Subgroups — #37576196

Order 24448.

528 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259301	C₂	1	1	yes	maximal, characteristic
2	C₂×#20259281	C₂	1	1	yes	maximal, characteristic
3	#27132605	C₂	1	1	yes	maximal, characteristic, complemented
4	#27132597	C₂	1	1	yes	maximal, characteristic, complemented
5	#27132595	C₂	1	1	yes	maximal, characteristic, complemented
6	#27132584	C₂	1	1	yes	maximal, characteristic, complemented
7	#27132567	C₂	1	1	yes	maximal, characteristic, complemented
8	#27132560	C₂	1	1	yes	maximal, characteristic, complemented
9	#27132550	C₂	1	1	yes	maximal, characteristic, complemented
10	#27132546	C₂	1	1	yes	maximal, characteristic, complemented
11	#27132536	C₂	1	1	yes	maximal, characteristic
12	#27132536	C₂	1	1	yes	maximal, characteristic
13	#27132526	C₂	1	1	yes	maximal, characteristic
14	#27132523	C₂	1	1	yes	maximal, characteristic
15	C₂×#95×C₁₉₁	C₂	1	1	yes	maximal, characteristic
16	C₂²×Dic₃₈₂	C₂²	1	1	yes	characteristic
17	#20259301	—	2	4	no	—
18	#20259281	—	2	4	no	—
19	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×Dic₁₉₁⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Dic₁₉₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×Dic₁₉₁	C₂²	1	1	yes	characteristic
36	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
37	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
38	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
39	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
40	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
41	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
42	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
43	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
44	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
45	C₁₉₁⋊#95	C₂²	1	1	yes	characteristic
46	C₂³×C₄×C₁₉₁	C₂²	1	1	yes	characteristic
47	C₂³×C₄×C₁₉₁	C₂²	1	1	yes	characteristic
48	C₂³×C₄×C₁₉₁	C₂²	1	1	yes	characteristic
49	#95×C₁₉₁	C₂²	1	1	yes	characteristic
50	#95×C₁₉₁	C₂²	1	1	yes	characteristic
51	#95×C₁₉₁	C₂²	1	1	yes	characteristic
52	#95×C₁₉₁	C₂²	1	1	yes	characteristic
53	C₂×Dic₃₈₂	—	2	2	no	—
54	C₂×Dic₃₈₂	—	2	2	no	—
55	C₂×Dic₃₈₂	—	4	1	no	—
56	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
57	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
58	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
59	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
60	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
61	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
62	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
63	C₂²×Dic₁₉₁	C₂³	1	1	yes	characteristic
64	C₄⋊Dic₁₉₁	—	2	2	no	—
65	C₄⋊Dic₁₉₁	—	2	2	no	—
66	C₄⋊Dic₁₉₁	—	2	2	no	—
67	C₄⋊Dic₁₉₁	—	2	2	no	—
68	C₄⋊Dic₁₉₁	—	4	1	no	—
69	Dic₁₉₁⋊C₄	—	2	2	no	—
70	Dic₁₉₁⋊C₄	—	2	2	no	—
71	Dic₁₉₁⋊C₄	—	2	2	no	—
72	Dic₁₉₁⋊C₄	—	2	2	no	—
73	Dic₁₉₁⋊C₄	—	4	1	no	—
74	Dic₁₉₁⋊C₄	—	4	1	no	—
75	C₂²⋊Dic₁₉₁	—	2	2	no	—
76	C₂²⋊Dic₁₉₁	—	2	2	no	—
77	C₂²⋊Dic₁₉₁	—	2	2	no	—
78	C₂²⋊Dic₁₉₁	D₄	1	4	yes	—
79	C₄×Dic₁₉₁	—	2	2	no	—
80	C₄×Dic₁₉₁	—	2	2	no	—
81	C₂⁴×C₁₉₁	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₉₁	—	2	2	no	—
83	C₂²×C₄×C₁₉₁	—	2	2	no	—
84	C₂²×C₄×C₁₉₁	—	2	2	no	—
85	C₂²×C₄×C₁₉₁	—	2	2	no	—
86	C₂²×C₄×C₁₉₁	—	2	2	no	—
87	C₂²×C₄×C₁₉₁	—	2	2	no	—
88	C₂²×C₄×C₁₉₁	—	4	1	no	—
89	C₂²×C₄×C₁₉₁	—	4	1	no	—
90	C₂²×C₄×C₁₉₁	Q₈	1	4	yes	complemented
91	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₁₉₁	C₂³	1	1	yes	characteristic
97	Dic₃₈₂	—	4	4	no	—
98	C₂×Dic₁₉₁	—	2	1	no	—
99	C₂×Dic₁₉₁	—	2	1	no	—
100	C₂×Dic₁₉₁	—	2	1	no	—
101	C₂×Dic₁₉₁	—	2	1	no	—
102	C₂×Dic₁₉₁	—	2	1	no	—
103	C₂×Dic₁₉₁	—	2	1	no	—
104	C₂×Dic₁₉₁	—	2	1	no	—
105	C₂×Dic₁₉₁	—	2	1	no	—
106	C₂×Dic₁₉₁	—	2	1	no	—
107	C₂×Dic₁₉₁	—	2	1	no	—
108	C₂×Dic₁₉₁	—	2	1	no	—
109	C₂×Dic₁₉₁	—	2	1	no	—
110	C₂×Dic₁₉₁	—	2	1	no	—
111	C₂×Dic₁₉₁	—	2	1	no	—
112	C₂×Dic₁₉₁	—	2	1	no	—
113	C₂×Dic₁₉₁	—	2	1	no	—
114	C₂×Dic₁₉₁	—	2	1	no	—
115	C₂×Dic₁₉₁	—	2	1	no	—
116	C₂×Dic₁₉₁	—	2	1	no	—
117	C₂×Dic₁₉₁	—	2	1	no	—
118	C₂×Dic₁₉₁	—	2	1	no	—
119	C₂×Dic₁₉₁	—	2	1	no	—
120	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
121	C₂×Dic₁₉₁	C₂×D₄	1	2	yes	—
122	C₂³×C₁₉₁	—	2	1	no	—
123	C₂³×C₁₉₁	—	2	1	no	—
124	C₂³×C₁₉₁	—	2	1	no	—
125	C₂³×C₁₉₁	—	2	1	no	—
126	C₂³×C₁₉₁	C₂×D₄	1	2	yes	—
127	C₂³×C₁₉₁	C₂×Q₈	1	2	yes	—
128	C₂³×C₁₉₁	#41	1	2	yes	—
129	C₂³×C₁₉₁	C₂⁴	1	1	yes	characteristic
130	C₂×C₄×C₁₉₁	—	2	8	no	—
131	C₂×C₄×C₁₉₁	—	2	1	no	—
132	C₂×C₄×C₁₉₁	—	2	1	no	—
133	C₂×C₄×C₁₉₁	—	2	1	no	—
134	C₂×C₄×C₁₉₁	—	2	1	no	—
135	C₂×C₄×C₁₉₁	—	2	1	no	—
136	C₂×C₄×C₁₉₁	—	2	1	no	—
137	C₂×C₄×C₁₉₁	—	2	1	no	—
138	C₂×C₄×C₁₉₁	—	2	1	no	—
139	C₂×C₄×C₁₉₁	—	2	1	no	—
140	C₂×C₄×C₁₉₁	—	2	1	no	—
141	C₂×C₄×C₁₉₁	—	2	1	no	—
142	C₂×C₄×C₁₉₁	—	2	1	no	—
143	C₂×C₄×C₁₉₁	—	2	1	no	—
144	C₂×C₄×C₁₉₁	—	2	1	no	—
145	C₂×C₄×C₁₉₁	—	4	4	no	—
146	C₂×C₄×C₁₉₁	—	4	4	no	—
147	C₂×C₄×C₁₉₁	C₂×Q₈	1	2	yes	—
148	C₂×C₄×C₁₉₁	C₂×Q₈	1	2	yes	—
149	C₂×C₄×C₁₉₁	#41	1	2	yes	—
150	C₂×C₄×C₁₉₁	#41	1	2	yes	—
151	C₂²×C₁₉₁	—	2	2	no	—
152	C₂²×C₁₉₁	—	2	2	no	—
153	C₂²×C₁₉₁	—	2	2	no	—
154	C₂²×C₁₉₁	—	2	2	no	—
155	C₂²×C₁₉₁	—	2	2	no	—
156	C₂²×C₁₉₁	—	2	2	no	—
157	C₂²×C₁₉₁	C₂²⋊Q₈	1	4	yes	—
158	C₂²×C₁₉₁	C₂²×D₄	1	1	yes	characteristic
159	C₂²×C₁₉₁	C₂²×Q₈	1	1	yes	characteristic
160	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
161	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
162	C₂²×C₁₉₁	C₂×#41	1	1	yes	characteristic
163	C₂²×C₁₉₁	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂²×C₁₉₁	2₋¹⁺⁴	1	1	yes	characteristic
165	C₄×C₁₉₁	—	2	2	no	—
166	C₄×C₁₉₁	—	2	2	no	—
167	C₄×C₁₉₁	—	2	2	no	—
168	C₄×C₁₉₁	—	2	2	no	—
169	C₄×C₁₉₁	—	4	1	no	—
170	C₄×C₁₉₁	—	4	1	no	—
171	Dic₁₉₁	—	2	2	no	—
172	Dic₁₉₁	—	2	2	no	—
173	Dic₁₉₁	—	4	1	no	—
174	Dic₁₉₁	—	4	1	no	—
175	Dic₁₉₁	—	4	1	no	—
176	Dic₁₉₁	—	4	1	no	—
177	Dic₁₉₁	—	4	1	no	—
178	Dic₁₉₁	—	4	1	no	—
179	C₂×C₁₉₁	—	2	4	no	—
180	C₂×C₁₉₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₁₉₁	#533	1	1	yes	characteristic
182	C₂×C₁₉₁	#544	1	1	yes	characteristic
183	C₂×C₁₉₁	#546	1	1	yes	characteristic
184	C₂×C₁₉₁	#547	1	1	yes	characteristic
185	C₂×C₁₉₁	#551	1	1	yes	characteristic
186	C₂×C₁₉₁	#552	1	1	yes	characteristic
187	C₁₉₁	#2438	1	1	yes	characteristic, complemented, Sylow
188	#2438	—	191	1	no	maximal, Sylow
189	C₂×C₂²⋊Q₈	—	191	1	no	—
190	C₂×#117	—	191	1	no	—
191	#400	—	191	1	no	—
192	#398	—	191	1	no	—
193	#398	—	191	1	no	—
194	#395	—	191	1	no	—
195	#391	—	191	1	no	—
196	#389	—	191	1	no	—
197	#387	—	191	1	no	—
198	#387	—	191	1	no	—
199	#385	—	191	1	no	—
200	#385	—	191	1	no	—
201	#381	—	191	1	no	—
202	#380	—	191	1	no	—
203	C₂×#95	D₁₉₁	1	1	yes	characteristic
204	C₂²×Q₈	—	191	1	no	—
205	C₂³×C₄	C₂×D₁₉₁	1	1	yes	characteristic
206	C₂³×C₄	C₂×D₁₉₁	1	1	yes	characteristic
207	C₂³×C₄	C₂×D₁₉₁	1	1	yes	characteristic
208	C₂²⋊Q₈	—	382	4	no	—
209	#117	—	382	4	no	—
210	C₂×C₄⋊C₄	—	191	1	no	—
211	C₂×C₄⋊C₄	—	191	1	no	—
212	C₂×C₄⋊C₄	—	191	1	no	—
213	C₂×C₄⋊C₄	—	191	1	no	—
214	C₂×C₄⋊C₄	—	191	1	no	—
215	C₂×C₄⋊C₄	—	191	1	no	—
216	C₂×C₄⋊C₄	—	191	1	no	—
217	C₂×C₄⋊C₄	—	191	1	no	—
218	C₂×C₄⋊C₄	—	191	1	no	—
219	C₂×C₄⋊C₄	—	191	1	no	—
220	C₂×C₄⋊C₄	—	191	1	no	—
221	C₂×C₂²⋊C₄	—	191	1	no	—
222	C₂×C₂²⋊C₄	—	191	1	no	—
223	C₂×C₂²⋊C₄	—	191	1	no	—
224	C₂×C₂²⋊C₄	—	191	1	no	—
225	C₂×C₄²	—	191	1	no	—
226	C₂×C₄²	—	191	1	no	—
227	#95	—	191	1	no	—
228	#95	—	191	1	no	—
229	#95	—	191	1	no	—
230	#95	—	191	1	no	—
231	#95	—	191	1	no	—
232	#95	—	191	1	no	—
233	#95	—	191	1	no	—
234	#95	—	191	1	no	—
235	#95	—	191	1	no	—
236	#95	—	191	1	no	—
237	#95	C₂×D₁₉₁	1	1	yes	characteristic
238	#95	C₂×D₁₉₁	1	1	yes	characteristic
239	#95	C₂×D₁₉₁	1	1	yes	characteristic
240	#95	C₂×D₁₉₁	1	1	yes	characteristic
241	C₂⁴	C₂²×D₁₉₁	1	1	yes	characteristic
242	C₂×Q₈	—	382	2	no	—
243	C₂×Q₈	—	382	2	no	—
244	C₂×Q₈	—	764	1	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	4	1	no	—
252	C₂²×C₄	—	4	1	no	—
253	C₂²×C₄	—	191	1	no	—
254	C₂²×C₄	—	191	1	no	—
255	C₂²×C₄	—	191	1	no	—
256	C₂²×C₄	—	191	1	no	—
257	C₂²×C₄	—	191	1	no	—
258	C₂²×C₄	—	191	1	no	—
259	C₂²×C₄	—	191	1	no	—
260	C₂²×C₄	—	191	1	no	—
261	C₂²×C₄	Dic₃₈₂	1	4	yes	complemented
262	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
263	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
264	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²×D₁₉₁	1	1	yes	characteristic
268	C₄⋊C₄	—	382	2	no	—
269	C₄⋊C₄	—	382	2	no	—
270	C₄⋊C₄	—	382	2	no	—
271	C₄⋊C₄	—	382	2	no	—
272	C₄⋊C₄	—	382	2	no	—
273	C₄⋊C₄	—	382	2	no	—
274	C₄⋊C₄	—	382	2	no	—
275	C₄⋊C₄	—	382	2	no	—
276	C₄⋊C₄	—	764	1	no	—
277	C₄⋊C₄	—	764	1	no	—
278	C₄⋊C₄	—	764	1	no	—
279	C₂²⋊C₄	—	382	2	no	—
280	C₂²⋊C₄	—	382	2	no	—
281	C₂²⋊C₄	—	382	2	no	—
282	C₂²⋊C₄	—	191	4	no	—
283	C₄²	—	382	2	no	—
284	C₄²	—	382	2	no	—
285	C₂³	—	2	1	no	—
286	C₂³	—	2	1	no	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	D₄×D₁₉₁	1	2	yes	—
290	C₂³	C₂×Dic₃₈₂	1	2	yes	—
291	C₂³	#15690286	1	2	yes	—
292	C₂³	C₂³×D₁₉₁	1	1	yes	characteristic
293	Q₈	—	764	4	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	382	1	no	—
312	C₂×C₄	—	382	1	no	—
313	C₂×C₄	—	382	1	no	—
314	C₂×C₄	—	382	1	no	—
315	C₂×C₄	—	382	1	no	—
316	C₂×C₄	—	382	1	no	—
317	C₂×C₄	—	382	1	no	—
318	C₂×C₄	—	382	1	no	—
319	C₂×C₄	—	382	1	no	—
320	C₂×C₄	—	382	1	no	—
321	C₂×C₄	—	382	1	no	—
322	C₂×C₄	—	382	1	no	—
323	C₂×C₄	—	382	1	no	—
324	C₂×C₄	—	382	1	no	—
325	C₂×C₄	—	382	1	no	—
326	C₂×C₄	—	382	1	no	—
327	C₂×C₄	—	382	1	no	—
328	C₂×C₄	—	382	1	no	—
329	C₂×C₄	—	382	1	no	—
330	C₂×C₄	—	382	1	no	—
331	C₂×C₄	—	382	1	no	—
332	C₂×C₄	—	382	1	no	—
333	C₂×C₄	—	191	2	no	—
334	C₂×C₄	—	191	2	no	—
335	C₂×C₄	C₂×Dic₃₈₂	1	2	yes	—
336	C₂×C₄	C₂×Dic₃₈₂	1	2	yes	—
337	C₂×C₄	#15690287	1	2	yes	—
338	C₂×C₄	#15690287	1	2	yes	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	#20259299	1	4	yes	—
346	C₂²	C₂×D₄×D₁₉₁	1	1	yes	characteristic
347	C₂²	C₂²×Dic₃₈₂	1	1	yes	characteristic
348	C₂²	C₂×#15690286	1	1	yes	characteristic
349	C₂²	C₂×#15690287	1	1	yes	characteristic
350	C₂²	C₂×#15690287	1	1	yes	characteristic
351	C₂²	#20259367	1	1	yes	characteristic
352	C₂²	#20259370	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	382	2	no	—
360	C₄	—	382	2	no	—
361	C₄	—	764	1	no	—
362	C₄	—	764	1	no	—
363	C₄	—	764	1	no	—
364	C₄	—	764	1	no	—
365	C₄	—	764	1	no	—
366	C₄	—	764	1	no	—
367	C₂	—	2	4	no	—
368	C₂	C₂×#20259299	1	1	yes	characteristic
369	C₂	#27133220	1	1	yes	characteristic
370	C₂	#27133294	1	1	yes	characteristic
371	C₂	#27133303	1	1	yes	characteristic
372	C₂	#27133314	1	1	yes	characteristic
373	C₂	#27133339	1	1	yes	characteristic
374	C₂	#27133348	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉₁
commutator, socle, cosocle	C₂³×C₁₉₁	C₂⁴
Fitting	C₂×#95×C₁₉₁	C₂
prime radical	C₂⁴×C₁₉₁	C₂³
hypercenter	C₂×#95	D₁₉₁
hypocenter	C₁₉₁	#2438
LCS	G ▷ C₂³×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂³ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
3. #27132605	C₂	semidirect
4. #27132597	C₂	semidirect
5. #27132595	C₂	semidirect
6. #27132584	C₂	semidirect
7. #27132567	C₂	semidirect
8. #27132560	C₂	semidirect
9. #27132550	C₂	semidirect
10. #27132546	C₂	semidirect
90. C₂²×C₄×C₁₉₁	Q₈	semidirect
187. C₁₉₁	#2438	semidirect
261. C₂²×C₄	Dic₃₈₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20259301	2
C₂×#20259281	2
#27132605	2
#27132597	2
#27132595	2
#27132584	2
#27132567	2
#27132560	2
#27132550	2
#27132546	2
#27132536	2
#27132526	2
#27132523	2
C₂×#95×C₁₉₁	2
#2438	191