Subgroups — #27098753

Order 12032.

1900 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257349	C₂	1	2	yes	maximal, complemented
2	#20256398	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256178	C₂	1	2	yes	maximal, complemented
5	#20255820	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255808	C₂	1	2	yes	maximal, complemented
7	#20255621	C₂	1	2	yes	maximal, complemented
8	#20255540	C₂	1	4	yes	maximal, complemented
9	#20255067	C₂	1	2	yes	maximal, complemented
10	D₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#20254029	C₂	1	2	yes	maximal, complemented
12	#20253967	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253578	C₂	1	4	yes	maximal, complemented
14	#20253539	C₂	1	2	yes	maximal, complemented
15	#20252363	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252235	C₂	1	2	yes	maximal, complemented
17	C₄×#135×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×D₈×D₄₇	C₂²	1	2	yes	—
19	#15689858	C₂²	1	2	yes	complemented
20	#15689846	C₂²	1	2	yes	—
21	#15689836	C₂²	1	4	yes	complemented
22	#15689797	—	2	4	no	—
23	D₄×Dic₉₄	C₂²	1	2	yes	complemented
24	#15689782	—	2	2	no	—
25	#15689769	—	2	2	no	—
26	#15689761	C₂²	1	4	yes	complemented
27	D₄×D₁₈₈	C₂²	1	2	yes	—
28	#15689745	C₂²	1	4	yes	complemented
29	#15689706	—	2	4	no	—
30	#15689673	C₂²	1	2	yes	complemented
31	#15689657	—	2	2	no	—
32	#15689657	C₂²	1	1	yes	characteristic
33	C₂×#13094012	—	2	2	no	—
34	#15689595	C₂²	1	4	yes	complemented
35	#15689528	C₂²	1	1	yes	characteristic, complemented
36	#15689527	C₂²	1	2	yes	complemented
37	#15689508	C₂²	1	2	yes	complemented
38	#15689500	C₂²	1	1	yes	characteristic
39	#15689484	C₂²	1	4	yes	complemented
40	#15689470	C₂²	1	2	yes	complemented
41	#15689463	C₂²	1	4	yes	complemented
42	#15689449	C₂²	1	4	yes	complemented
43	#15689447	C₂²	1	4	yes	complemented
44	#15689412	C₂²	1	4	yes	complemented
45	#15689408	C₂²	1	2	yes	complemented
46	#15689403	C₂²	1	2	yes	complemented
47	#15689401	C₂²	1	4	yes	complemented
48	#15689372	C₂²	1	4	yes	complemented
49	#15689361	C₂²	1	2	yes	complemented
50	#15689360	C₂²	1	2	yes	—
51	#15689359	C₂²	1	2	yes	complemented
52	#15689359	C₂²	1	2	yes	complemented
53	#15689341	C₂²	1	4	yes	complemented
54	#15689340	C₂²	1	4	yes	complemented
55	#15689323	C₂²	1	2	yes	complemented
56	#15689318	C₂²	1	2	yes	—
57	#15689272	C₂²	1	4	yes	complemented
58	#15689268	C₂²	1	4	yes	complemented
59	#15689258	C₂²	1	4	yes	—
60	#15689253	C₂²	1	1	yes	characteristic, complemented
61	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
62	#15689233	C₂²	1	4	yes	complemented
63	#15689232	C₂²	1	4	yes	complemented
64	#15689221	C₂²	1	4	yes	complemented
65	C₄×D₃₇₆	C₂²	1	2	yes	complemented
66	C₄×D₃₇₆	C₂²	1	2	yes	complemented
67	D₈×Dic₄₇	C₂²	1	2	yes	—
68	#15689205	C₂²	1	2	yes	complemented
69	#15689202	C₂²	1	1	yes	characteristic
70	#15689194	C₂²	1	2	yes	complemented
71	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
72	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
73	#15689182	C₂²	1	2	yes	complemented
74	#15689180	C₂²	1	1	yes	characteristic, complemented
75	#15689160	C₂²	1	2	yes	complemented
76	#15689126	C₂²	1	4	yes	complemented
77	#15689077	C₂²	1	2	yes	complemented
78	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
79	C₄×#41×C₄₇	C₂²	1	2	yes	complemented
80	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
82	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
84	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
85	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
86	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
87	C₄₇×#416	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
89	C₂×#10625350	—	2	2	no	—
90	C₂²×Dic₉₄	—	2	2	no	—
91	C₂²×D₁₈₈	—	2	2	no	—
92	C₂×D₄×D₄₇	C₂³	1	4	yes	—
93	C₂×#10625336	C₂³	1	4	yes	—
94	C₂×D₃₇₆	C₂³	1	2	yes	—
95	C₂×D₃₇₆	C₂³	1	2	yes	—
96	C₂×#10625334	C₂³	1	4	yes	—
97	D₈×D₄₇	—	2	8	no	—
98	C₂×#10625324	C₂³	1	2	yes	—
99	C₂×C₈×D₄₇	C₂³	1	2	yes	—
100	#13094024	C₂³	1	2	yes	—
101	#13094023	C₂³	1	4	yes	—
102	#13094021	C₂³	1	2	yes	—
103	#13094019	—	2	4	no	—
104	#13094018	—	2	4	no	—
105	#13094018	D₄	1	2	yes	—
106	#13094016	D₄	1	1	yes	characteristic
107	#13094013	C₂³	1	4	yes	—
108	#13094012	—	2	2	no	—
109	#13094012	—	2	2	no	—
110	#13094012	—	2	2	no	—
111	#13094012	—	2	4	no	—
112	#13094012	—	2	4	no	—
113	#13094012	D₄	1	1	yes	characteristic
114	#13094010	—	2	4	no	—
115	#13094009	—	2	4	no	—
116	#13094009	—	2	4	no	—
117	#13094007	—	2	4	no	—
118	#13094007	D₄	1	2	yes	—
119	#13094003	—	2	2	no	—
120	#13094003	D₄	1	1	yes	characteristic
121	#13094002	—	2	4	no	—
122	#13094001	—	2	4	no	—
123	#13094000	C₂³	1	4	yes	—
124	#13093999	C₂³	1	4	yes	—
125	#13093998	—	2	2	no	—
126	#13093998	—	2	2	no	—
127	#13093998	D₄	1	1	yes	characteristic
128	#13093998	C₂³	1	4	yes	—
129	#13093997	—	2	4	no	—
130	#13093996	—	2	4	no	—
131	#13093994	—	2	4	no	—
132	#13093992	—	2	4	no	—
133	C₄×Dic₉₄	—	2	2	no	—
134	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
135	C₄×D₁₈₈	—	2	2	no	—
136	C₄×D₁₈₈	—	2	2	no	—
137	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
138	C₄×D₁₈₈	C₂³	1	4	yes	—
139	D₄×Dic₄₇	C₂³	1	4	yes	—
140	#13093986	C₂³	1	4	yes	—
141	C₄×C₂²⋊D₄₇	—	2	4	no	—
142	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
143	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
144	#13093982	C₂³	1	4	yes	—
145	#13093981	—	2	4	no	—
146	#13093981	C₂³	1	2	yes	—
147	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
148	C₂×(C₂×D₄₇)⋊C₄	—	2	4	no	—
149	C₂²⋊C₄×D₄₇	—	2	4	no	—
150	#13093958	C₂³	1	2	yes	—
151	#13093958	C₂³	1	2	yes	—
152	#13093957	C₂³	1	4	yes	—
153	#13093955	C₂³	1	4	yes	—
154	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
155	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
156	Dic₄₇⋊C₈	C₂³	1	2	yes	—
157	Dic₄₇⋊C₈	C₂³	1	2	yes	—
158	#13093948	C₂³	1	4	yes	—
159	#13093946	C₂³	1	4	yes	—
160	#13093946	C₂³	1	4	yes	—
161	#13093945	C₂³	1	4	yes	—
162	#13093944	C₂³	1	4	yes	—
163	#13093944	C₂³	1	4	yes	—
164	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
165	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
166	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
167	#13093935	C₂³	1	2	yes	—
168	#13093934	C₂³	1	2	yes	—
169	C₈×Dic₄₇	C₂³	1	2	yes	—
170	C₂×#41×C₄₇	C₂³	1	2	yes	—
171	#135×C₄₇	—	2	4	no	—
172	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
173	C₂×SD₁₆×C₄₇	C₂³	1	2	yes	—
174	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
178	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
179	C₄×D₄×C₄₇	—	2	2	no	—
180	C₄×D₄×C₄₇	—	2	2	no	—
181	C₄×D₄×C₄₇	C₂³	1	2	yes	—
182	C₄×D₄×C₄₇	C₂³	1	2	yes	—
183	#117×C₄₇	—	2	2	no	—
184	#117×C₄₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₄₇	—	2	2	no	—
186	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
187	#107×C₄₇	C₂³	1	1	yes	characteristic
188	#107×C₄₇	C₂³	1	1	yes	characteristic
189	#106×C₄₇	C₂³	1	2	yes	—
190	#103×C₄₇	C₂³	1	2	yes	—
191	#103×C₄₇	C₂³	1	2	yes	—
192	#102×C₄₇	C₂³	1	2	yes	—
193	#102×C₄₇	C₂³	1	2	yes	—
194	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
198	C₂³×D₄₇	—	2	4	no	—
199	#41×C₄₇	—	2	4	no	—
200	#41×C₄₇	—	4	2	no	—
201	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
202	C₂×D₄×C₄₇	—	2	2	no	—
203	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₄₇	—	2	2	no	—
205	C₂²×C₄×C₄₇	—	2	2	no	—
206	C₂²×C₄×C₄₇	—	2	2	no	—
207	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
210	C₂×C₂²⋊D₄₇	—	2	4	no	—
211	C₂×C₂²⋊D₄₇	—	2	4	no	—
212	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
213	C₂²×Dic₄₇	—	2	4	no	—
214	D₄×D₄₇	—	2	8	no	—
215	D₄×D₄₇	—	4	4	no	—
216	#10625350	—	8	4	no	—
217	C₂×D₁₈₈	—	2	2	no	—
218	C₂×D₁₈₈	—	2	4	no	—
219	C₂×D₁₈₈	—	2	2	no	—
220	C₂×D₁₈₈	—	8	4	no	—
221	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
222	C₂×D₁₈₈	C₂⁴	1	4	yes	—
223	C₂×C₄×D₄₇	—	2	4	no	—
224	C₂×C₄×D₄₇	—	2	4	no	—
225	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
226	C₂×Dic₉₄	—	2	2	no	—
227	C₂×Dic₉₄	—	2	4	no	—
228	C₂×Dic₉₄	—	8	4	no	—
229	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
230	Q₁₆×C₄₇	—	2	2	no	—
231	SD₁₆×C₄₇	—	2	4	no	—
232	D₈×C₄₇	#41	1	4	yes	complemented
233	C₂×C₈×C₄₇	—	2	2	no	—
234	C₂×C₈×C₄₇	—	4	1	no	—
235	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
239	C₄⋊C₄×C₄₇	—	2	2	no	—
240	C₄⋊C₄×C₄₇	—	2	2	no	—
241	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
242	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
243	C₂²⋊C₄×C₄₇	—	2	2	no	—
244	C₂²⋊C₄×C₄₇	—	2	2	no	—
245	C₂²⋊C₄×C₄₇	—	2	2	no	—
246	C₄²×C₄₇	—	2	2	no	—
247	C₄²×C₄₇	—	2	2	no	—
248	C₄²×C₄₇	—	2	2	no	—
249	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
252	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
253	C₂²⋊Dic₄₇	—	2	4	no	—
254	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
255	#10625336	—	4	4	no	—
256	#10625334	—	2	8	no	—
257	(C₂×D₄₇)⋊C₄	—	2	4	no	—
258	(C₂×D₄₇)⋊C₄	—	2	4	no	—
259	(C₂×D₄₇)⋊C₄	—	2	4	no	—
260	(C₂×D₄₇)⋊C₄	—	2	4	no	—
261	(C₂×D₄₇)⋊C₄	—	2	4	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	C₂×D₄	1	2	yes	—
266	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
267	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
268	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
269	C₄⋊Dic₄₇	—	2	2	no	—
270	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
271	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
272	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
273	Dic₄₇⋊C₄	—	2	4	no	—
274	Dic₄₇⋊C₄	—	2	4	no	—
275	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
276	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
277	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
278	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
279	C₄×Dic₄₇	—	2	4	no	—
280	C₄×Dic₄₇	C₂⁴	1	2	yes	—
281	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
282	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
283	D₃₇₆	—	2	4	no	—
284	D₃₇₆	—	4	2	no	—
285	#10625324	—	4	2	no	—
286	C₈×D₄₇	—	2	4	no	—
287	C₂³×C₄₇	—	2	2	no	—
288	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
289	C₂²×D₄₇	—	2	4	no	—
290	C₂²×D₄₇	—	4	8	no	—
291	C₂²×D₄₇	—	8	4	no	—
292	C₂²×D₄₇	—	8	4	no	—
293	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
294	Q₈×C₄₇	—	2	2	no	—
295	Q₈×C₄₇	—	2	2	no	—
296	D₄×C₄₇	—	2	2	no	—
297	D₄×C₄₇	—	4	4	no	—
298	D₄×C₄₇	C₂×#41	1	4	yes	—
299	C₂×C₄×C₄₇	—	2	2	no	—
300	C₂×C₄×C₄₇	—	2	1	no	—
301	C₂×C₄×C₄₇	—	2	1	no	—
302	C₂×C₄×C₄₇	—	2	2	no	—
303	C₂×C₄×C₄₇	—	2	2	no	—
304	C₂×C₄×C₄₇	—	2	2	no	—
305	C₂×C₄×C₄₇	—	4	1	no	—
306	C₂×C₄×C₄₇	—	4	4	no	—
307	C₂×C₄×C₄₇	—	4	4	no	—
308	C₂×C₄×C₄₇	—	8	2	no	—
309	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	2	no	—
316	C₂²⋊D₄₇	—	4	8	no	—
317	C₂²⋊D₄₇	—	8	4	no	—
318	C₂×Dic₄₇	—	2	4	no	—
319	C₂×Dic₄₇	—	8	4	no	—
320	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
321	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
322	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
323	D₁₈₈	—	2	2	no	—
324	D₁₈₈	—	2	4	no	—
325	D₁₈₈	—	2	4	no	—
326	D₁₈₈	—	4	4	no	—
327	D₁₈₈	—	8	2	no	—
328	D₁₈₈	—	8	4	no	—
329	C₄×D₄₇	—	2	2	no	—
330	C₄×D₄₇	—	2	2	no	—
331	C₄×D₄₇	—	8	4	no	—
332	C₄×D₄₇	—	8	4	no	—
333	Dic₉₄	—	2	2	no	—
334	Dic₉₄	—	4	4	no	—
335	Dic₉₄	—	8	4	no	—
336	C₈×C₄₇	—	2	1	no	—
337	C₈×C₄₇	—	2	1	no	—
338	C₈×C₄₇	—	2	1	no	—
339	C₈×C₄₇	C₂×#41	1	2	yes	—
340	C₄₇⋊C₈	—	2	2	no	—
341	C₄₇⋊C₈	—	2	2	no	—
342	#61475	—	47	1	no	maximal, Sylow
343	C₂²×C₄₇	—	2	1	no	—
344	C₂²×C₄₇	—	2	4	no	—
345	C₂²×C₄₇	—	2	1	no	—
346	C₂²×C₄₇	—	2	1	no	—
347	C₂²×C₄₇	—	4	2	no	—
348	C₂²×C₄₇	—	4	2	no	—
349	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
350	C₂×D₄₇	—	2	2	no	—
351	C₂×D₄₇	—	2	2	no	—
352	C₂×D₄₇	—	2	2	no	—
353	C₂×D₄₇	—	4	4	no	—
354	C₂×D₄₇	—	4	4	no	—
355	C₂×D₄₇	—	4	4	no	—
356	C₂×D₄₇	—	16	8	no	—
357	C₄×C₄₇	—	2	1	no	—
358	C₄×C₄₇	—	2	1	no	—
359	C₄×C₄₇	—	2	1	no	—
360	C₄×C₄₇	—	2	1	no	—
361	C₄×C₄₇	—	4	2	no	—
362	C₄×C₄₇	—	4	2	no	—
363	C₄×C₄₇	—	4	2	no	—
364	C₄×C₄₇	#576	1	2	yes	—
365	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
366	C₄×C₄₇	#585	1	1	yes	characteristic
367	Dic₄₇	—	2	2	no	—
368	Dic₄₇	—	2	2	no	—
369	Dic₄₇	—	2	2	no	—
370	Dic₄₇	—	4	4	no	—
371	#3514	—	47	2	no	—
372	#3396	—	47	1	no	—
373	Q₈×D₈	—	47	1	no	—
374	#3373	—	47	2	no	—
375	#3342	—	47	1	no	—
376	#3341	—	47	2	no	—
377	#3324	—	47	2	no	—
378	#3319	—	47	4	no	—
379	#3280	—	47	2	no	—
380	D₄×D₈	—	47	1	no	—
381	#3175	—	47	2	no	—
382	#3169	—	47	1	no	—
383	#3118	—	47	4	no	—
384	#3115	—	47	2	no	—
385	#2966	—	47	1	no	—
386	#2948	—	47	2	no	—
387	C₄×#135	D₄₇	1	1	yes	characteristic, complemented
388	C₂×C₄₇	—	4	4	no	—
389	C₂×C₄₇	—	4	1	no	—
390	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
391	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
392	C₂×C₄₇	#3584	1	1	yes	characteristic
393	D₄₇	—	4	2	no	—
394	D₄₇	—	8	4	no	—
395	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
396	C₂²×D₈	—	47	2	no	—
397	#559	—	47	2	no	—
398	#556	—	47	2	no	—
399	#555	—	47	4	no	—
400	#551	—	94	4	no	—
401	D₄×Q₈	—	47	2	no	—
402	#548	—	94	2	no	—
403	#546	—	47	4	no	—
404	#546	—	94	2	no	—
405	D₄²	—	47	2	no	—
406	#542	—	47	4	no	—
407	#538	—	94	4	no	—
408	#532	—	47	2	no	—
409	#529	—	47	1	no	—
410	#529	—	94	2	no	—
411	C₂×#124	—	94	2	no	—
412	#518	—	47	4	no	—
413	C₄×#41	C₂×D₄₇	1	2	yes	complemented
414	#500	—	47	2	no	—
415	#500	—	47	1	no	—
416	#495	—	47	2	no	—
417	#493	—	47	1	no	—
418	#489	—	47	4	no	—
419	#486	—	47	2	no	—
420	#485	—	47	4	no	—
421	#482	—	47	4	no	—
422	#482	—	47	4	no	—
423	#476	—	47	4	no	—
424	#475	—	47	2	no	—
425	#474	—	47	2	no	—
426	#474	—	47	4	no	—
427	#468	—	47	4	no	—
428	#467	—	47	2	no	—
429	#466	—	47	2	no	—
430	#466	—	47	2	no	—
431	#466	—	47	2	no	—
432	#463	—	47	4	no	—
433	#463	—	47	4	no	—
434	#460	—	47	2	no	—
435	#459	—	47	2	no	—
436	#450	—	47	4	no	—
437	#449	—	47	4	no	—
438	#447	—	47	4	no	—
439	#446	—	47	1	no	—
440	C₈×Q₈	—	47	1	no	—
441	#442	—	47	4	no	—
442	#442	—	47	4	no	—
443	#440	—	47	4	no	—
444	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
445	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
446	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
447	C₄×SD₁₆	C₂×D₄₇	1	2	yes	complemented
448	C₄×D₈	—	47	2	no	—
449	C₄×D₈	—	47	2	no	—
450	C₄×D₈	—	47	2	no	—
451	C₄×D₈	—	47	2	no	—
452	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
453	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
454	#436	—	47	1	no	—
455	#435	—	47	2	no	—
456	C₈×D₄	—	47	2	no	—
457	C₈×D₄	—	47	1	no	—
458	#433	—	47	2	no	—
459	#432	—	47	1	no	—
460	#427	—	47	2	no	—
461	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
462	#418	—	47	4	no	—
463	#416	C₂×D₄₇	1	2	yes	complemented
464	#405	—	47	2	no	—
465	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic, complemented
466	C₄₇	#61475	1	1	yes	characteristic, complemented, Sylow
467	C₂×#41	—	94	2	no	—
468	C₂×#41	C₂²×D₄₇	1	2	yes	—
469	C₂²×Q₈	—	94	2	no	—
470	C₂²×D₄	—	47	4	no	—
471	C₂²×D₄	—	94	2	no	—
472	#135	—	2	4	no	—
473	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
474	C₂×SD₁₆	—	47	4	no	—
475	C₂×SD₁₆	C₂²×D₄₇	1	2	yes	—
476	C₂×D₈	—	47	4	no	—
477	C₂×D₈	—	47	2	no	—
478	C₂×D₈	—	47	2	no	—
479	C₂×D₈	—	94	8	no	—
480	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
481	C₂×M₁₆	—	47	2	no	—
482	C₂²×C₈	—	47	2	no	—
483	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
484	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
485	C₄⋊Q₈	—	47	4	no	—
486	C₄⋊Q₈	—	47	2	no	—
487	#127	—	47	2	no	—
488	#126	—	47	2	no	—
489	#126	—	94	4	no	—
490	#126	—	94	4	no	—
491	#125	—	47	1	no	—
492	#124	—	47	4	no	—
493	#124	—	47	1	no	—
494	#124	—	94	4	no	—
495	#124	—	94	4	no	—
496	#124	—	94	2	no	—
497	#124	—	94	2	no	—
498	#124	—	94	4	no	—
499	#124	—	94	2	no	—
500	#123	—	47	2	no	—
501	#123	—	94	4	no	—
502	#123	—	94	4	no	—
503	#123	—	94	4	no	—
504	C₂²⋊Q₈	—	47	1	no	—
505	C₂²⋊Q₈	—	47	4	no	—
506	C₂²⋊Q₈	—	94	4	no	—
507	C₂²⋊Q₈	—	94	4	no	—
508	C₂²⋊Q₈	—	94	2	no	—
509	#121	—	47	1	no	—
510	#121	—	47	4	no	—
511	#121	—	47	4	no	—
512	#121	—	94	4	no	—
513	#121	—	94	4	no	—
514	#121	—	94	2	no	—
515	#121	—	94	2	no	—
516	#120	—	94	4	no	—
517	#120	—	94	4	no	—
518	C₄×Q₈	—	47	1	no	—
519	C₄×Q₈	—	94	2	no	—
520	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
521	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	47	2	no	—
525	C₄×D₄	—	47	4	no	—
526	C₄×D₄	—	47	4	no	—
527	C₄×D₄	—	47	1	no	—
528	C₄×D₄	—	47	4	no	—
529	C₄×D₄	—	94	2	no	—
530	C₄×D₄	—	94	4	no	—
531	C₄×D₄	—	94	4	no	—
532	C₄×D₄	—	94	2	no	—
533	C₄×D₄	C₂²×D₄₇	1	2	yes	—
534	C₄×D₄	C₂²×D₄₇	1	2	yes	—
535	#117	—	2	2	no	—
536	#117	—	47	2	no	—
537	#117	—	47	4	no	—
538	#117	—	94	4	no	—
539	#117	C₂²×D₄₇	1	2	yes	—
540	C₂×C₂²⋊C₄	—	94	4	no	—
541	C₂×C₂²⋊C₄	—	94	4	no	—
542	C₂×C₂²⋊C₄	—	94	4	no	—
543	C₂×C₄²	—	2	2	no	—
544	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
545	#107	—	47	2	no	—
546	#107	—	47	2	no	—
547	#107	—	47	4	no	—
548	#107	C₂²×D₄₇	1	1	yes	characteristic
549	#107	C₂²×D₄₇	1	1	yes	characteristic
550	#106	—	47	4	no	—
551	#106	C₂²×D₄₇	1	2	yes	—
552	C₄⋊C₈	—	47	2	no	—
553	C₄⋊C₈	—	47	2	no	—
554	C₄⋊C₈	—	47	1	no	—
555	C₄⋊C₈	—	47	1	no	—
556	#103	—	47	4	no	—
557	#103	C₂²×D₄₇	1	2	yes	—
558	#103	C₂²×D₄₇	1	2	yes	—
559	#102	—	47	4	no	—
560	#102	—	47	4	no	—
561	#102	—	47	4	no	—
562	#102	—	47	4	no	—
563	#102	—	47	4	no	—
564	#102	C₂²×D₄₇	1	2	yes	—
565	#102	C₂²×D₄₇	1	2	yes	—
566	C₂²⋊C₈	—	47	2	no	—
567	C₂²⋊C₈	—	47	2	no	—
568	C₂²⋊C₈	—	47	2	no	—
569	#97	—	47	2	no	—
570	#97	—	47	2	no	—
571	C₄×C₈	—	47	2	no	—
572	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
573	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
574	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
575	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
576	C₂⁴	—	94	4	no	—
577	#41	—	2	4	no	—
578	#41	—	4	2	no	—
579	#41	—	376	4	no	—
580	C₂×Q₈	—	47	1	no	—
581	C₂×Q₈	—	94	4	no	—
582	C₂×Q₈	—	94	2	no	—
583	C₂×Q₈	—	376	4	no	—
584	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	47	2	no	—
587	C₂×D₄	—	47	1	no	—
588	C₂×D₄	—	47	4	no	—
589	C₂×D₄	—	94	4	no	—
590	C₂×D₄	—	94	4	no	—
591	C₂×D₄	—	94	8	no	—
592	C₂×D₄	—	94	4	no	—
593	C₂×D₄	—	94	2	no	—
594	C₂×D₄	—	94	2	no	—
595	C₂×D₄	—	376	4	no	—
596	C₂×D₄	—	188	4	no	—
597	C₂×D₄	C₂³×D₄₇	1	2	yes	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	47	2	no	—
602	C₂²×C₄	—	94	4	no	—
603	C₂²×C₄	—	94	4	no	—
604	C₂²×C₄	—	94	4	no	—
605	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
606	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
607	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
608	Q₁₆	—	2	2	no	—
609	SD₁₆	—	2	4	no	—
610	SD₁₆	—	188	4	no	—
611	D₈	—	94	8	no	—
612	D₈	—	94	4	no	—
613	D₈	—	188	2	no	—
614	D₈	#10625350	1	4	yes	complemented
615	M₁₆	—	188	2	no	—
616	C₂×C₈	—	2	2	no	—
617	C₂×C₈	—	4	1	no	—
618	C₂×C₈	—	47	2	no	—
619	C₂×C₈	—	47	2	no	—
620	C₂×C₈	—	94	4	no	—
621	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
622	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
623	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
624	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	47	2	no	—
628	C₄⋊C₄	—	47	2	no	—
629	C₄⋊C₄	—	47	2	no	—
630	C₄⋊C₄	—	47	2	no	—
631	C₄⋊C₄	—	47	1	no	—
632	C₄⋊C₄	—	47	1	no	—
633	C₄⋊C₄	—	47	4	no	—
634	C₄⋊C₄	—	94	4	no	—
635	C₄⋊C₄	—	94	4	no	—
636	C₄⋊C₄	—	94	2	no	—
637	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
638	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	47	2	no	—
643	C₂²⋊C₄	—	47	2	no	—
644	C₂²⋊C₄	—	47	2	no	—
645	C₂²⋊C₄	—	47	2	no	—
646	C₂²⋊C₄	—	47	2	no	—
647	C₂²⋊C₄	—	94	4	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	4	no	—
654	C₂²⋊C₄	—	94	4	no	—
655	C₂²⋊C₄	—	94	4	no	—
656	C₄²	—	2	2	no	—
657	C₄²	—	2	2	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	47	2	no	—
660	C₄²	—	94	4	no	—
661	C₄²	D₄×D₄₇	1	1	yes	characteristic
662	C₄²	D₄×D₄₇	1	1	yes	characteristic
663	C₄²	C₂³×D₄₇	1	1	yes	characteristic
664	C₄²	C₂³×D₄₇	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	47	2	no	—
667	C₂³	—	94	4	no	—
668	C₂³	—	376	4	no	—
669	C₂³	—	376	4	no	—
670	C₂³	—	188	8	no	—
671	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	94	2	no	—
675	Q₈	—	376	4	no	—
676	Q₈	—	188	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	4	no	—
679	D₄	—	94	2	no	—
680	D₄	—	94	4	no	—
681	D₄	—	94	4	no	—
682	D₄	—	376	2	no	—
683	D₄	—	376	4	no	—
684	D₄	—	376	4	no	—
685	D₄	—	188	2	no	—
686	D₄	—	188	8	no	—
687	D₄	—	188	4	no	—
688	D₄	C₂×#10625350	1	4	yes	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	—	47	2	no	—
700	C₂×C₄	—	47	2	no	—
701	C₂×C₄	—	47	2	no	—
702	C₂×C₄	—	94	2	no	—
703	C₂×C₄	—	94	2	no	—
704	C₂×C₄	—	94	4	no	—
705	C₂×C₄	—	376	4	no	—
706	C₂×C₄	—	376	4	no	—
707	C₂×C₄	—	376	4	no	—
708	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
709	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
710	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
711	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
712	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
713	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
714	C₈	—	2	1	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	94	2	no	—
718	C₈	—	94	2	no	—
719	C₈	C₂×#10625350	1	2	yes	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	94	2	no	—
727	C₂²	—	94	2	no	—
728	C₂²	—	94	2	no	—
729	C₂²	—	188	4	no	—
730	C₂²	—	188	4	no	—
731	C₂²	—	188	4	no	—
732	C₂²	—	752	8	no	—
733	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	—	4	2	no	—
741	C₄	—	94	2	no	—
742	C₄	—	94	2	no	—
743	C₄	—	94	2	no	—
744	C₄	—	188	4	no	—
745	C₄	#15689925	1	2	yes	—
746	C₄	C₂²×#10625350	1	1	yes	characteristic
747	C₄	#15689959	1	1	yes	characteristic
748	C₂	—	4	1	no	—
749	C₂	—	4	4	no	—
750	C₂	—	376	4	no	—
751	C₂	—	188	2	no	—
752	C₂	D₄×#10625350	1	1	yes	characteristic
753	C₂	C₂×#15689925	1	1	yes	characteristic
754	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#135×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	C₄×#135	D₄₇
hypocenter	C₄₇	#61475
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #20257349	C₂	semidirect
2. #20256398	C₂	semidirect
3. D₈×Dic₉₄	C₂	semidirect
4. #20256178	C₂	semidirect
5. #20255820	C₂	semidirect
6. #20255808	C₂	semidirect
7. #20255621	C₂	semidirect
8. #20255540	C₂	semidirect
9. #20255067	C₂	semidirect
10. D₈×D₁₈₈	C₂	semidirect
11. #20254029	C₂	semidirect
12. #20253967	C₂	semidirect
13. #20253578	C₂	semidirect
14. #20253539	C₂	semidirect
15. #20252363	C₂	semidirect
16. #20252235	C₂	semidirect
17. C₄×#135×C₄₇	C₂	semidirect
19. #15689858	C₂²	semidirect
21. #15689836	C₂²	semidirect
23. D₄×Dic₉₄	C₂²	semidirect
26. #15689761	C₂²	semidirect
28. #15689745	C₂²	semidirect
30. #15689673	C₂²	semidirect
34. #15689595	C₂²	semidirect
35. #15689528	C₂²	semidirect
36. #15689527	C₂²	semidirect
37. #15689508	C₂²	semidirect
39. #15689484	C₂²	semidirect
40. #15689470	C₂²	semidirect
41. #15689463	C₂²	semidirect
42. #15689449	C₂²	semidirect
43. #15689447	C₂²	semidirect
44. #15689412	C₂²	semidirect
45. #15689408	C₂²	semidirect
46. #15689403	C₂²	semidirect
47. #15689401	C₂²	semidirect
48. #15689372	C₂²	semidirect
49. #15689361	C₂²	semidirect
51. #15689359	C₂²	semidirect
52. #15689359	C₂²	semidirect
53. #15689341	C₂²	semidirect
54. #15689340	C₂²	semidirect
55. #15689323	C₂²	semidirect
57. #15689272	C₂²	semidirect
58. #15689268	C₂²	semidirect
60. #15689253	C₂²	semidirect
61. C₈×Dic₉₄	C₂²	semidirect
62. #15689233	C₂²	semidirect
63. #15689232	C₂²	semidirect
64. #15689221	C₂²	semidirect
65. C₄×D₃₇₆	C₂²	semidirect
66. C₄×D₃₇₆	C₂²	semidirect
68. #15689205	C₂²	semidirect
70. #15689194	C₂²	semidirect
72. C₈×C₂²⋊D₄₇	C₂²	semidirect
73. #15689182	C₂²	semidirect
74. #15689180	C₂²	semidirect
75. #15689160	C₂²	semidirect
76. #15689126	C₂²	semidirect
77. #15689077	C₂²	semidirect
79. C₄×#41×C₄₇	C₂²	semidirect
80. C₄×Q₁₆×C₄₇	C₂²	semidirect
81. C₄×Q₁₆×C₄₇	C₂²	semidirect
82. C₄×SD₁₆×C₄₇	C₂²	semidirect
83. C₄×SD₁₆×C₄₇	C₂²	semidirect
86. C₄₇×#427	C₂²	semidirect
87. C₄₇×#416	C₂²	semidirect
88. C₂×C₄×C₈×C₄₇	C₂²	semidirect
232. D₈×C₄₇	#41	semidirect
387. C₄×#135	D₄₇	semidirect
413. C₄×#41	C₂×D₄₇	semidirect
444. C₄×Q₁₆	C₂×D₄₇	semidirect
445. C₄×Q₁₆	C₂×D₄₇	semidirect
446. C₄×SD₁₆	C₂×D₄₇	semidirect
447. C₄×SD₁₆	C₂×D₄₇	semidirect
461. #427	C₂×D₄₇	semidirect
463. #416	C₂×D₄₇	semidirect
465. C₂×C₄×C₈	C₂×D₄₇	semidirect
466. C₄₇	#61475	semidirect
614. D₈	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257349	2
#20256398	2
D₈×Dic₉₄	2
#20256178	2
#20255820	2
#20255808	2
#20255621	2
#20255540	2
#20255067	2
D₈×D₁₈₈	2
#20254029	2
#20253967	2
#20253578	2
#20253539	2
#20252363	2
#20252235	2
C₄×#135×C₄₇	2
#61475	47