Subgroups — #26204273

Order 12032.

750 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254529	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254329	C₂	1	1	yes	maximal, characteristic
3	#20253970	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253769	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15689469	C₂	1	1	yes	maximal, characteristic
6	#20243049	C₂	1	2	yes	maximal, complemented
7	#20243038	C₂	1	2	yes	maximal, complemented
8	#20242999	C₂	1	2	yes	maximal, complemented
9	#20242988	C₂	1	2	yes	maximal, complemented
10	M₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3138	C₂	1	1	yes	maximal, characteristic
12	#15689680	C₂²	1	1	yes	characteristic
13	C₂×#13094024	C₂²	1	1	yes	characteristic
14	#15689526	C₂²	1	1	yes	characteristic, complemented
15	#15689519	C₂²	1	2	yes	complemented
16	#15689502	C₂²	1	1	yes	characteristic, complemented
17	#15689495	C₂²	1	2	yes	—
18	#15689492	—	2	2	no	—
19	#15689475	C₂²	1	1	yes	characteristic, complemented
20	#15689474	C₂²	1	2	yes	complemented
21	#15689474	C₂²	1	2	yes	complemented
22	#15689473	C₂²	1	1	yes	characteristic, complemented
23	#15689473	C₂²	1	2	yes	complemented
24	#15689469	—	2	2	no	—
25	#15689469	C₂²	1	2	yes	—
26	#15689469	C₂²	1	2	yes	—
27	#15689469	C₂²	1	2	yes	—
28	#15689451	—	2	2	no	—
29	#15689408	—	2	2	no	—
30	#15689362	—	2	2	no	—
31	#15689320	—	2	2	no	—
32	#15689274	—	2	2	no	—
33	C₄×#10625337	—	2	2	no	—
34	#15689176	C₂²	1	1	yes	characteristic
35	#15689133	—	2	2	no	—
36	C₂×#13093945	—	2	2	no	—
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688844	C₂²	1	2	yes	complemented
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
40	C₄₇×#533	C₂²	1	1	yes	characteristic
41	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#490	—	2	2	no	—
43	C₄₇×#486	C₂²	1	2	yes	—
44	C₄₇×#486	C₂²	1	2	yes	—
45	C₄₇×#418	—	2	2	no	—
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×Dic₉₄	—	2	1	no	—
48	C₂×#10625337	—	2	2	no	—
49	C₂×#10625335	—	2	4	no	—
50	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
51	#13094024	—	2	1	no	—
52	#13094024	—	2	1	no	—
53	#13094024	—	2	1	no	—
54	#13094024	C₂³	1	1	yes	characteristic
55	#13094024	C₂³	1	2	yes	—
56	#13094024	C₂³	1	1	yes	characteristic
57	#13094016	—	2	1	no	—
58	#13094003	—	2	1	no	—
59	#13094003	—	2	1	no	—
60	C₄×Dic₉₄	—	2	1	no	—
61	C₄×Dic₉₄	—	2	1	no	—
62	#13093983	—	2	1	no	—
63	C₂×C₄⋊Dic₄₇	—	2	1	no	—
64	C₂×C₄⋊Dic₄₇	—	2	1	no	—
65	#13093957	—	2	2	no	—
66	#13093955	—	2	4	no	—
67	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
68	#13093949	—	2	4	no	—
69	#13093949	—	2	4	no	—
70	#13093948	—	2	2	no	—
71	#13093948	—	2	4	no	—
72	#13093947	—	2	2	no	—
73	#13093945	—	2	4	no	—
74	#13093945	—	2	4	no	—
75	#13093945	—	2	4	no	—
76	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
77	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
80	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₄₇	—	2	1	no	—
82	C₂²×D₄×C₄₇	—	2	1	no	—
83	C₂²×D₄×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
85	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
87	#127×C₄₇	—	2	1	no	—
88	#127×C₄₇	—	2	1	no	—
89	#127×C₄₇	—	2	1	no	—
90	#127×C₄₇	C₂³	1	2	yes	—
91	#125×C₄₇	—	2	1	no	—
92	C₂²⋊Q₈×C₄₇	—	2	1	no	—
93	C₂²⋊Q₈×C₄₇	—	2	1	no	—
94	C₄×Q₈×C₄₇	—	2	1	no	—
95	C₄×Q₈×C₄₇	—	2	1	no	—
96	#117×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	#102×C₄₇	—	2	4	no	—
99	#102×C₄₇	—	2	4	no	—
100	#97×C₄₇	D₄	1	2	yes	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	C₂⁴×C₄₇	—	4	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	4	4	no	—
109	C₂×D₄×C₄₇	—	4	1	no	—
110	C₂×D₄×C₄₇	—	4	1	no	—
111	C₂×D₄×C₄₇	—	4	1	no	—
112	C₂×D₄×C₄₇	—	4	4	no	—
113	C₂×D₄×C₄₇	—	8	2	no	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×Dic₄₇	—	4	1	no	—
118	C₂×Dic₉₄	—	2	1	no	—
119	C₂×Dic₉₄	—	2	2	no	—
120	C₂×Dic₉₄	—	2	1	no	—
121	C₂×Dic₉₄	—	4	4	no	—
122	C₂×Dic₉₄	—	4	1	no	—
123	M₁₆×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	4	1	no	—
130	C₄⋊C₄×C₄₇	—	4	1	no	—
131	C₂²⋊C₄×C₄₇	—	4	1	no	—
132	C₄²×C₄₇	—	4	1	no	—
133	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂²⋊Dic₄₇	—	4	1	no	—
138	#10625337	—	4	4	no	—
139	#10625335	—	8	4	no	—
140	C₄⋊Dic₄₇	—	2	2	no	—
141	C₄⋊Dic₄₇	—	2	1	no	—
142	C₄⋊Dic₄₇	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	1	no	—
144	C₄⋊Dic₄₇	—	2	1	no	—
145	C₄⋊Dic₄₇	—	2	1	no	—
146	C₄⋊Dic₄₇	—	4	1	no	—
147	C₄⋊Dic₄₇	—	4	1	no	—
148	Dic₄₇⋊C₄	—	4	1	no	—
149	Dic₄₇⋊C₄	—	4	1	no	—
150	C₄×Dic₄₇	—	4	1	no	—
151	C₂×C₄₇⋊C₈	—	4	2	no	—
152	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	—	8	2	no	—
157	C₂³×C₄₇	—	8	2	no	—
158	C₂³×C₄₇	—	8	2	no	—
159	C₂³×C₄₇	#127	1	1	yes	characteristic
160	Q₈×C₄₇	—	4	2	no	—
161	Q₈×C₄₇	—	4	2	no	—
162	D₄×C₄₇	—	4	4	no	—
163	D₄×C₄₇	—	4	4	no	—
164	D₄×C₄₇	—	4	4	no	—
165	D₄×C₄₇	—	8	2	no	—
166	D₄×C₄₇	—	8	2	no	—
167	D₄×C₄₇	—	8	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
173	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#135	1	4	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×Dic₄₇	—	4	1	no	—
180	C₂×Dic₄₇	—	4	1	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	8	2	no	—
183	Dic₉₄	—	4	4	no	—
184	Dic₉₄	—	4	2	no	—
185	Dic₉₄	—	4	2	no	—
186	Dic₉₄	—	8	2	no	—
187	C₈×C₄₇	—	2	4	no	—
188	C₄₇⋊C₈	—	2	2	no	—
189	C₄₇⋊C₈	—	2	2	no	—
190	C₄₇⋊C₈	—	2	4	no	—
191	#19637	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	8	2	no	—
195	C₂²×C₄₇	—	8	2	no	—
196	C₂²×C₄₇	—	8	2	no	—
197	C₂²×C₄₇	—	16	4	no	—
198	C₂²×C₄₇	#495	1	2	yes	—
199	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	8	1	no	—
203	C₄×C₄₇	—	8	1	no	—
204	C₄×C₄₇	#495	1	2	yes	—
205	C₄×C₄₇	C₂×#135	1	2	yes	—
206	C₄×C₄₇	#575	1	2	yes	—
207	C₄×C₄₇	#577	1	2	yes	—
208	Dic₄₇	—	8	2	no	—
209	Dic₄₇	—	8	1	no	—
210	Dic₄₇	—	8	1	no	—
211	#3229	—	47	1	no	—
212	#3208	—	47	1	no	—
213	#3170	—	47	1	no	—
214	#3139	—	47	1	no	—
215	#3138	D₄₇	1	1	yes	characteristic
216	C₂×#486	—	47	1	no	—
217	#1720	—	47	2	no	—
218	#1719	—	47	2	no	—
219	#1711	—	47	2	no	—
220	#1708	—	47	2	no	—
221	C₈×M₁₆	—	47	1	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	—	16	2	no	—
224	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
225	C₂×C₄₇	#3153	1	1	yes	characteristic
226	C₂×C₄₇	#3154	1	1	yes	characteristic
227	#533	—	47	1	no	—
228	#533	C₂×D₄₇	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	—	47	1	no	—
230	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
231	#500	—	47	1	no	—
232	#498	—	47	2	no	—
233	#494	—	47	1	no	—
234	#492	—	47	2	no	—
235	#491	—	94	2	no	—
236	#490	—	2	2	no	—
237	#487	—	47	1	no	—
238	#487	—	47	2	no	—
239	#487	—	47	1	no	—
240	#487	—	47	2	no	—
241	#487	—	47	2	no	—
242	#486	—	47	2	no	—
243	#486	—	47	2	no	—
244	#486	—	47	2	no	—
245	#486	—	94	2	no	—
246	#486	C₂×D₄₇	1	2	yes	—
247	#486	C₂×D₄₇	1	2	yes	—
248	#483	—	94	2	no	—
249	#475	—	94	2	no	—
250	#467	—	94	2	no	—
251	#460	—	94	2	no	—
252	#450	—	94	2	no	—
253	C₄×Q₁₆	—	94	2	no	—
254	#431	—	47	1	no	—
255	#419	—	94	2	no	—
256	#418	—	2	2	no	—
257	C₂×#102	—	94	2	no	—
258	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
259	C₂×C₄×C₈	—	47	1	no	—
260	#322	—	47	2	no	—
261	C₈²	—	47	2	no	—
262	C₄₇	#19637	1	1	yes	characteristic, complemented, Sylow
263	C₂²×Q₈	—	94	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂×Q₁₆	—	94	2	no	—
268	C₂×SD₁₆	—	94	4	no	—
269	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
270	C₂²×C₈	—	47	2	no	—
271	C₄⋊Q₈	—	47	2	no	—
272	C₄⋊Q₈	—	47	1	no	—
273	C₄⋊Q₈	—	47	1	no	—
274	C₄⋊Q₈	—	94	1	no	—
275	C₄⋊Q₈	—	94	1	no	—
276	C₄⋊Q₈	—	94	1	no	—
277	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
278	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
279	#127	—	2	1	no	—
280	#127	—	2	1	no	—
281	#127	—	2	1	no	—
282	#127	C₂²×D₄₇	1	2	yes	—
283	#125	—	2	1	no	—
284	#125	—	94	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	C₂²⋊Q₈	—	2	1	no	—
287	C₂²⋊Q₈	—	94	1	no	—
288	C₂²⋊Q₈	—	94	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	94	1	no	—
292	C₄×Q₈	—	94	1	no	—
293	#117	—	2	1	no	—
294	#117	—	94	1	no	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₄⋊C₄	—	94	1	no	—
297	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
298	#107	—	94	2	no	—
299	#106	—	94	4	no	—
300	C₄⋊C₈	—	47	2	no	—
301	#103	—	94	2	no	—
302	#103	—	94	2	no	—
303	#103	—	94	4	no	—
304	#103	—	94	4	no	—
305	#103	—	94	4	no	—
306	#102	—	2	4	no	—
307	#102	—	2	4	no	—
308	#102	—	94	4	no	—
309	#102	—	94	4	no	—
310	#102	—	94	4	no	—
311	C₂²⋊C₈	—	47	2	no	—
312	#97	C₂²⋊D₄₇	1	2	yes	—
313	C₄×C₈	—	47	2	no	—
314	C₄×C₈	—	47	1	no	—
315	C₄×C₈	—	47	2	no	—
316	C₄×C₈	—	47	1	no	—
317	C₄×C₈	C₂²×D₄₇	1	2	yes	—
318	C₂⁴	—	4	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	94	1	no	—
322	C₂×Q₈	—	94	1	no	—
323	C₂×Q₈	—	94	2	no	—
324	C₂×Q₈	—	188	4	no	—
325	C₂×Q₈	—	188	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	8	2	no	—
335	C₂²×C₄	—	188	1	no	—
336	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
339	Q₁₆	—	188	4	no	—
340	SD₁₆	—	376	4	no	—
341	M₁₆	—	2	4	no	—
342	C₂×C₈	—	47	2	no	—
343	C₂×C₈	—	47	2	no	—
344	C₂×C₈	—	47	4	no	—
345	C₂×C₈	—	188	2	no	—
346	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	94	2	no	—
354	C₄⋊C₄	—	94	1	no	—
355	C₄⋊C₄	—	94	2	no	—
356	C₄⋊C₄	—	94	1	no	—
357	C₄⋊C₄	—	94	1	no	—
358	C₄⋊C₄	—	94	1	no	—
359	C₄⋊C₄	—	188	1	no	—
360	C₄⋊C₄	—	188	1	no	—
361	C₄⋊C₄	—	188	1	no	—
362	C₄⋊C₄	—	188	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	188	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	—	188	1	no	—
367	C₄²	D₄×D₄₇	1	1	yes	characteristic
368	C₄²	D₄×D₄₇	1	1	yes	characteristic
369	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₄²	C₂³×D₄₇	1	1	yes	characteristic
371	C₂³	—	4	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	#13094020	1	1	yes	characteristic
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	376	2	no	—
379	Q₈	—	188	4	no	—
380	Q₈	—	188	2	no	—
381	Q₈	—	188	2	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	4	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	376	2	no	—
393	C₂×C₄	—	188	1	no	—
394	C₂×C₄	—	188	1	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	#13094020	1	1	yes	characteristic
397	C₂×C₄	#13094020	1	1	yes	characteristic
398	C₂×C₄	#13094020	1	1	yes	characteristic
399	C₂×C₄	#13094044	1	4	yes	—
400	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
403	C₈	—	2	4	no	—
404	C₈	—	94	2	no	—
405	C₈	—	94	2	no	—
406	C₈	—	94	4	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	16	4	no	—
413	C₂²	#15689505	1	2	yes	—
414	C₂²	C₂×#13094020	1	1	yes	characteristic
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	376	2	no	—
420	C₄	—	376	1	no	—
421	C₄	—	376	1	no	—
422	C₄	#15689505	1	2	yes	—
423	C₄	C₂×#13094044	1	2	yes	—
424	C₄	#15689919	1	2	yes	—
425	C₄	#15689933	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	16	2	no	—
428	C₂	C₂×#15689505	1	1	yes	characteristic
429	C₂	#20253850	1	1	yes	characteristic
430	C₂	#20253862	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3138	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	C₂×#127×C₄₇	C₂²
hypercenter	#3138	D₄₇
hypocenter	C₄₇	#19637
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3138

Complements

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

N	H ≅ G/N	type
1. #20254529	C₂	semidirect
3. #20253970	C₂	semidirect
4. #20253769	C₂	semidirect
6. #20243049	C₂	semidirect
7. #20243038	C₂	semidirect
8. #20242999	C₂	semidirect
9. #20242988	C₂	semidirect
10. M₁₆×C₄₇⋊C₈	C₂	semidirect
14. #15689526	C₂²	semidirect
15. #15689519	C₂²	semidirect
16. #15689502	C₂²	semidirect
19. #15689475	C₂²	semidirect
20. #15689474	C₂²	semidirect
21. #15689474	C₂²	semidirect
22. #15689473	C₂²	semidirect
23. #15689473	C₂²	semidirect
38. #15688844	C₂²	semidirect
39. C₈×C₄₇⋊C₈	C₂²	semidirect
262. C₄₇	#19637	semidirect

Maximal subgroups

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

subgroup	index
#20254529	2
#20254329	2
#20253970	2
#20253769	2
C₂×#15689469	2
#20243049	2
#20243038	2
#20242999	2
#20242988	2
M₁₆×C₄₇⋊C₈	2
C₄₇×#3138	2
#19637	47