Subgroups — #26216860

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689078	C₂	1	1	yes	maximal, characteristic
2	#20245995	C₂	1	2	yes	maximal
3	#20243555	C₂	1	2	yes	maximal, complemented
4	#20243517	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243514	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243419	C₂	1	2	yes	maximal
7	#20243413	C₂	1	1	yes	maximal, characteristic
8	#20243287	C₂	1	2	yes	maximal, complemented
9	#20243280	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243276	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1808	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂×#13093983	C₂²	1	1	yes	characteristic
14	C₂×#13093957	C₂²	1	2	yes	—
15	C₂×#13093956	C₂²	1	2	yes	—
16	C₂×#13093955	C₂²	1	2	yes	—
17	#15689078	C₄	1	8	yes	complemented
18	C₂×#13093934	C₂²	1	1	yes	characteristic
19	C₂×#13093934	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
22	#15689017	—	2	2	no	—
23	#15689011	—	2	2	no	—
24	#15689008	—	2	2	no	—
25	#15689006	—	2	2	no	—
26	#15688992	C₂²	1	2	yes	—
27	#15688988	C₂²	1	2	yes	—
28	#15688983	C₂²	1	2	yes	—
29	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	#15688886	C₂²	1	1	yes	characteristic
32	#15688886	C₂²	1	1	yes	characteristic
33	#15688885	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₇	C₂²	1	2	yes	—
37	C₄₇×#380	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	1	yes	characteristic
39	C₄₇×#340	C₂²	1	1	yes	characteristic
40	C₂×#10625329	—	2	4	no	—
41	C₂×#10625329	C₂×C₄	1	4	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	#13093983	C₂×C₄	1	4	yes	—
45	#13093983	Q₈	1	4	yes	—
46	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×Dic₄₇⋊C₄	—	2	2	no	—
51	C₂×Dic₄₇⋊C₄	—	2	2	no	—
52	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
53	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	#13093957	—	2	4	no	—
60	#13093956	—	2	4	no	—
61	#13093955	—	2	4	no	—
62	#13093934	C₂×C₄	1	4	yes	—
63	#13093934	C₂×C₄	1	4	yes	—
64	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
65	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₄₇⋊#95	—	2	2	no	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	—	2	4	no	—
73	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
79	#107×C₄₇	—	2	4	no	—
80	#95×C₄₇	—	2	2	no	—
81	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₇	—	2	2	no	—
91	C₂²×Dic₄₇	—	2	2	no	—
92	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	2	8	no	—
98	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₄₇	#41	1	4	yes	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	2	no	—
105	C₂²⋊C₄×C₄₇	—	8	2	no	—
106	C₂²⋊Dic₄₇	—	8	2	no	—
107	C₂²⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
108	C₂²⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
109	C₄⋊Dic₄₇	—	2	2	no	—
110	C₄⋊Dic₄₇	—	2	2	no	—
111	C₄⋊Dic₄₇	—	2	2	no	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
114	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
115	Dic₄₇⋊C₄	—	8	2	no	—
116	Dic₄₇⋊C₄	—	8	2	no	—
117	C₄×Dic₄₇	—	8	2	no	—
118	C₄×Dic₄₇	—	8	2	no	—
119	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
120	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
121	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
122	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
123	#10625329	—	2	8	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
127	C₂×C₄₇⋊C₈	#41	1	4	yes	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	1	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	1	no	—
132	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
133	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	4	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	2	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	2	yes	—
148	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
149	C₂×Dic₄₇	—	2	1	no	—
150	C₂×Dic₄₇	—	2	1	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	1	no	—
154	C₂×Dic₄₇	—	2	1	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	2	yes	—
162	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
165	C₈×C₄₇	—	2	2	no	—
166	C₈×C₄₇	#117	1	4	yes	—
167	C₄₇⋊C₈	—	2	2	no	—
168	C₄₇⋊C₈	#117	1	4	yes	—
169	#20822	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	—	2	2	no	—
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	4	2	no	—
174	C₂²×C₄₇	—	4	2	no	—
175	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₄₇	#532	1	2	yes	—
177	C₂²×C₄₇	#576	1	1	yes	characteristic
178	C₂²×C₄₇	#577	1	2	yes	—
179	C₂²×C₄₇	#578	1	1	yes	characteristic
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	8	2	no	—
182	C₄×C₄₇	—	8	2	no	—
183	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
184	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
185	C₄×C₄₇	#533	1	2	yes	—
186	Dic₄₇	—	2	2	no	—
187	Dic₄₇	—	2	2	no	—
188	Dic₄₇	—	2	2	no	—
189	Dic₄₇	—	2	2	no	—
190	Dic₄₇	—	8	2	no	—
191	Dic₄₇	—	8	2	no	—
192	C₂×#405	—	47	1	no	—
193	#2314	—	47	2	no	—
194	#1847	—	47	2	no	—
195	#1835	—	47	1	no	—
196	#1834	—	47	1	no	—
197	#1809	—	47	2	no	—
198	#1808	D₄₇	1	1	yes	characteristic
199	#1807	—	47	1	no	—
200	#1776	—	47	2	no	—
201	C₄×#107	—	47	1	no	—
202	C₄×#106	—	47	1	no	—
203	C₂×C₄₇	—	4	2	no	—
204	C₂×C₄₇	#2285	1	1	yes	characteristic
205	C₂×C₄₇	#2912	1	1	yes	characteristic
206	C₂×C₄₇	#2913	1	1	yes	characteristic
207	C₂×C₄₇	#3178	1	2	yes	—
208	C₂×C₄₇	#3179	1	2	yes	—
209	C₂²×M₁₆	—	47	1	no	—
210	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
211	C₂×#117	—	47	1	no	—
212	C₂×#107	—	47	2	no	—
213	C₂×#107	C₂×D₄₇	1	2	yes	—
214	C₂×#106	—	47	2	no	—
215	C₂×#106	—	47	2	no	—
216	#405	—	47	8	no	—
217	C₂×#97	—	47	1	no	—
218	C₂×#97	—	47	1	no	—
219	C₂×C₄×C₈	—	47	1	no	—
220	C₂×C₄×C₈	—	47	1	no	—
221	#388	—	94	2	no	—
222	#388	—	94	2	no	—
223	#387	—	94	2	no	—
224	#387	—	94	2	no	—
225	#384	—	47	2	no	—
226	#382	—	47	2	no	—
227	#380	—	47	2	no	—
228	#380	C₂×D₄₇	1	2	yes	—
229	C₄×C₄⋊C₄	—	47	2	no	—
230	C₄×C₄⋊C₄	—	47	2	no	—
231	#340	—	47	1	no	—
232	#340	—	47	1	no	—
233	#340	—	47	2	no	—
234	#340	—	47	2	no	—
235	#340	C₂×D₄₇	1	1	yes	characteristic
236	#340	C₂×D₄₇	1	1	yes	characteristic
237	C₄₇	#20822	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₂×M₁₆	—	47	4	no	—
240	C₂×M₁₆	—	94	4	no	—
241	C₂²×C₈	—	2	4	no	—
242	C₂²×C₈	—	47	1	no	—
243	C₂²×C₈	—	47	1	no	—
244	C₂²×C₈	C₄×D₄₇	1	4	yes	—
245	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
246	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
247	#117	—	47	4	no	—
248	#117	—	47	4	no	—
249	C₂×C₄⋊C₄	—	47	1	no	—
250	C₂×C₄⋊C₄	—	47	1	no	—
251	C₂×C₄⋊C₄	—	47	2	no	—
252	C₂×C₄⋊C₄	—	47	2	no	—
253	C₂×C₄⋊C₄	—	94	2	no	—
254	C₂×C₄⋊C₄	—	94	2	no	—
255	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
256	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	47	1	no	—
259	C₂×C₂²⋊C₄	—	47	1	no	—
260	C₂×C₂²⋊C₄	—	94	2	no	—
261	C₂×C₄²	—	47	1	no	—
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	94	2	no	—
264	C₂×C₄²	—	94	2	no	—
265	#107	—	2	4	no	—
266	#107	—	94	4	no	—
267	#106	—	94	4	no	—
268	#106	—	94	4	no	—
269	#97	—	47	4	no	—
270	#97	—	47	4	no	—
271	C₄×C₈	—	47	4	no	—
272	C₄×C₈	—	47	4	no	—
273	#95	—	2	2	no	—
274	#95	—	94	2	no	—
275	#95	—	94	2	no	—
276	#95	—	94	2	no	—
277	#95	—	94	2	no	—
278	#95	—	94	2	no	—
279	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	47	1	no	—
285	C₂²×C₄	—	47	1	no	—
286	C₂²×C₄	—	47	1	no	—
287	C₂²×C₄	—	47	1	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
291	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
293	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
294	M₁₆	—	94	8	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	—	47	2	no	—
298	C₂×C₈	—	47	4	no	—
299	C₂×C₈	—	47	2	no	—
300	C₂×C₈	—	94	2	no	—
301	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
302	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
303	C₂×C₈	#10625352	1	4	yes	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	47	4	no	—
309	C₄⋊C₄	—	47	4	no	—
310	C₄⋊C₄	—	94	2	no	—
311	C₄⋊C₄	—	94	2	no	—
312	C₄⋊C₄	—	94	2	no	—
313	C₄⋊C₄	—	94	2	no	—
314	C₄⋊C₄	—	376	2	no	—
315	C₄⋊C₄	—	376	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	—	47	4	no	—
318	C₂²⋊C₄	—	47	4	no	—
319	C₂²⋊C₄	—	376	2	no	—
320	C₄²	—	47	2	no	—
321	C₄²	—	47	2	no	—
322	C₄²	—	47	2	no	—
323	C₄²	—	47	2	no	—
324	C₄²	—	376	2	no	—
325	C₄²	—	376	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	1	no	—
330	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
331	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	4	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	—	47	2	no	—
343	C₂×C₄	—	47	2	no	—
344	C₂×C₄	—	47	2	no	—
345	C₂×C₄	—	47	2	no	—
346	C₂×C₄	—	94	1	no	—
347	C₂×C₄	—	94	1	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	94	1	no	—
351	C₂×C₄	—	94	1	no	—
352	C₂×C₄	—	188	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	C₄⋊C₄×D₄₇	1	2	yes	—
359	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
361	C₂×C₄	#41×D₄₇	1	2	yes	—
362	C₂×C₄	C₂×#10625352	1	2	yes	—
363	C₈	—	2	2	no	—
364	C₈	—	47	4	no	—
365	C₈	—	94	2	no	—
366	C₈	#13093980	1	4	yes	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
373	C₂²	#15689668	1	2	yes	—
374	C₂²	#15689924	1	1	yes	characteristic
375	C₂²	#15689930	1	2	yes	—
376	C₂²	#15689936	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	—	94	2	no	—
381	C₄	—	94	2	no	—
382	C₄	—	94	2	no	—
383	C₄	—	94	2	no	—
384	C₄	—	376	2	no	—
385	C₄	—	376	2	no	—
386	C₄	#117×D₄₇	1	1	yes	characteristic
387	C₄	C₂×#13093980	1	1	yes	characteristic
388	C₄	#15689675	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	#20245790	1	1	yes	characteristic
391	C₂	#20251980	1	1	yes	characteristic
392	C₂	#20251984	1	1	yes	characteristic
393	C₂	#20254059	1	2	yes	—
394	C₂	#20254074	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1808	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1808	D₄₇
hypocenter	C₄₇	#20822
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #1808

Complements

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

N	H ≅ G/N	type
3. #20243555	C₂	semidirect
4. #20243517	C₂	semidirect
5. #20243514	C₂	semidirect
8. #20243287	C₂	semidirect
9. #20243280	C₂	semidirect
10. #20243276	C₂	semidirect
17. #15689078	C₄	semidirect
237. C₄₇	#20822	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689078	2
#20245995	2
#20243555	2
#20243517	2
#20243514	2
#20243419	2
#20243413	2
#20243287	2
#20243280	2
#20243276	2
C₄₇×#1808	2
#20822	47