Subgroups — #31720482

Order 17152.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573767	C₂	1	1	yes	maximal, characteristic
2	#22569219	C₂	1	2	yes	maximal, complemented
3	#22569206	C₂	1	2	yes	maximal, complemented
4	#22569204	C₂	1	2	yes	maximal, complemented
5	#22569200	C₂	1	2	yes	maximal, complemented
6	#22569191	C₂	1	2	yes	maximal, complemented
7	#22569188	C₂	1	2	yes	maximal, complemented
8	#22569179	C₂	1	2	yes	maximal, complemented
9	#22569169	C₂	1	2	yes	maximal, complemented
10	#22569152	C₂	1	1	yes	maximal, characteristic, complemented
11	#22569149	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×#11761612	C₂	1	1	yes	maximal, characteristic, complemented
13	#22568930	C₂	1	1	yes	maximal, characteristic, complemented
14	#22568930	C₂	1	1	yes	maximal, characteristic, complemented
15	#22568912	C₂	1	1	yes	maximal, characteristic, complemented
16	#22568903	C₂	1	1	yes	maximal, characteristic, complemented
17	#22568874	C₂	1	1	yes	maximal, characteristic, complemented
18	#22568863	C₂	1	1	yes	maximal, characteristic, complemented
19	#22568863	C₂	1	1	yes	maximal, characteristic, complemented
20	#22568634	C₂	1	1	yes	maximal, characteristic, complemented
21	#22568627	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863351	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524049	C₂²	1	1	yes	characteristic
25	C₂×#14524049	C₂²	1	1	yes	characteristic
26	C₂²×#11761612	C₂²	1	1	yes	characteristic
27	C₂²×#11761612	C₂²	1	1	yes	characteristic
28	#16864116	C₄	1	1	yes	characteristic
29	#16864111	C₄	1	1	yes	characteristic
30	#16864103	C₄	1	1	yes	characteristic
31	#16864092	C₄	1	1	yes	characteristic
32	#16864092	C₄	1	1	yes	characteristic
33	#16864086	C₄	1	1	yes	characteristic
34	#16864086	C₄	1	1	yes	characteristic
35	#16864081	C₄	1	2	yes	—
36	#16864072	C₄	1	2	yes	—
37	#16864072	C₄	1	2	yes	—
38	#16864050	C₄	1	1	yes	characteristic
39	#16864040	C₄	1	2	yes	—
40	#16863953	C₂²	1	1	yes	characteristic
41	#16863928	C₂²	1	2	yes	—
42	#16863926	C₂²	1	2	yes	—
43	#16863926	C₂²	1	2	yes	—
44	#16863907	C₂²	1	1	yes	characteristic
45	#16863907	C₂²	1	1	yes	characteristic
46	C₄×#11761628	C₂²	1	1	yes	characteristic
47	C₄×#11761627	C₂²	1	2	yes	—
48	C₂×#14524002	C₂²	1	1	yes	characteristic
49	C₂×#14524002	C₂²	1	1	yes	characteristic
50	#16863525	C₂²	1	2	yes	complemented
51	#16863525	C₂²	1	2	yes	complemented
52	#16863524	C₂²	1	2	yes	complemented
53	#16863524	C₂²	1	2	yes	complemented
54	#16863524	C₂²	1	2	yes	complemented
55	#16863524	C₂²	1	2	yes	complemented
56	#16863523	C₂²	1	2	yes	complemented
57	#16863520	C₂²	1	2	yes	complemented
58	#16863474	C₂²	1	2	yes	—
59	#16863472	C₂²	1	2	yes	complemented
60	#16863472	C₂²	1	2	yes	complemented
61	#16863471	C₂²	1	2	yes	complemented
62	#16863471	C₂²	1	2	yes	complemented
63	#16863470	C₂²	1	2	yes	complemented
64	#16863470	C₂²	1	2	yes	complemented
65	#16863468	C₂²	1	2	yes	—
66	#16863468	C₂²	1	2	yes	—
67	#16863467	C₂²	1	2	yes	complemented
68	#16863467	C₂²	1	2	yes	complemented
69	#16863465	C₂²	1	2	yes	complemented
70	#16863465	C₂²	1	2	yes	complemented
71	#16863464	C₂²	1	2	yes	complemented
72	#16863464	C₂²	1	2	yes	complemented
73	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
74	C₈×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
75	C₈×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
76	(C₂²⋊D₆₇)⋊C₈	C₂²	1	2	yes	complemented
77	(C₂²⋊D₆₇)⋊C₈	C₂²	1	2	yes	complemented
78	#16863456	C₂²	1	2	yes	complemented
79	#16863456	C₂²	1	2	yes	complemented
80	#16863454	C₂²	1	2	yes	complemented
81	#16863454	C₂²	1	2	yes	complemented
82	#16863454	C₂²	1	2	yes	complemented
83	#16863454	C₂²	1	2	yes	complemented
84	#16863452	C₂²	1	2	yes	complemented
85	#16863450	C₂²	1	2	yes	complemented
86	#16863450	C₂²	1	2	yes	complemented
87	#16863448	C₂²	1	2	yes	complemented
88	#16863446	C₂²	1	2	yes	complemented
89	#16863446	C₂²	1	2	yes	complemented
90	#16863422	C₂²	1	1	yes	characteristic
91	#16863422	C₂²	1	1	yes	characteristic
92	#16863422	C₂²	1	1	yes	characteristic
93	#16863422	C₂²	1	1	yes	characteristic
94	#16863420	C₂²	1	1	yes	characteristic
95	#16863362	C₂²	1	1	yes	characteristic
96	#16863362	C₂²	1	1	yes	characteristic
97	#16863360	C₂²	1	1	yes	characteristic
98	#16863360	C₂²	1	1	yes	characteristic
99	#16863354	C₂²	1	2	yes	complemented
100	#16863354	C₂²	1	2	yes	complemented
101	#16863353	C₂²	1	2	yes	complemented
102	#16863353	C₂²	1	2	yes	complemented
103	#16863351	C₂²	1	1	yes	characteristic
104	#16863351	C₂²	1	1	yes	characteristic
105	#16863351	C₂²	1	1	yes	characteristic
106	#16863351	C₂²	1	1	yes	characteristic
107	#16863351	C₂²	1	1	yes	characteristic
108	#16863351	C₂²	1	1	yes	characteristic
109	#16863351	C₂²	1	1	yes	characteristic
110	#16863351	C₂²	1	1	yes	characteristic
111	#16863351	C₂²	1	2	yes	complemented
112	#16863351	C₂²	1	2	yes	complemented
113	C₄×#11761612	C₂²	1	1	yes	characteristic
114	#16863348	C₂²	1	2	yes	complemented
115	M₁₆×Dic₆₇	C₂²	1	2	yes	complemented
116	M₁₆×Dic₆₇	C₂²	1	2	yes	complemented
117	C₂×#14523953	C₂²	1	2	yes	complemented
118	#97×D₆₇	C₂²	1	2	yes	complemented
119	C₂×C₈×Dic₆₇	C₂²	1	2	yes	complemented
120	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
121	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
123	#435×C₆₇	C₂²	1	1	yes	characteristic
124	#435×C₆₇	C₂²	1	1	yes	characteristic
125	#435×C₆₇	C₂²	1	1	yes	characteristic
126	#435×C₆₇	C₂²	1	1	yes	characteristic
127	#435×C₆₇	C₂²	1	1	yes	characteristic
128	#435×C₆₇	C₂²	1	1	yes	characteristic
129	#435×C₆₇	C₂²	1	1	yes	characteristic
130	#435×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
132	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
133	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
134	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#11761628	C₂³	1	1	yes	characteristic
136	C₂×#11761627	C₂×C₄	1	2	yes	—
137	#14524049	—	2	4	no	—
138	#14524049	—	2	4	no	—
139	C₂×#11761612	—	2	4	no	—
140	C₂×#11761612	—	2	4	no	—
141	C₂×#11761612	C₂³	1	2	yes	—
142	C₂×#11761612	C₂³	1	1	yes	characteristic
143	C₂×#11761612	C₂³	1	1	yes	characteristic
144	C₂×#11761612	C₂³	1	1	yes	characteristic
145	C₂×#11761612	C₂³	1	2	yes	—
146	C₂×#11761612	C₂³	1	1	yes	characteristic
147	C₂×#11761611	C₂³	1	2	yes	—
148	C₂×#11761611	C₂³	1	2	yes	—
149	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
150	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
151	C₂×C₈×D₆₇	C₂³	1	2	yes	—
152	C₂×C₈×D₆₇	C₂³	1	2	yes	—
153	#14524043	C₂×C₄	1	1	yes	characteristic
154	#14524043	C₂×C₄	1	1	yes	characteristic
155	#14524038	C₂×C₄	1	2	yes	—
156	#14524038	C₂×C₄	1	2	yes	—
157	#14524036	C₂×C₄	1	2	yes	—
158	#14524036	C₂×C₄	1	2	yes	—
159	#14524036	C₂×C₄	1	2	yes	—
160	#14524036	C₂×C₄	1	2	yes	—
161	#14524035	C₂×C₄	1	1	yes	characteristic
162	#14524035	C₂×C₄	1	1	yes	characteristic
163	#14524034	C₂×C₄	1	2	yes	—
164	#14524033	C₂×C₄	1	2	yes	—
165	#14524033	C₂×C₄	1	2	yes	—
166	#14524030	C₂×C₄	1	2	yes	—
167	#14524029	C₂×C₄	1	2	yes	—
168	#14524029	C₂×C₄	1	2	yes	—
169	#14524027	C₂×C₄	1	2	yes	—
170	#14524027	C₂×C₄	1	2	yes	—
171	#14524026	C₂×C₄	1	2	yes	—
172	#14524026	C₂×C₄	1	2	yes	—
173	#14524025	C₂×C₄	1	2	yes	—
174	#14524025	C₂×C₄	1	2	yes	—
175	#14524024	C₂×C₄	1	2	yes	—
176	#14524024	C₂×C₄	1	2	yes	—
177	#14524023	C₂×C₄	1	2	yes	—
178	#14524022	C₂×C₄	1	2	yes	—
179	#14524022	C₂×C₄	1	2	yes	—
180	#14524022	C₂×C₄	1	1	yes	characteristic
181	#14524022	C₂×C₄	1	1	yes	characteristic
182	#14524022	C₂×C₄	1	1	yes	characteristic
183	#14524022	C₂×C₄	1	1	yes	characteristic
184	#14524020	C₂×C₄	1	2	yes	—
185	#14524020	C₂×C₄	1	2	yes	—
186	#14524017	C₂×C₄	1	1	yes	characteristic
187	#14524017	C₂×C₄	1	1	yes	characteristic
188	#14524017	C₂×C₄	1	1	yes	characteristic
189	#14524017	C₂×C₄	1	1	yes	characteristic
190	#14524015	C₂×C₄	1	2	yes	—
191	#14524015	C₂×C₄	1	2	yes	—
192	#14524014	C₂×C₄	1	2	yes	—
193	#14524012	C₂×C₄	1	2	yes	—
194	#14524012	C₂×C₄	1	2	yes	—
195	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
196	C₄×Dic₁₃₄	C₂×C₄	1	1	yes	characteristic
197	C₄×Dic₁₃₄	C₂³	1	2	yes	—
198	C₄×Dic₁₃₄	C₂³	1	2	yes	—
199	#14524008	C₂×C₄	1	2	yes	—
200	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
201	C₄×D₂₆₈	C₂×C₄	1	1	yes	characteristic
202	D₄×Dic₆₇	C₂×C₄	1	2	yes	—
203	C₄×C₂²⋊D₆₇	C₂×C₄	1	2	yes	—
204	C₄×C₂²⋊D₆₇	C₂×C₄	1	2	yes	—
205	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
206	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
207	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
208	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
209	(C₂²⋊D₆₇)⋊C₄	C₂×C₄	1	2	yes	—
210	(C₂²⋊D₆₇)⋊C₄	C₂×C₄	1	2	yes	—
211	#14524002	C₂×C₄	1	2	yes	—
212	#14524002	C₂×C₄	1	2	yes	—
213	#14524002	C₂×C₄	1	1	yes	characteristic
214	#14524002	C₂×C₄	1	1	yes	characteristic
215	#14524002	C₂×C₄	1	1	yes	characteristic
216	#14524002	C₂×C₄	1	1	yes	characteristic
217	#14524002	C₂³	1	1	yes	characteristic
218	#14524002	C₂³	1	1	yes	characteristic
219	#14524002	C₂³	1	1	yes	characteristic
220	#14524002	C₂³	1	2	yes	—
221	#14524002	C₂³	1	2	yes	—
222	#14524001	C₂×C₄	1	2	yes	—
223	#14524000	C₂³	1	2	yes	—
224	#14523999	C₂×C₄	1	2	yes	—
225	#14523999	C₂×C₄	1	2	yes	—
226	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
227	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
228	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
229	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
230	C₂×C₂²⋊Dic₆₇	C₂×C₄	1	2	yes	—
231	C₂×C₂²⋊Dic₆₇	C₂×C₄	1	2	yes	—
232	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
233	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
234	C₄²×D₆₇	C₂³	1	2	yes	—
235	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
236	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
237	Dic₆₇⋊C₈	C₂³	1	2	yes	—
238	Dic₆₇⋊C₈	C₂³	1	2	yes	—
239	Dic₆₇⋊C₈	C₂³	1	2	yes	—
240	Dic₆₇⋊C₈	C₂³	1	2	yes	—
241	Dic₆₇⋊C₈	C₂³	1	2	yes	—
242	Dic₆₇⋊C₈	C₂³	1	2	yes	—
243	Dic₆₇⋊C₈	C₂³	1	2	yes	—
244	Dic₆₇⋊C₈	C₂³	1	2	yes	—
245	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
246	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
247	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
248	C₂²⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
249	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
250	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
251	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
252	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	—
253	#14523954	C₂³	1	2	yes	—
254	#14523953	C₂³	1	2	yes	—
255	#14523953	C₂³	1	2	yes	—
256	#14523953	C₂³	1	2	yes	—
257	#14523953	C₂³	1	2	yes	—
258	#14523953	C₂³	1	2	yes	—
259	#14523953	C₂³	1	2	yes	—
260	#14523953	C₂³	1	2	yes	—
261	#14523953	C₂³	1	2	yes	—
262	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
263	C₈×Dic₆₇	C₂³	1	2	yes	—
264	C₈×Dic₆₇	C₂³	1	2	yes	—
265	C₈×Dic₆₇	C₂³	1	2	yes	—
266	C₈×Dic₆₇	C₂³	1	2	yes	—
267	C₈×Dic₆₇	C₂³	1	2	yes	—
268	C₈×Dic₆₇	C₂³	1	2	yes	—
269	C₈×Dic₆₇	C₂³	1	2	yes	—
270	C₈×Dic₆₇	C₂³	1	2	yes	—
271	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
272	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
273	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
274	C₂×M₁₆×C₆₇	—	2	4	no	—
275	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
277	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₆₇	—	2	4	no	—
280	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
289	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
290	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
291	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
292	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
299	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
312	#97×C₆₇	C₂³	1	1	yes	characteristic
313	#97×C₆₇	C₂³	1	1	yes	characteristic
314	#97×C₆₇	C₂³	1	1	yes	characteristic
315	#97×C₆₇	C₂³	1	1	yes	characteristic
316	#11761628	—	2	2	no	—
317	#11761628	—	2	2	no	—
318	#11761627	—	4	4	no	—
319	C₂×Dic₁₃₄	C₂²×C₄	1	1	yes	characteristic
320	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
321	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
322	C₂×D₂₆₈	C₂²×C₄	1	1	yes	characteristic
323	C₂×C₂²⋊D₆₇	C₂²×C₄	1	2	yes	—
324	C₂×C₂²⋊D₆₇	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₆₇	C₂²×C₄	1	2	yes	—
326	C₂×C₂²⋊D₆₇	C₂²×C₄	1	2	yes	—
327	C₂×C₂²⋊D₆₇	C₂²×C₄	1	2	yes	—
328	C₂²×Dic₆₇	C₂²×C₄	1	2	yes	—
329	C₂²×Dic₆₇	C₂²×C₄	1	2	yes	—
330	C₂²×Dic₆₇	C₂²×C₄	1	2	yes	—
331	C₂²×Dic₆₇	C₂²×C₄	1	2	yes	—
332	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
333	C₂×C₄×D₆₇	C₂²×C₄	1	2	yes	—
334	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
335	#11761612	—	2	2	no	—
336	#11761612	—	2	2	no	—
337	#11761612	—	2	2	no	—
338	#11761612	—	2	4	no	—
339	#11761612	—	2	4	no	—
340	#11761612	#41	1	4	yes	complemented
341	#11761611	—	2	4	no	—
342	#11761611	—	2	4	no	—
343	C₂×C₆₇⋊C₈	—	2	4	no	—
344	C₂×C₆₇⋊C₈	—	2	4	no	—
345	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
346	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
347	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
348	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
349	C₈×D₆₇	—	2	4	no	—
350	C₈×D₆₇	—	2	4	no	—
351	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
352	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
353	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
354	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
355	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
356	C₄⋊Dic₆₇	C₂²×C₄	1	1	yes	characteristic
357	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
358	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
359	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
360	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
361	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
362	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
363	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
364	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
365	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
366	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
367	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
368	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
369	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
370	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
371	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
372	Dic₆₇⋊C₄	C₂²×C₄	1	2	yes	—
373	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
374	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
375	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
376	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
377	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
378	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
380	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
381	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
382	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
383	C₂²⋊Dic₆₇	C₂²×C₄	1	2	yes	—
384	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
385	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
386	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
387	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
388	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
389	(C₂×D₆₇)⋊C₄	C₂²×C₄	1	2	yes	—
390	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
391	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
392	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
393	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
394	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
395	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
396	C₄×Dic₆₇	C₂⁴	1	2	yes	—
397	C₄×Dic₆₇	C₂⁴	1	2	yes	—
398	C₄×Dic₆₇	C₂⁴	1	2	yes	—
399	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
400	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
401	C₂×D₄×C₆₇	—	4	2	no	—
402	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
403	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
404	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
405	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
406	C₂²×C₄×C₆₇	—	2	2	no	—
407	C₂²×C₄×C₆₇	—	2	2	no	—
408	C₂²×C₄×C₆₇	—	2	2	no	—
409	C₂²×C₄×C₆₇	—	2	2	no	—
410	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
411	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
412	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
413	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
414	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
415	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
416	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
418	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	M₁₆×C₆₇	—	2	2	no	—
424	M₁₆×C₆₇	—	2	2	no	—
425	M₁₆×C₆₇	—	2	2	no	—
426	M₁₆×C₆₇	—	2	2	no	—
427	C₂×C₈×C₆₇	—	2	2	no	—
428	C₂×C₈×C₆₇	—	2	2	no	—
429	C₂×C₈×C₆₇	—	2	2	no	—
430	C₂×C₈×C₆₇	—	2	2	no	—
431	C₂×C₈×C₆₇	—	2	2	no	—
432	C₂×C₈×C₆₇	—	2	2	no	—
433	C₂×C₈×C₆₇	—	2	2	no	—
434	C₂×C₈×C₆₇	#41	1	4	yes	complemented
435	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
437	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
444	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
445	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
446	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
447	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
448	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
449	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
450	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
451	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
452	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
453	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
454	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
455	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
456	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
457	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
458	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
459	C₂³×C₆₇	—	2	2	no	—
460	C₂³×C₆₇	—	2	2	no	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	4	1	no	—
463	C₂³×C₆₇	—	4	1	no	—
464	C₂³×C₆₇	—	4	1	no	—
465	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
466	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
467	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
468	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
469	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
470	C₂²×D₆₇	C₂³×C₄	1	2	yes	—
471	D₄×C₆₇	—	2	2	no	—
472	D₄×C₆₇	—	2	2	no	—
473	D₄×C₆₇	—	4	1	no	—
474	D₄×C₆₇	—	4	1	no	—
475	C₂×C₄×C₆₇	—	2	2	no	—
476	C₂×C₄×C₆₇	—	2	2	no	—
477	C₂×C₄×C₆₇	—	2	2	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	2	2	no	—
480	C₂×C₄×C₆₇	—	2	2	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	2	1	no	—
484	C₂×C₄×C₆₇	—	2	1	no	—
485	C₂×C₄×C₆₇	—	2	1	no	—
486	C₂×C₄×C₆₇	—	2	1	no	—
487	C₂×C₄×C₆₇	—	2	1	no	—
488	C₂×C₄×C₆₇	—	2	1	no	—
489	C₂×C₄×C₆₇	—	4	1	no	—
490	C₂×C₄×C₆₇	—	4	1	no	—
491	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
492	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
494	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
497	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
498	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
499	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
500	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
501	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
502	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
503	C₂²⋊D₆₇	—	2	4	no	—
504	C₂²⋊D₆₇	—	2	4	no	—
505	C₂²⋊D₆₇	—	4	2	no	—
506	C₂²⋊D₆₇	—	4	2	no	—
507	C₂²⋊D₆₇	—	4	2	no	—
508	C₂×Dic₆₇	—	2	4	no	—
509	C₂×Dic₆₇	—	4	2	no	—
510	C₂×Dic₆₇	—	4	2	no	—
511	C₂×Dic₆₇	—	4	2	no	—
512	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
513	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
514	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
515	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
516	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
517	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
518	C₂×Dic₆₇	C₂³×C₄	1	2	yes	—
519	D₂₆₈	—	2	2	no	—
520	C₄×D₆₇	—	2	2	no	—
521	C₄×D₆₇	—	2	2	no	—
522	C₄×D₆₇	—	4	2	no	—
523	C₄×D₆₇	—	4	2	no	—
524	Dic₁₃₄	—	2	2	no	—
525	Dic₁₃₄	—	4	2	no	—
526	Dic₁₃₄	—	4	2	no	—
527	C₈×C₆₇	—	2	1	no	—
528	C₈×C₆₇	—	2	1	no	—
529	C₈×C₆₇	—	2	1	no	—
530	C₈×C₆₇	—	2	1	no	—
531	C₈×C₆₇	—	2	1	no	—
532	C₈×C₆₇	—	2	1	no	—
533	C₈×C₆₇	C₂×#41	1	2	yes	—
534	C₈×C₆₇	C₂×#41	1	2	yes	—
535	C₆₇⋊C₈	—	2	2	no	—
536	C₆₇⋊C₈	—	2	2	no	—
537	C₆₇⋊C₈	—	2	2	no	—
538	C₆₇⋊C₈	C₂×#41	1	4	yes	—
539	C₂²×C₆₇	—	2	1	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	1	no	—
542	C₂²×C₆₇	—	2	1	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	1	no	—
545	C₂²×C₆₇	—	2	1	no	—
546	C₂²×C₆₇	—	2	1	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	1	no	—
552	C₂²×C₆₇	—	4	4	no	—
553	C₂²×C₆₇	—	8	2	no	—
554	C₂²×C₆₇	C₄×#41	1	2	yes	—
555	C₂²×C₆₇	#568	1	2	yes	—
556	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
557	C₂×D₆₇	—	2	2	no	—
558	C₂×D₆₇	—	2	2	no	—
559	C₂×D₆₇	—	2	2	no	—
560	C₄×C₆₇	—	2	1	no	—
561	C₄×C₆₇	—	2	1	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	1	no	—
564	C₄×C₆₇	—	2	1	no	—
565	C₄×C₆₇	—	2	1	no	—
566	C₄×C₆₇	—	2	1	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	C₄×#41	1	2	yes	—
569	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
570	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
571	Dic₆₇	—	2	2	no	—
572	Dic₆₇	—	2	2	no	—
573	Dic₆₇	—	2	2	no	—
574	Dic₆₇	—	2	2	no	—
575	Dic₆₇	—	2	2	no	—
576	Dic₆₇	—	2	2	no	—
577	Dic₆₇	—	2	2	no	—
578	#60216	—	67	1	no	maximal, Sylow
579	C₂×C₆₇	—	2	2	no	—
580	C₂×C₆₇	—	2	2	no	—
581	C₂×C₆₇	—	4	1	no	—
582	C₂×C₆₇	—	4	1	no	—
583	C₂×C₆₇	—	4	1	no	—
584	C₂×C₆₇	C₂×C₄×#41	1	1	yes	characteristic
585	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
586	C₂×C₆₇	#3573	1	1	yes	characteristic
587	D₆₇	—	4	2	no	—
588	#3475	—	67	1	no	—
589	#2970	—	67	2	no	—
590	#2969	—	67	2	no	—
591	#2968	—	67	2	no	—
592	#2968	—	67	2	no	—
593	#2967	—	67	2	no	—
594	#2967	—	67	2	no	—
595	#2966	—	67	2	no	—
596	#2965	—	67	2	no	—
597	#2962	—	67	1	no	—
598	#2961	—	67	1	no	—
599	D₄×M₁₆	—	67	1	no	—
600	#2933	—	67	1	no	—
601	#2933	—	67	1	no	—
602	#2930	—	67	1	no	—
603	#2929	—	67	1	no	—
604	C₂×#435	D₆₇	1	1	yes	characteristic, complemented
605	#2925	—	67	1	no	—
606	#2924	—	67	1	no	—
607	#2924	—	67	1	no	—
608	#2875	—	67	1	no	—
609	#2873	—	67	1	no	—
610	C₂×#405	—	67	1	no	—
611	C₆₇	#60216	1	1	yes	characteristic, complemented, Sylow
612	C₂×#131	—	67	1	no	—
613	C₂×#131	—	67	1	no	—
614	C₂²×M₁₆	—	67	1	no	—
615	C₂²×M₁₆	—	67	1	no	—
616	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
617	C₂³×C₈	C₂×D₆₇	1	1	yes	characteristic
618	#556	—	67	1	no	—
619	#555	—	67	1	no	—
620	#554	—	67	1	no	—
621	#553	—	67	1	no	—
622	#553	—	67	1	no	—
623	#552	—	67	1	no	—
624	#552	—	67	1	no	—
625	#552	—	67	2	no	—
626	#551	—	67	2	no	—
627	#551	—	67	2	no	—
628	#547	—	67	1	no	—
629	#546	—	67	2	no	—
630	#533	—	67	1	no	—
631	#529	—	67	2	no	—
632	#529	—	67	2	no	—
633	#529	—	67	2	no	—
634	#525	—	67	1	no	—
635	#525	—	67	1	no	—
636	C₄×#41	—	67	2	no	—
637	C₄×#41	—	67	1	no	—
638	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
639	C₂×#117	—	67	1	no	—
640	C₂×#117	—	67	1	no	—
641	#446	—	67	2	no	—
642	#446	—	67	2	no	—
643	#446	—	67	2	no	—
644	#446	—	67	2	no	—
645	#446	—	67	2	no	—
646	#446	—	67	2	no	—
647	#446	—	67	2	no	—
648	C₈×Q₈	—	67	2	no	—
649	#436	—	67	2	no	—
650	#436	—	67	2	no	—
651	#436	—	67	2	no	—
652	#436	—	67	2	no	—
653	#436	—	67	2	no	—
654	#435	—	67	2	no	—
655	#435	—	67	2	no	—
656	#435	—	67	2	no	—
657	#435	—	67	2	no	—
658	#435	—	67	2	no	—
659	#435	—	67	2	no	—
660	#435	—	67	2	no	—
661	#435	—	67	2	no	—
662	#435	—	67	2	no	—
663	#435	—	67	2	no	—
664	#435	C₂×D₆₇	1	1	yes	characteristic
665	#435	C₂×D₆₇	1	1	yes	characteristic
666	#435	C₂×D₆₇	1	1	yes	characteristic
667	#435	C₂×D₆₇	1	1	yes	characteristic
668	#435	C₂×D₆₇	1	1	yes	characteristic
669	#435	C₂×D₆₇	1	1	yes	characteristic
670	#435	C₂×D₆₇	1	1	yes	characteristic
671	#435	C₂×D₆₇	1	1	yes	characteristic
672	C₈×D₄	—	67	2	no	—
673	C₈×D₄	—	67	2	no	—
674	C₈×D₄	—	67	2	no	—
675	C₈×D₄	—	67	2	no	—
676	C₈×D₄	—	67	2	no	—
677	#433	—	67	2	no	—
678	#433	—	67	2	no	—
679	#433	—	67	2	no	—
680	#433	—	67	2	no	—
681	#433	—	67	2	no	—
682	#433	—	67	2	no	—
683	#432	—	67	2	no	—
684	#432	—	67	2	no	—
685	#432	—	67	2	no	—
686	#431	—	67	2	no	—
687	#431	—	67	2	no	—
688	#431	—	67	2	no	—
689	#424	—	67	1	no	—
690	#424	—	67	1	no	—
691	#424	—	67	1	no	—
692	#424	—	67	1	no	—
693	#423	—	67	1	no	—
694	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
695	#408	—	67	1	no	—
696	#408	—	67	1	no	—
697	#407	—	67	1	no	—
698	#407	—	67	1	no	—
699	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic
700	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic
701	#405	—	67	2	no	—
702	#405	—	67	2	no	—
703	#405	—	67	1	no	—
704	#405	—	67	1	no	—
705	#405	—	67	1	no	—
706	#405	—	67	1	no	—
707	#405	—	67	2	no	—
708	#405	—	67	2	no	—
709	#405	—	67	1	no	—
710	#405	—	67	1	no	—
711	#405	—	67	1	no	—
712	#405	—	67	1	no	—
713	#405	—	67	2	no	—
714	#405	—	67	2	no	—
715	C₄×M₁₆	—	67	2	no	—
716	C₄×M₁₆	—	67	2	no	—
717	C₄×M₁₆	—	67	1	no	—
718	C₄×M₁₆	—	67	2	no	—
719	C₂×#97	—	67	2	no	—
720	C₂×#97	—	67	2	no	—
721	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
722	C₂×C₄×C₈	—	67	2	no	—
723	C₂×#41	—	67	2	no	—
724	C₂×#41	—	67	1	no	—
725	C₂²×D₄	C₄×D₆₇	1	1	yes	characteristic
726	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
727	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
728	#131	—	134	4	no	—
729	#131	—	134	4	no	—
730	C₂×M₁₆	—	2	4	no	—
731	C₂×M₁₆	—	67	1	no	—
732	C₂×M₁₆	—	67	2	no	—
733	C₂×M₁₆	—	67	1	no	—
734	C₂×M₁₆	—	67	1	no	—
735	C₂×M₁₆	—	67	2	no	—
736	C₂×M₁₆	—	67	1	no	—
737	C₂×M₁₆	—	67	2	no	—
738	C₂×M₁₆	—	67	2	no	—
739	C₂×M₁₆	—	134	4	no	—
740	C₂×M₁₆	—	134	4	no	—
741	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
742	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
743	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
744	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
745	C₂²×C₈	—	2	4	no	—
746	C₂²×C₈	—	67	2	no	—
747	C₂²×C₈	—	67	2	no	—
748	C₂²×C₈	—	67	2	no	—
749	C₂²×C₈	—	67	2	no	—
750	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
751	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
752	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
753	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
754	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
755	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
756	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
757	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
758	C₄⋊Q₈	—	67	1	no	—
759	C₄⋊Q₈	—	67	1	no	—
760	#126	—	67	2	no	—
761	#126	—	67	2	no	—
762	#126	—	67	2	no	—
763	#126	—	67	2	no	—
764	#126	—	67	2	no	—
765	#126	—	67	2	no	—
766	#125	—	67	2	no	—
767	#125	—	67	2	no	—
768	#125	—	67	2	no	—
769	#125	—	67	1	no	—
770	#125	—	67	1	no	—
771	#124	—	67	2	no	—
772	#124	—	67	2	no	—
773	#124	—	67	2	no	—
774	#123	—	67	2	no	—
775	#123	—	67	2	no	—
776	#123	—	67	2	no	—
777	#123	—	67	2	no	—
778	#123	—	67	2	no	—
779	#123	—	67	2	no	—
780	#123	—	67	2	no	—
781	#123	—	67	2	no	—
782	C₂²⋊Q₈	—	67	1	no	—
783	C₂²⋊Q₈	—	67	1	no	—
784	C₂²⋊Q₈	—	67	1	no	—
785	C₂²⋊Q₈	—	67	1	no	—
786	C₂²⋊Q₈	—	67	2	no	—
787	C₂²⋊Q₈	—	67	2	no	—
788	C₂²⋊Q₈	—	67	2	no	—
789	C₂²⋊Q₈	—	67	2	no	—
790	C₂²⋊Q₈	—	67	2	no	—
791	#121	—	67	2	no	—
792	#121	—	67	2	no	—
793	#121	—	67	2	no	—
794	#121	—	67	1	no	—
795	#121	—	67	1	no	—
796	#121	—	67	1	no	—
797	#121	—	67	1	no	—
798	#120	—	67	2	no	—
799	#120	—	67	2	no	—
800	C₄×Q₈	—	67	2	no	—
801	C₄×Q₈	—	67	1	no	—
802	C₄×Q₈	—	67	1	no	—
803	C₄×Q₈	—	67	2	no	—
804	C₄×Q₈	—	67	2	no	—
805	C₄×D₄	—	67	2	no	—
806	C₄×D₄	—	67	2	no	—
807	C₄×D₄	—	67	2	no	—
808	C₄×D₄	—	67	2	no	—
809	C₄×D₄	—	67	2	no	—
810	C₄×D₄	—	67	2	no	—
811	C₄×D₄	—	67	2	no	—
812	C₄×D₄	—	67	2	no	—
813	C₄×D₄	—	67	2	no	—
814	C₄×D₄	—	67	1	no	—
815	C₄×D₄	—	67	1	no	—
816	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
817	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
818	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
819	C₄×D₄	C₄×D₆₇	1	1	yes	characteristic
820	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
821	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
822	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
823	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
824	#117	—	67	2	no	—
825	#117	—	67	2	no	—
826	#117	—	67	1	no	—
827	#117	—	67	1	no	—
828	#117	—	67	1	no	—
829	#117	—	67	1	no	—
830	#117	—	67	1	no	—
831	#117	—	67	1	no	—
832	#117	—	67	1	no	—
833	#117	—	67	2	no	—
834	#117	—	67	2	no	—
835	#117	—	67	2	no	—
836	#117	—	67	2	no	—
837	#117	—	67	2	no	—
838	#117	—	67	2	no	—
839	C₂×C₄⋊C₄	—	67	1	no	—
840	C₂×C₄⋊C₄	—	67	1	no	—
841	C₂×C₄⋊C₄	—	67	1	no	—
842	C₂×C₄⋊C₄	—	67	1	no	—
843	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	—	67	2	no	—
845	C₂×C₂²⋊C₄	—	67	2	no	—
846	C₂×C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	C₄×D₆₇	1	1	yes	characteristic
848	C₂×C₄²	—	67	2	no	—
849	C₂×C₄²	—	67	2	no	—
850	C₂×C₄²	—	67	2	no	—
851	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
852	C₄⋊C₈	—	67	2	no	—
853	C₄⋊C₈	—	67	2	no	—
854	C₄⋊C₈	—	67	2	no	—
855	C₄⋊C₈	—	67	2	no	—
856	C₄⋊C₈	—	67	2	no	—
857	C₄⋊C₈	—	67	2	no	—
858	C₄⋊C₈	—	67	2	no	—
859	C₄⋊C₈	—	67	2	no	—
860	C₄⋊C₈	—	67	2	no	—
861	C₄⋊C₈	—	67	2	no	—
862	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
863	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
864	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
865	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
866	C₂²⋊C₈	—	67	2	no	—
867	C₂²⋊C₈	—	67	2	no	—
868	C₂²⋊C₈	—	67	2	no	—
869	C₂²⋊C₈	—	67	2	no	—
870	C₂²⋊C₈	—	67	2	no	—
871	C₂²⋊C₈	—	67	2	no	—
872	C₂²⋊C₈	—	67	2	no	—
873	C₂²⋊C₈	—	67	2	no	—
874	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
875	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
876	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
877	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
878	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
879	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
880	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
881	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
882	#97	—	67	2	no	—
883	#97	—	67	2	no	—
884	#97	—	67	2	no	—
885	#97	—	67	2	no	—
886	#97	—	67	2	no	—
887	#97	—	67	2	no	—
888	#97	—	67	2	no	—
889	#97	—	67	2	no	—
890	#97	—	67	2	no	—
891	#97	C₂²×D₆₇	1	1	yes	characteristic
892	#97	C₂²×D₆₇	1	1	yes	characteristic
893	#97	C₂²×D₆₇	1	1	yes	characteristic
894	#97	C₂²×D₆₇	1	1	yes	characteristic
895	C₄×C₈	—	67	2	no	—
896	C₄×C₈	—	67	2	no	—
897	C₄×C₈	—	67	2	no	—
898	C₄×C₈	—	67	2	no	—
899	C₄×C₈	—	67	2	no	—
900	C₄×C₈	—	67	2	no	—
901	C₄×C₈	—	67	2	no	—
902	C₄×C₈	—	67	2	no	—
903	C₄×C₈	—	67	2	no	—
904	C₂⁴	C₂×C₄×D₆₇	1	1	yes	characteristic
905	C₂⁴	C₂×C₄×D₆₇	1	1	yes	characteristic
906	#41	—	268	4	no	—
907	#41	—	134	2	no	—
908	#41	—	134	2	no	—
909	C₂×Q₈	—	67	2	no	—
910	C₂×Q₈	—	67	2	no	—
911	C₂×Q₈	—	67	1	no	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	67	2	no	—
914	C₂×D₄	—	67	2	no	—
915	C₂×D₄	—	67	2	no	—
916	C₂×D₄	—	67	2	no	—
917	C₂×D₄	—	67	2	no	—
918	C₂×D₄	—	67	1	no	—
919	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
920	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
921	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
922	C₂×D₄	C₂×C₄×D₆₇	1	1	yes	characteristic
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	67	2	no	—
928	C₂²×C₄	—	67	2	no	—
929	C₂²×C₄	—	67	2	no	—
930	C₂²×C₄	—	67	2	no	—
931	C₂²×C₄	—	67	2	no	—
932	C₂²×C₄	—	67	2	no	—
933	C₂²×C₄	—	67	2	no	—
934	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
935	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
936	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
937	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
938	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
939	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
940	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
941	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
943	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
944	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
945	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
946	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	2	no	—
951	M₁₆	—	67	4	no	—
952	M₁₆	—	134	4	no	—
953	M₁₆	—	134	4	no	—
954	M₁₆	—	134	4	no	—
955	M₁₆	—	134	2	no	—
956	M₁₆	—	134	2	no	—
957	M₁₆	—	134	2	no	—
958	M₁₆	—	134	4	no	—
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	—	2	2	no	—
962	C₂×C₈	—	2	2	no	—
963	C₂×C₈	—	2	2	no	—
964	C₂×C₈	—	2	2	no	—
965	C₂×C₈	—	2	2	no	—
966	C₂×C₈	—	67	2	no	—
967	C₂×C₈	—	67	2	no	—
968	C₂×C₈	—	67	2	no	—
969	C₂×C₈	—	67	2	no	—
970	C₂×C₈	—	134	4	no	—
971	C₂×C₈	—	134	4	no	—
972	C₂×C₈	—	134	4	no	—
973	C₂×C₈	—	134	4	no	—
974	C₂×C₈	#11761627	1	4	yes	complemented
975	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
976	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
977	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
978	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
979	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
980	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
981	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
982	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
983	C₄⋊C₄	—	67	1	no	—
984	C₄⋊C₄	—	67	1	no	—
985	C₄⋊C₄	—	67	1	no	—
986	C₄⋊C₄	—	67	1	no	—
987	C₄⋊C₄	—	67	1	no	—
988	C₄⋊C₄	—	67	1	no	—
989	C₄⋊C₄	—	67	2	no	—
990	C₄⋊C₄	—	67	2	no	—
991	C₄⋊C₄	—	67	2	no	—
992	C₄⋊C₄	—	67	2	no	—
993	C₄⋊C₄	—	67	2	no	—
994	C₄⋊C₄	—	67	2	no	—
995	C₄⋊C₄	—	67	2	no	—
996	C₄⋊C₄	—	67	2	no	—
997	C₄⋊C₄	—	67	2	no	—
998	C₄⋊C₄	—	67	2	no	—
999	C₄⋊C₄	—	67	2	no	—
1000	C₄⋊C₄	—	67	2	no	—
1001	C₄⋊C₄	—	67	2	no	—
1002	C₄⋊C₄	—	67	2	no	—
1003	C₄⋊C₄	—	67	2	no	—
1004	C₄⋊C₄	—	67	2	no	—
1005	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1006	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1008	C₄⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1009	C₂²⋊C₄	—	67	2	no	—
1010	C₂²⋊C₄	—	67	2	no	—
1011	C₂²⋊C₄	—	67	2	no	—
1012	C₂²⋊C₄	—	67	2	no	—
1013	C₂²⋊C₄	—	67	2	no	—
1014	C₂²⋊C₄	—	67	2	no	—
1015	C₂²⋊C₄	—	67	2	no	—
1016	C₂²⋊C₄	—	67	2	no	—
1017	C₂²⋊C₄	—	67	2	no	—
1018	C₂²⋊C₄	—	67	2	no	—
1019	C₂²⋊C₄	—	67	2	no	—
1020	C₂²⋊C₄	—	67	2	no	—
1021	C₂²⋊C₄	—	67	2	no	—
1022	C₂²⋊C₄	—	67	2	no	—
1023	C₂²⋊C₄	—	67	2	no	—
1024	C₂²⋊C₄	—	67	2	no	—
1025	C₂²⋊C₄	—	67	2	no	—
1026	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1027	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1028	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1029	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1030	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1031	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1032	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1033	C₂²⋊C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
1034	C₄²	—	67	2	no	—
1035	C₄²	—	67	2	no	—
1036	C₄²	—	67	2	no	—
1037	C₄²	—	67	2	no	—
1038	C₄²	—	67	2	no	—
1039	C₄²	—	67	2	no	—
1040	C₄²	—	67	2	no	—
1041	C₄²	—	67	2	no	—
1042	C₄²	—	67	2	no	—
1043	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
1044	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
1045	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1046	C₄²	C₂³×D₆₇	1	1	yes	characteristic
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	—	67	2	no	—
1054	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1055	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1056	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1057	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1058	C₂³	C₂²×C₄×D₆₇	1	1	yes	characteristic
1059	Q₈	—	268	2	no	—
1060	Q₈	—	268	2	no	—
1061	Q₈	—	134	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	4	1	no	—
1065	D₄	—	4	1	no	—
1066	D₄	—	268	2	no	—
1067	D₄	—	268	2	no	—
1068	D₄	—	268	2	no	—
1069	D₄	—	134	4	no	—
1070	D₄	—	134	4	no	—
1071	D₄	—	134	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	4	1	no	—
1087	C₂×C₄	—	4	1	no	—
1088	C₂×C₄	—	268	2	no	—
1089	C₂×C₄	—	268	2	no	—
1090	C₂×C₄	—	268	2	no	—
1091	C₂×C₄	—	268	2	no	—
1092	C₂×C₄	—	268	2	no	—
1093	C₂×C₄	—	67	2	no	—
1094	C₂×C₄	—	67	2	no	—
1095	C₂×C₄	—	67	2	no	—
1096	C₂×C₄	—	67	2	no	—
1097	C₂×C₄	—	67	2	no	—
1098	C₂×C₄	—	67	2	no	—
1099	C₂×C₄	—	67	2	no	—
1100	C₂×C₄	—	134	4	no	—
1101	C₂×C₄	—	134	2	no	—
1102	C₂×C₄	—	134	2	no	—
1103	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1104	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1106	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1107	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1108	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1109	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1110	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1111	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
1112	C₂×C₄	#41×D₆₇	1	2	yes	—
1113	C₂×C₄	C₂×#11761627	1	2	yes	—
1114	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	67	4	no	—
1122	C₈	—	134	2	no	—
1123	C₈	—	134	2	no	—
1124	C₈	—	134	2	no	—
1125	C₈	C₂×#11761627	1	2	yes	—
1126	C₈	C₂×#11761627	1	2	yes	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	1	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	4	4	no	—
1141	C₂²	—	8	2	no	—
1142	C₂²	—	134	2	no	—
1143	C₂²	—	134	2	no	—
1144	C₂²	—	134	2	no	—
1145	C₂²	C₄×#11761627	1	2	yes	—
1146	C₂²	#16864162	1	2	yes	—
1147	C₂²	C₂³×C₄×D₆₇	1	1	yes	characteristic
1148	C₄	—	2	1	no	—
1149	C₄	—	2	1	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	134	2	no	—
1157	C₄	—	134	2	no	—
1158	C₄	—	134	2	no	—
1159	C₄	—	134	2	no	—
1160	C₄	—	134	2	no	—
1161	C₄	—	134	2	no	—
1162	C₄	—	134	2	no	—
1163	C₄	C₄×#11761627	1	2	yes	—
1164	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1165	C₄	C₂²×#11761627	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	2	2	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	1	no	—
1171	C₂	—	268	2	no	—
1172	C₂	C₂×C₄×#11761627	1	1	yes	characteristic
1173	C₂	C₂×#16864162	1	1	yes	characteristic
1174	C₂	#22574920	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁴×C₄
Fitting	C₂×#435×C₆₇	C₂
prime radical	#22573767	C₂
cosocle	C₂×C₄×C₆₇	C₂⁵
hypercenter	C₂×#435	D₆₇
hypocenter	C₆₇	#60216
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. #22569219	C₂	semidirect
3. #22569206	C₂	semidirect
4. #22569204	C₂	semidirect
5. #22569200	C₂	semidirect
6. #22569191	C₂	semidirect
7. #22569188	C₂	semidirect
8. #22569179	C₂	semidirect
9. #22569169	C₂	semidirect
10. #22569152	C₂	semidirect
11. #22569149	C₂	semidirect
12. D₄×#11761612	C₂	semidirect
13. #22568930	C₂	semidirect
14. #22568930	C₂	semidirect
15. #22568912	C₂	semidirect
16. #22568903	C₂	semidirect
17. #22568874	C₂	semidirect
18. #22568863	C₂	semidirect
19. #22568863	C₂	semidirect
20. #22568634	C₂	semidirect
21. #22568627	C₂	semidirect
22. C₂×#16863351	C₂	semidirect
23. C₂×#435×C₆₇	C₂	semidirect
50. #16863525	C₂²	semidirect
51. #16863525	C₂²	semidirect
52. #16863524	C₂²	semidirect
53. #16863524	C₂²	semidirect
54. #16863524	C₂²	semidirect
55. #16863524	C₂²	semidirect
56. #16863523	C₂²	semidirect
57. #16863520	C₂²	semidirect
59. #16863472	C₂²	semidirect
60. #16863472	C₂²	semidirect
61. #16863471	C₂²	semidirect
62. #16863471	C₂²	semidirect
63. #16863470	C₂²	semidirect
64. #16863470	C₂²	semidirect
67. #16863467	C₂²	semidirect
68. #16863467	C₂²	semidirect
69. #16863465	C₂²	semidirect
70. #16863465	C₂²	semidirect
71. #16863464	C₂²	semidirect
72. #16863464	C₂²	semidirect
74. C₈×C₂²⋊D₆₇	C₂²	semidirect
75. C₈×C₂²⋊D₆₇	C₂²	semidirect
76. (C₂²⋊D₆₇)⋊C₈	C₂²	semidirect
77. (C₂²⋊D₆₇)⋊C₈	C₂²	semidirect
78. #16863456	C₂²	semidirect
79. #16863456	C₂²	semidirect
80. #16863454	C₂²	semidirect
81. #16863454	C₂²	semidirect
82. #16863454	C₂²	semidirect
83. #16863454	C₂²	semidirect
84. #16863452	C₂²	semidirect
85. #16863450	C₂²	semidirect
86. #16863450	C₂²	semidirect
87. #16863448	C₂²	semidirect
88. #16863446	C₂²	semidirect
89. #16863446	C₂²	semidirect
99. #16863354	C₂²	semidirect
100. #16863354	C₂²	semidirect
101. #16863353	C₂²	semidirect
102. #16863353	C₂²	semidirect
111. #16863351	C₂²	semidirect
112. #16863351	C₂²	semidirect
114. #16863348	C₂²	semidirect
115. M₁₆×Dic₆₇	C₂²	semidirect
116. M₁₆×Dic₆₇	C₂²	semidirect
117. C₂×#14523953	C₂²	semidirect
118. #97×D₆₇	C₂²	semidirect
119. C₂×C₈×Dic₆₇	C₂²	semidirect
340. #11761612	#41	semidirect
434. C₂×C₈×C₆₇	#41	semidirect
604. C₂×#435	D₆₇	semidirect
611. C₆₇	#60216	semidirect
974. C₂×C₈	#11761627	semidirect

Maximal subgroups

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

subgroup	index
#22573767	2
#22569219	2
#22569206	2
#22569204	2
#22569200	2
#22569191	2
#22569188	2
#22569179	2
#22569169	2
#22569152	2
#22569149	2
D₄×#11761612	2
#22568930	2
#22568912	2
#22568903	2
#22568874	2
#22568863	2
#22568634	2
#22568627	2
C₂×#16863351	2
C₂×#435×C₆₇	2
#60216	67