Subgroups — C₂²×#15689003 #26374592

Order 12032.

11630 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	C₂⁵×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
3	C₂³×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689003	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₄₇⋊#95	C₂	1	2	yes	maximal, complemented
6	C₂⁴×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×Dic₄₇	—	2	16	no	—
8	C₂⁴×Dic₄₇	—	2	8	no	—
9	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
10	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
11	C₂⁴×Dic₄₇	C₂²	1	12	yes	complemented
12	C₂²×C₂²⋊Dic₄₇	—	2	16	no	—
13	C₂²×C₂²⋊Dic₄₇	—	2	8	no	—
14	C₂²×C₂²⋊Dic₄₇	C₂²	1	24	yes	complemented
15	C₂²×C₂²⋊Dic₄₇	C₂²	1	12	yes	complemented
16	#15689003	C₂²	1	64	yes	direct product factor
17	C₂×C₄₇⋊#95	C₂²	1	24	yes	complemented
18	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
19	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
20	C₂³×D₄×C₄₇	—	2	8	no	—
21	C₂³×D₄×C₄₇	—	2	8	no	—
22	C₂³×D₄×C₄₇	C₄	1	16	yes	complemented
23	C₂³×D₄×C₄₇	C₂²	1	12	yes	—
24	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂³×Dic₄₇	—	2	128	no	—
26	C₂³×Dic₄₇	—	2	8	no	—
27	C₂³×Dic₄₇	—	2	8	no	—
28	C₂³×Dic₄₇	—	2	48	no	—
29	C₂³×Dic₄₇	—	2	96	no	—
30	C₂³×Dic₄₇	—	2	8	no	—
31	C₂³×Dic₄₇	—	2	8	no	—
32	C₂³×Dic₄₇	—	2	8	no	—
33	C₂³×Dic₄₇	D₄	1	16	yes	complemented
34	C₂³×Dic₄₇	C₂³	1	12	yes	—
35	C₂³×Dic₄₇	C₂³	1	12	yes	—
36	C₂³×Dic₄₇	C₂³	1	16	yes	complemented
37	C₂×C₂²⋊Dic₄₇	—	2	48	no	—
38	C₂×C₂²⋊Dic₄₇	—	2	96	no	—
39	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
40	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	complemented
41	C₄₇⋊#95	C₂³	1	32	yes	complemented
42	C₂⁵×C₄₇	—	2	8	no	—
43	C₂⁵×C₄₇	—	2	8	no	—
44	C₂⁵×C₄₇	—	2	8	no	—
45	C₂⁵×C₄₇	—	2	4	no	—
46	C₂⁵×C₄₇	—	2	4	no	—
47	C₂⁵×C₄₇	—	2	8	no	—
48	C₂⁵×C₄₇	C₂×C₄	1	8	yes	—
49	C₂⁵×C₄₇	C₂×C₄	1	8	yes	complemented
50	C₂⁵×C₄₇	D₄	1	8	yes	—
51	C₂⁵×C₄₇	D₄	1	8	yes	—
52	C₂⁵×C₄₇	C₂³	1	6	yes	—
53	C₂⁵×C₄₇	C₂³	1	6	yes	—
54	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
55	C₂²×D₄×C₄₇	—	2	128	no	—
56	C₂²×D₄×C₄₇	—	2	48	no	—
57	C₂²×D₄×C₄₇	—	2	48	no	—
58	C₂²×D₄×C₄₇	C₂×C₄	1	96	yes	complemented
59	C₂²×D₄×C₄₇	C₂³	1	16	yes	—
60	C₂³×C₄×C₄₇	—	2	4	no	—
61	C₂³×C₄×C₄₇	—	2	4	no	—
62	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
63	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
64	C₂⁴×C₄₇	—	2	64	no	—
65	C₂⁴×C₄₇	—	2	32	no	—
66	C₂⁴×C₄₇	—	2	64	no	—
67	C₂⁴×C₄₇	—	2	32	no	—
68	C₂⁴×C₄₇	—	2	24	no	—
69	C₂⁴×C₄₇	—	2	24	no	—
70	C₂⁴×C₄₇	—	2	32	no	—
71	C₂⁴×C₄₇	—	2	64	no	—
72	C₂⁴×C₄₇	—	2	12	no	—
73	C₂⁴×C₄₇	—	2	12	no	—
74	C₂⁴×C₄₇	—	2	24	no	—
75	C₂⁴×C₄₇	—	2	24	no	—
76	C₂⁴×C₄₇	—	4	16	no	—
77	C₂⁴×C₄₇	—	4	32	no	—
78	C₂⁴×C₄₇	—	4	16	no	—
79	C₂⁴×C₄₇	C₂²⋊C₄	1	64	yes	complemented
80	C₂⁴×C₄₇	C₂²×C₄	1	24	yes	—
81	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
82	C₂⁴×C₄₇	C₂²×C₄	1	24	yes	complemented
83	C₂⁴×C₄₇	C₂×D₄	1	24	yes	—
84	C₂⁴×C₄₇	C₂×D₄	1	24	yes	—
85	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
86	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
87	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
88	C₂⁴×C₄₇	#41	1	8	yes	—
89	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
90	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
91	C₂⁴×C₄₇	C₂⁴	1	3	yes	—
92	C₂×D₄×C₄₇	—	2	384	no	—
93	C₂×D₄×C₄₇	—	2	32	no	—
94	C₂×D₄×C₄₇	—	2	32	no	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	64	yes	complemented
96	C₂²×C₄×C₄₇	—	2	32	no	—
97	C₂²×C₄×C₄₇	—	2	12	no	—
98	C₂²×C₄×C₄₇	—	2	12	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	complemented
100	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
101	C₂²×Dic₄₇	—	2	384	no	—
102	C₂²×Dic₄₇	—	2	64	no	—
103	C₂²×Dic₄₇	—	2	24	no	—
104	C₂²×Dic₄₇	—	2	24	no	—
105	C₂²×Dic₄₇	—	2	32	no	—
106	C₂²×Dic₄₇	—	2	64	no	—
107	C₂²×Dic₄₇	—	2	24	no	—
108	C₂²×Dic₄₇	—	2	24	no	—
109	C₂²×Dic₄₇	—	2	24	no	—
110	C₂²×Dic₄₇	—	4	32	no	—
111	C₂²×Dic₄₇	C₂×D₄	1	48	yes	complemented
112	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
113	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
114	C₂²⋊Dic₄₇	—	2	32	no	—
115	C₂²⋊Dic₄₇	—	2	64	no	—
116	C₂³×C₄₇	—	2	96	no	—
117	C₂³×C₄₇	—	2	48	no	—
118	C₂³×C₄₇	—	2	96	no	—
119	C₂³×C₄₇	—	2	48	no	—
120	C₂³×C₄₇	—	2	8	no	—
121	C₂³×C₄₇	—	2	8	no	—
122	C₂³×C₄₇	—	2	256	no	—
123	C₂³×C₄₇	—	2	48	no	—
124	C₂³×C₄₇	—	2	96	no	—
125	C₂³×C₄₇	—	2	8	no	—
126	C₂³×C₄₇	—	2	4	no	—
127	C₂³×C₄₇	—	2	4	no	—
128	C₂³×C₄₇	—	2	8	no	—
129	C₂³×C₄₇	—	4	24	no	—
130	C₂³×C₄₇	—	4	48	no	—
131	C₂³×C₄₇	—	4	24	no	—
132	C₂³×C₄₇	—	4	128	no	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
134	C₂³×C₄₇	C₂×C₂²⋊C₄	1	96	yes	complemented
135	C₂³×C₄₇	C₄×D₄	1	32	yes	—
136	C₂³×C₄₇	#120	1	16	yes	—
137	C₂³×C₄₇	#121	1	32	yes	—
138	C₂³×C₄₇	#123	1	16	yes	—
139	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
140	C₂³×C₄₇	C₂³×C₄	1	6	yes	—
141	C₂³×C₄₇	C₂³×C₄	1	8	yes	complemented
142	C₂³×C₄₇	C₂²×D₄	1	12	yes	—
143	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
144	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
145	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
146	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
147	C₂³×C₄₇	C₂×#41	1	12	yes	—
148	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
149	D₄×C₄₇	—	2	128	no	—
150	C₂×C₄×C₄₇	—	2	48	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	complemented
154	C₂×Dic₄₇	—	2	128	no	—
155	C₂×Dic₄₇	—	2	96	no	—
156	C₂×Dic₄₇	—	2	8	no	—
157	C₂×Dic₄₇	—	2	8	no	—
158	C₂×Dic₄₇	—	2	8	no	—
159	C₂×Dic₄₇	—	2	8	no	—
160	C₂×Dic₄₇	—	2	8	no	—
161	C₂×Dic₄₇	—	4	48	no	—
162	C₂×Dic₄₇	C₂²×D₄	1	16	yes	complemented
163	C₂²×#386	—	47	1	no	maximal, Sylow
164	C₂²×C₄₇	—	2	16	no	—
165	C₂²×C₄₇	—	2	8	no	—
166	C₂²×C₄₇	—	2	16	no	—
167	C₂²×C₄₇	—	2	8	no	—
168	C₂²×C₄₇	—	2	192	no	—
169	C₂²×C₄₇	—	2	8	no	—
170	C₂²×C₄₇	—	2	16	no	—
171	C₂²×C₄₇	—	4	4	no	—
172	C₂²×C₄₇	—	4	8	no	—
173	C₂²×C₄₇	—	4	4	no	—
174	C₂²×C₄₇	—	4	96	no	—
175	C₂²×C₄₇	#386	1	64	yes	complemented
176	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	12	yes	—
177	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	16	yes	complemented
178	C₂²×C₄₇	C₂×C₄×D₄	1	24	yes	—
179	C₂²×C₄₇	C₂×#120	1	12	yes	—
180	C₂²×C₄₇	C₂×#121	1	24	yes	—
181	C₂²×C₄₇	C₂×#123	1	12	yes	—
182	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
183	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
184	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
185	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
186	C₂²×C₄₇	C₂²×#41	1	2	yes	—
187	C₄×C₄₇	—	2	8	no	—
188	Dic₄₇	—	2	16	no	—
189	Dic₄₇	—	4	8	no	—
190	C₂⁴×D₄	D₄₇	1	1	yes	characteristic
191	C₂⁵×C₄	—	47	1	no	—
192	C₂³×C₂²⋊C₄	—	47	2	no	—
193	C₂³×C₂²⋊C₄	—	47	1	no	—
194	C₂×#386	—	47	24	no	—
195	C₂²×#95	—	47	2	no	—
196	C₂×C₄₇	—	2	16	no	—
197	C₂×C₄₇	—	4	8	no	—
198	C₂×C₄₇	C₂×#386	1	24	yes	complemented
199	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄₇	C₂²×C₄×D₄	1	2	yes	—
201	C₂×C₄₇	C₂²×#120	1	1	yes	characteristic
202	C₂×C₄₇	C₂²×#121	1	2	yes	—
203	C₂×C₄₇	C₂²×#123	1	1	yes	characteristic
204	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
205	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
206	C₂³×D₄	—	2	8	no	—
207	C₂³×D₄	—	2	8	no	—
208	C₂³×D₄	Dic₄₇	1	16	yes	complemented
209	C₂³×D₄	C₂×D₄₇	1	12	yes	—
210	C₂⁴×C₄	—	47	2	no	—
211	C₂⁴×C₄	—	47	12	no	—
212	C₂⁴×C₄	—	47	2	no	—
213	C₂⁴×C₄	—	94	16	no	—
214	C₂⁴×C₄	—	94	8	no	—
215	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
216	C₂²×C₂²⋊C₄	—	47	24	no	—
217	C₂²×C₂²⋊C₄	—	47	12	no	—
218	C₂²×C₂²⋊C₄	—	94	16	no	—
219	C₂²×C₂²⋊C₄	—	94	8	no	—
220	#386	—	47	64	no	—
221	C₂×#95	—	47	24	no	—
222	C₄₇	C₂²×#386	1	1	yes	characteristic, complemented, Sylow
223	C₂⁵	—	2	8	no	—
224	C₂⁵	—	2	8	no	—
225	C₂⁵	—	2	8	no	—
226	C₂⁵	—	2	8	no	—
227	C₂⁵	—	2	4	no	—
228	C₂⁵	—	2	4	no	—
229	C₂⁵	C₂×Dic₄₇	1	8	yes	—
230	C₂⁵	C₂×Dic₄₇	1	8	yes	complemented
231	C₂⁵	C₂²⋊D₄₇	1	8	yes	—
232	C₂⁵	C₂²⋊D₄₇	1	8	yes	—
233	C₂⁵	C₂²×D₄₇	1	6	yes	—
234	C₂⁵	C₂²×D₄₇	1	6	yes	—
235	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
236	C₂²×D₄	—	2	128	no	—
237	C₂²×D₄	—	2	48	no	—
238	C₂²×D₄	—	2	48	no	—
239	C₂²×D₄	C₂×Dic₄₇	1	96	yes	complemented
240	C₂²×D₄	C₂²×D₄₇	1	16	yes	—
241	C₂³×C₄	—	2	4	no	—
242	C₂³×C₄	—	2	4	no	—
243	C₂³×C₄	—	47	16	no	—
244	C₂³×C₄	—	47	12	no	—
245	C₂³×C₄	—	47	12	no	—
246	C₂³×C₄	—	47	16	no	—
247	C₂³×C₄	—	94	96	no	—
248	C₂³×C₄	—	94	128	no	—
249	C₂³×C₄	—	94	8	no	—
250	C₂³×C₄	—	94	48	no	—
251	C₂³×C₄	—	94	8	no	—
252	C₂³×C₄	—	94	8	no	—
253	C₂³×C₄	—	94	8	no	—
254	C₂³×C₄	—	94	8	no	—
255	C₂³×C₄	C₂×Dic₄₇	1	8	yes	complemented
256	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
257	C₂×C₂²⋊C₄	—	47	32	no	—
258	C₂×C₂²⋊C₄	—	47	16	no	—
259	C₂×C₂²⋊C₄	—	94	96	no	—
260	C₂×C₂²⋊C₄	—	94	48	no	—
261	#95	—	47	32	no	—
262	C₂⁴	—	2	64	no	—
263	C₂⁴	—	2	32	no	—
264	C₂⁴	—	2	64	no	—
265	C₂⁴	—	2	32	no	—
266	C₂⁴	—	2	24	no	—
267	C₂⁴	—	2	24	no	—
268	C₂⁴	—	2	32	no	—
269	C₂⁴	—	2	64	no	—
270	C₂⁴	—	2	24	no	—
271	C₂⁴	—	2	12	no	—
272	C₂⁴	—	2	12	no	—
273	C₂⁴	—	2	24	no	—
274	C₂⁴	—	4	16	no	—
275	C₂⁴	—	4	32	no	—
276	C₂⁴	—	4	16	no	—
277	C₂⁴	C₂²⋊Dic₄₇	1	64	yes	complemented
278	C₂⁴	D₄×D₄₇	1	8	yes	—
279	C₂⁴	#10625352	1	8	yes	—
280	C₂⁴	C₂²×Dic₄₇	1	24	yes	—
281	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
282	C₂⁴	C₂²×Dic₄₇	1	24	yes	complemented
283	C₂⁴	C₂×C₂²⋊D₄₇	1	24	yes	—
284	C₂⁴	C₂×C₂²⋊D₄₇	1	24	yes	—
285	C₂⁴	C₂×C₂²⋊D₄₇	1	4	yes	—
286	C₂⁴	C₂×C₂²⋊D₄₇	1	4	yes	—
287	C₂⁴	C₂³×D₄₇	1	4	yes	—
288	C₂⁴	C₂³×D₄₇	1	4	yes	—
289	C₂⁴	C₂³×D₄₇	1	3	yes	—
290	C₂×D₄	—	2	384	no	—
291	C₂×D₄	—	2	32	no	—
292	C₂×D₄	—	2	32	no	—
293	C₂×D₄	C₂²×Dic₄₇	1	64	yes	complemented
294	C₂²×C₄	—	2	32	no	—
295	C₂²×C₄	—	2	12	no	—
296	C₂²×C₄	—	2	12	no	—
297	C₂²×C₄	—	47	48	no	—
298	C₂²×C₄	—	47	8	no	—
299	C₂²×C₄	—	47	8	no	—
300	C₂²×C₄	—	94	64	no	—
301	C₂²×C₄	—	94	384	no	—
302	C₂²×C₄	—	94	64	no	—
303	C₂²×C₄	—	94	24	no	—
304	C₂²×C₄	—	94	32	no	—
305	C₂²×C₄	—	94	24	no	—
306	C₂²×C₄	—	94	24	no	—
307	C₂²×C₄	—	94	24	no	—
308	C₂²×C₄	—	94	24	no	—
309	C₂²×C₄	—	188	32	no	—
310	C₂²×C₄	C₂²×Dic₄₇	1	24	yes	complemented
311	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
312	C₂²⋊C₄	—	94	64	no	—
313	C₂²⋊C₄	—	94	32	no	—
314	C₂³	—	2	256	no	—
315	C₂³	—	2	96	no	—
316	C₂³	—	2	48	no	—
317	C₂³	—	2	96	no	—
318	C₂³	—	2	48	no	—
319	C₂³	—	2	8	no	—
320	C₂³	—	2	8	no	—
321	C₂³	—	2	48	no	—
322	C₂³	—	2	96	no	—
323	C₂³	—	2	8	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	2	8	no	—
327	C₂³	—	4	128	no	—
328	C₂³	—	4	24	no	—
329	C₂³	—	4	48	no	—
330	C₂³	—	4	24	no	—
331	C₂³	C₂×C₂²⋊Dic₄₇	1	16	yes	—
332	C₂³	C₂×C₂²⋊Dic₄₇	1	96	yes	complemented
333	C₂³	D₄×Dic₄₇	1	32	yes	—
334	C₂³	#13093992	1	16	yes	—
335	C₂³	#13093996	1	32	yes	—
336	C₂³	#13094005	1	16	yes	—
337	C₂³	C₂³×Dic₄₇	1	8	yes	—
338	C₂³	C₂³×Dic₄₇	1	6	yes	—
339	C₂³	C₂³×Dic₄₇	1	8	yes	complemented
340	C₂³	C₂×D₄×D₄₇	1	12	yes	—
341	C₂³	C₂²×C₂²⋊D₄₇	1	8	yes	—
342	C₂³	C₂²×C₂²⋊D₄₇	1	8	yes	—
343	C₂³	C₂²×C₂²⋊D₄₇	1	6	yes	—
344	C₂³	C₂²×C₂²⋊D₄₇	1	6	yes	—
345	C₂³	C₂×#10625352	1	12	yes	—
346	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
347	D₄	—	2	128	no	—
348	C₂×C₄	—	2	48	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	47	16	no	—
352	C₂×C₄	—	94	128	no	—
353	C₂×C₄	—	94	96	no	—
354	C₂×C₄	—	94	8	no	—
355	C₂×C₄	—	94	8	no	—
356	C₂×C₄	—	94	8	no	—
357	C₂×C₄	—	94	8	no	—
358	C₂×C₄	—	94	8	no	—
359	C₂×C₄	—	188	48	no	—
360	C₂×C₄	C₂³×Dic₄₇	1	8	yes	complemented
361	C₂²	—	2	16	no	—
362	C₂²	—	2	192	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	2	16	no	—
365	C₂²	—	2	8	no	—
366	C₂²	—	2	8	no	—
367	C₂²	—	2	16	no	—
368	C₂²	—	4	96	no	—
369	C₂²	—	4	4	no	—
370	C₂²	—	4	8	no	—
371	C₂²	—	4	4	no	—
372	C₂²	#15689003	1	64	yes	direct product factor
373	C₂²	C₂²×C₂²⋊Dic₄₇	1	12	yes	—
374	C₂²	C₂²×C₂²⋊Dic₄₇	1	16	yes	complemented
375	C₂²	C₂×D₄×Dic₄₇	1	24	yes	—
376	C₂²	C₂×#13093992	1	12	yes	—
377	C₂²	C₂×#13093996	1	24	yes	—
378	C₂²	C₂×#13094005	1	12	yes	—
379	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
380	C₂²	C₂²×D₄×D₄₇	1	2	yes	—
381	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
383	C₂²	C₂²×#10625352	1	2	yes	—
384	C₄	—	2	8	no	—
385	C₄	—	94	16	no	—
386	C₄	—	188	8	no	—
387	C₂	—	2	16	no	—
388	C₂	—	4	8	no	—
389	C₂	C₂×#15689003	1	24	yes	direct product factor
390	C₂	C₂³×C₂²⋊Dic₄₇	1	1	yes	characteristic
391	C₂	C₂²×D₄×Dic₄₇	1	2	yes	—
392	C₂	C₂²×#13093992	1	1	yes	characteristic
393	C₂	C₂²×#13093996	1	2	yes	—
394	C₂	C₂²×#13094005	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting, prime radical	C₂⁴×D₄×C₄₇	C₂
socle	C₂⁵×C₄₇	C₂³
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂⁴×D₄	D₄₇
hypocenter	C₄₇	C₂²×#386
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁵×Dic₄₇	C₂	semidirect
2. C₂³×C₂²⋊Dic₄₇	C₂	semidirect
3. C₂³×C₂²⋊Dic₄₇	C₂	semidirect
4. C₂×#15689003	C₂	direct (N × H)
5. C₂²×C₄₇⋊#95	C₂	semidirect
11. C₂⁴×Dic₄₇	C₂²	semidirect
14. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
15. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
16. #15689003	C₂²	direct (N × H)
17. C₂×C₄₇⋊#95	C₂²	semidirect
22. C₂³×D₄×C₄₇	C₄	semidirect
33. C₂³×Dic₄₇	D₄	semidirect
36. C₂³×Dic₄₇	C₂³	semidirect
39. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
40. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
41. C₄₇⋊#95	C₂³	semidirect
49. C₂⁵×C₄₇	C₂×C₄	semidirect
58. C₂²×D₄×C₄₇	C₂×C₄	semidirect
62. C₂³×C₄×C₄₇	C₂×C₄	semidirect
79. C₂⁴×C₄₇	C₂²⋊C₄	semidirect
82. C₂⁴×C₄₇	C₂²×C₄	semidirect
95. C₂×D₄×C₄₇	C₂²×C₄	semidirect
99. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
111. C₂²×Dic₄₇	C₂×D₄	semidirect
134. C₂³×C₄₇	C₂×C₂²⋊C₄	semidirect
141. C₂³×C₄₇	C₂³×C₄	semidirect
153. C₂×C₄×C₄₇	C₂³×C₄	semidirect
162. C₂×Dic₄₇	C₂²×D₄	semidirect
175. C₂²×C₄₇	#386	semidirect
177. C₂²×C₄₇	C₂²×C₂²⋊C₄	semidirect
198. C₂×C₄₇	C₂×#386	semidirect
208. C₂³×D₄	Dic₄₇	semidirect
222. C₄₇	C₂²×#386	semidirect
230. C₂⁵	C₂×Dic₄₇	semidirect
239. C₂²×D₄	C₂×Dic₄₇	semidirect
255. C₂³×C₄	C₂×Dic₄₇	semidirect
277. C₂⁴	C₂²⋊Dic₄₇	semidirect
282. C₂⁴	C₂²×Dic₄₇	semidirect
293. C₂×D₄	C₂²×Dic₄₇	semidirect
310. C₂²×C₄	C₂²×Dic₄₇	semidirect
332. C₂³	C₂×C₂²⋊Dic₄₇	semidirect
339. C₂³	C₂³×Dic₄₇	semidirect
360. C₂×C₄	C₂³×Dic₄₇	semidirect
372. C₂²	#15689003	direct (N × H)
374. C₂²	C₂²×C₂²⋊Dic₄₇	semidirect
389. C₂	C₂×#15689003	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×Dic₄₇	2
C₂³×C₂²⋊Dic₄₇	2
C₂×#15689003	2
C₂²×C₄₇⋊#95	2
C₂⁴×D₄×C₄₇	2
C₂²×#386	47

Subgroups — C22×#15689003 #26374592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689003 #26374592