Subgroups — #26106381

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
3	#20241271	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#384	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10625329	—	2	1	no	—
6	#15689176	—	2	2	no	—
7	#15689176	C₄	1	4	yes	complemented
8	#15689147	—	2	2	no	—
9	#15689147	C₄	1	4	yes	complemented
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
14	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#384	—	2	1	no	—
20	C₄₇×#384	—	2	1	no	—
21	C₄₇×#384	C₄	1	2	yes	—
22	C₄₇×#384	C₂²	1	2	yes	—
23	C₂×#10625329	—	2	4	no	—
24	C₂×#10625329	—	4	2	no	—
25	C₂×#10625329	—	4	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
29	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
30	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
31	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
32	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
33	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
34	C₄×C₄₇⋊C₈	—	2	4	no	—
35	C₂³×C₄×C₄₇	—	2	2	no	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
45	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
48	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	D₄	1	2	yes	—
55	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
56	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
57	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	—	2	2	no	—
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	4	no	—
63	C₂²×C₄×C₄₇	—	4	4	no	—
64	C₂²×C₄×C₄₇	—	4	4	no	—
65	C₂²×C₄×C₄₇	—	4	4	no	—
66	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
72	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
74	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
75	C₂²×C₄×C₄₇	D₈	1	2	yes	—
76	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₄⋊C₄×C₄₇	—	4	4	no	—
83	C₄⋊C₄×C₄₇	—	4	4	no	—
84	C₄⋊C₄×C₄₇	—	4	4	no	—
85	C₄⋊C₄×C₄₇	—	4	4	no	—
86	C₄⋊C₄×C₄₇	—	4	2	no	—
87	C₄⋊C₄×C₄₇	—	4	2	no	—
88	C₄⋊C₄×C₄₇	—	4	4	no	—
89	C₄²×C₄₇	C₄²	1	2	yes	—
90	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
93	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
94	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
99	#10625329	—	4	8	no	—
100	C₂×C₄₇⋊C₈	—	2	4	no	—
101	C₂×C₄₇⋊C₈	—	2	4	no	—
102	C₂×C₄₇⋊C₈	—	4	2	no	—
103	C₂×C₄₇⋊C₈	—	4	2	no	—
104	C₂×C₄₇⋊C₈	—	4	2	no	—
105	C₂×C₄₇⋊C₈	—	4	2	no	—
106	C₂³×C₄₇	—	2	1	no	—
107	C₂³×C₄₇	—	2	1	no	—
108	C₂³×C₄₇	—	2	1	no	—
109	C₂³×C₄₇	—	2	1	no	—
110	C₂³×C₄₇	#95	1	2	yes	—
111	C₂³×C₄₇	#102	1	2	yes	—
112	C₂³×C₄₇	#103	1	2	yes	—
113	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₄×C₄₇	—	2	1	no	—
115	C₂×C₄×C₄₇	—	2	1	no	—
116	C₂×C₄×C₄₇	—	2	1	no	—
117	C₂×C₄×C₄₇	—	2	1	no	—
118	C₂×C₄×C₄₇	—	2	4	no	—
119	C₂×C₄×C₄₇	—	2	4	no	—
120	C₂×C₄×C₄₇	—	2	4	no	—
121	C₂×C₄×C₄₇	—	2	4	no	—
122	C₂×C₄×C₄₇	—	4	4	no	—
123	C₂×C₄×C₄₇	—	4	4	no	—
124	C₂×C₄×C₄₇	—	4	4	no	—
125	C₂×C₄×C₄₇	—	8	8	no	—
126	C₂×C₄×C₄₇	#95	1	2	yes	—
127	C₂×C₄×C₄₇	#95	1	2	yes	—
128	C₂×C₄×C₄₇	#95	1	2	yes	—
129	C₂×C₄×C₄₇	#100	1	2	yes	—
130	C₂×C₄×C₄₇	#101	1	2	yes	—
131	C₂×C₄×C₄₇	#102	1	4	yes	—
132	C₂×C₄×C₄₇	#102	1	2	yes	—
133	C₂×C₄×C₄₇	#103	1	4	yes	—
134	C₂×C₄×C₄₇	#103	1	2	yes	—
135	C₂×C₄×C₄₇	#106	1	4	yes	—
136	C₂×C₄×C₄₇	#107	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
147	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
148	C₂×C₄×C₄₇	#137	1	2	yes	—
149	C₄₇⋊C₈	—	4	4	no	—
150	C₄₇⋊C₈	—	4	4	no	—
151	#8043	—	47	1	no	maximal, Sylow
152	C₂²×C₄₇	—	2	2	no	—
153	C₂²×C₄₇	—	2	2	no	—
154	C₂²×C₄₇	—	2	2	no	—
155	C₂²×C₄₇	—	2	2	no	—
156	C₂²×C₄₇	—	2	2	no	—
157	C₂²×C₄₇	—	2	2	no	—
158	C₂²×C₄₇	#340	1	4	yes	—
159	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
160	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
161	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
162	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
163	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
164	C₂²×C₄₇	#418	1	1	yes	characteristic
165	C₂²×C₄₇	#419	1	1	yes	characteristic
166	C₄×C₄₇	—	2	2	no	—
167	C₄×C₄₇	—	2	1	no	—
168	C₄×C₄₇	—	2	1	no	—
169	C₄×C₄₇	—	8	4	no	—
170	C₄×C₄₇	#340	1	4	yes	—
171	C₄×C₄₇	#343	1	4	yes	—
172	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
173	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
174	C₄×C₄₇	#417	1	2	yes	—
175	C₄×C₄₇	C₂×#106	1	1	yes	characteristic
176	C₄×C₄₇	C₂×#107	1	1	yes	characteristic
177	C₄×C₄₇	#428	1	2	yes	—
178	C₂×#431	—	47	1	no	—
179	C₂×#423	—	47	1	no	—
180	C₂×#384	D₄₇	1	1	yes	characteristic
181	#1296	—	47	4	no	—
182	C₂×C₄₇	—	2	4	no	—
183	C₂×C₄₇	#1545	1	1	yes	characteristic
184	C₂×C₄₇	#1546	1	1	yes	characteristic
185	C₂×C₄₇	#1548	1	1	yes	characteristic
186	C₂×C₄₇	#1549	1	1	yes	characteristic
187	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
188	C₂×C₄₇	#1736	1	1	yes	characteristic
189	C₂×C₄₇	C₂×#343	1	1	yes	characteristic
190	C₂²×M₁₆	—	94	1	no	—
191	C₂²×C₄⋊C₄	—	2	1	no	—
192	C₂²×C₄⋊C₄	—	2	1	no	—
193	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
194	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
195	#431	—	47	4	no	—
196	#431	—	94	2	no	—
197	#423	—	47	4	no	—
198	#423	—	94	2	no	—
199	C₂×C₄⋊C₈	—	47	2	no	—
200	C₂×C₄⋊C₈	—	47	2	no	—
201	C₂×C₄⋊C₈	—	94	1	no	—
202	C₂×C₂²⋊C₈	—	94	1	no	—
203	C₂×C₄×C₈	—	94	1	no	—
204	#384	—	2	1	no	—
205	#384	—	2	1	no	—
206	#384	Dic₄₇	1	2	yes	—
207	#384	C₂×D₄₇	1	2	yes	—
208	C₄₇	#8043	1	1	yes	characteristic, complemented, Sylow
209	C₂³×C₄	—	2	2	no	—
210	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
211	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
212	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
213	C₂×M₁₆	—	94	4	no	—
214	C₂×M₁₆	—	188	2	no	—
215	C₂×M₁₆	—	188	2	no	—
216	C₂²×C₈	—	94	2	no	—
217	C₂²×C₈	—	94	2	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	4	4	no	—
224	C₂×C₄⋊C₄	—	4	2	no	—
225	C₂×C₄⋊C₄	—	4	2	no	—
226	C₂×C₄⋊C₄	—	4	4	no	—
227	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
228	C₂×C₄²	Dic₉₄	1	2	yes	—
229	C₂×C₄²	C₄×D₄₇	1	2	yes	—
230	C₂×C₄²	C₄×D₄₇	1	2	yes	—
231	C₂×C₄²	D₁₈₈	1	2	yes	—
232	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
236	C₄⋊C₈	—	47	4	no	—
237	C₄⋊C₈	—	47	4	no	—
238	C₄⋊C₈	—	94	4	no	—
239	C₄⋊C₈	—	94	2	no	—
240	C₄⋊C₈	—	94	2	no	—
241	C₂²⋊C₈	—	94	4	no	—
242	C₄×C₈	—	94	4	no	—
243	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	4	no	—
250	C₂²×C₄	—	4	4	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
253	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
254	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
255	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
256	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
257	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
258	C₂²×C₄	#10625334	1	2	yes	—
259	C₂²×C₄	#10625335	1	2	yes	—
260	C₂²×C₄	#10625336	1	2	yes	—
261	C₂²×C₄	#10625337	1	2	yes	—
262	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
263	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
265	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
268	M₁₆	—	188	8	no	—
269	C₂×C₈	—	94	4	no	—
270	C₂×C₈	—	94	4	no	—
271	C₂×C₈	—	188	2	no	—
272	C₂×C₈	—	188	2	no	—
273	C₂×C₈	—	188	2	no	—
274	C₂×C₈	—	188	2	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₄⋊C₄	—	4	4	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄²	C₄×Dic₄₇	1	2	yes	—
283	C₄²	Dic₄₇⋊C₄	1	2	yes	—
284	C₄²	Dic₄₇⋊C₄	1	2	yes	—
285	C₄²	C₄⋊Dic₄₇	1	2	yes	—
286	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
287	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
288	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
289	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
290	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
291	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
292	C₂³	—	2	1	no	—
293	C₂³	—	2	1	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	C₄₇⋊#95	1	2	yes	—
297	C₂³	#13093945	1	2	yes	—
298	C₂³	#13093948	1	2	yes	—
299	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	4	no	—
311	C₂×C₄	—	8	8	no	—
312	C₂×C₄	C₄₇⋊#95	1	2	yes	—
313	C₂×C₄	C₄₇⋊#95	1	2	yes	—
314	C₂×C₄	C₄₇⋊#95	1	2	yes	—
315	C₂×C₄	#13093941	1	2	yes	—
316	C₂×C₄	#13093943	1	2	yes	—
317	C₂×C₄	#13093944	1	4	yes	—
318	C₂×C₄	#13093945	1	2	yes	—
319	C₂×C₄	#13093947	1	4	yes	—
320	C₂×C₄	#13093948	1	2	yes	—
321	C₂×C₄	#13093955	1	4	yes	—
322	C₂×C₄	#13093957	1	4	yes	—
323	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
324	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
329	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
330	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
331	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
332	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
333	C₂×C₄	#13094050	1	2	yes	—
334	C₂×C₄	#13094055	1	2	yes	—
335	C₈	—	188	4	no	—
336	C₈	—	188	4	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	#15688885	1	4	yes	—
344	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
345	C₂²	C₂×#13093941	1	1	yes	characteristic
346	C₂²	C₂×#13093943	1	1	yes	characteristic
347	C₂²	C₂×#13093945	1	1	yes	characteristic
348	C₂²	C₂×#13093948	1	1	yes	characteristic
349	C₂²	#15689128	1	1	yes	characteristic
350	C₂²	#15689132	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	8	4	no	—
355	C₄	#15688885	1	4	yes	—
356	C₄	#15688892	1	4	yes	—
357	C₄	C₂×#13093944	1	1	yes	characteristic
358	C₄	C₂×#13093947	1	1	yes	characteristic
359	C₄	#15689122	1	2	yes	—
360	C₄	C₂×#13093955	1	1	yes	characteristic
361	C₄	C₂×#13093957	1	1	yes	characteristic
362	C₄	#15689163	1	2	yes	—
363	C₂	—	2	4	no	—
364	C₂	#20242056	1	1	yes	characteristic
365	C₂	#20242060	1	1	yes	characteristic
366	C₂	#20242069	1	1	yes	characteristic
367	C₂	#20242073	1	1	yes	characteristic
368	C₂	C₂×#15688885	1	1	yes	characteristic
369	C₂	#20243107	1	1	yes	characteristic
370	C₂	C₂×#15688892	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#384	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#384	D₄₇
hypocenter	C₄₇	#8043
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#384

Complements

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

N	H ≅ G/N	type
3. #20241271	C₂	semidirect
7. #15689176	C₄	semidirect
9. #15689147	C₄	semidirect
31. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
32. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
208. C₄₇	#8043	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689176	2
C₂×#15689147	2
#20241271	2
C₂×C₄₇×#384	2
#8043	47