Subgroups — C₄₇×#15091 #26054789

Order 12032.

2322 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#386	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#386	C₂	1	2	yes	maximal
4	C₄₇×#1442	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1439	C₂	1	4	yes	maximal, complemented
6	C₄₇×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₇	—	2	8	no	—
12	C₂²×C₄⋊C₄×C₄₇	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
18	C₄₇×#386	—	2	4	no	—
19	C₄₇×#386	—	2	8	no	—
20	C₂×#95×C₄₇	C₂²	1	4	yes	—
21	C₂×#95×C₄₇	C₂²	1	2	yes	—
22	C₂×#95×C₄₇	C₂²	1	4	yes	—
23	C₂×#95×C₄₇	C₂²	1	8	yes	—
24	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
25	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
26	C₂²×D₄×C₄₇	—	2	2	no	—
27	C₂²×D₄×C₄₇	—	2	4	no	—
28	C₂²×D₄×C₄₇	—	2	4	no	—
29	C₂²×D₄×C₄₇	—	2	2	no	—
30	C₂²×D₄×C₄₇	Q₈	1	4	yes	—
31	C₂³×C₄×C₄₇	—	2	4	no	—
32	C₂³×C₄×C₄₇	—	2	8	no	—
33	C₂³×C₄×C₄₇	—	2	4	no	—
34	C₂³×C₄×C₄₇	—	2	4	no	—
35	C₂³×C₄×C₄₇	—	4	8	no	—
36	C₂³×C₄×C₄₇	D₄	1	4	yes	—
37	C₂³×C₄×C₄₇	D₄	1	8	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂×C₄⋊C₄×C₄₇	—	2	32	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	16	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
46	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
52	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
55	#95×C₄₇	—	2	8	no	—
56	#95×C₄₇	—	2	4	no	—
57	#95×C₄₇	—	2	8	no	—
58	#95×C₄₇	—	4	8	no	—
59	C₂⁴×C₄₇	—	2	4	no	—
60	C₂⁴×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	—	2	1	no	—
62	C₂⁴×C₄₇	—	2	2	no	—
63	C₂⁴×C₄₇	—	2	4	no	—
64	C₂⁴×C₄₇	—	2	2	no	—
65	C₂⁴×C₄₇	—	2	1	no	—
66	C₂⁴×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
68	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
69	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
70	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
71	C₂⁴×C₄₇	#41	1	4	yes	—
72	C₂⁴×C₄₇	#41	1	2	yes	—
73	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
74	C₂×D₄×C₄₇	—	2	16	no	—
75	C₂×D₄×C₄₇	—	2	8	no	—
76	C₂×D₄×C₄₇	—	4	4	no	—
77	C₂×D₄×C₄₇	—	4	8	no	—
78	C₂×D₄×C₄₇	—	4	4	no	—
79	C₂²×C₄×C₄₇	—	2	32	no	—
80	C₂²×C₄×C₄₇	—	2	8	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	16	no	—
84	C₂²×C₄×C₄₇	—	2	16	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	8	no	—
92	C₂²×C₄×C₄₇	—	2	8	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	8	no	—
100	C₂²×C₄×C₄₇	—	2	8	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	4	16	no	—
103	C₂²×C₄×C₄₇	—	4	16	no	—
104	C₂²×C₄×C₄₇	—	4	16	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	8	yes	—
109	C₄⋊C₄×C₄₇	—	2	32	no	—
110	C₂²⋊C₄×C₄₇	—	4	16	no	—
111	C₂²⋊C₄×C₄₇	—	4	8	no	—
112	C₂²⋊C₄×C₄₇	—	4	4	no	—
113	C₂²⋊C₄×C₄₇	—	4	8	no	—
114	C₂³×C₄₇	—	2	4	no	—
115	C₂³×C₄₇	—	2	8	no	—
116	C₂³×C₄₇	—	2	8	no	—
117	C₂³×C₄₇	—	2	4	no	—
118	C₂³×C₄₇	—	2	16	no	—
119	C₂³×C₄₇	—	2	8	no	—
120	C₂³×C₄₇	—	2	8	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	2	no	—
123	C₂³×C₄₇	—	2	8	no	—
124	C₂³×C₄₇	—	4	1	no	—
125	C₂³×C₄₇	—	4	2	no	—
126	C₂³×C₄₇	—	4	4	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	1	no	—
129	C₂³×C₄₇	—	4	4	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	—	4	8	no	—
132	C₂³×C₄₇	—	4	4	no	—
133	C₂³×C₄₇	#120	1	4	yes	—
134	C₂³×C₄₇	C₂²⋊Q₈	1	8	yes	—
135	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
136	C₂³×C₄₇	#124	1	8	yes	—
137	C₂³×C₄₇	#124	1	4	yes	—
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
140	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
141	C₂³×C₄₇	C₂×#41	1	2	yes	—
142	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
143	C₂³×C₄₇	C₂×#41	1	4	yes	—
144	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
145	D₄×C₄₇	—	4	16	no	—
146	C₂×C₄×C₄₇	—	2	32	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	16	no	—
150	C₂×C₄×C₄₇	—	2	8	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	8	no	—
154	C₂×C₄×C₄₇	—	2	8	no	—
155	C₂×C₄×C₄₇	—	4	32	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	8	no	—
160	C₂×C₄×C₄₇	—	4	8	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	4	4	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	4	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	8	no	—
168	C₂×C₄×C₄₇	—	4	8	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	#123	1	8	yes	—
171	#15091	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₇	—	2	16	no	—
173	C₂²×C₄₇	—	2	16	no	—
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	—	2	8	no	—
177	C₂²×C₄₇	—	2	8	no	—
178	C₂²×C₄₇	—	4	8	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	—	8	4	no	—
182	C₂²×C₄₇	—	8	1	no	—
183	C₂²×C₄₇	—	8	1	no	—
184	C₂²×C₄₇	—	8	2	no	—
185	C₂²×C₄₇	#393	1	8	yes	—
186	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
188	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#123	1	2	yes	—
190	C₂²×C₄₇	#525	1	4	yes	—
191	C₂²×C₄₇	C₂×#124	1	2	yes	—
192	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
193	C₂²×C₄₇	#534	1	4	yes	—
194	C₂²×C₄₇	#535	1	2	yes	—
195	C₂²×C₄₇	#553	1	8	yes	—
196	C₂²×C₄₇	#553	1	4	yes	—
197	C₂²×C₄₇	#554	1	4	yes	—
198	C₄×C₄₇	—	2	8	no	—
199	C₄×C₄₇	—	4	8	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	—	8	4	no	—
202	C₄×C₄₇	—	8	2	no	—
203	C₂³×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
204	C₂×#386	C₂×C₄₇	1	1	yes	characteristic
205	C₂×#386	C₂×C₄₇	1	2	yes	—
206	#1442	C₂×C₄₇	1	4	yes	complemented
207	#1439	C₂×C₄₇	1	4	yes	complemented
208	C₂²⋊#95	C₂×C₄₇	1	1	yes	characteristic, complemented
209	C₂²⋊#95	C₂×C₄₇	1	2	yes	complemented
210	C₂×C₄₇	—	2	8	no	—
211	C₂×C₄₇	—	8	2	no	—
212	C₂×C₄₇	C₂×#393	1	1	yes	characteristic
213	C₂×C₄₇	#2487	1	2	yes	—
214	C₂×C₄₇	#2504	1	2	yes	—
215	C₂×C₄₇	#2579	1	4	yes	—
216	C₂×C₄₇	#2591	1	4	yes	—
217	C₂×C₄₇	#2613	1	1	yes	characteristic
218	C₂×C₄₇	#2849	1	1	yes	characteristic
219	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
220	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
221	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
222	C₂²×C₄⋊C₄	—	2	8	no	—
223	C₂²×C₄⋊C₄	—	2	4	no	—
224	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
225	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
226	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
227	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
228	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
229	#386	—	2	4	no	—
230	#386	—	2	8	no	—
231	C₂×#95	C₂²×C₄₇	1	4	yes	—
232	C₂×#95	C₂²×C₄₇	1	4	yes	—
233	C₂×#95	C₂²×C₄₇	1	2	yes	—
234	C₂×#95	C₂²×C₄₇	1	8	yes	—
235	C₄₇	#15091	1	1	yes	characteristic, direct product factor, Sylow
236	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
237	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	—	2	4	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	Q₈×C₄₇	1	4	yes	—
243	C₂³×C₄	—	2	4	no	—
244	C₂³×C₄	—	2	8	no	—
245	C₂³×C₄	—	2	4	no	—
246	C₂³×C₄	—	2	4	no	—
247	C₂³×C₄	—	4	8	no	—
248	C₂³×C₄	D₄×C₄₇	1	4	yes	—
249	C₂³×C₄	D₄×C₄₇	1	8	yes	—
250	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
251	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
252	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
253	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
255	C₂×C₄⋊C₄	—	2	32	no	—
256	C₂×C₄⋊C₄	—	2	16	no	—
257	C₂×C₄⋊C₄	—	2	8	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	8	no	—
264	C₂×C₂²⋊C₄	—	2	4	no	—
265	C₂×C₂²⋊C₄	—	2	8	no	—
266	C₂×C₂²⋊C₄	—	4	8	no	—
267	#95	—	2	8	no	—
268	#95	—	2	4	no	—
269	#95	—	2	8	no	—
270	#95	—	4	8	no	—
271	C₂⁴	—	2	4	no	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	—	2	2	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	2	no	—
277	C₂⁴	—	2	1	no	—
278	C₂⁴	—	2	4	no	—
279	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
280	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
281	C₂⁴	C₂×Q₈×C₄₇	1	2	yes	—
282	C₂⁴	C₂×Q₈×C₄₇	1	2	yes	—
283	C₂⁴	#41×C₄₇	1	4	yes	—
284	C₂⁴	#41×C₄₇	1	2	yes	—
285	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
286	C₂×D₄	—	2	16	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	—	4	8	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂²×C₄	—	2	32	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	16	no	—
296	C₂²×C₄	—	2	16	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	4	16	no	—
315	C₂²×C₄	—	4	16	no	—
316	C₂²×C₄	—	4	16	no	—
317	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
318	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
319	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
320	C₂²×C₄	#41×C₄₇	1	8	yes	—
321	C₄⋊C₄	—	2	32	no	—
322	C₂²⋊C₄	—	4	16	no	—
323	C₂²⋊C₄	—	4	8	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	8	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	8	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	16	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	8	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	4	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	4	no	—
345	C₂³	#120×C₄₇	1	4	yes	—
346	C₂³	C₂²⋊Q₈×C₄₇	1	8	yes	—
347	C₂³	C₂²⋊Q₈×C₄₇	1	4	yes	—
348	C₂³	#124×C₄₇	1	8	yes	—
349	C₂³	#124×C₄₇	1	4	yes	—
350	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
351	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
352	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
353	C₂³	C₂×#41×C₄₇	1	2	yes	—
354	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
355	C₂³	C₂×#41×C₄₇	1	4	yes	—
356	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
357	D₄	—	4	16	no	—
358	C₂×C₄	—	2	32	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	16	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	4	32	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	8	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	#123×C₄₇	1	8	yes	—
383	C₂²	—	2	16	no	—
384	C₂²	—	2	16	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	8	4	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	2	no	—
396	C₂²	C₄₇×#393	1	8	yes	—
397	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
398	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
399	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
400	C₂²	C₂×#123×C₄₇	1	2	yes	—
401	C₂²	C₄₇×#525	1	4	yes	—
402	C₂²	C₂×#124×C₄₇	1	2	yes	—
403	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
404	C₂²	C₄₇×#534	1	4	yes	—
405	C₂²	C₄₇×#535	1	2	yes	—
406	C₂²	C₄₇×#553	1	8	yes	—
407	C₂²	C₄₇×#553	1	4	yes	—
408	C₂²	C₄₇×#554	1	4	yes	—
409	C₄	—	2	8	no	—
410	C₄	—	4	8	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	4	no	—
413	C₄	—	8	2	no	—
414	C₂	—	2	8	no	—
415	C₂	—	8	2	no	—
416	C₂	C₂×C₄₇×#393	1	1	yes	characteristic
417	C₂	C₄₇×#2487	1	2	yes	—
418	C₂	C₄₇×#2504	1	2	yes	—
419	C₂	C₄₇×#2579	1	4	yes	—
420	C₂	C₄₇×#2591	1	4	yes	—
421	C₂	C₄₇×#2613	1	1	yes	characteristic
422	C₂	C₄₇×#2849	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄⋊C₄×C₄₇	C₂	semidirect
4. C₄₇×#1442	C₂	semidirect
5. C₄₇×#1439	C₂	semidirect
6. C₄₇×C₂²⋊#95	C₂	semidirect
7. C₄₇×C₂²⋊#95	C₂	semidirect
171. #15091	C₄₇	direct (N × H)
203. C₂³×C₄⋊C₄	C₂×C₄₇	semidirect
206. #1442	C₂×C₄₇	semidirect
207. #1439	C₂×C₄₇	semidirect
208. C₂²⋊#95	C₂×C₄₇	semidirect
209. C₂²⋊#95	C₂×C₄₇	semidirect
235. C₄₇	#15091	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₄₇	2
C₂×C₄₇×#386	2
C₄₇×#1442	2
C₄₇×#1439	2
C₄₇×C₂²⋊#95	2
#15091	47

Subgroups — C47×#15091 #26054789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15091 #26054789