Subgroups — #26220950

Order 12032.

1114 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	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
3	#20244382	C₂	1	4	yes	maximal, complemented
4	#20244378	C₂	1	4	yes	maximal, complemented
5	#20243127	C₂	1	4	yes	maximal
6	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂²×#10625329	C₂²	1	2	yes	—
9	#15689147	—	2	2	no	—
10	#15689147	C₂²	1	2	yes	—
11	#15689147	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
13	C₄×#10625329	—	2	1	no	—
14	C₄×#10625329	—	2	1	no	—
15	C₄×#10625329	C₂²	1	2	yes	—
16	C₄×#10625329	C₂²	1	2	yes	—
17	C₂×#13093935	—	2	1	no	—
18	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
19	#15688892	C₂²	1	16	yes	—
20	C₄₇×#533	—	2	1	no	—
21	C₄₇×#533	—	2	1	no	—
22	C₄₇×#533	—	2	1	no	—
23	C₄₇×#533	—	2	1	no	—
24	C₄₇×#533	—	2	2	no	—
25	C₄₇×#533	—	2	2	no	—
26	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
27	C₂×#125×C₄₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊Q₈×C₄₇	C₄	1	4	yes	—
29	C₂×C₄×Q₈×C₄₇	C₄	1	4	yes	—
30	C₂×#117×C₄₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	8	no	—
36	C₂×#10625329	Q₈	1	8	yes	complemented
37	C₂×#10625329	C₂³	1	4	yes	—
38	C₂×#10625329	C₂³	1	4	yes	—
39	C₂²×C₄₇⋊C₈	—	2	2	no	—
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
42	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
43	#13093935	—	2	2	no	—
44	#13093935	—	2	2	no	—
45	C₄×C₄₇⋊C₈	—	2	2	no	—
46	C₄×C₄₇⋊C₈	—	2	2	no	—
47	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₄₇	—	2	2	no	—
51	C₄⋊Q₈×C₄₇	—	2	2	no	—
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	—	2	2	no	—
54	#125×C₄₇	—	2	2	no	—
55	#125×C₄₇	—	2	2	no	—
56	#125×C₄₇	—	2	4	no	—
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	—	2	4	no	—
59	C₂²⋊Q₈×C₄₇	—	2	4	no	—
60	C₂²⋊Q₈×C₄₇	—	2	4	no	—
61	C₄×Q₈×C₄₇	—	2	4	no	—
62	C₄×Q₈×C₄₇	—	2	4	no	—
63	C₄×Q₈×C₄₇	—	2	4	no	—
64	C₄×Q₈×C₄₇	—	2	4	no	—
65	#117×C₄₇	—	2	2	no	—
66	#117×C₄₇	—	2	2	no	—
67	#117×C₄₇	—	2	2	no	—
68	#117×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
73	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	D₄	1	2	yes	—
80	C₂×C₄²×C₄₇	D₄	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
84	C₂×Q₈×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	4	8	no	—
87	C₂²×C₄×C₄₇	—	4	4	no	—
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₄₇	#41	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₄⋊C₄×C₄₇	—	2	8	no	—
104	C₄⋊C₄×C₄₇	—	2	8	no	—
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	2	4	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	—	2	4	no	—
109	C₂²⋊C₄×C₄₇	—	2	4	no	—
110	C₂²⋊C₄×C₄₇	—	2	4	no	—
111	C₄²×C₄₇	—	2	4	no	—
112	C₄²×C₄₇	—	2	4	no	—
113	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
114	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
115	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
116	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂×D₄	1	2	yes	—
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	2	yes	—
123	#10625329	—	2	8	no	—
124	#10625329	—	2	4	no	—
125	#10625329	—	2	8	no	—
126	#10625329	—	4	4	no	—
127	#10625329	C₂×Q₈	1	8	yes	—
128	C₂×C₄₇⋊C₈	—	2	8	no	—
129	C₂×C₄₇⋊C₈	—	2	4	no	—
130	C₂×C₄₇⋊C₈	—	2	4	no	—
131	C₂×C₄₇⋊C₈	—	4	4	no	—
132	C₂³×C₄₇	—	4	2	no	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂³×C₄₇	C₄×Q₈	1	4	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	Q₈×C₄₇	—	4	8	no	—
138	Q₈×C₄₇	—	4	8	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	8	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	8	no	—
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
156	C₂×C₄×C₄₇	#124	1	2	yes	—
157	C₂×C₄×C₄₇	#124	1	2	yes	—
158	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
159	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
164	C₄₇⋊C₈	—	2	8	no	—
165	C₄₇⋊C₈	—	4	4	no	—
166	#21337	—	47	1	no	maximal, Sylow
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	4	4	no	—
171	C₂²×C₄₇	#391	1	2	yes	—
172	C₂²×C₄₇	#391	1	2	yes	—
173	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	4	8	no	—
179	C₄×C₄₇	#391	1	2	yes	—
180	C₄×C₄₇	#391	1	2	yes	—
181	C₄×C₄₇	#413	1	4	yes	—
182	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
183	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
184	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
185	C₂×#533	D₄₇	1	1	yes	characteristic
186	C₂×#423	—	47	1	no	—
187	C₂×C₄×M₁₆	—	47	1	no	—
188	#1998	—	47	4	no	—
189	#1997	—	47	4	no	—
190	#1742	—	47	4	no	—
191	C₂×C₄₇	—	2	2	no	—
192	C₂×C₄₇	—	2	2	no	—
193	C₂×C₄₇	—	2	2	no	—
194	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#413	1	2	yes	—
196	C₂²×M₁₆	—	47	2	no	—
197	C₂²×M₁₆	—	47	2	no	—
198	#533	—	2	1	no	—
199	#533	—	2	1	no	—
200	#533	—	2	1	no	—
201	#533	—	2	1	no	—
202	#533	—	2	2	no	—
203	#533	—	2	2	no	—
204	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
205	C₂×#125	C₂×D₄₇	1	2	yes	—
206	C₂×C₂²⋊Q₈	Dic₄₇	1	4	yes	—
207	C₂×C₄×Q₈	Dic₄₇	1	4	yes	—
208	C₂×#117	C₂×D₄₇	1	2	yes	—
209	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
210	#423	—	47	2	no	—
211	#423	—	47	2	no	—
212	#423	—	94	2	no	—
213	C₂×C₄⋊C₈	—	94	2	no	—
214	C₄×M₁₆	—	47	2	no	—
215	C₄×M₁₆	—	47	2	no	—
216	C₄×M₁₆	—	94	1	no	—
217	C₄×M₁₆	—	94	1	no	—
218	C₂×#97	—	94	1	no	—
219	C₂×C₄×C₈	—	94	1	no	—
220	#343	—	47	16	no	—
221	C₄₇	#21337	1	1	yes	characteristic, complemented, Sylow
222	C₂²×Q₈	C₂×Dic₄₇	1	4	yes	—
223	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
224	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
225	C₂×M₁₆	—	47	8	no	—
226	C₂×M₁₆	—	47	4	no	—
227	C₂×M₁₆	—	47	4	no	—
228	C₂×M₁₆	—	94	4	no	—
229	C₂×M₁₆	—	94	2	no	—
230	C₂×M₁₆	—	94	2	no	—
231	C₂×M₁₆	—	94	8	no	—
232	C₂²×C₈	—	94	2	no	—
233	C₂²×C₈	—	94	2	no	—
234	C₄⋊Q₈	—	2	2	no	—
235	C₄⋊Q₈	—	2	2	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	#125	—	2	2	no	—
239	#125	—	2	2	no	—
240	#125	—	2	4	no	—
241	C₂²⋊Q₈	—	2	4	no	—
242	C₂²⋊Q₈	—	2	4	no	—
243	C₂²⋊Q₈	—	2	4	no	—
244	C₂²⋊Q₈	—	2	4	no	—
245	C₄×Q₈	—	2	4	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	4	no	—
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
254	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
255	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
256	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
257	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
258	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
259	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
264	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
265	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
266	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
267	C₄⋊C₈	—	94	4	no	—
268	C₄⋊C₈	—	94	4	no	—
269	#97	—	94	2	no	—
270	#97	—	94	2	no	—
271	C₄×C₈	—	94	2	no	—
272	C₄×C₈	—	94	2	no	—
273	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	4	8	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
279	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
280	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
281	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
282	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
283	C₂²×C₄	#10625354	1	4	yes	—
284	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
285	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
286	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
287	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
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	C₂³×D₄₇	1	1	yes	characteristic
293	M₁₆	—	47	8	no	—
294	M₁₆	—	94	8	no	—
295	M₁₆	—	94	4	no	—
296	M₁₆	—	94	8	no	—
297	M₁₆	—	188	4	no	—
298	C₂×C₈	—	94	8	no	—
299	C₂×C₈	—	94	4	no	—
300	C₂×C₈	—	94	4	no	—
301	C₂×C₈	—	188	4	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	8	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	4	no	—
309	C₂²⋊C₄	—	2	4	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	4	no	—
312	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
313	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
314	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
315	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
316	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
317	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
318	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
319	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
320	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
321	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
324	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
325	C₂³	Q₈×Dic₄₇	1	4	yes	—
326	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
327	Q₈	—	4	8	no	—
328	Q₈	—	4	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	8	no	—
337	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
340	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
342	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
343	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
344	C₂×C₄	#13094000	1	4	yes	—
345	C₂×C₄	#13094000	1	4	yes	—
346	C₂×C₄	#13094013	1	2	yes	—
347	C₂×C₄	#13094013	1	2	yes	—
348	C₂×C₄	#13094022	1	2	yes	—
349	C₂×C₄	#13094022	1	2	yes	—
350	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
351	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
353	C₂×C₄	C₂×#10625354	1	2	yes	—
354	C₈	—	94	8	no	—
355	C₈	—	188	4	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	4	no	—
360	C₂²	#15689030	1	2	yes	—
361	C₂²	#15689030	1	2	yes	—
362	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
363	C₂²	C₂×Q₈×Dic₄₇	1	2	yes	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	8	no	—
368	C₄	#15689030	1	2	yes	—
369	C₄	#15689030	1	2	yes	—
370	C₄	#15689107	1	4	yes	—
371	C₄	C₂×#13094000	1	2	yes	—
372	C₄	C₂×#13094013	1	1	yes	characteristic
373	C₄	C₂×#13094022	1	1	yes	characteristic
374	C₂	—	2	2	no	—
375	C₂	—	2	2	no	—
376	C₂	—	2	2	no	—
377	C₂	C₂×#15689030	1	1	yes	characteristic
378	C₂	C₂×#15689107	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₄₇
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#21337
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20244382	C₂	semidirect
4. #20244378	C₂	semidirect
36. C₂×#10625329	Q₈	semidirect
221. C₄₇	#21337	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂×C₄×#10625329	2
#20244382	2
#20244378	2
#20243127	2
C₂×C₄₇×#533	2
#21337	47