Subgroups — #31733431

Order 17152.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573961	C₂	1	1	yes	maximal, characteristic, complemented
2	#22573842	C₂	1	1	yes	maximal, characteristic
3	#22572438	C₂	1	2	yes	maximal, complemented
4	#22572423	C₂	1	2	yes	maximal, complemented
5	#22572288	C₂	1	2	yes	maximal, complemented
6	#22572248	C₂	1	2	yes	maximal, complemented
7	#22572233	C₂	1	2	yes	maximal, complemented
8	#22572228	C₂	1	2	yes	maximal, complemented
9	#22572042	C₂	1	2	yes	maximal, complemented
10	#22572031	C₂	1	2	yes	maximal, complemented
11	#22570567	C₂	1	1	yes	maximal, characteristic, complemented
12	#22570170	C₂	1	1	yes	maximal, characteristic, complemented
13	#22570043	C₂	1	1	yes	maximal, characteristic, complemented
14	#22569849	C₂	1	1	yes	maximal, characteristic, complemented
15	#22569841	C₂	1	1	yes	maximal, characteristic, complemented
16	#22569733	C₂	1	1	yes	maximal, characteristic, complemented
17	#22569489	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#16863549	C₂	1	1	yes	maximal, characteristic, complemented
19	#22569067	C₂	1	1	yes	maximal, characteristic, complemented
20	#22568930	C₂	1	1	yes	maximal, characteristic, complemented
21	#22568731	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16863400	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#3091	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14524089	C₂²	1	1	yes	characteristic
25	C₂³×D₂₆₈	C₂²	1	1	yes	characteristic
26	C₂×#14524073	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#11761617	C₂²	1	1	yes	characteristic
28	C₂²×#11761617	C₂²	1	1	yes	characteristic, complemented
29	C₂×#14524049	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#11761612	C₂²	1	1	yes	characteristic, complemented
31	#16864114	C₂²	1	2	yes	complemented
32	#16864101	C₂²	1	2	yes	complemented
33	#16864085	C₂²	1	2	yes	complemented
34	#16864081	C₂²	1	2	yes	complemented
35	#16864079	—	2	2	no	—
36	#16864072	—	2	2	no	—
37	#16864042	—	2	1	no	—
38	#16864042	—	2	1	no	—
39	#16864037	C₂²	1	2	yes	—
40	#16864037	C₂²	1	2	yes	—
41	D₄×D₂₆₈	—	2	1	no	—
42	D₄×D₂₆₈	—	2	1	no	—
43	#16864030	C₂²	1	2	yes	—
44	#16864030	C₂²	1	2	yes	—
45	#16864024	C₂²	1	1	yes	characteristic, complemented
46	#16864017	—	2	1	no	—
47	#16864008	—	2	1	no	—
48	#16863972	C₂²	1	1	yes	characteristic, complemented
49	#16863965	C₂²	1	1	yes	characteristic
50	#16863960	C₂²	1	1	yes	characteristic
51	#16863957	—	2	2	no	—
52	#16863953	—	2	1	no	—
53	#16863930	—	2	1	no	—
54	#16863907	C₂²	1	1	yes	characteristic
55	C₂×#14524022	C₂²	1	1	yes	characteristic, complemented
56	#120×D₆₇	—	2	2	no	—
57	#16863876	C₂²	1	1	yes	characteristic, complemented
58	#16863873	C₂²	1	1	yes	characteristic, complemented
59	#16863870	C₂²	1	1	yes	characteristic
60	#16863759	C₂²	1	2	yes	complemented
61	#16863757	C₂²	1	2	yes	complemented
62	#16863752	C₂²	1	2	yes	complemented
63	#16863741	C₂²	1	2	yes	complemented
64	#16863723	C₂²	1	2	yes	complemented
65	#16863722	C₂²	1	2	yes	complemented
66	#16863716	C₂²	1	2	yes	complemented
67	#16863711	C₂²	1	2	yes	complemented
68	#16863699	C₂²	1	2	yes	complemented
69	#16863695	C₂²	1	2	yes	complemented
70	#16863685	C₂²	1	2	yes	complemented
71	#16863675	C₂²	1	2	yes	complemented
72	#16863652	C₂²	1	2	yes	complemented
73	#16863643	C₂²	1	2	yes	complemented
74	#16863643	C₂²	1	2	yes	complemented
75	#16863640	C₂²	1	2	yes	complemented
76	#16863635	C₂²	1	2	yes	complemented
77	#16863626	C₂²	1	2	yes	complemented
78	#16863626	C₂²	1	2	yes	complemented
79	#16863623	C₂²	1	2	yes	complemented
80	#16863621	C₂²	1	2	yes	complemented
81	#16863621	C₂²	1	2	yes	complemented
82	#16863595	C₂²	1	2	yes	complemented
83	#16863595	C₂²	1	2	yes	complemented
84	#16863561	C₂²	1	2	yes	complemented
85	#16863561	C₂²	1	2	yes	complemented
86	#16863549	C₂²	1	2	yes	complemented
87	#16863549	C₂²	1	2	yes	complemented
88	#16863549	C₂²	1	2	yes	complemented
89	#16863549	C₂²	1	2	yes	complemented
90	#16863548	C₂²	1	2	yes	complemented
91	#16863548	C₂²	1	2	yes	complemented
92	#16863495	C₂²	1	2	yes	complemented
93	#16863495	C₂²	1	2	yes	complemented
94	#16863483	C₂²	1	2	yes	complemented
95	#16863483	C₂²	1	2	yes	complemented
96	#16863471	C₂²	1	2	yes	complemented
97	#16863470	C₂²	1	2	yes	complemented
98	#16863464	C₂²	1	2	yes	complemented
99	(C₂²⋊D₆₇)⋊C₈	C₂²	1	2	yes	complemented
100	#16863439	C₂²	1	1	yes	characteristic, complemented
101	#16863422	C₂²	1	1	yes	characteristic, complemented
102	#16863404	C₂²	1	1	yes	characteristic, complemented
103	#16863400	C₂²	1	1	yes	characteristic
104	#16863400	C₂²	1	1	yes	characteristic
105	#16863400	C₂²	1	1	yes	characteristic, complemented
106	#16863400	C₂²	1	1	yes	characteristic, complemented
107	#16863400	C₂²	1	2	yes	complemented
108	#16863400	C₂²	1	2	yes	complemented
109	#16863399	C₂²	1	2	yes	complemented
110	#16863397	C₂²	1	1	yes	characteristic, complemented
111	#16863396	C₂²	1	2	yes	complemented
112	#16863391	C₂²	1	2	yes	complemented
113	C₂×#14523965	C₂²	1	1	yes	characteristic
114	C₂×#14523965	C₂²	1	1	yes	characteristic, complemented
115	C₂×#14523963	C₂²	1	2	yes	complemented
116	C₂×#14523963	C₂²	1	2	yes	complemented
117	#102×D₆₇	C₂²	1	2	yes	complemented
118	#16863362	C₂²	1	1	yes	characteristic, complemented
119	#16863351	C₂²	1	1	yes	characteristic, complemented
120	#525×C₆₇	C₂²	1	1	yes	characteristic
121	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#485×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#484×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#483×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	#481×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	#480×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
131	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂⁴×D₆₇	—	2	1	no	—
136	#14524089	—	2	4	no	—
137	#14524089	—	4	2	no	—
138	C₂×#11761629	C₂³	1	2	yes	—
139	C₂×#11761628	—	2	1	no	—
140	C₂×#11761628	C₂³	1	1	yes	characteristic
141	C₂²×Dic₁₃₄	C₂³	1	1	yes	characteristic
142	C₂²×D₂₆₈	—	2	4	no	—
143	C₂²×D₂₆₈	—	2	1	no	—
144	C₂²×D₂₆₈	—	2	1	no	—
145	C₂²×D₂₆₈	—	2	1	no	—
146	C₂²×D₂₆₈	—	2	1	no	—
147	C₂²×D₂₆₈	—	4	2	no	—
148	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
149	C₂²×D₂₆₈	C₂³	1	2	yes	—
150	C₂²×D₂₆₈	C₂³	1	2	yes	—
151	C₂²×D₂₆₈	C₂³	1	1	yes	characteristic
152	C₂×D₄×D₆₇	—	2	2	no	—
153	C₂×D₄×D₆₇	—	2	2	no	—
154	C₂×D₄×D₆₇	—	2	2	no	—
155	C₂×D₄×D₆₇	C₂³	1	2	yes	—
156	#14524073	—	4	2	no	—
157	C₂×#11761618	C₂³	1	2	yes	complemented
158	C₂×#11761617	—	2	4	no	—
159	C₂×#11761617	—	4	2	no	—
160	C₂×#11761617	C₂³	1	2	yes	—
161	C₂×#11761617	C₂³	1	2	yes	—
162	C₂×#11761617	C₂³	1	2	yes	—
163	C₂×#11761617	C₂³	1	2	yes	—
164	C₂×#11761616	C₂³	1	2	yes	complemented
165	#14524049	—	4	2	no	—
166	C₂×#11761612	—	4	2	no	—
167	C₂×#11761612	C₂³	1	1	yes	characteristic
168	C₂×#11761612	C₂³	1	1	yes	characteristic
169	C₂×#11761612	C₂³	1	2	yes	—
170	C₂×#11761611	C₂³	1	2	yes	complemented
171	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
172	C₂×C₈×D₆₇	C₂³	1	2	yes	complemented
173	#14524043	—	2	1	no	—
174	#14524043	—	2	1	no	—
175	#14524042	C₂³	1	2	yes	complemented
176	#14524040	—	2	1	no	—
177	#14524039	C₂³	1	2	yes	—
178	#14524038	—	2	2	no	—
179	#14524037	—	2	2	no	—
180	#14524036	—	2	2	no	—
181	#14524036	—	2	2	no	—
182	#14524035	—	2	1	no	—
183	#14524035	—	2	2	no	—
184	#14524034	C₂³	1	2	yes	complemented
185	#14524033	—	2	2	no	—
186	#14524033	—	2	2	no	—
187	#14524032	C₂³	1	2	yes	—
188	#14524031	—	2	1	no	—
189	#14524031	—	2	1	no	—
190	#14524029	—	2	2	no	—
191	#14524028	—	2	2	no	—
192	#14524028	—	2	2	no	—
193	#14524027	—	2	2	no	—
194	#14524026	—	2	2	no	—
195	#14524026	D₄	1	2	yes	—
196	#14524025	—	2	2	no	—
197	#14524023	C₂³	1	2	yes	complemented
198	#14524023	C₂³	1	2	yes	complemented
199	#14524022	—	2	2	no	—
200	#14524022	—	2	1	no	—
201	#14524022	—	2	1	no	—
202	#14524022	D₄	1	1	yes	characteristic
203	#14524022	D₄	1	1	yes	characteristic
204	#14524022	C₂³	1	2	yes	—
205	#14524022	C₂³	1	2	yes	—
206	#14524021	—	2	2	no	—
207	#14524020	—	2	2	no	—
208	#14524018	—	2	2	no	—
209	#14524018	—	2	2	no	—
210	#14524018	C₂³	1	2	yes	—
211	#14524018	C₂³	1	2	yes	—
212	#14524017	—	2	1	no	—
213	#14524017	—	2	1	no	—
214	#14524017	D₄	1	1	yes	characteristic
215	#14524017	D₄	1	1	yes	characteristic
216	#14524016	—	2	2	no	—
217	#14524016	—	2	2	no	—
218	#14524013	—	2	2	no	—
219	#14524013	—	2	2	no	—
220	#14524013	—	2	2	no	—
221	#14524013	—	2	2	no	—
222	#14524013	—	2	2	no	—
223	#14524012	D₄	1	2	yes	—
224	#14524011	—	2	2	no	—
225	#14524011	—	2	2	no	—
226	#14524011	—	2	2	no	—
227	C₄×Dic₁₃₄	—	2	1	no	—
228	C₄×Dic₁₃₄	—	2	1	no	—
229	C₄×Dic₁₃₄	—	2	1	no	—
230	C₄×Dic₁₃₄	—	2	2	no	—
231	#14524008	C₂³	1	2	yes	complemented
232	#14524008	C₂³	1	2	yes	complemented
233	C₄×D₂₆₈	—	2	1	no	—
234	C₄×D₂₆₈	—	2	1	no	—
235	C₄×D₂₆₈	—	2	1	no	—
236	#14524005	C₂³	1	2	yes	—
237	#14524005	C₂³	1	2	yes	—
238	C₄×C₂²⋊D₆₇	—	2	2	no	—
239	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
240	C₄×C₂²⋊D₆₇	C₂³	1	2	yes	—
241	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
242	#14524002	—	2	2	no	—
243	#14524002	C₂³	1	1	yes	characteristic
244	#14524001	C₂³	1	2	yes	complemented
245	#14524000	—	2	2	no	—
246	#14523999	—	2	2	no	—
247	C₂×C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
248	C₂×Dic₆₇⋊C₄	—	2	1	no	—
249	C₄⋊C₄×D₆₇	C₂³	1	2	yes	complemented
250	C₂×C₂²⋊Dic₆₇	—	2	1	no	—
251	C₂²⋊C₄×D₆₇	—	2	2	no	—
252	C₂²⋊C₄×D₆₇	—	2	2	no	—
253	C₂²⋊C₄×D₆₇	—	2	2	no	—
254	#14523976	C₂³	1	2	yes	complemented
255	#14523974	C₂³	1	2	yes	complemented
256	Dic₆₇⋊C₈	C₂³	1	2	yes	complemented
257	Dic₆₇⋊C₈	C₂³	1	2	yes	complemented
258	#14523967	C₂³	1	2	yes	complemented
259	#14523966	C₂³	1	2	yes	complemented
260	#14523966	C₂³	1	2	yes	complemented
261	#14523965	C₂³	1	2	yes	—
262	#14523965	C₂³	1	2	yes	—
263	#14523965	C₂³	1	2	yes	—
264	#14523965	C₂³	1	2	yes	—
265	#14523964	C₂³	1	2	yes	complemented
266	#14523963	C₂³	1	2	yes	—
267	#14523963	C₂³	1	2	yes	—
268	#14523963	C₂³	1	2	yes	—
269	#14523963	C₂³	1	2	yes	—
270	#14523963	C₂³	1	2	yes	—
271	#14523963	C₂³	1	2	yes	—
272	#14523963	C₂³	1	2	yes	—
273	#14523963	C₂³	1	2	yes	—
274	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	complemented
275	(C₂×D₆₇)⋊C₈	C₂³	1	2	yes	complemented
276	#14523953	C₂³	1	2	yes	complemented
277	C₈×Dic₆₇	C₂³	1	2	yes	complemented
278	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
279	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
280	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
282	#123×C₆₇	—	2	1	no	—
283	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
285	#121×C₆₇	C₂³	1	1	yes	characteristic
286	#121×C₆₇	C₂³	1	1	yes	characteristic
287	#120×C₆₇	—	2	1	no	—
288	C₄×D₄×C₆₇	—	2	1	no	—
289	C₄×D₄×C₆₇	—	2	1	no	—
290	#117×C₆₇	—	2	1	no	—
291	#117×C₆₇	—	2	1	no	—
292	#117×C₆₇	C₂³	1	1	yes	characteristic
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	#117×C₆₇	C₂³	1	1	yes	characteristic
296	#117×C₆₇	C₂³	1	1	yes	characteristic
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	#107×C₆₇	C₂³	1	1	yes	characteristic, complemented
302	#107×C₆₇	C₂³	1	1	yes	characteristic, complemented
303	#107×C₆₇	C₂³	1	1	yes	characteristic, complemented
304	#107×C₆₇	C₂³	1	1	yes	characteristic, complemented
305	#106×C₆₇	C₂³	1	1	yes	characteristic, complemented
306	#106×C₆₇	C₂³	1	1	yes	characteristic, complemented
307	#106×C₆₇	C₂³	1	1	yes	characteristic, complemented
308	#106×C₆₇	C₂³	1	1	yes	characteristic, complemented
309	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
310	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
311	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
312	#103×C₆₇	C₂³	1	1	yes	characteristic, complemented
313	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
314	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
315	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
316	#102×C₆₇	C₂³	1	1	yes	characteristic, complemented
317	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
319	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
320	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
321	C₂³×D₆₇	—	2	1	no	—
322	C₂³×D₆₇	—	2	2	no	—
323	C₂³×D₆₇	—	2	2	no	—
324	C₂³×D₆₇	—	2	1	no	—
325	C₂³×D₆₇	—	2	2	no	—
326	C₂³×D₆₇	—	4	4	no	—
327	C₂³×D₆₇	—	8	2	no	—
328	C₂³×D₆₇	—	8	2	no	—
329	#11761629	—	2	4	no	—
330	#11761629	—	4	2	no	—
331	#11761628	—	2	2	no	—
332	#11761628	—	2	2	no	—
333	#11761628	—	4	4	no	—
334	C₂×Dic₁₃₄	—	2	2	no	—
335	C₂×Dic₁₃₄	—	2	2	no	—
336	C₂×Dic₁₃₄	—	2	1	no	—
337	C₂×Dic₁₃₄	—	2	2	no	—
338	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
339	C₂×Dic₁₃₄	C₂⁴	1	2	yes	—
340	C₂×D₂₆₈	—	2	1	no	—
341	C₂×D₂₆₈	—	2	2	no	—
342	C₂×D₂₆₈	—	2	2	no	—
343	C₂×D₂₆₈	—	2	2	no	—
344	C₂×D₂₆₈	—	2	4	no	—
345	C₂×D₂₆₈	—	2	4	no	—
346	C₂×D₂₆₈	—	2	2	no	—
347	C₂×D₂₆₈	—	2	2	no	—
348	C₂×D₂₆₈	—	2	2	no	—
349	C₂×D₂₆₈	—	2	1	no	—
350	C₂×D₂₆₈	—	2	2	no	—
351	C₂×D₂₆₈	—	2	2	no	—
352	C₂×D₂₆₈	—	4	2	no	—
353	C₂×D₂₆₈	—	4	2	no	—
354	C₂×D₂₆₈	—	4	4	no	—
355	C₂×D₂₆₈	—	4	4	no	—
356	C₂×D₂₆₈	—	4	4	no	—
357	C₂×D₂₆₈	—	4	4	no	—
358	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
359	C₂×D₂₆₈	#41	1	4	yes	—
360	C₂×D₂₆₈	C₂⁴	1	2	yes	—
361	C₂×D₂₆₈	C₂⁴	1	2	yes	—
362	C₂×C₂²⋊D₆₇	—	2	2	no	—
363	C₂×C₂²⋊D₆₇	—	2	2	no	—
364	C₂×C₂²⋊D₆₇	—	2	2	no	—
365	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
366	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
367	C₂×C₂²⋊D₆₇	C₂×D₄	1	2	yes	—
368	D₄×D₆₇	—	2	4	no	—
369	D₄×D₆₇	—	4	2	no	—
370	D₄×D₆₇	—	4	8	no	—
371	D₄×D₆₇	—	8	4	no	—
372	D₄×D₆₇	—	8	4	no	—
373	C₂²×Dic₆₇	—	2	1	no	—
374	C₂²×Dic₆₇	—	2	1	no	—
375	C₂×C₄×D₆₇	—	2	2	no	—
376	C₂×C₄×D₆₇	—	2	2	no	—
377	C₂×C₄×D₆₇	—	2	2	no	—
378	C₂×C₄×D₆₇	—	2	2	no	—
379	C₂×C₄×D₆₇	C₂⁴	1	2	yes	—
380	#11761618	—	4	2	no	—
381	#11761617	—	2	4	no	—
382	#11761617	—	2	4	no	—
383	#11761617	—	4	2	no	—
384	#11761617	—	4	2	no	—
385	#11761616	—	4	2	no	—
386	#11761612	—	2	2	no	—
387	#11761612	—	2	2	no	—
388	#11761612	—	4	2	no	—
389	#11761611	—	4	2	no	—
390	C₂×C₆₇⋊C₈	—	4	2	no	—
391	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
392	C₂×C₆₇⋊C₈	C₂⁴	1	2	yes	—
393	C₈×D₆₇	—	4	2	no	—
394	C₄⋊Dic₆₇	—	2	1	no	—
395	C₄⋊Dic₆₇	—	2	2	no	—
396	C₄⋊Dic₆₇	—	2	2	no	—
397	C₄⋊Dic₆₇	—	2	2	no	—
398	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
399	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
400	C₄⋊Dic₆₇	C₂⁴	1	2	yes	—
401	Dic₆₇⋊C₄	—	2	2	no	—
402	Dic₆₇⋊C₄	—	2	2	no	—
403	Dic₆₇⋊C₄	—	2	2	no	—
404	Dic₆₇⋊C₄	—	2	2	no	—
405	Dic₆₇⋊C₄	—	2	2	no	—
406	Dic₆₇⋊C₄	—	2	2	no	—
407	Dic₆₇⋊C₄	—	2	2	no	—
408	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
409	Dic₆₇⋊C₄	C₂×D₄	1	2	yes	—
410	C₂²⋊Dic₆₇	—	2	2	no	—
411	C₂²⋊Dic₆₇	—	2	2	no	—
412	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
413	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
414	C₂²⋊Dic₆₇	C₂×D₄	1	2	yes	—
415	(C₂×D₆₇)⋊C₄	—	2	2	no	—
416	(C₂×D₆₇)⋊C₄	—	2	2	no	—
417	(C₂×D₆₇)⋊C₄	—	2	2	no	—
418	(C₂×D₆₇)⋊C₄	—	2	2	no	—
419	(C₂×D₆₇)⋊C₄	—	2	2	no	—
420	(C₂×D₆₇)⋊C₄	—	2	2	no	—
421	(C₂×D₆₇)⋊C₄	—	2	2	no	—
422	(C₂×D₆₇)⋊C₄	—	2	2	no	—
423	(C₂×D₆₇)⋊C₄	—	2	2	no	—
424	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
425	(C₂×D₆₇)⋊C₄	C₂×D₄	1	2	yes	—
426	C₄×Dic₆₇	—	2	2	no	—
427	C₄×Dic₆₇	—	2	2	no	—
428	C₄×Dic₆₇	—	2	2	no	—
429	C₄×Dic₆₇	C₂⁴	1	2	yes	—
430	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
431	#41×C₆₇	—	2	2	no	—
432	#41×C₆₇	—	2	2	no	—
433	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₂×D₄×C₆₇	—	2	1	no	—
435	C₂×D₄×C₆₇	—	2	1	no	—
436	C₂×D₄×C₆₇	—	2	1	no	—
437	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₆₇	—	2	2	no	—
439	C₂²×C₄×C₆₇	—	2	2	no	—
440	C₂²×C₄×C₆₇	—	2	1	no	—
441	C₂²×C₄×C₆₇	—	2	1	no	—
442	C₂²×C₄×C₆₇	—	2	1	no	—
443	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
444	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
445	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
446	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₂×C₈×C₆₇	—	2	2	no	—
450	C₂×C₈×C₆₇	—	2	2	no	—
451	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₆₇	—	2	1	no	—
456	C₄⋊C₄×C₆₇	—	2	1	no	—
457	C₄⋊C₄×C₆₇	—	2	1	no	—
458	C₄⋊C₄×C₆₇	—	2	1	no	—
459	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
460	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
461	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
462	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
465	C₂²⋊C₄×C₆₇	—	2	1	no	—
466	C₂²⋊C₄×C₆₇	—	2	1	no	—
467	C₂²⋊C₄×C₆₇	—	2	1	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	—	2	1	no	—
472	C₂²⋊C₄×C₆₇	—	2	1	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₄²×C₆₇	—	2	1	no	—
475	C₄²×C₆₇	—	2	1	no	—
476	C₄²×C₆₇	—	2	1	no	—
477	C₄²×C₆₇	—	2	1	no	—
478	C₄²×C₆₇	—	2	1	no	—
479	C₂³×C₆₇	—	2	2	no	—
480	C₂³×C₆₇	—	2	2	no	—
481	C₂³×C₆₇	—	2	1	no	—
482	C₂³×C₆₇	—	4	1	no	—
483	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
484	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
485	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
486	C₂²×D₆₇	—	2	2	no	—
487	C₂²×D₆₇	—	2	4	no	—
488	C₂²×D₆₇	—	2	2	no	—
489	C₂²×D₆₇	—	4	4	no	—
490	C₂²×D₆₇	—	4	4	no	—
491	C₂²×D₆₇	—	4	4	no	—
492	C₂²×D₆₇	—	4	4	no	—
493	C₂²×D₆₇	—	4	2	no	—
494	C₂²×D₆₇	—	4	4	no	—
495	C₂²×D₆₇	—	8	2	no	—
496	C₂²×D₆₇	—	8	2	no	—
497	C₂²×D₆₇	—	8	1	no	—
498	C₂²×D₆₇	—	8	2	no	—
499	C₂²×D₆₇	—	8	1	no	—
500	C₂²×D₆₇	—	8	2	no	—
501	C₂²×D₆₇	—	8	1	no	—
502	C₂²×D₆₇	—	8	1	no	—
503	C₂²×D₆₇	—	8	16	no	—
504	C₂²×D₆₇	C₂²×D₄	1	2	yes	—
505	Q₈×C₆₇	—	2	1	no	—
506	Q₈×C₆₇	—	2	1	no	—
507	D₄×C₆₇	—	2	1	no	—
508	D₄×C₆₇	—	2	1	no	—
509	D₄×C₆₇	—	4	2	no	—
510	D₄×C₆₇	—	4	2	no	—
511	D₄×C₆₇	—	4	2	no	—
512	C₂×C₄×C₆₇	—	2	2	no	—
513	C₂×C₄×C₆₇	—	2	2	no	—
514	C₂×C₄×C₆₇	—	2	2	no	—
515	C₂×C₄×C₆₇	—	2	1	no	—
516	C₂×C₄×C₆₇	—	2	1	no	—
517	C₂×C₄×C₆₇	—	2	1	no	—
518	C₂×C₄×C₆₇	—	2	1	no	—
519	C₂×C₄×C₆₇	—	2	1	no	—
520	C₂×C₄×C₆₇	—	2	1	no	—
521	C₂×C₄×C₆₇	—	2	1	no	—
522	C₂×C₄×C₆₇	—	2	1	no	—
523	C₂×C₄×C₆₇	—	2	1	no	—
524	C₂×C₄×C₆₇	—	2	1	no	—
525	C₂×C₄×C₆₇	—	2	1	no	—
526	C₂×C₄×C₆₇	—	4	2	no	—
527	C₂×C₄×C₆₇	—	4	2	no	—
528	C₂×C₄×C₆₇	—	8	1	no	—
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
533	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
534	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
535	C₂²⋊D₆₇	—	2	4	no	—
536	C₂²⋊D₆₇	—	2	4	no	—
537	C₂²⋊D₆₇	—	4	2	no	—
538	C₂²⋊D₆₇	—	4	4	no	—
539	C₂²⋊D₆₇	—	8	2	no	—
540	C₂²⋊D₆₇	—	8	2	no	—
541	C₂×Dic₆₇	—	2	2	no	—
542	C₂×Dic₆₇	—	2	2	no	—
543	C₂×Dic₆₇	—	4	2	no	—
544	C₂×Dic₆₇	—	8	1	no	—
545	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
546	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
547	C₂×Dic₆₇	C₂²×D₄	1	2	yes	—
548	D₂₆₈	—	2	4	no	—
549	D₂₆₈	—	2	2	no	—
550	D₂₆₈	—	2	2	no	—
551	D₂₆₈	—	2	2	no	—
552	D₂₆₈	—	2	2	no	—
553	D₂₆₈	—	4	4	no	—
554	D₂₆₈	—	4	4	no	—
555	D₂₆₈	—	4	4	no	—
556	D₂₆₈	—	4	2	no	—
557	D₂₆₈	—	8	2	no	—
558	D₂₆₈	—	8	2	no	—
559	D₂₆₈	C₂×#41	1	4	yes	—
560	C₄×D₆₇	—	2	2	no	—
561	C₄×D₆₇	—	2	2	no	—
562	C₄×D₆₇	—	4	4	no	—
563	C₄×D₆₇	—	8	2	no	—
564	C₄×D₆₇	—	8	2	no	—
565	C₄×D₆₇	—	8	2	no	—
566	Dic₁₃₄	—	2	2	no	—
567	Dic₁₃₄	—	2	2	no	—
568	Dic₁₃₄	—	2	2	no	—
569	Dic₁₃₄	—	4	2	no	—
570	Dic₁₃₄	—	8	2	no	—
571	C₈×C₆₇	—	2	1	no	—
572	C₈×C₆₇	—	2	1	no	—
573	C₈×C₆₇	—	2	1	no	—
574	C₈×C₆₇	—	2	1	no	—
575	C₆₇⋊C₈	—	2	2	no	—
576	C₆₇⋊C₈	—	2	2	no	—
577	C₂²×C₆₇	—	2	1	no	—
578	C₂²×C₆₇	—	2	1	no	—
579	C₂²×C₆₇	—	2	1	no	—
580	C₂²×C₆₇	—	2	1	no	—
581	C₂²×C₆₇	—	2	1	no	—
582	C₂²×C₆₇	—	2	1	no	—
583	C₂²×C₆₇	—	2	1	no	—
584	C₂²×C₆₇	—	4	4	no	—
585	C₂²×C₆₇	—	4	1	no	—
586	C₂²×C₆₇	—	4	1	no	—
587	C₂²×C₆₇	—	4	1	no	—
588	C₂²×C₆₇	#546	1	2	yes	—
589	C₂²×C₆₇	#577	1	2	yes	—
590	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
591	C₂×D₆₇	—	2	2	no	—
592	C₂×D₆₇	—	2	2	no	—
593	C₂×D₆₇	—	2	4	no	—
594	C₂×D₆₇	—	2	2	no	—
595	C₂×D₆₇	—	4	2	no	—
596	C₂×D₆₇	—	4	2	no	—
597	C₂×D₆₇	—	4	2	no	—
598	C₂×D₆₇	—	4	2	no	—
599	C₂×D₆₇	—	4	2	no	—
600	C₂×D₆₇	—	8	4	no	—
601	C₂×D₆₇	—	8	8	no	—
602	C₂×D₆₇	—	8	8	no	—
603	C₂×D₆₇	—	8	4	no	—
604	C₂×D₆₇	—	16	4	no	—
605	C₄×C₆₇	—	2	1	no	—
606	C₄×C₆₇	—	2	1	no	—
607	C₄×C₆₇	—	4	1	no	—
608	C₄×C₆₇	—	4	1	no	—
609	C₄×C₆₇	—	4	1	no	—
610	C₄×C₆₇	—	4	1	no	—
611	C₄×C₆₇	—	4	1	no	—
612	C₄×C₆₇	—	4	1	no	—
613	C₄×C₆₇	—	4	1	no	—
614	C₄×C₆₇	#546	1	2	yes	—
615	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
616	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
617	Dic₆₇	—	2	2	no	—
618	Dic₆₇	—	2	2	no	—
619	Dic₆₇	—	2	2	no	—
620	Dic₆₇	—	4	2	no	—
621	Dic₆₇	—	4	2	no	—
622	#61184	—	67	1	no	maximal, Sylow
623	C₂×C₆₇	—	2	2	no	—
624	C₂×C₆₇	—	2	2	no	—
625	C₂×C₆₇	—	4	1	no	—
626	C₂×C₆₇	—	8	1	no	—
627	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
628	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
629	C₂×C₆₇	#3585	1	1	yes	characteristic
630	D₆₇	—	4	2	no	—
631	D₆₇	—	4	4	no	—
632	D₆₇	—	8	2	no	—
633	#3495	—	67	1	no	—
634	#3484	—	67	1	no	—
635	#3324	—	67	2	no	—
636	#3323	—	67	2	no	—
637	#3314	—	67	2	no	—
638	#3311	—	67	2	no	—
639	#3310	—	67	2	no	—
640	#3310	—	67	2	no	—
641	#3296	—	67	2	no	—
642	#3295	—	67	2	no	—
643	#3136	—	67	1	no	—
644	#3096	—	67	1	no	—
645	#3091	D₆₇	1	1	yes	characteristic, complemented
646	#3081	—	67	1	no	—
647	#3057	—	67	1	no	—
648	#3056	—	67	1	no	—
649	#3043	—	67	1	no	—
650	#3009	—	67	1	no	—
651	C₂×#450	—	67	1	no	—
652	#2949	—	67	1	no	—
653	#2933	—	67	1	no	—
654	#2897	—	67	1	no	—
655	C₂×#418	—	67	1	no	—
656	C₆₇	#61184	1	1	yes	characteristic, complemented, Sylow
657	C₂×H(5,𝔽₂)	—	67	1	no	—
658	C₂³×D₄	—	67	1	no	—
659	C₂×#137	—	67	1	no	—
660	C₂²×SD₁₆	—	67	1	no	—
661	C₂²×SD₁₆	—	67	1	no	—
662	C₂×#131	—	67	1	no	—
663	C₂²×M₁₆	—	67	1	no	—
664	#556	—	67	2	no	—
665	#554	—	67	2	no	—
666	#552	—	67	2	no	—
667	#552	—	67	2	no	—
668	#552	—	134	2	no	—
669	#551	—	134	2	no	—
670	#546	—	67	2	no	—
671	#546	—	67	2	no	—
672	#546	—	134	1	no	—
673	#546	—	134	1	no	—
674	D₄²	—	67	2	no	—
675	D₄²	—	67	2	no	—
676	D₄²	—	134	1	no	—
677	D₄²	—	134	1	no	—
678	#544	—	67	1	no	—
679	#542	—	134	1	no	—
680	#541	—	134	1	no	—
681	#536	—	67	1	no	—
682	#535	—	67	1	no	—
683	#535	—	67	1	no	—
684	#534	—	134	2	no	—
685	#533	—	134	1	no	—
686	#529	—	134	1	no	—
687	#525	—	67	1	no	—
688	#525	C₂×D₆₇	1	1	yes	characteristic
689	C₂×C₂²⋊Q₈	—	67	1	no	—
690	C₂×#120	—	134	2	no	—
691	#520	—	67	1	no	—
692	#519	—	67	1	no	—
693	#518	—	67	1	no	—
694	C₂×#117	C₂×D₆₇	1	1	yes	characteristic, complemented
695	#490	—	67	2	no	—
696	#489	—	67	2	no	—
697	#488	—	67	2	no	—
698	#486	—	67	2	no	—
699	#485	C₂×D₆₇	1	1	yes	characteristic, complemented
700	#485	C₂×D₆₇	1	1	yes	characteristic, complemented
701	#484	C₂×D₆₇	1	1	yes	characteristic, complemented
702	#483	C₂×D₆₇	1	1	yes	characteristic, complemented
703	#482	—	67	2	no	—
704	#482	—	67	2	no	—
705	#482	C₂×D₆₇	1	1	yes	characteristic, complemented
706	#482	C₂×D₆₇	1	1	yes	characteristic, complemented
707	#481	—	67	2	no	—
708	#481	C₂×D₆₇	1	1	yes	characteristic, complemented
709	#480	—	67	2	no	—
710	#480	C₂×D₆₇	1	1	yes	characteristic, complemented
711	#478	—	67	2	no	—
712	#478	—	67	2	no	—
713	#476	—	67	2	no	—
714	#474	—	67	2	no	—
715	#470	—	67	2	no	—
716	#468	—	67	2	no	—
717	#468	—	67	2	no	—
718	#468	—	67	2	no	—
719	#467	—	67	2	no	—
720	#465	—	67	2	no	—
721	#465	—	67	2	no	—
722	#465	—	67	2	no	—
723	#464	—	67	2	no	—
724	#464	—	67	2	no	—
725	#460	—	67	2	no	—
726	#460	—	67	2	no	—
727	#452	—	67	2	no	—
728	#452	—	67	2	no	—
729	#450	—	67	2	no	—
730	#450	—	67	2	no	—
731	#450	—	67	2	no	—
732	#450	—	67	2	no	—
733	#450	—	67	2	no	—
734	#450	—	67	2	no	—
735	#440	—	67	2	no	—
736	#440	—	67	2	no	—
737	C₄×SD₁₆	—	67	2	no	—
738	C₄×SD₁₆	—	67	2	no	—
739	#436	—	67	2	no	—
740	#435	—	67	2	no	—
741	#435	—	67	2	no	—
742	C₈×D₄	—	67	2	no	—
743	#428	—	67	1	no	—
744	#427	C₂×D₆₇	1	1	yes	characteristic, complemented
745	#427	C₂×D₆₇	1	1	yes	characteristic, complemented
746	#424	—	67	1	no	—
747	#419	—	67	1	no	—
748	#418	—	67	1	no	—
749	#418	—	67	1	no	—
750	#418	—	67	1	no	—
751	#418	—	67	1	no	—
752	#418	—	67	2	no	—
753	#418	—	67	2	no	—
754	#418	—	67	2	no	—
755	#417	—	67	1	no	—
756	#417	—	67	2	no	—
757	#416	—	67	2	no	—
758	#416	C₂×D₆₇	1	1	yes	characteristic, complemented
759	#416	C₂×D₆₇	1	1	yes	characteristic, complemented
760	C₂×#102	—	67	1	no	—
761	C₂×#102	—	67	1	no	—
762	C₂×#102	—	67	2	no	—
763	C₂×#102	—	67	2	no	—
764	C₂×#102	—	67	2	no	—
765	#408	—	67	1	no	—
766	C₂×C₂²⋊C₈	C₂×D₆₇	1	1	yes	characteristic, complemented
767	#405	—	67	1	no	—
768	C₂⁵	—	134	1	no	—
769	H(5,𝔽₂)	—	268	2	no	—
770	H(5,𝔽₂)	—	134	4	no	—
771	C₂×#41	—	67	1	no	—
772	C₂×#41	—	67	2	no	—
773	C₂×#41	—	134	1	no	—
774	C₂×#41	C₂²×D₆₇	1	1	yes	characteristic
775	C₂²×Q₈	—	67	1	no	—
776	C₂²×D₄	—	268	2	no	—
777	C₂²×D₄	—	67	2	no	—
778	C₂²×D₄	—	67	2	no	—
779	C₂²×D₄	—	67	2	no	—
780	C₂²×D₄	—	67	1	no	—
781	C₂²×D₄	—	67	1	no	—
782	C₂²×D₄	—	134	1	no	—
783	C₂²×D₄	—	134	4	no	—
784	C₂²×D₄	—	134	2	no	—
785	C₂²×D₄	—	134	2	no	—
786	C₂²×D₄	—	134	2	no	—
787	C₂²×D₄	—	134	1	no	—
788	C₂²×D₄	—	134	1	no	—
789	C₂²×D₄	—	134	1	no	—
790	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
791	#137	—	268	2	no	—
792	C₂×Q₁₆	—	67	2	no	—
793	C₂×SD₁₆	—	268	2	no	—
794	C₂×SD₁₆	—	67	2	no	—
795	C₂×SD₁₆	—	67	2	no	—
796	C₂×SD₁₆	—	67	2	no	—
797	C₂×SD₁₆	—	67	2	no	—
798	C₂×SD₁₆	—	67	2	no	—
799	C₂×SD₁₆	—	134	4	no	—
800	#131	—	268	2	no	—
801	C₂×M₁₆	—	268	2	no	—
802	C₂×M₁₆	—	67	2	no	—
803	C₂×M₁₆	—	67	1	no	—
804	C₂×M₁₆	—	67	1	no	—
805	C₂×M₁₆	—	67	2	no	—
806	C₂²×C₈	—	67	2	no	—
807	C₂²×C₈	—	67	2	no	—
808	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
809	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
810	C₄⋊Q₈	—	67	2	no	—
811	C₄⋊Q₈	—	134	1	no	—
812	C₄⋊Q₈	—	134	1	no	—
813	#127	—	67	2	no	—
814	#127	—	134	1	no	—
815	#126	—	134	2	no	—
816	#126	—	134	2	no	—
817	#126	—	134	2	no	—
818	#126	—	134	2	no	—
819	#125	—	67	2	no	—
820	#125	—	134	1	no	—
821	#125	—	134	2	no	—
822	#125	—	134	2	no	—
823	#125	—	134	2	no	—
824	#124	—	67	2	no	—
825	#124	—	134	1	no	—
826	#124	—	134	1	no	—
827	#124	—	134	2	no	—
828	#123	—	2	1	no	—
829	#123	—	67	2	no	—
830	#123	—	134	2	no	—
831	#123	—	134	2	no	—
832	#123	—	134	2	no	—
833	#123	—	134	2	no	—
834	#123	—	134	2	no	—
835	C₂²⋊Q₈	—	67	1	no	—
836	C₂²⋊Q₈	—	67	1	no	—
837	C₂²⋊Q₈	—	67	2	no	—
838	C₂²⋊Q₈	—	67	2	no	—
839	C₂²⋊Q₈	—	67	2	no	—
840	C₂²⋊Q₈	—	67	2	no	—
841	C₂²⋊Q₈	—	134	2	no	—
842	C₂²⋊Q₈	—	134	2	no	—
843	C₂²⋊Q₈	—	134	2	no	—
844	C₂²⋊Q₈	—	134	1	no	—
845	C₂²⋊Q₈	—	134	1	no	—
846	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
847	C₂²⋊Q₈	C₂²×D₆₇	1	1	yes	characteristic
848	#121	—	67	1	no	—
849	#121	—	67	1	no	—
850	#121	—	67	2	no	—
851	#121	—	67	2	no	—
852	#121	—	134	2	no	—
853	#121	—	134	2	no	—
854	#121	—	134	2	no	—
855	#121	—	134	2	no	—
856	#121	—	134	1	no	—
857	#121	—	134	1	no	—
858	#121	C₂²×D₆₇	1	1	yes	characteristic
859	#121	C₂²×D₆₇	1	1	yes	characteristic
860	#120	—	2	1	no	—
861	#120	—	67	2	no	—
862	#120	—	134	2	no	—
863	#120	—	134	2	no	—
864	#120	—	134	2	no	—
865	#120	—	134	2	no	—
866	#120	—	134	2	no	—
867	#120	—	134	2	no	—
868	#120	—	134	2	no	—
869	#120	—	134	2	no	—
870	C₄×Q₈	—	67	2	no	—
871	C₄×Q₈	—	67	2	no	—
872	C₄×Q₈	—	134	1	no	—
873	C₄×Q₈	—	134	1	no	—
874	C₄×Q₈	—	134	2	no	—
875	C₄×Q₈	—	134	1	no	—
876	C₄×D₄	—	2	1	no	—
877	C₄×D₄	—	2	1	no	—
878	C₄×D₄	—	67	2	no	—
879	C₄×D₄	—	67	2	no	—
880	C₄×D₄	—	67	2	no	—
881	C₄×D₄	—	67	2	no	—
882	C₄×D₄	—	134	1	no	—
883	C₄×D₄	—	134	1	no	—
884	C₄×D₄	—	134	1	no	—
885	C₄×D₄	—	134	2	no	—
886	C₄×D₄	—	134	2	no	—
887	#117	—	2	1	no	—
888	#117	—	2	1	no	—
889	#117	—	67	1	no	—
890	#117	—	67	2	no	—
891	#117	—	134	2	no	—
892	#117	—	134	2	no	—
893	#117	—	134	2	no	—
894	#117	C₂²×D₆₇	1	1	yes	characteristic
895	#117	C₂²×D₆₇	1	1	yes	characteristic
896	#117	C₂²×D₆₇	1	1	yes	characteristic
897	#117	C₂²×D₆₇	1	1	yes	characteristic
898	#117	C₂²×D₆₇	1	1	yes	characteristic
899	C₂×C₄⋊C₄	—	67	1	no	—
900	C₂×C₄⋊C₄	—	67	2	no	—
901	C₂×C₄⋊C₄	—	134	1	no	—
902	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
904	C₂×C₂²⋊C₄	—	2	1	no	—
905	C₂×C₂²⋊C₄	—	134	2	no	—
906	C₂×C₂²⋊C₄	—	134	2	no	—
907	C₂×C₂²⋊C₄	—	134	2	no	—
908	C₂×C₂²⋊C₄	—	134	1	no	—
909	C₂×C₄²	—	2	1	no	—
910	#107	—	67	2	no	—
911	#107	C₂²×D₆₇	1	1	yes	characteristic, complemented
912	#107	C₂²×D₆₇	1	1	yes	characteristic, complemented
913	#107	C₂²×D₆₇	1	1	yes	characteristic, complemented
914	#107	C₂²×D₆₇	1	1	yes	characteristic, complemented
915	#106	—	67	2	no	—
916	#106	C₂²×D₆₇	1	1	yes	characteristic, complemented
917	#106	C₂²×D₆₇	1	1	yes	characteristic, complemented
918	#106	C₂²×D₆₇	1	1	yes	characteristic, complemented
919	#106	C₂²×D₆₇	1	1	yes	characteristic, complemented
920	C₄⋊C₈	—	67	2	no	—
921	C₄⋊C₈	—	67	2	no	—
922	#103	—	67	2	no	—
923	#103	—	67	2	no	—
924	#103	—	67	2	no	—
925	#103	C₂²×D₆₇	1	1	yes	characteristic, complemented
926	#103	C₂²×D₆₇	1	1	yes	characteristic, complemented
927	#103	C₂²×D₆₇	1	1	yes	characteristic, complemented
928	#103	C₂²×D₆₇	1	1	yes	characteristic, complemented
929	#102	—	67	2	no	—
930	#102	—	67	2	no	—
931	#102	—	67	2	no	—
932	#102	—	67	2	no	—
933	#102	—	67	2	no	—
934	#102	—	67	2	no	—
935	#102	—	67	2	no	—
936	#102	—	67	2	no	—
937	#102	—	67	2	no	—
938	#102	—	67	2	no	—
939	#102	—	67	2	no	—
940	#102	—	67	2	no	—
941	#102	—	67	2	no	—
942	#102	C₂²×D₆₇	1	1	yes	characteristic, complemented
943	#102	C₂²×D₆₇	1	1	yes	characteristic, complemented
944	#102	C₂²×D₆₇	1	1	yes	characteristic, complemented
945	#102	C₂²×D₆₇	1	1	yes	characteristic, complemented
946	C₂²⋊C₈	—	67	2	no	—
947	C₂²⋊C₈	—	67	2	no	—
948	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
949	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
950	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
951	C₂²⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
952	#97	—	67	2	no	—
953	C₄×C₈	—	67	2	no	—
954	C₂⁴	—	268	4	no	—
955	C₂⁴	—	536	2	no	—
956	C₂⁴	—	536	2	no	—
957	C₂⁴	—	134	2	no	—
958	C₂⁴	—	134	2	no	—
959	C₂⁴	—	134	2	no	—
960	C₂⁴	—	134	1	no	—
961	C₂⁴	—	134	1	no	—
962	C₂⁴	D₄×D₆₇	1	1	yes	characteristic
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	268	4	no	—
966	#41	—	268	2	no	—
967	#41	—	134	4	no	—
968	#41	—	134	2	no	—
969	#41	—	134	2	no	—
970	C₂×Q₈	—	67	1	no	—
971	C₂×Q₈	—	67	2	no	—
972	C₂×Q₈	—	134	2	no	—
973	C₂×Q₈	—	134	2	no	—
974	C₂×Q₈	—	134	2	no	—
975	C₂×Q₈	—	134	1	no	—
976	C₂×Q₈	C₂³×D₆₇	1	1	yes	characteristic
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	268	4	no	—
981	C₂×D₄	—	268	4	no	—
982	C₂×D₄	—	268	4	no	—
983	C₂×D₄	—	268	2	no	—
984	C₂×D₄	—	268	2	no	—
985	C₂×D₄	—	268	4	no	—
986	C₂×D₄	—	268	8	no	—
987	C₂×D₄	—	268	2	no	—
988	C₂×D₄	—	536	4	no	—
989	C₂×D₄	—	536	4	no	—
990	C₂×D₄	—	67	2	no	—
991	C₂×D₄	—	67	2	no	—
992	C₂×D₄	—	67	2	no	—
993	C₂×D₄	—	67	1	no	—
994	C₂×D₄	—	67	4	no	—
995	C₂×D₄	—	67	2	no	—
996	C₂×D₄	—	67	2	no	—
997	C₂×D₄	—	134	2	no	—
998	C₂×D₄	—	134	4	no	—
999	C₂×D₄	—	134	4	no	—
1000	C₂×D₄	—	134	2	no	—
1001	C₂×D₄	—	134	2	no	—
1002	C₂×D₄	—	134	2	no	—
1003	C₂×D₄	—	134	2	no	—
1004	C₂×D₄	—	134	2	no	—
1005	C₂×D₄	—	134	4	no	—
1006	C₂×D₄	—	134	2	no	—
1007	C₂×D₄	—	134	2	no	—
1008	C₂×D₄	—	134	1	no	—
1009	C₂×D₄	—	134	1	no	—
1010	C₂×D₄	—	134	2	no	—
1011	C₂×D₄	—	134	2	no	—
1012	C₂×D₄	—	134	2	no	—
1013	C₂×D₄	C₂³×D₆₇	1	1	yes	characteristic
1014	C₂²×C₄	—	2	2	no	—
1015	C₂²×C₄	—	2	2	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	67	2	no	—
1020	C₂²×C₄	—	134	2	no	—
1021	C₂²×C₄	—	134	2	no	—
1022	C₂²×C₄	—	134	2	no	—
1023	C₂²×C₄	—	134	2	no	—
1024	C₂²×C₄	—	134	1	no	—
1025	C₂²×C₄	—	134	1	no	—
1026	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
1027	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
1028	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
1029	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1030	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1031	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
1032	Q₁₆	—	268	2	no	—
1033	SD₁₆	—	268	2	no	—
1034	SD₁₆	—	268	2	no	—
1035	SD₁₆	—	268	2	no	—
1036	SD₁₆	—	134	4	no	—
1037	SD₁₆	—	134	4	no	—
1038	M₁₆	—	268	2	no	—
1039	M₁₆	—	268	2	no	—
1040	M₁₆	—	134	2	no	—
1041	M₁₆	—	134	2	no	—
1042	C₂×C₈	—	2	2	no	—
1043	C₂×C₈	—	2	2	no	—
1044	C₂×C₈	—	268	2	no	—
1045	C₂×C₈	—	268	2	no	—
1046	C₂×C₈	—	67	2	no	—
1047	C₂×C₈	—	67	2	no	—
1048	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
1049	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
1050	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
1051	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	67	1	no	—
1057	C₄⋊C₄	—	67	1	no	—
1058	C₄⋊C₄	—	67	2	no	—
1059	C₄⋊C₄	—	67	2	no	—
1060	C₄⋊C₄	—	67	2	no	—
1061	C₄⋊C₄	—	134	2	no	—
1062	C₄⋊C₄	—	134	2	no	—
1063	C₄⋊C₄	—	134	2	no	—
1064	C₄⋊C₄	—	134	2	no	—
1065	C₄⋊C₄	—	134	2	no	—
1066	C₄⋊C₄	—	134	2	no	—
1067	C₄⋊C₄	—	134	2	no	—
1068	C₄⋊C₄	—	134	2	no	—
1069	C₄⋊C₄	—	134	1	no	—
1070	C₄⋊C₄	—	134	2	no	—
1071	C₄⋊C₄	—	134	2	no	—
1072	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1073	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1074	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1075	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1076	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1077	C₄⋊C₄	C₂³×D₆₇	1	1	yes	characteristic
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	1	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	67	2	no	—
1088	C₂²⋊C₄	—	67	2	no	—
1089	C₂²⋊C₄	—	67	2	no	—
1090	C₂²⋊C₄	—	67	2	no	—
1091	C₂²⋊C₄	—	67	2	no	—
1092	C₂²⋊C₄	—	134	2	no	—
1093	C₂²⋊C₄	—	134	2	no	—
1094	C₂²⋊C₄	—	134	2	no	—
1095	C₂²⋊C₄	—	134	2	no	—
1096	C₂²⋊C₄	—	134	2	no	—
1097	C₂²⋊C₄	—	134	2	no	—
1098	C₂²⋊C₄	—	134	2	no	—
1099	C₂²⋊C₄	—	134	2	no	—
1100	C₂²⋊C₄	—	134	2	no	—
1101	C₂²⋊C₄	—	134	2	no	—
1102	C₂²⋊C₄	—	134	2	no	—
1103	C₄²	—	2	1	no	—
1104	C₄²	—	2	1	no	—
1105	C₄²	—	2	1	no	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	2	1	no	—
1108	C₄²	—	67	2	no	—
1109	C₄²	—	134	2	no	—
1110	C₄²	—	134	2	no	—
1111	C₄²	—	134	2	no	—
1112	C₂³	—	2	2	no	—
1113	C₂³	—	2	2	no	—
1114	C₂³	—	2	1	no	—
1115	C₂³	—	4	1	no	—
1116	C₂³	—	268	4	no	—
1117	C₂³	—	268	4	no	—
1118	C₂³	—	268	4	no	—
1119	C₂³	—	268	4	no	—
1120	C₂³	—	268	2	no	—
1121	C₂³	—	268	4	no	—
1122	C₂³	—	536	1	no	—
1123	C₂³	—	536	1	no	—
1124	C₂³	—	536	2	no	—
1125	C₂³	—	536	1	no	—
1126	C₂³	—	536	1	no	—
1127	C₂³	—	536	2	no	—
1128	C₂³	—	536	2	no	—
1129	C₂³	—	536	2	no	—
1130	C₂³	—	536	16	no	—
1131	C₂³	—	67	2	no	—
1132	C₂³	—	134	2	no	—
1133	C₂³	—	134	2	no	—
1134	C₂³	—	134	4	no	—
1135	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1136	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1137	C₂³	C₂×D₄×D₆₇	1	1	yes	characteristic
1138	Q₈	—	2	1	no	—
1139	Q₈	—	2	1	no	—
1140	Q₈	—	268	2	no	—
1141	Q₈	—	536	2	no	—
1142	Q₈	—	134	2	no	—
1143	Q₈	—	134	2	no	—
1144	Q₈	—	134	2	no	—
1145	D₄	—	2	1	no	—
1146	D₄	—	2	1	no	—
1147	D₄	—	4	2	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	268	4	no	—
1151	D₄	—	268	4	no	—
1152	D₄	—	268	4	no	—
1153	D₄	—	268	2	no	—
1154	D₄	—	268	4	no	—
1155	D₄	—	268	2	no	—
1156	D₄	—	536	2	no	—
1157	D₄	—	536	2	no	—
1158	D₄	—	536	2	no	—
1159	D₄	—	536	2	no	—
1160	D₄	—	67	4	no	—
1161	D₄	—	134	4	no	—
1162	D₄	—	134	4	no	—
1163	D₄	—	134	4	no	—
1164	D₄	—	134	2	no	—
1165	D₄	—	134	2	no	—
1166	D₄	—	134	2	no	—
1167	D₄	—	134	2	no	—
1168	C₂×C₄	—	2	2	no	—
1169	C₂×C₄	—	2	2	no	—
1170	C₂×C₄	—	2	2	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	4	2	no	—
1183	C₂×C₄	—	4	2	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	—	268	4	no	—
1186	C₂×C₄	—	268	2	no	—
1187	C₂×C₄	—	536	2	no	—
1188	C₂×C₄	—	536	2	no	—
1189	C₂×C₄	—	536	2	no	—
1190	C₂×C₄	—	536	1	no	—
1191	C₂×C₄	—	67	2	no	—
1192	C₂×C₄	—	67	2	no	—
1193	C₂×C₄	—	67	2	no	—
1194	C₂×C₄	—	134	2	no	—
1195	C₂×C₄	—	134	2	no	—
1196	C₂×C₄	—	134	2	no	—
1197	C₂×C₄	—	134	2	no	—
1198	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1199	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1200	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
1201	C₂×C₄	#41×D₆₇	1	2	yes	—
1202	C₂×C₄	#14524089	1	2	yes	—
1203	C₂×C₄	C₂⁴×D₆₇	1	1	yes	characteristic
1204	C₈	—	2	1	no	—
1205	C₈	—	2	1	no	—
1206	C₈	—	2	1	no	—
1207	C₈	—	2	1	no	—
1208	C₈	—	134	2	no	—
1209	C₈	—	134	2	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	4	4	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	268	2	no	—
1222	C₂²	—	268	2	no	—
1223	C₂²	—	268	2	no	—
1224	C₂²	—	268	2	no	—
1225	C₂²	—	268	2	no	—
1226	C₂²	—	536	4	no	—
1227	C₂²	—	536	8	no	—
1228	C₂²	—	536	4	no	—
1229	C₂²	—	536	8	no	—
1230	C₂²	—	1072	4	no	—
1231	C₂²	—	134	4	no	—
1232	C₂²	—	134	2	no	—
1233	C₂²	—	134	2	no	—
1234	C₂²	—	134	2	no	—
1235	C₂²	#16864038	1	2	yes	—
1236	C₂²	#16864203	1	2	yes	—
1237	C₂²	C₂²×D₄×D₆₇	1	1	yes	characteristic
1238	C₄	—	2	1	no	—
1239	C₄	—	2	1	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	1	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	—	268	2	no	—
1248	C₄	—	268	2	no	—
1249	C₄	—	134	2	no	—
1250	C₄	—	134	2	no	—
1251	C₄	—	134	2	no	—
1252	C₄	#16864038	1	2	yes	—
1253	C₄	C₂×#41×D₆₇	1	1	yes	characteristic
1254	C₄	C₂×#14524089	1	1	yes	characteristic
1255	C₂	—	2	2	no	—
1256	C₂	—	2	2	no	—
1257	C₂	—	4	1	no	—
1258	C₂	—	8	1	no	—
1259	C₂	—	268	4	no	—
1260	C₂	—	268	2	no	—
1261	C₂	—	536	2	no	—
1262	C₂	C₂×#16864038	1	1	yes	characteristic
1263	C₂	C₂×#16864203	1	1	yes	characteristic
1264	C₂	#22574986	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₆₇
commutator, cosocle	C₂×C₄×C₆₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₆₇
Fitting	C₆₇×#3091	C₂
socle	C₂²×C₆₇	C₂³×D₄
prime radical	#22573842	C₂
hypercenter	#3091	D₆₇
hypocenter	C₆₇	#61184
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3091

Complements

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

N	H ≅ G/N	type
1. #22573961	C₂	semidirect
3. #22572438	C₂	semidirect
4. #22572423	C₂	semidirect
5. #22572288	C₂	semidirect
6. #22572248	C₂	semidirect
7. #22572233	C₂	semidirect
8. #22572228	C₂	semidirect
9. #22572042	C₂	semidirect
10. #22572031	C₂	semidirect
11. #22570567	C₂	semidirect
12. #22570170	C₂	semidirect
13. #22570043	C₂	semidirect
14. #22569849	C₂	semidirect
15. #22569841	C₂	semidirect
16. #22569733	C₂	semidirect
17. #22569489	C₂	semidirect
18. C₂×#16863549	C₂	semidirect
19. #22569067	C₂	semidirect
20. #22568930	C₂	semidirect
21. #22568731	C₂	semidirect
22. C₂×#16863400	C₂	semidirect
23. C₆₇×#3091	C₂	semidirect
26. C₂×#14524073	C₂²	semidirect
28. C₂²×#11761617	C₂²	semidirect
29. C₂×#14524049	C₂²	semidirect
30. C₂²×#11761612	C₂²	semidirect
31. #16864114	C₂²	semidirect
32. #16864101	C₂²	semidirect
33. #16864085	C₂²	semidirect
34. #16864081	C₂²	semidirect
45. #16864024	C₂²	semidirect
48. #16863972	C₂²	semidirect
55. C₂×#14524022	C₂²	semidirect
57. #16863876	C₂²	semidirect
58. #16863873	C₂²	semidirect
60. #16863759	C₂²	semidirect
61. #16863757	C₂²	semidirect
62. #16863752	C₂²	semidirect
63. #16863741	C₂²	semidirect
64. #16863723	C₂²	semidirect
65. #16863722	C₂²	semidirect
66. #16863716	C₂²	semidirect
67. #16863711	C₂²	semidirect
68. #16863699	C₂²	semidirect
69. #16863695	C₂²	semidirect
70. #16863685	C₂²	semidirect
71. #16863675	C₂²	semidirect
72. #16863652	C₂²	semidirect
73. #16863643	C₂²	semidirect
74. #16863643	C₂²	semidirect
75. #16863640	C₂²	semidirect
76. #16863635	C₂²	semidirect
77. #16863626	C₂²	semidirect
78. #16863626	C₂²	semidirect
79. #16863623	C₂²	semidirect
80. #16863621	C₂²	semidirect
81. #16863621	C₂²	semidirect
82. #16863595	C₂²	semidirect
83. #16863595	C₂²	semidirect
84. #16863561	C₂²	semidirect
85. #16863561	C₂²	semidirect
86. #16863549	C₂²	semidirect
87. #16863549	C₂²	semidirect
88. #16863549	C₂²	semidirect
89. #16863549	C₂²	semidirect
90. #16863548	C₂²	semidirect
91. #16863548	C₂²	semidirect
92. #16863495	C₂²	semidirect
93. #16863495	C₂²	semidirect
94. #16863483	C₂²	semidirect
95. #16863483	C₂²	semidirect
96. #16863471	C₂²	semidirect
97. #16863470	C₂²	semidirect
98. #16863464	C₂²	semidirect
99. (C₂²⋊D₆₇)⋊C₈	C₂²	semidirect
100. #16863439	C₂²	semidirect
101. #16863422	C₂²	semidirect
102. #16863404	C₂²	semidirect
105. #16863400	C₂²	semidirect
106. #16863400	C₂²	semidirect
107. #16863400	C₂²	semidirect
108. #16863400	C₂²	semidirect
109. #16863399	C₂²	semidirect
110. #16863397	C₂²	semidirect
111. #16863396	C₂²	semidirect
112. #16863391	C₂²	semidirect
114. C₂×#14523965	C₂²	semidirect
115. C₂×#14523963	C₂²	semidirect
116. C₂×#14523963	C₂²	semidirect
117. #102×D₆₇	C₂²	semidirect
118. #16863362	C₂²	semidirect
119. #16863351	C₂²	semidirect
121. C₂×#117×C₆₇	C₂²	semidirect
122. #485×C₆₇	C₂²	semidirect
123. #485×C₆₇	C₂²	semidirect
124. #484×C₆₇	C₂²	semidirect
125. #483×C₆₇	C₂²	semidirect
126. #482×C₆₇	C₂²	semidirect
127. #482×C₆₇	C₂²	semidirect
128. #481×C₆₇	C₂²	semidirect
129. #480×C₆₇	C₂²	semidirect
130. #427×C₆₇	C₂²	semidirect
131. #427×C₆₇	C₂²	semidirect
132. #416×C₆₇	C₂²	semidirect
133. #416×C₆₇	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
157. C₂×#11761618	C₂³	semidirect
164. C₂×#11761616	C₂³	semidirect
170. C₂×#11761611	C₂³	semidirect
172. C₂×C₈×D₆₇	C₂³	semidirect
175. #14524042	C₂³	semidirect
184. #14524034	C₂³	semidirect
197. #14524023	C₂³	semidirect
198. #14524023	C₂³	semidirect
231. #14524008	C₂³	semidirect
232. #14524008	C₂³	semidirect
244. #14524001	C₂³	semidirect
249. C₄⋊C₄×D₆₇	C₂³	semidirect
254. #14523976	C₂³	semidirect
255. #14523974	C₂³	semidirect
256. Dic₆₇⋊C₈	C₂³	semidirect
257. Dic₆₇⋊C₈	C₂³	semidirect
258. #14523967	C₂³	semidirect
259. #14523966	C₂³	semidirect
260. #14523966	C₂³	semidirect
265. #14523964	C₂³	semidirect
274. (C₂×D₆₇)⋊C₈	C₂³	semidirect
275. (C₂×D₆₇)⋊C₈	C₂³	semidirect
276. #14523953	C₂³	semidirect
277. C₈×Dic₆₇	C₂³	semidirect
301. #107×C₆₇	C₂³	semidirect
302. #107×C₆₇	C₂³	semidirect
303. #107×C₆₇	C₂³	semidirect
304. #107×C₆₇	C₂³	semidirect
305. #106×C₆₇	C₂³	semidirect
306. #106×C₆₇	C₂³	semidirect
307. #106×C₆₇	C₂³	semidirect
308. #106×C₆₇	C₂³	semidirect
309. #103×C₆₇	C₂³	semidirect
310. #103×C₆₇	C₂³	semidirect
311. #103×C₆₇	C₂³	semidirect
312. #103×C₆₇	C₂³	semidirect
313. #102×C₆₇	C₂³	semidirect
314. #102×C₆₇	C₂³	semidirect
315. #102×C₆₇	C₂³	semidirect
316. #102×C₆₇	C₂³	semidirect
645. #3091	D₆₇	semidirect
656. C₆₇	#61184	semidirect
694. C₂×#117	C₂×D₆₇	semidirect
699. #485	C₂×D₆₇	semidirect
700. #485	C₂×D₆₇	semidirect
701. #484	C₂×D₆₇	semidirect
702. #483	C₂×D₆₇	semidirect
705. #482	C₂×D₆₇	semidirect
706. #482	C₂×D₆₇	semidirect
708. #481	C₂×D₆₇	semidirect
710. #480	C₂×D₆₇	semidirect
744. #427	C₂×D₆₇	semidirect
745. #427	C₂×D₆₇	semidirect
758. #416	C₂×D₆₇	semidirect
759. #416	C₂×D₆₇	semidirect
766. C₂×C₂²⋊C₈	C₂×D₆₇	semidirect
911. #107	C₂²×D₆₇	semidirect
912. #107	C₂²×D₆₇	semidirect
913. #107	C₂²×D₆₇	semidirect
914. #107	C₂²×D₆₇	semidirect
916. #106	C₂²×D₆₇	semidirect
917. #106	C₂²×D₆₇	semidirect
918. #106	C₂²×D₆₇	semidirect
919. #106	C₂²×D₆₇	semidirect
925. #103	C₂²×D₆₇	semidirect
926. #103	C₂²×D₆₇	semidirect
927. #103	C₂²×D₆₇	semidirect
928. #103	C₂²×D₆₇	semidirect
942. #102	C₂²×D₆₇	semidirect
943. #102	C₂²×D₆₇	semidirect
944. #102	C₂²×D₆₇	semidirect
945. #102	C₂²×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573961	2
#22573842	2
#22572438	2
#22572423	2
#22572288	2
#22572248	2
#22572233	2
#22572228	2
#22572042	2
#22572031	2
#22570567	2
#22570170	2
#22570043	2
#22569849	2
#22569841	2
#22569733	2
#22569489	2
C₂×#16863549	2
#22569067	2
#22568930	2
#22568731	2
C₂×#16863400	2
C₆₇×#3091	2
#61184	67