆₇	1	1	yes	characteristic, complemented
719	#3488	C₂×C₆₇	1	1	yes	characteristic, complemented
720	#3485	C₂×C₆₇	1	1	yes	characteristic, complemented
721	#3284	C₂×C₆₇	1	2	yes	complemented
722	#3280	C₂×C₆₇	1	2	yes	complemented
723	#3275	C₂×C₆₇	1	2	yes	complemented
724	#3272	C₂×C₆₇	1	2	yes	complemented
725	#3269	C₂×C₆₇	1	2	yes	complemented
726	#3268	C₂×C₆₇	1	2	yes	complemented
727	#3267	C₂×C₆₇	1	2	yes	complemented
728	#3264	C₂×C₆₇	1	2	yes	complemented
729	#3154	C₂×C₆₇	1	1	yes	characteristic, complemented
730	#3063	C₂×C₆₇	1	1	yes	characteristic, complemented
731	#3055	C₂×C₆₇	1	1	yes	characteristic, complemented
732	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
733	#3041	C₂×C₆₇	1	1	yes	characteristic, complemented
734	#3012	C₂×C₆₇	1	1	yes	characteristic, complemented
735	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
736	#3002	C₂×C₆₇	1	1	yes	characteristic, complemented
737	C₂×#449	C₂×C₆₇	1	1	yes	characteristic, complemented
738	#2946	C₂×C₆₇	1	1	yes	characteristic, complemented
739	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
740	C₆₇	#61074	1	1	yes	characteristic, direct product factor, Sylow
741	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
742	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic, complemented
743	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
744	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
745	#576	—	2	8	no	—
746	#575	—	2	8	no	—
747	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
749	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
750	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
751	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
752	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
753	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
754	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
755	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
756	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
757	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
758	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
759	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
760	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
761	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
762	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
764	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
765	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
766	#550	C₂²×C₆₇	1	2	yes	complemented
767	#548	C₂²×C₆₇	1	2	yes	complemented
768	#547	—	2	1	no	—
769	#547	—	2	1	no	—
770	#547	C₂²×C₆₇	1	2	yes	complemented
771	#547	C₂²×C₆₇	1	2	yes	complemented
772	#546	—	2	2	no	—
773	#546	—	2	1	no	—
774	#546	—	2	1	no	—
775	#546	C₂²×C₆₇	1	2	yes	complemented
776	#546	C₂²×C₆₇	1	2	yes	complemented
777	#546	C₂²×C₆₇	1	2	yes	complemented
778	D₄²	—	2	2	no	—
779	D₄²	C₂²×C₆₇	1	2	yes	complemented
780	#537	—	2	1	no	—
781	#537	C₂²×C₆₇	1	1	yes	characteristic
782	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
783	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	#535	—	2	1	no	—
785	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
786	#534	—	2	2	no	—
787	#525	—	2	1	no	—
788	#525	C₂²×C₆₇	1	1	yes	characteristic
789	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
790	C₂×#123	—	2	2	no	—
791	C₂×#121	—	2	1	no	—
792	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
793	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
794	#518	C₂²×C₆₇	1	1	yes	characteristic, complemented
795	#497	C₂²×C₆₇	1	2	yes	complemented
796	#496	C₂²×C₆₇	1	2	yes	complemented
797	#495	C₂²×C₆₇	1	2	yes	complemented
798	#492	C₂²×C₆₇	1	2	yes	complemented
799	#470	C₂²×C₆₇	1	2	yes	complemented
800	#469	C₂²×C₆₇	1	2	yes	complemented
801	#468	C₂²×C₆₇	1	2	yes	complemented
802	#468	C₂²×C₆₇	1	2	yes	complemented
803	#467	C₂²×C₆₇	1	2	yes	complemented
804	#466	C₂²×C₆₇	1	2	yes	complemented
805	#465	C₂²×C₆₇	1	2	yes	complemented
806	#465	C₂²×C₆₇	1	2	yes	complemented
807	#464	C₂²×C₆₇	1	2	yes	complemented
808	#463	C₂²×C₆₇	1	2	yes	complemented
809	#463	C₂²×C₆₇	1	2	yes	complemented
810	#463	C₂²×C₆₇	1	2	yes	complemented
811	#462	C₂²×C₆₇	1	2	yes	complemented
812	#461	C₂²×C₆₇	1	2	yes	complemented
813	#459	C₂²×C₆₇	1	2	yes	complemented
814	#459	C₂²×C₆₇	1	2	yes	complemented
815	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
816	#452	C₂²×C₆₇	1	1	yes	characteristic, complemented
817	#452	C₂²×C₆₇	1	2	yes	complemented
818	#452	C₂²×C₆₇	1	2	yes	complemented
819	#452	C₂²×C₆₇	1	2	yes	complemented
820	#451	C₂²×C₆₇	1	1	yes	characteristic, complemented
821	#450	C₂²×C₆₇	1	1	yes	characteristic, complemented
822	#450	C₂²×C₆₇	1	2	yes	complemented
823	#450	C₂²×C₆₇	1	2	yes	complemented
824	#450	C₂²×C₆₇	1	2	yes	complemented
825	#449	C₂²×C₆₇	1	2	yes	complemented
826	#449	C₂²×C₆₇	1	2	yes	complemented
827	#449	C₂²×C₆₇	1	2	yes	complemented
828	#449	C₂²×C₆₇	1	2	yes	complemented
829	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
830	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
831	#449	C₂²×C₆₇	1	2	yes	complemented
832	#448	C₂²×C₆₇	1	1	yes	characteristic, complemented
833	#447	C₂²×C₆₇	1	1	yes	characteristic, complemented
834	#447	C₂²×C₆₇	1	2	yes	complemented
835	#442	C₂²×C₆₇	1	2	yes	complemented
836	#440	C₂²×C₆₇	1	2	yes	complemented
837	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
838	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
839	#436	C₂²×C₆₇	1	2	yes	complemented
840	#435	C₂²×C₆₇	1	2	yes	complemented
841	#435	C₂²×C₆₇	1	2	yes	complemented
842	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
843	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
844	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
845	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
846	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
847	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
848	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
849	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
850	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic, complemented
851	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
852	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
853	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
854	H(5,𝔽₂)	—	2	4	no	—
855	H(5,𝔽₂)	—	2	4	no	—
856	H(5,𝔽₂)	—	4	2	no	—
857	H(5,𝔽₂)	—	4	2	no	—
858	C₂×#41	—	2	1	no	—
859	C₂×#41	—	2	1	no	—
860	C₂×#41	—	2	1	no	—
861	C₂×#41	—	2	1	no	—
862	C₂×#41	—	2	1	no	—
863	C₂×#41	—	2	1	no	—
864	C₂×#41	—	2	4	no	—
865	C₂×#41	—	2	4	no	—
866	C₂×#41	—	4	2	no	—
867	C₂×#41	—	4	2	no	—
868	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
869	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
870	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
871	C₂×#41	C₂³×C₆₇	1	2	yes	—
872	C₂×#41	C₂³×C₆₇	1	2	yes	—
873	C₂×#41	C₂³×C₆₇	1	2	yes	—
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	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
879	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
880	C₂²×D₄	—	2	1	no	—
881	C₂²×D₄	—	2	1	no	—
882	C₂²×D₄	—	2	1	no	—
883	C₂²×D₄	—	2	1	no	—
884	C₂²×D₄	—	2	2	no	—
885	C₂²×D₄	—	2	2	no	—
886	C₂²×D₄	—	2	1	no	—
887	C₂²×D₄	—	2	2	no	—
888	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
889	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
890	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
891	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
892	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
893	C₂³×C₄	—	2	1	no	—
894	C₂³×C₄	—	2	1	no	—
895	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
896	#137	—	2	4	no	—
897	#137	—	2	8	no	—
898	#137	—	2	4	no	—
899	AGL(1,ℤ/8)	—	2	4	no	—
900	AGL(1,ℤ/8)	—	2	8	no	—
901	AGL(1,ℤ/8)	—	2	8	no	—
902	AGL(1,ℤ/8)	—	2	8	no	—
903	AGL(1,ℤ/8)	—	2	4	no	—
904	AGL(1,ℤ/8)	D₄×C₆₇	1	8	yes	complemented
905	#135	—	2	4	no	—
906	#135	—	2	8	no	—
907	#135	—	2	8	no	—
908	#135	—	2	8	no	—
909	#135	—	4	2	no	—
910	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
911	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
912	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
913	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
914	C₂×SD₁₆	—	4	2	no	—
915	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
916	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
917	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
918	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
919	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
920	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
921	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
922	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
923	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
924	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
925	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
926	C₂×D₈	—	2	4	no	—
927	C₂×D₈	—	2	8	no	—
928	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
929	C₂×D₈	C₂³×C₆₇	1	2	yes	—
930	C₂×D₈	C₂³×C₆₇	1	2	yes	—
931	C₂×D₈	C₂³×C₆₇	1	2	yes	—
932	C₂×D₈	C₂³×C₆₇	1	2	yes	—
933	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
934	C₂×D₈	C₂³×C₆₇	1	2	yes	—
935	#131	—	2	4	no	—
936	C₂×M₁₆	—	2	4	no	—
937	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
938	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
939	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
940	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
941	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
942	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
943	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
944	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
945	C₄⋊Q₈	—	2	1	no	—
946	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
947	#127	—	2	2	no	—
948	#127	C₂³×C₆₇	1	2	yes	—
949	#124	—	2	1	no	—
950	#124	—	2	2	no	—
951	#124	C₂³×C₆₇	1	2	yes	—
952	#124	C₂³×C₆₇	1	2	yes	—
953	#123	—	2	2	no	—
954	#123	—	2	1	no	—
955	#123	—	2	2	no	—
956	#123	—	2	2	no	—
957	#123	—	2	2	no	—
958	#123	—	2	2	no	—
959	#123	—	2	2	no	—
960	#123	—	2	2	no	—
961	#123	—	2	2	no	—
962	#123	—	2	2	no	—
963	#123	D₄×C₆₇	1	2	yes	—
964	C₂²⋊Q₈	—	2	1	no	—
965	C₂²⋊Q₈	—	2	1	no	—
966	C₂²⋊Q₈	—	2	1	no	—
967	C₂²⋊Q₈	—	2	2	no	—
968	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
969	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
970	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
971	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
972	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
973	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
974	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
975	#121	—	2	1	no	—
976	#121	—	2	2	no	—
977	#121	—	2	2	no	—
978	#121	—	2	2	no	—
979	#121	—	2	2	no	—
980	#121	—	2	1	no	—
981	#121	—	2	1	no	—
982	#121	—	2	1	no	—
983	#121	—	2	1	no	—
984	#121	—	2	2	no	—
985	#121	—	2	2	no	—
986	#121	—	2	2	no	—
987	#121	—	2	2	no	—
988	#121	—	2	2	no	—
989	#121	—	2	2	no	—
990	#121	D₄×C₆₇	1	1	yes	characteristic
991	#121	D₄×C₆₇	1	1	yes	characteristic
992	#121	C₂³×C₆₇	1	2	yes	—
993	#121	C₂³×C₆₇	1	2	yes	—
994	#121	C₂³×C₆₇	1	1	yes	characteristic
995	#121	C₂³×C₆₇	1	1	yes	characteristic
996	#121	C₂³×C₆₇	1	2	yes	—
997	#120	—	2	1	no	—
998	#120	—	2	2	no	—
999	#120	—	2	2	no	—
1000	#120	—	2	2	no	—
1001	#120	—	2	2	no	—
1002	#120	—	2	2	no	—
1003	#120	—	2	2	no	—
1004	#120	D₄×C₆₇	1	2	yes	—
1005	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
1006	C₄×D₄	—	2	1	no	—
1007	C₄×D₄	—	2	1	no	—
1008	C₄×D₄	—	2	1	no	—
1009	C₄×D₄	—	2	1	no	—
1010	C₄×D₄	—	2	2	no	—
1011	C₄×D₄	—	2	2	no	—
1012	C₄×D₄	—	2	2	no	—
1013	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1014	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1015	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1016	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1017	C₄×D₄	C₂³×C₆₇	1	2	yes	—
1018	#117	—	2	1	no	—
1019	#117	C₂³×C₆₇	1	1	yes	characteristic
1020	#117	C₂³×C₆₇	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	—	2	1	no	—
1022	C₂×C₄⋊C₄	—	2	2	no	—
1023	C₂×C₄⋊C₄	—	2	2	no	—
1024	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	—	2	1	no	—
1026	C₂×C₂²⋊C₄	—	2	2	no	—
1027	C₂×C₂²⋊C₄	—	2	2	no	—
1028	C₂×C₂²⋊C₄	—	2	2	no	—
1029	C₂×C₂²⋊C₄	—	2	2	no	—
1030	#107	C₂³×C₆₇	1	2	yes	—
1031	#106	C₂³×C₆₇	1	2	yes	—
1032	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1033	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
1034	#103	C₂³×C₆₇	1	2	yes	—
1035	#103	C₂³×C₆₇	1	2	yes	—
1036	#103	C₂³×C₆₇	1	1	yes	characteristic
1037	#103	C₂³×C₆₇	1	1	yes	characteristic
1038	#103	C₂³×C₆₇	1	1	yes	characteristic
1039	#103	C₂³×C₆₇	1	1	yes	characteristic
1040	#103	C₂³×C₆₇	1	2	yes	—
1041	#102	C₂³×C₆₇	1	2	yes	—
1042	#102	C₂³×C₆₇	1	2	yes	—
1043	#102	C₂³×C₆₇	1	1	yes	characteristic
1044	#102	C₂³×C₆₇	1	1	yes	characteristic
1045	#102	C₂³×C₆₇	1	1	yes	characteristic
1046	#102	C₂³×C₆₇	1	1	yes	characteristic
1047	#102	C₂³×C₆₇	1	2	yes	—
1048	#102	C₂³×C₆₇	1	2	yes	—
1049	#102	C₂³×C₆₇	1	2	yes	—
1050	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1051	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1052	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1053	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
1054	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1055	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1056	#97	C₂³×C₆₇	1	2	yes	—
1057	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1058	C₂⁴	—	2	1	no	—
1059	C₂⁴	—	2	1	no	—
1060	C₂⁴	—	2	2	no	—
1061	C₂⁴	—	2	2	no	—
1062	C₂⁴	—	2	1	no	—
1063	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
1064	#41	—	2	2	no	—
1065	#41	—	2	2	no	—
1066	#41	—	2	2	no	—
1067	#41	—	2	2	no	—
1068	#41	—	2	4	no	—
1069	#41	—	2	4	no	—
1070	#41	—	2	2	no	—
1071	#41	—	2	4	no	—
1072	#41	—	2	4	no	—
1073	#41	—	2	2	no	—
1074	#41	—	2	2	no	—
1075	#41	—	2	2	no	—
1076	#41	—	2	2	no	—
1077	#41	—	4	4	no	—
1078	#41	—	4	2	no	—
1079	#41	—	4	1	no	—
1080	#41	—	4	2	no	—
1081	#41	—	4	1	no	—
1082	#41	—	4	2	no	—
1083	#41	—	4	2	no	—
1084	#41	—	4	4	no	—
1085	#41	—	4	4	no	—
1086	#41	—	4	4	no	—
1087	#41	—	4	4	no	—
1088	#41	—	4	4	no	—
1089	#41	C₂×D₄×C₆₇	1	4	yes	—
1090	C₂×Q₈	—	2	1	no	—
1091	C₂×Q₈	—	2	1	no	—
1092	C₂×Q₈	—	2	2	no	—
1093	C₂×Q₈	—	2	2	no	—
1094	C₂×Q₈	—	2	2	no	—
1095	C₂×Q₈	—	4	1	no	—
1096	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1097	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1098	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
1099	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1100	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1101	C₂×D₄	—	2	1	no	—
1102	C₂×D₄	—	2	4	no	—
1103	C₂×D₄	—	2	4	no	—
1104	C₂×D₄	—	2	2	no	—
1105	C₂×D₄	—	2	2	no	—
1106	C₂×D₄	—	2	1	no	—
1107	C₂×D₄	—	2	1	no	—
1108	C₂×D₄	—	2	2	no	—
1109	C₂×D₄	—	2	2	no	—
1110	C₂×D₄	—	2	1	no	—
1111	C₂×D₄	—	2	2	no	—
1112	C₂×D₄	—	2	2	no	—
1113	C₂×D₄	—	2	1	no	—
1114	C₂×D₄	—	2	1	no	—
1115	C₂×D₄	—	2	1	no	—
1116	C₂×D₄	—	2	2	no	—
1117	C₂×D₄	—	2	2	no	—
1118	C₂×D₄	—	2	1	no	—
1119	C₂×D₄	—	2	2	no	—
1120	C₂×D₄	—	2	1	no	—
1121	C₂×D₄	—	2	2	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	2	no	—
1127	C₂×D₄	—	2	2	no	—
1128	C₂×D₄	—	4	1	no	—
1129	C₂×D₄	—	4	2	no	—
1130	C₂×D₄	—	4	2	no	—
1131	C₂×D₄	—	4	4	no	—
1132	C₂×D₄	—	4	8	no	—
1133	C₂×D₄	—	4	4	no	—
1134	C₂×D₄	—	4	4	no	—
1135	C₂×D₄	—	4	8	no	—
1136	C₂×D₄	—	4	4	no	—
1137	C₂×D₄	—	8	4	no	—
1138	C₂×D₄	—	8	2	no	—
1139	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1140	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1141	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1142	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
1143	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	complemented
1144	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1145	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1146	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1147	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1148	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1149	C₂²×C₄	—	2	1	no	—
1150	C₂²×C₄	—	2	2	no	—
1151	C₂²×C₄	—	2	2	no	—
1152	C₂²×C₄	—	2	1	no	—
1153	C₂²×C₄	—	2	1	no	—
1154	C₂²×C₄	—	2	1	no	—
1155	C₂²×C₄	—	2	1	no	—
1156	C₂²×C₄	—	2	2	no	—
1157	C₂²×C₄	—	2	2	no	—
1158	C₂²×C₄	—	2	2	no	—
1159	C₂²×C₄	—	2	1	no	—
1160	C₂²×C₄	—	2	2	no	—
1161	C₂²×C₄	—	2	1	no	—
1162	C₂²×C₄	—	2	1	no	—
1163	C₂²×C₄	—	2	2	no	—
1164	C₂²×C₄	—	2	2	no	—
1165	C₂²×C₄	—	2	2	no	—
1166	C₂²×C₄	—	4	4	no	—
1167	C₂²×C₄	—	4	4	no	—
1168	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1169	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1170	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1171	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1172	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1173	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1174	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1175	Q₁₆	—	2	2	no	—
1176	Q₁₆	—	2	4	no	—
1177	Q₁₆	—	2	4	no	—
1178	Q₁₆	—	4	1	no	—
1179	SD₁₆	—	2	2	no	—
1180	SD₁₆	—	2	2	no	—
1181	SD₁₆	—	2	4	no	—
1182	SD₁₆	—	2	4	no	—
1183	SD₁₆	—	2	4	no	—
1184	SD₁₆	—	2	4	no	—
1185	SD₁₆	—	4	2	no	—
1186	SD₁₆	—	4	2	no	—
1187	SD₁₆	—	4	1	no	—
1188	SD₁₆	—	4	1	no	—
1189	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
1190	D₈	—	2	4	no	—
1191	D₈	—	2	2	no	—
1192	D₈	—	2	4	no	—
1193	D₈	—	2	4	no	—
1194	D₈	—	2	4	no	—
1195	D₈	—	4	1	no	—
1196	D₈	C₂×D₄×C₆₇	1	8	yes	complemented
1197	M₁₆	—	2	2	no	—
1198	M₁₆	—	2	4	no	—
1199	M₁₆	—	2	4	no	—
1200	M₁₆	C₂×D₄×C₆₇	1	4	yes	complemented
1201	C₂×C₈	—	2	2	no	—
1202	C₂×C₈	—	2	2	no	—
1203	C₂×C₈	—	2	4	no	—
1204	C₂×C₈	—	2	4	no	—
1205	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1206	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1207	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1208	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1209	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1210	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1211	C₄⋊C₄	—	2	1	no	—
1212	C₄⋊C₄	—	2	1	no	—
1213	C₄⋊C₄	—	2	1	no	—
1214	C₄⋊C₄	—	2	2	no	—
1215	C₄⋊C₄	—	2	2	no	—
1216	C₄⋊C₄	—	2	2	no	—
1217	C₄⋊C₄	—	2	2	no	—
1218	C₄⋊C₄	—	2	2	no	—
1219	C₄⋊C₄	—	2	2	no	—
1220	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1221	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1222	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1223	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1224	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1225	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1226	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1227	C₂²⋊C₄	—	2	1	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	2	no	—
1230	C₂²⋊C₄	—	2	2	no	—
1231	C₂²⋊C₄	—	2	1	no	—
1232	C₂²⋊C₄	—	2	1	no	—
1233	C₂²⋊C₄	—	2	2	no	—
1234	C₂²⋊C₄	—	2	1	no	—
1235	C₂²⋊C₄	—	2	1	no	—
1236	C₂²⋊C₄	—	2	2	no	—
1237	C₂²⋊C₄	—	2	2	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	C₂×D₄×C₆₇	1	2	yes	—
1246	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1247	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1248	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1249	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1250	C₄²	—	2	2	no	—
1251	C₄²	—	2	1	no	—
1252	C₄²	C₂⁴×C₆₇	1	2	yes	—
1253	C₂³	—	2	2	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	2	no	—
1256	C₂³	—	2	4	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	2	2	no	—
1259	C₂³	—	2	1	no	—
1260	C₂³	—	4	1	no	—
1261	C₂³	—	4	1	no	—
1262	C₂³	—	4	2	no	—
1263	C₂³	—	4	4	no	—
1264	C₂³	—	4	4	no	—
1265	C₂³	—	4	2	no	—
1266	C₂³	—	4	2	no	—
1267	C₂³	—	8	1	no	—
1268	C₂³	—	8	1	no	—
1269	C₂³	—	8	1	no	—
1270	C₂³	—	8	1	no	—
1271	C₂³	—	8	2	no	—
1272	C₂³	—	8	1	no	—
1273	C₂³	—	8	2	no	—
1274	C₂³	—	8	2	no	—
1275	C₂³	—	8	2	no	—
1276	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1277	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1278	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1279	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1280	Q₈	—	2	2	no	—
1281	Q₈	—	2	1	no	—
1282	Q₈	—	2	1	no	—
1283	Q₈	—	2	1	no	—
1284	Q₈	—	2	2	no	—
1285	Q₈	—	2	2	no	—
1286	Q₈	—	2	1	no	—
1287	Q₈	—	2	1	no	—
1288	Q₈	—	4	2	no	—
1289	Q₈	—	4	2	no	—
1290	Q₈	C₂²×D₄×C₆₇	1	2	yes	—
1291	D₄	—	2	4	no	—
1292	D₄	—	2	4	no	—
1293	D₄	—	2	4	no	—
1294	D₄	—	2	2	no	—
1295	D₄	—	2	2	no	—
1296	D₄	—	2	1	no	—
1297	D₄	—	2	1	no	—
1298	D₄	—	2	2	no	—
1299	D₄	—	2	1	no	—
1300	D₄	—	2	1	no	—
1301	D₄	—	2	1	no	—
1302	D₄	—	2	2	no	—
1303	D₄	—	4	2	no	—
1304	D₄	—	4	2	no	—
1305	D₄	—	4	4	no	—
1306	D₄	—	4	4	no	—
1307	D₄	—	4	2	no	—
1308	D₄	—	4	4	no	—
1309	D₄	—	4	2	no	—
1310	D₄	—	4	4	no	—
1311	D₄	—	4	4	no	—
1312	D₄	—	4	2	no	—
1313	D₄	—	4	4	no	—
1314	D₄	—	4	4	no	—
1315	D₄	—	4	2	no	—
1316	D₄	—	4	2	no	—
1317	D₄	—	4	2	no	—
1318	D₄	—	8	2	no	—
1319	D₄	—	8	2	no	—
1320	D₄	—	8	2	no	—
1321	D₄	—	8	2	no	—
1322	D₄	—	8	1	no	—
1323	D₄	—	8	1	no	—
1324	D₄	C₂²×D₄×C₆₇	1	4	yes	—
1325	D₄	C₂²×D₄×C₆₇	1	2	yes	—
1326	C₂×C₄	—	2	2	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	2	no	—
1329	C₂×C₄	—	2	2	no	—
1330	C₂×C₄	—	2	4	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	2	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	2	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	2	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	2	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	4	2	no	—
1344	C₂×C₄	—	4	4	no	—
1345	C₂×C₄	—	4	2	no	—
1346	C₂×C₄	—	4	2	no	—
1347	C₂×C₄	—	4	4	no	—
1348	C₂×C₄	—	4	4	no	—
1349	C₂×C₄	—	4	4	no	—
1350	C₂×C₄	—	4	2	no	—
1351	C₂×C₄	—	4	2	no	—
1352	C₂×C₄	—	4	2	no	—
1353	C₂×C₄	—	8	2	no	—
1354	C₂×C₄	—	8	2	no	—
1355	C₂×C₄	—	8	2	no	—
1356	C₂×C₄	—	8	1	no	—
1357	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1358	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1359	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1360	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1361	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1362	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1363	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1364	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1365	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1366	C₈	—	2	1	no	—
1367	C₈	—	2	1	no	—
1368	C₈	—	2	2	no	—
1369	C₈	—	2	1	no	—
1370	C₈	—	2	1	no	—
1371	C₈	C₂²×D₄×C₆₇	1	4	yes	—
1372	C₂²	—	2	1	no	—
1373	C₂²	—	2	1	no	—
1374	C₂²	—	2	1	no	—
1375	C₂²	—	2	2	no	—
1376	C₂²	—	2	1	no	—
1377	C₂²	—	2	1	no	—
1378	C₂²	—	2	2	no	—
1379	C₂²	—	2	1	no	—
1380	C₂²	—	2	1	no	—
1381	C₂²	—	2	1	no	—
1382	C₂²	—	2	2	no	—
1383	C₂²	—	2	2	no	—
1384	C₂²	—	2	4	no	—
1385	C₂²	—	4	2	no	—
1386	C₂²	—	4	1	no	—
1387	C₂²	—	4	1	no	—
1388	C₂²	—	4	2	no	—
1389	C₂²	—	4	1	no	—
1390	C₂²	—	4	2	no	—
1391	C₂²	—	4	1	no	—
1392	C₂²	—	4	2	no	—
1393	C₂²	—	4	1	no	—
1394	C₂²	—	4	1	no	—
1395	C₂²	—	4	1	no	—
1396	C₂²	—	4	2	no	—
1397	C₂²	—	4	1	no	—
1398	C₂²	—	8	2	no	—
1399	C₂²	—	8	4	no	—
1400	C₂²	—	8	4	no	—
1401	C₂²	—	16	2	no	—
1402	C₂²	—	16	4	no	—
1403	C₂²	—	16	4	no	—
1404	C₂²	D₄²×C₆₇	1	2	yes	—
1405	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1406	C₄	—	2	2	no	—
1407	C₄	—	2	2	no	—
1408	C₄	—	2	1	no	—
1409	C₄	—	2	1	no	—
1410	C₄	—	2	2	no	—
1411	C₄	—	2	2	no	—
1412	C₄	—	4	1	no	—
1413	C₄	—	4	2	no	—
1414	C₄	—	4	1	no	—
1415	C₄	—	4	1	no	—
1416	C₄	—	4	1	no	—
1417	C₄	—	4	2	no	—
1418	C₄	D₄²×C₆₇	1	2	yes	—
1419	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1420	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1421	C₂	—	2	2	no	—
1422	C₂	—	4	1	no	—
1423	C₂	—	4	1	no	—
1424	C₂	—	4	2	no	—
1425	C₂	—	4	2	no	—
1426	C₂	—	4	4	no	—
1427	C₂	—	8	1	no	—
1428	C₂	—	8	2	no	—
1429	C₂	—	8	1	no	—
1430	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1431	C₂	C₆₇×#3584	1	1	yes	characteristic
1432	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. C₂×#575×C₆₇	C₂	semidirect
3. C₆₇×#3488	C₂	semidirect
4. C₆₇×#3485	C₂	semidirect
5. C₆₇×#3284	C₂	semidirect
6. C₆₇×#3280	C₂	semidirect
7. C₆₇×#3275	C₂	semidirect
8. C₆₇×#3272	C₂	semidirect
9. C₆₇×#3269	C₂	semidirect
10. C₆₇×#3268	C₂	semidirect
11. C₆₇×#3267	C₂	semidirect
12. C₆₇×#3264	C₂	semidirect
13. C₆₇×#3154	C₂	semidirect
14. C₆₇×#3063	C₂	semidirect
15. C₆₇×#3055	C₂	semidirect
16. C₆₇×#3046	C₂	semidirect
17. C₆₇×#3041	C₂	semidirect
18. C₆₇×#3012	C₂	semidirect
19. C₆₇×#3009	C₂	semidirect
20. C₆₇×#3002	C₂	semidirect
21. C₂×#449×C₆₇	C₂	semidirect
22. C₆₇×#2946	C₂	semidirect
23. C₆₇×#2933	C₂	semidirect
25. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
26. C₂²×#41×C₆₇	C₂²	semidirect
27. C₂²×#41×C₆₇	C₂²	semidirect
30. C₂×#137×C₆₇	C₂²	semidirect
31. C₂×#137×C₆₇	C₂²	semidirect
32. 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
40. C₂×#135×C₆₇	C₂²	semidirect
41. C₂×#135×C₆₇	C₂²	semidirect
42. C₂×#135×C₆₇	C₂²	semidirect
43. C₂×#135×C₆₇	C₂²	semidirect
44. C₂²×SD₁₆×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
53. #547×C₆₇	C₂²	semidirect
54. #547×C₆₇	C₂²	semidirect
58. #546×C₆₇	C₂²	semidirect
59. #546×C₆₇	C₂²	semidirect
60. #546×C₆₇	C₂²	semidirect
62. D₄²×C₆₇	C₂²	semidirect
65. #536×C₆₇	C₂²	semidirect
66. #536×C₆₇	C₂²	semidirect
68. #535×C₆₇	C₂²	semidirect
72. #525×C₆₇	C₂²	semidirect
75. C₂×#121×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. #462×C₆₇	C₂²	semidirect
95. #461×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. #452×C₆₇	C₂²	semidirect
102. #452×C₆₇	C₂²	semidirect
103. #451×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. #449×C₆₇	C₂²	semidirect
114. #449×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. #418×C₆₇	C₂²	semidirect
129. #417×C₆₇	C₂²	semidirect
130. #416×C₆₇	C₂²	semidirect
131. #416×C₆₇	C₂²	semidirect
132. C₂×#103×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
187. AGL(1,ℤ/8)×C₆₇	D₄	semidirect
426. C₂×D₄×C₆₇	C₂×D₄	semidirect
472. SD₁₆×C₆₇	C₂×D₄	semidirect
479. D₈×C₆₇	C₂×D₄	semidirect
483. M₁₆×C₆₇	C₂×D₄	semidirect
704. #61074	C₆₇	direct (N × H)
717. C₂×#576	C₂×C₆₇	semidirect
718. C₂×#575	C₂×C₆₇	semidirect
719. #3488	C₂×C₆₇	semidirect
720. #3485	C₂×C₆₇	semidirect
721. #3284	C₂×C₆₇	semidirect
722. #3280	C₂×C₆₇	semidirect
723. #3275	C₂×C₆₇	semidirect
724. #3272	C₂×C₆₇	semidirect
725. #3269	C₂×C₆₇	semidirect
726. #3268	C₂×C₆₇	semidirect
727. #3267	C₂×C₆₇	semidirect
728. #3264	C₂×C₆₇	semidirect
729. #3154	C₂×C₆₇	semidirect
730. #3063	C₂×C₆₇	semidirect
731. #3055	C₂×C₆₇	semidirect
732. #3046	C₂×C₆₇	semidirect
733. #3041	C₂×C₆₇	semidirect
734. #3012	C₂×C₆₇	semidirect
735. #3009	C₂×C₆₇	semidirect
736. #3002	C₂×C₆₇	semidirect
737. C₂×#449	C₂×C₆₇	semidirect
738. #2946	C₂×C₆₇	semidirect
739. #2933	C₂×C₆₇	semidirect
740. C₆₇	#61074	direct (N × H)
742. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
743. C₂²×#41	C₂²×C₆₇	semidirect
744. C₂²×#41	C₂²×C₆₇	semidirect
747. C₂×#137	C₂²×C₆₇	semidirect
748. C₂×#137	C₂²×C₆₇	semidirect
749. C₂×#137	C₂²×C₆₇	semidirect
751. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
752. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
753. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
754. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
755. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
757. C₂×#135	C₂²×C₆₇	semidirect
758. C₂×#135	C₂²×C₆₇	semidirect
759. C₂×#135	C₂²×C₆₇	semidirect
760. C₂×#135	C₂²×C₆₇	semidirect
761. C₂²×SD₁₆	C₂²×C₆₇	semidirect
762. C₂²×D₈	C₂²×C₆₇	semidirect
763. C₂²×D₈	C₂²×C₆₇	semidirect
764. C₂×#131	C₂²×C₆₇	semidirect
765. C₂²×M₁₆	C₂²×C₆₇	semidirect
766. #550	C₂²×C₆₇	semidirect
767. #548	C₂²×C₆₇	semidirect
770. #547	C₂²×C₆₇	semidirect
771. #547	C₂²×C₆₇	semidirect
775. #546	C₂²×C₆₇	semidirect
776. #546	C₂²×C₆₇	semidirect
777. #546	C₂²×C₆₇	semidirect
779. D₄²	C₂²×C₆₇	semidirect
782. #536	C₂²×C₆₇	semidirect
783. #536	C₂²×C₆₇	semidirect
785. #535	C₂²×C₆₇	semidirect
789. #525	C₂²×C₆₇	semidirect
792. C₂×#121	C₂²×C₆₇	semidirect
793. #520	C₂²×C₆₇	semidirect
794. #518	C₂²×C₆₇	semidirect
795. #497	C₂²×C₆₇	semidirect
796. #496	C₂²×C₆₇	semidirect
797. #495	C₂²×C₆₇	semidirect
798. #492	C₂²×C₆₇	semidirect
799. #470	C₂²×C₆₇	semidirect
800. #469	C₂²×C₆₇	semidirect
801. #468	C₂²×C₆₇	semidirect
802. #468	C₂²×C₆₇	semidirect
803. #467	C₂²×C₆₇	semidirect
804. #466	C₂²×C₆₇	semidirect
805. #465	C₂²×C₆₇	semidirect
806. #465	C₂²×C₆₇	semidirect
807. #464	C₂²×C₆₇	semidirect
808. #463	C₂²×C₆₇	semidirect
809. #463	C₂²×C₆₇	semidirect
810. #463	C₂²×C₆₇	semidirect
811. #462	C₂²×C₆₇	semidirect
812. #461	C₂²×C₆₇	semidirect
813. #459	C₂²×C₆₇	semidirect
814. #459	C₂²×C₆₇	semidirect
815. #452	C₂²×C₆₇	semidirect
816. #452	C₂²×C₆₇	semidirect
817. #452	C₂²×C₆₇	semidirect
818. #452	C₂²×C₆₇	semidirect
819. #452	C₂²×C₆₇	semidirect
820. #451	C₂²×C₆₇	semidirect
821. #450	C₂²×C₆₇	semidirect
822. #450	C₂²×C₆₇	semidirect
823. #450	C₂²×C₆₇	semidirect
824. #450	C₂²×C₆₇	semidirect
825. #449	C₂²×C₆₇	semidirect
826. #449	C₂²×C₆₇	semidirect
827. #449	C₂²×C₆₇	semidirect
828. #449	C₂²×C₆₇	semidirect
829. #449	C₂²×C₆₇	semidirect
830. #449	C₂²×C₆₇	semidirect
831. #449	C₂²×C₆₇	semidirect
832. #448	C₂²×C₆₇	semidirect
833. #447	C₂²×C₆₇	semidirect
834. #447	C₂²×C₆₇	semidirect
835. #442	C₂²×C₆₇	semidirect
836. #440	C₂²×C₆₇	semidirect
837. C₄×SD₁₆	C₂²×C₆₇	semidirect
838. C₄×D₈	C₂²×C₆₇	semidirect
839. #436	C₂²×C₆₇	semidirect
840. #435	C₂²×C₆₇	semidirect
841. #435	C₂²×C₆₇	semidirect
842. C₈×D₄	C₂²×C₆₇	semidirect
843. #428	C₂²×C₆₇	semidirect
844. #424	C₂²×C₆₇	semidirect
845. #418	C₂²×C₆₇	semidirect
846. #417	C₂²×C₆₇	semidirect
847. #416	C₂²×C₆₇	semidirect
848. #416	C₂²×C₆₇	semidirect
849. C₂×#103	C₂²×C₆₇	semidirect
850. C₂×#102	C₂²×C₆₇	semidirect
851. #408	C₂²×C₆₇	semidirect
852. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
853. #405	C₂²×C₆₇	semidirect
904. AGL(1,ℤ/8)	D₄×C₆₇	semidirect
1143. C₂×D₄	C₂×D₄×C₆₇	semidirect
1189. SD₁₆	C₂×D₄×C₆₇	semidirect
1196. D₈	C₂×D₄×C₆₇	semidirect
1200. M₁₆	C₂×D₄×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
C₂×#575×C₆₇	2
C₆₇×#3488	2
C₆₇×#3485	2
C₆₇×#3284	2
C₆₇×#3280	2
C₆₇×#3275	2
C₆₇×#3272	2
C₆₇×#3269	2
C₆₇×#3268	2
C₆₇×#3267	2
C₆₇×#3264	2
C₆₇×#3154	2
C₆₇×#3063	2
C₆₇×#3055	2
C₆₇×#3046	2
C₆₇×#3041	2
C₆₇×#3012	2
C₆₇×#3009	2
C₆₇×#3002	2
C₂×#449×C₆₇	2
C₆₇×#2946	2
C₆₇×#2933	2
#61074	67

Subgroups — C67×#61074 #30740325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61074 #30740325