Subgroups — C₄₇×#12978 #26052676

Order 12032.

494 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#2929	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#350	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1379	C₂	1	2	yes	maximal, complemented
6	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₄₇×#525	C₄	1	1	yes	characteristic
9	C₂×M₃₂×C₄₇	—	2	1	no	—
10	C₂×M₃₂×C₄₇	—	2	4	no	—
11	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₄₇	—	2	1	no	—
13	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	—
14	C₄₇×#435	—	2	1	no	—
15	C₄₇×#435	—	2	1	no	—
16	C₈×D₄×C₄₇	—	2	1	no	—
17	C₈×D₄×C₄₇	—	2	1	no	—
18	C₄₇×#424	C₄	1	1	yes	characteristic
19	C₄₇×#408	C₄	1	1	yes	characteristic
20	C₄₇×#407	C₄	1	1	yes	characteristic
21	C₄₇×#405	C₂²	1	1	yes	characteristic
22	C₄₇×#350	—	2	4	no	—
23	C₄₇×C₂²⋊C₁₆	—	2	1	no	—
24	C₄₇×C₂²⋊C₁₆	—	2	1	no	—
25	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
27	#131×C₄₇	—	2	2	no	—
28	#131×C₄₇	—	2	2	no	—
29	C₂×M₁₆×C₄₇	—	2	1	no	—
30	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₄₇	—	2	2	no	—
33	C₂²×C₈×C₄₇	—	2	2	no	—
34	C₂²×C₈×C₄₇	—	2	1	no	—
35	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
40	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
41	#123×C₄₇	—	2	1	no	—
42	C₂²⋊Q₈×C₄₇	C₈	1	1	yes	characteristic
43	C₂²⋊Q₈×C₄₇	C₈	1	1	yes	characteristic
44	#121×C₄₇	C₈	1	1	yes	characteristic
45	#121×C₄₇	C₈	1	1	yes	characteristic
46	#120×C₄₇	—	2	1	no	—
47	C₄×D₄×C₄₇	—	2	1	no	—
48	C₄×D₄×C₄₇	—	2	1	no	—
49	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
50	M₃₂×C₄₇	—	2	4	no	—
51	M₃₂×C₄₇	—	2	2	no	—
52	M₃₂×C₄₇	D₄	1	4	yes	complemented
53	C₂×C₁₆×C₄₇	—	2	4	no	—
54	C₂×C₁₆×C₄₇	—	2	2	no	—
55	C₂×C₁₆×C₄₇	—	2	2	no	—
56	C₂×C₁₆×C₄₇	—	2	2	no	—
57	C₂×C₁₆×C₄₇	—	2	2	no	—
58	C₄⋊C₈×C₄₇	—	2	1	no	—
59	C₄⋊C₈×C₄₇	—	2	1	no	—
60	C₂²⋊C₈×C₄₇	—	2	1	no	—
61	C₂²⋊C₈×C₄₇	—	2	1	no	—
62	C₂²⋊C₈×C₄₇	—	2	1	no	—
63	C₂²⋊C₈×C₄₇	—	2	1	no	—
64	#97×C₄₇	—	2	1	no	—
65	C₄×C₈×C₄₇	—	2	1	no	—
66	C₂⁴×C₄₇	M₁₆	1	1	yes	characteristic
67	#41×C₄₇	—	2	2	no	—
68	#41×C₄₇	—	2	2	no	—
69	C₂×Q₈×C₄₇	C₂×C₈	1	1	yes	characteristic
70	C₂×D₄×C₄₇	—	2	1	no	—
71	C₂×D₄×C₄₇	—	2	1	no	—
72	C₂×D₄×C₄₇	—	2	1	no	—
73	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	M₁₆	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	M₁₆×C₄₇	—	2	2	no	—
84	M₁₆×C₄₇	—	2	2	no	—
85	M₁₆×C₄₇	—	4	2	no	—
86	C₂×C₈×C₄₇	—	2	2	no	—
87	C₂×C₈×C₄₇	—	2	1	no	—
88	C₂×C₈×C₄₇	—	2	1	no	—
89	C₂×C₈×C₄₇	—	2	2	no	—
90	C₂×C₈×C₄₇	—	2	2	no	—
91	C₂×C₈×C₄₇	—	2	1	no	—
92	C₂×C₈×C₄₇	—	2	1	no	—
93	C₂×C₈×C₄₇	—	2	1	no	—
94	C₂×C₈×C₄₇	—	2	1	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₂×C₈×C₄₇	—	4	1	no	—
97	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₄₇	#41	1	2	yes	—
103	C₄⋊C₄×C₄₇	—	2	1	no	—
104	C₄⋊C₄×C₄₇	—	2	1	no	—
105	C₄⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
106	C₄⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
107	C₂²⋊C₄×C₄₇	—	2	1	no	—
108	C₂²⋊C₄×C₄₇	—	2	1	no	—
109	C₂²⋊C₄×C₄₇	—	2	1	no	—
110	C₂²⋊C₄×C₄₇	—	2	1	no	—
111	C₂²⋊C₄×C₄₇	—	2	1	no	—
112	C₄²×C₄₇	—	2	1	no	—
113	C₁₆×C₄₇	—	2	4	no	—
114	C₁₆×C₄₇	—	4	2	no	—
115	C₂³×C₄₇	—	2	2	no	—
116	C₂³×C₄₇	—	2	2	no	—
117	C₂³×C₄₇	—	2	1	no	—
118	C₂³×C₄₇	—	4	1	no	—
119	C₂³×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
120	C₂³×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
121	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
122	Q₈×C₄₇	—	2	2	no	—
123	D₄×C₄₇	—	2	2	no	—
124	D₄×C₄₇	—	4	2	no	—
125	D₄×C₄₇	—	4	2	no	—
126	D₄×C₄₇	—	4	2	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	4	1	no	—
138	C₂×C₄×C₄₇	—	4	1	no	—
139	C₂×C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	#131	1	2	yes	—
145	C₈×C₄₇	—	2	1	no	—
146	C₈×C₄₇	—	2	1	no	—
147	C₈×C₄₇	—	4	1	no	—
148	C₈×C₄₇	—	4	1	no	—
149	C₈×C₄₇	#120	1	1	yes	characteristic
150	C₈×C₄₇	#121	1	2	yes	—
151	C₈×C₄₇	#123	1	1	yes	characteristic
152	#12978	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂²×C₄₇	—	2	1	no	—
154	C₂²×C₄₇	—	2	1	no	—
155	C₂²×C₄₇	—	2	1	no	—
156	C₂²×C₄₇	—	2	1	no	—
157	C₂²×C₄₇	—	2	1	no	—
158	C₂²×C₄₇	—	2	1	no	—
159	C₂²×C₄₇	—	2	1	no	—
160	C₂²×C₄₇	—	4	4	no	—
161	C₂²×C₄₇	—	4	1	no	—
162	C₂²×C₄₇	—	4	1	no	—
163	C₂²×C₄₇	—	4	1	no	—
164	C₂²×C₄₇	#350	1	2	yes	complemented
165	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
166	C₂²×C₄₇	#435	1	2	yes	—
167	C₄×C₄₇	—	2	1	no	—
168	C₄×C₄₇	—	2	1	no	—
169	C₄×C₄₇	—	4	1	no	—
170	C₄×C₄₇	—	4	1	no	—
171	C₄×C₄₇	—	4	1	no	—
172	C₄×C₄₇	#386	1	1	yes	characteristic
173	C₄×C₄₇	#408	1	1	yes	characteristic
174	C₄×C₄₇	C₈×D₄	1	2	yes	—
175	C₂²×M₃₂	C₂×C₄₇	1	1	yes	characteristic, complemented
176	#2929	C₂×C₄₇	1	1	yes	characteristic
177	C₂×#350	C₂×C₄₇	1	2	yes	complemented
178	C₂×C₂²⋊C₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
179	#1379	C₂×C₄₇	1	2	yes	complemented
180	C₂×C₄₇	—	2	2	no	—
181	C₂×C₄₇	—	2	2	no	—
182	C₂×C₄₇	—	4	1	no	—
183	C₂×C₄₇	—	8	1	no	—
184	C₂×C₄₇	#1869	1	1	yes	characteristic
185	C₂×C₄₇	C₂×#350	1	1	yes	characteristic
186	C₂×C₄₇	#2117	1	1	yes	characteristic
187	C₂×#131	C₂²×C₄₇	1	1	yes	characteristic
188	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
189	#525	C₄×C₄₇	1	1	yes	characteristic
190	C₂×M₃₂	—	2	1	no	—
191	C₂×M₃₂	—	2	4	no	—
192	C₂×M₃₂	C₂²×C₄₇	1	2	yes	—
193	C₂²×C₁₆	—	2	1	no	—
194	C₂²×C₁₆	C₂²×C₄₇	1	2	yes	—
195	#435	—	2	1	no	—
196	#435	—	2	1	no	—
197	C₈×D₄	—	2	1	no	—
198	C₈×D₄	—	2	1	no	—
199	#424	C₄×C₄₇	1	1	yes	characteristic
200	#408	C₄×C₄₇	1	1	yes	characteristic
201	#407	C₄×C₄₇	1	1	yes	characteristic
202	#405	C₂²×C₄₇	1	1	yes	characteristic
203	#350	—	2	4	no	—
204	C₂²⋊C₁₆	—	2	1	no	—
205	C₂²⋊C₁₆	—	2	1	no	—
206	C₄₇	#12978	1	1	yes	characteristic, direct product factor, Sylow
207	C₂×#41	C₂×C₄×C₄₇	1	1	yes	characteristic
208	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
209	#131	—	2	2	no	—
210	#131	—	2	2	no	—
211	C₂×M₁₆	—	2	1	no	—
212	C₂×M₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
213	C₂×M₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
218	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
219	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
220	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
221	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
223	#123	—	2	1	no	—
224	C₂²⋊Q₈	C₈×C₄₇	1	1	yes	characteristic
225	C₂²⋊Q₈	C₈×C₄₇	1	1	yes	characteristic
226	#121	C₈×C₄₇	1	1	yes	characteristic
227	#121	C₈×C₄₇	1	1	yes	characteristic
228	#120	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	#117	C₂×C₄×C₄₇	1	1	yes	characteristic
232	M₃₂	—	2	4	no	—
233	M₃₂	—	2	2	no	—
234	M₃₂	D₄×C₄₇	1	4	yes	complemented
235	C₂×C₁₆	—	2	4	no	—
236	C₂×C₁₆	—	2	2	no	—
237	C₂×C₁₆	—	2	2	no	—
238	C₂×C₁₆	—	2	2	no	—
239	C₂×C₁₆	—	2	2	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₂²⋊C₈	—	2	1	no	—
243	C₂²⋊C₈	—	2	1	no	—
244	C₂²⋊C₈	—	2	1	no	—
245	C₂²⋊C₈	—	2	1	no	—
246	#97	—	2	1	no	—
247	C₄×C₈	—	2	1	no	—
248	C₂⁴	M₁₆×C₄₇	1	1	yes	characteristic
249	#41	—	2	2	no	—
250	#41	—	2	2	no	—
251	C₂×Q₈	C₂×C₈×C₄₇	1	1	yes	characteristic
252	C₂×D₄	—	2	1	no	—
253	C₂×D₄	—	2	1	no	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	C₂×C₈×C₄₇	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₈×C₄₇	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₈×C₄₇	1	1	yes	characteristic
263	C₂²×C₄	M₁₆×C₄₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
265	M₁₆	—	2	2	no	—
266	M₁₆	—	2	2	no	—
267	M₁₆	—	4	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	1	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	4	1	no	—
278	C₂×C₈	—	4	1	no	—
279	C₂×C₈	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
280	C₂×C₈	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
281	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
282	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
283	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
284	C₂×C₈	#41×C₄₇	1	2	yes	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	C₂×C₈×C₄₇	1	1	yes	characteristic
288	C₄⋊C₄	C₂×C₈×C₄₇	1	1	yes	characteristic
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₄²	—	2	1	no	—
295	C₁₆	—	2	4	no	—
296	C₁₆	—	4	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	4	1	no	—
301	C₂³	C₂²⋊C₈×C₄₇	1	1	yes	characteristic
302	C₂³	C₂²⋊C₈×C₄₇	1	1	yes	characteristic
303	C₂³	C₂×M₁₆×C₄₇	1	1	yes	characteristic
304	Q₈	—	2	2	no	—
305	D₄	—	2	2	no	—
306	D₄	—	4	2	no	—
307	D₄	—	4	2	no	—
308	D₄	—	4	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	C₂²⋊C₈×C₄₇	1	1	yes	characteristic
322	C₂×C₄	C₂²⋊C₈×C₄₇	1	1	yes	characteristic
323	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
324	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
325	C₂×C₄	C₂²×C₈×C₄₇	1	1	yes	characteristic
326	C₂×C₄	#131×C₄₇	1	2	yes	—
327	C₈	—	2	1	no	—
328	C₈	—	2	1	no	—
329	C₈	—	4	1	no	—
330	C₈	—	4	1	no	—
331	C₈	#120×C₄₇	1	1	yes	characteristic
332	C₈	#121×C₄₇	1	2	yes	—
333	C₈	#123×C₄₇	1	1	yes	characteristic
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	4	1	no	—
343	C₂²	—	4	1	no	—
344	C₂²	—	4	1	no	—
345	C₂²	C₄₇×#350	1	2	yes	complemented
346	C₂²	C₂×C₂²⋊C₈×C₄₇	1	1	yes	characteristic
347	C₂²	C₄₇×#435	1	2	yes	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	1	no	—
351	C₄	—	4	1	no	—
352	C₄	—	4	1	no	—
353	C₄	C₄₇×#386	1	1	yes	characteristic
354	C₄	C₄₇×#408	1	1	yes	characteristic
355	C₄	C₈×D₄×C₄₇	1	2	yes	—
356	C₂	—	2	2	no	—
357	C₂	—	2	2	no	—
358	C₂	—	4	1	no	—
359	C₂	—	8	1	no	—
360	C₂	C₄₇×#1869	1	1	yes	characteristic
361	C₂	C₂×C₄₇×#350	1	1	yes	characteristic
362	C₂	C₄₇×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₄₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₄₇
Frattini, cosocle	C₂²×C₈	C₂³×C₄₇
socle	C₂²×C₄₇	C₂×C₂²⋊C₈
prime radical	C₄₇×#525	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₄₇ ◁ C₂³×C₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×M₃₂×C₄₇	C₂	semidirect
3. C₂×C₄₇×#350	C₂	semidirect
4. C₂×C₄₇×C₂²⋊C₁₆	C₂	semidirect
5. C₄₇×#1379	C₂	semidirect
52. M₃₂×C₄₇	D₄	semidirect
152. #12978	C₄₇	direct (N × H)
164. C₂²×C₄₇	#350	semidirect
175. C₂²×M₃₂	C₂×C₄₇	semidirect
177. C₂×#350	C₂×C₄₇	semidirect
178. C₂×C₂²⋊C₁₆	C₂×C₄₇	semidirect
179. #1379	C₂×C₄₇	semidirect
206. C₄₇	#12978	direct (N × H)
234. M₃₂	D₄×C₄₇	semidirect
345. C₂²	C₄₇×#350	semidirect

Maximal subgroups

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

subgroup	index
C₂²×M₃₂×C₄₇	2
C₄₇×#2929	2
C₂×C₄₇×#350	2
C₂×C₄₇×C₂²⋊C₁₆	2
C₄₇×#1379	2
#12978	47

Subgroups — C47×#12978 #26052676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#12978 #26052676