Subgroups — #26220766

Order 12032.

1154 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×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
2	#20245795	C₂	1	1	yes	maximal, characteristic
3	#20244333	C₂	1	8	yes	maximal, complemented
4	#20243097	C₂	1	4	yes	maximal
5	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	C₄×#10625329	—	2	2	no	—
9	C₄×#10625329	C₂²	1	4	yes	—
10	C₂×#13093935	—	2	1	no	—
11	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
12	#15688993	—	2	1	no	—
13	#15688989	—	2	1	no	—
14	#15688983	—	2	2	no	—
15	C₄×C₄⋊Dic₄₇	C₂²	1	4	yes	—
16	#15688882	C₂²	1	16	yes	—
17	C₄₇×#533	—	2	1	no	—
18	C₄₇×#533	—	2	1	no	—
19	C₄₇×#533	—	2	1	no	—
20	C₄₇×#533	—	2	1	no	—
21	C₄₇×#533	C₄	1	4	yes	complemented
22	C₄₇×#533	C₂²	1	4	yes	—
23	C₂×C₄⋊Q₈×C₄₇	C₄	1	2	yes	complemented
24	C₂×#125×C₄₇	C₄	1	2	yes	complemented
25	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
26	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
27	C₂×#117×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	4	no	—
31	C₂×#10625329	Q₈	1	8	yes	complemented
32	C₂×#10625329	C₂³	1	4	yes	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	#13093983	—	2	8	no	—
35	C₂×C₄⋊Dic₄₇	—	2	4	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
39	#13093935	—	2	4	no	—
40	C₄×C₄₇⋊C₈	—	2	4	no	—
41	C₄₇⋊#95	—	2	4	no	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂³×C₄×C₄₇	D₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₄⋊Q₈×C₄₇	—	2	2	no	—
46	C₄⋊Q₈×C₄₇	—	2	2	no	—
47	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
48	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
49	#125×C₄₇	—	2	2	no	—
50	#125×C₄₇	—	2	2	no	—
51	#125×C₄₇	C₂×C₄	1	8	yes	—
52	C₂²⋊Q₈×C₄₇	—	2	4	no	—
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	2	4	no	—
55	C₂²⋊Q₈×C₄₇	—	2	4	no	—
56	C₄×Q₈×C₄₇	—	2	4	no	—
57	C₄×Q₈×C₄₇	—	2	4	no	—
58	C₄×Q₈×C₄₇	—	2	4	no	—
59	C₄×Q₈×C₄₇	—	2	4	no	—
60	#117×C₄₇	—	2	2	no	—
61	#117×C₄₇	—	2	2	no	—
62	#117×C₄₇	C₂×C₄	1	4	yes	—
63	#117×C₄₇	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂×C₄	1	2	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	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
78	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₄₇	—	2	4	no	—
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	4	8	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	4	4	no	—
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	4	yes	—
96	C₂²×C₄×C₄₇	#41	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	—	2	8	no	—
100	C₄⋊C₄×C₄₇	—	2	8	no	—
101	C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₄⋊C₄×C₄₇	—	2	4	no	—
103	C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
105	C₂²⋊C₄×C₄₇	—	2	4	no	—
106	C₂²⋊C₄×C₄₇	—	2	4	no	—
107	C₄²×C₄₇	—	2	4	no	—
108	C₄²×C₄₇	—	2	4	no	—
109	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
110	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
111	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²⋊Dic₄₇	—	4	4	no	—
120	C₄⋊Dic₄₇	—	4	8	no	—
121	C₄⋊Dic₄₇	—	4	4	no	—
122	C₄×Dic₄₇	—	2	8	no	—
123	#10625329	—	2	8	no	—
124	#10625329	—	2	4	no	—
125	#10625329	C₂×Q₈	1	8	yes	complemented
126	C₂×C₄₇⋊C₈	—	2	8	no	—
127	C₂×C₄₇⋊C₈	—	2	4	no	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₄₇	#124	1	2	yes	—
132	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
133	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₄₇	—	4	8	no	—
135	Q₈×C₄₇	—	4	8	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	8	no	—
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
151	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
152	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
153	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
154	C₂×C₄×C₄₇	#124	1	2	yes	—
155	C₂×C₄×C₄₇	C₄⋊Q₈	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	C₂²×Q₈	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
160	C₂×Dic₄₇	—	4	8	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₄₇⋊C₈	—	2	8	no	—
163	#21306	—	47	1	no	maximal, Sylow
164	C₂²×C₄₇	—	2	2	no	—
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	4	2	no	—
168	C₂²×C₄₇	—	4	2	no	—
169	C₂²×C₄₇	#391	1	2	yes	—
170	C₂²×C₄₇	#391	1	2	yes	—
171	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	4	8	no	—
178	C₄×C₄₇	#391	1	2	yes	—
179	C₄×C₄₇	#391	1	2	yes	—
180	C₄×C₄₇	#421	1	4	yes	—
181	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
182	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
183	Dic₄₇	—	8	4	no	—
184	C₂×#533	D₄₇	1	1	yes	characteristic
185	C₂×C₄×M₁₆	—	47	1	no	—
186	#2285	—	47	1	no	—
187	#1986	—	47	8	no	—
188	#1733	—	47	4	no	—
189	C₂×C₄₇	—	2	1	no	—
190	C₂×C₄₇	—	2	1	no	—
191	C₂×C₄₇	—	2	2	no	—
192	C₂×C₄₇	—	2	2	no	—
193	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
194	C₂×C₄₇	C₂×#421	1	2	yes	—
195	C₂²×M₁₆	—	47	2	no	—
196	#533	—	2	1	no	—
197	#533	—	2	1	no	—
198	#533	—	2	1	no	—
199	#533	—	2	1	no	—
200	#533	Dic₄₇	1	4	yes	complemented
201	#533	C₂×D₄₇	1	4	yes	—
202	C₂×C₄⋊Q₈	Dic₄₇	1	2	yes	complemented
203	C₂×#125	Dic₄₇	1	2	yes	complemented
204	C₂×C₂²⋊Q₈	—	2	2	no	—
205	C₂×C₄×Q₈	—	2	2	no	—
206	C₂×#117	—	47	2	no	—
207	C₂×#117	C₂×D₄₇	1	2	yes	—
208	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
209	C₄×M₁₆	—	47	4	no	—
210	C₄×M₁₆	—	94	2	no	—
211	C₂×#97	—	94	1	no	—
212	C₂×C₄×C₈	—	94	1	no	—
213	#384	—	94	1	no	—
214	#382	—	94	1	no	—
215	#380	—	94	2	no	—
216	C₄×C₄⋊C₄	—	47	4	no	—
217	#339	—	47	16	no	—
218	C₄₇	#21306	1	1	yes	characteristic, complemented, Sylow
219	C₂²×Q₈	—	2	2	no	—
220	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
221	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
222	C₂×M₁₆	—	47	8	no	—
223	C₂×M₁₆	—	47	4	no	—
224	C₂×M₁₆	—	94	4	no	—
225	C₂×M₁₆	—	94	2	no	—
226	C₂²×C₈	—	94	2	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
230	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
231	#125	—	2	2	no	—
232	#125	—	2	2	no	—
233	#125	C₂×Dic₄₇	1	8	yes	—
234	C₂²⋊Q₈	—	2	4	no	—
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₂²⋊Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×Q₈	—	2	4	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	94	8	no	—
245	#117	C₂×Dic₄₇	1	4	yes	—
246	#117	C₂²×D₄₇	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	94	2	no	—
250	C₂×C₄⋊C₄	—	94	4	no	—
251	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	94	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	47	4	no	—
256	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
257	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
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	2	yes	—
262	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
265	#97	—	94	4	no	—
266	C₄×C₈	—	94	4	no	—
267	#95	—	94	4	no	—
268	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	4	8	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	—	94	4	no	—
275	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
276	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
277	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
278	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
279	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
280	C₂²×C₄	#10625354	1	4	yes	—
281	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
289	M₁₆	—	47	8	no	—
290	M₁₆	—	94	8	no	—
291	M₁₆	—	94	4	no	—
292	C₂×C₈	—	94	8	no	—
293	C₂×C₈	—	94	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	188	8	no	—
300	C₄⋊C₄	—	188	4	no	—
301	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	188	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	4	no	—
307	C₄²	—	94	8	no	—
308	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
309	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
310	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
311	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
312	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
313	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
314	C₄²	C₂²×Dic₄₇	1	2	yes	—
315	C₄²	C₂²×Dic₄₇	1	2	yes	—
316	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
317	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
318	C₂³	—	4	2	no	—
319	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
320	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
321	C₂³	#13094013	1	2	yes	—
322	C₂³	#13094022	1	2	yes	—
323	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
324	Q₈	—	4	8	no	—
325	Q₈	—	4	8	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	188	8	no	—
335	C₂×C₄	—	188	4	no	—
336	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
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	1	yes	characteristic
340	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
342	C₂×C₄	Q₈×Dic₄₇	1	4	yes	—
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	#13094022	1	2	yes	—
348	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
350	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
351	C₂×C₄	C₂×#10625354	1	2	yes	—
352	C₈	—	94	8	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	#15689030	1	2	yes	—
359	C₂²	#15689030	1	2	yes	—
360	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
361	C₂²	C₂×#13094013	1	1	yes	characteristic
362	C₂²	C₂×#13094022	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	8	no	—
367	C₄	—	376	4	no	—
368	C₄	#15689030	1	2	yes	—
369	C₄	#15689030	1	2	yes	—
370	C₄	#15689140	1	4	yes	—
371	C₄	C₂×Q₈×Dic₄₇	1	2	yes	—
372	C₄	C₂×#13094000	1	2	yes	—
373	C₂	—	2	1	no	—
374	C₂	—	2	2	no	—
375	C₂	—	2	2	no	—
376	C₂	—	2	1	no	—
377	C₂	C₂×#15689030	1	1	yes	characteristic
378	C₂	C₂×#15689140	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#21306
LCS	G ▷ C₂×C₄×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. #20244333	C₂	semidirect
21. C₄₇×#533	C₄	semidirect
23. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
24. C₂×#125×C₄₇	C₄	semidirect
31. C₂×#10625329	Q₈	semidirect
125. #10625329	C₂×Q₈	semidirect
200. #533	Dic₄₇	semidirect
202. C₂×C₄⋊Q₈	Dic₄₇	semidirect
203. C₂×#125	Dic₄₇	semidirect
218. C₄₇	#21306	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625329	2
#20245795	2
#20244333	2
#20243097	2
C₂×C₄₇×#533	2
#21306	47