Subgroups — #26219584

Order 12032.

1010 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689150	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689150	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
5	#20244112	C₂	1	4	yes	maximal, complemented
6	#20244107	C₂	1	4	yes	maximal, complemented
7	#20243085	C₂	1	1	yes	maximal, characteristic
8	#20243082	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#2296	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	#15689150	—	2	4	no	—
15	#15689150	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	#15689079	—	2	4	no	—
23	C₂×#13093935	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
25	#15688878	C₂²	1	4	yes	—
26	#15688878	C₂²	1	4	yes	—
27	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#389	C₄	1	2	yes	—
31	C₄₇×#389	C₄	1	2	yes	—
32	C₄₇×#385	C₄	1	2	yes	—
33	C₄₇×#385	C₄	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	—	2	2	no	—
39	C₂×#10625329	—	2	2	no	—
40	C₂×#10625329	Q₈	1	4	yes	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	2	no	—
45	C₂²×C₄₇⋊C₈	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
57	#13093935	—	2	4	no	—
58	C₄×C₄₇⋊C₈	—	2	4	no	—
59	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	#117×C₄₇	—	2	2	no	—
63	#117×C₄₇	—	2	2	no	—
64	#117×C₄₇	D₄	1	4	yes	—
65	#117×C₄₇	Q₈	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	—	2	2	no	—
75	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
79	#95×C₄₇	C₂×C₄	1	4	yes	—
80	#95×C₄₇	C₂×C₄	1	4	yes	—
81	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
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	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₄₇	#41	1	2	yes	—
97	C₂²×C₄×C₄₇	#41	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₄⋊C₄×C₄₇	—	2	2	no	—
100	C₄⋊C₄×C₄₇	—	2	2	no	—
101	C₄⋊C₄×C₄₇	—	2	8	no	—
102	C₄⋊C₄×C₄₇	—	4	4	no	—
103	C₄⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
104	C₂²⋊C₄×C₄₇	—	2	4	no	—
105	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
106	C₄²×C₄₇	—	2	4	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	C₂×D₄	1	4	yes	—
112	C₄²×C₄₇	C₂×Q₈	1	4	yes	—
113	#10625329	—	2	8	no	—
114	#10625329	—	4	4	no	—
115	C₂×C₄₇⋊C₈	—	2	8	no	—
116	C₂×C₄₇⋊C₈	—	2	1	no	—
117	C₂×C₄₇⋊C₈	—	2	2	no	—
118	C₂×C₄₇⋊C₈	—	2	1	no	—
119	C₂×C₄₇⋊C₈	—	2	1	no	—
120	C₂×C₄₇⋊C₈	—	2	1	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	4	4	no	—
129	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
130	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
131	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂³×C₄₇	C₄×D₄	1	2	yes	—
136	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
137	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	—	2	8	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	#121	1	4	yes	—
156	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
157	C₂×C₄×C₄₇	#125	1	4	yes	—
158	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
159	C₂×C₄×C₄₇	#131	1	4	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	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₄₇⋊C₈	—	2	2	no	—
167	C₄₇⋊C₈	—	2	2	no	—
168	C₄₇⋊C₈	—	2	4	no	—
169	C₄₇⋊C₈	—	4	2	no	—
170	C₄₇⋊C₈	—	4	2	no	—
171	#21147	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	2	4	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	#389	1	4	yes	—
177	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
180	C₂²×C₄₇	C₂×#131	1	2	yes	—
181	C₂²×C₄₇	#568	1	2	yes	—
182	C₄×C₄₇	—	2	8	no	—
183	C₄×C₄₇	—	2	4	no	—
184	C₄×C₄₇	—	4	2	no	—
185	C₄×C₄₇	—	4	2	no	—
186	C₄×C₄₇	—	4	2	no	—
187	C₄×C₄₇	#389	1	4	yes	—
188	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
189	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
191	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
192	C₂×#424	—	47	1	no	—
193	C₂×#424	—	47	1	no	—
194	C₂²×C₄⋊C₈	—	47	1	no	—
195	C₂×#405	—	47	1	no	—
196	#2296	D₄₇	1	1	yes	characteristic
197	#1940	—	47	4	no	—
198	#1939	—	47	4	no	—
199	#1729	—	47	1	no	—
200	#1728	—	47	1	no	—
201	C₂×C₄₇	—	2	4	no	—
202	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
203	C₂×C₄₇	#2906	1	2	yes	—
204	C₂×C₄₇	#2929	1	1	yes	characteristic
205	C₂×C₄₇	#2930	1	1	yes	characteristic
206	C₂×C₄₇	#2962	1	2	yes	—
207	C₂²×M₁₆	—	47	1	no	—
208	C₂²×M₁₆	—	47	1	no	—
209	C₂³×C₈	—	47	1	no	—
210	C₂³×C₈	—	47	1	no	—
211	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
212	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
213	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
214	#424	—	94	4	no	—
215	#424	—	94	4	no	—
216	C₂×C₄⋊C₈	—	47	2	no	—
217	C₂×C₄⋊C₈	—	47	2	no	—
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×C₄⋊C₈	—	47	4	no	—
220	C₂×C₄⋊C₈	—	47	2	no	—
221	C₂×C₄⋊C₈	—	94	4	no	—
222	#405	—	94	4	no	—
223	C₂×#97	—	47	2	no	—
224	C₂×C₄×C₈	—	47	2	no	—
225	#389	Dic₄₇	1	2	yes	—
226	#389	Dic₄₇	1	2	yes	—
227	#385	Dic₄₇	1	2	yes	—
228	#385	Dic₄₇	1	2	yes	—
229	C₄×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
230	#336	—	47	4	no	—
231	#336	—	47	4	no	—
232	C₄₇	#21147	1	1	yes	characteristic, complemented, Sylow
233	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
234	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
235	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
236	C₂×M₁₆	—	47	4	no	—
237	C₂×M₁₆	—	94	2	no	—
238	C₂×M₁₆	—	94	2	no	—
239	C₂×M₁₆	—	94	2	no	—
240	C₂×M₁₆	—	94	2	no	—
241	C₂×M₁₆	—	94	2	no	—
242	C₂²×C₈	—	47	4	no	—
243	C₂²×C₈	—	47	1	no	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	2	no	—
246	C₂²×C₈	—	47	2	no	—
247	C₂²×C₈	—	47	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂²×C₈	—	94	2	no	—
250	C₂²×C₈	—	94	2	no	—
251	C₂²×C₈	—	94	2	no	—
252	C₂²×C₈	—	94	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	Dic₉₄	1	4	yes	—
256	#117	D₁₈₈	1	4	yes	—
257	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
260	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
261	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
267	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
268	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
269	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
270	C₄⋊C₈	—	94	4	no	—
271	C₄⋊C₈	—	94	4	no	—
272	C₄⋊C₈	—	94	4	no	—
273	C₄⋊C₈	—	94	4	no	—
274	C₄⋊C₈	—	94	8	no	—
275	#97	—	94	4	no	—
276	C₄×C₈	—	94	4	no	—
277	#95	C₂×Dic₄₇	1	4	yes	—
278	#95	C₂×Dic₄₇	1	4	yes	—
279	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
285	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
286	C₂²×C₄	D₄×D₄₇	1	2	yes	—
287	C₂²×C₄	#10625352	1	2	yes	—
288	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
289	C₂²×C₄	#10625354	1	2	yes	—
290	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
292	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
293	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
294	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
295	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
297	M₁₆	—	94	8	no	—
298	M₁₆	—	188	4	no	—
299	C₂×C₈	—	47	2	no	—
300	C₂×C₈	—	47	2	no	—
301	C₂×C₈	—	47	4	no	—
302	C₂×C₈	—	94	8	no	—
303	C₂×C₈	—	94	1	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	94	1	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	1	no	—
308	C₂×C₈	—	94	1	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	94	2	no	—
312	C₂×C₈	—	94	2	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	—	94	2	no	—
315	C₂×C₈	—	188	4	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₄⋊C₄	C₄⋊Dic₄₇	1	8	yes	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	C₄⋊Dic₄₇	1	8	yes	—
323	C₄²	—	2	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	C₂×Dic₉₄	1	4	yes	—
329	C₄²	C₂×D₁₈₈	1	4	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
333	C₂³	D₄×Dic₄₇	1	2	yes	—
334	C₂³	Q₈×Dic₄₇	1	2	yes	—
335	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	C₂×C₄⋊Dic₄₇	1	8	yes	—
350	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
351	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
352	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
353	C₂×C₄	#13093999	1	4	yes	—
354	C₂×C₄	#13094004	1	4	yes	—
355	C₂×C₄	#13094015	1	4	yes	—
356	C₂×C₄	#13094023	1	4	yes	—
357	C₂×C₄	#13094031	1	4	yes	—
358	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
360	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
362	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
363	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
364	C₈	—	94	2	no	—
365	C₈	—	94	2	no	—
366	C₈	—	94	4	no	—
367	C₈	—	188	2	no	—
368	C₈	—	188	2	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	4	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	#15689022	1	4	yes	—
374	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
375	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
376	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
377	C₂²	C₂×#13094031	1	2	yes	—
378	C₂²	#15689890	1	2	yes	—
379	C₄	—	2	8	no	—
380	C₄	—	2	4	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	#15689022	1	4	yes	—
385	C₄	C₂×#13093999	1	1	yes	characteristic
386	C₄	C₂×#13094004	1	1	yes	characteristic
387	C₄	C₂×#13094015	1	1	yes	characteristic
388	C₄	C₂×#13094023	1	1	yes	characteristic
389	C₂	—	2	4	no	—
390	C₂	C₂×#15689022	1	1	yes	characteristic
391	C₂	#20251956	1	2	yes	—
392	C₂	#20252083	1	1	yes	characteristic
393	C₂	#20252092	1	1	yes	characteristic
394	C₂	#20252337	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#2296	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2296	D₄₇
hypocenter	C₄₇	#21147
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2296

Complements

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

N	H ≅ G/N	type
5. #20244112	C₂	semidirect
6. #20244107	C₂	semidirect
232. C₄₇	#21147	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689150	2
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂×#15689079	2
#20244112	2
#20244107	2
#20243085	2
#20243082	2
C₄₇×#2296	2
#21147	47