Subgroups — C₄₇×#13922 #26053620

Order 12032.

4166 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#391	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1446	C₂	1	4	yes	maximal, complemented
6	C₄₇×C₂²⋊#95	C₂	1	4	yes	maximal
7	C₂³×Q₈×C₄₇	—	2	16	no	—
8	C₂³×Q₈×C₄₇	—	2	4	no	—
9	C₂³×Q₈×C₄₇	—	2	4	no	—
10	C₂³×Q₈×C₄₇	C₄	1	8	yes	complemented
11	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
12	C₂³×Q₈×C₄₇	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#391	—	2	16	no	—
20	C₄₇×#380	—	2	4	no	—
21	C₄×C₂²⋊C₄×C₄₇	—	2	4	no	—
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	16	yes	—
25	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
26	C₂²×Q₈×C₄₇	—	2	64	no	—
27	C₂²×Q₈×C₄₇	—	2	64	no	—
28	C₂²×Q₈×C₄₇	—	2	64	no	—
29	C₂²×Q₈×C₄₇	—	2	32	no	—
30	C₂²×Q₈×C₄₇	—	2	16	no	—
31	C₂²×Q₈×C₄₇	—	2	4	no	—
32	C₂²×Q₈×C₄₇	—	2	4	no	—
33	C₂²×Q₈×C₄₇	—	2	4	no	—
34	C₂²×Q₈×C₄₇	—	2	8	no	—
35	C₂²×Q₈×C₄₇	—	2	4	no	—
36	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	—
37	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	—
38	C₂²×Q₈×C₄₇	D₄	1	16	yes	—
39	C₂³×C₄×C₄₇	—	2	4	no	—
40	C₂³×C₄×C₄₇	—	2	4	no	—
41	C₂³×C₄×C₄₇	—	2	16	no	—
42	C₂³×C₄×C₄₇	—	2	8	no	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₄₇	D₄	1	4	yes	—
46	C₂³×C₄×C₄₇	D₄	1	4	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
48	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₄₇	Q₈	1	8	yes	complemented
59	C₂×C₄²×C₄₇	—	2	4	no	—
60	C₂×C₄²×C₄₇	—	2	8	no	—
61	#95×C₄₇	—	2	4	no	—
62	#95×C₄₇	—	2	4	no	—
63	#95×C₄₇	—	2	32	no	—
64	C₂⁴×C₄₇	—	2	4	no	—
65	C₂⁴×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
67	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
68	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
69	C₂⁴×C₄₇	C₂×Q₈	1	4	yes	—
70	C₂⁴×C₄₇	#41	1	4	yes	—
71	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
72	C₂×Q₈×C₄₇	—	2	256	no	—
73	C₂×Q₈×C₄₇	—	2	32	no	—
74	C₂×Q₈×C₄₇	—	2	32	no	—
75	C₂×Q₈×C₄₇	—	2	32	no	—
76	C₂×Q₈×C₄₇	—	2	16	no	—
77	C₂×Q₈×C₄₇	—	2	16	no	—
78	C₂×Q₈×C₄₇	—	2	16	no	—
79	C₂×Q₈×C₄₇	—	2	32	no	—
80	C₂×Q₈×C₄₇	—	2	32	no	—
81	C₂×Q₈×C₄₇	C₂²⋊C₄	1	32	yes	complemented
82	C₂²×C₄×C₄₇	—	2	32	no	—
83	C₂²×C₄×C₄₇	—	2	32	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	8	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	32	no	—
90	C₂²×C₄×C₄₇	—	2	16	no	—
91	C₂²×C₄×C₄₇	—	2	16	no	—
92	C₂²×C₄×C₄₇	—	2	16	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	8	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	8	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	8	no	—
99	C₂²×C₄×C₄₇	—	2	8	no	—
100	C₂²×C₄×C₄₇	—	2	8	no	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	16	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×Q₈	1	8	yes	complemented
112	C₄⋊C₄×C₄₇	—	4	8	no	—
113	C₂²⋊C₄×C₄₇	—	2	16	no	—
114	C₂²⋊C₄×C₄₇	—	4	8	no	—
115	C₄²×C₄₇	—	4	8	no	—
116	C₂³×C₄₇	—	2	4	no	—
117	C₂³×C₄₇	—	2	4	no	—
118	C₂³×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	—	2	4	no	—
120	C₂³×C₄₇	—	2	4	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	16	no	—
123	C₂³×C₄₇	—	2	16	no	—
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
125	C₂³×C₄₇	C₄×Q₈	1	8	yes	—
126	C₂³×C₄₇	C₂²⋊Q₈	1	8	yes	—
127	C₂³×C₄₇	#124	1	4	yes	—
128	C₂³×C₄₇	C₄⋊Q₈	1	4	yes	—
129	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
131	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
133	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
134	C₂³×C₄₇	C₂×#41	1	2	yes	—
135	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
136	Q₈×C₄₇	—	2	64	no	—
137	Q₈×C₄₇	—	2	64	no	—
138	C₂×C₄×C₄₇	—	2	64	no	—
139	C₂×C₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	2	8	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	16	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	16	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	32	no	—
147	C₂×C₄×C₄₇	—	2	8	no	—
148	C₂×C₄×C₄₇	—	2	16	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	8	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	16	no	—
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂×C₄×C₄₇	#120	1	8	yes	—
161	C₂×C₄×C₄₇	#120	1	8	yes	—
162	#13922	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₄₇	—	2	4	no	—
164	C₂²×C₄₇	—	2	16	no	—
165	C₂²×C₄₇	—	2	16	no	—
166	C₂²×C₄₇	—	2	8	no	—
167	C₂²×C₄₇	—	2	8	no	—
168	C₂²×C₄₇	—	2	4	no	—
169	C₂²×C₄₇	#391	1	8	yes	complemented
170	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	2	yes	—
172	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
173	C₂²×C₄₇	#519	1	2	yes	—
174	C₂²×C₄₇	C₂×#120	1	2	yes	—
175	C₂²×C₄₇	C₂×#120	1	2	yes	—
176	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
177	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
179	C₂²×C₄₇	#536	1	2	yes	—
180	C₂²×C₄₇	#536	1	2	yes	—
181	C₂²×C₄₇	#548	1	8	yes	—
182	C₂²×C₄₇	D₄×Q₈	1	8	yes	—
183	C₄×C₄₇	—	2	16	no	—
184	C₄×C₄₇	—	2	4	no	—
185	C₄×C₄₇	—	4	8	no	—
186	C₄×C₄₇	—	8	4	no	—
187	C₄×C₄₇	#379	1	8	yes	—
188	C₂⁴×Q₈	C₂×C₄₇	1	1	yes	characteristic
189	C₂×#391	C₂×C₄₇	1	4	yes	complemented
190	C₂×#380	C₂×C₄₇	1	1	yes	characteristic
191	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
192	#1446	C₂×C₄₇	1	4	yes	complemented
193	C₂²⋊#95	C₂×C₄₇	1	4	yes	—
194	C₂×C₄₇	—	2	8	no	—
195	C₂×C₄₇	C₂×#379	1	1	yes	characteristic
196	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
197	C₂×C₄₇	#2310	1	1	yes	characteristic
198	C₂×C₄₇	Q₈×C₂²⋊C₄	1	4	yes	—
199	C₂×C₄₇	#2409	1	4	yes	—
200	C₂×C₄₇	#2434	1	2	yes	—
201	C₂×C₄₇	#2436	1	2	yes	—
202	C₂³×Q₈	—	2	16	no	—
203	C₂³×Q₈	—	2	4	no	—
204	C₂³×Q₈	—	2	4	no	—
205	C₂³×Q₈	C₄×C₄₇	1	8	yes	complemented
206	C₂³×Q₈	C₂²×C₄₇	1	2	yes	—
207	C₂³×Q₈	C₂²×C₄₇	1	2	yes	—
208	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
209	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
211	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
212	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
213	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
214	#391	—	2	16	no	—
215	#380	—	2	4	no	—
216	C₄×C₂²⋊C₄	—	2	4	no	—
217	C₂×#95	C₂²×C₄₇	1	16	yes	—
218	C₂×#95	C₂²×C₄₇	1	2	yes	—
219	C₂×#95	C₂²×C₄₇	1	2	yes	—
220	C₄₇	#13922	1	1	yes	characteristic, direct product factor, Sylow
221	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
222	C₂²×Q₈	—	2	64	no	—
223	C₂²×Q₈	—	2	64	no	—
224	C₂²×Q₈	—	2	64	no	—
225	C₂²×Q₈	—	2	32	no	—
226	C₂²×Q₈	—	2	16	no	—
227	C₂²×Q₈	—	2	4	no	—
228	C₂²×Q₈	—	2	4	no	—
229	C₂²×Q₈	—	2	4	no	—
230	C₂²×Q₈	—	2	8	no	—
231	C₂²×Q₈	—	2	4	no	—
232	C₂²×Q₈	C₂×C₄×C₄₇	1	8	yes	—
233	C₂²×Q₈	C₂×C₄×C₄₇	1	8	yes	—
234	C₂²×Q₈	D₄×C₄₇	1	16	yes	—
235	C₂³×C₄	—	2	4	no	—
236	C₂³×C₄	—	2	4	no	—
237	C₂³×C₄	—	2	16	no	—
238	C₂³×C₄	—	2	8	no	—
239	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	—
240	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
241	C₂³×C₄	D₄×C₄₇	1	4	yes	—
242	C₂³×C₄	D₄×C₄₇	1	4	yes	—
243	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
244	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
245	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
246	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	—	2	8	no	—
250	C₂×C₂²⋊C₄	—	2	4	no	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	8	no	—
254	C₂×C₂²⋊C₄	Q₈×C₄₇	1	8	yes	complemented
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	—	2	8	no	—
257	#95	—	2	4	no	—
258	#95	—	2	4	no	—
259	#95	—	2	32	no	—
260	C₂⁴	—	2	4	no	—
261	C₂⁴	—	2	4	no	—
262	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
263	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
264	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
265	C₂⁴	C₂×Q₈×C₄₇	1	4	yes	—
266	C₂⁴	#41×C₄₇	1	4	yes	—
267	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
268	C₂×Q₈	—	2	256	no	—
269	C₂×Q₈	—	2	32	no	—
270	C₂×Q₈	—	2	32	no	—
271	C₂×Q₈	—	2	32	no	—
272	C₂×Q₈	—	2	16	no	—
273	C₂×Q₈	—	2	16	no	—
274	C₂×Q₈	—	2	16	no	—
275	C₂×Q₈	—	2	32	no	—
276	C₂×Q₈	—	2	32	no	—
277	C₂×Q₈	C₂²⋊C₄×C₄₇	1	32	yes	complemented
278	C₂²×C₄	—	2	32	no	—
279	C₂²×C₄	—	2	32	no	—
280	C₂²×C₄	—	2	16	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	32	no	—
286	C₂²×C₄	—	2	16	no	—
287	C₂²×C₄	—	2	16	no	—
288	C₂²×C₄	—	2	16	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	C₂²⋊C₄×C₄₇	1	16	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
299	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₄₇	1	16	yes	—
302	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
306	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
307	C₂²×C₄	C₂×Q₈×C₄₇	1	8	yes	complemented
308	C₄⋊C₄	—	4	8	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₂²⋊C₄	—	4	8	no	—
311	C₄²	—	4	8	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	4	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	4	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	2	16	no	—
319	C₂³	—	2	16	no	—
320	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
321	C₂³	C₄×Q₈×C₄₇	1	8	yes	—
322	C₂³	C₂²⋊Q₈×C₄₇	1	8	yes	—
323	C₂³	#124×C₄₇	1	4	yes	—
324	C₂³	C₄⋊Q₈×C₄₇	1	4	yes	—
325	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
326	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
327	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
328	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
329	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
330	C₂³	C₂×#41×C₄₇	1	2	yes	—
331	C₂³	2₋¹⁺⁴×C₄₇	1	4	yes	—
332	Q₈	—	2	64	no	—
333	Q₈	—	2	64	no	—
334	C₂×C₄	—	2	64	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	16	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	16	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	32	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	16	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	16	no	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	16	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
356	C₂×C₄	#120×C₄₇	1	8	yes	—
357	C₂×C₄	#120×C₄₇	1	8	yes	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	16	no	—
361	C₂²	—	2	16	no	—
362	C₂²	—	2	8	no	—
363	C₂²	—	2	8	no	—
364	C₂²	C₄₇×#391	1	8	yes	complemented
365	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
366	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	2	yes	—
367	C₂²	C₂×C₄×Q₈×C₄₇	1	2	yes	—
368	C₂²	C₄₇×#519	1	2	yes	—
369	C₂²	C₂×#120×C₄₇	1	2	yes	—
370	C₂²	C₂×#120×C₄₇	1	2	yes	—
371	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
372	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
373	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
374	C₂²	C₄₇×#536	1	2	yes	—
375	C₂²	C₄₇×#536	1	2	yes	—
376	C₂²	C₄₇×#548	1	8	yes	—
377	C₂²	D₄×Q₈×C₄₇	1	8	yes	—
378	C₄	—	2	16	no	—
379	C₄	—	2	4	no	—
380	C₄	—	4	8	no	—
381	C₄	—	8	4	no	—
382	C₄	C₄₇×#379	1	8	yes	—
383	C₂	—	2	8	no	—
384	C₂	C₂×C₄₇×#379	1	1	yes	characteristic
385	C₂	C₂×C₄₇×#391	1	1	yes	characteristic
386	C₂	C₄₇×#2310	1	1	yes	characteristic
387	C₂	Q₈×C₂²⋊C₄×C₄₇	1	4	yes	—
388	C₂	C₄₇×#2409	1	4	yes	—
389	C₂	C₄₇×#2434	1	2	yes	—
390	C₂	C₄₇×#2436	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂⁵×C₄₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#391	C₂	semidirect
5. C₄₇×#1446	C₂	semidirect
10. C₂³×Q₈×C₄₇	C₄	semidirect
58. C₂×C₂²⋊C₄×C₄₇	Q₈	semidirect
81. C₂×Q₈×C₄₇	C₂²⋊C₄	semidirect
111. C₂²×C₄×C₄₇	C₂×Q₈	semidirect
162. #13922	C₄₇	direct (N × H)
169. C₂²×C₄₇	#391	semidirect
189. C₂×#391	C₂×C₄₇	semidirect
192. #1446	C₂×C₄₇	semidirect
205. C₂³×Q₈	C₄×C₄₇	semidirect
220. C₄₇	#13922	direct (N × H)
254. C₂×C₂²⋊C₄	Q₈×C₄₇	semidirect
277. C₂×Q₈	C₂²⋊C₄×C₄₇	semidirect
307. C₂²×C₄	C₂×Q₈×C₄₇	semidirect
364. C₂²	C₄₇×#391	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₄₇	2
C₂×C₄₇×#391	2
C₂×C₄₇×#380	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₄₇×#1446	2
C₄₇×C₂²⋊#95	2
#13922	47

Subgroups — C47×#13922 #26053620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13922 #26053620