Subgroups — #26186141

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253386	C₂	1	1	yes	maximal, characteristic
2	#20252095	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242220	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242218	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242216	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242214	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#10625334	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#10625334	C₂	1	1	yes	maximal, characteristic, complemented
11	#20242161	C₂	1	1	yes	maximal, characteristic, complemented
12	#20241811	C₂	1	1	yes	maximal, characteristic, complemented
13	#20241785	C₂	1	1	yes	maximal, characteristic, complemented
14	#20241670	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13094030	—	2	1	no	—
17	C₂²×C₈×D₄₇	—	2	1	no	—
18	#15689670	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₄₇	C₂²	1	1	yes	characteristic
20	#15689438	C₄	1	1	yes	characteristic
21	#15689435	C₄	1	1	yes	characteristic
22	#15689402	C₄	1	1	yes	characteristic
23	#15689401	C₄	1	1	yes	characteristic
24	#15689317	C₄	1	1	yes	characteristic
25	#15689316	C₄	1	1	yes	characteristic
26	#15689258	C₄	1	1	yes	characteristic
27	#15689255	C₄	1	1	yes	characteristic
28	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
29	C₄×#10625334	C₂²	1	1	yes	characteristic
30	C₄×#10625334	C₂²	1	1	yes	characteristic
31	#15689201	C₂²	1	1	yes	characteristic, complemented
32	#15689200	C₂²	1	1	yes	characteristic, complemented
33	#15689198	—	2	1	no	—
34	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
35	C₈×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
36	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	#15689188	C₂²	1	1	yes	characteristic
38	C₈×C₂²⋊D₄₇	—	2	1	no	—
39	C₈×C₂²⋊D₄₇	—	2	1	no	—
40	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
41	#15689174	C₂²	1	1	yes	characteristic
42	#15689174	C₂²	1	1	yes	characteristic
43	#15689145	C₂²	1	1	yes	characteristic
44	C₄⋊C₈×D₄₇	C₂²	1	1	yes	characteristic
45	#15689088	—	2	1	no	—
46	C₂²⋊C₈×D₄₇	—	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	#15688875	C₂²	1	1	yes	characteristic, complemented
51	#15688852	C₂²	1	1	yes	characteristic
52	#15688852	C₂²	1	1	yes	characteristic, complemented
53	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
54	D₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#15688850	C₂²	1	1	yes	characteristic
56	#15688850	C₂²	1	1	yes	characteristic, complemented
57	#15688845	C₂²	1	1	yes	characteristic, complemented
58	#15688845	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×#335	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	C₈²×C₄₇	C₂²	1	1	yes	characteristic, complemented
67	C₂×#10625350	—	2	1	no	—
68	C₂×D₄×D₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₄₇	—	2	1	no	—
70	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
71	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
72	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
73	#13094030	—	4	4	no	—
74	C₂×#10625329	—	2	1	no	—
75	C₂×#10625324	—	2	1	no	—
76	C₂×#10625324	—	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	—	2	1	no	—
82	C₂×C₈×D₄₇	—	4	4	no	—
83	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
84	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
85	#13094023	C₂×C₄	1	1	yes	characteristic
86	#13094020	C₂×C₄	1	1	yes	characteristic
87	#13094010	—	2	1	no	—
88	#13093999	C₂×C₄	1	1	yes	characteristic
89	#13093997	—	2	1	no	—
90	#13093995	C₂×C₄	1	1	yes	characteristic
91	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
92	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
93	D₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	#13093986	C₂×C₄	1	1	yes	characteristic
95	C₄×C₂²⋊D₄₇	—	2	1	no	—
96	C₄×C₂²⋊D₄₇	—	2	1	no	—
97	(C₂²⋊D₄₇)⋊C₄	—	2	1	no	—
98	C₄⋊C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂²⋊C₄×D₄₇	—	2	1	no	—
100	C₄²×D₄₇	C₂³	1	1	yes	characteristic
101	#13093958	C₂×C₄	1	1	yes	characteristic
102	#13093957	C₂×C₄	1	1	yes	characteristic
103	#13093957	C₂×C₄	1	1	yes	characteristic
104	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
105	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
106	Dic₄₇⋊C₈	—	2	1	no	—
107	Dic₄₇⋊C₈	—	2	1	no	—
108	Dic₄₇⋊C₈	—	2	1	no	—
109	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
110	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
111	#13093946	C₂×C₄	1	1	yes	characteristic
112	#13093946	C₂×C₄	1	1	yes	characteristic
113	#13093945	C₂×C₄	1	1	yes	characteristic
114	#13093945	C₂×C₄	1	1	yes	characteristic
115	#13093944	C₂×C₄	1	1	yes	characteristic
116	#13093944	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
118	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
119	(C₂×D₄₇)⋊C₈	—	2	1	no	—
120	(C₂×D₄₇)⋊C₈	—	2	1	no	—
121	(C₂×D₄₇)⋊C₈	—	2	1	no	—
122	(C₂×D₄₇)⋊C₈	—	2	1	no	—
123	(C₂×D₄₇)⋊C₈	—	2	1	no	—
124	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
125	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
127	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
128	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₄₇	—	2	1	no	—
154	C₂×C₂²⋊D₄₇	—	2	1	no	—
155	C₂²×Dic₄₇	—	2	1	no	—
156	D₄×D₄₇	—	2	2	no	—
157	D₄×D₄₇	—	2	2	no	—
158	#10625350	—	4	2	no	—
159	#10625350	—	4	2	no	—
160	C₂×D₁₈₈	—	2	1	no	—
161	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄×D₄₇	—	2	1	no	—
164	C₂×C₄×D₄₇	—	2	1	no	—
165	C₂×C₄×D₄₇	—	2	1	no	—
166	C₂×C₄×D₄₇	—	2	1	no	—
167	C₂×C₄×D₄₇	—	4	2	no	—
168	C₂×C₄×D₄₇	—	4	2	no	—
169	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
172	C₂×Dic₉₄	—	2	1	no	—
173	D₈×C₄₇	—	2	2	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	1	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	4	2	no	—
178	C₂×C₈×C₄₇	—	4	2	no	—
179	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
183	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²⋊C₄×C₄₇	—	2	1	no	—
186	C₂²⋊C₄×C₄₇	—	2	1	no	—
187	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
188	C₂²⋊Dic₄₇	—	2	1	no	—
189	C₂²⋊Dic₄₇	—	2	1	no	—
190	#10625334	—	2	2	no	—
191	#10625334	—	2	2	no	—
192	(C₂×D₄₇)⋊C₄	—	2	1	no	—
193	(C₂×D₄₇)⋊C₄	—	2	1	no	—
194	(C₂×D₄₇)⋊C₄	—	2	1	no	—
195	(C₂×D₄₇)⋊C₄	—	2	1	no	—
196	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
197	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
198	Dic₄₇⋊C₄	—	2	1	no	—
199	Dic₄₇⋊C₄	—	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	#10625329	—	4	2	no	—
204	C₂×C₄₇⋊C₈	—	2	1	no	—
205	C₂×C₄₇⋊C₈	—	2	1	no	—
206	C₂×C₄₇⋊C₈	—	2	1	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	D₃₇₆	—	2	2	no	—
213	#10625324	—	4	2	no	—
214	#10625324	—	4	2	no	—
215	C₈×D₄₇	—	2	2	no	—
216	C₈×D₄₇	—	4	2	no	—
217	C₈×D₄₇	—	4	2	no	—
218	C₈×D₄₇	—	4	2	no	—
219	C₈×D₄₇	—	4	2	no	—
220	C₈×D₄₇	D₈	1	4	yes	complemented
221	C₂³×C₄₇	—	2	1	no	—
222	C₂³×C₄₇	—	2	1	no	—
223	C₂²×D₄₇	—	2	4	no	—
224	C₂²×D₄₇	—	2	1	no	—
225	C₂²×D₄₇	—	2	1	no	—
226	C₂²×D₄₇	—	4	2	no	—
227	C₂²×D₄₇	—	4	2	no	—
228	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
229	D₄×C₄₇	—	2	1	no	—
230	D₄×C₄₇	—	2	1	no	—
231	D₄×C₄₇	—	2	1	no	—
232	D₄×C₄₇	#131	1	2	yes	complemented
233	C₂×C₄×C₄₇	—	2	1	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	4	1	no	—
236	C₂×C₄×C₄₇	—	4	1	no	—
237	C₂×C₄×C₄₇	—	4	1	no	—
238	C₂×C₄×C₄₇	—	4	1	no	—
239	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
242	C₂²⋊D₄₇	—	2	4	no	—
243	C₂²⋊D₄₇	—	4	2	no	—
244	C₂²⋊D₄₇	—	4	2	no	—
245	C₂²⋊D₄₇	—	4	2	no	—
246	C₂×Dic₄₇	—	2	1	no	—
247	C₂×Dic₄₇	—	2	1	no	—
248	C₂×Dic₄₇	—	4	2	no	—
249	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
250	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
251	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
252	D₁₈₈	—	2	1	no	—
253	D₁₈₈	—	2	1	no	—
254	D₁₈₈	—	2	1	no	—
255	D₁₈₈	—	4	2	no	—
256	D₁₈₈	#131	1	2	yes	complemented
257	C₄×D₄₇	—	2	1	no	—
258	C₄×D₄₇	—	2	1	no	—
259	C₄×D₄₇	—	4	1	no	—
260	C₄×D₄₇	—	4	2	no	—
261	C₄×D₄₇	—	4	1	no	—
262	C₄×D₄₇	—	4	1	no	—
263	C₄×D₄₇	—	4	1	no	—
264	C₄×D₄₇	—	4	1	no	—
265	C₄×D₄₇	—	4	2	no	—
266	C₄×D₄₇	C₂×D₈	1	2	yes	—
267	C₄×D₄₇	#135	1	2	yes	—
268	Dic₉₄	—	4	2	no	—
269	C₈×C₄₇	—	2	1	no	—
270	C₈×C₄₇	—	2	1	no	—
271	C₈×C₄₇	—	2	1	no	—
272	C₈×C₄₇	—	4	1	no	—
273	C₈×C₄₇	—	4	1	no	—
274	C₈×C₄₇	—	4	1	no	—
275	C₈×C₄₇	C₂×D₈	1	2	yes	—
276	C₄₇⋊C₈	—	2	1	no	—
277	C₄₇⋊C₈	—	2	1	no	—
278	C₄₇⋊C₈	—	2	1	no	—
279	C₄₇⋊C₈	—	4	1	no	—
280	C₄₇⋊C₈	—	4	1	no	—
281	C₄₇⋊C₈	—	4	1	no	—
282	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
283	#17900	—	47	1	no	maximal, Sylow
284	C₂²×C₄₇	—	2	2	no	—
285	C₂²×C₄₇	—	4	1	no	—
286	C₂²×C₄₇	—	4	1	no	—
287	C₂²×C₄₇	—	4	1	no	—
288	C₂²×C₄₇	—	4	1	no	—
289	C₂²×C₄₇	—	4	1	no	—
290	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×D₄₇	—	2	1	no	—
292	C₂×D₄₇	—	2	1	no	—
293	C₂×D₄₇	—	2	2	no	—
294	C₂×D₄₇	—	4	8	no	—
295	C₂×D₄₇	—	4	1	no	—
296	C₂×D₄₇	—	4	1	no	—
297	C₂×D₄₇	—	4	1	no	—
298	C₂×D₄₇	—	4	1	no	—
299	C₂×D₄₇	—	4	1	no	—
300	C₂×D₄₇	C₄×D₈	1	2	yes	—
301	C₄×C₄₇	—	2	1	no	—
302	C₄×C₄₇	—	4	1	no	—
303	C₄×C₄₇	—	4	1	no	—
304	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
305	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
306	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
307	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
308	Dic₄₇	—	2	1	no	—
309	Dic₄₇	—	2	1	no	—
310	Dic₄₇	—	4	1	no	—
311	Dic₄₇	—	4	1	no	—
312	Dic₄₇	C₄×D₈	1	2	yes	—
313	#3100	—	47	1	no	—
314	#2931	—	47	1	no	—
315	C₂×C₈×D₄	—	47	1	no	—
316	#1581	—	47	1	no	—
317	#1581	—	47	1	no	—
318	#1581	—	47	1	no	—
319	#1581	—	47	1	no	—
320	C₈×D₈	—	47	1	no	—
321	C₈×D₈	—	47	1	no	—
322	C₈×D₈	—	47	1	no	—
323	C₈×D₈	D₄₇	1	1	yes	characteristic, complemented
324	#1571	—	47	1	no	—
325	#1486	—	47	1	no	—
326	#1480	—	47	1	no	—
327	#1450	—	47	1	no	—
328	C₂×C₄₇	—	4	2	no	—
329	C₂×C₄₇	—	8	1	no	—
330	C₂×C₄₇	#2929	1	1	yes	characteristic
331	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
332	C₂×C₄₇	#2955	1	1	yes	characteristic
333	D₄₇	—	2	2	no	—
334	D₄₇	—	4	2	no	—
335	D₄₇	—	8	1	no	—
336	C₂×#131	—	94	1	no	—
337	C₂³×C₈	—	94	1	no	—
338	#532	—	47	1	no	—
339	C₂×C₄×D₄	—	47	1	no	—
340	#480	—	47	1	no	—
341	#480	—	47	1	no	—
342	#474	—	47	1	no	—
343	#474	—	47	1	no	—
344	#459	—	47	1	no	—
345	#459	—	47	1	no	—
346	#447	—	47	1	no	—
347	#447	—	47	1	no	—
348	C₄×D₈	—	47	1	no	—
349	C₄×D₈	—	47	1	no	—
350	C₄×D₈	—	47	1	no	—
351	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
352	#436	—	47	1	no	—
353	#436	—	47	1	no	—
354	#436	—	94	1	no	—
355	C₈×D₄	—	47	1	no	—
356	C₈×D₄	—	47	1	no	—
357	C₈×D₄	—	47	1	no	—
358	C₈×D₄	—	47	1	no	—
359	C₈×D₄	—	94	1	no	—
360	C₈×D₄	—	94	1	no	—
361	C₈×D₄	—	94	1	no	—
362	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
363	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
364	#431	—	47	1	no	—
365	#431	—	47	1	no	—
366	#423	—	47	1	no	—
367	C₂×C₄⋊C₈	—	47	1	no	—
368	#408	—	94	1	no	—
369	C₂×C₂²⋊C₈	—	94	1	no	—
370	C₂×C₄×C₈	—	47	1	no	—
371	#335	—	47	1	no	—
372	#335	—	47	1	no	—
373	#335	—	47	1	no	—
374	#335	C₂×D₄₇	1	1	yes	characteristic, complemented
375	D₄⋊C₈	—	47	1	no	—
376	D₄⋊C₈	—	47	1	no	—
377	D₄⋊C₈	—	47	1	no	—
378	D₄⋊C₈	—	47	1	no	—
379	D₄⋊C₈	—	47	1	no	—
380	D₄⋊C₈	—	47	1	no	—
381	D₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
382	D₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
383	#322	—	47	1	no	—
384	#322	—	47	1	no	—
385	C₈²	—	47	1	no	—
386	C₈²	C₂×D₄₇	1	1	yes	characteristic, complemented
387	C₄₇	#17900	1	1	yes	characteristic, complemented, Sylow
388	C₂×#41	—	94	1	no	—
389	C₂²×D₄	—	47	1	no	—
390	C₂³×C₄	—	94	1	no	—
391	C₂×D₈	—	47	1	no	—
392	C₂×D₈	—	47	1	no	—
393	C₂×D₈	—	47	1	no	—
394	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
395	#131	—	188	4	no	—
396	C₂×M₁₆	—	94	1	no	—
397	C₂×M₁₆	—	94	1	no	—
398	C₂×M₁₆	—	94	1	no	—
399	C₂²×C₈	—	2	1	no	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	47	1	no	—
402	C₂²×C₈	—	47	1	no	—
403	C₂²×C₈	—	94	1	no	—
404	C₂²×C₈	—	94	1	no	—
405	C₂²×C₈	—	94	1	no	—
406	C₂²×C₈	—	94	1	no	—
407	C₂²×C₈	—	94	1	no	—
408	C₂²×C₈	—	188	4	no	—
409	C₄⋊Q₈	—	47	1	no	—
410	#127	—	47	1	no	—
411	#124	—	94	1	no	—
412	#121	—	47	1	no	—
413	#121	—	47	1	no	—
414	#121	—	94	1	no	—
415	C₄×D₄	—	47	1	no	—
416	C₄×D₄	—	47	1	no	—
417	C₄×D₄	—	47	1	no	—
418	C₄×D₄	—	47	1	no	—
419	C₄×D₄	—	94	1	no	—
420	C₄×D₄	—	94	1	no	—
421	C₄×D₄	—	94	1	no	—
422	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
423	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
424	C₂×C₄⋊C₄	—	47	1	no	—
425	C₂×C₂²⋊C₄	—	94	1	no	—
426	C₂×C₄²	—	47	1	no	—
427	#107	—	47	1	no	—
428	#107	—	47	1	no	—
429	#107	—	47	1	no	—
430	#107	C₄×D₄₇	1	1	yes	characteristic
431	C₄⋊C₈	—	47	1	no	—
432	C₄⋊C₈	—	47	1	no	—
433	C₄⋊C₈	—	47	1	no	—
434	C₄⋊C₈	—	47	1	no	—
435	C₄⋊C₈	—	94	1	no	—
436	C₄⋊C₈	—	94	1	no	—
437	C₄⋊C₈	—	94	1	no	—
438	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
439	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
440	#102	—	47	1	no	—
441	#102	—	47	1	no	—
442	#102	—	47	1	no	—
443	#102	—	47	1	no	—
444	#102	—	47	1	no	—
445	#102	—	47	1	no	—
446	#102	C₄×D₄₇	1	1	yes	characteristic
447	#102	C₄×D₄₇	1	1	yes	characteristic
448	C₂²⋊C₈	—	2	1	no	—
449	C₂²⋊C₈	—	2	1	no	—
450	C₂²⋊C₈	—	47	1	no	—
451	C₂²⋊C₈	—	47	1	no	—
452	C₂²⋊C₈	—	94	1	no	—
453	C₂²⋊C₈	—	94	1	no	—
454	C₂²⋊C₈	—	94	1	no	—
455	C₂²⋊C₈	—	94	1	no	—
456	C₂²⋊C₈	—	94	1	no	—
457	C₂²⋊C₈	—	94	1	no	—
458	C₂²⋊C₈	—	94	1	no	—
459	C₄×C₈	—	47	1	no	—
460	C₄×C₈	—	47	1	no	—
461	C₄×C₈	—	47	1	no	—
462	C₄×C₈	—	47	1	no	—
463	C₄×C₈	—	47	1	no	—
464	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
465	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
466	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
467	C₂⁴	—	94	1	no	—
468	#41	—	188	2	no	—
469	#41	—	188	2	no	—
470	C₂×Q₈	—	94	1	no	—
471	C₂×D₄	—	47	1	no	—
472	C₂×D₄	—	47	1	no	—
473	C₂×D₄	—	94	1	no	—
474	C₂×D₄	—	94	1	no	—
475	C₂×D₄	—	94	1	no	—
476	C₂×D₄	—	94	1	no	—
477	C₂×D₄	—	94	2	no	—
478	C₂×D₄	—	94	2	no	—
479	C₂×D₄	—	94	1	no	—
480	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
481	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	47	1	no	—
485	C₂²×C₄	—	47	1	no	—
486	C₂²×C₄	—	47	1	no	—
487	C₂²×C₄	—	94	1	no	—
488	C₂²×C₄	—	94	1	no	—
489	C₂²×C₄	—	94	1	no	—
490	C₂²×C₄	—	94	1	no	—
491	C₂²×C₄	—	94	1	no	—
492	C₂²×C₄	—	188	2	no	—
493	C₂²×C₄	—	188	2	no	—
494	D₈	—	2	2	no	—
495	D₈	—	94	2	no	—
496	D₈	—	94	2	no	—
497	D₈	—	94	2	no	—
498	M₁₆	—	188	2	no	—
499	M₁₆	—	188	2	no	—
500	M₁₆	—	188	2	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	4	2	no	—
505	C₂×C₈	—	4	2	no	—
506	C₂×C₈	—	47	1	no	—
507	C₂×C₈	—	47	4	no	—
508	C₂×C₈	—	47	1	no	—
509	C₂×C₈	—	47	1	no	—
510	C₂×C₈	—	47	1	no	—
511	C₂×C₈	—	94	2	no	—
512	C₂×C₈	—	94	1	no	—
513	C₂×C₈	—	94	1	no	—
514	C₂×C₈	—	94	1	no	—
515	C₂×C₈	—	188	2	no	—
516	C₂×C₈	—	188	2	no	—
517	C₂×C₈	—	188	2	no	—
518	C₂×C₈	—	188	2	no	—
519	C₂×C₈	—	188	2	no	—
520	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
521	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
522	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
523	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
524	C₄⋊C₄	—	47	1	no	—
525	C₄⋊C₄	—	47	1	no	—
526	C₄⋊C₄	—	94	1	no	—
527	C₄⋊C₄	—	94	1	no	—
528	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
529	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
530	C₂²⋊C₄	—	2	1	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	94	1	no	—
533	C₂²⋊C₄	—	94	1	no	—
534	C₂²⋊C₄	—	94	1	no	—
535	C₂²⋊C₄	—	94	1	no	—
536	C₂²⋊C₄	—	94	1	no	—
537	C₂²⋊C₄	—	94	1	no	—
538	C₄²	—	47	1	no	—
539	C₄²	—	47	1	no	—
540	C₄²	—	47	1	no	—
541	C₄²	C₂³×D₄₇	1	1	yes	characteristic
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	47	1	no	—
545	C₂³	—	94	4	no	—
546	C₂³	—	94	1	no	—
547	C₂³	—	94	1	no	—
548	C₂³	—	188	2	no	—
549	C₂³	—	188	2	no	—
550	Q₈	—	188	2	no	—
551	D₄	—	2	1	no	—
552	D₄	—	2	1	no	—
553	D₄	—	2	1	no	—
554	D₄	—	47	2	no	—
555	D₄	—	94	4	no	—
556	D₄	—	94	1	no	—
557	D₄	—	94	1	no	—
558	D₄	—	94	1	no	—
559	D₄	—	188	2	no	—
560	D₄	—	188	2	no	—
561	D₄	—	188	2	no	—
562	D₄	—	188	2	no	—
563	D₄	#13094030	1	2	yes	complemented
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	47	1	no	—
571	C₂×C₄	—	47	2	no	—
572	C₂×C₄	—	47	2	no	—
573	C₂×C₄	—	47	1	no	—
574	C₂×C₄	—	47	1	no	—
575	C₂×C₄	—	94	1	no	—
576	C₂×C₄	—	94	1	no	—
577	C₂×C₄	—	94	1	no	—
578	C₂×C₄	—	94	1	no	—
579	C₂×C₄	—	188	1	no	—
580	C₂×C₄	—	188	2	no	—
581	C₂×C₄	—	188	2	no	—
582	C₂×C₄	—	188	2	no	—
583	C₂×C₄	—	188	1	no	—
584	C₂×C₄	—	188	1	no	—
585	C₂×C₄	—	188	1	no	—
586	C₂×C₄	—	188	1	no	—
587	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
588	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
589	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
590	C₈	—	2	1	no	—
591	C₈	—	2	1	no	—
592	C₈	—	2	1	no	—
593	C₈	—	4	1	no	—
594	C₈	—	4	1	no	—
595	C₈	—	4	1	no	—
596	C₈	—	47	2	no	—
597	C₈	—	94	1	no	—
598	C₈	—	94	1	no	—
599	C₈	—	94	1	no	—
600	C₈	—	188	1	no	—
601	C₈	—	188	1	no	—
602	C₈	—	188	1	no	—
603	C₈	D₈×D₄₇	1	2	yes	—
604	C₂²	—	2	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	47	2	no	—
611	C₂²	—	94	1	no	—
612	C₂²	—	94	1	no	—
613	C₂²	—	94	2	no	—
614	C₂²	—	188	8	no	—
615	C₂²	—	188	1	no	—
616	C₂²	—	188	1	no	—
617	C₂²	—	188	1	no	—
618	C₂²	—	188	1	no	—
619	C₂²	—	188	1	no	—
620	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
621	C₄	—	2	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	47	2	no	—
625	C₄	—	94	1	no	—
626	C₄	—	94	1	no	—
627	C₄	—	188	1	no	—
628	C₄	—	188	1	no	—
629	C₄	#131×D₄₇	1	1	yes	characteristic
630	C₄	C₂×#13094030	1	1	yes	characteristic
631	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
632	C₄	#135×D₄₇	1	1	yes	characteristic
633	C₂	—	4	2	no	—
634	C₂	—	8	1	no	—
635	C₂	—	94	2	no	—
636	C₂	—	376	1	no	—
637	C₂	—	188	2	no	—
638	C₂	#20252077	1	1	yes	characteristic
639	C₂	C₄×D₈×D₄₇	1	1	yes	characteristic
640	C₂	#20252286	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253386	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×D₈	D₄₇
hypocenter	C₄₇	#17900
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
2. #20252095	C₂	semidirect
3. C₈×D₄×D₄₇	C₂	semidirect
4. #20242220	C₂	semidirect
5. #20242218	C₂	semidirect
6. #20242216	C₂	semidirect
7. #20242214	C₂	semidirect
8. C₈×D₃₇₆	C₂	semidirect
9. C₈×#10625334	C₂	semidirect
10. C₈×#10625334	C₂	semidirect
11. #20242161	C₂	semidirect
12. #20241811	C₂	semidirect
13. #20241785	C₂	semidirect
14. #20241670	C₂	semidirect
15. C₈×D₈×C₄₇	C₂	semidirect
31. #15689201	C₂²	semidirect
32. #15689200	C₂²	semidirect
35. C₈×D₁₈₈	C₂²	semidirect
48. #15688876	C₂²	semidirect
49. #15688875	C₂²	semidirect
50. #15688875	C₂²	semidirect
52. #15688852	C₂²	semidirect
54. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
56. #15688850	C₂²	semidirect
57. #15688845	C₂²	semidirect
58. #15688845	C₂²	semidirect
59. C₈×C₄₇⋊C₈	C₂²	semidirect
62. C₈×D₄×C₄₇	C₂²	semidirect
63. C₄₇×#335	C₂²	semidirect
65. C₄₇×D₄⋊C₈	C₂²	semidirect
66. C₈²×C₄₇	C₂²	semidirect
220. C₈×D₄₇	D₈	semidirect
232. D₄×C₄₇	#131	semidirect
256. D₁₈₈	#131	semidirect
323. C₈×D₈	D₄₇	semidirect
363. C₈×D₄	C₂×D₄₇	semidirect
374. #335	C₂×D₄₇	semidirect
382. D₄⋊C₈	C₂×D₄₇	semidirect
386. C₈²	C₂×D₄₇	semidirect
387. C₄₇	#17900	semidirect
563. D₄	#13094030	semidirect

Maximal subgroups

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

subgroup	index
#20253386	2
#20252095	2
C₈×D₄×D₄₇	2
#20242220	2
#20242218	2
#20242216	2
#20242214	2
C₈×D₃₇₆	2
C₈×#10625334	2
#20242161	2
#20241811	2
#20241785	2
#20241670	2
C₈×D₈×C₄₇	2
#17900	47