Subgroups — #26186840

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253963	C₂	1	1	yes	maximal, characteristic
2	#20252100	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252099	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242299	C₂	1	4	yes	maximal, complemented
5	#20242209	C₂	1	4	yes	maximal, complemented
6	#20242143	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241840	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15688845	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094032	—	2	1	no	—
11	C₂×#13094031	—	2	1	no	—
12	#15689673	C₂²	1	1	yes	characteristic
13	#15689526	C₄	1	1	yes	characteristic
14	#15689499	C₄	1	1	yes	characteristic
15	#15689471	C₄	1	1	yes	characteristic
16	#15689469	C₄	1	1	yes	characteristic
17	#15689357	C₄	1	4	yes	—
18	C₄×#10625334	C₂²	1	4	yes	—
19	#15689201	—	2	1	no	—
20	#15689201	C₂²	1	2	yes	—
21	#15689200	—	2	1	no	—
22	#15689200	C₂²	1	2	yes	—
23	D₄×C₄₇⋊C₈	—	2	1	no	—
24	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
25	#15689188	—	2	1	no	—
26	#15689188	C₂²	1	2	yes	—
27	#15689147	C₂²	1	1	yes	characteristic
28	#15689091	—	2	1	no	—
29	#15689090	—	2	1	no	—
30	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	#15688873	C₂²	1	4	yes	—
33	#15688852	C₂²	1	4	yes	—
34	#15688845	C₂²	1	2	yes	—
35	#15688845	C₂²	1	2	yes	—
36	C₄₇×#532	C₂²	1	1	yes	characteristic
37	C₄₇×#423	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×D₄⋊C₈	C₂²	1	4	yes	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625334	C₂×C₄	1	4	yes	—
42	#13094032	—	4	4	no	—
43	#13094031	—	4	4	no	—
44	C₂×#10625329	—	2	1	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625324	—	2	2	no	—
47	C₂²×C₄₇⋊C₈	—	2	2	no	—
48	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
49	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
51	C₂×C₈×D₄₇	—	2	2	no	—
52	#13094024	C₂×C₄	1	1	yes	characteristic
53	#13094021	C₂×C₄	1	1	yes	characteristic
54	#13094012	—	2	1	no	—
55	#13093998	—	2	1	no	—
56	#13093998	C₂×C₄	1	2	yes	—
57	C₄×D₁₈₈	—	2	1	no	—
58	C₄×D₁₈₈	C₂³	1	2	yes	—
59	#13093957	C₂×C₄	1	4	yes	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	#13093945	C₂×C₄	1	4	yes	—
63	#13093944	C₂×C₄	1	4	yes	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
66	(C₂×D₄₇)⋊C₈	—	2	2	no	—
67	(C₂×D₄₇)⋊C₈	—	2	2	no	—
68	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
69	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
71	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
72	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
73	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂×#41×C₄₇	—	2	1	no	—
76	C₂×M₁₆×C₄₇	—	2	1	no	—
77	C₂²×C₈×C₄₇	—	2	1	no	—
78	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
80	#124×C₄₇	—	2	1	no	—
81	#121×C₄₇	—	2	1	no	—
82	#121×C₄₇	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	—	2	1	no	—
87	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
88	C₄×C₈×C₄₇	—	2	1	no	—
89	C₄×C₈×C₄₇	C₂³	1	2	yes	—
90	#41×C₄₇	—	4	2	no	—
91	#41×C₄₇	—	4	2	no	—
92	C₂×Q₈×C₄₇	—	2	1	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	—	2	1	no	—
96	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	C₂×C₂²⋊D₄₇	—	2	2	no	—
102	#10625350	—	4	2	no	—
103	#10625350	—	4	2	no	—
104	C₂×D₁₈₈	—	2	1	no	—
105	C₂×D₁₈₈	—	2	1	no	—
106	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₄₇	—	2	2	no	—
108	C₂×Dic₉₄	—	2	1	no	—
109	M₁₆×C₄₇	—	4	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	4	2	no	—
113	C₄⋊C₄×C₄₇	—	2	1	no	—
114	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₄₇	#41	1	1	yes	characteristic
120	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
121	#10625334	—	2	8	no	—
122	(C₂×D₄₇)⋊C₄	—	2	2	no	—
123	(C₂×D₄₇)⋊C₄	—	2	2	no	—
124	C₄⋊Dic₄₇	—	2	1	no	—
125	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
126	#10625329	—	4	4	no	—
127	#10625329	—	4	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	4	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	4	4	no	—
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
139	#10625324	—	4	4	no	—
140	C₈×D₄₇	—	4	4	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
143	C₂²×D₄₇	—	2	2	no	—
144	Q₈×C₄₇	—	4	2	no	—
145	D₄×C₄₇	—	2	4	no	—
146	D₄×C₄₇	—	4	4	no	—
147	D₄×C₄₇	—	4	2	no	—
148	D₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂²⋊D₄₇	—	4	4	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	D₁₈₈	—	2	4	no	—
165	D₁₈₈	—	4	2	no	—
166	D₁₈₈	—	4	2	no	—
167	C₄×D₄₇	—	4	2	no	—
168	C₄×D₄₇	—	4	2	no	—
169	Dic₉₄	—	4	2	no	—
170	C₈×C₄₇	—	4	2	no	—
171	C₈×C₄₇	—	4	2	no	—
172	C₄₇⋊C₈	—	2	2	no	—
173	C₄₇⋊C₈	—	2	1	no	—
174	C₄₇⋊C₈	—	2	1	no	—
175	C₄₇⋊C₈	—	2	1	no	—
176	C₄₇⋊C₈	—	2	1	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	C₄₇⋊C₈	#131	1	4	yes	complemented
179	#17962	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	2	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	#442	1	2	yes	—
186	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂×D₄₇	—	4	2	no	—
188	C₂×D₄₇	—	4	2	no	—
189	C₂×D₄₇	—	4	2	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	4	2	no	—
193	C₄×C₄₇	#442	1	2	yes	—
194	C₄×C₄₇	#444	1	2	yes	—
195	C₄×C₄₇	C₂×#131	1	2	yes	—
196	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	Dic₄₇	—	4	2	no	—
199	#3169	—	47	1	no	—
200	#2931	—	47	1	no	—
201	#2931	—	47	1	no	—
202	#1594	—	47	4	no	—
203	#1580	—	47	4	no	—
204	#1566	—	47	1	no	—
205	#1492	—	47	1	no	—
206	#1492	D₄₇	1	1	yes	characteristic, complemented
207	C₂×#322	—	47	1	no	—
208	C₂×C₄₇	—	2	2	no	—
209	C₂×C₄₇	—	8	2	no	—
210	C₂×C₄₇	#2931	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
212	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
213	D₄₇	—	8	2	no	—
214	C₂×#131	—	94	1	no	—
215	C₂×#131	—	94	1	no	—
216	#532	—	47	1	no	—
217	#532	C₂×D₄₇	1	1	yes	characteristic
218	#500	—	47	1	no	—
219	#493	—	47	1	no	—
220	#486	—	47	1	no	—
221	#486	—	47	1	no	—
222	#466	—	47	4	no	—
223	C₄×D₈	—	47	4	no	—
224	#436	—	47	2	no	—
225	#436	—	47	2	no	—
226	#436	—	94	1	no	—
227	#436	—	94	1	no	—
228	C₈×D₄	—	47	2	no	—
229	C₈×D₄	—	47	2	no	—
230	C₈×D₄	—	94	1	no	—
231	C₈×D₄	—	94	1	no	—
232	#423	—	47	1	no	—
233	#423	C₂×D₄₇	1	1	yes	characteristic
234	#408	—	94	1	no	—
235	#408	—	94	1	no	—
236	C₂×C₄×C₈	—	47	1	no	—
237	C₂×C₄×C₈	—	47	1	no	—
238	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
239	#334	—	47	4	no	—
240	D₄⋊C₈	—	47	4	no	—
241	D₄⋊C₈	C₂×D₄₇	1	4	yes	—
242	#322	—	47	2	no	—
243	#322	—	47	2	no	—
244	C₄₇	#17962	1	1	yes	characteristic, complemented, Sylow
245	C₂×#41	—	2	1	no	—
246	C₂×#41	—	94	1	no	—
247	C₂×D₈	—	47	4	no	—
248	#131	—	188	4	no	—
249	#131	—	188	4	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	47	2	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	47	1	no	—
258	C₂²×C₈	—	94	2	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₄⋊Q₈	—	47	1	no	—
261	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
262	#127	—	47	1	no	—
263	#127	C₄×D₄₇	1	1	yes	characteristic
264	#124	—	2	1	no	—
265	#124	—	94	1	no	—
266	#121	—	2	1	no	—
267	#121	—	47	2	no	—
268	#121	—	94	1	no	—
269	#121	C₄×D₄₇	1	2	yes	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	47	2	no	—
272	C₄×D₄	—	94	1	no	—
273	C₄×D₄	C₂²×D₄₇	1	2	yes	—
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	#107	—	47	4	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	47	2	no	—
278	C₄⋊C₈	—	94	1	no	—
279	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
280	#102	—	47	4	no	—
281	#102	—	47	4	no	—
282	C₂²⋊C₈	—	94	2	no	—
283	C₂²⋊C₈	—	94	2	no	—
284	C₂²⋊C₈	—	94	2	no	—
285	C₂²⋊C₈	—	94	2	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	47	1	no	—
288	C₄×C₈	—	47	1	no	—
289	C₄×C₈	—	47	1	no	—
290	C₄×C₈	—	47	1	no	—
291	C₄×C₈	—	47	2	no	—
292	C₄×C₈	—	47	1	no	—
293	C₄×C₈	—	47	1	no	—
294	C₄×C₈	C₂²×D₄₇	1	2	yes	—
295	#41	—	4	2	no	—
296	#41	—	4	2	no	—
297	#41	—	188	2	no	—
298	#41	—	188	2	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	94	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	47	2	no	—
305	C₂×D₄	—	94	2	no	—
306	C₂×D₄	—	94	1	no	—
307	C₂×D₄	—	94	1	no	—
308	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	94	2	no	—
311	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
313	C₂²×C₄	#10625352	1	1	yes	characteristic
314	D₈	—	94	8	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	188	4	no	—
317	M₁₆	—	188	4	no	—
318	M₁₆	—	188	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	47	2	no	—
324	C₂×C₈	—	47	1	no	—
325	C₂×C₈	—	47	1	no	—
326	C₂×C₈	—	47	1	no	—
327	C₂×C₈	—	47	1	no	—
328	C₂×C₈	—	94	4	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	—	94	2	no	—
332	C₂×C₈	—	188	4	no	—
333	C₂×C₈	—	188	4	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	47	2	no	—
336	C₄⋊C₄	—	94	1	no	—
337	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	94	2	no	—
341	C₂²⋊C₄	—	94	2	no	—
342	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
343	C₄²	D₄×D₄₇	1	1	yes	characteristic
344	C₄²	#10625352	1	1	yes	characteristic
345	C₄²	C₂³×D₄₇	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	—	94	2	no	—
348	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
349	Q₈	—	4	2	no	—
350	Q₈	—	188	2	no	—
351	D₄	—	2	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	94	4	no	—
356	D₄	—	188	4	no	—
357	D₄	—	188	2	no	—
358	D₄	—	188	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
368	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
369	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	#13094048	1	2	yes	—
371	C₂×C₄	#13094051	1	2	yes	—
372	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₈	—	47	4	no	—
378	C₈	—	94	2	no	—
379	C₈	—	94	1	no	—
380	C₈	—	94	1	no	—
381	C₈	—	94	1	no	—
382	C₈	—	94	1	no	—
383	C₈	—	188	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	188	2	no	—
390	C₂²	—	188	2	no	—
391	C₂²	—	188	2	no	—
392	C₂²	#15689232	1	2	yes	—
393	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	188	2	no	—
398	C₄	#15689232	1	2	yes	—
399	C₄	#15689242	1	2	yes	—
400	C₄	#131×D₄₇	1	2	yes	—
401	C₄	C₂×#13094048	1	1	yes	characteristic
402	C₄	C₂×#13094051	1	1	yes	characteristic
403	C₂	—	2	2	no	—
404	C₂	—	8	2	no	—
405	C₂	—	376	2	no	—
406	C₂	#20252096	1	1	yes	characteristic
407	C₂	C₂×#15689232	1	1	yes	characteristic
408	C₂	C₂×#15689242	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1492	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253963	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1492	D₄₇
hypocenter	C₄₇	#17962
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1492

Complements

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

N	H ≅ G/N	type
2. #20252100	C₂	semidirect
3. #20252099	C₂	semidirect
4. #20242299	C₂	semidirect
5. #20242209	C₂	semidirect
6. #20242143	C₂	semidirect
7. #20241840	C₂	semidirect
8. C₂×#15688845	C₂	semidirect
9. C₄₇×#1492	C₂	semidirect
178. C₄₇⋊C₈	#131	semidirect
206. #1492	D₄₇	semidirect
244. C₄₇	#17962	semidirect

Maximal subgroups

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

subgroup	index
#20253963	2
#20252100	2
#20252099	2
#20242299	2
#20242209	2
#20242143	2
#20241840	2
C₂×#15688845	2
C₄₇×#1492	2
#17962	47