Subgroups — C₂×C₄₇×#2849 #26076311

Order 12032.

7738 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₂²×#120×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2849	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₄₇×#386	C₂	1	4	yes	maximal, complemented
6	C₂×C₄₇×#385	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#381	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#379	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
11	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₄₇	—	2	8	no	—
13	C₂⁴×C₄×C₄₇	—	2	16	no	—
14	C₂⁴×C₄×C₄₇	C₂²	1	4	yes	—
15	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₄₇	C₂²	1	8	yes	complemented
17	C₂×#123×C₄₇	—	2	16	no	—
18	C₂×#123×C₄₇	C₂²	1	16	yes	complemented
19	C₂×#120×C₄₇	—	2	8	no	—
20	C₂×#120×C₄₇	C₂²	1	8	yes	—
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	complemented
22	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
24	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	complemented
27	C₄₇×#386	C₂²	1	32	yes	complemented
28	C₄₇×#385	C₂²	1	32	yes	complemented
29	C₄₇×#381	C₂²	1	16	yes	complemented
30	C₄₇×#379	C₂²	1	8	yes	complemented
31	C₂×#95×C₄₇	C₂²	1	8	yes	complemented
32	C₂⁵×C₄₇	—	2	8	no	—
33	C₂⁵×C₄₇	—	2	16	no	—
34	C₂⁵×C₄₇	D₄	1	8	yes	—
35	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
36	C₂⁵×C₄₇	C₂³	1	4	yes	—
37	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
38	C₂⁵×C₄₇	C₂³	1	2	yes	—
39	C₂²×D₄×C₄₇	—	2	4	no	—
40	C₂²×D₄×C₄₇	—	2	8	no	—
41	C₂²×D₄×C₄₇	—	2	8	no	—
42	C₂²×D₄×C₄₇	—	2	16	no	—
43	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
44	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
45	C₂³×C₄×C₄₇	—	2	128	no	—
46	C₂³×C₄×C₄₇	—	2	16	no	—
47	C₂³×C₄×C₄₇	—	2	8	no	—
48	C₂³×C₄×C₄₇	—	2	8	no	—
49	C₂³×C₄×C₄₇	—	2	32	no	—
50	C₂³×C₄×C₄₇	—	2	32	no	—
51	C₂³×C₄×C₄₇	—	2	64	no	—
52	C₂³×C₄×C₄₇	D₄	1	16	yes	complemented
53	C₂³×C₄×C₄₇	C₂³	1	16	yes	—
54	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
59	#123×C₄₇	—	2	64	no	—
60	#120×C₄₇	—	2	32	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	16	no	—
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	16	yes	complemented
63	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
68	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	complemented
73	#95×C₄₇	C₂³	1	32	yes	complemented
74	C₂⁴×C₄₇	—	2	128	no	—
75	C₂⁴×C₄₇	—	2	32	no	—
76	C₂⁴×C₄₇	—	2	64	no	—
77	C₂⁴×C₄₇	—	2	16	no	—
78	C₂⁴×C₄₇	—	2	8	no	—
79	C₂⁴×C₄₇	—	2	32	no	—
80	C₂⁴×C₄₇	—	2	8	no	—
81	C₂⁴×C₄₇	—	2	8	no	—
82	C₂⁴×C₄₇	—	2	4	no	—
83	C₂⁴×C₄₇	—	2	2	no	—
84	C₂⁴×C₄₇	—	2	8	no	—
85	C₂⁴×C₄₇	C₂×D₄	1	16	yes	—
86	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
87	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
88	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
89	C₂⁴×C₄₇	#41	1	16	yes	—
90	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
91	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
92	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
93	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂×D₄×C₄₇	—	2	8	no	—
95	C₂×D₄×C₄₇	—	2	16	no	—
96	C₂×D₄×C₄₇	—	2	16	no	—
97	C₂×D₄×C₄₇	—	2	32	no	—
98	C₂×D₄×C₄₇	—	4	16	no	—
99	C₂×D₄×C₄₇	—	4	32	no	—
100	C₂²×C₄×C₄₇	—	2	128	no	—
101	C₂²×C₄×C₄₇	—	2	256	no	—
102	C₂²×C₄×C₄₇	—	2	64	no	—
103	C₂²×C₄×C₄₇	—	2	32	no	—
104	C₂²×C₄×C₄₇	—	2	8	no	—
105	C₂²×C₄×C₄₇	—	2	8	no	—
106	C₂²×C₄×C₄₇	—	2	16	no	—
107	C₂²×C₄×C₄₇	—	2	16	no	—
108	C₂²×C₄×C₄₇	—	2	64	no	—
109	C₂²×C₄×C₄₇	—	2	8	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	16	no	—
114	C₂²×C₄×C₄₇	—	2	8	no	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	32	yes	complemented
117	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
121	C₄⋊C₄×C₄₇	—	2	32	no	—
122	C₂²⋊C₄×C₄₇	—	2	8	no	—
123	C₂²⋊C₄×C₄₇	—	2	16	no	—
124	C₂²⋊C₄×C₄₇	—	2	16	no	—
125	C₂²⋊C₄×C₄₇	—	2	32	no	—
126	C₂²⋊C₄×C₄₇	—	2	32	no	—
127	C₂³×C₄₇	—	2	256	no	—
128	C₂³×C₄₇	—	2	128	no	—
129	C₂³×C₄₇	—	2	32	no	—
130	C₂³×C₄₇	—	2	16	no	—
131	C₂³×C₄₇	—	2	16	no	—
132	C₂³×C₄₇	—	2	16	no	—
133	C₂³×C₄₇	—	2	64	no	—
134	C₂³×C₄₇	—	2	32	no	—
135	C₂³×C₄₇	—	2	64	no	—
136	C₂³×C₄₇	—	2	8	no	—
137	C₂³×C₄₇	—	2	8	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	8	no	—
142	C₂³×C₄₇	—	4	4	no	—
143	C₂³×C₄₇	—	4	8	no	—
144	C₂³×C₄₇	—	4	16	no	—
145	C₂³×C₄₇	#120	1	16	yes	—
146	C₂³×C₄₇	#123	1	32	yes	complemented
147	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
148	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
149	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
150	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
151	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
152	C₂³×C₄₇	C₂×#41	1	16	yes	—
153	C₂³×C₄₇	C₂×#41	1	8	yes	—
154	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
155	D₄×C₄₇	—	4	16	no	—
156	D₄×C₄₇	—	4	32	no	—
157	C₂×C₄×C₄₇	—	2	128	no	—
158	C₂×C₄×C₄₇	—	2	32	no	—
159	C₂×C₄×C₄₇	—	2	64	no	—
160	C₂×C₄×C₄₇	—	2	8	no	—
161	C₂×C₄×C₄₇	—	2	8	no	—
162	C₂×C₄×C₄₇	—	2	8	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	16	no	—
167	C₂×C₄×C₄₇	—	2	8	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	—	4	16	no	—
171	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
172	C₂×#2849	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₇	—	2	128	no	—
174	C₂²×C₄₇	—	2	32	no	—
175	C₂²×C₄₇	—	2	64	no	—
176	C₂²×C₄₇	—	2	8	no	—
177	C₂²×C₄₇	—	2	8	no	—
178	C₂²×C₄₇	—	2	8	no	—
179	C₂²×C₄₇	—	2	16	no	—
180	C₂²×C₄₇	—	2	32	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	4	no	—
183	C₂²×C₄₇	—	4	8	no	—
184	C₂²×C₄₇	—	8	8	no	—
185	C₂²×C₄₇	C₂×#120	1	8	yes	—
186	C₂²×C₄₇	C₂×#120	1	4	yes	—
187	C₂²×C₄₇	C₂×#123	1	8	yes	—
188	C₂²×C₄₇	C₂×#123	1	16	yes	complemented
189	C₂²×C₄₇	#525	1	16	yes	—
190	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
191	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
192	C₂²×C₄₇	C₂²×#41	1	4	yes	—
193	C₄×C₄₇	—	2	16	no	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	—	4	8	no	—
197	C₂⁵×C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
198	C₂²×#123	C₂×C₄₇	1	2	yes	complemented
199	C₂²×#120	C₂×C₄₇	1	1	yes	characteristic
200	#2849	C₂×C₄₇	1	16	yes	direct product factor
201	C₂×#386	C₂×C₄₇	1	4	yes	complemented
202	C₂×#385	C₂×C₄₇	1	4	yes	complemented
203	C₂×#381	C₂×C₄₇	1	2	yes	complemented
204	C₂×#379	C₂×C₄₇	1	1	yes	characteristic, complemented
205	C₂×C₄₇	—	2	8	no	—
206	C₂×C₄₇	—	2	16	no	—
207	C₂×C₄₇	—	8	2	no	—
208	C₂×C₄₇	#2849	1	8	yes	direct product factor
209	C₂×C₄₇	C₂²×#120	1	1	yes	characteristic
210	C₂×C₄₇	C₂²×#123	1	2	yes	—
211	C₂×C₄₇	C₂×#525	1	4	yes	—
212	C₂⁶	C₂²×C₄₇	1	1	yes	characteristic
213	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
214	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
215	C₂⁴×C₄	—	2	8	no	—
216	C₂⁴×C₄	—	2	16	no	—
217	C₂⁴×C₄	C₂²×C₄₇	1	4	yes	—
218	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
219	C₂⁴×C₄	C₂²×C₄₇	1	8	yes	complemented
220	C₂×#123	—	2	16	no	—
221	C₂×#123	C₂²×C₄₇	1	16	yes	complemented
222	C₂×#120	—	2	8	no	—
223	C₂×#120	C₂²×C₄₇	1	8	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	complemented
225	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
226	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
228	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
229	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	complemented
230	#386	C₂²×C₄₇	1	32	yes	complemented
231	#385	C₂²×C₄₇	1	32	yes	complemented
232	#381	C₂²×C₄₇	1	16	yes	complemented
233	#379	C₂²×C₄₇	1	8	yes	complemented
234	C₂×#95	C₂²×C₄₇	1	8	yes	complemented
235	C₄₇	C₂×#2849	1	1	yes	characteristic, direct product factor, Sylow
236	C₂⁵	—	2	8	no	—
237	C₂⁵	—	2	16	no	—
238	C₂⁵	D₄×C₄₇	1	8	yes	—
239	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
240	C₂⁵	C₂³×C₄₇	1	4	yes	—
241	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
242	C₂⁵	C₂³×C₄₇	1	2	yes	—
243	C₂²×D₄	—	2	4	no	—
244	C₂²×D₄	—	2	8	no	—
245	C₂²×D₄	—	2	8	no	—
246	C₂²×D₄	—	2	16	no	—
247	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
248	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
249	C₂³×C₄	—	2	128	no	—
250	C₂³×C₄	—	2	16	no	—
251	C₂³×C₄	—	2	8	no	—
252	C₂³×C₄	—	2	8	no	—
253	C₂³×C₄	—	2	32	no	—
254	C₂³×C₄	—	2	32	no	—
255	C₂³×C₄	—	2	64	no	—
256	C₂³×C₄	D₄×C₄₇	1	16	yes	complemented
257	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
258	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
260	C₂³×C₄	C₂³×C₄₇	1	16	yes	—
261	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
262	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
263	#123	—	2	64	no	—
264	#120	—	2	32	no	—
265	C₂×C₄⋊C₄	—	2	16	no	—
266	C₂×C₄⋊C₄	C₂³×C₄₇	1	16	yes	complemented
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	8	no	—
269	C₂×C₂²⋊C₄	—	2	8	no	—
270	C₂×C₂²⋊C₄	—	2	16	no	—
271	C₂×C₂²⋊C₄	—	2	16	no	—
272	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
274	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₄₇	1	16	yes	complemented
277	#95	C₂³×C₄₇	1	32	yes	complemented
278	C₂⁴	—	2	128	no	—
279	C₂⁴	—	2	32	no	—
280	C₂⁴	—	2	64	no	—
281	C₂⁴	—	2	16	no	—
282	C₂⁴	—	2	8	no	—
283	C₂⁴	—	2	32	no	—
284	C₂⁴	—	2	8	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	—	2	2	no	—
288	C₂⁴	—	2	8	no	—
289	C₂⁴	C₂×D₄×C₄₇	1	16	yes	—
290	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
291	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
292	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
293	C₂⁴	#41×C₄₇	1	16	yes	—
294	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
295	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
296	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
297	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	16	no	—
300	C₂×D₄	—	2	16	no	—
301	C₂×D₄	—	2	32	no	—
302	C₂×D₄	—	4	16	no	—
303	C₂×D₄	—	4	32	no	—
304	C₂²×C₄	—	2	128	no	—
305	C₂²×C₄	—	2	256	no	—
306	C₂²×C₄	—	2	64	no	—
307	C₂²×C₄	—	2	32	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	16	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	2	64	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	16	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	C₂×D₄×C₄₇	1	16	yes	—
320	C₂²×C₄	C₂×D₄×C₄₇	1	32	yes	complemented
321	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
323	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₄₇	1	8	yes	—
325	C₄⋊C₄	—	2	32	no	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	2	16	no	—
328	C₂²⋊C₄	—	2	16	no	—
329	C₂²⋊C₄	—	2	32	no	—
330	C₂²⋊C₄	—	2	32	no	—
331	C₂³	—	2	256	no	—
332	C₂³	—	2	128	no	—
333	C₂³	—	2	32	no	—
334	C₂³	—	2	16	no	—
335	C₂³	—	2	16	no	—
336	C₂³	—	2	16	no	—
337	C₂³	—	2	64	no	—
338	C₂³	—	2	32	no	—
339	C₂³	—	2	64	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	8	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	8	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	8	no	—
348	C₂³	—	4	16	no	—
349	C₂³	#120×C₄₇	1	16	yes	—
350	C₂³	#123×C₄₇	1	32	yes	complemented
351	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
352	C₂³	C₂²×D₄×C₄₇	1	8	yes	—
353	C₂³	C₂²×D₄×C₄₇	1	8	yes	—
354	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
355	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
356	C₂³	C₂×#41×C₄₇	1	16	yes	—
357	C₂³	C₂×#41×C₄₇	1	8	yes	—
358	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
359	D₄	—	4	16	no	—
360	D₄	—	4	32	no	—
361	C₂×C₄	—	2	128	no	—
362	C₂×C₄	—	2	32	no	—
363	C₂×C₄	—	2	64	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	16	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	8	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	C₂²×D₄×C₄₇	1	16	yes	—
376	C₂²	—	2	128	no	—
377	C₂²	—	2	32	no	—
378	C₂²	—	2	64	no	—
379	C₂²	—	2	8	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	2	8	no	—
382	C₂²	—	2	16	no	—
383	C₂²	—	2	32	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	8	8	no	—
388	C₂²	C₂×#120×C₄₇	1	8	yes	—
389	C₂²	C₂×#120×C₄₇	1	4	yes	—
390	C₂²	C₂×#123×C₄₇	1	8	yes	—
391	C₂²	C₂×#123×C₄₇	1	16	yes	complemented
392	C₂²	C₄₇×#525	1	16	yes	—
393	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
394	C₂²	C₂³×D₄×C₄₇	1	2	yes	—
395	C₂²	C₂²×#41×C₄₇	1	4	yes	—
396	C₄	—	2	16	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	8	no	—
400	C₂	—	2	8	no	—
401	C₂	—	2	16	no	—
402	C₂	—	8	2	no	—
403	C₂	C₄₇×#2849	1	8	yes	direct product factor
404	C₂	C₂²×#120×C₄₇	1	1	yes	characteristic
405	C₂	C₂²×#123×C₄₇	1	2	yes	—
406	C₂	C₂×C₄₇×#525	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂²×#120×C₄₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₄×C₄₇	C₂	semidirect
2. C₂²×#123×C₄₇	C₂	semidirect
4. C₄₇×#2849	C₂	direct (N × H)
5. C₂×C₄₇×#386	C₂	semidirect
6. C₂×C₄₇×#385	C₂	semidirect
7. C₂×C₄₇×#381	C₂	semidirect
8. C₂×C₄₇×#379	C₂	semidirect
16. C₂⁴×C₄×C₄₇	C₂²	semidirect
18. C₂×#123×C₄₇	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
26. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
27. C₄₇×#386	C₂²	semidirect
28. C₄₇×#385	C₂²	semidirect
29. C₄₇×#381	C₂²	semidirect
30. C₄₇×#379	C₂²	semidirect
31. C₂×#95×C₄₇	C₂²	semidirect
52. C₂³×C₄×C₄₇	D₄	semidirect
62. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
72. C₂×C₂²⋊C₄×C₄₇	C₂³	semidirect
73. #95×C₄₇	C₂³	semidirect
116. C₂²×C₄×C₄₇	C₂×D₄	semidirect
146. C₂³×C₄₇	#123	semidirect
172. C₂×#2849	C₄₇	direct (N × H)
188. C₂²×C₄₇	C₂×#123	semidirect
197. C₂⁵×C₄	C₂×C₄₇	semidirect
198. C₂²×#123	C₂×C₄₇	semidirect
200. #2849	C₂×C₄₇	direct (N × H)
201. C₂×#386	C₂×C₄₇	semidirect
202. C₂×#385	C₂×C₄₇	semidirect
203. C₂×#381	C₂×C₄₇	semidirect
204. C₂×#379	C₂×C₄₇	semidirect
208. C₂×C₄₇	#2849	direct (N × H)
219. C₂⁴×C₄	C₂²×C₄₇	semidirect
221. C₂×#123	C₂²×C₄₇	semidirect
224. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
229. C₂²×C₂²⋊C₄	C₂²×C₄₇	semidirect
230. #386	C₂²×C₄₇	semidirect
231. #385	C₂²×C₄₇	semidirect
232. #381	C₂²×C₄₇	semidirect
233. #379	C₂²×C₄₇	semidirect
234. C₂×#95	C₂²×C₄₇	semidirect
235. C₄₇	C₂×#2849	direct (N × H)
256. C₂³×C₄	D₄×C₄₇	semidirect
266. C₂×C₄⋊C₄	C₂³×C₄₇	semidirect
276. C₂×C₂²⋊C₄	C₂³×C₄₇	semidirect
277. #95	C₂³×C₄₇	semidirect
320. C₂²×C₄	C₂×D₄×C₄₇	semidirect
350. C₂³	#123×C₄₇	semidirect
391. C₂²	C₂×#123×C₄₇	semidirect
403. C₂	C₄₇×#2849	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×C₄×C₄₇	2
C₂²×#123×C₄₇	2
C₂²×#120×C₄₇	2
C₄₇×#2849	2
C₂×C₄₇×#386	2
C₂×C₄₇×#385	2
C₂×C₄₇×#381	2
C₂×C₄₇×#379	2
C₂×#2849	47

Subgroups — C2×C47×#2849 #26076311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2849 #26076311