Subgroups — #26198520

Order 12032.

802 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	#20253816	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253388	C₂	1	2	yes	maximal, complemented
3	#20242753	C₂	1	2	yes	maximal, complemented
4	#20242743	C₂	1	2	yes	maximal, complemented
5	#20242729	C₂	1	4	yes	maximal, complemented
6	#20242136	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242038	C₂	1	2	yes	maximal, complemented
8	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13094046	—	2	1	no	—
10	C₂×#13094046	—	2	1	no	—
11	#15689673	C₂²	1	2	yes	—
12	#15689507	—	2	1	no	—
13	#15689507	—	2	1	no	—
14	#15689503	C₂²	1	1	yes	characteristic, complemented
15	#15689500	C₂²	1	1	yes	characteristic, complemented
16	#15689496	C₂²	1	2	yes	complemented
17	#15689436	—	2	2	no	—
18	#15689403	C₂²	1	4	yes	—
19	#15689318	C₂²	1	4	yes	—
20	#15689257	—	2	2	no	—
21	C₄×#10625334	—	2	4	no	—
22	#15689176	C₂²	1	2	yes	—
23	#15688876	C₂²	1	2	yes	complemented
24	#15688874	C₂²	1	2	yes	complemented
25	#15688870	C₂²	1	4	yes	complemented
26	#15688866	C₂²	1	4	yes	complemented
27	C₂³×C₈×C₄₇	—	2	1	no	—
28	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₈×D₄×C₄₇	—	2	1	no	—
30	C₈×D₄×C₄₇	—	2	1	no	—
31	C₈×D₄×C₄₇	C₂²	1	2	yes	—
32	C₈×D₄×C₄₇	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
35	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#10625350	—	2	2	no	—
37	#13094046	—	4	4	no	—
38	#13094046	—	4	4	no	—
39	C₂×Dic₁₈₈	—	2	1	no	—
40	C₂×Dic₁₈₈	—	2	1	no	—
41	C₂×#10625325	—	2	2	no	—
42	C₂×#10625325	—	2	2	no	—
43	C₂×D₃₇₆	—	2	1	no	—
44	C₂×D₃₇₆	—	2	1	no	—
45	C₂×#10625334	—	2	4	no	—
46	#13094024	C₂³	1	2	yes	—
47	#13094021	C₂³	1	2	yes	—
48	#13094012	—	2	2	no	—
49	#13093998	—	2	2	no	—
50	#13093998	—	2	2	no	—
51	C₄×D₁₈₈	—	2	2	no	—
52	C₄×D₁₈₈	—	2	2	no	—
53	#13093957	—	2	4	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
55	#13093945	—	2	4	no	—
56	#13093944	—	2	4	no	—
57	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₄×C₄₇⋊C₈	—	2	2	no	—
59	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	—	2	1	no	—
61	C₂²×C₈×C₄₇	—	2	1	no	—
62	C₂²×C₈×C₄₇	—	2	2	no	—
63	C₂²×C₈×C₄₇	—	2	2	no	—
64	C₂²×C₈×C₄₇	—	4	4	no	—
65	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
66	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
67	C₄×D₄×C₄₇	—	2	1	no	—
68	C₄×D₄×C₄₇	—	2	1	no	—
69	C₄×D₄×C₄₇	D₄	1	2	yes	—
70	C₄×D₄×C₄₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₇	—	2	1	no	—
75	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
76	C₂²⋊C₈×C₄₇	—	2	2	no	—
77	C₂²⋊C₈×C₄₇	—	2	2	no	—
78	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
79	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
80	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂⁴×C₄₇	—	2	1	no	—
83	C₂×D₄×C₄₇	—	2	4	no	—
84	C₂×D₄×C₄₇	—	2	1	no	—
85	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
94	C₂×C₂²⋊D₄₇	—	4	2	no	—
95	#10625350	—	4	4	no	—
96	#10625350	—	4	4	no	—
97	C₂×D₁₈₈	—	2	2	no	—
98	C₂×D₁₈₈	—	2	2	no	—
99	C₂×D₁₈₈	—	2	2	no	—
100	C₂×C₄×D₄₇	—	4	2	no	—
101	C₂×Dic₉₄	—	2	2	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	4	2	no	—
105	C₂×C₈×C₄₇	—	4	4	no	—
106	C₂×C₈×C₄₇	—	4	4	no	—
107	C₂×C₈×C₄₇	D₈	1	4	yes	complemented
108	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₄⋊C₄×C₄₇	—	2	1	no	—
113	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₄₇	#41	1	1	yes	characteristic
119	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
120	#10625334	—	4	8	no	—
121	(C₂×D₄₇)⋊C₄	—	4	2	no	—
122	(C₂×D₄₇)⋊C₄	—	4	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	4	no	—
126	Dic₁₈₈	—	4	2	no	—
127	Dic₁₈₈	—	4	2	no	—
128	D₃₇₆	—	4	2	no	—
129	D₃₇₆	—	4	2	no	—
130	#10625325	—	4	4	no	—
131	#10625325	—	4	4	no	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	4	2	no	—
136	C₂³×C₄₇	#121	1	1	yes	characteristic
137	C₂²×D₄₇	—	4	2	no	—
138	D₄×C₄₇	—	2	4	no	—
139	D₄×C₄₇	—	2	2	no	—
140	D₄×C₄₇	#135	1	4	yes	complemented
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	4	1	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
152	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂²⋊D₄₇	—	8	4	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	D₁₈₈	—	4	2	no	—
159	D₁₈₈	—	4	4	no	—
160	D₁₈₈	—	4	2	no	—
161	D₁₈₈	—	8	2	no	—
162	C₄×D₄₇	—	8	4	no	—
163	Dic₉₄	—	4	2	no	—
164	Dic₉₄	—	4	2	no	—
165	C₈×C₄₇	—	2	1	no	—
166	C₈×C₄₇	—	2	1	no	—
167	C₈×C₄₇	—	4	2	no	—
168	C₈×C₄₇	C₂×D₈	1	2	yes	—
169	C₈×C₄₇	C₂×D₈	1	2	yes	—
170	C₄₇⋊C₈	—	4	4	no	—
171	#19101	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	4	8	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	#459	1	2	yes	—
179	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
180	C₂×D₄₇	—	8	2	no	—
181	C₂×D₄₇	—	8	2	no	—
182	C₂×D₄₇	—	8	2	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	2	1	no	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	4	2	no	—
187	C₄×C₄₇	#459	1	2	yes	—
188	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
189	C₄×C₄₇	C₂×#135	1	2	yes	—
190	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	Dic₄₇	—	8	2	no	—
192	#3147	—	47	1	no	—
193	#3100	—	47	2	no	—
194	C₂×C₈×D₄	D₄₇	1	1	yes	characteristic, complemented
195	#1669	—	47	2	no	—
196	#1667	—	47	2	no	—
197	#1665	—	47	4	no	—
198	#1564	—	47	1	no	—
199	#1540	—	47	2	no	—
200	C₂×C₄₇	—	2	2	no	—
201	C₂×C₄₇	—	4	4	no	—
202	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
203	C₂×C₄₇	#3050	1	1	yes	characteristic
204	C₂×C₄₇	#3067	1	1	yes	characteristic
205	D₄₇	—	16	2	no	—
206	C₂×#135	—	94	1	no	—
207	C₂×#135	—	94	1	no	—
208	C₂³×C₈	—	2	1	no	—
209	#532	—	47	2	no	—
210	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
211	#495	—	94	1	no	—
212	#495	—	94	1	no	—
213	#494	—	47	1	no	—
214	#493	—	47	1	no	—
215	#492	—	47	2	no	—
216	#480	—	94	2	no	—
217	#474	—	47	4	no	—
218	#459	—	47	4	no	—
219	#447	—	94	2	no	—
220	C₄×D₈	—	94	4	no	—
221	C₈×D₄	—	2	1	no	—
222	C₈×D₄	—	2	1	no	—
223	C₈×D₄	C₂×D₄₇	1	2	yes	—
224	C₈×D₄	C₂×D₄₇	1	2	yes	—
225	#431	—	47	2	no	—
226	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	—	2	1	no	—
228	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
229	#335	—	47	2	no	—
230	#334	—	47	2	no	—
231	#332	—	47	4	no	—
232	#331	—	47	4	no	—
233	C₄₇	#19101	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	94	2	no	—
235	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
236	C₂³×C₄	—	2	1	no	—
237	#135	—	188	4	no	—
238	#135	—	188	4	no	—
239	C₂×Q₁₆	—	94	1	no	—
240	C₂×Q₁₆	—	94	1	no	—
241	C₂×SD₁₆	—	94	2	no	—
242	C₂×SD₁₆	—	94	2	no	—
243	C₂×D₈	—	94	4	no	—
244	C₂×D₈	—	94	1	no	—
245	C₂×D₈	—	94	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	4	4	no	—
250	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
251	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
252	C₄⋊Q₈	—	47	2	no	—
253	#127	—	47	2	no	—
254	#124	—	94	2	no	—
255	#121	—	94	2	no	—
256	#121	—	94	2	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	94	2	no	—
260	C₄×D₄	—	94	2	no	—
261	C₄×D₄	D₁₈₈	1	2	yes	—
262	C₄×D₄	C₂²×D₄₇	1	2	yes	—
263	C₂×C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
266	#107	—	94	4	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	47	4	no	—
269	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
270	#102	—	94	4	no	—
271	#102	—	94	4	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₂²⋊C₈	—	94	2	no	—
275	C₄×C₈	—	94	2	no	—
276	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
277	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
279	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
280	C₂⁴	—	2	1	no	—
281	#41	—	188	4	no	—
282	#41	—	188	4	no	—
283	C₂×Q₈	—	94	2	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	94	2	no	—
287	C₂×D₄	—	94	2	no	—
288	C₂×D₄	—	94	2	no	—
289	C₂×D₄	—	188	2	no	—
290	C₂×D₄	C₂×D₁₈₈	1	2	yes	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
298	C₂²×C₄	#10625350	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	Q₁₆	—	188	2	no	—
301	Q₁₆	—	188	2	no	—
302	SD₁₆	—	188	4	no	—
303	SD₁₆	—	188	4	no	—
304	D₈	—	188	2	no	—
305	D₈	—	188	8	no	—
306	D₈	—	188	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	—	4	4	no	—
311	C₂×C₈	—	4	4	no	—
312	C₂×C₈	—	94	4	no	—
313	C₂×C₈	#10625334	1	4	yes	complemented
314	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
315	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
316	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
317	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	94	2	no	—
320	C₄⋊C₄	—	94	2	no	—
321	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	188	2	no	—
325	C₂²⋊C₄	—	188	2	no	—
326	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
327	C₄²	#10625350	1	1	yes	characteristic
328	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
329	C₄²	C₂³×D₄₇	1	1	yes	characteristic
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	188	2	no	—
335	C₂³	#13093998	1	1	yes	characteristic
336	Q₈	—	188	2	no	—
337	Q₈	—	188	2	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	—	376	2	no	—
341	D₄	—	376	4	no	—
342	D₄	—	188	2	no	—
343	D₄	—	188	4	no	—
344	D₄	—	188	2	no	—
345	D₄	#13094046	1	4	yes	complemented
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	376	4	no	—
354	C₂×C₄	—	188	2	no	—
355	C₂×C₄	#13093998	1	1	yes	characteristic
356	C₂×C₄	#13093998	1	1	yes	characteristic
357	C₂×C₄	#13093998	1	1	yes	characteristic
358	C₂×C₄	C₂×#10625334	1	2	yes	—
359	C₂×C₄	#13094049	1	2	yes	—
360	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
362	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	188	4	no	—
367	C₈	C₂×#10625334	1	2	yes	—
368	C₈	C₂×#10625334	1	2	yes	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	376	2	no	—
376	C₂²	—	376	2	no	—
377	C₂²	—	376	2	no	—
378	C₂²	#15689318	1	2	yes	—
379	C₂²	C₂×#13093998	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	376	2	no	—
385	C₄	#15689318	1	2	yes	—
386	C₄	C₂²×#10625334	1	1	yes	characteristic
387	C₄	C₂×#13094046	1	2	yes	—
388	C₄	C₂×#13094049	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	4	4	no	—
391	C₂	—	752	2	no	—
392	C₂	C₂×#15689318	1	1	yes	characteristic
393	C₂	#20252969	1	1	yes	characteristic
394	C₂	#20253108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093998
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₈×D₄×C₄₇	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	C₂×C₈×D₄	D₄₇
hypocenter	C₄₇	#19101
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #20253816	C₂	semidirect
2. #20253388	C₂	semidirect
3. #20242753	C₂	semidirect
4. #20242743	C₂	semidirect
5. #20242729	C₂	semidirect
6. #20242136	C₂	semidirect
7. #20242038	C₂	semidirect
8. C₂×C₈×D₄×C₄₇	C₂	semidirect
14. #15689503	C₂²	semidirect
15. #15689500	C₂²	semidirect
16. #15689496	C₂²	semidirect
23. #15688876	C₂²	semidirect
24. #15688874	C₂²	semidirect
25. #15688870	C₂²	semidirect
26. #15688866	C₂²	semidirect
107. C₂×C₈×C₄₇	D₈	semidirect
140. D₄×C₄₇	#135	semidirect
194. C₂×C₈×D₄	D₄₇	semidirect
233. C₄₇	#19101	semidirect
313. C₂×C₈	#10625334	semidirect
345. D₄	#13094046	semidirect

Maximal subgroups

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

subgroup	index
#20253816	2
#20253388	2
#20242753	2
#20242743	2
#20242729	2
#20242136	2
#20242038	2
C₂×C₈×D₄×C₄₇	2
#19101	47