Subgroups — #34257757

Order 20224.

714 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772507	C₂	1	2	yes	maximal, complemented
2	C₄×#14579180	C₂	1	1	yes	maximal, characteristic
3	#23762224	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762220	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762218	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762203	C₂	1	2	yes	maximal, complemented
7	C₈×#11929612	C₂	1	2	yes	maximal, complemented
8	#334×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761784	C₂	1	2	yes	maximal, complemented
10	#23761685	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579180	C₄	1	1	yes	characteristic
13	C₄×#11929623	C₂²	1	2	yes	—
14	C₈×Dic₁₅₈	C₂²	1	2	yes	—
15	#19098687	C₂²	1	2	yes	—
16	C₄×Dic₃₁₆	C₂²	1	1	yes	characteristic
17	#19098657	C₄	1	1	yes	characteristic
18	#19098654	C₄	1	2	yes	—
19	C₄×#11929612	C₂²	1	2	yes	—
20	D₈×Dic₇₉	C₄	1	1	yes	characteristic
21	D₄×C₇₉⋊C₈	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₇₉	—	2	2	no	—
23	(C₂²⋊D₇₉)⋊C₈	—	2	2	no	—
24	#19098614	C₂²	1	1	yes	characteristic
25	#19098614	C₂²	1	1	yes	characteristic
26	#19098613	—	2	2	no	—
27	#19098600	C₄	1	1	yes	characteristic
28	C₂×Dic₇₉⋊C₈	—	2	2	no	—
29	C₄⋊C₈×D₇₉	C₂²	1	2	yes	—
30	#19098556	C₄	1	2	yes	—
31	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
32	#19098314	C₂²	1	1	yes	characteristic
33	#19098313	C₂²	1	2	yes	—
34	#19098295	C₂²	1	2	yes	—
35	#19098293	C₂²	1	2	yes	—
36	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
37	#19098284	C₂²	1	1	yes	characteristic
38	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
39	C₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₇₉	C₂²	1	2	yes	—
42	#334×C₇₉	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
44	#322×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×#11929623	C₂×C₄	1	2	yes	—
46	#14579180	C₈	1	8	yes	complemented
47	C₂×Dic₃₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#11929612	C₂×C₄	1	2	yes	—
49	C₂²×C₇₉⋊C₈	—	2	2	no	—
50	C₂×C₈×D₇₉	—	2	2	no	—
51	C₂×C₈×D₇₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₇₉	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₁₅₈	C₂³	1	2	yes	—
54	#14579126	C₂×C₄	1	2	yes	—
55	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
56	C₄×C₂²⋊D₇₉	—	2	2	no	—
57	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
58	#14579119	C₂×C₄	1	2	yes	—
59	#14579117	—	2	2	no	—
60	C₂×C₄×Dic₇₉	—	2	2	no	—
61	C₄²×D₇₉	C₂³	1	1	yes	characteristic
62	#14579095	C₂×C₄	1	1	yes	characteristic
63	#14579092	C₂×C₄	1	2	yes	—
64	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
65	Dic₇₉⋊C₈	—	2	2	no	—
66	Dic₇₉⋊C₈	—	2	2	no	—
67	Dic₇₉⋊C₈	—	2	2	no	—
68	Dic₇₉⋊C₈	—	2	1	no	—
69	Dic₇₉⋊C₈	D₄	1	2	yes	—
70	#14579086	C₂×C₄	1	2	yes	—
71	#14579084	C₂×C₄	1	2	yes	—
72	#14579082	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
74	(C₂×D₇₉)⋊C₈	—	2	1	no	—
75	(C₂×D₇₉)⋊C₈	D₄	1	2	yes	—
76	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
79	C₈×Dic₇₉	—	2	2	no	—
80	C₈×Dic₇₉	—	2	2	no	—
81	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
83	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₇₉	—	2	2	no	—
85	C₄×D₄×C₇₉	C₂³	1	2	yes	—
86	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
88	#102×C₇₉	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₇₉	—	2	2	no	—
90	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
93	#11929623	—	2	4	no	—
94	#11929623	C₂×C₈	1	8	yes	complemented
95	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
96	C₂×C₂²⋊D₇₉	—	2	2	no	—
97	C₂²×Dic₇₉	—	2	2	no	—
98	C₂²×Dic₇₉	—	2	2	no	—
99	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₇₉	#41	1	1	yes	characteristic
102	Dic₃₁₆	C₂×C₈	1	4	yes	complemented
103	#11929612	C₂×C₈	1	8	yes	complemented
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	—	2	1	no	—
106	C₂×C₇₉⋊C₈	—	8	2	no	—
107	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
110	C₈×D₇₉	—	2	2	no	—
111	C₈×D₇₉	—	8	2	no	—
112	C₈×D₇₉	C₂×C₈	1	4	yes	complemented
113	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
114	Dic₇₉⋊C₄	—	2	2	no	—
115	Dic₇₉⋊C₄	—	2	2	no	—
116	C₂²⋊Dic₇₉	—	2	2	no	—
117	(C₂×D₇₉)⋊C₄	—	2	2	no	—
118	C₄×Dic₇₉	—	2	2	no	—
119	C₄×Dic₇₉	—	2	2	no	—
120	C₄×Dic₇₉	—	2	2	no	—
121	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
123	C₄×Dic₇₉	#41	1	1	yes	characteristic
124	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇₉	—	2	2	no	—
126	D₈×C₇₉	C₂×C₈	1	4	yes	complemented
127	C₂×C₈×C₇₉	—	2	2	no	—
128	C₂×C₈×C₇₉	—	2	1	no	—
129	C₂×C₈×C₇₉	—	8	2	no	—
130	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
134	C₂²⋊C₄×C₇₉	—	2	2	no	—
135	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
136	C₂³×C₇₉	—	2	2	no	—
137	C₂²×D₇₉	C₄×D₄	1	1	yes	characteristic
138	D₄×C₇₉	—	2	2	no	—
139	D₄×C₇₉	C₂²×C₈	1	4	yes	—
140	C₂×C₄×C₇₉	—	2	2	no	—
141	C₂×C₄×C₇₉	—	4	2	no	—
142	C₂×C₄×C₇₉	—	4	2	no	—
143	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
146	C₂²⋊D₇₉	—	2	8	no	—
147	C₂×Dic₇₉	—	2	2	no	—
148	C₂×Dic₇₉	—	2	8	no	—
149	C₂×Dic₇₉	—	2	2	no	—
150	C₂×Dic₇₉	—	8	2	no	—
151	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
154	C₄×D₇₉	—	2	2	no	—
155	C₄×D₇₉	—	4	1	no	—
156	C₄×D₇₉	C₂²×C₈	1	2	yes	—
157	C₄×D₇₉	#131	1	2	yes	—
158	Dic₁₅₈	—	2	2	no	—
159	Dic₁₅₈	C₂²×C₈	1	4	yes	—
160	C₈×C₇₉	—	2	1	no	—
161	C₈×C₇₉	—	2	2	no	—
162	C₈×C₇₉	—	4	1	no	—
163	C₈×C₇₉	—	4	2	no	—
164	C₈×C₇₉	C₂²×C₈	1	2	yes	—
165	C₇₉⋊C₈	—	2	1	no	—
166	C₇₉⋊C₈	—	2	2	no	—
167	C₇₉⋊C₈	—	4	1	no	—
168	C₇₉⋊C₈	—	4	2	no	—
169	C₇₉⋊C₈	C₂²×C₈	1	2	yes	—
170	C₂²×C₇₉	—	2	4	no	—
171	C₂²×C₇₉	—	4	2	no	—
172	C₂²×C₇₉	—	4	2	no	—
173	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
174	C₂×D₇₉	—	2	1	no	—
175	C₂×D₇₉	—	2	1	no	—
176	C₂×D₇₉	C₈×D₄	1	2	yes	—
177	C₄×C₇₉	—	2	1	no	—
178	C₄×C₇₉	—	4	2	no	—
179	C₄×C₇₉	C₂³×C₈	1	1	yes	characteristic
180	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
181	C₄×C₇₉	#577	1	2	yes	—
182	Dic₇₉	—	2	4	no	—
183	Dic₇₉	—	2	1	no	—
184	Dic₇₉	—	2	1	no	—
185	Dic₇₉	—	4	2	no	—
186	Dic₇₉	C₈×D₄	1	2	yes	—
187	#17858	—	79	1	no	maximal, Sylow
188	C₂×C₇₉	—	4	4	no	—
189	C₂×C₇₉	C₂×C₈×D₄	1	1	yes	characteristic
190	C₂×C₇₉	#2952	1	1	yes	characteristic
191	C₂×C₇₉	#2957	1	1	yes	characteristic
192	D₇₉	—	2	2	no	—
193	#2988	—	79	2	no	—
194	C₄×#135	—	79	1	no	—
195	#1580	—	79	1	no	—
196	#1580	D₇₉	1	1	yes	characteristic, complemented
197	#1579	—	79	1	no	—
198	#1579	—	79	1	no	—
199	C₈×SD₁₆	—	79	2	no	—
200	C₈×SD₁₆	—	79	2	no	—
201	C₂×#334	—	79	1	no	—
202	#1477	—	79	2	no	—
203	#1450	—	79	1	no	—
204	C₇₉	#17858	1	1	yes	characteristic, complemented, Sylow
205	C₂×#135	—	79	1	no	—
206	C₄×#41	—	79	2	no	—
207	C₈×Q₈	—	79	2	no	—
208	C₈×Q₈	—	79	2	no	—
209	C₄×Q₁₆	—	79	1	no	—
210	C₄×Q₁₆	—	79	1	no	—
211	C₄×SD₁₆	—	79	2	no	—
212	C₄×SD₁₆	—	79	2	no	—
213	C₄×D₈	—	79	1	no	—
214	C₄×D₈	C₂×D₇₉	1	1	yes	characteristic
215	C₈×D₄	—	79	2	no	—
216	C₈×D₄	—	158	2	no	—
217	C₈×D₄	—	158	2	no	—
218	C₈×D₄	C₂×D₇₉	1	2	yes	—
219	#431	—	79	1	no	—
220	#431	—	79	1	no	—
221	#431	—	158	2	no	—
222	#427	—	79	1	no	—
223	C₂×C₄⋊C₈	—	79	2	no	—
224	C₂×C₄⋊C₈	—	158	2	no	—
225	#416	—	79	2	no	—
226	C₂×C₄×C₈	—	79	1	no	—
227	#334	—	79	2	no	—
228	#334	—	79	1	no	—
229	#334	C₂×D₇₉	1	1	yes	characteristic
230	Q₈⋊C₈	—	79	2	no	—
231	Q₈⋊C₈	—	79	2	no	—
232	D₄⋊C₈	—	79	2	no	—
233	D₄⋊C₈	C₂×D₇₉	1	2	yes	—
234	#322	—	79	1	no	—
235	#322	C₂×D₇₉	1	1	yes	characteristic
236	C₈²	—	79	1	no	—
237	C₈²	—	79	1	no	—
238	C₂×#41	—	79	2	no	—
239	#135	—	79	8	no	—
240	C₂×Q₁₆	—	79	1	no	—
241	C₂×SD₁₆	—	79	2	no	—
242	C₂×D₈	C₄×D₇₉	1	1	yes	characteristic
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	79	1	no	—
245	C₂²×C₈	—	79	1	no	—
246	C₂²×C₈	—	158	2	no	—
247	C₂²×C₈	—	158	2	no	—
248	C₄×Q₈	—	79	2	no	—
249	C₄×Q₈	—	79	2	no	—
250	C₄×D₄	—	79	2	no	—
251	C₄×D₄	—	158	2	no	—
252	C₄×D₄	—	158	2	no	—
253	C₄×D₄	C₂²×D₇₉	1	2	yes	—
254	#117	—	79	2	no	—
255	#117	—	158	2	no	—
256	C₂×C₄²	—	79	1	no	—
257	C₂×C₄²	—	158	2	no	—
258	#107	—	79	1	no	—
259	#107	C₄×D₇₉	1	1	yes	characteristic
260	#106	—	79	2	no	—
261	C₄⋊C₈	—	79	2	no	—
262	C₄⋊C₈	—	79	2	no	—
263	C₄⋊C₈	—	158	2	no	—
264	C₄⋊C₈	—	158	1	no	—
265	C₄⋊C₈	—	158	2	no	—
266	C₄⋊C₈	—	158	2	no	—
267	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
268	#103	—	79	2	no	—
269	#103	—	79	2	no	—
270	#102	—	79	2	no	—
271	#102	C₄×D₇₉	1	2	yes	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	79	2	no	—
274	C₂²⋊C₈	—	158	1	no	—
275	C₂²⋊C₈	—	158	2	no	—
276	C₄×C₈	—	79	1	no	—
277	C₄×C₈	—	79	1	no	—
278	C₄×C₈	—	79	1	no	—
279	C₄×C₈	—	79	1	no	—
280	C₄×C₈	—	79	1	no	—
281	C₄×C₈	—	158	2	no	—
282	C₄×C₈	—	158	2	no	—
283	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
285	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
286	#41	—	79	8	no	—
287	#41	—	158	4	no	—
288	C₂×Q₈	—	79	2	no	—
289	C₂×D₄	—	158	2	no	—
290	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	79	1	no	—
293	C₂²×C₄	—	79	1	no	—
294	C₂²×C₄	—	79	1	no	—
295	C₂²×C₄	—	158	2	no	—
296	C₂²×C₄	—	158	2	no	—
297	Q₁₆	—	79	4	no	—
298	SD₁₆	—	79	8	no	—
299	D₈	C₈×D₇₉	1	4	yes	complemented
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	8	2	no	—
303	C₂×C₈	—	79	1	no	—
304	C₂×C₈	—	79	4	no	—
305	C₂×C₈	—	79	1	no	—
306	C₂×C₈	—	79	2	no	—
307	C₂×C₈	—	632	2	no	—
308	C₂×C₈	—	632	2	no	—
309	C₂×C₈	—	158	2	no	—
310	C₂×C₈	—	158	1	no	—
311	C₂×C₈	—	158	2	no	—
312	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
313	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
314	C₂×C₈	D₄×D₇₉	1	2	yes	—
315	C₄⋊C₄	—	79	2	no	—
316	C₄⋊C₄	—	158	2	no	—
317	C₄⋊C₄	—	158	2	no	—
318	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	158	2	no	—
321	C₂²⋊C₄	—	158	2	no	—
322	C₄²	—	79	1	no	—
323	C₄²	—	79	1	no	—
324	C₄²	—	79	1	no	—
325	C₄²	—	158	2	no	—
326	C₄²	—	158	2	no	—
327	C₄²	—	158	2	no	—
328	C₄²	C₂³×D₇₉	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	—	79	1	no	—
331	Q₈	—	79	4	no	—
332	Q₈	—	158	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	158	8	no	—
335	D₄	C₂×C₈×D₇₉	1	4	yes	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	316	1	no	—
340	C₂×C₄	—	79	1	no	—
341	C₂×C₄	—	79	2	no	—
342	C₂×C₄	—	79	2	no	—
343	C₂×C₄	—	79	1	no	—
344	C₂×C₄	—	79	1	no	—
345	C₂×C₄	—	632	2	no	—
346	C₂×C₄	—	158	2	no	—
347	C₂×C₄	—	158	8	no	—
348	C₂×C₄	—	158	2	no	—
349	C₂×C₄	—	158	2	no	—
350	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
351	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
352	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
353	C₈	—	2	1	no	—
354	C₈	—	2	2	no	—
355	C₈	—	4	1	no	—
356	C₈	—	4	2	no	—
357	C₈	—	316	1	no	—
358	C₈	—	316	2	no	—
359	C₈	—	79	2	no	—
360	C₈	—	158	1	no	—
361	C₈	—	158	2	no	—
362	C₈	C₂×C₈×D₇₉	1	2	yes	—
363	C₂²	—	2	4	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	79	2	no	—
367	C₂²	—	158	1	no	—
368	C₂²	—	158	1	no	—
369	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	4	2	no	—
372	C₄	—	316	2	no	—
373	C₄	—	79	2	no	—
374	C₄	—	158	1	no	—
375	C₄	—	158	1	no	—
376	C₄	—	158	4	no	—
377	C₄	C₂²×C₈×D₇₉	1	1	yes	characteristic
378	C₄	#131×D₇₉	1	1	yes	characteristic
379	C₄	#19099373	1	2	yes	—
380	C₂	—	4	4	no	—
381	C₂	—	158	2	no	—
382	C₂	C₈×D₄×D₇₉	1	1	yes	characteristic
383	C₂	#23772282	1	1	yes	characteristic
384	C₂	#23772314	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₄×C₇₉	C₂³×C₈
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1580	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#14579180	C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1580	D₇₉
hypocenter	C₇₉	#17858
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1580

Complements

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

N	H ≅ G/N	type
1. #23772507	C₂	semidirect
3. #23762224	C₂	semidirect
4. #23762220	C₂	semidirect
5. #23762218	C₂	semidirect
6. #23762203	C₂	semidirect
7. C₈×#11929612	C₂	semidirect
8. #334×D₇₉	C₂	semidirect
9. #23761784	C₂	semidirect
10. #23761685	C₂	semidirect
11. C₇₉×#1580	C₂	semidirect
46. #14579180	C₈	semidirect
94. #11929623	C₂×C₈	semidirect
102. Dic₃₁₆	C₂×C₈	semidirect
103. #11929612	C₂×C₈	semidirect
112. C₈×D₇₉	C₂×C₈	semidirect
126. D₈×C₇₉	C₂×C₈	semidirect
196. #1580	D₇₉	semidirect
204. C₇₉	#17858	semidirect
299. D₈	C₈×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23772507	2
C₄×#14579180	2
#23762224	2
#23762220	2
#23762218	2
#23762203	2
C₈×#11929612	2
#334×D₇₉	2
#23761784	2
#23761685	2
C₇₉×#1580	2
#17858	79