Subgroups — #26221398

Order 12032.

1238 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689180	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20244341	C₂	1	2	yes	maximal, complemented
4	#20244312	C₂	1	2	yes	maximal, complemented
5	#20243696	C₂	1	4	yes	maximal
6	#20243218	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₄₇	—	2	1	no	—
10	#15689180	—	2	4	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×#13093948	C₂²	1	8	yes	—
13	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×#13093935	C₂²	1	2	yes	—
15	C₄×C₄⋊Dic₄₇	—	2	1	no	—
16	C₄×C₄⋊Dic₄₇	—	2	1	no	—
17	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
18	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
19	C₂×C₄₇⋊#95	—	2	1	no	—
20	#15688885	C₂²	1	8	yes	—
21	C₄₇×#533	—	2	4	no	—
22	C₄₇×#533	C₄	1	8	yes	complemented
23	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₄₇	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
29	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
30	C₂×#117×C₄₇	—	2	1	no	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂³×Dic₄₇	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	—	2	8	no	—
36	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	2	2	no	—
39	C₂×C₄×Dic₄₇	—	4	4	no	—
40	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
41	#13093948	—	2	16	no	—
42	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
43	#13093935	—	2	4	no	—
44	C₄₇⋊#95	—	2	2	no	—
45	C₄₇⋊#95	—	2	2	no	—
46	C₂²×Q₈×C₄₇	—	2	1	no	—
47	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₄₇	—	2	2	no	—
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
54	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
55	#125×C₄₇	—	2	8	no	—
56	C₂²⋊Q₈×C₄₇	—	2	8	no	—
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
59	C₄×Q₈×C₄₇	—	2	8	no	—
60	C₄×Q₈×C₄₇	—	2	4	no	—
61	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
62	#117×C₄₇	—	2	8	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄²×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	D₄	1	4	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₄₇	—	2	4	no	—
79	C₂×Q₈×C₄₇	—	2	2	no	—
80	C₂×Q₈×C₄₇	—	2	8	no	—
81	C₂×Q₈×C₄₇	—	4	2	no	—
82	C₂×Q₈×C₄₇	—	4	2	no	—
83	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
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	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	2	8	no	—
101	C₂²×Dic₄₇	—	2	4	no	—
102	C₂²×Dic₄₇	—	4	4	no	—
103	C₂²×Dic₄₇	—	4	4	no	—
104	C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	2	4	no	—
107	C₄⋊C₄×C₄₇	—	2	8	no	—
108	C₄⋊C₄×C₄₇	—	2	8	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
111	C₂²⋊C₄×C₄₇	—	2	8	no	—
112	C₄²×C₄₇	—	2	8	no	—
113	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
114	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
115	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
116	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₇	C₂×D₄	1	2	yes	—
118	C₄²×C₄₇	C₂×D₄	1	2	yes	—
119	C₄⋊Dic₄₇	—	2	8	no	—
120	C₄⋊Dic₄₇	—	2	4	no	—
121	C₄⋊Dic₄₇	#41	1	8	yes	—
122	C₄×Dic₄₇	—	4	4	no	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₂×C₄₇⋊C₈	—	2	4	no	—
125	C₂×C₄₇⋊C₈	—	2	8	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	1	no	—
128	C₂³×C₄₇	—	2	1	no	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂³×C₄₇	#137	1	4	yes	—
131	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₄₇	—	2	8	no	—
133	Q₈×C₄₇	—	4	4	no	—
134	Q₈×C₄₇	—	4	8	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	8	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	8	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₄₇	#137	1	2	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
159	C₂×Dic₄₇	—	2	8	no	—
160	C₂×Dic₄₇	—	4	16	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₂×Dic₄₇	—	4	4	no	—
163	C₄₇⋊C₈	—	4	4	no	—
164	#21394	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	4	no	—
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	#419	1	4	yes	—
170	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₄₇	#525	1	2	yes	—
172	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×#137	1	2	yes	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	4	4	no	—
180	C₄×C₄₇	—	4	4	no	—
181	C₄×C₄₇	#417	1	4	yes	—
182	C₄×C₄₇	C₄×#41	1	2	yes	—
183	C₄×C₄₇	#532	1	2	yes	—
184	Dic₄₇	—	4	8	no	—
185	C₂×#533	D₄₇	1	1	yes	characteristic
186	C₂×#432	—	47	1	no	—
187	C₂×C₄×C₄⋊C₄	—	47	1	no	—
188	#1988	—	47	2	no	—
189	#1981	—	47	2	no	—
190	#1872	—	47	4	no	—
191	#1763	—	47	4	no	—
192	C₂×C₄₇	—	2	4	no	—
193	C₂×C₄₇	#2297	1	1	yes	characteristic
194	C₂×C₄₇	C₂×#419	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
196	C₂×C₄₇	#3110	1	2	yes	—
197	C₂×C₄₇	#3113	1	2	yes	—
198	#533	—	2	4	no	—
199	#533	Dic₄₇	1	8	yes	complemented
200	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
201	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
202	C₂×#125	—	2	1	no	—
203	C₂×C₂²⋊Q₈	—	2	1	no	—
204	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
205	C₂×C₄×Q₈	—	2	1	no	—
206	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
207	C₂×#117	—	2	1	no	—
208	C₂²×C₄⋊C₄	—	47	2	no	—
209	C₂²×C₄²	—	94	1	no	—
210	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
211	#432	—	94	4	no	—
212	C₂×C₄⋊C₈	—	47	2	no	—
213	C₂×#103	—	47	8	no	—
214	C₂×C₂²⋊C₈	—	47	2	no	—
215	C₂×#97	—	47	2	no	—
216	C₄×C₄⋊C₄	—	47	2	no	—
217	C₄×C₄⋊C₄	—	47	2	no	—
218	C₄×C₄⋊C₄	—	94	1	no	—
219	C₄×C₄⋊C₄	—	94	1	no	—
220	C₂×#95	—	94	1	no	—
221	#340	—	47	8	no	—
222	C₄₇	#21394	1	1	yes	characteristic, complemented, Sylow
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
225	C₂³×C₄	—	94	2	no	—
226	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
227	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
228	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
229	C₂²×C₈	—	47	4	no	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
233	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
234	#125	—	2	8	no	—
235	C₂²⋊Q₈	—	2	8	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
238	C₄×Q₈	—	2	8	no	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
241	#117	—	2	8	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	47	4	no	—
248	C₂×C₄⋊C₄	—	94	8	no	—
249	C₂×C₄⋊C₄	—	94	2	no	—
250	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	94	2	no	—
254	C₂×C₄²	—	94	2	no	—
255	C₂×C₄²	—	188	4	no	—
256	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
257	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
259	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
260	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	C₄⋊C₈	—	94	4	no	—
263	#103	—	94	16	no	—
264	C₂²⋊C₈	—	94	4	no	—
265	#97	—	94	4	no	—
266	#95	—	94	2	no	—
267	#95	—	94	2	no	—
268	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	94	8	no	—
282	C₂²×C₄	—	94	4	no	—
283	C₂²×C₄	—	188	4	no	—
284	C₂²×C₄	—	188	4	no	—
285	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
286	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
287	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
288	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
293	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
295	C₂×C₈	—	94	4	no	—
296	C₂×C₈	—	94	8	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	8	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	47	8	no	—
304	C₄⋊C₄	—	94	8	no	—
305	C₄⋊C₄	—	94	4	no	—
306	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
307	C₂²⋊C₄	—	2	8	no	—
308	C₄²	—	2	8	no	—
309	C₄²	—	188	4	no	—
310	C₄²	—	188	4	no	—
311	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
312	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
313	C₄²	C₂²×Dic₄₇	1	2	yes	—
314	C₄²	C₂²×Dic₄₇	1	2	yes	—
315	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
316	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
321	C₂³	#13094055	1	4	yes	—
322	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
323	Q₈	—	2	8	no	—
324	Q₈	—	4	8	no	—
325	Q₈	—	4	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	94	8	no	—
341	C₂×C₄	—	188	16	no	—
342	C₂×C₄	—	188	4	no	—
343	C₂×C₄	—	188	4	no	—
344	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
345	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
346	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
347	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
348	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
349	C₂×C₄	#13094049	1	2	yes	—
350	C₂×C₄	#13094054	1	2	yes	—
351	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
352	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂×C₄	#41×D₄₇	1	4	yes	—
354	C₈	—	188	4	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	#15689132	1	4	yes	—
360	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
361	C₂²	#15689630	1	2	yes	—
362	C₂²	C₂×#13094049	1	1	yes	characteristic
363	C₂²	C₂×#13094054	1	1	yes	characteristic
364	C₂²	C₂×#13094055	1	2	yes	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	188	8	no	—
372	C₄	#15689124	1	4	yes	—
373	C₄	#41×Dic₄₇	1	2	yes	—
374	C₄	#15689669	1	2	yes	—
375	C₂	—	2	4	no	—
376	C₂	#20245879	1	1	yes	characteristic
377	C₂	C₂×#15689132	1	1	yes	characteristic
378	C₂	C₂×#15689124	1	1	yes	characteristic
379	C₂	#20253483	1	2	yes	—
380	C₂	#20253514	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#21394
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20244341	C₂	semidirect
4. #20244312	C₂	semidirect
6. #20243218	C₂	semidirect
22. C₄₇×#533	C₄	semidirect
53. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
54. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
61. C₄×Q₈×C₄₇	C₂×C₄	semidirect
199. #533	Dic₄₇	semidirect
222. C₄₇	#21394	semidirect
232. C₄⋊Q₈	C₂×Dic₄₇	semidirect
233. C₄⋊Q₈	C₂×Dic₄₇	semidirect
240. C₄×Q₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689180	2
C₂×C₄×C₄⋊Dic₄₇	2
#20244341	2
#20244312	2
#20243696	2
#20243218	2
C₂×C₄₇×#533	2
#21394	47