Subgroups — #26216840

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689080	C₂	1	1	yes	maximal, characteristic
2	#20245998	C₂	1	1	yes	maximal, characteristic
3	#20245996	C₂	1	1	yes	maximal, characteristic
4	#20243550	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243544	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243522	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243420	C₂	1	2	yes	maximal
8	#20243412	C₂	1	2	yes	maximal
9	#20243284	C₂	1	2	yes	maximal, complemented
10	#20243276	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1836	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13093981	C₂²	1	1	yes	characteristic
15	C₂×#13093957	C₂²	1	2	yes	—
16	C₂×#13093955	C₂²	1	2	yes	—
17	C₂×#13093955	C₂²	1	2	yes	—
18	C₂×#13093955	C₂²	1	2	yes	—
19	#15689080	C₄	1	8	yes	complemented
20	C₂×#13093934	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	#15689015	—	2	2	no	—
24	#15689013	—	2	2	no	—
25	#15689010	—	2	2	no	—
26	#15689004	—	2	2	no	—
27	#15688993	C₂²	1	1	yes	characteristic
28	#15688989	C₂²	1	1	yes	characteristic
29	#15688980	C₂²	1	2	yes	—
30	#15688980	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
32	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
33	#15688886	C₂²	1	2	yes	—
34	#15688886	C₂²	1	2	yes	—
35	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#384	C₂²	1	1	yes	characteristic
37	C₄₇×#382	C₂²	1	1	yes	characteristic
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
41	C₂×#10625324	—	2	2	no	—
42	C₂×#10625324	—	2	2	no	—
43	C₂×#10625324	C₂×C₄	1	4	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂×C₈×D₄₇	—	2	2	no	—
47	C₂×C₈×D₄₇	—	2	2	no	—
48	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
49	#13093981	C₂×C₄	1	4	yes	—
50	#13093981	Q₈	1	4	yes	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
54	C₂×Dic₄₇⋊C₄	D₄	1	2	yes	—
55	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
56	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	—	2	2	no	—
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	#13093957	—	2	4	no	—
62	#13093955	—	2	4	no	—
63	#13093955	—	2	4	no	—
64	#13093955	—	2	4	no	—
65	#13093934	C₂×C₄	1	4	yes	—
66	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
67	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	#97×C₄₇	C₂×C₄	1	4	yes	—
80	#95×C₄₇	—	2	2	no	—
81	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
90	C₂×C₄×D₄₇	—	2	1	no	—
91	C₂×C₄×D₄₇	—	2	1	no	—
92	C₂×C₄×D₄₇	—	2	1	no	—
93	C₂×C₄×D₄₇	—	2	1	no	—
94	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
95	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
96	C₂×C₈×C₄₇	—	2	1	no	—
97	C₂×C₈×C₄₇	—	2	1	no	—
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	2	no	—
105	C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₄⋊C₄×C₄₇	—	8	2	no	—
107	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
108	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
109	(C₂×D₄₇)⋊C₄	—	8	2	no	—
110	(C₂×D₄₇)⋊C₄	—	8	2	no	—
111	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	8	yes	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	8	2	no	—
117	Dic₄₇⋊C₄	C₄⋊C₄	1	8	yes	—
118	C₄×Dic₄₇	—	8	2	no	—
119	C₄×Dic₄₇	—	8	2	no	—
120	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
121	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
122	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₄₇⋊C₈	#41	1	2	yes	—
125	C₂×C₄₇⋊C₈	#41	1	2	yes	—
126	C₂×C₄₇⋊C₈	#41	1	2	yes	—
127	C₂×C₄₇⋊C₈	#41	1	2	yes	—
128	#10625324	—	2	8	no	—
129	C₈×D₄₇	—	2	8	no	—
130	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
131	C₂²×D₄₇	—	2	1	no	—
132	C₂²×D₄₇	—	2	1	no	—
133	C₂²×D₄₇	—	2	2	no	—
134	C₂²×D₄₇	—	2	2	no	—
135	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×Dic₄₇	—	2	1	no	—
152	C₂×Dic₄₇	—	2	1	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
163	C₄×D₄₇	—	2	2	no	—
164	C₄×D₄₇	—	2	2	no	—
165	C₄×D₄₇	—	2	2	no	—
166	C₄×D₄₇	—	2	2	no	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	—	2	2	no	—
169	C₄₇⋊C₈	#117	1	4	yes	—
170	C₄₇⋊C₈	#117	1	4	yes	—
171	#20820	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₄₇	#532	1	1	yes	characteristic
174	C₂²×C₄₇	#532	1	1	yes	characteristic
175	C₂²×C₄₇	#577	1	2	yes	—
176	C₂²×C₄₇	#577	1	2	yes	—
177	C₂×D₄₇	—	2	4	no	—
178	C₂×D₄₇	—	2	2	no	—
179	C₂×D₄₇	—	4	2	no	—
180	C₂×D₄₇	—	4	1	no	—
181	C₂×D₄₇	—	4	1	no	—
182	C₄×C₄₇	—	2	4	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	—	8	2	no	—
185	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
186	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
187	C₄×C₄₇	#533	1	1	yes	characteristic
188	C₄×C₄₇	#533	1	1	yes	characteristic
189	Dic₄₇	—	2	4	no	—
190	Dic₄₇	—	2	2	no	—
191	Dic₄₇	—	8	2	no	—
192	Dic₄₇	—	8	2	no	—
193	C₂×#405	—	47	1	no	—
194	#2314	—	47	1	no	—
195	#2314	—	47	1	no	—
196	#1846	—	47	1	no	—
197	#1844	—	47	1	no	—
198	#1836	—	47	1	no	—
199	#1836	D₄₇	1	1	yes	characteristic, complemented
200	#1809	—	47	2	no	—
201	#1807	—	47	2	no	—
202	#1776	—	47	2	no	—
203	C₄×#106	—	47	2	no	—
204	C₂×C₄₇	#2285	1	1	yes	characteristic
205	C₂×C₄₇	#2912	1	2	yes	—
206	C₂×C₄₇	#3173	1	2	yes	—
207	C₂×C₄₇	#3174	1	1	yes	characteristic
208	C₂×C₄₇	#3174	1	1	yes	characteristic
209	D₄₇	—	4	2	no	—
210	C₂²×M₁₆	—	47	1	no	—
211	C₂³×C₈	—	47	1	no	—
212	C₂×#117	—	47	1	no	—
213	C₂×#107	—	47	2	no	—
214	C₂×#106	—	47	2	no	—
215	C₂×#106	—	47	2	no	—
216	C₂×#106	—	47	2	no	—
217	#405	—	47	8	no	—
218	C₂×#97	—	47	1	no	—
219	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄×C₈	—	47	1	no	—
221	C₂×C₄×C₈	—	47	1	no	—
222	#388	—	94	2	no	—
223	#388	—	94	2	no	—
224	#387	—	94	2	no	—
225	#387	—	94	2	no	—
226	#384	—	47	1	no	—
227	#384	C₂×D₄₇	1	1	yes	characteristic
228	#382	—	47	1	no	—
229	#382	C₂×D₄₇	1	1	yes	characteristic
230	#380	—	47	2	no	—
231	#380	—	47	2	no	—
232	C₄×C₄⋊C₄	—	47	2	no	—
233	C₄×C₄⋊C₄	—	47	2	no	—
234	#340	—	47	2	no	—
235	#340	—	47	2	no	—
236	#340	C₂×D₄₇	1	2	yes	—
237	#340	C₂×D₄₇	1	2	yes	—
238	C₄₇	#20820	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	—	47	1	no	—
240	C₂×M₁₆	—	47	4	no	—
241	C₂×M₁₆	—	94	2	no	—
242	C₂×M₁₆	—	94	2	no	—
243	C₂²×C₈	—	47	1	no	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	4	no	—
246	C₂²×C₈	—	94	2	no	—
247	C₂²×C₈	—	94	2	no	—
248	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
249	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
250	#117	—	47	4	no	—
251	#117	—	47	4	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	47	2	no	—
254	C₂×C₄⋊C₄	—	47	2	no	—
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	47	2	no	—
260	C₂×C₂²⋊C₄	—	94	2	no	—
261	C₂×C₂²⋊C₄	—	94	2	no	—
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	94	2	no	—
264	C₂×C₄²	—	94	2	no	—
265	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
266	#107	—	94	4	no	—
267	#106	—	94	4	no	—
268	#106	—	94	4	no	—
269	#106	—	94	4	no	—
270	#97	—	47	4	no	—
271	#97	C₄×D₄₇	1	4	yes	—
272	C₄×C₈	—	47	4	no	—
273	C₄×C₈	—	47	4	no	—
274	#95	—	2	2	no	—
275	#95	—	94	2	no	—
276	#95	—	94	2	no	—
277	#95	—	94	2	no	—
278	#95	—	94	2	no	—
279	#95	—	94	2	no	—
280	C₂⁴	—	47	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	47	1	no	—
284	C₂²×C₄	—	47	2	no	—
285	C₂²×C₄	—	47	2	no	—
286	C₂²×C₄	—	47	2	no	—
287	C₂²×C₄	—	94	1	no	—
288	C₂²×C₄	—	94	1	no	—
289	C₂²×C₄	—	94	1	no	—
290	C₂²×C₄	—	94	1	no	—
291	C₂²×C₄	—	94	2	no	—
292	C₂²×C₄	—	94	2	no	—
293	C₂²×C₄	D₄×D₄₇	1	2	yes	—
294	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
295	M₁₆	—	94	8	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	47	2	no	—
301	C₂×C₈	—	47	2	no	—
302	C₂×C₈	—	47	2	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	47	2	no	—
306	C₂×C₈	—	94	8	no	—
307	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
308	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	8	2	no	—
314	C₄⋊C₄	—	47	8	no	—
315	C₄⋊C₄	—	94	2	no	—
316	C₄⋊C₄	—	94	2	no	—
317	C₄⋊C₄	—	94	2	no	—
318	C₄⋊C₄	—	94	2	no	—
319	C₄⋊C₄	—	376	2	no	—
320	C₂²⋊C₄	—	47	8	no	—
321	C₂²⋊C₄	—	376	2	no	—
322	C₂²⋊C₄	—	376	2	no	—
323	C₄²	—	47	2	no	—
324	C₄²	—	47	2	no	—
325	C₄²	—	376	2	no	—
326	C₄²	—	376	2	no	—
327	C₄²	C₂×C₄×D₄₇	1	2	yes	—
328	C₄²	Q₈×D₄₇	1	2	yes	—
329	C₂³	—	47	2	no	—
330	C₂³	—	94	1	no	—
331	C₂³	—	94	1	no	—
332	C₂³	—	94	2	no	—
333	C₂³	—	94	2	no	—
334	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	47	4	no	—
344	C₂×C₄	—	47	2	no	—
345	C₂×C₄	—	94	1	no	—
346	C₂×C₄	—	94	1	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	94	2	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	188	2	no	—
354	C₂×C₄	—	188	2	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
360	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
362	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
363	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
364	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
365	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	47	4	no	—
369	C₈	—	47	4	no	—
370	C₂²	—	94	2	no	—
371	C₂²	—	94	4	no	—
372	C₂²	—	188	2	no	—
373	C₂²	—	188	1	no	—
374	C₂²	—	188	1	no	—
375	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
376	C₂²	#15689672	1	1	yes	characteristic
377	C₂²	#15689672	1	1	yes	characteristic
378	C₂²	#15689932	1	2	yes	—
379	C₂²	#15689933	1	2	yes	—
380	C₄	—	2	4	no	—
381	C₄	—	8	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	94	2	no	—
384	C₄	—	94	4	no	—
385	C₄	—	376	2	no	—
386	C₄	—	376	2	no	—
387	C₄	#117×D₄₇	1	1	yes	characteristic
388	C₄	#117×D₄₇	1	1	yes	characteristic
389	C₄	#15689679	1	1	yes	characteristic
390	C₄	#15689679	1	1	yes	characteristic
391	C₂	—	188	2	no	—
392	C₂	#20245794	1	1	yes	characteristic
393	C₂	#20251982	1	2	yes	—
394	C₂	#20254004	1	2	yes	—
395	C₂	#20254015	1	1	yes	characteristic
396	C₂	#20254019	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1836	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1836	D₄₇
hypocenter	C₄₇	#20820
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1836

Complements

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

N	H ≅ G/N	type
4. #20243550	C₂	semidirect
5. #20243544	C₂	semidirect
6. #20243522	C₂	semidirect
9. #20243284	C₂	semidirect
10. #20243276	C₂	semidirect
11. C₄₇×#1836	C₂	semidirect
19. #15689080	C₄	semidirect
199. #1836	D₄₇	semidirect
238. C₄₇	#20820	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689080	2
#20245998	2
#20245996	2
#20243550	2
#20243544	2
#20243522	2
#20243420	2
#20243412	2
#20243284	2
#20243276	2
C₄₇×#1836	2
#20820	47