Subgroups — #30675912

Order 16768.

418 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22553878	C₂	1	1	yes	maximal, characteristic
2	#22553793	C₂	1	1	yes	maximal, characteristic, complemented
3	#22553639	C₂	1	1	yes	maximal, characteristic, complemented
4	#22553637	C₂	1	1	yes	maximal, characteristic, complemented
5	#22553634	C₂	1	1	yes	maximal, characteristic, complemented
6	#22553633	C₂	1	1	yes	maximal, characteristic, complemented
7	#22553630	C₂	1	1	yes	maximal, characteristic, complemented
8	#22553629	C₂	1	1	yes	maximal, characteristic, complemented
9	#22553627	C₂	1	1	yes	maximal, characteristic, complemented
10	#22553353	C₂	1	1	yes	maximal, characteristic, complemented
11	#22553349	C₂	1	1	yes	maximal, characteristic, complemented
12	#22553315	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
14	#22553277	C₂	1	1	yes	maximal, characteristic, complemented
15	#480×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14523513	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₃₁	C₂²	1	1	yes	characteristic
18	C₂×#14523496	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₁₃₁	C₂²	1	1	yes	characteristic
20	#16862242	—	2	1	no	—
21	#16862232	—	2	1	no	—
22	#16862221	C₂²	1	1	yes	characteristic
23	#16862220	C₂²	1	1	yes	characteristic
24	#16862217	C₂²	1	1	yes	characteristic
25	#16862216	—	2	1	no	—
26	#16862214	—	2	1	no	—
27	#16862211	—	2	1	no	—
28	#16862208	—	2	1	no	—
29	C₄×C₂²⋊D₁₃₁	—	2	1	no	—
30	C₄×C₂²⋊D₁₃₁	—	2	1	no	—
31	#16862205	C₂²	1	1	yes	characteristic, complemented
32	#16862204	C₂²	1	1	yes	characteristic
33	#16862204	C₂²	1	1	yes	characteristic
34	#16862204	C₂²	1	1	yes	characteristic, complemented
35	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic
36	C₄⋊C₄×D₁₃₁	C₂²	1	1	yes	characteristic, complemented
37	#16862180	C₂²	1	1	yes	characteristic, complemented
38	#16862179	C₂²	1	1	yes	characteristic, complemented
39	#16862178	C₂²	1	1	yes	characteristic, complemented
40	#16862177	C₂²	1	1	yes	characteristic, complemented
41	#16862177	C₂²	1	1	yes	characteristic, complemented
42	#16862177	C₂²	1	1	yes	characteristic, complemented
43	#16862168	C₂²	1	1	yes	characteristic
44	#16862168	C₂²	1	1	yes	characteristic
45	#16862167	C₂²	1	1	yes	characteristic
46	#16862167	C₂²	1	1	yes	characteristic
47	#16862166	C₂²	1	1	yes	characteristic
48	#16862166	C₂²	1	1	yes	characteristic
49	C₂²⋊(C₁₃₁⋊C₈)	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₁₃₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₁₃₁)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	#121×C₁₃₁	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
54	#107×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
55	#107×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
56	#102×C₁₃₁	C₂²	1	1	yes	characteristic
57	#102×C₁₃₁	C₂²	1	1	yes	characteristic
58	C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₃₁	—	2	1	no	—
60	#14523513	—	2	2	no	—
61	#14523513	—	2	2	no	—
62	C₂×Dic₂₆₂	D₄	1	1	yes	characteristic
63	C₂×D₅₂₄	—	2	1	no	—
64	C₂×D₅₂₄	D₄	1	1	yes	characteristic
65	C₂×D₅₂₄	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₃₁	—	2	1	no	—
67	C₂×C₂²⋊D₁₃₁	—	2	1	no	—
68	C₂×C₂²⋊D₁₃₁	—	2	1	no	—
69	C₂×C₂²⋊D₁₃₁	D₄	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₃₁	D₄	1	1	yes	characteristic
71	D₄×D₁₃₁	—	2	2	no	—
72	D₄×D₁₃₁	—	2	2	no	—
73	C₂×C₄×D₁₃₁	—	2	1	no	—
74	C₂×C₄×D₁₃₁	—	2	1	no	—
75	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₄×D₁₃₁	C₂³	1	1	yes	characteristic
77	#14523496	—	2	2	no	—
78	C₂×C₁₃₁⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₁₃₁⋊C₈	C₂³	1	1	yes	characteristic
80	C₈×D₁₃₁	—	2	2	no	—
81	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
82	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
83	C₄⋊Dic₁₃₁	C₂³	1	1	yes	characteristic
84	Dic₁₃₁⋊C₄	—	2	1	no	—
85	Dic₁₃₁⋊C₄	—	2	1	no	—
86	C₂²⋊Dic₁₃₁	—	2	1	no	—
87	C₂²⋊Dic₁₃₁	—	2	1	no	—
88	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
89	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
90	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
91	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
92	(C₂×D₁₃₁)⋊C₄	—	2	1	no	—
93	C₄×Dic₁₃₁	—	2	1	no	—
94	C₄×Dic₁₃₁	—	2	1	no	—
95	C₄×Dic₁₃₁	—	2	1	no	—
96	C₄×Dic₁₃₁	—	2	1	no	—
97	C₂×D₄×C₁₃₁	—	2	1	no	—
98	C₂×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₃₁	—	2	1	no	—
100	C₂²×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
101	C₂×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
102	C₂×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
103	C₄⋊C₄×C₁₃₁	—	2	1	no	—
104	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
105	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
106	C₄⋊C₄×C₁₃₁	C₂³	1	1	yes	characteristic
107	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
108	C₂²×D₁₃₁	—	2	1	no	—
109	C₂²×D₁₃₁	—	4	2	no	—
110	C₂²×D₁₃₁	—	8	1	no	—
111	C₂²×D₁₃₁	—	8	1	no	—
112	C₂²×D₁₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×D₁₃₁	C₂×D₄	1	1	yes	characteristic
114	Dic₂₆₂	—	2	2	no	—
115	D₅₂₄	—	2	2	no	—
116	D₅₂₄	—	2	1	no	—
117	D₅₂₄	—	2	1	no	—
118	D₅₂₄	—	8	1	no	—
119	C₂²⋊D₁₃₁	—	2	2	no	—
120	C₂²⋊D₁₃₁	—	2	2	no	—
121	C₂²⋊D₁₃₁	—	4	2	no	—
122	C₂²⋊D₁₃₁	—	8	1	no	—
123	C₂²⋊D₁₃₁	—	8	1	no	—
124	C₂×Dic₁₃₁	—	2	1	no	—
125	C₂×Dic₁₃₁	—	2	1	no	—
126	C₂×Dic₁₃₁	—	2	1	no	—
127	C₂×Dic₁₃₁	C₂×D₄	1	1	yes	characteristic
128	C₂×Dic₁₃₁	C₂×D₄	1	1	yes	characteristic
129	C₄×D₁₃₁	—	2	1	no	—
130	C₄×D₁₃₁	—	2	1	no	—
131	C₄×D₁₃₁	—	8	1	no	—
132	C₄×D₁₃₁	—	8	1	no	—
133	C₄×D₁₃₁	#41	1	2	yes	—
134	C₄×D₁₃₁	#41	1	2	yes	—
135	C₁₃₁⋊C₈	—	2	1	no	—
136	C₁₃₁⋊C₈	—	2	1	no	—
137	C₂³×C₁₃₁	—	2	1	no	—
138	C₂³×C₁₃₁	C₂×D₄	1	1	yes	characteristic
139	D₄×C₁₃₁	—	2	1	no	—
140	D₄×C₁₃₁	—	2	1	no	—
141	D₄×C₁₃₁	—	8	1	no	—
142	C₂×C₄×C₁₃₁	—	2	1	no	—
143	C₂×C₄×C₁₃₁	—	2	1	no	—
144	C₂×C₄×C₁₃₁	—	2	1	no	—
145	C₂×C₄×C₁₃₁	—	2	1	no	—
146	C₂×C₄×C₁₃₁	—	2	1	no	—
147	C₂×C₄×C₁₃₁	—	8	1	no	—
148	C₂×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
150	C₈×C₁₃₁	—	2	1	no	—
151	C₈×C₁₃₁	—	2	1	no	—
152	C₂²×C₁₃₁	—	2	1	no	—
153	C₂²×C₁₃₁	—	2	1	no	—
154	C₂²×C₁₃₁	—	2	1	no	—
155	C₂²×C₁₃₁	—	4	1	no	—
156	C₂²×C₁₃₁	—	4	1	no	—
157	C₂²×C₁₃₁	—	4	1	no	—
158	C₂²×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×D₁₃₁	—	2	1	no	—
160	C₂×D₁₃₁	—	2	1	no	—
161	C₂×D₁₃₁	—	2	1	no	—
162	C₂×D₁₃₁	—	2	1	no	—
163	C₂×D₁₃₁	—	2	1	no	—
164	C₂×D₁₃₁	—	4	1	no	—
165	C₂×D₁₃₁	—	4	1	no	—
166	C₂×D₁₃₁	—	4	1	no	—
167	C₂×D₁₃₁	—	8	4	no	—
168	C₂×D₁₃₁	#123	1	2	yes	—
169	C₄×C₁₃₁	—	2	1	no	—
170	C₄×C₁₃₁	—	4	1	no	—
171	C₄×C₁₃₁	—	4	1	no	—
172	C₄×C₁₃₁	—	4	1	no	—
173	C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
174	C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
175	Dic₁₃₁	—	2	1	no	—
176	Dic₁₃₁	—	4	1	no	—
177	Dic₁₃₁	—	4	1	no	—
178	Dic₁₃₁	—	4	1	no	—
179	Dic₁₃₁	#123	1	2	yes	—
180	C₂×C₁₃₁	—	4	1	no	—
181	C₂×C₁₃₁	—	8	1	no	—
182	C₂×C₁₃₁	C₂×#123	1	1	yes	characteristic
183	C₂×C₁₃₁	#576	1	1	yes	characteristic
184	C₂×C₁₃₁	#577	1	1	yes	characteristic
185	D₁₃₁	—	2	2	no	—
186	D₁₃₁	—	4	1	no	—
187	D₁₃₁	—	8	1	no	—
188	C₁₃₁	#3096	1	1	yes	characteristic, complemented, Sylow
189	#3096	—	131	1	no	maximal, Sylow
190	#535	—	131	1	no	—
191	#520	—	131	1	no	—
192	#482	—	131	1	no	—
193	#482	—	131	1	no	—
194	#482	—	131	1	no	—
195	#482	—	131	1	no	—
196	#481	—	131	1	no	—
197	#481	—	131	1	no	—
198	#480	—	131	1	no	—
199	#480	D₁₃₁	1	1	yes	characteristic, complemented
200	#428	—	131	1	no	—
201	#427	—	131	1	no	—
202	#418	—	131	1	no	—
203	C₂×#102	—	131	1	no	—
204	#408	—	131	1	no	—
205	C₂×#41	—	131	1	no	—
206	C₂²×D₄	—	131	1	no	—
207	C₂×M₁₆	—	131	1	no	—
208	C₂²×C₈	—	131	1	no	—
209	#127	—	262	1	no	—
210	#124	—	262	1	no	—
211	#121	—	131	1	no	—
212	#121	—	131	1	no	—
213	#121	—	131	1	no	—
214	#121	C₂×D₁₃₁	1	1	yes	characteristic
215	#120	—	262	1	no	—
216	#120	—	262	1	no	—
217	C₄×Q₈	—	262	1	no	—
218	C₄×D₄	—	262	1	no	—
219	C₄×D₄	—	262	1	no	—
220	C₄×D₄	—	262	1	no	—
221	#117	—	131	1	no	—
222	#117	—	131	1	no	—
223	#117	—	131	1	no	—
224	#117	—	131	1	no	—
225	C₂×C₄⋊C₄	—	131	1	no	—
226	C₂×C₄⋊C₄	—	131	1	no	—
227	C₂×C₄⋊C₄	C₂×D₁₃₁	1	1	yes	characteristic, complemented
228	#107	—	131	1	no	—
229	#107	—	131	1	no	—
230	#107	C₂×D₁₃₁	1	1	yes	characteristic, complemented
231	#107	C₂×D₁₃₁	1	1	yes	characteristic, complemented
232	#106	—	131	1	no	—
233	#106	—	131	1	no	—
234	#106	—	131	1	no	—
235	#106	—	131	1	no	—
236	#102	—	131	1	no	—
237	#102	—	131	1	no	—
238	#102	—	131	1	no	—
239	#102	—	131	1	no	—
240	#102	—	131	1	no	—
241	#102	—	131	1	no	—
242	#102	C₂×D₁₃₁	1	1	yes	characteristic
243	#102	C₂×D₁₃₁	1	1	yes	characteristic
244	C₂²⋊C₈	—	131	1	no	—
245	C₂²⋊C₈	—	131	1	no	—
246	C₂²⋊C₈	—	131	1	no	—
247	C₂²⋊C₈	C₂×D₁₃₁	1	1	yes	characteristic, complemented
248	C₂⁴	—	262	1	no	—
249	#41	—	262	2	no	—
250	#41	—	262	2	no	—
251	C₂×Q₈	—	131	1	no	—
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	—	262	1	no	—
254	C₂×D₄	—	262	1	no	—
255	C₂×D₄	—	262	1	no	—
256	C₂×D₄	—	262	2	no	—
257	C₂×D₄	—	262	2	no	—
258	C₂×D₄	—	262	1	no	—
259	C₂×D₄	—	131	1	no	—
260	C₂×D₄	—	131	1	no	—
261	C₂×D₄	—	131	1	no	—
262	C₂×D₄	—	131	1	no	—
263	C₂×D₄	C₂²×D₁₃₁	1	1	yes	characteristic
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	262	1	no	—
266	C₂²×C₄	—	262	1	no	—
267	C₂²×C₄	—	131	1	no	—
268	C₂²×C₄	—	131	1	no	—
269	C₂²×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
270	M₁₆	—	262	2	no	—
271	C₂×C₈	—	262	2	no	—
272	C₂×C₈	—	131	1	no	—
273	C₂×C₈	—	131	1	no	—
274	C₂×C₈	C₂²×D₁₃₁	1	1	yes	characteristic
275	C₂×C₈	C₂²×D₁₃₁	1	1	yes	characteristic
276	C₄⋊C₄	—	2	1	no	—
277	C₄⋊C₄	—	262	1	no	—
278	C₄⋊C₄	—	262	1	no	—
279	C₄⋊C₄	—	131	1	no	—
280	C₄⋊C₄	—	131	1	no	—
281	C₄⋊C₄	—	131	1	no	—
282	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
283	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
284	C₄⋊C₄	C₂²×D₁₃₁	1	1	yes	characteristic
285	C₂²⋊C₄	—	2	1	no	—
286	C₂²⋊C₄	—	262	1	no	—
287	C₂²⋊C₄	—	262	1	no	—
288	C₂²⋊C₄	—	262	1	no	—
289	C₂²⋊C₄	—	262	1	no	—
290	C₂²⋊C₄	—	262	1	no	—
291	C₂²⋊C₄	—	262	1	no	—
292	C₂²⋊C₄	—	262	1	no	—
293	C₄²	—	262	1	no	—
294	C₄²	—	262	1	no	—
295	C₄²	—	262	1	no	—
296	C₄²	—	262	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	262	1	no	—
299	C₂³	—	524	2	no	—
300	C₂³	—	1048	1	no	—
301	C₂³	—	1048	1	no	—
302	C₂³	—	131	1	no	—
303	C₂³	—	131	1	no	—
304	C₂³	D₄×D₁₃₁	1	1	yes	characteristic
305	Q₈	—	262	2	no	—
306	D₄	—	2	1	no	—
307	D₄	—	2	1	no	—
308	D₄	—	262	2	no	—
309	D₄	—	262	2	no	—
310	D₄	—	262	2	no	—
311	D₄	—	262	1	no	—
312	D₄	—	262	1	no	—
313	D₄	—	8	1	no	—
314	D₄	—	524	2	no	—
315	D₄	—	1048	1	no	—
316	D₄	—	1048	1	no	—
317	D₄	—	1048	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	262	1	no	—
324	C₂×C₄	—	262	1	no	—
325	C₂×C₄	—	262	1	no	—
326	C₂×C₄	—	262	1	no	—
327	C₂×C₄	—	262	1	no	—
328	C₂×C₄	—	8	1	no	—
329	C₂×C₄	—	1048	1	no	—
330	C₂×C₄	—	1048	1	no	—
331	C₂×C₄	—	131	1	no	—
332	C₂×C₄	—	131	1	no	—
333	C₂×C₄	—	131	2	no	—
334	C₂×C₄	—	131	2	no	—
335	C₂×C₄	D₄×D₁₃₁	1	1	yes	characteristic
336	C₂×C₄	C₂³×D₁₃₁	1	1	yes	characteristic
337	C₈	—	2	1	no	—
338	C₈	—	2	1	no	—
339	C₈	—	262	1	no	—
340	C₈	—	262	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	—	4	1	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	262	1	no	—
348	C₂²	—	262	1	no	—
349	C₂²	—	262	1	no	—
350	C₂²	—	262	1	no	—
351	C₂²	—	262	1	no	—
352	C₂²	—	524	1	no	—
353	C₂²	—	524	1	no	—
354	C₂²	—	524	1	no	—
355	C₂²	—	1048	4	no	—
356	C₂²	—	131	2	no	—
357	C₂²	C₂×D₄×D₁₃₁	1	1	yes	characteristic
358	C₄	—	2	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	262	1	no	—
363	C₄	—	524	1	no	—
364	C₄	—	524	1	no	—
365	C₄	—	524	1	no	—
366	C₄	—	131	2	no	—
367	C₄	#41×D₁₃₁	1	1	yes	characteristic
368	C₄	#41×D₁₃₁	1	1	yes	characteristic
369	C₂	—	4	1	no	—
370	C₂	—	262	2	no	—
371	C₂	—	8	1	no	—
372	C₂	—	524	1	no	—
373	C₂	—	1048	1	no	—
374	C₂	#123×D₁₃₁	1	1	yes	characteristic
375	C₂	#22554113	1	1	yes	characteristic
376	C₂	#22554121	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₁
commutator, cosocle	C₂×C₄×C₁₃₁	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₁
Fitting	#480×C₁₃₁	C₂
socle	C₂²×C₁₃₁	C₂²×D₄
prime radical	#22553878	C₂
hypercenter	#480	D₁₃₁
hypocenter	C₁₃₁	#3096
LCS	G ▷ C₂×C₄×C₁₃₁ ▷ C₂×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #480

Complements

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

N	H ≅ G/N	type
2. #22553793	C₂	semidirect
3. #22553639	C₂	semidirect
4. #22553637	C₂	semidirect
5. #22553634	C₂	semidirect
6. #22553633	C₂	semidirect
7. #22553630	C₂	semidirect
8. #22553629	C₂	semidirect
9. #22553627	C₂	semidirect
10. #22553353	C₂	semidirect
11. #22553349	C₂	semidirect
12. #22553315	C₂	semidirect
13. #102×D₁₃₁	C₂	semidirect
14. #22553277	C₂	semidirect
15. #480×C₁₃₁	C₂	semidirect
31. #16862205	C₂²	semidirect
34. #16862204	C₂²	semidirect
36. C₄⋊C₄×D₁₃₁	C₂²	semidirect
37. #16862180	C₂²	semidirect
38. #16862179	C₂²	semidirect
39. #16862178	C₂²	semidirect
40. #16862177	C₂²	semidirect
41. #16862177	C₂²	semidirect
42. #16862177	C₂²	semidirect
49. C₂²⋊(C₁₃₁⋊C₈)	C₂²	semidirect
50. (C₂×D₁₃₁)⋊C₈	C₂²	semidirect
51. (C₂×D₁₃₁)⋊C₈	C₂²	semidirect
53. C₂×C₄⋊C₄×C₁₃₁	C₂²	semidirect
54. #107×C₁₃₁	C₂²	semidirect
55. #107×C₁₃₁	C₂²	semidirect
58. C₂²⋊C₈×C₁₃₁	C₂²	semidirect
188. C₁₃₁	#3096	semidirect
199. #480	D₁₃₁	semidirect
227. C₂×C₄⋊C₄	C₂×D₁₃₁	semidirect
230. #107	C₂×D₁₃₁	semidirect
231. #107	C₂×D₁₃₁	semidirect
247. C₂²⋊C₈	C₂×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#22553878	2
#22553793	2
#22553639	2
#22553637	2
#22553634	2
#22553633	2
#22553630	2
#22553629	2
#22553627	2
#22553353	2
#22553349	2
#22553315	2
#102×D₁₃₁	2
#22553277	2
#480×C₁₃₁	2
#3096	131