Subgroups — #26108976

Order 12032.

568 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243505	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal
4	#20241229	C₂	1	2	yes	maximal
5	C₄²×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
7	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
9	#15688878	—	2	1	no	—
10	#15688878	—	2	1	no	—
11	#15688878	—	2	1	no	—
12	Q₈⋊(C₄₇⋊C₈)	—	2	4	no	—
13	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
17	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
18	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
19	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₄³×C₄₇	—	2	1	no	—
23	C₄³×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
27	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
29	C₄×C₄₇⋊C₈	—	2	2	no	—
30	C₄×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₄×Q₈×C₄₇	—	2	2	no	—
33	C₄×Q₈×C₄₇	—	2	2	no	—
34	C₄×Q₈×C₄₇	—	2	2	no	—
35	C₄×Q₈×C₄₇	—	2	1	no	—
36	C₄×Q₈×C₄₇	—	2	1	no	—
37	C₄×Q₈×C₄₇	C₈	1	4	yes	complemented
38	C₄×Q₈×C₄₇	D₄	1	2	yes	—
39	C₄×Q₈×C₄₇	Q₈	1	2	yes	—
40	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
41	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
43	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₇	—	2	1	no	—
47	C₂×C₄²×C₄₇	—	2	1	no	—
48	C₂×C₄²×C₄₇	—	2	1	no	—
49	C₂×C₄²×C₄₇	—	2	1	no	—
50	C₂×C₄²×C₄₇	—	2	1	no	—
51	C₂×C₄²×C₄₇	—	2	1	no	—
52	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
59	#95×C₄₇	—	2	1	no	—
60	#95×C₄₇	—	2	1	no	—
61	#95×C₄₇	—	2	1	no	—
62	C₂×Q₈×C₄₇	—	2	1	no	—
63	C₂×Q₈×C₄₇	—	2	1	no	—
64	C₂×Q₈×C₄₇	—	2	1	no	—
65	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
66	C₂×Q₈×C₄₇	C₂×C₈	1	2	yes	—
67	C₂×Q₈×C₄₇	M₁₆	1	2	yes	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	1	no	—
71	C₂²×C₄×C₄₇	—	2	1	no	—
72	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₄⋊C₄×C₄₇	—	2	4	no	—
80	C₄⋊C₄×C₄₇	—	2	4	no	—
81	C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₄⋊C₄×C₄₇	—	2	2	no	—
83	C₄⋊C₄×C₄₇	—	2	2	no	—
84	C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₄⋊C₄×C₄₇	—	2	1	no	—
86	C₄⋊C₄×C₄₇	C₄⋊C₄	1	2	yes	—
87	C₄⋊C₄×C₄₇	C₂×C₈	1	2	yes	—
88	C₄⋊C₄×C₄₇	M₁₆	1	2	yes	—
89	C₄²×C₄₇	—	2	4	no	—
90	C₄²×C₄₇	—	2	4	no	—
91	C₄²×C₄₇	—	2	2	no	—
92	C₄²×C₄₇	—	2	2	no	—
93	C₄²×C₄₇	—	2	2	no	—
94	C₄²×C₄₇	—	2	1	no	—
95	C₄²×C₄₇	—	2	1	no	—
96	C₄²×C₄₇	—	2	2	no	—
97	C₄²×C₄₇	—	2	2	no	—
98	C₄²×C₄₇	—	4	1	no	—
99	C₄²×C₄₇	—	4	2	no	—
100	C₄²×C₄₇	—	4	2	no	—
101	C₄²×C₄₇	—	4	2	no	—
102	C₄²×C₄₇	C₂×C₈	1	2	yes	—
103	C₄²×C₄₇	M₁₆	1	2	yes	—
104	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
106	C₄²×C₄₇	#41	1	1	yes	characteristic
107	C₄²×C₄₇	#41	1	1	yes	characteristic
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	4	2	no	—
110	C₂×C₄₇⋊C₈	—	4	2	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂×C₄₇⋊C₈	—	4	2	no	—
114	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	Q₈×C₄₇	—	2	2	no	—
116	Q₈×C₄₇	—	2	2	no	—
117	Q₈×C₄₇	—	2	2	no	—
118	Q₈×C₄₇	C₄⋊C₈	1	4	yes	complemented
119	C₂×C₄×C₄₇	—	2	2	no	—
120	C₂×C₄×C₄₇	—	2	2	no	—
121	C₂×C₄×C₄₇	—	2	1	no	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	2	1	no	—
124	C₂×C₄×C₄₇	—	2	1	no	—
125	C₂×C₄×C₄₇	—	2	1	no	—
126	C₂×C₄×C₄₇	—	2	1	no	—
127	C₂×C₄×C₄₇	—	2	1	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	4	1	no	—
137	C₂×C₄×C₄₇	—	4	1	no	—
138	C₂×C₄×C₄₇	—	4	1	no	—
139	C₂×C₄×C₄₇	—	4	1	no	—
140	C₂×C₄×C₄₇	—	4	1	no	—
141	C₂×C₄×C₄₇	—	4	1	no	—
142	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
143	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
144	C₂×C₄×C₄₇	#104	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#135	1	2	yes	—
156	C₂×C₄×C₄₇	#137	1	2	yes	—
157	C₄₇⋊C₈	—	4	4	no	—
158	C₄₇⋊C₈	—	8	2	no	—
159	#8566	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	#380	1	1	yes	characteristic
161	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
162	C₂²×C₄₇	#407	1	1	yes	characteristic
163	C₂²×C₄₇	#416	1	1	yes	characteristic
164	C₂²×C₄₇	#419	1	1	yes	characteristic
165	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
166	C₂²×C₄₇	#421	1	1	yes	characteristic
167	C₄×C₄₇	—	2	4	no	—
168	C₄×C₄₇	—	2	1	no	—
169	C₄×C₄₇	—	2	1	no	—
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	—	2	2	no	—
172	C₄×C₄₇	—	2	2	no	—
173	C₄×C₄₇	—	4	2	no	—
174	C₄×C₄₇	—	4	2	no	—
175	C₄×C₄₇	—	4	1	no	—
176	C₄×C₄₇	—	4	2	no	—
177	C₄×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
178	C₄×C₄₇	#423	1	1	yes	characteristic
179	C₄×C₄₇	#431	1	1	yes	characteristic
180	C₄×C₄₇	#432	1	1	yes	characteristic
181	C₄×C₄₇	#464	1	2	yes	—
182	C₄×C₄₇	#479	1	2	yes	—
183	C₄²×Q₈	D₄₇	1	1	yes	characteristic
184	#1831	—	47	1	no	—
185	C₄×C₄⋊C₈	—	47	1	no	—
186	C₂×Q₈⋊C₈	—	47	2	no	—
187	#1279	—	47	2	no	—
188	C₂×C₄₇	#1476	1	1	yes	characteristic
189	C₂×C₄₇	#1479	1	1	yes	characteristic
190	C₂×C₄₇	#1488	1	1	yes	characteristic
191	C₂×C₄₇	#1491	1	1	yes	characteristic
192	C₂×C₄₇	#1797	1	1	yes	characteristic
193	C₂×C₄₇	#1805	1	1	yes	characteristic
194	C₂×C₄₇	#1806	1	1	yes	characteristic
195	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic
196	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
198	C₂×C₄⋊C₈	—	47	2	no	—
199	C₂×C₄⋊C₈	—	94	1	no	—
200	C₂×C₄×C₈	—	47	2	no	—
201	C₄×C₄⋊C₄	—	2	1	no	—
202	C₄×C₄⋊C₄	—	2	1	no	—
203	C₄×C₄⋊C₄	—	2	1	no	—
204	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
205	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
207	C₄³	—	2	1	no	—
208	C₄³	C₂×D₄₇	1	1	yes	characteristic
209	#336	—	94	1	no	—
210	#336	—	94	1	no	—
211	#336	—	94	1	no	—
212	Q₈⋊C₈	—	94	4	no	—
213	C₄₇	#8566	1	1	yes	characteristic, complemented, Sylow
214	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
215	C₂²×C₈	—	94	2	no	—
216	C₂²×C₈	—	94	2	no	—
217	C₄×Q₈	—	2	2	no	—
218	C₄×Q₈	—	2	2	no	—
219	C₄×Q₈	—	2	2	no	—
220	C₄×Q₈	—	2	1	no	—
221	C₄×Q₈	—	2	1	no	—
222	C₄×Q₈	C₄₇⋊C₈	1	4	yes	complemented
223	C₄×Q₈	Dic₉₄	1	2	yes	—
224	C₄×Q₈	D₁₈₈	1	2	yes	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	2	1	no	—
228	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	—	2	1	no	—
237	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
238	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
241	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
244	C₄⋊C₈	—	94	4	no	—
245	C₄⋊C₈	—	94	2	no	—
246	C₄⋊C₈	—	94	2	no	—
247	C₄×C₈	—	94	2	no	—
248	C₄×C₈	—	94	2	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	#95	—	2	1	no	—
252	C₂×Q₈	—	2	1	no	—
253	C₂×Q₈	—	2	1	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×Q₈	C₂×C₄₇⋊C₈	1	2	yes	—
256	C₂×Q₈	#10625329	1	2	yes	—
257	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
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	C₂²×Dic₄₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
269	C₂×C₈	—	94	4	no	—
270	C₂×C₈	—	188	2	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	—	2	4	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	C₂×C₄₇⋊C₈	1	2	yes	—
283	C₄⋊C₄	#10625329	1	2	yes	—
284	C₄⋊C₄	C₄⋊Dic₄₇	1	2	yes	—
285	C₄²	—	2	4	no	—
286	C₄²	—	2	4	no	—
287	C₄²	—	2	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	1	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	4	1	no	—
295	C₄²	—	4	2	no	—
296	C₄²	—	4	2	no	—
297	C₄²	—	4	2	no	—
298	C₄²	C₂×C₄₇⋊C₈	1	2	yes	—
299	C₄²	#10625329	1	2	yes	—
300	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
301	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
302	C₄²	#10625350	1	1	yes	characteristic
303	C₄²	#10625350	1	1	yes	characteristic
304	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
305	Q₈	—	2	2	no	—
306	Q₈	—	2	2	no	—
307	Q₈	—	2	2	no	—
308	Q₈	C₄⋊(C₄₇⋊C₈)	1	4	yes	complemented
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
333	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
334	C₂×C₄	#13093951	1	2	yes	—
335	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
336	C₂×C₄	#13093983	1	1	yes	characteristic
337	C₂×C₄	#13093998	1	1	yes	characteristic
338	C₂×C₄	#13093998	1	1	yes	characteristic
339	C₂×C₄	#13094003	1	1	yes	characteristic
340	C₂×C₄	#13094003	1	1	yes	characteristic
341	C₂×C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
342	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
343	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
344	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
345	C₂×C₄	#13094044	1	2	yes	—
346	C₂×C₄	#13094055	1	2	yes	—
347	C₈	—	376	2	no	—
348	C₈	—	188	4	no	—
349	C₂²	#15688983	1	1	yes	characteristic
350	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
351	C₂²	#15689087	1	1	yes	characteristic
352	C₂²	#15689119	1	1	yes	characteristic
353	C₂²	#15689132	1	1	yes	characteristic
354	C₂²	C₂×#13093951	1	1	yes	characteristic
355	C₂²	#15689140	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	C₂×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
367	C₄	#15689147	1	1	yes	characteristic
368	C₄	#15689176	1	1	yes	characteristic
369	C₄	#15689180	1	1	yes	characteristic
370	C₄	#15689345	1	2	yes	—
371	C₄	#15689430	1	2	yes	—
372	C₂	#20241770	1	1	yes	characteristic
373	C₂	#20241783	1	1	yes	characteristic
374	C₂	#20241822	1	1	yes	characteristic
375	C₂	#20241835	1	1	yes	characteristic
376	C₂	#20243368	1	1	yes	characteristic
377	C₂	#20243403	1	1	yes	characteristic
378	C₂	#20243408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄²×Q₈×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄²×Q₈	D₄₇
hypocenter	C₄₇	#8566
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
37. C₄×Q₈×C₄₇	C₈	semidirect
118. Q₈×C₄₇	C₄⋊C₈	semidirect
213. C₄₇	#8566	semidirect
222. C₄×Q₈	C₄₇⋊C₈	semidirect
308. Q₈	C₄⋊(C₄₇⋊C₈)	semidirect

Maximal subgroups

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

subgroup	index
#20243505	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
#20241229	2
C₄²×Q₈×C₄₇	2
#8566	47