Subgroups — #26182103

Order 12032.

1278 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252412	C₂	1	2	yes	maximal, complemented
2	#20241712	C₂	1	2	yes	maximal, complemented
3	#20241706	C₂	1	4	yes	maximal, complemented
4	#20241702	C₂	1	2	yes	maximal, complemented
5	C₂×#15688849	C₂	1	4	yes	maximal, complemented
6	C₂×C₄₇×#520	C₂	1	1	yes	maximal, characteristic
7	D₄×C₄₇⋊C₈	—	2	8	no	—
8	#15689176	C₂²	1	4	yes	—
9	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	8	yes	—
10	#15688849	C₂²	1	4	yes	—
11	#15688849	C₂²	1	8	yes	—
12	#15688847	C₂²	1	4	yes	—
13	C₂²×#41×C₄₇	C₄	1	1	yes	characteristic
14	C₄₇×#520	—	2	8	no	—
15	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₇	C₄	1	2	yes	—
22	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₄₇⋊C₈	—	2	8	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
28	C₂²⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
29	C₄×C₄₇⋊C₈	—	2	4	no	—
30	C₂×#41×C₄₇	—	2	4	no	—
31	C₂×#41×C₄₇	—	2	4	no	—
32	C₂×#41×C₄₇	C₈	1	8	yes	complemented
33	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
35	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₄×Q₈×C₄₇	—	2	4	no	—
42	C₄×Q₈×C₄₇	—	2	4	no	—
43	C₄×D₄×C₄₇	—	2	4	no	—
44	C₄×D₄×C₄₇	—	2	8	no	—
45	C₄×D₄×C₄₇	—	2	8	no	—
46	C₄×D₄×C₄₇	D₄	1	8	yes	—
47	#117×C₄₇	—	2	8	no	—
48	#117×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
68	#41×C₄₇	—	2	32	no	—
69	C₂×Q₈×C₄₇	—	2	2	no	—
70	C₂×Q₈×C₄₇	—	2	2	no	—
71	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	complemented
72	C₂×D₄×C₄₇	—	2	4	no	—
73	C₂×D₄×C₄₇	—	2	4	no	—
74	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
75	C₂×D₄×C₄₇	C₂×C₈	1	4	yes	—
76	C₂×D₄×C₄₇	C₂×C₈	1	8	yes	complemented
77	C₂×D₄×C₄₇	M₁₆	1	4	yes	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	8	2	no	—
85	C₂²×C₄×C₄₇	—	8	2	no	—
86	C₂²×C₄×C₄₇	—	8	2	no	—
87	C₂²×C₄×C₄₇	C₂×C₈	1	8	yes	complemented
88	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	complemented
89	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₄⋊C₄×C₄₇	—	2	4	no	—
100	C₄⋊C₄×C₄₇	—	2	4	no	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
106	C₂²⋊C₄×C₄₇	—	2	4	no	—
107	C₂²⋊C₄×C₄₇	—	2	2	no	—
108	C₂²⋊C₄×C₄₇	—	2	2	no	—
109	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
110	C₄²×C₄₇	—	2	4	no	—
111	C₄²×C₄₇	—	2	4	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	C₂×D₄	1	4	yes	—
114	C₂×C₄₇⋊C₈	—	2	8	no	—
115	C₂×C₄₇⋊C₈	—	8	8	no	—
116	C₂³×C₄₇	—	2	1	no	—
117	C₂³×C₄₇	—	2	1	no	—
118	C₂³×C₄₇	—	4	2	no	—
119	C₂³×C₄₇	—	4	2	no	—
120	C₂³×C₄₇	—	4	1	no	—
121	C₂³×C₄₇	—	4	1	no	—
122	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
123	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
124	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
125	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
126	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
127	Q₈×C₄₇	—	2	8	no	—
128	D₄×C₄₇	—	2	16	no	—
129	D₄×C₄₇	C₂²⋊C₈	1	16	yes	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	16	no	—
135	C₂×C₄×C₄₇	—	2	8	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	4	8	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	1	no	—
142	C₂×C₄×C₄₇	—	4	1	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	8	4	no	—
147	C₂×C₄×C₄₇	—	8	4	no	—
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
153	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
156	C₄₇⋊C₈	—	4	8	no	—
157	#17351	—	47	1	no	maximal, Sylow
158	C₂²×C₄₇	—	2	1	no	—
159	C₂²×C₄₇	—	2	4	no	—
160	C₂²×C₄₇	—	2	1	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	—	4	4	no	—
164	C₂²×C₄₇	—	4	4	no	—
165	C₂²×C₄₇	—	4	2	no	—
166	C₂²×C₄₇	—	4	2	no	—
167	C₂²×C₄₇	—	4	1	no	—
168	C₂²×C₄₇	—	4	1	no	—
169	C₂²×C₄₇	C₂×C₂²⋊C₈	1	8	yes	—
170	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
172	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
173	C₄×C₄₇	—	2	2	no	—
174	C₄×C₄₇	—	2	4	no	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	—	2	4	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	4	2	no	—
179	C₄×C₄₇	—	4	1	no	—
180	C₄×C₄₇	—	4	1	no	—
181	C₄×C₄₇	C₂×C₂²⋊C₈	1	4	yes	—
182	C₂×#520	D₄₇	1	1	yes	characteristic
183	#2972	—	47	2	no	—
184	#1461	—	47	2	no	—
185	#1459	—	47	4	no	—
186	#1458	—	47	2	no	—
187	C₂×#324	—	47	4	no	—
188	C₂×C₄₇	—	2	1	no	—
189	C₂×C₄₇	—	2	1	no	—
190	C₂×C₄₇	—	2	8	no	—
191	C₂×C₄₇	—	4	2	no	—
192	C₂×C₄₇	C₂²×C₂²⋊C₈	1	1	yes	characteristic
193	C₂×C₄₇	#2883	1	1	yes	characteristic
194	C₂×C₄₇	#2889	1	1	yes	characteristic
195	C₂²×#41	Dic₄₇	1	1	yes	characteristic
196	#520	—	2	8	no	—
197	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic
198	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
199	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
200	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic
201	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
202	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
203	C₂×#117	Dic₄₇	1	2	yes	—
204	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
205	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
207	C₈×D₄	—	94	8	no	—
208	#431	—	47	4	no	—
209	C₂×C₂²⋊C₈	—	47	8	no	—
210	#324	—	47	4	no	—
211	#324	—	47	8	no	—
212	#323	—	47	4	no	—
213	C₄₇	#17351	1	1	yes	characteristic, complemented, Sylow
214	C₂×#41	—	2	4	no	—
215	C₂×#41	—	2	4	no	—
216	C₂×#41	C₄₇⋊C₈	1	8	yes	complemented
217	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
218	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
219	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
220	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
222	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
223	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
224	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
225	C₂²×C₈	—	94	8	no	—
226	C₄×Q₈	—	2	4	no	—
227	C₄×Q₈	—	2	4	no	—
228	C₄×D₄	—	2	4	no	—
229	C₄×D₄	—	2	8	no	—
230	C₄×D₄	—	2	8	no	—
231	C₄×D₄	C₂²⋊D₄₇	1	8	yes	—
232	#117	—	2	8	no	—
233	#117	—	2	4	no	—
234	C₂×C₄⋊C₄	—	2	8	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
243	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
244	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
248	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
249	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
250	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
251	C₄⋊C₈	—	94	4	no	—
252	C₂²⋊C₈	—	47	8	no	—
253	C₂²⋊C₈	—	94	8	no	—
254	C₄×C₈	—	94	4	no	—
255	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
256	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
257	#41	—	2	32	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	C₂×C₄₇⋊C₈	1	4	yes	complemented
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	C₂×C₄₇⋊C₈	1	4	yes	—
264	C₂×D₄	C₂×C₄₇⋊C₈	1	8	yes	complemented
265	C₂×D₄	#10625329	1	4	yes	—
266	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	8	2	no	—
274	C₂²×C₄	—	8	2	no	—
275	C₂²×C₄	—	8	2	no	—
276	C₂²×C₄	C₂×C₄₇⋊C₈	1	8	yes	complemented
277	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	complemented
278	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
279	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
285	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
287	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
288	C₂×C₈	—	94	8	no	—
289	C₂×C₈	—	376	8	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₂²⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	2	no	—
304	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
312	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
313	C₂³	C₂²×C₄₇⋊C₈	1	4	yes	—
314	C₂³	C₂×#10625329	1	4	yes	—
315	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
316	Q₈	—	2	8	no	—
317	D₄	—	2	16	no	—
318	D₄	C₂²⋊(C₄₇⋊C₈)	1	16	yes	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	8	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	8	4	no	—
336	C₂×C₄	—	8	4	no	—
337	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
339	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
340	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
341	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
342	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
343	C₂×C₄	C₂×#10625329	1	2	yes	—
344	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
345	C₈	—	188	8	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	4	4	no	—
352	C₂²	—	4	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	8	yes	—
358	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
359	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
360	C₂²	C₂²×#10625329	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	4	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	1	no	—
369	C₄	C₂×C₂²⋊(C₄₇⋊C₈)	1	4	yes	—
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	2	8	no	—
373	C₂	—	4	2	no	—
374	C₂	C₂²×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
375	C₂	#20251849	1	1	yes	characteristic
376	C₂	#20251871	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#520	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#520	D₄₇
hypocenter	C₄₇	#17351
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ C₂×#520

Complements

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

N	H ≅ G/N	type
1. #20252412	C₂	semidirect
2. #20241712	C₂	semidirect
3. #20241706	C₂	semidirect
4. #20241702	C₂	semidirect
5. C₂×#15688849	C₂	semidirect
32. C₂×#41×C₄₇	C₈	semidirect
71. C₂×Q₈×C₄₇	C₂×C₈	semidirect
76. C₂×D₄×C₄₇	C₂×C₈	semidirect
87. C₂²×C₄×C₄₇	C₂×C₈	semidirect
88. C₂²×C₄×C₄₇	C₂×C₈	semidirect
213. C₄₇	#17351	semidirect
216. C₂×#41	C₄₇⋊C₈	semidirect
260. C₂×Q₈	C₂×C₄₇⋊C₈	semidirect
264. C₂×D₄	C₂×C₄₇⋊C₈	semidirect
276. C₂²×C₄	C₂×C₄₇⋊C₈	semidirect
277. C₂²×C₄	C₂×C₄₇⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#20252412	2
#20241712	2
#20241706	2
#20241702	2
C₂×#15688849	2
C₂×C₄₇×#520	2
#17351	47