Subgroups — #26124880

Order 12032.

958 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₄₇⋊C₈	C₂	1	2	yes	maximal
2	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688877	C₂	1	2	yes	maximal
4	C₄×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
9	C₂×Dic₄₇⋊C₈	—	2	4	no	—
10	C₂×Dic₄₇⋊C₈	—	2	4	no	—
11	C₂×Dic₄₇⋊C₈	—	2	4	no	—
12	C₂×C₄₇⋊#95	C₄	1	2	yes	—
13	C₂×C₄₇⋊#95	C₄	1	1	yes	characteristic
14	C₂×C₄₇⋊#95	C₄	1	1	yes	characteristic
15	#15688878	—	2	2	no	—
16	#15688877	—	2	4	no	—
17	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₇	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
21	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
22	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	1	no	—
25	C₂²×C₄₇⋊C₈	—	2	1	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	1	no	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	2	1	no	—
31	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
32	C₂²×C₄₇⋊C₈	Q₈	1	2	yes	—
33	C₂×C₄×Dic₄₇	—	2	2	no	—
34	C₂×C₄×Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
38	C₂×C₄×Dic₄₇	Q₈	1	4	yes	—
39	Dic₄₇⋊C₈	—	2	16	no	—
40	C₄₇⋊#95	—	2	2	no	—
41	C₄₇⋊#95	—	2	4	no	—
42	C₄₇⋊#95	C₈	1	4	yes	complemented
43	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₇	—	2	2	no	—
47	C₂²×C₈×C₄₇	—	2	2	no	—
48	C₂²×C₈×C₄₇	—	2	2	no	—
49	C₂²×C₈×C₄₇	—	2	2	no	—
50	C₂²×C₈×C₄₇	—	2	2	no	—
51	C₂²×C₈×C₄₇	—	2	2	no	—
52	C₂²×C₈×C₄₇	D₄	1	4	yes	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	—	2	2	no	—
55	C₂×C₄²×C₄₇	D₄	1	2	yes	—
56	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
57	C₄⋊C₈×C₄₇	—	2	8	no	—
58	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	2	1	no	—
64	C₂²×C₄×C₄₇	—	2	1	no	—
65	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
68	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
76	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	#41	1	2	yes	—
78	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
79	C₂²×Dic₄₇	—	2	2	no	—
80	C₂²×Dic₄₇	—	2	2	no	—
81	C₂²×Dic₄₇	—	2	2	no	—
82	C₂²×Dic₄₇	—	2	2	no	—
83	C₂²×Dic₄₇	—	2	2	no	—
84	C₂²×Dic₄₇	—	2	2	no	—
85	C₂²×Dic₄₇	—	2	2	no	—
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	—	2	2	no	—
89	C₂²×Dic₄₇	C₄⋊C₄	1	4	yes	—
90	C₂²×Dic₄₇	C₄⋊C₄	1	4	yes	—
91	C₂²×Dic₄₇	C₂×C₈	1	4	yes	—
92	C₂²×Dic₄₇	M₁₆	1	4	yes	—
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₂×C₈×C₄₇	—	2	4	no	—
95	C₂×C₈×C₄₇	—	2	4	no	—
96	C₂×C₈×C₄₇	—	4	2	no	—
97	C₂×C₈×C₄₇	—	4	2	no	—
98	C₂×C₈×C₄₇	—	4	2	no	—
99	C₂×C₈×C₄₇	—	4	2	no	—
100	C₄²×C₄₇	—	2	2	no	—
101	C₄²×C₄₇	—	2	4	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄×Dic₄₇	—	2	4	no	—
104	C₄×Dic₄₇	—	2	4	no	—
105	C₄×Dic₄₇	—	2	4	no	—
106	C₄×Dic₄₇	—	2	4	no	—
107	C₂×C₄₇⋊C₈	—	2	4	no	—
108	C₂×C₄₇⋊C₈	—	2	2	no	—
109	C₂×C₄₇⋊C₈	—	2	2	no	—
110	C₂×C₄₇⋊C₈	—	2	4	no	—
111	C₂×C₄₇⋊C₈	—	4	1	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂×C₄₇⋊C₈	—	4	1	no	—
114	C₂×C₄₇⋊C₈	—	4	2	no	—
115	C₂×C₄₇⋊C₈	—	4	1	no	—
116	C₂×C₄₇⋊C₈	—	4	1	no	—
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₇	C₄×D₄	1	2	yes	—
120	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
121	C₂³×C₄₇	C₄×Q₈	1	1	yes	characteristic
122	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
123	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
124	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
125	C₂³×C₄₇	#131	1	2	yes	—
126	C₂³×C₄₇	#131	1	1	yes	characteristic
127	C₂³×C₄₇	#131	1	1	yes	characteristic
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	C₄⋊C₈	1	4	yes	complemented
138	C₂×C₄×C₄₇	#120	1	2	yes	—
139	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
140	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#121	1	2	yes	—
142	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
146	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
147	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#123	1	2	yes	—
149	C₂×C₄×C₄₇	#125	1	2	yes	—
150	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	—	2	4	no	—
160	C₂×Dic₄₇	—	2	4	no	—
161	C₂×Dic₄₇	—	2	4	no	—
162	C₂×Dic₄₇	—	2	4	no	—
163	C₂×Dic₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	C₄⋊C₈	1	8	yes	complemented
170	C₈×C₄₇	—	4	4	no	—
171	C₄₇⋊C₈	—	4	2	no	—
172	C₄₇⋊C₈	—	4	2	no	—
173	#11322	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	#384	1	1	yes	characteristic
175	C₂²×C₄₇	#385	1	2	yes	—
176	C₂²×C₄₇	#385	1	1	yes	characteristic
177	C₂²×C₄₇	#389	1	2	yes	—
178	C₂²×C₄₇	#389	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×C₄⋊C₈	1	2	yes	—
180	C₂²×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
181	C₂²×C₄₇	#423	1	2	yes	—
182	C₂²×C₄₇	#423	1	1	yes	characteristic
183	C₂²×C₄₇	#424	1	2	yes	—
184	C₂²×C₄₇	#424	1	2	yes	—
185	C₂²×C₄₇	#424	1	1	yes	characteristic
186	C₂²×C₄₇	#424	1	1	yes	characteristic
187	C₂²×C₄₇	C₈×D₄	1	2	yes	—
188	C₂²×C₄₇	C₈×D₄	1	1	yes	characteristic
189	C₂²×C₄₇	#435	1	2	yes	—
190	C₂²×C₄₇	#435	1	2	yes	—
191	C₂²×C₄₇	#435	1	2	yes	—
192	C₂²×C₄₇	#436	1	2	yes	—
193	C₂²×C₄₇	#436	1	1	yes	characteristic
194	C₂²×C₄₇	C₈×Q₈	1	1	yes	characteristic
195	C₂²×C₄₇	#446	1	1	yes	characteristic
196	C₂²×C₄₇	#446	1	2	yes	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	#392	1	1	yes	characteristic
200	C₄×C₄₇	#395	1	1	yes	characteristic
201	C₄×C₄₇	#395	1	2	yes	—
202	C₄×C₄₇	#398	1	1	yes	characteristic
203	C₄×C₄₇	#398	1	2	yes	—
204	C₄×C₄₇	#399	1	1	yes	characteristic
205	Dic₄₇	—	2	8	no	—
206	Dic₄₇	—	4	4	no	—
207	C₂²×C₄⋊C₈	—	47	2	no	—
208	C₂²×C₄⋊C₈	D₄₇	1	1	yes	characteristic
209	C₂×#336	—	47	1	no	—
210	C₂×#336	—	47	2	no	—
211	C₄×#95	—	47	1	no	—
212	C₂×C₄₇	#1444	1	1	yes	characteristic
213	C₂×C₄₇	#1842	1	1	yes	characteristic
214	C₂×C₄₇	#1843	1	1	yes	characteristic
215	C₂×C₄₇	#1850	1	2	yes	—
216	C₂×C₄₇	#1850	1	1	yes	characteristic
217	C₂×C₄₇	#1851	1	2	yes	—
218	C₂×C₄₇	#1851	1	1	yes	characteristic
219	C₂×C₄₇	#1939	1	2	yes	—
220	C₂×C₄₇	#1939	1	1	yes	characteristic
221	C₂×C₄₇	#1940	1	2	yes	—
222	C₂×C₄₇	#1940	1	1	yes	characteristic
223	C₂³×C₈	—	47	1	no	—
224	C₂³×C₈	—	47	1	no	—
225	C₂³×C₈	C₂×D₄₇	1	2	yes	—
226	C₂²×C₄²	—	47	2	no	—
227	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
228	C₂×C₄⋊C₈	—	2	4	no	—
229	C₂×C₄⋊C₈	—	2	2	no	—
230	C₂×C₄⋊C₈	—	94	4	no	—
231	C₂×C₄⋊C₈	—	94	4	no	—
232	C₂×C₄⋊C₈	—	94	4	no	—
233	C₂×#95	—	47	1	no	—
234	C₂×#95	—	47	2	no	—
235	C₂×#95	—	47	1	no	—
236	#336	—	94	4	no	—
237	#336	—	94	2	no	—
238	C₄₇	#11322	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	—	47	2	no	—
240	C₂³×C₄	—	47	2	no	—
241	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
242	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
243	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	47	2	no	—
251	C₂²×C₈	—	47	2	no	—
252	C₂²×C₈	—	94	2	no	—
253	C₂²×C₈	—	94	2	no	—
254	C₂²×C₈	—	94	2	no	—
255	C₂²×C₈	—	94	1	no	—
256	C₂²×C₈	—	94	1	no	—
257	C₂²×C₈	—	94	1	no	—
258	C₂²×C₈	—	94	1	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	47	4	no	—
264	C₂×C₄²	—	47	4	no	—
265	C₂×C₄²	—	94	2	no	—
266	C₂×C₄²	—	94	2	no	—
267	C₂×C₄²	—	94	2	no	—
268	C₂×C₄²	—	94	2	no	—
269	C₂×C₄²	Dic₉₄	1	2	yes	—
270	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
271	C₄⋊C₈	—	2	8	no	—
272	C₄⋊C₈	—	94	16	no	—
273	#95	—	47	4	no	—
274	#95	—	94	4	no	—
275	#95	—	94	2	no	—
276	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	47	4	no	—
284	C₂²×C₄	—	47	4	no	—
285	C₂²×C₄	—	47	4	no	—
286	C₂²×C₄	—	47	4	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	2	no	—
291	C₂²×C₄	—	94	2	no	—
292	C₂²×C₄	—	94	2	no	—
293	C₂²×C₄	—	94	2	no	—
294	C₂²×C₄	—	94	2	no	—
295	C₂²×C₄	—	94	2	no	—
296	C₂²×C₄	—	94	2	no	—
297	C₂²×C₄	C₈×D₄₇	1	2	yes	—
298	C₂²×C₄	#10625324	1	2	yes	—
299	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
300	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
301	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
302	C₂²×C₄	#10625350	1	2	yes	—
303	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
304	C₂²×C₄	D₄×D₄₇	1	2	yes	—
305	C₂²×C₄	#10625352	1	1	yes	characteristic
306	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
308	C₂²×C₄	#10625354	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	94	4	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	94	4	no	—
322	C₂×C₈	—	188	1	no	—
323	C₂×C₈	—	188	2	no	—
324	C₂×C₈	—	188	1	no	—
325	C₂×C₈	—	188	2	no	—
326	C₂×C₈	—	188	1	no	—
327	C₂×C₈	—	188	1	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	4	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	94	4	no	—
332	C₄²	—	94	4	no	—
333	C₄²	—	94	4	no	—
334	C₄²	—	94	4	no	—
335	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
336	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
337	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
338	C₂³	#13093986	1	1	yes	characteristic
339	C₂³	#13093989	1	1	yes	characteristic
340	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
341	C₂³	M₁₆×D₄₇	1	2	yes	—
342	C₂³	C₂×#10625324	1	1	yes	characteristic
343	C₂³	#13094030	1	2	yes	—
344	C₂³	#13094032	1	1	yes	characteristic
345	C₂³	#13094032	1	1	yes	characteristic
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	47	8	no	—
356	C₂×C₄	—	94	4	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	94	4	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	94	4	no	—
361	C₂×C₄	—	94	4	no	—
362	C₂×C₄	—	94	4	no	—
363	C₂×C₄	—	94	4	no	—
364	C₂×C₄	—	94	4	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	Dic₄₇⋊C₈	1	4	yes	complemented
370	C₂×C₄	#13093992	1	2	yes	—
371	C₂×C₄	#13093993	1	1	yes	characteristic
372	C₂×C₄	#13093995	1	1	yes	characteristic
373	C₂×C₄	#13093996	1	2	yes	—
374	C₂×C₄	#13094000	1	2	yes	—
375	C₂×C₄	#13094000	1	1	yes	characteristic
376	C₂×C₄	#13094002	1	2	yes	—
377	C₂×C₄	#13094002	1	2	yes	—
378	C₂×C₄	#13094003	1	2	yes	—
379	C₂×C₄	#13094007	1	1	yes	characteristic
380	C₂×C₄	#13094009	1	2	yes	—
381	C₂×C₄	#13094014	1	2	yes	—
382	C₂×C₄	#13094015	1	1	yes	characteristic
383	C₂×C₄	#13094020	1	1	yes	characteristic
384	C₂×C₄	#13094022	1	2	yes	—
385	C₂×C₄	#13094022	1	1	yes	characteristic
386	C₂×C₄	#13094023	1	1	yes	characteristic
387	C₂×C₄	#13094023	1	2	yes	—
388	C₈	—	4	4	no	—
389	C₈	—	188	2	no	—
390	C₈	—	188	2	no	—
391	C₂²	#15688992	1	1	yes	characteristic
392	C₂²	#15688994	1	2	yes	—
393	C₂²	#15688996	1	1	yes	characteristic
394	C₂²	#15689018	1	2	yes	—
395	C₂²	#15689019	1	1	yes	characteristic
396	C₂²	C₄⋊C₈×D₄₇	1	2	yes	—
397	C₂²	C₂×Dic₄₇⋊C₈	1	1	yes	characteristic
398	C₂²	#15689145	1	2	yes	—
399	C₂²	#15689146	1	1	yes	characteristic
400	C₂²	#15689148	1	2	yes	—
401	C₂²	#15689148	1	2	yes	—
402	C₂²	#15689149	1	1	yes	characteristic
403	C₂²	#15689151	1	1	yes	characteristic
404	C₂²	C₈×C₂²⋊D₄₇	1	2	yes	—
405	C₂²	#15689188	1	1	yes	characteristic
406	C₂²	#15689192	1	2	yes	—
407	C₂²	#15689193	1	2	yes	—
408	C₂²	#15689194	1	2	yes	—
409	C₂²	#15689199	1	2	yes	—
410	C₂²	#15689200	1	1	yes	characteristic
411	C₂²	#15689247	1	1	yes	characteristic
412	C₂²	#15689250	1	1	yes	characteristic
413	C₂²	#15689252	1	2	yes	—
414	C₄	—	2	4	no	—
415	C₄	—	4	2	no	—
416	C₄	—	94	8	no	—
417	C₄	—	188	4	no	—
418	C₄	#15689031	1	1	yes	characteristic
419	C₄	#15689042	1	1	yes	characteristic
420	C₄	#15689043	1	2	yes	—
421	C₄	#15689054	1	1	yes	characteristic
422	C₄	#15689056	1	2	yes	—
423	C₄	#15689058	1	1	yes	characteristic
424	C₂	#20241651	1	1	yes	characteristic
425	C₂	#20243539	1	1	yes	characteristic
426	C₂	#20243541	1	1	yes	characteristic
427	C₂	#20243564	1	2	yes	—
428	C₂	#20243566	1	1	yes	characteristic
429	C₂	#20243569	1	2	yes	—
430	C₂	#20243571	1	1	yes	characteristic
431	C₂	#20244103	1	2	yes	—
432	C₂	#20244104	1	1	yes	characteristic
433	C₂	#20244108	1	2	yes	—
434	C₂	#20244109	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₈
Fitting	C₂²×C₄⋊C₈×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂²×C₄⋊C₈	D₄₇
hypocenter	C₄₇	#11322
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
42. C₄₇⋊#95	C₈	semidirect
137. C₂×C₄×C₄₇	C₄⋊C₈	semidirect
169. C₂×Dic₄₇	C₄⋊C₈	semidirect
238. C₄₇	#11322	semidirect
369. C₂×C₄	Dic₄₇⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂²×Dic₄₇⋊C₈	2
C₂×#15688878	2
C₂×#15688877	2
C₄×C₄₇⋊#95	2
C₂²×C₄⋊C₈×C₄₇	2
#11322	47