Subgroups — #27097783

Order 12032.

2000 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256998	C₂	1	2	yes	maximal, complemented
2	#20256401	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256256	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256050	C₂	1	2	yes	maximal, complemented
5	#20255791	C₂	1	2	yes	maximal, complemented
6	#20255781	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255240	C₂	1	4	yes	maximal, complemented
8	#20255213	C₂	1	2	yes	maximal, complemented
9	#20255075	C₂	1	2	yes	maximal, complemented
10	D₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253967	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253958	C₂	1	2	yes	maximal, complemented
13	#20253449	C₂	1	2	yes	maximal, complemented
14	#20253437	C₂	1	4	yes	maximal, complemented
15	C₄×#13094046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×D₃₇₆	C₂	1	2	yes	maximal, complemented
17	C₈×#41×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13094046	C₂²	1	1	yes	characteristic
19	C₂²×D₃₇₆	C₂²	1	2	yes	—
20	#15689858	C₂²	1	2	yes	complemented
21	#15689833	C₂²	1	2	yes	complemented
22	#15689830	C₂²	1	2	yes	—
23	#15689819	C₂²	1	4	yes	complemented
24	#15689817	—	2	2	no	—
25	#15689797	—	2	4	no	—
26	#15689769	C₂²	1	4	yes	complemented
27	#15689761	—	2	2	no	—
28	D₄×D₁₈₈	C₂²	1	2	yes	—
29	#15689673	C₂²	1	2	yes	complemented
30	#15689660	—	2	2	no	—
31	#15689657	C₂²	1	4	yes	complemented
32	#15689632	—	2	4	no	—
33	C₄×#10625350	C₂²	1	2	yes	complemented
34	C₂×C₄×D₁₈₈	C₂²	1	4	yes	complemented
35	C₄×D₄×D₄₇	—	2	2	no	—
36	#15689528	C₂²	1	1	yes	characteristic, complemented
37	#15689525	C₂²	1	2	yes	complemented
38	#15689507	C₂²	1	2	yes	complemented
39	#15689500	C₂²	1	1	yes	characteristic
40	#15689478	C₂²	1	4	yes	complemented
41	#15689470	C₂²	1	2	yes	complemented
42	#15689459	C₂²	1	4	yes	complemented
43	#15689448	C₂²	1	4	yes	complemented
44	#15689442	C₂²	1	4	yes	complemented
45	#15689424	C₂²	1	4	yes	complemented
46	#15689424	C₂²	1	4	yes	complemented
47	#15689419	C₂²	1	2	yes	complemented
48	#15689414	C₂²	1	2	yes	complemented
49	#15689364	C₂²	1	2	yes	complemented
50	#15689359	C₂²	1	2	yes	—
51	#15689359	C₂²	1	2	yes	complemented
52	#15689359	C₂²	1	2	yes	complemented
53	#15689352	C₂²	1	4	yes	complemented
54	#15689339	C₂²	1	4	yes	complemented
55	#15689339	C₂²	1	4	yes	complemented
56	#15689324	C₂²	1	2	yes	complemented
57	#15689319	C₂²	1	2	yes	—
58	#15689276	C₂²	1	4	yes	complemented
59	#15689270	C₂²	1	4	yes	complemented
60	#15689259	C₂²	1	4	yes	—
61	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
62	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic, complemented
63	C₄×#10625325	C₂²	1	2	yes	complemented
64	C₄×#10625325	C₂²	1	2	yes	complemented
65	C₄×#10625325	C₂²	1	4	yes	complemented
66	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
67	C₄×D₃₇₆	C₂²	1	2	yes	—
68	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
69	C₄×D₃₇₆	C₂²	1	2	yes	complemented
70	C₄×D₃₇₆	C₂²	1	4	yes	complemented
71	C₄×D₃₇₆	C₂²	1	4	yes	complemented
72	C₄×D₃₇₆	C₂²	1	2	yes	complemented
73	C₄×D₃₇₆	C₂²	1	2	yes	complemented
74	#15689161	C₂²	1	1	yes	characteristic, complemented
75	C₂×#13093958	C₂²	1	2	yes	complemented
76	#15689120	C₂²	1	2	yes	complemented
77	C₂×#13093946	C₂²	1	4	yes	complemented
78	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
79	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
80	C₈×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
81	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
82	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
83	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
84	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
85	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
86	C₄₇×#431	C₂²	1	2	yes	complemented
87	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
89	C₂×#10625350	—	2	2	no	—
90	C₂×#10625350	C₂³	1	2	yes	—
91	C₂²×D₁₈₈	C₂³	1	4	yes	—
92	C₂×D₄×D₄₇	—	2	2	no	—
93	C₂²×C₄×D₄₇	—	2	4	no	—
94	#13094046	—	2	4	no	—
95	C₂×Dic₁₈₈	C₂³	1	1	yes	characteristic
96	C₂×#10625325	C₂³	1	2	yes	—
97	C₂×#10625325	C₂³	1	4	yes	—
98	C₂×D₃₇₆	—	2	8	no	—
99	C₂×D₃₇₆	C₂³	1	2	yes	—
100	C₂×D₃₇₆	C₂³	1	4	yes	—
101	C₂×D₃₇₆	C₂³	1	2	yes	—
102	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
103	#13094024	C₂³	1	2	yes	—
104	#13094021	C₂³	1	2	yes	—
105	#13094019	—	2	4	no	—
106	#13094018	—	2	4	no	—
107	#13094016	C₂³	1	4	yes	—
108	#13094015	—	2	2	no	—
109	#13094013	—	2	2	no	—
110	#13094012	—	2	2	no	—
111	#13094012	C₂³	1	4	yes	—
112	#13094009	—	2	4	no	—
113	#13094009	—	2	4	no	—
114	#13094007	—	2	4	no	—
115	#13094006	—	2	4	no	—
116	#13094003	C₂³	1	4	yes	—
117	#13094002	—	2	4	no	—
118	#13094001	—	2	4	no	—
119	#13094000	—	2	2	no	—
120	#13093999	—	2	2	no	—
121	#13093998	—	2	2	no	—
122	#13093998	C₂³	1	4	yes	—
123	#13093998	C₂³	1	4	yes	—
124	#13093997	—	2	4	no	—
125	#13093996	—	2	4	no	—
126	#13093994	—	2	4	no	—
127	#13093992	—	2	4	no	—
128	C₄×Dic₉₄	C₂³	1	2	yes	—
129	C₄×Dic₉₄	C₂³	1	2	yes	—
130	C₄×D₁₈₈	—	2	4	no	—
131	C₄×D₁₈₈	—	2	2	no	—
132	C₄×D₁₈₈	—	2	4	no	—
133	C₄×D₁₈₈	C₂³	1	2	yes	—
134	C₄×D₁₈₈	C₂³	1	4	yes	—
135	C₄×D₁₈₈	C₂³	1	4	yes	—
136	C₄×D₁₈₈	C₂³	1	2	yes	—
137	C₄×D₁₈₈	C₂³	1	4	yes	—
138	D₄×Dic₄₇	—	2	2	no	—
139	#13093986	—	2	2	no	—
140	C₄×C₂²⋊D₄₇	—	2	2	no	—
141	C₄×C₂²⋊D₄₇	—	2	4	no	—
142	C₄×C₂²⋊D₄₇	—	2	2	no	—
143	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
144	#13093983	C₂³	1	2	yes	—
145	#13093981	—	2	2	no	—
146	#13093981	—	2	4	no	—
147	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
148	C₄⋊C₄×D₄₇	—	2	2	no	—
149	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
150	C₂²⋊C₄×D₄₇	—	2	4	no	—
151	C₄²×D₄₇	—	2	2	no	—
152	#13093958	C₂³	1	1	yes	characteristic
153	#13093958	C₂³	1	1	yes	characteristic
154	#13093958	C₂³	1	2	yes	—
155	#13093958	C₂³	1	2	yes	—
156	#13093958	C₂³	1	4	yes	—
157	#13093956	C₂³	1	4	yes	—
158	#13093956	C₂³	1	2	yes	—
159	#13093949	C₂³	1	2	yes	—
160	#13093949	C₂³	1	2	yes	—
161	#13093949	C₂³	1	4	yes	—
162	#13093946	C₂³	1	4	yes	—
163	#13093946	C₂³	1	4	yes	—
164	#13093946	C₂³	1	2	yes	—
165	#13093946	C₂³	1	4	yes	—
166	#13093946	C₂³	1	4	yes	—
167	#13093946	C₂³	1	4	yes	—
168	#13093946	C₂³	1	2	yes	—
169	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
170	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
171	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
172	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
173	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
175	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
177	C₄×D₄×C₄₇	D₄	1	2	yes	—
178	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₄₇	C₂³	1	2	yes	—
180	#117×C₄₇	D₄	1	2	yes	—
181	#117×C₄₇	D₄	1	1	yes	characteristic
182	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
184	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
185	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
186	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
187	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
188	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₄₇	C₂³	1	2	yes	—
191	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₄₇	C₂³	1	2	yes	—
194	C₄×C₈×C₄₇	C₂³	1	2	yes	—
195	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₇	C₂³	1	2	yes	—
197	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
198	C₂³×D₄₇	—	2	4	no	—
199	#41×C₄₇	—	2	4	no	—
200	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
209	C₂×C₂²⋊D₄₇	—	2	4	no	—
210	C₂×C₂²⋊D₄₇	—	2	2	no	—
211	C₂×C₂²⋊D₄₇	—	2	4	no	—
212	C₂²×Dic₄₇	—	2	4	no	—
213	D₄×D₄₇	—	4	8	no	—
214	#10625350	—	2	4	no	—
215	#10625350	—	4	2	no	—
216	#10625350	—	8	4	no	—
217	C₂×D₁₈₈	—	2	8	no	—
218	C₂×D₁₈₈	—	2	2	no	—
219	C₂×D₁₈₈	—	2	4	no	—
220	C₂×D₁₈₈	—	2	2	no	—
221	C₂×D₁₈₈	—	4	4	no	—
222	C₂×D₁₈₈	C₂⁴	1	4	yes	—
223	C₂×D₁₈₈	C₂⁴	1	2	yes	—
224	C₂×C₄×D₄₇	—	2	2	no	—
225	C₂×C₄×D₄₇	—	2	2	no	—
226	C₂×C₄×D₄₇	—	2	2	no	—
227	C₂×C₄×D₄₇	—	2	4	no	—
228	C₂×C₄×D₄₇	—	2	4	no	—
229	C₂×C₄×D₄₇	—	2	4	no	—
230	C₂×C₄×D₄₇	—	8	8	no	—
231	C₂×Dic₉₄	—	2	2	no	—
232	C₂×Dic₉₄	C₂⁴	1	2	yes	—
233	C₂×C₈×C₄₇	—	2	4	no	—
234	C₂×C₈×C₄₇	—	2	2	no	—
235	C₂×C₈×C₄₇	—	4	2	no	—
236	C₂×C₈×C₄₇	—	4	1	no	—
237	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
239	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
240	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
244	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
246	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
247	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
249	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
250	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₄₇	C₂×D₄	1	2	yes	—
252	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
253	C₄²×C₄₇	C₂×D₄	1	2	yes	—
254	C₄²×C₄₇	C₂⁴	1	2	yes	—
255	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
256	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
257	C₂²⋊Dic₄₇	—	2	4	no	—
258	C₂²⋊Dic₄₇	—	2	2	no	—
259	(C₂×D₄₇)⋊C₄	—	2	4	no	—
260	(C₂×D₄₇)⋊C₄	—	2	4	no	—
261	(C₂×D₄₇)⋊C₄	—	2	2	no	—
262	(C₂×D₄₇)⋊C₄	—	2	4	no	—
263	(C₂×D₄₇)⋊C₄	—	2	4	no	—
264	(C₂×D₄₇)⋊C₄	—	2	4	no	—
265	(C₂×D₄₇)⋊C₄	—	2	2	no	—
266	(C₂×D₄₇)⋊C₄	—	2	4	no	—
267	(C₂×D₄₇)⋊C₄	—	2	4	no	—
268	C₄⋊Dic₄₇	—	2	2	no	—
269	C₄⋊Dic₄₇	—	2	4	no	—
270	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
271	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
272	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
273	Dic₄₇⋊C₄	—	2	4	no	—
274	Dic₄₇⋊C₄	—	2	2	no	—
275	Dic₄₇⋊C₄	—	2	2	no	—
276	Dic₄₇⋊C₄	—	2	4	no	—
277	Dic₄₇⋊C₄	—	2	4	no	—
278	C₄×Dic₄₇	—	2	2	no	—
279	C₄×Dic₄₇	—	2	2	no	—
280	C₄×Dic₄₇	—	2	2	no	—
281	Dic₁₈₈	—	2	2	no	—
282	D₃₇₆	—	2	8	no	—
283	D₃₇₆	—	2	4	no	—
284	D₃₇₆	—	4	2	no	—
285	D₃₇₆	#41	1	4	yes	complemented
286	#10625325	—	2	4	no	—
287	#10625325	—	4	4	no	—
288	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
289	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
290	C₂²×D₄₇	—	2	2	no	—
291	C₂²×D₄₇	—	2	4	no	—
292	C₂²×D₄₇	—	4	8	no	—
293	C₂²×D₄₇	—	4	8	no	—
294	C₂²×D₄₇	—	8	4	no	—
295	Q₈×C₄₇	—	2	2	no	—
296	D₄×C₄₇	—	2	4	no	—
297	D₄×C₄₇	#135	1	4	yes	complemented
298	C₂×C₄×C₄₇	—	2	4	no	—
299	C₂×C₄×C₄₇	—	2	2	no	—
300	C₂×C₄×C₄₇	—	2	4	no	—
301	C₂×C₄×C₄₇	—	2	2	no	—
302	C₂×C₄×C₄₇	—	2	2	no	—
303	C₂×C₄×C₄₇	—	2	1	no	—
304	C₂×C₄×C₄₇	—	2	2	no	—
305	C₂×C₄×C₄₇	—	2	1	no	—
306	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
315	C₂²⋊D₄₇	—	4	4	no	—
316	C₂²⋊D₄₇	—	4	8	no	—
317	C₂²⋊D₄₇	—	8	4	no	—
318	C₂×Dic₄₇	—	2	2	no	—
319	C₂×Dic₄₇	—	2	2	no	—
320	C₂×Dic₄₇	—	2	2	no	—
321	C₂×Dic₄₇	—	2	4	no	—
322	C₂×Dic₄₇	—	8	4	no	—
323	D₁₈₈	—	2	4	no	—
324	D₁₈₈	—	2	2	no	—
325	D₁₈₈	—	2	4	no	—
326	D₁₈₈	—	4	8	no	—
327	D₁₈₈	—	4	4	no	—
328	D₁₈₈	—	8	2	no	—
329	D₁₈₈	C₂×#41	1	4	yes	—
330	C₄×D₄₇	—	4	4	no	—
331	C₄×D₄₇	—	4	4	no	—
332	C₄×D₄₇	—	4	4	no	—
333	C₄×D₄₇	—	4	8	no	—
334	C₄×D₄₇	—	8	4	no	—
335	C₄×D₄₇	—	8	4	no	—
336	Dic₉₄	—	2	2	no	—
337	Dic₉₄	—	2	2	no	—
338	Dic₉₄	—	8	2	no	—
339	C₈×C₄₇	—	2	1	no	—
340	C₈×C₄₇	—	2	2	no	—
341	C₈×C₄₇	—	2	2	no	—
342	C₈×C₄₇	—	2	1	no	—
343	C₈×C₄₇	—	2	1	no	—
344	C₈×C₄₇	C₂×#41	1	2	yes	—
345	#61431	—	47	1	no	maximal, Sylow
346	C₂²×C₄₇	—	2	2	no	—
347	C₂²×C₄₇	—	2	2	no	—
348	C₂²×C₄₇	—	2	1	no	—
349	C₂²×C₄₇	—	2	1	no	—
350	C₂²×C₄₇	—	2	1	no	—
351	C₂²×C₄₇	C₂×#135	1	4	yes	—
352	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
353	C₂×D₄₇	—	2	4	no	—
354	C₂×D₄₇	—	4	2	no	—
355	C₂×D₄₇	—	4	2	no	—
356	C₂×D₄₇	—	4	4	no	—
357	C₂×D₄₇	—	4	4	no	—
358	C₂×D₄₇	—	4	4	no	—
359	C₂×D₄₇	—	8	16	no	—
360	C₄×C₄₇	—	2	1	no	—
361	C₄×C₄₇	—	2	2	no	—
362	C₄×C₄₇	—	2	1	no	—
363	C₄×C₄₇	—	2	2	no	—
364	C₄×C₄₇	—	2	1	no	—
365	C₄×C₄₇	—	2	2	no	—
366	C₄×C₄₇	C₂×#135	1	2	yes	—
367	C₄×C₄₇	#576	1	2	yes	—
368	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
369	C₄×C₄₇	#585	1	1	yes	characteristic
370	Dic₄₇	—	4	2	no	—
371	Dic₄₇	—	4	2	no	—
372	Dic₄₇	—	4	4	no	—
373	Dic₄₇	—	4	2	no	—
374	#3481	—	47	2	no	—
375	#3396	—	47	1	no	—
376	#3380	—	47	1	no	—
377	#3361	—	47	2	no	—
378	#3339	—	47	2	no	—
379	#3338	—	47	1	no	—
380	#3297	—	47	4	no	—
381	#3295	—	47	2	no	—
382	#3280	—	47	2	no	—
383	D₄×D₈	—	47	1	no	—
384	#3169	—	47	1	no	—
385	#3168	—	47	2	no	—
386	#3106	—	47	2	no	—
387	#3105	—	47	4	no	—
388	C₈×#41	D₄₇	1	1	yes	characteristic, complemented
389	C₄×#135	—	47	1	no	—
390	C₂×C₄×D₈	—	47	2	no	—
391	C₂×C₄₇	—	2	4	no	—
392	C₂×C₄₇	—	4	1	no	—
393	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
394	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
395	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
396	D₄₇	—	4	4	no	—
397	D₄₇	—	8	4	no	—
398	C₂×#135	—	47	1	no	—
399	C₂²×D₈	—	47	2	no	—
400	#559	—	47	2	no	—
401	#554	—	47	2	no	—
402	#554	—	47	2	no	—
403	#553	—	47	4	no	—
404	#553	—	94	2	no	—
405	#551	—	94	4	no	—
406	#546	—	47	4	no	—
407	#546	—	94	2	no	—
408	D₄²	—	47	2	no	—
409	#532	—	47	2	no	—
410	#529	—	47	4	no	—
411	#529	—	94	2	no	—
412	#525	—	94	4	no	—
413	C₄×#41	—	47	2	no	—
414	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
415	C₂×C₄×D₄	—	47	4	no	—
416	C₂×C₄×D₄	—	94	2	no	—
417	#500	—	47	1	no	—
418	#499	—	47	2	no	—
419	#495	—	47	2	no	—
420	#493	—	47	1	no	—
421	#488	—	47	4	no	—
422	#486	—	47	2	no	—
423	#484	—	47	4	no	—
424	#482	—	47	4	no	—
425	#481	—	47	4	no	—
426	#478	—	47	4	no	—
427	#478	—	47	4	no	—
428	#477	—	47	2	no	—
429	#476	—	47	2	no	—
430	#467	—	47	2	no	—
431	#466	—	47	2	no	—
432	#466	—	47	2	no	—
433	#466	—	47	2	no	—
434	#465	—	47	4	no	—
435	#463	—	47	4	no	—
436	#463	—	47	4	no	—
437	#460	—	47	2	no	—
438	#459	—	47	2	no	—
439	#450	—	47	4	no	—
440	#449	—	47	4	no	—
441	#447	—	47	4	no	—
442	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
443	C₈×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
444	C₄×Q₁₆	—	47	1	no	—
445	C₄×Q₁₆	—	47	1	no	—
446	C₄×SD₁₆	—	47	2	no	—
447	C₄×SD₁₆	—	47	4	no	—
448	C₄×SD₁₆	—	47	2	no	—
449	C₄×D₈	—	47	2	no	—
450	C₄×D₈	—	47	2	no	—
451	C₄×D₈	—	47	4	no	—
452	C₄×D₈	—	47	4	no	—
453	C₄×D₈	—	47	2	no	—
454	C₄×D₈	—	47	1	no	—
455	C₄×D₈	—	47	2	no	—
456	C₄×D₈	—	47	1	no	—
457	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
458	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
459	C₈×D₄	C₂×D₄₇	1	2	yes	complemented
460	C₈×D₄	C₂×D₄₇	1	2	yes	complemented
461	#431	C₂×D₄₇	1	2	yes	complemented
462	#431	C₂×D₄₇	1	1	yes	characteristic, complemented
463	#427	—	47	1	no	—
464	C₂×#107	—	47	2	no	—
465	#416	—	47	2	no	—
466	C₂×#102	—	47	4	no	—
467	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	complemented
468	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
469	C₄₇	#61431	1	1	yes	characteristic, complemented, Sylow
470	C₂×#41	—	47	2	no	—
471	C₂×#41	—	94	2	no	—
472	C₂×#41	D₁₈₈	1	1	yes	characteristic
473	C₂²×D₄	—	47	4	no	—
474	C₂²×D₄	—	94	2	no	—
475	C₂³×C₄	—	94	4	no	—
476	#135	—	94	4	no	—
477	C₂×Q₁₆	—	47	1	no	—
478	C₂×SD₁₆	—	47	2	no	—
479	C₂×SD₁₆	—	47	4	no	—
480	C₂×D₈	—	47	1	no	—
481	C₂×D₈	—	47	4	no	—
482	C₂×D₈	—	47	2	no	—
483	C₂×D₈	—	47	2	no	—
484	C₂×D₈	—	94	8	no	—
485	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
486	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
487	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
488	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
489	C₄⋊Q₈	—	47	2	no	—
490	#127	—	47	2	no	—
491	#126	—	94	4	no	—
492	#126	—	94	4	no	—
493	#125	—	47	4	no	—
494	#125	—	94	2	no	—
495	#124	—	47	4	no	—
496	#124	—	94	2	no	—
497	#124	—	94	2	no	—
498	#123	—	94	4	no	—
499	#123	—	94	4	no	—
500	#123	—	94	4	no	—
501	#123	—	94	4	no	—
502	C₂²⋊Q₈	—	47	4	no	—
503	C₂²⋊Q₈	—	94	2	no	—
504	C₂²⋊Q₈	—	94	4	no	—
505	C₂²⋊Q₈	—	94	4	no	—
506	#121	—	47	4	no	—
507	#121	—	47	4	no	—
508	#121	—	94	4	no	—
509	#121	—	94	2	no	—
510	#121	—	94	2	no	—
511	#121	—	94	4	no	—
512	#120	—	94	4	no	—
513	#120	—	94	4	no	—
514	C₄×Q₈	—	47	2	no	—
515	C₄×Q₈	—	47	2	no	—
516	C₄×Q₈	D₁₈₈	1	1	yes	characteristic
517	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
518	C₄×D₄	—	47	2	no	—
519	C₄×D₄	—	47	4	no	—
520	C₄×D₄	—	47	4	no	—
521	C₄×D₄	—	47	4	no	—
522	C₄×D₄	—	47	2	no	—
523	C₄×D₄	—	94	2	no	—
524	C₄×D₄	—	94	4	no	—
525	C₄×D₄	—	94	2	no	—
526	C₄×D₄	—	94	2	no	—
527	C₄×D₄	—	94	2	no	—
528	C₄×D₄	—	94	4	no	—
529	C₄×D₄	—	94	4	no	—
530	C₄×D₄	—	94	4	no	—
531	C₄×D₄	—	94	2	no	—
532	C₄×D₄	D₁₈₈	1	1	yes	characteristic
533	C₄×D₄	D₁₈₈	1	2	yes	—
534	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
535	C₄×D₄	C₂²×D₄₇	1	2	yes	—
536	#117	—	47	2	no	—
537	#117	—	94	2	no	—
538	#117	—	94	4	no	—
539	#117	D₁₈₈	1	2	yes	—
540	#117	D₁₈₈	1	1	yes	characteristic
541	C₂×C₄⋊C₄	—	47	4	no	—
542	C₂×C₄⋊C₄	—	94	2	no	—
543	C₂×C₂²⋊C₄	—	94	4	no	—
544	C₂×C₂²⋊C₄	—	94	4	no	—
545	C₂×C₄²	—	94	2	no	—
546	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
547	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
548	#107	—	47	1	no	—
549	#107	—	47	2	no	—
550	#107	—	47	4	no	—
551	#107	—	47	1	no	—
552	#107	—	47	2	no	—
553	#106	—	47	2	no	—
554	#106	—	47	4	no	—
555	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
556	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
557	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
558	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
559	#103	—	47	2	no	—
560	#103	—	47	2	no	—
561	#103	—	47	4	no	—
562	#102	—	47	2	no	—
563	#102	—	47	4	no	—
564	#102	—	47	4	no	—
565	#102	—	47	4	no	—
566	#102	—	47	2	no	—
567	#102	—	47	4	no	—
568	#102	—	47	4	no	—
569	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
570	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
571	C₂²⋊C₈	C₂²×D₄₇	1	2	yes	—
572	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
573	C₄×C₈	C₂²×D₄₇	1	2	yes	—
574	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
575	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
576	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
577	C₄×C₈	C₂²×D₄₇	1	2	yes	—
578	C₄×C₈	C₂²×D₄₇	1	2	yes	—
579	C₂⁴	—	94	4	no	—
580	#41	—	2	4	no	—
581	#41	—	94	4	no	—
582	#41	—	376	4	no	—
583	#41	—	188	2	no	—
584	C₂×Q₈	—	47	2	no	—
585	C₂×Q₈	—	94	2	no	—
586	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
587	C₂×D₄	—	47	2	no	—
588	C₂×D₄	—	47	4	no	—
589	C₂×D₄	—	94	8	no	—
590	C₂×D₄	—	94	4	no	—
591	C₂×D₄	—	94	2	no	—
592	C₂×D₄	—	94	4	no	—
593	C₂×D₄	—	94	2	no	—
594	C₂×D₄	—	94	4	no	—
595	C₂×D₄	—	94	2	no	—
596	C₂×D₄	—	188	4	no	—
597	C₂×D₄	—	188	8	no	—
598	C₂×D₄	C₂×D₁₈₈	1	2	yes	—
599	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
600	C₂²×C₄	—	94	4	no	—
601	C₂²×C₄	—	94	4	no	—
602	C₂²×C₄	—	94	4	no	—
603	C₂²×C₄	—	94	2	no	—
604	C₂²×C₄	—	94	2	no	—
605	C₂²×C₄	—	94	2	no	—
606	C₂²×C₄	—	94	4	no	—
607	C₂²×C₄	—	376	8	no	—
608	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
609	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
611	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
612	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
613	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
614	Q₁₆	—	94	2	no	—
615	SD₁₆	—	94	4	no	—
616	SD₁₆	—	188	4	no	—
617	D₈	—	47	4	no	—
618	D₈	—	94	8	no	—
619	D₈	—	94	4	no	—
620	D₈	—	188	2	no	—
621	C₂×C₈	—	2	4	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	4	1	no	—
624	C₂×C₈	—	4	2	no	—
625	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
626	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
627	C₂×C₈	C₂³×D₄₇	1	2	yes	—
628	C₂×C₈	C₂³×D₄₇	1	2	yes	—
629	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
630	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
631	C₄⋊C₄	—	47	2	no	—
632	C₄⋊C₄	—	47	2	no	—
633	C₄⋊C₄	—	47	4	no	—
634	C₄⋊C₄	—	94	4	no	—
635	C₄⋊C₄	—	94	2	no	—
636	C₄⋊C₄	—	94	2	no	—
637	C₄⋊C₄	—	94	4	no	—
638	C₄⋊C₄	—	94	4	no	—
639	C₄⋊C₄	—	94	4	no	—
640	C₄⋊C₄	—	94	2	no	—
641	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
642	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
643	C₄⋊C₄	C₂×D₁₈₈	1	1	yes	characteristic
644	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
645	C₂²⋊C₄	—	94	4	no	—
646	C₂²⋊C₄	—	94	2	no	—
647	C₂²⋊C₄	—	94	2	no	—
648	C₂²⋊C₄	—	94	4	no	—
649	C₂²⋊C₄	—	94	4	no	—
650	C₂²⋊C₄	—	94	4	no	—
651	C₂²⋊C₄	—	94	4	no	—
652	C₂²⋊C₄	—	94	4	no	—
653	C₂²⋊C₄	—	94	2	no	—
654	C₂²⋊C₄	—	94	4	no	—
655	C₂²⋊C₄	—	94	4	no	—
656	C₂²⋊C₄	C₂×D₁₈₈	1	2	yes	—
657	C₂²⋊C₄	C₂×D₁₈₈	1	2	yes	—
658	C₂²⋊C₄	C₂×D₁₈₈	1	2	yes	—
659	C₄²	—	94	2	no	—
660	C₄²	—	94	2	no	—
661	C₄²	—	94	2	no	—
662	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
663	C₄²	C₂×D₁₈₈	1	2	yes	—
664	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
665	C₄²	C₂×D₁₈₈	1	2	yes	—
666	C₄²	C₂³×D₄₇	1	2	yes	—
667	C₄²	C₂³×D₄₇	1	1	yes	characteristic
668	C₄²	C₂³×D₄₇	1	1	yes	characteristic
669	C₂³	—	94	2	no	—
670	C₂³	—	94	4	no	—
671	C₂³	—	376	4	no	—
672	C₂³	—	188	8	no	—
673	C₂³	—	188	8	no	—
674	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
675	C₂³	C₂²×D₁₈₈	1	2	yes	—
676	Q₈	—	2	2	no	—
677	Q₈	—	94	2	no	—
678	Q₈	—	94	2	no	—
679	Q₈	—	376	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	47	4	no	—
682	D₄	—	94	4	no	—
683	D₄	—	94	2	no	—
684	D₄	—	94	4	no	—
685	D₄	—	376	2	no	—
686	D₄	—	376	4	no	—
687	D₄	—	188	8	no	—
688	D₄	—	188	4	no	—
689	D₄	—	188	8	no	—
690	D₄	—	188	4	no	—
691	D₄	#13094046	1	4	yes	complemented
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	94	2	no	—
701	C₂×C₄	—	94	2	no	—
702	C₂×C₄	—	94	2	no	—
703	C₂×C₄	—	94	4	no	—
704	C₂×C₄	—	376	4	no	—
705	C₂×C₄	—	376	4	no	—
706	C₂×C₄	—	376	4	no	—
707	C₂×C₄	—	188	4	no	—
708	C₂×C₄	—	188	4	no	—
709	C₂×C₄	—	188	4	no	—
710	C₂×C₄	—	188	8	no	—
711	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
714	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
715	C₂×C₄	C₂²×D₁₈₈	1	2	yes	—
716	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
719	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
720	C₈	—	2	2	no	—
721	C₈	—	2	1	no	—
722	C₈	—	2	1	no	—
723	C₈	—	2	1	no	—
724	C₈	—	2	2	no	—
725	C₈	#41×D₄₇	1	2	yes	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	94	4	no	—
732	C₂²	—	376	16	no	—
733	C₂²	—	188	4	no	—
734	C₂²	—	188	4	no	—
735	C₂²	—	188	4	no	—
736	C₂²	—	188	2	no	—
737	C₂²	—	188	2	no	—
738	C₂²	C₂×#13094046	1	4	yes	—
739	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
740	C₄	—	2	1	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	2	no	—
746	C₄	—	188	2	no	—
747	C₄	—	188	2	no	—
748	C₄	—	188	4	no	—
749	C₄	—	188	2	no	—
750	C₄	C₂×#13094046	1	2	yes	—
751	C₄	#15689928	1	2	yes	—
752	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
753	C₄	#15689959	1	1	yes	characteristic
754	C₂	—	2	4	no	—
755	C₂	—	4	1	no	—
756	C₂	—	376	4	no	—
757	C₂	—	188	4	no	—
758	C₂	#41×D₁₈₈	1	1	yes	characteristic
759	C₂	C₂²×#13094046	1	1	yes	characteristic
760	C₂	C₂×#15689928	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₈×#41×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₈×#41	D₄₇
hypocenter	C₄₇	#61431
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₈×#41

Complements

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

N	H ≅ G/N	type
1. #20256998	C₂	semidirect
2. #20256401	C₂	semidirect
3. #20256256	C₂	semidirect
4. #20256050	C₂	semidirect
5. #20255791	C₂	semidirect
6. #20255781	C₂	semidirect
7. #20255240	C₂	semidirect
8. #20255213	C₂	semidirect
9. #20255075	C₂	semidirect
10. D₄×D₃₇₆	C₂	semidirect
11. #20253967	C₂	semidirect
12. #20253958	C₂	semidirect
13. #20253449	C₂	semidirect
14. #20253437	C₂	semidirect
15. C₄×#13094046	C₂	semidirect
16. C₂×C₄×D₃₇₆	C₂	semidirect
17. C₈×#41×C₄₇	C₂	semidirect
20. #15689858	C₂²	semidirect
21. #15689833	C₂²	semidirect
23. #15689819	C₂²	semidirect
26. #15689769	C₂²	semidirect
29. #15689673	C₂²	semidirect
31. #15689657	C₂²	semidirect
33. C₄×#10625350	C₂²	semidirect
34. C₂×C₄×D₁₈₈	C₂²	semidirect
36. #15689528	C₂²	semidirect
37. #15689525	C₂²	semidirect
38. #15689507	C₂²	semidirect
40. #15689478	C₂²	semidirect
41. #15689470	C₂²	semidirect
42. #15689459	C₂²	semidirect
43. #15689448	C₂²	semidirect
44. #15689442	C₂²	semidirect
45. #15689424	C₂²	semidirect
46. #15689424	C₂²	semidirect
47. #15689419	C₂²	semidirect
48. #15689414	C₂²	semidirect
49. #15689364	C₂²	semidirect
51. #15689359	C₂²	semidirect
52. #15689359	C₂²	semidirect
53. #15689352	C₂²	semidirect
54. #15689339	C₂²	semidirect
55. #15689339	C₂²	semidirect
56. #15689324	C₂²	semidirect
58. #15689276	C₂²	semidirect
59. #15689270	C₂²	semidirect
61. C₄×Dic₁₈₈	C₂²	semidirect
62. C₄×Dic₁₈₈	C₂²	semidirect
63. C₄×#10625325	C₂²	semidirect
64. C₄×#10625325	C₂²	semidirect
65. C₄×#10625325	C₂²	semidirect
69. C₄×D₃₇₆	C₂²	semidirect
70. C₄×D₃₇₆	C₂²	semidirect
71. C₄×D₃₇₆	C₂²	semidirect
72. C₄×D₃₇₆	C₂²	semidirect
73. C₄×D₃₇₆	C₂²	semidirect
74. #15689161	C₂²	semidirect
75. C₂×#13093958	C₂²	semidirect
76. #15689120	C₂²	semidirect
77. C₂×#13093946	C₂²	semidirect
79. C₈×Q₈×C₄₇	C₂²	semidirect
80. C₈×Q₈×C₄₇	C₂²	semidirect
83. C₈×D₄×C₄₇	C₂²	semidirect
84. C₈×D₄×C₄₇	C₂²	semidirect
85. C₄₇×#431	C₂²	semidirect
86. C₄₇×#431	C₂²	semidirect
87. C₂×C₄×C₈×C₄₇	C₂²	semidirect
88. C₂×C₄×C₈×C₄₇	C₂²	semidirect
285. D₃₇₆	#41	semidirect
297. D₄×C₄₇	#135	semidirect
388. C₈×#41	D₄₇	semidirect
442. C₈×Q₈	C₂×D₄₇	semidirect
443. C₈×Q₈	C₂×D₄₇	semidirect
459. C₈×D₄	C₂×D₄₇	semidirect
460. C₈×D₄	C₂×D₄₇	semidirect
461. #431	C₂×D₄₇	semidirect
462. #431	C₂×D₄₇	semidirect
467. C₂×C₄×C₈	C₂×D₄₇	semidirect
468. C₂×C₄×C₈	C₂×D₄₇	semidirect
469. C₄₇	#61431	semidirect
691. D₄	#13094046	semidirect

Maximal subgroups

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

subgroup	index
#20256998	2
#20256401	2
#20256256	2
#20256050	2
#20255791	2
#20255781	2
#20255240	2
#20255213	2
#20255075	2
D₄×D₃₇₆	2
#20253967	2
#20253958	2
#20253449	2
#20253437	2
C₄×#13094046	2
C₂×C₄×D₃₇₆	2
C₈×#41×C₄₇	2
#61431	47