Subgroups — #26215253

Order 12032.

1002 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#20245853	C₂	1	1	yes	maximal, characteristic
3	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243169	C₂	1	2	yes	maximal, complemented
7	#20243162	C₂	1	2	yes	maximal, complemented
8	#20243156	C₂	1	2	yes	maximal, complemented
9	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243086	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#436	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×#13093983	C₂²	1	2	yes	—
14	D₄×C₄₇⋊C₈	C₄	1	8	yes	complemented
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×#13093934	C₂²	1	2	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	#15689026	C₄	1	2	yes	—
22	#15689022	C₄	1	2	yes	—
23	#15689016	C₄	1	4	yes	—
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
26	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
27	#15688877	C₂²	1	2	yes	—
28	#15688877	C₂²	1	2	yes	—
29	#15688877	C₂²	1	2	yes	—
30	#15688877	C₂²	1	1	yes	characteristic
31	#15688877	C₂²	1	1	yes	characteristic
32	#15688877	C₂²	1	1	yes	characteristic
33	#15688877	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#436	C₄	1	8	yes	complemented
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄₇⋊C₈	—	4	2	no	—
41	C₂²×C₄₇⋊C₈	—	4	2	no	—
42	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	#13093983	—	4	2	no	—
47	#13093983	—	4	2	no	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
50	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
51	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
58	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
59	#13093934	—	4	2	no	—
60	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
61	C₈×Dic₄₇	—	4	2	no	—
62	C₈×Dic₄₇	—	4	2	no	—
63	C₄₇⋊#95	C₂×C₄	1	4	yes	—
64	C₄₇⋊#95	C₂×C₄	1	2	yes	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
67	C₂×M₁₆×C₄₇	—	4	2	no	—
68	C₂×M₁₆×C₄₇	—	4	2	no	—
69	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
74	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
79	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
80	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
81	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₄₇	—	2	4	no	—
83	C₂×D₄×C₄₇	C₄²	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
95	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	M₁₆×C₄₇	—	4	8	no	—
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
105	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
108	C₂²⋊C₄×C₄₇	C₄²	1	8	yes	—
109	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
110	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²⋊Dic₄₇	—	2	8	no	—
112	C₂²⋊Dic₄₇	—	4	4	no	—
113	C₄⋊Dic₄₇	—	2	4	no	—
114	C₄⋊Dic₄₇	—	4	4	no	—
115	C₄×Dic₄₇	—	2	4	no	—
116	C₄×Dic₄₇	—	2	1	no	—
117	C₄×Dic₄₇	—	2	2	no	—
118	C₄×Dic₄₇	—	2	2	no	—
119	C₄×Dic₄₇	—	2	1	no	—
120	C₄×Dic₄₇	—	2	1	no	—
121	C₄×Dic₄₇	—	2	1	no	—
122	C₄×Dic₄₇	—	2	4	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	4	8	no	—
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
138	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
139	D₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
149	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
150	C₂×C₄×C₄₇	#131	1	4	yes	—
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	2	4	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	#131	1	4	yes	—
166	C₈×C₄₇	—	2	4	no	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	—	2	2	no	—
169	C₄₇⋊C₈	—	2	2	no	—
170	C₄₇⋊C₈	—	2	4	no	—
171	C₄₇⋊C₈	—	2	2	no	—
172	#20562	—	47	1	no	maximal, Sylow
173	C₂²×C₄₇	—	2	4	no	—
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	—	4	4	no	—
177	C₂²×C₄₇	—	4	4	no	—
178	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
179	C₂²×C₄₇	#518	1	1	yes	characteristic
180	C₂²×C₄₇	#520	1	1	yes	characteristic
181	C₂²×C₄₇	C₂×#131	1	2	yes	—
182	C₂²×C₄₇	C₂×#131	1	2	yes	—
183	C₄×C₄₇	—	2	2	no	—
184	C₄×C₄₇	—	2	4	no	—
185	C₄×C₄₇	#405	1	4	yes	—
186	C₄×C₄₇	#518	1	1	yes	characteristic
187	C₄×C₄₇	#518	1	1	yes	characteristic
188	C₄×C₄₇	#520	1	1	yes	characteristic
189	C₄×C₄₇	#520	1	1	yes	characteristic
190	Dic₄₇	—	2	4	no	—
191	Dic₄₇	—	4	2	no	—
192	Dic₄₇	—	4	4	no	—
193	C₂×#436	D₄₇	1	1	yes	characteristic
194	C₂×C₈×D₄	—	47	1	no	—
195	#2293	—	47	1	no	—
196	#1770	—	47	1	no	—
197	C₈×C₄⋊C₄	—	47	1	no	—
198	C₄×C₄⋊C₈	—	47	1	no	—
199	#1753	—	47	2	no	—
200	C₈×C₂²⋊C₄	—	47	2	no	—
201	#1750	—	47	2	no	—
202	#1744	—	47	1	no	—
203	#1729	—	47	2	no	—
204	C₂×C₄₇	—	4	4	no	—
205	C₂×C₄₇	#2275	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
207	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
208	C₂×C₄₇	#2979	1	2	yes	—
209	C₂×C₄₇	#2994	1	2	yes	—
210	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
211	C₂³×C₈	—	47	2	no	—
212	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
213	C₂×#117	—	47	2	no	—
214	#436	Dic₄₇	1	8	yes	complemented
215	C₈×D₄	—	47	8	no	—
216	C₂×C₄⋊C₈	—	47	1	no	—
217	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	—	47	2	no	—
219	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
220	C₂×#97	—	47	2	no	—
221	C₂×C₄×C₈	—	47	1	no	—
222	C₂×C₄×C₈	—	47	2	no	—
223	C₂×C₄×C₈	—	47	2	no	—
224	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
225	#390	—	47	2	no	—
226	#389	—	47	2	no	—
227	#388	—	47	4	no	—
228	C₄×C₄⋊C₄	—	47	1	no	—
229	C₄×C₂²⋊C₄	—	47	2	no	—
230	C₄³	—	47	1	no	—
231	#336	—	47	1	no	—
232	#336	—	47	2	no	—
233	#336	—	47	2	no	—
234	#336	—	47	2	no	—
235	#336	—	47	1	no	—
236	#336	—	47	1	no	—
237	#336	—	47	1	no	—
238	C₄₇	#20562	1	1	yes	characteristic, complemented, Sylow
239	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
241	C₂×M₁₆	—	4	2	no	—
242	C₂×M₁₆	—	4	2	no	—
243	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	2	no	—
246	C₂²×C₈	—	47	1	no	—
247	C₂²×C₈	—	47	8	no	—
248	C₂²×C₈	—	188	2	no	—
249	C₂²×C₈	—	188	2	no	—
250	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
252	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
253	C₄×D₄	C₄×D₄₇	1	4	yes	—
254	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
255	#117	—	188	2	no	—
256	#117	—	188	2	no	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	—	47	4	no	—
259	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	47	4	no	—
261	C₂×C₂²⋊C₄	—	47	4	no	—
262	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
263	C₂×C₄²	—	47	2	no	—
264	C₂×C₄²	—	47	2	no	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	2	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	C₄⋊C₈	—	47	4	no	—
270	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
271	C₂²⋊C₈	—	47	8	no	—
272	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	—
273	#97	—	188	2	no	—
274	C₄×C₈	—	47	4	no	—
275	C₄×C₈	—	188	2	no	—
276	C₄×C₈	—	188	2	no	—
277	C₄×C₈	C₂×Dic₄₇	1	4	yes	—
278	#95	—	47	4	no	—
279	#95	—	47	2	no	—
280	C₂⁴	C₂×C₄×D₄₇	1	2	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	47	2	no	—
288	C₂²×C₄	—	47	4	no	—
289	C₂²×C₄	—	47	2	no	—
290	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
292	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
293	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
295	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
296	M₁₆	—	4	8	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	47	4	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	1	no	—
308	C₂×C₈	—	94	1	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	94	1	no	—
311	C₂×C₈	—	94	1	no	—
312	C₂×C₈	—	188	8	no	—
313	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
314	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
315	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
316	C₄⋊C₄	—	94	4	no	—
317	C₄⋊C₄	—	188	4	no	—
318	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
319	C₂²⋊C₄	—	94	8	no	—
320	C₂²⋊C₄	—	188	4	no	—
321	C₂²⋊C₄	C₄×Dic₄₇	1	8	yes	—
322	C₄²	—	94	4	no	—
323	C₄²	—	94	4	no	—
324	C₄²	—	94	1	no	—
325	C₄²	—	94	2	no	—
326	C₄²	—	94	1	no	—
327	C₄²	—	94	2	no	—
328	C₄²	—	94	1	no	—
329	C₄²	—	94	1	no	—
330	C₄²	C₂×C₄×D₄₇	1	2	yes	—
331	C₄²	C₂²×Dic₄₇	1	2	yes	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
337	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
338	D₄	—	2	8	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	47	4	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	94	4	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	4	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	4	no	—
355	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
356	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
357	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
358	C₂×C₄	#13094032	1	4	yes	—
359	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
361	C₂×C₄	#13094069	1	1	yes	characteristic
362	C₂×C₄	#13094069	1	1	yes	characteristic
363	C₂×C₄	#13094070	1	1	yes	characteristic
364	C₂×C₄	#13094071	1	1	yes	characteristic
365	C₈	—	2	4	no	—
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	94	4	no	—
369	C₈	—	94	2	no	—
370	C₈	—	94	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
377	C₂²	#15689595	1	1	yes	characteristic
378	C₂²	#15689602	1	1	yes	characteristic
379	C₂²	#131×D₄₇	1	2	yes	—
380	C₂²	C₂×#13094032	1	2	yes	—
381	C₄	—	2	2	no	—
382	C₄	—	2	4	no	—
383	C₄	—	94	4	no	—
384	C₄	—	188	2	no	—
385	C₄	—	188	4	no	—
386	C₄	#15689081	1	4	yes	—
387	C₄	#15689595	1	1	yes	characteristic
388	C₄	#15689598	1	1	yes	characteristic
389	C₄	#15689602	1	1	yes	characteristic
390	C₄	#15689606	1	1	yes	characteristic
391	C₂	—	4	4	no	—
392	C₂	#20245749	1	1	yes	characteristic
393	C₂	C₂×#15689081	1	1	yes	characteristic
394	C₂	#131×Dic₄₇	1	1	yes	characteristic
395	C₂	#20252453	1	2	yes	—
396	C₂	#20252549	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄₇×#436	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#436	D₄₇
hypocenter	C₄₇	#20562
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
3. #20243258	C₂	semidirect
4. C₈×C₄⋊Dic₄₇	C₂	semidirect
5. C₄⋊C₈×Dic₄₇	C₂	semidirect
6. #20243169	C₂	semidirect
7. #20243162	C₂	semidirect
8. #20243156	C₂	semidirect
9. #20243133	C₂	semidirect
10. #20243086	C₂	semidirect
14. D₄×C₄₇⋊C₈	C₄	semidirect
36. C₄₇×#436	C₄	semidirect
214. #436	Dic₄₇	semidirect
238. C₄₇	#20562	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
#20245853	2
#20243258	2
C₈×C₄⋊Dic₄₇	2
C₄⋊C₈×Dic₄₇	2
#20243169	2
#20243162	2
#20243156	2
#20243133	2
#20243086	2
C₂×C₄₇×#436	2
#20562	47