Subgroups — #123×C₄₇⋊C₈ #26223238

Order 12032.

1034 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243996	C₂	1	2	yes	maximal, complemented
4	#20243947	C₂	1	2	yes	maximal, complemented
5	#20243681	C₂	1	1	yes	maximal, characteristic
6	#20243568	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
10	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#123×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	D₄×C₄₇⋊C₈	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	#15688878	C₂²	1	2	yes	—
28	#15688878	C₂²	1	2	yes	—
29	#15688878	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	C₂×#123×C₄₇	C₄	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#388	C₄	1	2	yes	—
36	C₄₇×#387	C₄	1	2	yes	—
37	C₄₇×#386	C₄	1	1	yes	characteristic
38	C₄₇×#385	C₄	1	1	yes	characteristic
39	C₄₇×#381	C₄	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
42	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	—	2	4	no	—
45	C₂²×C₄₇⋊C₈	—	2	4	no	—
46	C₂²×C₄₇⋊C₈	—	2	2	no	—
47	C₂²×C₄₇⋊C₈	—	2	4	no	—
48	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
57	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
61	C₄×C₄₇⋊C₈	—	2	4	no	—
62	C₄×C₄₇⋊C₈	—	2	4	no	—
63	C₄×C₄₇⋊C₈	—	2	2	no	—
64	C₄×C₄₇⋊C₈	—	2	4	no	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	#123×C₄₇	C₈	1	8	yes	complemented
71	C₄×D₄×C₄₇	—	2	2	no	—
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
88	#95×C₄₇	C₂×C₄	1	2	yes	—
89	#95×C₄₇	C₂×C₄	1	2	yes	—
90	#95×C₄₇	C₂×C₄	1	2	yes	—
91	#95×C₄₇	C₂×C₄	1	2	yes	—
92	#95×C₄₇	C₂×C₄	1	2	yes	—
93	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	C₂×C₈	1	4	yes	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	complemented
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	#41	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	4	no	—
122	C₄⋊C₄×C₄₇	C₂×C₈	1	8	yes	complemented
123	C₂²⋊C₄×C₄₇	—	2	2	no	—
124	C₂²⋊C₄×C₄₇	—	2	2	no	—
125	C₂²⋊C₄×C₄₇	—	2	2	no	—
126	C₂²⋊C₄×C₄₇	—	2	4	no	—
127	C₂²⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
128	C₂²⋊C₄×C₄₇	C₂×C₈	1	8	yes	complemented
129	C₄²×C₄₇	—	2	4	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	8	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	8	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	4	4	no	—
149	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	#41	1	4	yes	—
152	C₂×C₄₇⋊C₈	#41	1	4	yes	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	C₄×D₄	1	2	yes	—
160	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
161	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
162	C₂³×C₄₇	#131	1	2	yes	—
163	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	D₄×C₄₇	—	2	8	no	—
165	C₂×C₄×C₄₇	—	2	8	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	8	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
191	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
192	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
193	C₂×C₄×C₄₇	#131	1	4	yes	—
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
196	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₄₇⋊C₈	—	2	2	no	—
199	C₄₇⋊C₈	—	2	4	no	—
200	C₄₇⋊C₈	—	4	1	no	—
201	C₄₇⋊C₈	—	4	1	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₄₇⋊C₈	#123	1	4	yes	direct product factor
204	C₈×#123	—	47	1	no	maximal, Sylow
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	4	no	—
207	C₂²×C₄₇	—	2	4	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	2	2	no	—
210	C₂²×C₄₇	—	2	4	no	—
211	C₂²×C₄₇	—	4	1	no	—
212	C₂²×C₄₇	—	4	2	no	—
213	C₂²×C₄₇	—	4	1	no	—
214	C₂²×C₄₇	C₈×D₄	1	4	yes	—
215	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂²×C₄₇	C₄×#41	1	2	yes	—
217	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#131	1	2	yes	—
220	C₄×C₄₇	—	2	4	no	—
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	—	2	4	no	—
223	C₄×C₄₇	—	2	4	no	—
224	C₄×C₄₇	—	2	2	no	—
225	C₄×C₄₇	—	4	1	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	—	4	1	no	—
228	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
229	C₄×C₄₇	#525	1	1	yes	characteristic
230	C₄×C₄₇	#529	1	2	yes	—
231	C₂×C₈×D₄	—	47	1	no	—
232	C₂²×C₄×C₈	—	47	1	no	—
233	C₄×#123	D₄₇	1	1	yes	characteristic
234	#1923	—	47	2	no	—
235	#1916	—	47	2	no	—
236	#1869	—	47	1	no	—
237	#1850	—	47	1	no	—
238	#1817	—	47	1	no	—
239	C₈×C₄⋊C₄	—	47	2	no	—
240	C₈×C₂²⋊C₄	—	47	1	no	—
241	C₈×C₂²⋊C₄	—	47	2	no	—
242	C₂×C₄₇	—	2	4	no	—
243	C₂×C₄₇	—	4	2	no	—
244	C₂×C₄₇	C₄×#123	1	1	yes	characteristic
245	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
246	C₂×C₄₇	#2929	1	1	yes	characteristic
247	C₂×C₄₇	C₈×#41	1	2	yes	—
248	C₂×C₄₇	#2966	1	2	yes	—
249	C₂³×C₈	—	47	1	no	—
250	C₂³×C₈	—	47	1	no	—
251	C₂³×C₈	—	47	1	no	—
252	C₂×#123	Dic₄₇	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
254	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
255	C₈×D₄	—	94	4	no	—
256	C₂×C₄⋊C₈	—	47	2	no	—
257	C₂×C₄⋊C₈	—	47	1	no	—
258	C₂×C₂²⋊C₈	—	47	1	no	—
259	C₂×C₂²⋊C₈	—	47	1	no	—
260	C₂×C₂²⋊C₈	—	47	2	no	—
261	C₂×C₂²⋊C₈	—	47	1	no	—
262	C₂×C₄×C₈	—	47	2	no	—
263	C₂×C₄×C₈	—	47	2	no	—
264	C₂×C₄×C₈	—	47	1	no	—
265	C₂×C₄×C₈	—	47	2	no	—
266	C₂×C₄×C₈	—	94	4	no	—
267	#388	Dic₄₇	1	2	yes	—
268	#387	Dic₄₇	1	2	yes	—
269	#386	Dic₄₇	1	1	yes	characteristic
270	#385	Dic₄₇	1	1	yes	characteristic
271	#381	Dic₄₇	1	1	yes	characteristic
272	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
273	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
274	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
275	#336	—	47	2	no	—
276	#336	—	47	2	no	—
277	#336	—	47	2	no	—
278	#336	—	47	2	no	—
279	#336	—	47	2	no	—
280	C₄₇	C₈×#123	1	1	yes	characteristic, complemented, Sylow
281	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
282	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
283	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
284	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
285	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
286	C₂²×C₈	—	47	1	no	—
287	C₂²×C₈	—	47	4	no	—
288	C₂²×C₈	—	47	1	no	—
289	C₂²×C₈	—	47	2	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	47	2	no	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	94	4	no	—
294	C₂²×C₈	—	94	4	no	—
295	C₂²×C₈	—	94	4	no	—
296	C₂²×C₈	—	94	2	no	—
297	C₂²×C₈	—	94	2	no	—
298	#123	C₄₇⋊C₈	1	8	yes	direct product factor
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
303	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
313	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
314	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
315	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
316	C₄⋊C₈	—	94	4	no	—
317	C₄⋊C₈	—	94	2	no	—
318	C₂²⋊C₈	—	94	4	no	—
319	C₂²⋊C₈	—	94	2	no	—
320	C₂²⋊C₈	—	94	2	no	—
321	C₂²⋊C₈	—	94	2	no	—
322	C₄×C₈	—	94	4	no	—
323	C₄×C₈	—	94	4	no	—
324	C₄×C₈	—	94	4	no	—
325	C₄×C₈	—	94	2	no	—
326	#95	C₂×Dic₄₇	1	2	yes	—
327	#95	C₂×Dic₄₇	1	2	yes	—
328	#95	C₂×Dic₄₇	1	2	yes	—
329	#95	C₂×Dic₄₇	1	2	yes	—
330	#95	C₂×Dic₄₇	1	2	yes	—
331	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
332	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	C₂×C₄₇⋊C₈	1	4	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	complemented
347	C₂²×C₄	D₄×D₄₇	1	2	yes	—
348	C₂²×C₄	#10625352	1	2	yes	—
349	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
350	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
354	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
355	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
356	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
357	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
358	C₂×C₈	—	47	2	no	—
359	C₂×C₈	—	47	4	no	—
360	C₂×C₈	—	47	2	no	—
361	C₂×C₈	—	47	4	no	—
362	C₂×C₈	—	94	8	no	—
363	C₂×C₈	—	94	8	no	—
364	C₂×C₈	—	94	2	no	—
365	C₂×C₈	—	94	2	no	—
366	C₂×C₈	—	94	2	no	—
367	C₂×C₈	—	94	1	no	—
368	C₂×C₈	—	94	1	no	—
369	C₂×C₈	—	94	2	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	94	2	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	188	4	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	C₂×C₄₇⋊C₈	1	8	yes	complemented
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	C₂×C₄₇⋊C₈	1	4	yes	complemented
383	C₂²⋊C₄	C₂×C₄₇⋊C₈	1	8	yes	complemented
384	C₄²	—	2	4	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	1	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	1	no	—
397	C₂³	D₄×Dic₄₇	1	2	yes	—
398	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
399	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
400	C₂³	#13094031	1	2	yes	—
401	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
402	D₄	—	2	8	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
428	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
429	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
430	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
431	C₂×C₄	#13094031	1	4	yes	—
432	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
433	C₂×C₄	#41×D₄₇	1	2	yes	—
434	C₂×C₄	#41×D₄₇	1	2	yes	—
435	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
436	C₈	—	47	4	no	—
437	C₈	—	94	2	no	—
438	C₈	—	94	4	no	—
439	C₈	—	188	1	no	—
440	C₈	—	188	1	no	—
441	C₈	—	188	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	2	no	—
451	C₂²	D₄×C₄₇⋊C₈	1	4	yes	—
452	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
453	C₂²	#41×Dic₄₇	1	2	yes	—
454	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
455	C₂²	C₂×#13094031	1	1	yes	characteristic
456	C₂²	C₂×#13094031	1	2	yes	—
457	C₄	—	2	2	no	—
458	C₄	—	2	4	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	4	no	—
461	C₄	—	2	4	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	2	no	—
465	C₄	#123×D₄₇	1	1	yes	characteristic
466	C₄	#15689631	1	1	yes	characteristic
467	C₄	#15689650	1	2	yes	—
468	C₂	—	2	4	no	—
469	C₂	—	4	2	no	—
470	C₂	#123×Dic₄₇	1	1	yes	characteristic
471	C₂	C₂×D₄×C₄₇⋊C₈	1	1	yes	characteristic
472	C₂	#20252083	1	1	yes	characteristic
473	C₂	#41×C₄₇⋊C₈	1	2	yes	—
474	C₂	#20252364	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄×#123×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#123	D₄₇
hypocenter	C₄₇	C₈×#123
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#123

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₄₇⋊C₈	C₂	semidirect
3. #20243996	C₂	semidirect
4. #20243947	C₂	semidirect
6. #20243568	C₂	semidirect
7. #20243456	C₂	semidirect
8. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
9. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
10. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
70. #123×C₄₇	C₈	semidirect
108. C₂²×C₄×C₄₇	C₂×C₈	semidirect
122. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
127. C₂²⋊C₄×C₄₇	C₂×C₈	semidirect
128. C₂²⋊C₄×C₄₇	C₂×C₈	semidirect
203. C₄₇⋊C₈	#123	direct (N × H)
280. C₄₇	C₈×#123	semidirect
298. #123	C₄₇⋊C₈	direct (N × H)
346. C₂²×C₄	C₂×C₄₇⋊C₈	semidirect
377. C₄⋊C₄	C₂×C₄₇⋊C₈	semidirect
382. C₂²⋊C₄	C₂×C₄₇⋊C₈	semidirect
383. C₂²⋊C₄	C₂×C₄₇⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
C₂²×C₄×C₄₇⋊C₈	2
#20243996	2
#20243947	2
#20243681	2
#20243568	2
#20243456	2
C₄⋊C₄×C₄₇⋊C₈	2
C₂²⋊C₄×C₄₇⋊C₈	2
C₄×#123×C₄₇	2
C₈×#123	47

Subgroups — #123×C47⋊C8 #26223238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #123×C₄₇⋊C₈ #26223238