Subgroups — #30839683

Order 17152.

602 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570796	C₂	1	1	yes	maximal, characteristic
2	#22570015	C₂	1	2	yes	maximal
3	C₈×Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic
4	#22559670	C₂	1	2	yes	maximal, complemented
5	#22559669	C₂	1	2	yes	maximal, complemented
6	#22559610	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559580	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559579	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558966	C₂	1	1	yes	maximal, characteristic
10	#22558896	C₂	1	2	yes	maximal
11	C₆₇×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863951	C₂²	1	2	yes	—
13	C₄×Q₈×D₆₇	C₂²	1	1	yes	characteristic
14	#16863776	C₂²	1	1	yes	characteristic
15	#16863748	C₂²	1	2	yes	—
16	#16863702	—	2	2	no	—
17	#16863701	—	2	2	no	—
18	#16863688	C₂²	1	2	yes	—
19	#16863682	C₂²	1	2	yes	—
20	#16863681	C₂²	1	2	yes	—
21	#16863638	—	2	1	no	—
22	#16863638	—	2	1	no	—
23	Q₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₈×Dic₁₃₄	—	2	1	no	—
25	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
26	#16863520	—	2	1	no	—
27	#16863520	C₂²	1	1	yes	characteristic
28	#16863490	—	2	1	no	—
29	#16863490	—	2	1	no	—
30	#16863437	—	2	2	no	—
31	#16863418	C₂²	1	2	yes	—
32	C₄⋊C₈×D₆₇	—	2	1	no	—
33	C₄⋊C₈×D₆₇	C₂²	1	1	yes	characteristic
34	#16863403	—	2	2	no	—
35	C₄×C₈×D₆₇	—	2	1	no	—
36	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
37	#16863149	C₂²	1	1	yes	characteristic
38	#16863148	C₂²	1	2	yes	—
39	#16863145	C₂²	1	2	yes	—
40	#16863143	C₂²	1	2	yes	—
41	#16863141	C₂²	1	2	yes	—
42	#500×C₆₇	C₂²	1	1	yes	characteristic
43	#477×C₆₇	C₂²	1	2	yes	—
44	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
45	#335×C₆₇	C₂²	1	1	yes	characteristic
46	#333×C₆₇	C₂²	1	2	yes	—
47	C₂×Q₈×D₆₇	D₄	1	1	yes	characteristic
48	C₂×Dic₂₆₈	—	2	1	no	—
49	C₂×Dic₂₆₈	—	2	1	no	—
50	C₂×#11761611	—	2	2	no	—
51	C₂×C₈×D₆₇	—	2	1	no	—
52	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
53	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
54	#14524043	C₂³	1	2	yes	—
55	#14524034	—	2	2	no	—
56	#14524023	—	2	2	no	—
57	#14524019	—	2	2	no	—
58	Q₈×Dic₆₇	—	2	2	no	—
59	Q₈×Dic₆₇	D₄	1	1	yes	characteristic
60	C₄×Dic₁₃₄	—	2	1	no	—
61	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
62	#14524008	—	2	1	no	—
63	#14524008	—	2	2	no	—
64	#14524008	D₄	1	1	yes	characteristic
65	#14524001	—	2	2	no	—
66	C₄⋊C₄×D₆₇	—	2	1	no	—
67	C₄⋊C₄×D₆₇	D₄	1	1	yes	characteristic
68	C₄²×D₆₇	—	2	1	no	—
69	C₄²×D₆₇	C₂³	1	1	yes	characteristic
70	#14523976	—	2	2	no	—
71	#14523975	—	2	2	no	—
72	#14523974	—	2	2	no	—
73	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
74	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
75	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
76	Dic₆₇⋊C₈	—	2	1	no	—
77	Dic₆₇⋊C₈	—	2	1	no	—
78	Dic₆₇⋊C₈	—	2	2	no	—
79	Dic₆₇⋊C₈	—	2	1	no	—
80	#14523968	—	2	2	no	—
81	#14523967	—	2	2	no	—
82	#14523966	—	2	2	no	—
83	#14523966	—	2	2	no	—
84	#14523966	—	2	2	no	—
85	C₄×C₆₇⋊C₈	—	2	1	no	—
86	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
87	C₈×Dic₆₇	—	2	1	no	—
88	C₈×Dic₆₇	—	2	1	no	—
89	C₈×Dic₆₇	D₄	1	1	yes	characteristic
90	C₈×Dic₆₇	D₄	1	1	yes	characteristic
91	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
92	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
93	#107×C₆₇	—	2	1	no	—
94	#107×C₆₇	—	2	1	no	—
95	#107×C₆₇	—	2	2	no	—
96	C₄⋊C₈×C₆₇	—	2	1	no	—
97	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
98	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
99	#103×C₆₇	—	2	2	no	—
100	C₄×C₈×C₆₇	—	2	1	no	—
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×Dic₁₃₄	—	2	1	no	—
103	C₂×Dic₁₃₄	—	2	2	no	—
104	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
105	Q₈×D₆₇	—	2	2	no	—
106	Q₈×D₆₇	Q₁₆	1	4	yes	complemented
107	C₂×C₄×D₆₇	—	2	1	no	—
108	C₂×C₄×D₆₇	—	2	1	no	—
109	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₆₇	#41	1	1	yes	characteristic
112	Dic₂₆₈	—	4	2	no	—
113	Dic₂₆₈	—	4	2	no	—
114	#11761611	—	4	4	no	—
115	C₂×C₆₇⋊C₈	—	2	1	no	—
116	C₂×C₆₇⋊C₈	—	2	2	no	—
117	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₆₇⋊C₈	C₂×D₄	1	1	yes	characteristic
119	C₈×D₆₇	—	2	2	no	—
120	C₈×D₆₇	—	4	1	no	—
121	C₈×D₆₇	—	4	2	no	—
122	C₄⋊Dic₆₇	—	2	1	no	—
123	C₄⋊Dic₆₇	—	2	2	no	—
124	C₄⋊Dic₆₇	—	2	2	no	—
125	C₄⋊Dic₆₇	—	4	2	no	—
126	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
127	Dic₆₇⋊C₄	—	2	1	no	—
128	Dic₆₇⋊C₄	—	2	1	no	—
129	Dic₆₇⋊C₄	—	2	1	no	—
130	Dic₆₇⋊C₄	—	4	2	no	—
131	(C₂×D₆₇)⋊C₄	—	4	2	no	—
132	C₄×Dic₆₇	—	2	1	no	—
133	C₄×Dic₆₇	—	2	1	no	—
134	C₄×Dic₆₇	—	2	1	no	—
135	C₄×Dic₆₇	—	4	2	no	—
136	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₆₇	#41	1	1	yes	characteristic
139	C₂×Q₈×C₆₇	—	2	2	no	—
140	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	—	2	2	no	—
142	C₂×C₈×C₆₇	—	2	1	no	—
143	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₆₇	—	2	1	no	—
146	C₄⋊C₄×C₆₇	—	2	2	no	—
147	C₄⋊C₄×C₆₇	—	2	2	no	—
148	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₆₇	—	2	1	no	—
150	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
151	C₂²×D₆₇	#121	1	1	yes	characteristic
152	Q₈×C₆₇	—	2	1	no	—
153	Q₈×C₆₇	—	8	2	no	—
154	Q₈×C₆₇	C₂×Q₁₆	1	2	yes	—
155	C₂×C₄×C₆₇	—	2	1	no	—
156	C₂×C₄×C₆₇	—	2	1	no	—
157	C₂×C₄×C₆₇	—	4	2	no	—
158	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₆₇	—	2	1	no	—
162	C₂×Dic₆₇	—	2	1	no	—
163	C₂×Dic₆₇	—	4	2	no	—
164	C₂×Dic₆₇	#121	1	1	yes	characteristic
165	C₂×Dic₆₇	#121	1	1	yes	characteristic
166	C₂×Dic₆₇	#121	1	1	yes	characteristic
167	C₄×D₆₇	—	2	4	no	—
168	C₄×D₆₇	—	2	1	no	—
169	C₄×D₆₇	—	2	1	no	—
170	C₄×D₆₇	—	4	1	no	—
171	C₄×D₆₇	—	4	2	no	—
172	C₄×D₆₇	C₂×Q₁₆	1	2	yes	—
173	C₄×D₆₇	#135	1	2	yes	—
174	Dic₁₃₄	—	2	1	no	—
175	Dic₁₃₄	—	2	4	no	—
176	Dic₁₃₄	—	4	2	no	—
177	Dic₁₃₄	—	4	2	no	—
178	Dic₁₃₄	C₂×Q₁₆	1	2	yes	—
179	C₈×C₆₇	—	2	1	no	—
180	C₈×C₆₇	—	4	2	no	—
181	C₈×C₆₇	—	4	1	no	—
182	C₈×C₆₇	#137	1	2	yes	—
183	C₆₇⋊C₈	—	2	1	no	—
184	C₆₇⋊C₈	—	2	1	no	—
185	C₆₇⋊C₈	—	4	2	no	—
186	C₆₇⋊C₈	—	4	1	no	—
187	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
188	C₂×D₆₇	—	2	1	no	—
189	C₂×D₆₇	—	2	1	no	—
190	C₂×D₆₇	#467	1	2	yes	—
191	C₄×C₆₇	—	2	2	no	—
192	C₄×C₆₇	—	2	1	no	—
193	C₄×C₆₇	—	4	1	no	—
194	C₄×C₆₇	—	8	2	no	—
195	C₄×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
196	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
197	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
198	C₄×C₆₇	#575	1	1	yes	characteristic
199	Dic₆₇	—	2	1	no	—
200	Dic₆₇	—	2	2	no	—
201	Dic₆₇	—	2	1	no	—
202	Dic₆₇	—	4	1	no	—
203	Dic₆₇	—	8	2	no	—
204	Dic₆₇	#467	1	2	yes	—
205	#19262	—	67	1	no	maximal, Sylow
206	C₂×C₆₇	#3037	1	1	yes	characteristic
207	C₂×C₆₇	C₂×#467	1	1	yes	characteristic
208	C₂×C₆₇	#3067	1	1	yes	characteristic
209	D₆₇	—	2	2	no	—
210	#3170	—	67	1	no	—
211	#3078	—	67	2	no	—
212	C₂×C₈×Q₈	—	67	1	no	—
213	#1684	—	67	2	no	—
214	#1684	—	67	2	no	—
215	#1676	—	67	1	no	—
216	#1676	D₆₇	1	1	yes	characteristic, complemented
217	#1670	—	67	1	no	—
218	#1670	—	67	1	no	—
219	#1567	—	67	1	no	—
220	#1550	—	67	2	no	—
221	C₆₇	#19262	1	1	yes	characteristic, complemented, Sylow
222	#533	—	67	2	no	—
223	C₂×C₄×Q₈	—	67	1	no	—
224	#500	C₂×D₆₇	1	1	yes	characteristic
225	#494	—	67	1	no	—
226	#487	—	67	2	no	—
227	#479	—	134	2	no	—
228	#479	—	134	2	no	—
229	#477	—	67	2	no	—
230	#477	C₂×D₆₇	1	2	yes	—
231	#475	—	67	2	no	—
232	#475	—	67	2	no	—
233	#467	—	134	1	no	—
234	#467	—	134	1	no	—
235	C₈×Q₈	—	67	1	no	—
236	C₈×Q₈	—	67	1	no	—
237	C₈×Q₈	—	67	1	no	—
238	C₈×Q₈	—	134	1	no	—
239	C₈×Q₈	—	134	1	no	—
240	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
241	C₄×Q₁₆	—	134	1	no	—
242	C₄×Q₁₆	—	134	1	no	—
243	#428	—	134	2	no	—
244	#423	—	67	2	no	—
245	C₂×C₄⋊C₈	—	67	1	no	—
246	C₂×C₄⋊C₈	—	134	1	no	—
247	#419	—	134	2	no	—
248	C₂×C₄×C₈	—	67	1	no	—
249	C₂×C₄×C₈	—	134	1	no	—
250	#335	—	67	2	no	—
251	#335	—	67	1	no	—
252	#335	C₂×D₆₇	1	1	yes	characteristic
253	#333	—	67	2	no	—
254	#333	C₂×D₆₇	1	2	yes	—
255	#332	—	67	2	no	—
256	#332	—	67	2	no	—
257	C₂²×Q₈	—	67	1	no	—
258	C₂×Q₁₆	—	134	1	no	—
259	C₂×Q₁₆	—	134	1	no	—
260	C₂×M₁₆	—	134	2	no	—
261	C₂²×C₈	—	67	1	no	—
262	C₂²×C₈	—	67	1	no	—
263	C₂²×C₈	—	134	1	no	—
264	C₄⋊Q₈	—	67	2	no	—
265	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
266	#125	—	134	2	no	—
267	C₂²⋊Q₈	—	134	2	no	—
268	C₂²⋊Q₈	—	134	2	no	—
269	C₄×Q₈	—	67	1	no	—
270	C₄×Q₈	—	67	1	no	—
271	C₄×Q₈	—	67	1	no	—
272	C₄×Q₈	—	134	1	no	—
273	C₄×Q₈	—	134	2	no	—
274	C₄×Q₈	—	134	2	no	—
275	C₄×Q₈	—	134	1	no	—
276	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
277	#117	—	134	2	no	—
278	C₂×C₄⋊C₄	—	67	1	no	—
279	C₂×C₄⋊C₄	—	134	1	no	—
280	C₂×C₄²	—	67	1	no	—
281	C₂×C₄²	—	134	1	no	—
282	#107	—	2	1	no	—
283	#107	—	2	1	no	—
284	#107	—	2	2	no	—
285	#107	—	134	2	no	—
286	#106	—	134	2	no	—
287	#106	—	134	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	67	1	no	—
290	C₄⋊C₈	—	67	2	no	—
291	C₄⋊C₈	—	134	1	no	—
292	C₄⋊C₈	—	134	1	no	—
293	C₄⋊C₈	—	134	2	no	—
294	C₄⋊C₈	—	134	1	no	—
295	C₄⋊C₈	—	134	1	no	—
296	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
298	#103	—	2	2	no	—
299	#103	—	134	2	no	—
300	#103	—	134	2	no	—
301	#103	—	134	2	no	—
302	#103	—	134	2	no	—
303	#103	—	134	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	—	67	1	no	—
306	C₄×C₈	—	67	1	no	—
307	C₄×C₈	—	67	1	no	—
308	C₄×C₈	—	134	1	no	—
309	C₄×C₈	—	134	1	no	—
310	C₄×C₈	—	134	1	no	—
311	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	67	4	no	—
314	C₂×Q₈	—	67	1	no	—
315	C₂×Q₈	—	134	1	no	—
316	C₂×Q₈	—	134	2	no	—
317	C₂×Q₈	—	134	2	no	—
318	C₂×Q₈	D₄×D₆₇	1	1	yes	characteristic
319	C₂²×C₄	—	67	1	no	—
320	C₂²×C₄	—	67	1	no	—
321	C₂²×C₄	—	67	1	no	—
322	C₂²×C₄	—	134	1	no	—
323	C₂²×C₄	—	134	1	no	—
324	Q₁₆	—	268	2	no	—
325	Q₁₆	—	268	2	no	—
326	M₁₆	—	268	4	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	268	1	no	—
330	C₂×C₈	—	268	2	no	—
331	C₂×C₈	—	67	1	no	—
332	C₂×C₈	—	67	1	no	—
333	C₂×C₈	—	134	1	no	—
334	C₂×C₈	—	134	2	no	—
335	C₂×C₈	—	134	2	no	—
336	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
337	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	268	2	no	—
342	C₄⋊C₄	—	268	2	no	—
343	C₄⋊C₄	—	67	1	no	—
344	C₄⋊C₄	—	134	1	no	—
345	C₄⋊C₄	—	134	1	no	—
346	C₄⋊C₄	—	134	1	no	—
347	C₄⋊C₄	—	134	2	no	—
348	C₄⋊C₄	—	134	2	no	—
349	C₄⋊C₄	—	134	1	no	—
350	C₄⋊C₄	D₄×D₆₇	1	1	yes	characteristic
351	C₂²⋊C₄	—	268	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	268	2	no	—
354	C₄²	—	67	1	no	—
355	C₄²	—	67	1	no	—
356	C₄²	—	67	1	no	—
357	C₄²	—	134	1	no	—
358	C₄²	—	134	1	no	—
359	C₄²	—	134	1	no	—
360	C₄²	C₂³×D₆₇	1	1	yes	characteristic
361	C₂³	—	67	1	no	—
362	Q₈	—	2	1	no	—
363	Q₈	—	8	2	no	—
364	Q₈	—	268	2	no	—
365	Q₈	—	268	2	no	—
366	Q₈	—	67	2	no	—
367	Q₈	—	134	4	no	—
368	Q₈	—	134	1	no	—
369	Q₈	Q₁₆×D₆₇	1	2	yes	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	268	1	no	—
374	C₂×C₄	—	268	2	no	—
375	C₂×C₄	—	268	2	no	—
376	C₂×C₄	—	67	1	no	—
377	C₂×C₄	—	67	2	no	—
378	C₂×C₄	—	67	2	no	—
379	C₂×C₄	—	67	1	no	—
380	C₂×C₄	—	67	1	no	—
381	C₂×C₄	—	134	4	no	—
382	C₂×C₄	—	134	1	no	—
383	C₂×C₄	—	134	1	no	—
384	C₂×C₄	—	134	1	no	—
385	C₂×C₄	—	134	1	no	—
386	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
387	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
388	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
389	C₈	—	2	1	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	268	2	no	—
393	C₈	—	268	1	no	—
394	C₈	—	134	1	no	—
395	C₈	—	134	1	no	—
396	C₈	#14524075	1	2	yes	—
397	C₂²	—	67	2	no	—
398	C₂²	—	134	1	no	—
399	C₂²	—	134	1	no	—
400	C₂²	#121×D₆₇	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	8	2	no	—
405	C₄	—	268	1	no	—
406	C₄	—	536	2	no	—
407	C₄	—	67	2	no	—
408	C₄	—	134	2	no	—
409	C₄	—	134	1	no	—
410	C₄	—	134	1	no	—
411	C₄	C₂×Q₁₆×D₆₇	1	1	yes	characteristic
412	C₄	#135×D₆₇	1	1	yes	characteristic
413	C₄	C₂×#14524075	1	1	yes	characteristic
414	C₄	#16864195	1	1	yes	characteristic
415	C₂	—	134	2	no	—
416	C₂	#22569682	1	1	yes	characteristic
417	C₂	#467×D₆₇	1	1	yes	characteristic
418	C₂	#22569927	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₆₇
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#1676	C₂
socle	C₂²×C₆₇	C₂×#121
prime radical	C₂²×D₆₇	#121
hypercenter	#1676	D₆₇
hypocenter	C₆₇	#19262
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1676

Complements

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

N	H ≅ G/N	type
4. #22559670	C₂	semidirect
5. #22559669	C₂	semidirect
6. #22559610	C₂	semidirect
7. #22559580	C₂	semidirect
8. #22559579	C₂	semidirect
11. C₆₇×#1676	C₂	semidirect
106. Q₈×D₆₇	Q₁₆	semidirect
216. #1676	D₆₇	semidirect
221. C₆₇	#19262	semidirect

Maximal subgroups

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

subgroup	index
#22570796	2
#22570015	2
C₈×Q₈×D₆₇	2
#22559670	2
#22559669	2
#22559610	2
#22559580	2
#22559579	2
#22558966	2
#22558896	2
C₆₇×#1676	2
#19262	67