Subgroups — #432×Dic₄₇ #26214443

Order 12032.

1206 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689180	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20243243	C₂	1	2	yes	maximal, complemented
4	C₄⋊C₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
5	#20243152	C₂	1	2	yes	maximal
6	C₂²⋊C₈×Dic₄₇	C₂	1	2	yes	maximal
7	#20243136	C₂	1	2	yes	maximal, complemented
8	#97×Dic₄₇	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#432	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
11	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
12	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
14	#15689180	C₄	1	8	yes	complemented
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×#13093935	C₂²	1	2	yes	—
18	C₂×#13093934	C₂²	1	4	yes	—
19	C₂×C₈×Dic₄₇	C₂²	1	4	yes	—
20	C₄²×Dic₄₇	C₄	1	2	yes	—
21	C₄²×Dic₄₇	C₄	1	2	yes	—
22	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
26	#15688877	C₂²	1	4	yes	—
27	#15688877	C₂²	1	4	yes	—
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#432	C₄	1	8	yes	complemented
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
32	C₂×#97×C₄₇	C₂²	1	2	yes	—
33	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
34	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
35	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
36	C₂×C₄×Dic₄₇	—	2	8	no	—
37	C₂×C₄×Dic₄₇	—	2	8	no	—
38	C₂×C₄×Dic₄₇	—	2	4	no	—
39	C₂×C₄×Dic₄₇	—	2	4	no	—
40	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
46	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
54	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
55	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
56	#13093935	C₂×C₄	1	8	yes	complemented
57	#13093934	—	2	8	no	—
58	C₈×Dic₄₇	—	2	8	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	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
70	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
71	#97×C₄₇	C₂×C₄	1	8	yes	complemented
72	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
78	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
87	C₂²×Dic₄₇	—	2	4	no	—
88	C₂²×Dic₄₇	—	2	4	no	—
89	C₂²×Dic₄₇	—	2	4	no	—
90	C₂²×Dic₄₇	—	2	4	no	—
91	C₂²×Dic₄₇	—	2	4	no	—
92	C₂²×Dic₄₇	M₁₆	1	8	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₄₇	—	2	4	no	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
100	C₄²×C₄₇	C₄²	1	4	yes	—
101	C₄²×C₄₇	C₄²	1	4	yes	—
102	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
103	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
104	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
105	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
106	C₄×Dic₄₇	—	2	4	no	—
107	C₄×Dic₄₇	—	2	2	no	—
108	C₄×Dic₄₇	—	2	2	no	—
109	C₄×Dic₄₇	—	2	4	no	—
110	C₄×Dic₄₇	—	2	4	no	—
111	C₄×Dic₄₇	—	2	4	no	—
112	C₄×Dic₄₇	—	2	4	no	—
113	C₄×Dic₄₇	—	2	4	no	—
114	C₄×Dic₄₇	—	2	4	no	—
115	C₄×Dic₄₇	—	2	4	no	—
116	C₄×Dic₄₇	—	2	4	no	—
117	C₄×Dic₄₇	M₁₆	1	8	yes	—
118	C₄×Dic₄₇	#41	1	4	yes	—
119	C₄×Dic₄₇	#41	1	4	yes	—
120	C₂×C₄₇⋊C₈	—	2	4	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
123	C₂³×C₄₇	—	2	1	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
127	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
128	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	8	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
148	C₂×Dic₄₇	—	2	16	no	—
149	C₂×Dic₄₇	—	2	2	no	—
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	2	16	no	—
156	C₂×Dic₄₇	#117	1	4	yes	—
157	C₂×Dic₄₇	#117	1	4	yes	—
158	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
159	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
160	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
161	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
162	C₈×C₄₇	—	2	8	no	—
163	C₄₇⋊C₈	—	2	8	no	—
164	C₄×#432	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	2	4	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	C₄×M₁₆	1	4	yes	—
170	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
173	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
174	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
175	C₄×C₄₇	—	2	2	no	—
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	C₄×M₁₆	1	4	yes	—
180	C₄×C₄₇	C₄×#41	1	2	yes	—
181	C₄×C₄₇	C₄×#41	1	2	yes	—
182	Dic₄₇	—	2	4	no	—
183	Dic₄₇	—	2	4	no	—
184	Dic₄₇	—	2	4	no	—
185	Dic₄₇	#432	1	8	yes	direct product factor
186	C₂×#432	—	47	1	no	—
187	C₂×#432	D₄₇	1	1	yes	characteristic
188	C₂×C₄³	—	47	1	no	—
189	#1767	—	47	2	no	—
190	C₄×C₄⋊C₈	—	47	2	no	—
191	#1749	—	47	2	no	—
192	C₄×C₂²⋊C₈	—	47	2	no	—
193	#1745	—	47	2	no	—
194	C₄×#97	—	47	2	no	—
195	C₂×C₄₇	—	2	4	no	—
196	C₂×C₄₇	C₄×#117	1	1	yes	characteristic
197	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
198	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#432	1	2	yes	—
200	C₂×C₄₇	#2920	1	2	yes	—
201	C₂²×C₄²	—	47	2	no	—
202	C₂²×C₄²	—	47	2	no	—
203	C₂²×C₄²	—	47	1	no	—
204	C₂²×C₄²	—	47	1	no	—
205	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
206	#432	—	47	8	no	—
207	#432	Dic₄₇	1	8	yes	direct product factor
208	C₂×C₄⋊C₈	—	47	2	no	—
209	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
210	C₂×C₂²⋊C₈	—	47	2	no	—
211	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
212	C₂×#97	—	47	2	no	—
213	C₂×#97	—	47	4	no	—
214	C₂×#97	C₂×D₄₇	1	2	yes	—
215	C₂×C₄×C₈	—	47	4	no	—
216	C₄³	—	47	2	no	—
217	C₄³	—	47	2	no	—
218	C₄³	—	47	1	no	—
219	C₄³	—	47	1	no	—
220	C₄³	—	47	1	no	—
221	C₄³	—	47	1	no	—
222	#336	—	47	4	no	—
223	#336	—	47	4	no	—
224	C₄₇	C₄×#432	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₄	—	47	2	no	—
226	C₂³×C₄	—	47	2	no	—
227	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
228	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
230	C₂²×C₈	—	47	4	no	—
231	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
232	C₂×C₄²	—	47	2	no	—
233	C₂×C₄²	—	47	1	no	—
234	C₂×C₄²	—	47	1	no	—
235	C₂×C₄²	—	47	2	no	—
236	C₂×C₄²	—	47	2	no	—
237	C₂×C₄²	—	47	2	no	—
238	C₂×C₄²	—	47	2	no	—
239	C₂×C₄²	—	47	2	no	—
240	C₂×C₄²	—	47	2	no	—
241	C₂×C₄²	—	47	2	no	—
242	C₂×C₄²	—	47	2	no	—
243	C₂×C₄²	—	47	2	no	—
244	C₂×C₄²	—	47	1	no	—
245	C₂×C₄²	—	47	1	no	—
246	C₂×C₄²	—	94	8	no	—
247	C₂×C₄²	—	94	4	no	—
248	C₂×C₄²	—	94	4	no	—
249	C₂×C₄²	—	94	8	no	—
250	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
251	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
252	C₂×C₄²	C₄×D₄₇	1	4	yes	—
253	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
254	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
256	C₄⋊C₈	—	47	8	no	—
257	C₄⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
258	C₂²⋊C₈	—	47	8	no	—
259	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	—
260	#97	—	47	8	no	—
261	#97	—	94	8	no	—
262	#97	C₂×Dic₄₇	1	8	yes	complemented
263	C₄×C₈	—	94	8	no	—
264	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	47	2	no	—
270	C₂²×C₄	—	47	8	no	—
271	C₂²×C₄	—	47	2	no	—
272	C₂²×C₄	—	47	2	no	—
273	C₂²×C₄	—	47	2	no	—
274	C₂²×C₄	—	94	4	no	—
275	C₂²×C₄	—	94	4	no	—
276	C₂²×C₄	—	94	4	no	—
277	C₂²×C₄	—	94	4	no	—
278	C₂²×C₄	—	94	4	no	—
279	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
280	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
281	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
286	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
288	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	47	8	no	—
292	C₂×C₈	—	94	4	no	—
293	C₂×C₈	—	94	4	no	—
294	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
295	C₄²	—	47	8	no	—
296	C₄²	—	47	4	no	—
297	C₄²	—	47	4	no	—
298	C₄²	—	94	4	no	—
299	C₄²	—	94	4	no	—
300	C₄²	—	94	4	no	—
301	C₄²	—	94	4	no	—
302	C₄²	—	94	4	no	—
303	C₄²	—	94	4	no	—
304	C₄²	—	94	4	no	—
305	C₄²	—	94	4	no	—
306	C₄²	—	94	4	no	—
307	C₄²	—	94	2	no	—
308	C₄²	—	94	2	no	—
309	C₄²	C₄×Dic₄₇	1	4	yes	—
310	C₄²	C₄×Dic₄₇	1	4	yes	—
311	C₄²	C₂×C₄×D₄₇	1	2	yes	—
312	C₄²	C₂×C₄×D₄₇	1	2	yes	—
313	C₄²	C₂²×Dic₄₇	1	2	yes	—
314	C₄²	C₂²×Dic₄₇	1	2	yes	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	2	no	—
318	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
319	C₂³	M₁₆×D₄₇	1	4	yes	—
320	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	47	4	no	—
331	C₂×C₄	—	47	4	no	—
332	C₂×C₄	—	47	4	no	—
333	C₂×C₄	—	47	4	no	—
334	C₂×C₄	—	47	4	no	—
335	C₂×C₄	—	47	4	no	—
336	C₂×C₄	—	94	16	no	—
337	C₂×C₄	—	94	16	no	—
338	C₂×C₄	—	94	2	no	—
339	C₂×C₄	—	94	2	no	—
340	C₂×C₄	—	94	2	no	—
341	C₂×C₄	—	94	2	no	—
342	C₂×C₄	—	94	2	no	—
343	C₂×C₄	—	94	2	no	—
344	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
345	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
346	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
347	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
348	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
349	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
350	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
351	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
352	C₂×C₄	#41×D₄₇	1	2	yes	—
353	C₂×C₄	#41×D₄₇	1	2	yes	—
354	C₈	—	2	8	no	—
355	C₈	—	94	8	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	2	2	no	—
360	C₂²	M₁₆×Dic₄₇	1	4	yes	—
361	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
362	C₂²	#117×D₄₇	1	1	yes	characteristic
363	C₂²	#117×D₄₇	1	1	yes	characteristic
364	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
365	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	47	8	no	—
371	C₄	—	94	4	no	—
372	C₄	—	94	4	no	—
373	C₄	—	94	4	no	—
374	C₄	M₁₆×Dic₄₇	1	4	yes	—
375	C₄	#15689591	1	2	yes	—
376	C₄	#41×Dic₄₇	1	2	yes	—
377	C₂	—	2	4	no	—
378	C₂	#117×Dic₄₇	1	1	yes	characteristic
379	C₂	C₂×M₁₆×Dic₄₇	1	1	yes	characteristic
380	C₂	C₂×M₁₆×Dic₄₇	1	1	yes	characteristic
381	C₂	#432×D₄₇	1	2	yes	—
382	C₂	#20252018	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄₇×#432	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#432	D₄₇
hypocenter	C₄₇	C₄×#432
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
3. #20243243	C₂	semidirect
4. C₄⋊C₈×Dic₄₇	C₂	semidirect
7. #20243136	C₂	semidirect
8. #97×Dic₄₇	C₂	semidirect
14. #15689180	C₄	semidirect
29. C₄₇×#432	C₄	semidirect
54. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
56. #13093935	C₂×C₄	semidirect
69. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
71. #97×C₄₇	C₂×C₄	semidirect
185. Dic₄₇	#432	direct (N × H)
207. #432	Dic₄₇	direct (N × H)
224. C₄₇	C₄×#432	semidirect
257. C₄⋊C₈	C₂×Dic₄₇	semidirect
262. #97	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689180	2
C₂×C₄²×Dic₄₇	2
#20243243	2
C₄⋊C₈×Dic₄₇	2
#20243152	2
C₂²⋊C₈×Dic₄₇	2
#20243136	2
#97×Dic₄₇	2
C₂×C₄₇×#432	2
C₄×#432	47

Subgroups — #432×Dic47 #26214443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #432×Dic₄₇ #26214443