Subgroups — #26185695

Order 12032.

802 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#10625352	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094048	C₂	1	1	yes	maximal, characteristic
3	C₈×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242210	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242202	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242200	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242191	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242187	C₂	1	1	yes	maximal, characteristic, complemented
9	D₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242180	C₂	1	1	yes	maximal, characteristic, complemented
11	#20242137	C₂	1	1	yes	maximal, characteristic, complemented
12	#20241777	C₂	1	1	yes	maximal, characteristic, complemented
13	#20241772	C₂	1	1	yes	maximal, characteristic, complemented
14	#20241667	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13094048	C₄	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	—	2	1	no	—
18	C₄×#10625352	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₄₇	C₂²	1	1	yes	characteristic
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
21	#15689247	C₂²	1	1	yes	characteristic, complemented
22	#15689235	C₄	1	1	yes	characteristic
23	#15689232	C₄	1	1	yes	characteristic
24	#15689222	C₄	1	1	yes	characteristic
25	#15689220	C₄	1	1	yes	characteristic
26	C₄×#10625325	C₂²	1	1	yes	characteristic
27	C₄×#10625335	C₂²	1	1	yes	characteristic
28	C₄×#10625334	C₂²	1	1	yes	characteristic
29	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
30	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	#15689188	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₄₇	—	2	1	no	—
34	C₈×C₂²⋊D₄₇	—	2	1	no	—
35	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
36	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
37	#15689175	C₂²	1	1	yes	characteristic
38	#15689174	C₂²	1	1	yes	characteristic
39	#15689173	—	2	1	no	—
40	#15689164	C₄	1	1	yes	characteristic
41	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
42	#15689126	C₄	1	1	yes	characteristic
43	#15689121	C₄	1	1	yes	characteristic
44	C₂²⋊C₈×D₄₇	—	2	1	no	—
45	C₄×#10625324	C₂²	1	1	yes	characteristic
46	C₂×C₈×Dic₄₇	—	2	1	no	—
47	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
48	#15688876	C₂²	1	1	yes	characteristic, complemented
49	#15688875	C₂²	1	1	yes	characteristic, complemented
50	#15688873	C₂²	1	1	yes	characteristic, complemented
51	#15688855	C₂²	1	1	yes	characteristic, complemented
52	#15688853	C₂²	1	1	yes	characteristic, complemented
53	#15688852	C₂²	1	1	yes	characteristic
54	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
55	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
56	#15688850	C₂²	1	1	yes	characteristic
57	#15688845	C₂²	1	1	yes	characteristic, complemented
58	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
59	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
61	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
63	C₄₇×#334	C₂²	1	1	yes	characteristic, complemented
64	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
66	C₄₇×#322	C₂²	1	1	yes	characteristic, complemented
67	C₂×#10625352	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₄₇	—	2	1	no	—
70	#13094048	C₈	1	8	yes	complemented
71	C₂×#10625325	C₂×C₄	1	1	yes	characteristic
72	C₂×#10625335	C₂×C₄	1	1	yes	characteristic
73	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
74	C₂×#10625324	C₂×C₄	1	1	yes	characteristic
75	C₂×#10625324	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₄₇⋊C₈	—	2	1	no	—
77	C₂²×C₄₇⋊C₈	—	2	1	no	—
78	C₂×C₈×D₄₇	—	2	1	no	—
79	C₂×C₈×D₄₇	—	2	1	no	—
80	C₂×C₈×D₄₇	—	2	1	no	—
81	C₂×C₈×D₄₇	—	4	4	no	—
82	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
83	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
84	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
85	#13093989	C₂×C₄	1	1	yes	characteristic
86	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
87	D₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
88	D₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
89	#13093986	C₂×C₄	1	1	yes	characteristic
90	C₄×C₂²⋊D₄₇	—	2	1	no	—
91	C₄×C₂²⋊D₄₇	—	2	1	no	—
92	(C₂²⋊D₄₇)⋊C₄	—	2	1	no	—
93	(C₂²⋊D₄₇)⋊C₄	—	2	1	no	—
94	#13093982	C₂×C₄	1	1	yes	characteristic
95	#13093980	—	2	1	no	—
96	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊C₄×D₄₇	—	2	1	no	—
98	C₂×C₄×Dic₄₇	—	2	1	no	—
99	C₄²×D₄₇	C₂³	1	1	yes	characteristic
100	#13093957	C₂×C₄	1	1	yes	characteristic
101	#13093956	C₂×C₄	1	1	yes	characteristic
102	#13093955	C₂×C₄	1	1	yes	characteristic
103	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
104	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
105	Dic₄₇⋊C₈	—	2	1	no	—
106	Dic₄₇⋊C₈	—	2	1	no	—
107	Dic₄₇⋊C₈	—	2	1	no	—
108	Dic₄₇⋊C₈	—	2	1	no	—
109	#13093949	C₂×C₄	1	1	yes	characteristic
110	#13093947	C₂×C₄	1	1	yes	characteristic
111	#13093946	C₂×C₄	1	1	yes	characteristic
112	#13093945	C₂×C₄	1	1	yes	characteristic
113	#13093945	C₂×C₄	1	1	yes	characteristic
114	#13093944	C₂×C₄	1	1	yes	characteristic
115	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
116	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
117	(C₂×D₄₇)⋊C₈	—	2	1	no	—
118	(C₂×D₄₇)⋊C₈	—	2	1	no	—
119	(C₂×D₄₇)⋊C₈	—	2	1	no	—
120	(C₂×D₄₇)⋊C₈	—	2	1	no	—
121	#13093934	C₂×C₄	1	1	yes	characteristic
122	#13093934	C₂×C₄	1	1	yes	characteristic
123	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₄₇	—	2	1	no	—
127	C₈×Dic₄₇	—	2	1	no	—
128	C₈×Dic₄₇	—	2	1	no	—
129	C₈×Dic₄₇	D₄	1	1	yes	characteristic
130	C₈×Dic₄₇	D₄	1	1	yes	characteristic
131	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
132	C₂²×C₈×C₄₇	—	2	1	no	—
133	C₂²×C₈×C₄₇	—	2	1	no	—
134	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
136	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
137	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
139	#102×C₄₇	C₂×C₄	1	1	yes	characteristic
140	#102×C₄₇	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₄₇	—	2	1	no	—
142	C₂²⋊C₈×C₄₇	—	2	1	no	—
143	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
146	C₂³×D₄₇	—	2	1	no	—
147	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂×C₂²⋊D₄₇	—	2	1	no	—
152	C₂×C₂²⋊D₄₇	—	2	1	no	—
153	C₂²×Dic₄₇	—	2	1	no	—
154	C₂²×Dic₄₇	—	2	1	no	—
155	C₂²×Dic₄₇	—	2	1	no	—
156	#10625352	—	2	2	no	—
157	#10625352	C₂×C₈	1	4	yes	complemented
158	D₄×D₄₇	—	2	2	no	—
159	D₄×D₄₇	C₂×C₈	1	4	yes	complemented
160	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₄₇	—	2	1	no	—
162	C₂×C₄×D₄₇	—	2	1	no	—
163	C₂×C₄×D₄₇	—	2	1	no	—
164	C₂×C₄×D₄₇	—	4	2	no	—
165	C₂×C₄×D₄₇	—	4	2	no	—
166	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
169	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
170	D₈×C₄₇	C₂×C₈	1	4	yes	complemented
171	C₂×C₈×C₄₇	—	2	1	no	—
172	C₂×C₈×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	4	2	no	—
175	C₂×C₈×C₄₇	—	4	2	no	—
176	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
180	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²⋊C₄×C₄₇	—	2	1	no	—
183	C₂²⋊C₄×C₄₇	—	2	1	no	—
184	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
185	C₂²⋊Dic₄₇	—	2	1	no	—
186	C₂²⋊Dic₄₇	—	2	1	no	—
187	#10625335	C₂×C₈	1	4	yes	complemented
188	#10625334	C₂×C₈	1	4	yes	complemented
189	(C₂×D₄₇)⋊C₄	—	2	1	no	—
190	(C₂×D₄₇)⋊C₄	—	2	1	no	—
191	(C₂×D₄₇)⋊C₄	—	2	1	no	—
192	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
194	Dic₄₇⋊C₄	—	2	1	no	—
195	Dic₄₇⋊C₄	—	2	1	no	—
196	Dic₄₇⋊C₄	—	2	1	no	—
197	C₄×Dic₄₇	—	2	1	no	—
198	C₄×Dic₄₇	—	2	1	no	—
199	C₄×Dic₄₇	—	2	1	no	—
200	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
202	C₄×Dic₄₇	#41	1	1	yes	characteristic
203	C₂×C₄₇⋊C₈	—	2	1	no	—
204	C₂×C₄₇⋊C₈	—	2	1	no	—
205	C₂×C₄₇⋊C₈	—	2	1	no	—
206	C₂×C₄₇⋊C₈	—	4	2	no	—
207	C₂×C₄₇⋊C₈	—	4	2	no	—
208	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
209	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
211	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
212	#10625325	C₂×C₈	1	4	yes	complemented
213	#10625324	—	2	2	no	—
214	#10625324	C₂×C₈	1	4	yes	complemented
215	C₈×D₄₇	—	2	2	no	—
216	C₈×D₄₇	—	4	1	no	—
217	C₈×D₄₇	—	4	2	no	—
218	C₈×D₄₇	—	4	2	no	—
219	C₈×D₄₇	—	4	2	no	—
220	C₂³×C₄₇	—	2	1	no	—
221	C₂³×C₄₇	—	2	1	no	—
222	C₂²×D₄₇	—	2	1	no	—
223	C₂²×D₄₇	—	2	4	no	—
224	C₂²×D₄₇	—	4	2	no	—
225	C₂²×D₄₇	—	4	2	no	—
226	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
227	D₄×C₄₇	—	2	1	no	—
228	D₄×C₄₇	—	2	1	no	—
229	D₄×C₄₇	C₂²×C₈	1	2	yes	—
230	D₄×C₄₇	C₂²×C₈	1	2	yes	complemented
231	C₂×C₄×C₄₇	—	2	1	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	4	1	no	—
234	C₂×C₄×C₄₇	—	4	1	no	—
235	C₂×C₄×C₄₇	—	4	1	no	—
236	C₂×C₄×C₄₇	—	4	1	no	—
237	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
240	C₂²⋊D₄₇	—	2	4	no	—
241	C₂²⋊D₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	2	1	no	—
243	C₂×Dic₄₇	—	2	4	no	—
244	C₂×Dic₄₇	—	2	1	no	—
245	C₂×Dic₄₇	—	2	1	no	—
246	C₂×Dic₄₇	—	4	2	no	—
247	C₂×Dic₄₇	—	4	2	no	—
248	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
249	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
250	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
251	D₁₈₈	—	2	1	no	—
252	D₁₈₈	C₂²×C₈	1	2	yes	—
253	C₄×D₄₇	—	2	1	no	—
254	C₄×D₄₇	—	2	1	no	—
255	C₄×D₄₇	—	4	1	no	—
256	C₄×D₄₇	—	4	2	no	—
257	C₄×D₄₇	—	4	2	no	—
258	C₄×D₄₇	—	4	1	no	—
259	C₄×D₄₇	—	4	1	no	—
260	C₄×D₄₇	C₂²×C₈	1	2	yes	—
261	C₄×D₄₇	#131	1	2	yes	—
262	Dic₉₄	—	2	1	no	—
263	Dic₉₄	C₂²×C₈	1	2	yes	complemented
264	C₈×C₄₇	—	2	1	no	—
265	C₈×C₄₇	—	2	1	no	—
266	C₈×C₄₇	—	2	1	no	—
267	C₈×C₄₇	—	4	1	no	—
268	C₈×C₄₇	—	4	1	no	—
269	C₈×C₄₇	—	4	1	no	—
270	C₈×C₄₇	C₂²×C₈	1	2	yes	complemented
271	C₄₇⋊C₈	—	2	1	no	—
272	C₄₇⋊C₈	—	2	1	no	—
273	C₄₇⋊C₈	—	4	1	no	—
274	C₄₇⋊C₈	—	4	1	no	—
275	C₄₇⋊C₈	—	4	1	no	—
276	C₄₇⋊C₈	C₂²×C₈	1	2	yes	complemented
277	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	complemented
278	C₈×AGL(1,ℤ/8)	—	47	1	no	maximal, Sylow
279	C₂²×C₄₇	—	2	2	no	—
280	C₂²×C₄₇	—	2	2	no	—
281	C₂²×C₄₇	—	4	1	no	—
282	C₂²×C₄₇	—	4	1	no	—
283	C₂²×C₄₇	—	4	1	no	—
284	C₂²×C₄₇	—	4	1	no	—
285	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
286	C₂×D₄₇	—	2	1	no	—
287	C₂×D₄₇	—	2	1	no	—
288	C₂×D₄₇	—	2	2	no	—
289	C₂×D₄₇	—	4	8	no	—
290	C₂×D₄₇	—	4	1	no	—
291	C₂×D₄₇	—	4	1	no	—
292	C₂×D₄₇	C₈×D₄	1	2	yes	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	4	1	no	—
295	C₄×C₄₇	—	4	1	no	—
296	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
297	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
298	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₄×C₄₇	#575	1	1	yes	characteristic
300	Dic₄₇	—	2	2	no	—
301	Dic₄₇	—	2	1	no	—
302	Dic₄₇	—	2	1	no	—
303	Dic₄₇	—	4	1	no	—
304	Dic₄₇	—	4	1	no	—
305	Dic₄₇	C₈×D₄	1	2	yes	—
306	C₈×#41	—	47	1	no	—
307	C₄×AGL(1,ℤ/8)	—	47	1	no	—
308	C₂×C₈×D₄	—	47	1	no	—
309	#1580	—	47	1	no	—
310	#1580	D₄₇	1	1	yes	characteristic, complemented
311	SD₁₆⋊C₈	—	47	1	no	—
312	SD₁₆⋊C₈	—	47	1	no	—
313	C₈×SD₁₆	—	47	1	no	—
314	C₈×SD₁₆	—	47	1	no	—
315	C₈×D₈	—	47	1	no	—
316	C₈×D₈	—	47	1	no	—
317	#1565	—	47	1	no	—
318	#1478	—	47	1	no	—
319	#1477	—	47	1	no	—
320	C₈×M₁₆	—	47	1	no	—
321	C₂×C₄₇	—	4	2	no	—
322	C₂×C₄₇	—	4	2	no	—
323	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
324	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
325	C₂×C₄₇	#2955	1	1	yes	characteristic
326	D₄₇	—	2	2	no	—
327	D₄₇	—	4	2	no	—
328	C₂×AGL(1,ℤ/8)	—	47	1	no	—
329	C₂³×C₈	—	94	1	no	—
330	C₄×#41	—	47	1	no	—
331	C₂×C₄×D₄	—	47	1	no	—
332	C₈×Q₈	—	47	1	no	—
333	C₈×Q₈	—	47	1	no	—
334	#442	—	47	1	no	—
335	#442	—	47	1	no	—
336	#440	—	47	1	no	—
337	#440	—	47	1	no	—
338	C₄×SD₁₆	—	47	1	no	—
339	C₄×SD₁₆	—	47	1	no	—
340	C₄×D₈	—	47	1	no	—
341	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
342	C₈×D₄	—	47	1	no	—
343	C₈×D₄	—	47	1	no	—
344	C₈×D₄	—	47	1	no	—
345	C₈×D₄	—	47	1	no	—
346	C₈×D₄	—	94	1	no	—
347	C₈×D₄	—	94	1	no	—
348	C₈×D₄	—	94	1	no	—
349	C₈×D₄	—	94	1	no	—
350	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
351	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
352	#431	—	47	1	no	—
353	#431	—	47	1	no	—
354	#431	—	94	1	no	—
355	#428	—	47	1	no	—
356	C₂×C₄⋊C₈	—	47	1	no	—
357	#418	—	47	1	no	—
358	#417	—	47	1	no	—
359	C₂×C₂²⋊C₈	—	94	1	no	—
360	C₄×M₁₆	—	47	1	no	—
361	C₂×C₄×C₈	—	47	1	no	—
362	C₂×C₄×C₈	—	94	1	no	—
363	#335	—	47	1	no	—
364	#335	—	47	1	no	—
365	#334	—	47	1	no	—
366	#334	C₂×D₄₇	1	1	yes	characteristic, complemented
367	Q₈⋊C₈	—	47	1	no	—
368	Q₈⋊C₈	—	47	1	no	—
369	D₄⋊C₈	—	47	1	no	—
370	D₄⋊C₈	—	47	1	no	—
371	D₄⋊C₈	—	47	1	no	—
372	D₄⋊C₈	—	47	1	no	—
373	D₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
374	D₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
375	#322	—	47	1	no	—
376	#322	C₂×D₄₇	1	1	yes	characteristic, complemented
377	C₈²	—	47	1	no	—
378	C₈²	—	47	1	no	—
379	C₄₇	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
380	C₂×#41	—	47	1	no	—
381	C₂²×D₄	—	47	1	no	—
382	C₂³×C₄	—	94	1	no	—
383	AGL(1,ℤ/8)	—	47	8	no	—
384	C₂×SD₁₆	—	47	1	no	—
385	C₂×SD₁₆	—	47	1	no	—
386	C₂×D₈	—	47	1	no	—
387	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
388	C₂×M₁₆	—	47	1	no	—
389	C₂×M₁₆	—	47	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	47	1	no	—
393	C₂²×C₈	—	47	1	no	—
394	C₂²×C₈	—	94	1	no	—
395	C₂²×C₈	—	94	1	no	—
396	C₂²×C₈	—	94	1	no	—
397	C₂²×C₈	—	94	1	no	—
398	C₂²×C₈	—	94	1	no	—
399	C₂²×C₈	—	188	4	no	—
400	C₄×Q₈	—	47	1	no	—
401	C₄×Q₈	—	47	1	no	—
402	C₄×D₄	—	47	1	no	—
403	C₄×D₄	—	47	1	no	—
404	C₄×D₄	—	47	1	no	—
405	C₄×D₄	—	47	1	no	—
406	C₄×D₄	—	94	1	no	—
407	C₄×D₄	—	94	1	no	—
408	C₄×D₄	—	94	1	no	—
409	C₄×D₄	—	94	1	no	—
410	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
411	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
412	#117	—	47	1	no	—
413	#117	—	94	1	no	—
414	C₂×C₄⋊C₄	—	47	1	no	—
415	C₂×C₂²⋊C₄	—	94	1	no	—
416	C₂×C₄²	—	47	1	no	—
417	C₂×C₄²	—	94	1	no	—
418	#107	—	47	1	no	—
419	#107	C₄×D₄₇	1	1	yes	characteristic
420	#106	—	47	1	no	—
421	#106	—	47	1	no	—
422	C₄⋊C₈	—	47	1	no	—
423	C₄⋊C₈	—	47	1	no	—
424	C₄⋊C₈	—	94	1	no	—
425	C₄⋊C₈	—	94	1	no	—
426	C₄⋊C₈	—	94	1	no	—
427	C₄⋊C₈	—	94	1	no	—
428	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
429	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
430	#103	—	47	1	no	—
431	#103	—	47	1	no	—
432	#102	—	47	1	no	—
433	#102	—	47	1	no	—
434	#102	—	47	1	no	—
435	#102	—	47	1	no	—
436	#102	C₄×D₄₇	1	1	yes	characteristic
437	#102	C₄×D₄₇	1	1	yes	characteristic
438	C₂²⋊C₈	—	2	1	no	—
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	—	94	1	no	—
441	C₂²⋊C₈	—	94	1	no	—
442	C₂²⋊C₈	—	94	1	no	—
443	C₂²⋊C₈	—	94	1	no	—
444	C₂²⋊C₈	—	94	1	no	—
445	C₂²⋊C₈	—	94	1	no	—
446	#97	—	47	1	no	—
447	#97	—	47	1	no	—
448	C₄×C₈	—	47	1	no	—
449	C₄×C₈	—	47	1	no	—
450	C₄×C₈	—	47	1	no	—
451	C₄×C₈	—	47	1	no	—
452	C₄×C₈	—	47	1	no	—
453	C₄×C₈	—	94	1	no	—
454	C₄×C₈	—	94	1	no	—
455	C₄×C₈	—	94	1	no	—
456	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
457	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
458	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
459	C₂⁴	—	94	1	no	—
460	#41	—	47	4	no	—
461	#41	—	94	2	no	—
462	C₂×Q₈	—	47	1	no	—
463	C₂×D₄	—	47	4	no	—
464	C₂×D₄	—	47	1	no	—
465	C₂×D₄	—	94	2	no	—
466	C₂×D₄	—	94	1	no	—
467	C₂×D₄	—	94	1	no	—
468	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
469	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	47	1	no	—
473	C₂²×C₄	—	47	1	no	—
474	C₂²×C₄	—	47	1	no	—
475	C₂²×C₄	—	94	1	no	—
476	C₂²×C₄	—	94	1	no	—
477	C₂²×C₄	—	94	1	no	—
478	C₂²×C₄	—	94	1	no	—
479	C₂²×C₄	—	94	1	no	—
480	C₂²×C₄	—	94	1	no	—
481	C₂²×C₄	—	188	2	no	—
482	C₂²×C₄	—	188	2	no	—
483	SD₁₆	—	47	4	no	—
484	SD₁₆	—	47	4	no	—
485	D₈	—	47	4	no	—
486	D₈	C₈×D₄₇	1	4	yes	complemented
487	M₁₆	—	47	4	no	—
488	M₁₆	—	94	2	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	4	2	no	—
493	C₂×C₈	—	4	2	no	—
494	C₂×C₈	—	47	1	no	—
495	C₂×C₈	—	47	1	no	—
496	C₂×C₈	—	47	1	no	—
497	C₂×C₈	—	47	1	no	—
498	C₂×C₈	—	94	2	no	—
499	C₂×C₈	—	94	1	no	—
500	C₂×C₈	—	94	1	no	—
501	C₂×C₈	—	94	1	no	—
502	C₂×C₈	—	188	1	no	—
503	C₂×C₈	—	188	2	no	—
504	C₂×C₈	—	188	2	no	—
505	C₂×C₈	—	188	2	no	—
506	C₂×C₈	—	188	2	no	—
507	C₂×C₈	—	188	2	no	—
508	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
509	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
510	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
511	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
512	C₄⋊C₄	—	47	1	no	—
513	C₄⋊C₄	—	47	1	no	—
514	C₄⋊C₄	—	94	1	no	—
515	C₄⋊C₄	—	94	1	no	—
516	C₄⋊C₄	—	94	1	no	—
517	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
518	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	94	1	no	—
522	C₂²⋊C₄	—	94	1	no	—
523	C₂²⋊C₄	—	94	1	no	—
524	C₂²⋊C₄	—	94	1	no	—
525	C₂²⋊C₄	—	94	1	no	—
526	C₄²	—	47	1	no	—
527	C₄²	—	47	1	no	—
528	C₄²	—	47	1	no	—
529	C₄²	—	94	1	no	—
530	C₄²	—	94	1	no	—
531	C₄²	—	94	1	no	—
532	C₄²	C₂³×D₄₇	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	47	1	no	—
536	C₂³	—	94	4	no	—
537	C₂³	—	94	1	no	—
538	C₂³	—	188	2	no	—
539	C₂³	—	188	2	no	—
540	Q₈	—	47	2	no	—
541	Q₈	—	94	1	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	47	2	no	—
545	D₄	—	94	4	no	—
546	D₄	—	94	4	no	—
547	D₄	—	94	1	no	—
548	D₄	C₂×C₈×D₄₇	1	2	yes	—
549	D₄	C₂×C₈×D₄₇	1	2	yes	complemented
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	47	1	no	—
557	C₂×C₄	—	47	2	no	—
558	C₂×C₄	—	47	2	no	—
559	C₂×C₄	—	47	1	no	—
560	C₂×C₄	—	47	1	no	—
561	C₂×C₄	—	94	4	no	—
562	C₂×C₄	—	94	1	no	—
563	C₂×C₄	—	94	1	no	—
564	C₂×C₄	—	94	1	no	—
565	C₂×C₄	—	94	1	no	—
566	C₂×C₄	—	94	1	no	—
567	C₂×C₄	—	188	1	no	—
568	C₂×C₄	—	188	2	no	—
569	C₂×C₄	—	188	2	no	—
570	C₂×C₄	—	188	2	no	—
571	C₂×C₄	—	188	2	no	—
572	C₂×C₄	—	188	1	no	—
573	C₂×C₄	—	188	1	no	—
574	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
575	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
576	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	47	2	no	—
584	C₈	—	47	2	no	—
585	C₈	—	94	1	no	—
586	C₈	—	94	1	no	—
587	C₈	—	188	1	no	—
588	C₈	—	188	1	no	—
589	C₈	—	188	1	no	—
590	C₈	C₂×C₈×D₄₇	1	2	yes	complemented
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	47	2	no	—
598	C₂²	—	94	1	no	—
599	C₂²	—	94	1	no	—
600	C₂²	—	94	2	no	—
601	C₂²	—	188	8	no	—
602	C₂²	—	188	1	no	—
603	C₂²	—	188	1	no	—
604	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	47	2	no	—
609	C₄	—	94	1	no	—
610	C₄	—	94	1	no	—
611	C₄	—	94	2	no	—
612	C₄	—	188	1	no	—
613	C₄	—	188	1	no	—
614	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
615	C₄	#131×D₄₇	1	1	yes	characteristic
616	C₄	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
617	C₄	#15689919	1	1	yes	characteristic
618	C₂	—	4	2	no	—
619	C₂	—	4	2	no	—
620	C₂	—	94	2	no	—
621	C₂	—	188	2	no	—
622	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
623	C₂	#20252199	1	1	yes	characteristic
624	C₂	#20252288	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1580	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094048	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1580	D₄₇
hypocenter	C₄₇	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1580

Complements

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

N	H ≅ G/N	type
1. C₈×#10625352	C₂	semidirect
3. C₈×D₄×D₄₇	C₂	semidirect
4. #20242210	C₂	semidirect
5. #20242202	C₂	semidirect
6. #20242200	C₂	semidirect
7. #20242191	C₂	semidirect
8. #20242187	C₂	semidirect
9. D₈×C₄₇⋊C₈	C₂	semidirect
10. #20242180	C₂	semidirect
11. #20242137	C₂	semidirect
12. #20241777	C₂	semidirect
13. #20241772	C₂	semidirect
14. #20241667	C₂	semidirect
15. C₄₇×#1580	C₂	semidirect
20. C₈×Dic₉₄	C₂²	semidirect
21. #15689247	C₂²	semidirect
31. D₄×C₄₇⋊C₈	C₂²	semidirect
48. #15688876	C₂²	semidirect
49. #15688875	C₂²	semidirect
50. #15688873	C₂²	semidirect
51. #15688855	C₂²	semidirect
52. #15688853	C₂²	semidirect
55. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
57. #15688845	C₂²	semidirect
58. C₈×C₄₇⋊C₈	C₂²	semidirect
59. C₈×C₄₇⋊C₈	C₂²	semidirect
62. C₈×D₄×C₄₇	C₂²	semidirect
63. C₄₇×#334	C₂²	semidirect
65. C₄₇×D₄⋊C₈	C₂²	semidirect
66. C₄₇×#322	C₂²	semidirect
70. #13094048	C₈	semidirect
157. #10625352	C₂×C₈	semidirect
159. D₄×D₄₇	C₂×C₈	semidirect
170. D₈×C₄₇	C₂×C₈	semidirect
187. #10625335	C₂×C₈	semidirect
188. #10625334	C₂×C₈	semidirect
212. #10625325	C₂×C₈	semidirect
214. #10625324	C₂×C₈	semidirect
230. D₄×C₄₇	C₂²×C₈	semidirect
263. Dic₉₄	C₂²×C₈	semidirect
270. C₈×C₄₇	C₂²×C₈	semidirect
276. C₄₇⋊C₈	C₂²×C₈	semidirect
277. C₄₇⋊C₈	AGL(1,ℤ/8)	semidirect
310. #1580	D₄₇	semidirect
351. C₈×D₄	C₂×D₄₇	semidirect
366. #334	C₂×D₄₇	semidirect
374. D₄⋊C₈	C₂×D₄₇	semidirect
376. #322	C₂×D₄₇	semidirect
379. C₄₇	C₈×AGL(1,ℤ/8)	semidirect
486. D₈	C₈×D₄₇	semidirect
549. D₄	C₂×C₈×D₄₇	semidirect
590. C₈	C₂×C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₈×#10625352	2
C₄×#13094048	2
C₈×D₄×D₄₇	2
#20242210	2
#20242202	2
#20242200	2
#20242191	2
#20242187	2
D₈×C₄₇⋊C₈	2
#20242180	2
#20242137	2
#20241777	2
#20241772	2
#20241667	2
C₄₇×#1580	2
C₈×AGL(1,ℤ/8)	47