Subgroups — #26124473

Order 12032.

814 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688885	C₂	1	2	yes	maximal
3	C₂×#15688877	C₂	1	1	yes	maximal, characteristic
4	#20241617	C₂	1	2	yes	maximal
5	C₂²×#106×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄₇⋊#95	—	2	2	no	—
10	C₂×C₄₇⋊#95	—	2	2	no	—
11	#15688886	C₄	1	4	yes	complemented
12	#15688885	—	2	4	no	—
13	#15688877	—	2	2	no	—
14	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂×#106×C₄₇	—	2	2	no	—
17	C₂×#106×C₄₇	—	2	4	no	—
18	C₂³×Dic₄₇	—	2	2	no	—
19	C₂³×Dic₄₇	D₄	1	2	yes	—
20	C₂²×C₄₇⋊C₈	—	2	1	no	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	1	no	—
24	C₂²×C₄₇⋊C₈	Q₈	1	2	yes	—
25	C₂×C₄⋊Dic₄₇	—	2	2	no	—
26	C₂×C₄⋊Dic₄₇	—	2	2	no	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
31	C₂×C₄×Dic₄₇	—	2	1	no	—
32	C₂×C₄×Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	—	2	2	no	—
34	C₂×C₄×Dic₄₇	—	2	1	no	—
35	C₄₇⋊#95	—	4	4	no	—
36	C₄₇⋊#95	—	4	4	no	—
37	C₂³×C₄×C₄₇	—	2	2	no	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₄₇	—	2	2	no	—
40	C₂²×C₈×C₄₇	—	2	2	no	—
41	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₄₇	D₄	1	2	yes	—
43	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
50	#106×C₄₇	—	2	8	no	—
51	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₄₇	—	2	4	no	—
53	C₂²×C₄×C₄₇	—	4	2	no	—
54	C₂²×C₄×C₄₇	—	4	2	no	—
55	C₂²×C₄×C₄₇	—	4	2	no	—
56	C₂²×C₄×C₄₇	—	4	2	no	—
57	C₂²×C₄×C₄₇	—	4	2	no	—
58	C₂²×C₄×C₄₇	—	4	2	no	—
59	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	#41	1	2	yes	—
65	C₂²×C₄×C₄₇	#41	1	2	yes	—
66	C₂²×C₄×C₄₇	#41	1	2	yes	—
67	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
69	C₂²×Dic₄₇	—	2	2	no	—
70	C₂²×Dic₄₇	—	2	2	no	—
71	C₂²×Dic₄₇	—	2	2	no	—
72	C₂²×Dic₄₇	—	2	2	no	—
73	C₂²×Dic₄₇	—	2	2	no	—
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	—	2	4	no	—
76	C₂²×Dic₄₇	—	4	2	no	—
77	C₂²×Dic₄₇	—	4	2	no	—
78	C₂²×Dic₄₇	—	4	2	no	—
79	C₂²×Dic₄₇	—	4	2	no	—
80	C₂²×Dic₄₇	—	4	2	no	—
81	C₂²×Dic₄₇	—	4	2	no	—
82	C₂²×Dic₄₇	SD₁₆	1	4	yes	—
83	C₂×C₈×C₄₇	—	2	4	no	—
84	C₂×C₈×C₄₇	—	2	2	no	—
85	C₂×C₈×C₄₇	—	2	4	no	—
86	C₂×C₈×C₄₇	—	2	2	no	—
87	C₂×C₈×C₄₇	C₄⋊C₄	1	4	yes	—
88	C₄⋊C₄×C₄₇	—	2	4	no	—
89	C₄⋊C₄×C₄₇	—	2	4	no	—
90	C₄⋊C₄×C₄₇	—	4	2	no	—
91	C₄⋊C₄×C₄₇	—	4	2	no	—
92	C₄⋊Dic₄₇	—	2	4	no	—
93	C₄⋊Dic₄₇	—	2	4	no	—
94	C₄⋊Dic₄₇	—	4	2	no	—
95	C₄⋊Dic₄₇	—	4	2	no	—
96	C₄×Dic₄₇	—	4	1	no	—
97	C₄×Dic₄₇	—	4	1	no	—
98	C₄×Dic₄₇	—	4	2	no	—
99	C₂×C₄₇⋊C₈	—	2	4	no	—
100	C₂×C₄₇⋊C₈	—	2	2	no	—
101	C₂×C₄₇⋊C₈	—	4	1	no	—
102	C₂×C₄₇⋊C₈	—	4	1	no	—
103	C₂×C₄₇⋊C₈	—	4	2	no	—
104	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
105	C₂³×C₄₇	#121	1	1	yes	characteristic
106	C₂³×C₄₇	#121	1	2	yes	—
107	C₂³×C₄₇	#123	1	2	yes	—
108	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
109	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
110	C₂³×C₄₇	#135	1	2	yes	—
111	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
112	C₂³×C₄₇	#137	1	2	yes	—
113	C₂×C₄×C₄₇	—	4	4	no	—
114	C₂×C₄×C₄₇	—	4	4	no	—
115	C₂×C₄×C₄₇	—	4	4	no	—
116	C₂×C₄×C₄₇	—	8	2	no	—
117	C₂×C₄×C₄₇	—	8	2	no	—
118	C₂×C₄×C₄₇	—	8	2	no	—
119	C₂×C₄×C₄₇	—	8	2	no	—
120	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₄₇	#117	1	2	yes	—
122	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
123	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
124	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
125	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
126	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
128	C₂×C₄×C₄₇	#123	1	2	yes	—
129	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
130	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
131	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
132	C₂×C₄×C₄₇	#124	1	2	yes	—
133	C₂×C₄×C₄₇	#125	1	2	yes	—
134	C₂×C₄×C₄₇	#125	1	2	yes	—
135	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
136	C₂×C₄×C₄₇	#126	1	2	yes	—
137	C₂×C₄×C₄₇	#126	1	2	yes	—
138	C₂×Dic₄₇	—	2	4	no	—
139	C₂×Dic₄₇	—	2	4	no	—
140	C₂×Dic₄₇	—	2	4	no	—
141	C₂×Dic₄₇	—	4	2	no	—
142	C₂×Dic₄₇	—	4	2	no	—
143	C₂×Dic₄₇	—	4	2	no	—
144	C₂×Dic₄₇	—	4	2	no	—
145	C₂×Dic₄₇	—	4	4	no	—
146	C₂×Dic₄₇	—	4	4	no	—
147	C₂×Dic₄₇	—	4	4	no	—
148	C₂×Dic₄₇	—	8	2	no	—
149	C₂×Dic₄₇	—	8	2	no	—
150	C₂×Dic₄₇	—	8	2	no	—
151	C₂×Dic₄₇	—	8	2	no	—
152	C₈×C₄₇	—	2	4	no	—
153	C₄₇⋊C₈	—	4	2	no	—
154	#11257	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	#388	1	2	yes	—
156	C₂²×C₄₇	#389	1	1	yes	characteristic
157	C₂²×C₄₇	#394	1	1	yes	characteristic
158	C₂²×C₄₇	#397	1	1	yes	characteristic
159	C₂²×C₄₇	#398	1	2	yes	—
160	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
161	C₂²×C₄₇	#441	1	1	yes	characteristic
162	C₂²×C₄₇	#442	1	1	yes	characteristic
163	C₂²×C₄₇	#460	1	2	yes	—
164	C₂²×C₄₇	#461	1	2	yes	—
165	C₂²×C₄₇	#463	1	2	yes	—
166	C₂²×C₄₇	#464	1	2	yes	—
167	C₂²×C₄₇	#465	1	2	yes	—
168	C₂²×C₄₇	#468	1	2	yes	—
169	C₂²×C₄₇	#481	1	2	yes	—
170	C₂²×C₄₇	#482	1	2	yes	—
171	C₂²×C₄₇	#483	1	2	yes	—
172	C₂²×C₄₇	#485	1	2	yes	—
173	C₂²×C₄₇	#498	1	1	yes	characteristic
174	C₂²×C₄₇	#499	1	1	yes	characteristic
175	C₂²×C₄₇	#501	1	2	yes	—
176	C₄×C₄₇	—	8	4	no	—
177	C₄×C₄₇	#382	1	1	yes	characteristic
178	C₄×C₄₇	#385	1	1	yes	characteristic
179	C₄×C₄₇	#387	1	2	yes	—
180	C₄×C₄₇	#393	1	1	yes	characteristic
181	C₄×C₄₇	#400	1	1	yes	characteristic
182	C₄×C₄₇	#400	1	2	yes	—
183	Dic₄₇	—	4	4	no	—
184	Dic₄₇	—	8	4	no	—
185	C₂²×#106	D₄₇	1	1	yes	characteristic
186	C₂×#340	—	47	1	no	—
187	C₂×#340	—	47	2	no	—
188	C₂×#336	—	47	1	no	—
189	C₄⋊#95	—	47	2	no	—
190	C₂×C₄₇	#1442	1	1	yes	characteristic
191	C₂×C₄₇	#1926	1	2	yes	—
192	C₂×C₄₇	#1927	1	2	yes	—
193	C₂×C₄₇	#1941	1	1	yes	characteristic
194	C₂×C₄₇	#1943	1	1	yes	characteristic
195	C₂×C₄₇	#2055	1	2	yes	—
196	C₂×C₄₇	#2077	1	2	yes	—
197	C₂×C₄₇	#2084	1	2	yes	—
198	C₂×C₄₇	#2085	1	2	yes	—
199	C₂³×C₈	—	47	1	no	—
200	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
201	C₂²×C₄⋊C₄	—	47	2	no	—
202	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
203	C₂²×C₄²	—	47	1	no	—
204	C₂×#106	—	2	2	no	—
205	C₂×#106	—	2	4	no	—
206	C₂×#95	—	94	2	no	—
207	C₂×#95	—	94	2	no	—
208	#340	—	47	4	no	—
209	#340	—	94	4	no	—
210	#336	—	94	2	no	—
211	C₄₇	#11257	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₄	—	2	2	no	—
213	C₂³×C₄	—	47	2	no	—
214	C₂³×C₄	—	94	2	no	—
215	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	—	47	2	no	—
219	C₂²×C₈	—	94	2	no	—
220	C₂²×C₈	—	94	1	no	—
221	C₂²×C₈	—	94	1	no	—
222	C₂²×C₈	—	94	2	no	—
223	C₂²×C₈	Dic₉₄	1	2	yes	—
224	C₂²×C₈	C₄×D₄₇	1	2	yes	—
225	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	47	4	no	—
232	C₂×C₄⋊C₄	—	94	2	no	—
233	C₂×C₄⋊C₄	—	94	2	no	—
234	C₂×C₄⋊C₄	—	94	2	no	—
235	C₂×C₄⋊C₄	—	94	2	no	—
236	C₂×C₄⋊C₄	—	94	2	no	—
237	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	4	yes	—
238	C₂×C₄²	—	94	2	no	—
239	C₂×C₄²	—	94	1	no	—
240	C₂×C₄²	—	94	2	no	—
241	C₂×C₄²	—	94	1	no	—
242	#106	—	2	8	no	—
243	#95	—	188	4	no	—
244	#95	—	188	4	no	—
245	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	4	2	no	—
248	C₂²×C₄	—	4	2	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	47	4	no	—
254	C₂²×C₄	—	94	2	no	—
255	C₂²×C₄	—	94	2	no	—
256	C₂²×C₄	—	94	2	no	—
257	C₂²×C₄	—	94	2	no	—
258	C₂²×C₄	—	94	2	no	—
259	C₂²×C₄	—	94	2	no	—
260	C₂²×C₄	—	94	4	no	—
261	C₂²×C₄	—	188	2	no	—
262	C₂²×C₄	—	188	2	no	—
263	C₂²×C₄	—	188	2	no	—
264	C₂²×C₄	—	188	2	no	—
265	C₂²×C₄	—	188	2	no	—
266	C₂²×C₄	—	188	2	no	—
267	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
269	C₂²×C₄	#10625350	1	2	yes	—
270	C₂²×C₄	#10625352	1	2	yes	—
271	C₂²×C₄	#10625352	1	1	yes	characteristic
272	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
273	C₂²×C₄	#10625354	1	2	yes	—
274	C₂²×C₄	#10625354	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	94	4	no	—
282	C₂×C₈	—	94	2	no	—
283	C₂×C₈	—	188	1	no	—
284	C₂×C₈	—	188	1	no	—
285	C₂×C₈	—	188	2	no	—
286	C₂×C₈	Dic₄₇⋊C₄	1	4	yes	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	94	4	no	—
292	C₄⋊C₄	—	94	4	no	—
293	C₄⋊C₄	—	188	2	no	—
294	C₄⋊C₄	—	188	2	no	—
295	C₄²	—	188	1	no	—
296	C₄²	—	188	1	no	—
297	C₄²	—	188	2	no	—
298	C₂³	#13093986	1	1	yes	characteristic
299	C₂³	#13093995	1	1	yes	characteristic
300	C₂³	#13093996	1	2	yes	—
301	C₂³	#13094009	1	2	yes	—
302	C₂³	#13094023	1	1	yes	characteristic
303	C₂³	SD₁₆×D₄₇	1	2	yes	—
304	C₂³	#13094045	1	2	yes	—
305	C₂³	#13094051	1	2	yes	—
306	C₂³	#13094053	1	2	yes	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	8	2	no	—
311	C₂×C₄	—	8	2	no	—
312	C₂×C₄	—	8	2	no	—
313	C₂×C₄	—	8	2	no	—
314	C₂×C₄	—	94	4	no	—
315	C₂×C₄	—	94	4	no	—
316	C₂×C₄	—	94	4	no	—
317	C₂×C₄	—	376	2	no	—
318	C₂×C₄	—	376	2	no	—
319	C₂×C₄	—	376	2	no	—
320	C₂×C₄	—	376	2	no	—
321	C₂×C₄	—	188	4	no	—
322	C₂×C₄	—	188	4	no	—
323	C₂×C₄	—	188	4	no	—
324	C₂×C₄	—	188	2	no	—
325	C₂×C₄	—	188	2	no	—
326	C₂×C₄	—	188	2	no	—
327	C₂×C₄	—	188	2	no	—
328	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
329	C₂×C₄	#13093982	1	2	yes	—
330	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
331	C₂×C₄	#13093989	1	1	yes	characteristic
332	C₂×C₄	#13093993	1	1	yes	characteristic
333	C₂×C₄	#13094000	1	2	yes	—
334	C₂×C₄	#13094000	1	1	yes	characteristic
335	C₂×C₄	#13094003	1	2	yes	—
336	C₂×C₄	#13094005	1	2	yes	—
337	C₂×C₄	#13094007	1	1	yes	characteristic
338	C₂×C₄	#13094011	1	1	yes	characteristic
339	C₂×C₄	#13094013	1	1	yes	characteristic
340	C₂×C₄	#13094013	1	2	yes	—
341	C₂×C₄	#13094014	1	2	yes	—
342	C₂×C₄	#13094015	1	2	yes	—
343	C₂×C₄	#13094015	1	1	yes	characteristic
344	C₂×C₄	#13094019	1	2	yes	—
345	C₂×C₄	#13094019	1	2	yes	—
346	C₈	—	2	4	no	—
347	C₈	—	188	2	no	—
348	C₂²	#15689013	1	2	yes	—
349	C₂²	#15689019	1	1	yes	characteristic
350	C₂²	#15689037	1	1	yes	characteristic
351	C₂²	#15689049	1	1	yes	characteristic
352	C₂²	#15689056	1	2	yes	—
353	C₂²	#15689210	1	2	yes	—
354	C₂²	#15689229	1	1	yes	characteristic
355	C₂²	#15689234	1	1	yes	characteristic
356	C₂²	#15689321	1	2	yes	—
357	C₂²	#15689326	1	2	yes	—
358	C₂²	#15689340	1	2	yes	—
359	C₂²	#15689343	1	2	yes	—
360	C₂²	#15689349	1	2	yes	—
361	C₂²	#15689366	1	2	yes	—
362	C₂²	#15689443	1	2	yes	—
363	C₂²	#15689449	1	2	yes	—
364	C₂²	#15689455	1	2	yes	—
365	C₂²	#15689467	1	2	yes	—
366	C₂²	#15689520	1	1	yes	characteristic
367	C₂²	#15689523	1	1	yes	characteristic
368	C₂²	#15689530	1	2	yes	—
369	C₄	—	8	4	no	—
370	C₄	—	376	4	no	—
371	C₄	—	188	4	no	—
372	C₄	#15688988	1	1	yes	characteristic
373	C₄	#15688996	1	1	yes	characteristic
374	C₄	#15689004	1	2	yes	—
375	C₄	#15689034	1	1	yes	characteristic
376	C₄	#15689061	1	1	yes	characteristic
377	C₄	#15689062	1	2	yes	—
378	C₂	#20241647	1	1	yes	characteristic
379	C₂	#20244014	1	2	yes	—
380	C₂	#20244021	1	2	yes	—
381	C₂	#20244114	1	1	yes	characteristic
382	C₂	#20244124	1	1	yes	characteristic
383	C₂	#20244701	1	2	yes	—
384	C₂	#20244822	1	2	yes	—
385	C₂	#20244867	1	2	yes	—
386	C₂	#20244873	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂²×#106×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂²×#106	D₄₇
hypocenter	C₄₇	#11257
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂²×#106

Complements

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

N	H ≅ G/N	type
11. #15688886	C₄	semidirect
211. C₄₇	#11257	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15688886	2
C₂×#15688885	2
C₂×#15688877	2
#20241617	2
C₂²×#106×C₄₇	2
#11257	47