Subgroups — #26369491

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₄₇	C₂	1	2	yes	maximal, complemented
2	C₈×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20245220	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245216	C₂	1	2	yes	maximal, complemented
5	#20245211	C₂	1	2	yes	maximal, complemented
6	C₁₆×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245207	C₂	1	1	yes	maximal, characteristic, complemented
8	#20245142	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244997	C₂	1	2	yes	maximal, complemented
10	C₄×#13093963	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
13	C₄×D₄×D₄₇	C₄	1	1	yes	characteristic
14	C₂×#13093964	C₂²	1	2	yes	complemented
15	C₂×#13093963	C₂²	1	1	yes	characteristic
16	C₂×#13093963	C₂²	1	2	yes	—
17	C₂×#13093963	C₂²	1	1	yes	characteristic
18	M₃₂×D₄₇	—	2	8	no	—
19	C₂×C₁₆×D₄₇	C₂²	1	2	yes	complemented
20	C₂×C₁₆×D₄₇	C₂²	1	2	yes	complemented
21	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
22	D₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
23	#15689188	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
25	(C₂²⋊D₄₇)⋊C₈	C₄	1	2	yes	—
26	C₄⋊C₈×D₄₇	C₄	1	1	yes	characteristic
27	C₂²⋊C₈×D₄₇	C₄	1	2	yes	—
28	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
29	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
30	Dic₄₇⋊C₁₆	C₂²	1	2	yes	complemented
31	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
32	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	complemented
33	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	complemented
34	#15688898	C₂²	1	1	yes	characteristic, complemented
35	#15688898	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	C₂×M₃₂×C₄₇	C₂²	1	2	yes	complemented
38	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₄₇	C₈	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
45	C₂×C₈×D₄₇	—	2	4	no	—
46	C₂×C₈×D₄₇	—	2	4	no	—
47	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₈×D₄₇	C₂³	1	2	yes	—
51	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
52	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
53	D₄×Dic₄₇	C₈	1	1	yes	characteristic
54	#13093986	C₈	1	1	yes	characteristic
55	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
56	(C₂²⋊D₄₇)⋊C₄	C₈	1	2	yes	—
57	C₄⋊C₄×D₄₇	C₈	1	1	yes	characteristic
58	C₂²⋊C₄×D₄₇	C₈	1	2	yes	—
59	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
60	#13093964	—	2	4	no	—
61	#13093963	—	2	4	no	—
62	#13093963	—	2	2	no	—
63	#13093963	D₄	1	4	yes	complemented
64	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
65	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
67	C₁₆×D₄₇	—	2	4	no	—
68	C₁₆×D₄₇	—	2	4	no	—
69	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
70	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
71	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
72	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
73	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
74	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
78	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	M₃₂×C₄₇	—	2	4	no	—
80	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
81	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
85	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂³×D₄₇	C₂×C₈	1	2	yes	—
87	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
90	C₂²×Dic₄₇	C₂×C₈	1	2	yes	—
91	D₄×D₄₇	—	2	4	no	—
92	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₄₇	—	2	4	no	—
94	C₂×C₄×D₄₇	—	2	4	no	—
95	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
97	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
98	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
100	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₄⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
107	C₂²⋊C₄×C₄₇	C₂×C₈	1	2	yes	—
108	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
110	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
111	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
112	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
113	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
114	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
115	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
116	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄₇⋊C₈	—	2	4	no	—
118	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₄₇	—	2	4	no	—
122	C₈×D₄₇	—	2	2	no	—
123	C₈×D₄₇	—	2	2	no	—
124	C₈×D₄₇	—	2	2	no	—
125	C₈×D₄₇	—	2	4	no	—
126	C₈×D₄₇	C₂×D₄	1	2	yes	—
127	C₈×D₄₇	#41	1	2	yes	—
128	C₁₆×C₄₇	—	2	2	no	—
129	C₁₆×C₄₇	—	2	1	no	—
130	C₁₆×C₄₇	C₂×D₄	1	2	yes	complemented
131	C₄₇⋊C₁₆	—	2	2	no	—
132	C₄₇⋊C₁₆	—	2	1	no	—
133	C₄₇⋊C₁₆	C₂×D₄	1	2	yes	complemented
134	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
135	C₂²×D₄₇	—	2	4	no	—
136	C₂²×D₄₇	—	2	4	no	—
137	C₂²×D₄₇	—	4	2	no	—
138	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
139	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
140	D₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂²⋊D₄₇	—	2	4	no	—
148	C₂×Dic₄₇	—	2	4	no	—
149	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
150	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
151	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
152	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
153	D₁₈₈	M₃₂	1	4	yes	complemented
154	C₄×D₄₇	—	2	4	no	—
155	C₄×D₄₇	—	2	2	no	—
156	C₄×D₄₇	—	2	2	no	—
157	C₄×D₄₇	—	2	2	no	—
158	C₄×D₄₇	—	2	4	no	—
159	C₄×D₄₇	—	4	1	no	—
160	C₄×D₄₇	C₄×D₄	1	2	yes	—
161	C₄×D₄₇	#131	1	2	yes	—
162	C₈×C₄₇	—	2	2	no	—
163	C₈×C₄₇	—	2	1	no	—
164	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₄₇⋊C₈	—	2	2	no	—
167	C₄₇⋊C₈	—	2	1	no	—
168	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
169	D₄×M₃₂	—	47	1	no	maximal, Sylow
170	C₂²×C₄₇	—	2	2	no	—
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
174	C₂×D₄₇	—	2	1	no	—
175	C₂×D₄₇	—	2	1	no	—
176	C₂×D₄₇	—	2	2	no	—
177	C₂×D₄₇	—	2	2	no	—
178	C₂×D₄₇	—	4	8	no	—
179	C₂×D₄₇	C₈×D₄	1	2	yes	—
180	C₂×D₄₇	C₂×M₃₂	1	4	yes	complemented
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	2	2	no	—
183	C₄×C₄₇	C₂×M₃₂	1	2	yes	complemented
184	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
186	Dic₄₇	—	2	1	no	—
187	Dic₄₇	—	2	1	no	—
188	Dic₄₇	—	2	2	no	—
189	Dic₄₇	C₈×D₄	1	2	yes	—
190	C₂²×M₃₂	—	47	2	no	—
191	C₂×C₈×D₄	—	47	1	no	—
192	#2169	—	47	1	no	—
193	#2169	D₄₇	1	1	yes	characteristic, complemented
194	#2168	—	47	2	no	—
195	#2168	—	47	2	no	—
196	D₄×C₁₆	—	47	1	no	—
197	D₄×C₁₆	—	47	1	no	—
198	#2150	—	47	1	no	—
199	#2112	—	47	2	no	—
200	C₄×M₃₂	—	47	1	no	—
201	C₂×C₄₇	—	4	2	no	—
202	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
203	C₂×C₄₇	C₂²×M₃₂	1	1	yes	characteristic
204	C₂×C₄₇	#3407	1	1	yes	characteristic
205	D₄₇	—	2	2	no	—
206	D₄₇	—	2	4	no	—
207	C₂³×C₈	—	47	2	no	—
208	C₂×C₄×D₄	—	47	1	no	—
209	C₂×M₃₂	—	47	2	no	—
210	C₂×M₃₂	—	47	1	no	—
211	C₂×M₃₂	—	47	1	no	—
212	C₂×M₃₂	—	47	2	no	—
213	C₂×M₃₂	—	94	8	no	—
214	C₂×M₃₂	C₂×D₄₇	1	2	yes	complemented
215	C₂²×C₁₆	—	47	2	no	—
216	C₂²×C₁₆	—	47	2	no	—
217	C₈×D₄	—	47	2	no	—
218	C₈×D₄	—	47	1	no	—
219	C₈×D₄	—	47	1	no	—
220	C₈×D₄	—	47	2	no	—
221	C₈×D₄	—	47	1	no	—
222	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
223	C₂×C₄⋊C₈	—	47	1	no	—
224	C₂×C₂²⋊C₈	—	47	2	no	—
225	C₂×C₄×C₈	—	47	1	no	—
226	C₄⋊C₁₆	—	47	2	no	—
227	C₄⋊C₁₆	—	47	1	no	—
228	C₄⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
229	C₂²⋊C₁₆	—	47	2	no	—
230	C₂²⋊C₁₆	—	47	2	no	—
231	C₂²⋊C₁₆	—	47	2	no	—
232	C₂²⋊C₁₆	C₂×D₄₇	1	2	yes	complemented
233	#346	—	47	1	no	—
234	#346	—	47	1	no	—
235	C₄×C₁₆	—	47	1	no	—
236	C₄×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
237	C₄₇	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
238	C₂²×D₄	—	47	1	no	—
239	C₂³×C₄	—	47	2	no	—
240	C₂²×C₈	—	47	1	no	—
241	C₂²×C₈	—	47	2	no	—
242	C₂²×C₈	—	47	2	no	—
243	C₂²×C₈	—	47	2	no	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	2	no	—
246	C₂²×C₈	—	94	4	no	—
247	C₂²×C₈	—	94	4	no	—
248	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
249	C₄×D₄	—	47	1	no	—
250	C₄×D₄	—	47	2	no	—
251	C₄×D₄	—	47	1	no	—
252	C₄×D₄	—	47	2	no	—
253	C₄×D₄	—	47	1	no	—
254	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	47	1	no	—
256	C₂×C₂²⋊C₄	—	47	2	no	—
257	C₂×C₄²	—	47	1	no	—
258	M₃₂	—	2	4	no	—
259	M₃₂	—	47	4	no	—
260	M₃₂	—	94	2	no	—
261	M₃₂	—	94	4	no	—
262	M₃₂	—	94	4	no	—
263	C₂×C₁₆	—	47	1	no	—
264	C₂×C₁₆	—	47	1	no	—
265	C₂×C₁₆	—	47	2	no	—
266	C₂×C₁₆	—	94	4	no	—
267	C₂×C₁₆	—	94	4	no	—
268	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
269	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
270	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
271	C₄⋊C₈	—	47	2	no	—
272	C₄⋊C₈	—	47	1	no	—
273	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
274	C₂²⋊C₈	—	47	2	no	—
275	C₂²⋊C₈	—	47	2	no	—
276	C₂²⋊C₈	—	47	2	no	—
277	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
278	C₄×C₈	—	47	1	no	—
279	C₄×C₈	—	47	1	no	—
280	C₄×C₈	—	47	1	no	—
281	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₂⁴	—	47	2	no	—
283	C₂×D₄	—	47	2	no	—
284	C₂×D₄	—	47	1	no	—
285	C₂×D₄	—	94	4	no	—
286	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
287	C₂²×C₄	—	47	1	no	—
288	C₂²×C₄	—	47	2	no	—
289	C₂²×C₄	—	47	1	no	—
290	C₂²×C₄	—	47	2	no	—
291	C₂²×C₄	—	47	2	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	47	1	no	—
294	C₂²×C₄	—	94	4	no	—
295	C₂²×C₄	—	94	4	no	—
296	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	47	1	no	—
300	C₂×C₈	—	47	2	no	—
301	C₂×C₈	—	47	2	no	—
302	C₂×C₈	—	47	1	no	—
303	C₂×C₈	—	47	2	no	—
304	C₂×C₈	—	94	4	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	4	no	—
307	C₂×C₈	—	94	4	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
312	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
313	C₄⋊C₄	—	47	2	no	—
314	C₄⋊C₄	—	47	1	no	—
315	C₄⋊C₄	C₈×D₄₇	1	1	yes	characteristic
316	C₂²⋊C₄	—	47	2	no	—
317	C₂²⋊C₄	—	47	2	no	—
318	C₂²⋊C₄	—	47	2	no	—
319	C₂²⋊C₄	C₈×D₄₇	1	2	yes	—
320	C₄²	—	47	1	no	—
321	C₄²	—	47	1	no	—
322	C₄²	—	47	1	no	—
323	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
324	C₁₆	—	2	2	no	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	47	2	no	—
327	C₁₆	—	94	2	no	—
328	C₁₆	—	94	1	no	—
329	C₁₆	D₄×D₄₇	1	2	yes	complemented
330	C₂³	—	47	2	no	—
331	C₂³	—	47	1	no	—
332	C₂³	—	94	4	no	—
333	C₂³	—	94	4	no	—
334	C₂³	—	188	2	no	—
335	C₂³	C₂×C₈×D₄₇	1	2	yes	—
336	D₄	—	2	2	no	—
337	D₄	—	47	4	no	—
338	D₄	—	94	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	47	1	no	—
342	C₂×C₄	—	47	2	no	—
343	C₂×C₄	—	47	2	no	—
344	C₂×C₄	—	47	1	no	—
345	C₂×C₄	—	47	1	no	—
346	C₂×C₄	—	47	2	no	—
347	C₂×C₄	—	94	4	no	—
348	C₂×C₄	—	94	4	no	—
349	C₂×C₄	—	94	4	no	—
350	C₂×C₄	—	94	2	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	188	1	no	—
354	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
356	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	2	1	no	—
360	C₈	—	47	2	no	—
361	C₈	—	94	2	no	—
362	C₈	—	94	1	no	—
363	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
364	C₈	#41×D₄₇	1	1	yes	characteristic
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	47	2	no	—
369	C₂²	—	47	4	no	—
370	C₂²	—	94	2	no	—
371	C₂²	—	94	1	no	—
372	C₂²	—	94	1	no	—
373	C₂²	—	94	2	no	—
374	C₂²	—	188	8	no	—
375	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	2	1	no	—
378	C₄	—	47	2	no	—
379	C₄	—	94	2	no	—
380	C₄	—	94	1	no	—
381	C₄	—	94	1	no	—
382	C₄	M₃₂×D₄₇	1	2	yes	complemented
383	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
384	C₄	#131×D₄₇	1	1	yes	characteristic
385	C₂	—	4	2	no	—
386	C₂	—	94	2	no	—
387	C₂	—	94	4	no	—
388	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
389	C₂	C₂×M₃₂×D₄₇	1	1	yes	characteristic
390	C₂	#20256489	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#2169	C₂
prime radical	C₂×D₄×D₄₇	C₈
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2169	D₄₇
hypocenter	C₄₇	D₄×M₃₂
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ #2169

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₄₇	C₂	semidirect
3. #20245220	C₂	semidirect
4. #20245216	C₂	semidirect
5. #20245211	C₂	semidirect
6. C₁₆×D₁₈₈	C₂	semidirect
7. #20245207	C₂	semidirect
8. #20245142	C₂	semidirect
9. #20244997	C₂	semidirect
10. C₄×#13093963	C₂	semidirect
11. C₄₇×#2169	C₂	semidirect
14. C₂×#13093964	C₂²	semidirect
19. C₂×C₁₆×D₄₇	C₂²	semidirect
20. C₂×C₁₆×D₄₇	C₂²	semidirect
29. C₄⋊(C₄₇⋊C₁₆)	C₂²	semidirect
30. Dic₄₇⋊C₁₆	C₂²	semidirect
31. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
32. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
33. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
34. #15688898	C₂²	semidirect
35. #15688898	C₂²	semidirect
36. C₄×C₄₇⋊C₁₆	C₂²	semidirect
37. C₂×M₃₂×C₄₇	C₂²	semidirect
39. C₄₇×C₄⋊C₁₆	C₂²	semidirect
40. C₄₇×C₂²⋊C₁₆	C₂²	semidirect
41. C₄×C₁₆×C₄₇	C₂²	semidirect
63. #13093963	D₄	semidirect
130. C₁₆×C₄₇	C₂×D₄	semidirect
133. C₄₇⋊C₁₆	C₂×D₄	semidirect
153. D₁₈₈	M₃₂	semidirect
180. C₂×D₄₇	C₂×M₃₂	semidirect
183. C₄×C₄₇	C₂×M₃₂	semidirect
193. #2169	D₄₇	semidirect
214. C₂×M₃₂	C₂×D₄₇	semidirect
228. C₄⋊C₁₆	C₂×D₄₇	semidirect
232. C₂²⋊C₁₆	C₂×D₄₇	semidirect
236. C₄×C₁₆	C₂×D₄₇	semidirect
237. C₄₇	D₄×M₃₂	semidirect
329. C₁₆	D₄×D₄₇	semidirect
382. C₄	M₃₂×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₇	2
C₈×D₄×D₄₇	2
#20245220	2
#20245216	2
#20245211	2
C₁₆×D₁₈₈	2
#20245207	2
#20245142	2
#20244997	2
C₄×#13093963	2
C₄₇×#2169	2
D₄×M₃₂	47