Subgroups — #26199796

Order 12032.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254705	C₂	1	1	yes	maximal, characteristic
2	#20254518	C₂	1	1	yes	maximal, characteristic
3	#20253934	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252134	C₂	1	1	yes	maximal, characteristic
5	#20242912	C₂	1	2	yes	maximal, complemented
6	#20242888	C₂	1	2	yes	maximal, complemented
7	#20242788	C₂	1	2	yes	maximal, complemented
8	#20242764	C₂	1	2	yes	maximal, complemented
9	#20242043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094032	—	2	1	no	—
13	#15689680	C₂²	1	1	yes	characteristic
14	#15689673	C₂²	1	1	yes	characteristic
15	C₂×#13094024	C₂²	1	1	yes	characteristic
16	#15689532	—	2	2	no	—
17	#15689528	C₂²	1	2	yes	—
18	#15689521	—	2	1	no	—
19	#15689521	C₂²	1	2	yes	—
20	#15689470	—	2	1	no	—
21	#15689442	—	2	2	no	—
22	#15689414	C₂²	1	2	yes	—
23	#15689414	C₂²	1	2	yes	—
24	#15689414	C₂²	1	2	yes	—
25	#15689409	—	2	1	no	—
26	#15689352	—	2	2	no	—
27	#15689329	C₂²	1	2	yes	—
28	#15689324	—	2	1	no	—
29	#15689202	C₂²	1	2	yes	—
30	#15689196	—	2	2	no	—
31	C₈×D₁₈₈	C₂²	1	2	yes	—
32	#15689165	—	2	1	no	—
33	#15689165	—	2	1	no	—
34	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	#15689091	—	2	1	no	—
36	#15688871	C₂²	1	2	yes	—
37	#15688871	C₂²	1	1	yes	characteristic
38	#15688871	C₂²	1	2	yes	—
39	#15688871	C₂²	1	1	yes	characteristic
40	#15688870	C₂²	1	1	yes	characteristic
41	#15688870	C₂²	1	1	yes	characteristic
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	2	yes	—
46	C₄₇×#334	C₂²	1	2	yes	—
47	C₂×#10625350	—	2	1	no	—
48	C₂²×Dic₉₄	—	2	1	no	—
49	C₂×#10625325	—	2	2	no	—
50	#13094032	—	4	4	no	—
51	C₂×#10625324	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	2	no	—
54	#13094024	—	2	1	no	—
55	#13094024	—	2	1	no	—
56	#13094024	—	2	1	no	—
57	#13094024	D₄	1	1	yes	characteristic
58	#13094024	C₂³	1	1	yes	characteristic
59	#13094024	C₂³	1	2	yes	—
60	#13094024	C₂³	1	1	yes	characteristic
61	#13094021	D₄	1	1	yes	characteristic
62	#13094016	—	2	1	no	—
63	#13094012	—	2	1	no	—
64	#13094003	—	2	1	no	—
65	#13094003	—	2	1	no	—
66	#13093998	—	2	1	no	—
67	#13093998	D₄	1	2	yes	—
68	C₄×Dic₉₄	—	2	1	no	—
69	C₄×Dic₉₄	—	2	1	no	—
70	C₄×D₁₈₈	—	2	1	no	—
71	C₄×D₁₈₈	C₂³	1	2	yes	—
72	#13093983	—	2	1	no	—
73	C₂×C₄⋊Dic₄₇	—	2	1	no	—
74	C₂×C₄⋊Dic₄₇	—	2	1	no	—
75	#13093958	—	2	2	no	—
76	#13093958	—	2	2	no	—
77	#13093956	—	2	2	no	—
78	#13093956	—	2	2	no	—
79	#13093956	—	2	2	no	—
80	#13093956	—	2	2	no	—
81	#13093956	—	2	2	no	—
82	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
83	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
84	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
85	#13093949	—	2	2	no	—
86	#13093946	—	2	2	no	—
87	#13093946	—	2	2	no	—
88	#13093946	—	2	2	no	—
89	(C₂×D₄₇)⋊C₈	—	2	2	no	—
90	(C₂×D₄₇)⋊C₈	—	2	2	no	—
91	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
92	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	—	2	1	no	—
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	—	2	1	no	—
96	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₄₇	—	2	1	no	—
100	#97×C₄₇	D₄	1	2	yes	—
101	C₄×C₈×C₄₇	—	2	1	no	—
102	C₄×C₈×C₄₇	C₂³	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	2	no	—
107	C₂²×Dic₄₇	—	4	1	no	—
108	#10625350	—	4	2	no	—
109	#10625350	—	4	2	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×Dic₉₄	—	2	1	no	—
115	C₂×Dic₉₄	—	2	1	no	—
116	C₂×Dic₉₄	—	2	1	no	—
117	C₂×Dic₉₄	—	2	2	no	—
118	C₂×Dic₉₄	—	4	1	no	—
119	C₂×Dic₉₄	—	8	2	no	—
120	M₁₆×C₄₇	—	2	2	no	—
121	M₁₆×C₄₇	SD₁₆	1	4	yes	complemented
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	8	1	no	—
126	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	#41	1	1	yes	characteristic
131	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₄₇	—	4	1	no	—
133	(C₂×D₄₇)⋊C₄	—	2	2	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	1	no	—
138	C₄⋊Dic₄₇	—	2	1	no	—
139	C₄⋊Dic₄₇	—	2	2	no	—
140	C₄⋊Dic₄₇	—	2	1	no	—
141	C₄⋊Dic₄₇	—	2	1	no	—
142	C₄⋊Dic₄₇	—	4	1	no	—
143	C₄⋊Dic₄₇	—	4	1	no	—
144	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
145	Dic₄₇⋊C₄	—	4	1	no	—
146	Dic₄₇⋊C₄	—	4	1	no	—
147	C₄×Dic₄₇	—	4	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	4	2	no	—
151	#10625325	—	8	2	no	—
152	#10625324	—	4	4	no	—
153	C₈×D₄₇	—	4	4	no	—
154	C₂³×C₄₇	#121	1	1	yes	characteristic
155	C₂²×D₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
163	C₂×C₄×C₄₇	#137	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂²⋊D₄₇	—	4	4	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	4	1	no	—
170	C₂×Dic₄₇	—	4	1	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	8	2	no	—
173	D₁₈₈	—	2	2	no	—
174	D₁₈₈	—	2	2	no	—
175	D₁₈₈	—	4	2	no	—
176	D₁₈₈	—	8	1	no	—
177	C₄×D₄₇	—	4	2	no	—
178	C₄×D₄₇	—	4	2	no	—
179	Dic₉₄	—	4	2	no	—
180	Dic₉₄	—	4	1	no	—
181	Dic₉₄	—	4	1	no	—
182	Dic₉₄	—	8	2	no	—
183	Dic₉₄	—	8	1	no	—
184	Dic₉₄	—	8	2	no	—
185	C₈×C₄₇	—	2	2	no	—
186	C₈×C₄₇	—	4	2	no	—
187	C₈×C₄₇	—	4	1	no	—
188	C₈×C₄₇	—	4	1	no	—
189	C₈×C₄₇	C₂×SD₁₆	1	4	yes	—
190	C₄₇⋊C₈	—	4	1	no	—
191	C₄₇⋊C₈	—	4	1	no	—
192	#19233	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	1	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	#461	1	2	yes	—
196	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
197	C₂×D₄₇	—	4	2	no	—
198	C₂×D₄₇	—	4	2	no	—
199	C₂×D₄₇	—	4	2	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	#461	1	2	yes	—
204	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
205	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
206	C₄×C₄₇	#577	1	1	yes	characteristic
207	C₄×C₄₇	#578	1	1	yes	characteristic
208	Dic₄₇	—	4	2	no	—
209	Dic₄₇	—	8	1	no	—
210	Dic₄₇	—	8	2	no	—
211	Dic₄₇	—	8	1	no	—
212	#3246	—	47	1	no	—
213	#3227	—	47	1	no	—
214	#3165	—	47	1	no	—
215	#2935	—	47	1	no	—
216	#1695	—	47	2	no	—
217	#1691	—	47	2	no	—
218	#1675	—	47	2	no	—
219	#1671	—	47	2	no	—
220	#1565	D₄₇	1	1	yes	characteristic, complemented
221	#1542	—	47	1	no	—
222	C₂×#333	—	47	1	no	—
223	C₂×C₄₇	—	2	2	no	—
224	C₂×C₄₇	C₂×#461	1	1	yes	characteristic
225	C₂×C₄₇	#3063	1	1	yes	characteristic
226	C₂×C₄₇	#3068	1	1	yes	characteristic
227	D₄₇	—	8	2	no	—
228	C₂×#131	—	94	1	no	—
229	#533	—	47	1	no	—
230	#532	—	47	1	no	—
231	C₂×C₄⋊Q₈	—	47	1	no	—
232	#501	—	94	2	no	—
233	#500	—	47	2	no	—
234	#498	—	47	2	no	—
235	#498	—	94	1	no	—
236	#486	—	94	1	no	—
237	#481	—	94	2	no	—
238	#476	—	47	2	no	—
239	#476	—	47	2	no	—
240	#476	—	47	2	no	—
241	#475	—	94	1	no	—
242	#465	—	94	2	no	—
243	#461	—	47	2	no	—
244	#460	—	94	1	no	—
245	#436	—	47	2	no	—
246	#435	—	94	2	no	—
247	C₈×D₄	—	47	2	no	—
248	#431	C₂×D₄₇	1	1	yes	characteristic
249	#428	—	94	1	no	—
250	#428	—	94	1	no	—
251	C₂×C₄⋊C₈	—	47	1	no	—
252	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
253	#408	—	94	1	no	—
254	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
255	#335	C₂×D₄₇	1	2	yes	—
256	#334	C₂×D₄₇	1	2	yes	—
257	#333	—	47	2	no	—
258	#333	—	47	2	no	—
259	#333	—	47	1	no	—
260	#333	—	47	1	no	—
261	#332	—	47	1	no	—
262	#332	—	47	1	no	—
263	C₄₇	#19233	1	1	yes	characteristic, complemented, Sylow
264	C₂×#41	—	94	1	no	—
265	C₂²×Q₈	—	94	1	no	—
266	C₂×SD₁₆	—	94	2	no	—
267	#131	—	188	4	no	—
268	C₂×M₁₆	—	94	2	no	—
269	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
270	C₂×M₁₆	D₁₈₈	1	1	yes	characteristic
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	94	1	no	—
273	C₂²×C₈	—	94	2	no	—
274	C₄⋊Q₈	—	47	1	no	—
275	C₄⋊Q₈	—	47	2	no	—
276	C₄⋊Q₈	—	47	1	no	—
277	C₄⋊Q₈	—	47	1	no	—
278	C₄⋊Q₈	—	94	1	no	—
279	C₄⋊Q₈	—	94	1	no	—
280	C₄⋊Q₈	—	94	1	no	—
281	#127	—	47	1	no	—
282	#125	—	94	1	no	—
283	#124	—	94	1	no	—
284	C₂²⋊Q₈	—	94	1	no	—
285	C₂²⋊Q₈	—	94	1	no	—
286	#121	—	47	2	no	—
287	#121	—	94	1	no	—
288	C₄×Q₈	—	94	1	no	—
289	C₄×Q₈	—	94	1	no	—
290	C₄×D₄	—	47	2	no	—
291	C₄×D₄	—	94	1	no	—
292	#117	—	94	1	no	—
293	C₂×C₄⋊C₄	—	94	1	no	—
294	C₂×C₄⋊C₄	—	94	1	no	—
295	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
296	#107	—	94	2	no	—
297	#107	—	94	2	no	—
298	#106	—	94	2	no	—
299	#106	—	94	2	no	—
300	#106	—	94	2	no	—
301	#106	—	94	2	no	—
302	#106	—	94	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	47	1	no	—
305	C₄⋊C₈	—	47	1	no	—
306	C₄⋊C₈	—	94	1	no	—
307	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
310	#103	—	94	2	no	—
311	#102	—	94	2	no	—
312	#102	—	94	2	no	—
313	#102	—	94	2	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	94	2	no	—
316	C₂²⋊C₈	—	94	2	no	—
317	#97	D₁₈₈	1	2	yes	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	C₂²×D₄₇	1	2	yes	—
320	#41	—	188	2	no	—
321	#41	—	188	2	no	—
322	C₂×Q₈	—	94	1	no	—
323	C₂×Q₈	—	94	1	no	—
324	C₂×Q₈	—	94	1	no	—
325	C₂×Q₈	—	94	2	no	—
326	C₂×Q₈	—	376	2	no	—
327	C₂×Q₈	—	188	1	no	—
328	C₂×D₄	—	47	2	no	—
329	C₂×D₄	—	94	2	no	—
330	C₂×D₄	—	94	1	no	—
331	C₂×D₄	—	94	1	no	—
332	C₂²×C₄	—	94	2	no	—
333	C₂²×C₄	—	188	1	no	—
334	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	#10625354	1	1	yes	characteristic
337	SD₁₆	—	376	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	188	4	no	—
340	M₁₆	#10625325	1	4	yes	complemented
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	8	1	no	—
345	C₂×C₈	—	94	1	no	—
346	C₂×C₈	—	94	1	no	—
347	C₂×C₈	—	188	2	no	—
348	C₂×C₈	—	188	4	no	—
349	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
350	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
351	C₄⋊C₄	—	47	2	no	—
352	C₄⋊C₄	—	94	1	no	—
353	C₄⋊C₄	—	94	2	no	—
354	C₄⋊C₄	—	94	1	no	—
355	C₄⋊C₄	—	94	1	no	—
356	C₄⋊C₄	—	94	2	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	—	94	2	no	—
364	C₂²⋊C₄	—	94	2	no	—
365	C₂²⋊C₄	—	188	1	no	—
366	C₄²	—	188	1	no	—
367	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
368	C₄²	D₄×D₄₇	1	1	yes	characteristic
369	C₄²	#10625354	1	1	yes	characteristic
370	C₄²	C₂³×D₄₇	1	1	yes	characteristic
371	C₂³	—	94	2	no	—
372	C₂³	#13093999	1	1	yes	characteristic
373	Q₈	—	376	1	no	—
374	Q₈	—	376	2	no	—
375	Q₈	—	376	2	no	—
376	Q₈	—	188	1	no	—
377	Q₈	—	188	1	no	—
378	Q₈	—	188	2	no	—
379	D₄	—	94	2	no	—
380	D₄	—	94	2	no	—
381	D₄	—	376	1	no	—
382	D₄	—	188	4	no	—
383	D₄	—	188	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	376	2	no	—
389	C₂×C₄	—	188	1	no	—
390	C₂×C₄	—	188	1	no	—
391	C₂×C₄	—	188	2	no	—
392	C₂×C₄	—	188	2	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	#13093999	1	1	yes	characteristic
395	C₂×C₄	#13093999	1	1	yes	characteristic
396	C₂×C₄	#13093999	1	1	yes	characteristic
397	C₂×C₄	C₂×#10625325	1	2	yes	—
398	C₂×C₄	#13094057	1	2	yes	—
399	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
401	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	4	2	no	—
405	C₈	—	4	1	no	—
406	C₈	—	188	1	no	—
407	C₈	—	188	1	no	—
408	C₈	C₂×#10625325	1	4	yes	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	188	2	no	—
412	C₂²	—	188	2	no	—
413	C₂²	—	188	2	no	—
414	C₂²	#15689329	1	2	yes	—
415	C₂²	C₂×#13093999	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	376	1	no	—
420	C₄	—	376	2	no	—
421	C₄	—	376	1	no	—
422	C₄	—	188	2	no	—
423	C₄	#15689329	1	2	yes	—
424	C₄	C₂²×#10625325	1	1	yes	characteristic
425	C₄	C₂×#13094057	1	1	yes	characteristic
426	C₄	#15689933	1	1	yes	characteristic
427	C₄	#15689939	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	376	2	no	—
430	C₂	C₂×#15689329	1	1	yes	characteristic
431	C₂	#20253080	1	1	yes	characteristic
432	C₂	#20253117	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093999
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1565	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#15689673	C₂²
hypercenter	#1565	D₄₇
hypocenter	C₄₇	#19233
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
3. #20253934	C₂	semidirect
5. #20242912	C₂	semidirect
6. #20242888	C₂	semidirect
7. #20242788	C₂	semidirect
8. #20242764	C₂	semidirect
9. #20242043	C₂	semidirect
10. C₂×#15688871	C₂	semidirect
11. C₄₇×#1565	C₂	semidirect
121. M₁₆×C₄₇	SD₁₆	semidirect
220. #1565	D₄₇	semidirect
263. C₄₇	#19233	semidirect
340. M₁₆	#10625325	semidirect

Maximal subgroups

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

subgroup	index
#20254705	2
#20254518	2
#20253934	2
#20252134	2
#20242912	2
#20242888	2
#20242788	2
#20242764	2
#20242043	2
C₂×#15688871	2
C₄₇×#1565	2
#19233	47