Subgroups — #27086130

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256772	C₂	1	2	yes	maximal, complemented
2	#20254048	C₂	1	1	yes	maximal, characteristic, complemented
3	#20254047	C₂	1	1	yes	maximal, characteristic, complemented
4	#20254035	C₂	1	1	yes	maximal, characteristic, complemented
5	#20254023	C₂	1	2	yes	maximal, complemented
6	#20254020	C₂	1	2	yes	maximal, complemented
7	#20254015	C₂	1	2	yes	maximal, complemented
8	#20254010	C₂	1	2	yes	maximal, complemented
9	#20254003	C₂	1	2	yes	maximal, complemented
10	#20254000	C₂	1	2	yes	maximal, complemented
11	#20253901	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253815	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253732	C₂	1	2	yes	maximal, complemented
14	#20252995	C₂	1	2	yes	maximal, complemented
15	#20252967	C₂	1	2	yes	maximal, complemented
16	#20252185	C₂	1	2	yes	maximal, complemented
17	C₄×#13094043	C₂	1	2	yes	maximal, complemented
18	#405×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#3176	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13094043	C₂²	1	2	yes	—
21	C₂×#13094043	C₂²	1	2	yes	—
22	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
24	#15689740	C₂²	1	4	yes	—
25	#15689738	C₂²	1	4	yes	—
26	#15689736	C₂²	1	2	yes	—
27	#15689735	C₂²	1	2	yes	—
28	#15689727	C₂²	1	2	yes	—
29	#15689716	—	2	4	no	—
30	#15689705	—	2	4	no	—
31	#15689679	C₂²	1	2	yes	—
32	#15689671	C₂²	1	2	yes	—
33	#15689654	—	2	4	no	—
34	#15689650	—	2	4	no	—
35	#15689633	C₂²	1	4	yes	—
36	C₄×#10625352	C₂²	1	4	yes	—
37	#117×D₄₇	C₂²	1	1	yes	characteristic
38	#15689527	C₂²	1	2	yes	complemented
39	#15689525	C₂²	1	1	yes	characteristic, complemented
40	#15689522	C₂²	1	2	yes	complemented
41	#15689520	C₂²	1	2	yes	complemented
42	#15689506	C₂²	1	2	yes	complemented
43	#15689506	C₂²	1	2	yes	complemented
44	#15689503	C₂²	1	1	yes	characteristic, complemented
45	#15689495	C₂²	1	2	yes	complemented
46	#15689493	C₂²	1	2	yes	complemented
47	#15689492	C₂²	1	2	yes	complemented
48	#15689487	C₂²	1	2	yes	complemented
49	#15689481	C₂²	1	4	yes	complemented
50	#15689481	C₂²	1	4	yes	complemented
51	#15689382	C₂²	1	2	yes	—
52	#15689381	C₂²	1	2	yes	—
53	#15689373	C₂²	1	2	yes	—
54	#15689368	C₂²	1	4	yes	—
55	#15689367	C₂²	1	4	yes	—
56	#15689365	C₂²	1	2	yes	—
57	#15689364	C₂²	1	2	yes	—
58	#15689356	C₂²	1	2	yes	—
59	#15689351	C₂²	1	4	yes	—
60	#15689350	C₂²	1	4	yes	—
61	#15689235	C₂²	1	2	yes	complemented
62	#15689231	C₂²	1	2	yes	complemented
63	#15689229	C₂²	1	2	yes	complemented
64	#15689223	C₂²	1	4	yes	complemented
65	#15689220	C₂²	1	4	yes	complemented
66	C₄×Dic₁₈₈	C₂²	1	2	yes	complemented
67	#15689217	C₂²	1	2	yes	complemented
68	#15689214	C₂²	1	4	yes	complemented
69	C₄×#10625335	C₂²	1	4	yes	complemented
70	D₈×Dic₄₇	C₂²	1	2	yes	complemented
71	#15689160	C₂²	1	2	yes	—
72	#15689158	C₂²	1	2	yes	—
73	#15689116	C₂²	1	4	yes	—
74	#15689116	C₂²	1	4	yes	—
75	#15689081	C₂²	1	1	yes	characteristic
76	#15689080	C₂²	1	1	yes	characteristic
77	#15689080	C₂²	1	1	yes	characteristic
78	#15689079	C₂²	1	1	yes	characteristic
79	#15689078	C₂²	1	1	yes	characteristic
80	#15689077	C₂²	1	1	yes	characteristic
81	#15689077	C₂²	1	1	yes	characteristic
82	#97×D₄₇	C₂²	1	1	yes	characteristic
83	#97×D₄₇	C₂²	1	1	yes	characteristic
84	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
85	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
86	C₄₇×#540	C₂²	1	2	yes	—
87	C₄₇×#499	C₂²	1	1	yes	characteristic, complemented
88	C₄₇×#493	C₂²	1	1	yes	characteristic, complemented
89	C₄₇×#490	C₂²	1	2	yes	complemented
90	C₄₇×#469	C₂²	1	2	yes	—
91	C₄₇×#466	C₂²	1	2	yes	—
92	C₄₇×#442	C₂²	1	2	yes	complemented
93	C₄×D₈×C₄₇	C₂²	1	2	yes	complemented
94	C₄₇×#405	C₂²	1	1	yes	characteristic
95	C₂×#10625352	C₂³	1	4	yes	—
96	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
97	#13094043	—	2	8	no	—
98	#13094043	—	2	8	no	—
99	C₂×Dic₁₈₈	C₂³	1	2	yes	—
100	C₂×Dic₁₈₈	C₂³	1	2	yes	—
101	C₂×#10625335	C₂³	1	4	yes	—
102	C₂×#10625335	C₂³	1	4	yes	—
103	C₂×#10625329	C₂³	1	1	yes	characteristic
104	C₂×#10625324	C₂³	1	1	yes	characteristic
105	C₂×#10625324	C₂³	1	1	yes	characteristic
106	M₁₆×D₄₇	—	2	4	no	—
107	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
108	C₂×C₈×D₄₇	—	2	4	no	—
109	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
113	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
114	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
115	#13094024	C₂³	1	2	yes	—
116	#13094023	C₂³	1	4	yes	—
117	#13094019	—	2	4	no	—
118	#13094017	—	2	4	no	—
119	#13094017	—	2	4	no	—
120	#13094017	—	2	4	no	—
121	#13094016	C₂³	1	2	yes	—
122	#13094015	—	2	4	no	—
123	#13094014	—	2	4	no	—
124	#13094011	—	2	4	no	—
125	#13094011	C₂³	1	4	yes	—
126	#13094010	—	2	4	no	—
127	#13094007	—	2	4	no	—
128	#13094006	—	2	4	no	—
129	#13094005	—	2	4	no	—
130	#13094005	—	2	4	no	—
131	#13094004	C₂³	1	4	yes	—
132	#13094003	—	2	4	no	—
133	#13094003	C₂³	1	4	yes	—
134	#13094002	—	2	4	no	—
135	#13094001	—	2	4	no	—
136	#13093996	—	2	4	no	—
137	#13093995	—	2	4	no	—
138	#13093995	C₂³	1	4	yes	—
139	#13093992	—	2	4	no	—
140	C₄×Dic₉₄	C₂³	1	4	yes	—
141	#13093989	—	2	4	no	—
142	#13093989	C₂³	1	4	yes	—
143	D₄×Dic₄₇	—	2	4	no	—
144	D₄×Dic₄₇	—	2	4	no	—
145	D₄×Dic₄₇	C₂³	1	4	yes	—
146	C₄×C₂²⋊D₄₇	—	2	4	no	—
147	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
148	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
149	#13093983	C₂³	1	1	yes	characteristic
150	#13093982	D₄	1	2	yes	—
151	#13093982	C₂³	1	4	yes	—
152	#13093981	C₂³	1	1	yes	characteristic
153	#13093981	C₂³	1	1	yes	characteristic
154	#13093980	—	2	4	no	—
155	#13093980	D₄	1	2	yes	—
156	C₄⋊C₄×D₄₇	D₄	1	2	yes	—
157	C₂²⋊C₄×D₄₇	D₄	1	2	yes	—
158	C₂×C₄×Dic₄₇	—	2	4	no	—
159	C₄²×D₄₇	C₂³	1	1	yes	characteristic
160	C₄²×D₄₇	C₂³	1	1	yes	characteristic
161	#13093958	C₂³	1	2	yes	—
162	#13093957	C₂³	1	4	yes	—
163	#13093956	C₂³	1	2	yes	—
164	#13093955	C₂³	1	4	yes	—
165	#13093949	C₂³	1	4	yes	—
166	#13093949	C₂³	1	4	yes	—
167	#13093947	C₂³	1	4	yes	—
168	#13093947	C₂³	1	4	yes	—
169	#13093945	C₂³	1	4	yes	—
170	#13093945	C₂³	1	4	yes	—
171	#13093935	C₂³	1	1	yes	characteristic
172	#13093935	C₂³	1	1	yes	characteristic
173	#13093934	C₂³	1	1	yes	characteristic
174	#13093934	C₂³	1	1	yes	characteristic
175	#13093934	C₂³	1	1	yes	characteristic
176	#13093934	C₂³	1	1	yes	characteristic
177	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
178	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
179	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
180	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
181	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
182	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
183	C₂×D₈×C₄₇	C₂³	1	2	yes	—
184	C₂×D₈×C₄₇	C₂³	1	2	yes	—
185	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
187	#127×C₄₇	C₂³	1	2	yes	—
188	#125×C₄₇	C₂³	1	2	yes	—
189	#123×C₄₇	—	2	4	no	—
190	#121×C₄₇	—	2	4	no	—
191	#121×C₄₇	C₂³	1	4	yes	—
192	C₄×D₄×C₄₇	C₂³	1	4	yes	—
193	#117×C₄₇	C₂³	1	1	yes	characteristic
194	#107×C₄₇	C₂³	1	2	yes	—
195	#106×C₄₇	C₂³	1	2	yes	—
196	#102×C₄₇	C₂³	1	4	yes	—
197	#102×C₄₇	C₂³	1	4	yes	—
198	#97×C₄₇	C₂³	1	1	yes	characteristic
199	#97×C₄₇	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
202	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
203	C₂×D₄×C₄₇	—	2	4	no	—
204	C₂×D₄×C₄₇	—	2	4	no	—
205	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₄₇	—	2	4	no	—
207	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
208	C₂×C₂²⋊D₄₇	—	2	4	no	—
209	C₂×C₂²⋊D₄₇	—	2	4	no	—
210	C₂²×Dic₄₇	—	2	4	no	—
211	C₂²×Dic₄₇	—	2	4	no	—
212	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
213	#10625352	—	2	8	no	—
214	#10625352	—	2	8	no	—
215	C₂×C₄×D₄₇	—	2	2	no	—
216	C₂×C₄×D₄₇	—	2	2	no	—
217	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
218	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
219	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
220	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
221	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
222	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
223	C₂×Dic₉₄	—	2	4	no	—
224	C₂×Dic₉₄	C₂⁴	1	4	yes	—
225	D₈×C₄₇	—	2	4	no	—
226	D₈×C₄₇	—	2	4	no	—
227	M₁₆×C₄₇	—	2	2	no	—
228	C₂×C₈×C₄₇	—	2	2	no	—
229	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
230	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
231	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
232	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₄₇	—	2	4	no	—
234	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
236	C₂²⋊C₄×C₄₇	—	2	4	no	—
237	C₂²⋊C₄×C₄₇	—	2	4	no	—
238	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
239	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
241	C₂²⋊Dic₄₇	—	2	4	no	—
242	C₂²⋊Dic₄₇	—	2	4	no	—
243	C₂²⋊Dic₄₇	—	2	4	no	—
244	C₂²⋊Dic₄₇	—	2	4	no	—
245	C₂²⋊Dic₄₇	—	2	4	no	—
246	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
247	#10625335	—	2	8	no	—
248	#10625335	—	2	8	no	—
249	(C₂×D₄₇)⋊C₄	—	2	4	no	—
250	(C₂×D₄₇)⋊C₄	—	2	4	no	—
251	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
252	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
253	C₄⋊Dic₄₇	—	2	4	no	—
254	C₄⋊Dic₄₇	—	2	4	no	—
255	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
256	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
257	Dic₄₇⋊C₄	—	2	4	no	—
258	Dic₄₇⋊C₄	—	2	4	no	—
259	Dic₄₇⋊C₄	—	2	4	no	—
260	Dic₄₇⋊C₄	—	2	4	no	—
261	Dic₄₇⋊C₄	—	2	4	no	—
262	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
263	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
264	C₄×Dic₄₇	—	2	4	no	—
265	C₄×Dic₄₇	—	2	4	no	—
266	C₄×Dic₄₇	—	2	4	no	—
267	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
268	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
269	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
270	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
271	#10625329	—	2	2	no	—
272	C₂×C₄₇⋊C₈	—	2	2	no	—
273	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
274	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
276	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
277	Dic₁₈₈	—	2	4	no	—
278	Dic₁₈₈	—	2	4	no	—
279	#10625324	—	2	2	no	—
280	#10625324	—	2	2	no	—
281	C₈×D₄₇	—	2	2	no	—
282	C₈×D₄₇	—	2	2	no	—
283	C₈×D₄₇	—	2	2	no	—
284	C₈×D₄₇	—	2	2	no	—
285	C₈×D₄₇	#41	1	4	yes	—
286	C₈×D₄₇	#41	1	4	yes	—
287	C₂³×C₄₇	—	2	4	no	—
288	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
289	C₂²×D₄₇	—	2	2	no	—
290	C₂²×D₄₇	—	4	2	no	—
291	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
292	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
293	D₄×C₄₇	—	2	4	no	—
294	D₄×C₄₇	—	2	4	no	—
295	D₄×C₄₇	—	8	4	no	—
296	D₄×C₄₇	—	8	4	no	—
297	C₂×C₄×C₄₇	—	2	1	no	—
298	C₂×C₄×C₄₇	—	2	1	no	—
299	C₂×C₄×C₄₇	—	2	4	no	—
300	C₂×C₄×C₄₇	—	8	4	no	—
301	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
302	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
305	C₂²⋊D₄₇	—	4	8	no	—
306	C₂²⋊D₄₇	—	8	4	no	—
307	C₂×Dic₄₇	—	2	2	no	—
308	C₂×Dic₄₇	—	2	4	no	—
309	C₂×Dic₄₇	—	2	4	no	—
310	C₂×Dic₄₇	—	4	8	no	—
311	C₂×Dic₄₇	—	8	4	no	—
312	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
313	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
314	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
316	C₄×D₄₇	—	2	2	no	—
317	C₄×D₄₇	—	2	1	no	—
318	C₄×D₄₇	—	2	1	no	—
319	C₄×D₄₇	—	2	2	no	—
320	C₄×D₄₇	—	4	2	no	—
321	C₄×D₄₇	—	4	2	no	—
322	C₄×D₄₇	C₂×#41	1	2	yes	—
323	C₄×D₄₇	C₂×#41	1	2	yes	—
324	Dic₉₄	—	2	4	no	—
325	Dic₉₄	—	2	4	no	—
326	Dic₉₄	—	8	4	no	—
327	C₈×C₄₇	—	2	1	no	—
328	C₈×C₄₇	—	2	1	no	—
329	C₈×C₄₇	C₂×#41	1	2	yes	—
330	C₈×C₄₇	C₂×#41	1	2	yes	—
331	C₄₇⋊C₈	—	2	1	no	—
332	C₄₇⋊C₈	—	2	1	no	—
333	C₄₇⋊C₈	C₂×#41	1	2	yes	—
334	C₄₇⋊C₈	C₂×#41	1	2	yes	—
335	#60682	—	47	1	no	maximal, Sylow
336	C₂²×C₄₇	—	2	2	no	—
337	C₂²×C₄₇	—	2	1	no	—
338	C₂²×C₄₇	—	4	4	no	—
339	C₂²×C₄₇	—	4	4	no	—
340	C₂²×C₄₇	—	4	4	no	—
341	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
342	C₂×D₄₇	—	2	2	no	—
343	C₂×D₄₇	—	2	2	no	—
344	C₂×D₄₇	—	2	1	no	—
345	C₂×D₄₇	—	4	4	no	—
346	C₂×D₄₇	#532	1	2	yes	—
347	C₄×C₄₇	—	2	2	no	—
348	C₄×C₄₇	—	2	2	no	—
349	C₄×C₄₇	—	2	1	no	—
350	C₄×C₄₇	—	4	4	no	—
351	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
352	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
353	Dic₄₇	—	2	2	no	—
354	Dic₄₇	—	2	2	no	—
355	Dic₄₇	—	2	1	no	—
356	Dic₄₇	—	4	4	no	—
357	Dic₄₇	—	4	4	no	—
358	Dic₄₇	#532	1	2	yes	—
359	#3455	—	47	2	no	—
360	#3177	—	47	1	no	—
361	#3177	—	47	1	no	—
362	#3176	—	47	1	no	—
363	#3176	D₄₇	1	1	yes	characteristic, complemented
364	#3175	—	47	2	no	—
365	#3175	—	47	2	no	—
366	#3174	—	47	2	no	—
367	#3174	—	47	2	no	—
368	#3173	—	47	2	no	—
369	#3173	—	47	2	no	—
370	#3160	—	47	1	no	—
371	#3147	—	47	1	no	—
372	#3135	—	47	2	no	—
373	#3054	—	47	2	no	—
374	#3050	—	47	2	no	—
375	#2943	—	47	2	no	—
376	C₄×#135	—	47	2	no	—
377	C₂×#405	—	47	1	no	—
378	C₂×C₄₇	—	4	1	no	—
379	C₂×C₄₇	—	8	4	no	—
380	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
381	C₂×C₄₇	#3584	1	2	yes	—
382	D₄₇	—	2	2	no	—
383	D₄₇	—	4	1	no	—
384	C₂×#135	—	47	2	no	—
385	C₂×#135	—	47	2	no	—
386	C₂²×M₁₆	—	47	1	no	—
387	C₂³×C₈	—	47	1	no	—
388	#542	—	47	4	no	—
389	#542	—	47	4	no	—
390	#541	—	47	2	no	—
391	#541	—	47	2	no	—
392	#540	—	47	2	no	—
393	#540	C₂×D₄₇	1	2	yes	—
394	#539	—	94	4	no	—
395	#538	—	94	4	no	—
396	#533	—	47	2	no	—
397	#532	—	47	2	no	—
398	#529	—	94	4	no	—
399	#529	—	94	4	no	—
400	#525	—	47	4	no	—
401	C₄×#41	—	47	4	no	—
402	C₂×#117	—	47	1	no	—
403	#500	—	47	2	no	—
404	#499	—	47	2	no	—
405	#499	—	47	1	no	—
406	#499	C₂×D₄₇	1	1	yes	characteristic, complemented
407	#498	—	47	2	no	—
408	#495	—	47	2	no	—
409	#495	—	47	2	no	—
410	#494	—	47	1	no	—
411	#493	C₂×D₄₇	1	1	yes	characteristic, complemented
412	#492	—	47	2	no	—
413	#491	—	47	2	no	—
414	#491	—	47	2	no	—
415	#490	—	47	2	no	—
416	#490	C₂×D₄₇	1	2	yes	complemented
417	#489	—	47	4	no	—
418	#489	—	47	4	no	—
419	#470	—	47	2	no	—
420	#470	—	47	2	no	—
421	#469	—	47	2	no	—
422	#469	C₂×D₄₇	1	2	yes	—
423	#468	—	47	4	no	—
424	#468	—	47	4	no	—
425	#467	—	47	2	no	—
426	#467	—	47	2	no	—
427	#466	—	47	2	no	—
428	#466	C₂×D₄₇	1	2	yes	—
429	#465	—	47	4	no	—
430	#465	—	47	4	no	—
431	#442	—	47	2	no	—
432	#442	C₂×D₄₇	1	2	yes	complemented
433	#441	—	47	2	no	—
434	#441	—	47	2	no	—
435	#440	—	47	4	no	—
436	#440	—	47	4	no	—
437	C₄×Q₁₆	—	47	2	no	—
438	C₄×Q₁₆	—	47	2	no	—
439	C₄×SD₁₆	—	47	4	no	—
440	C₄×SD₁₆	—	47	4	no	—
441	C₄×D₈	—	47	2	no	—
442	C₄×D₈	C₂×D₄₇	1	2	yes	complemented
443	#427	—	47	2	no	—
444	#427	—	47	2	no	—
445	#416	—	47	4	no	—
446	#416	—	47	4	no	—
447	#405	—	47	1	no	—
448	#405	—	47	1	no	—
449	#405	—	47	1	no	—
450	#405	—	47	1	no	—
451	#405	—	47	1	no	—
452	#405	—	47	1	no	—
453	#405	—	47	1	no	—
454	#405	C₂×D₄₇	1	1	yes	characteristic
455	C₂×#97	—	47	1	no	—
456	C₂×#97	—	47	1	no	—
457	C₂×C₄×C₈	—	47	1	no	—
458	C₂×C₄×C₈	—	47	1	no	—
459	C₄₇	#60682	1	1	yes	characteristic, complemented, Sylow
460	C₂×#41	—	47	4	no	—
461	C₂³×C₄	—	47	1	no	—
462	#135	—	94	8	no	—
463	#135	—	94	8	no	—
464	C₂×Q₁₆	—	47	2	no	—
465	C₂×Q₁₆	—	47	2	no	—
466	C₂×SD₁₆	—	47	4	no	—
467	C₂×SD₁₆	—	47	4	no	—
468	C₂×D₈	C₂²×D₄₇	1	2	yes	—
469	C₂×D₈	C₂²×D₄₇	1	2	yes	—
470	C₂×M₁₆	—	47	1	no	—
471	C₂×M₁₆	—	47	1	no	—
472	C₂×M₁₆	—	47	1	no	—
473	C₂×M₁₆	—	94	4	no	—
474	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
475	C₂²×C₈	—	47	1	no	—
476	C₂²×C₈	—	47	1	no	—
477	C₂²×C₈	—	47	1	no	—
478	C₂²×C₈	—	47	1	no	—
479	C₂²×C₈	—	47	1	no	—
480	C₂²×C₈	—	47	1	no	—
481	C₂²×C₈	—	47	1	no	—
482	C₂²×C₈	—	94	4	no	—
483	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
484	C₄⋊Q₈	—	47	4	no	—
485	C₄⋊Q₈	—	47	2	no	—
486	#127	C₂²×D₄₇	1	2	yes	—
487	#126	—	94	4	no	—
488	#126	—	94	4	no	—
489	#126	—	94	4	no	—
490	#126	—	94	4	no	—
491	#125	—	47	2	no	—
492	#125	—	94	4	no	—
493	#125	—	94	4	no	—
494	#125	C₂²×D₄₇	1	2	yes	—
495	#124	—	47	4	no	—
496	#124	—	94	4	no	—
497	#124	—	94	4	no	—
498	#123	—	2	4	no	—
499	#123	—	94	4	no	—
500	#123	—	94	4	no	—
501	#123	—	94	4	no	—
502	#123	—	94	4	no	—
503	C₂²⋊Q₈	—	47	4	no	—
504	C₂²⋊Q₈	—	47	4	no	—
505	C₂²⋊Q₈	—	94	4	no	—
506	C₂²⋊Q₈	—	94	4	no	—
507	C₂²⋊Q₈	—	94	4	no	—
508	#121	—	2	4	no	—
509	#121	—	47	4	no	—
510	#121	—	94	4	no	—
511	#121	—	94	4	no	—
512	#121	C₂²×D₄₇	1	4	yes	—
513	#120	—	94	4	no	—
514	C₄×Q₈	—	47	4	no	—
515	C₄×Q₈	—	47	4	no	—
516	C₄×Q₈	—	94	4	no	—
517	C₄×D₄	—	47	4	no	—
518	C₄×D₄	—	94	4	no	—
519	C₄×D₄	—	94	4	no	—
520	C₄×D₄	—	94	4	no	—
521	C₄×D₄	—	94	4	no	—
522	C₄×D₄	—	94	4	no	—
523	C₄×D₄	C₂²×D₄₇	1	4	yes	—
524	#117	—	47	1	no	—
525	#117	—	47	2	no	—
526	#117	—	47	2	no	—
527	#117	—	47	1	no	—
528	#117	—	47	1	no	—
529	#117	—	47	4	no	—
530	#117	—	94	4	no	—
531	#117	C₂²×D₄₇	1	1	yes	characteristic
532	C₂×C₄⋊C₄	—	47	2	no	—
533	C₂×C₂²⋊C₄	—	47	2	no	—
534	C₂×C₄²	—	47	1	no	—
535	C₂×C₄²	—	47	1	no	—
536	C₂×C₄²	—	94	4	no	—
537	#107	—	47	2	no	—
538	#107	—	47	4	no	—
539	#107	C₂²×D₄₇	1	2	yes	—
540	#106	—	47	2	no	—
541	#106	—	47	4	no	—
542	#106	C₂²×D₄₇	1	2	yes	—
543	#103	—	47	4	no	—
544	#103	—	47	4	no	—
545	#103	—	47	4	no	—
546	#103	—	47	4	no	—
547	#102	—	47	4	no	—
548	#102	—	47	4	no	—
549	#102	C₂²×D₄₇	1	4	yes	—
550	#102	C₂²×D₄₇	1	4	yes	—
551	#97	—	47	1	no	—
552	#97	—	47	1	no	—
553	#97	—	47	1	no	—
554	#97	—	47	1	no	—
555	#97	—	47	1	no	—
556	#97	—	47	1	no	—
557	#97	C₂²×D₄₇	1	1	yes	characteristic
558	#97	C₂²×D₄₇	1	1	yes	characteristic
559	C₄×C₈	—	47	1	no	—
560	C₄×C₈	—	47	1	no	—
561	C₄×C₈	—	47	1	no	—
562	C₄×C₈	—	47	1	no	—
563	C₄×C₈	—	47	1	no	—
564	C₄×C₈	—	47	1	no	—
565	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
566	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
567	C₂⁴	—	47	1	no	—
568	#41	—	94	8	no	—
569	#41	—	94	8	no	—
570	C₂×Q₈	—	47	4	no	—
571	C₂×Q₈	—	94	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	94	4	no	—
575	C₂×D₄	—	94	4	no	—
576	C₂×D₄	C₂³×D₄₇	1	4	yes	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	47	1	no	—
579	C₂²×C₄	—	47	1	no	—
580	C₂²×C₄	—	47	1	no	—
581	C₂²×C₄	—	47	1	no	—
582	C₂²×C₄	—	47	1	no	—
583	C₂²×C₄	—	47	2	no	—
584	C₂²×C₄	—	47	2	no	—
585	C₂²×C₄	—	94	2	no	—
586	C₂²×C₄	—	94	2	no	—
587	C₂²×C₄	—	94	4	no	—
588	C₂²×C₄	—	94	4	no	—
589	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
590	Q₁₆	—	94	4	no	—
591	Q₁₆	—	94	4	no	—
592	SD₁₆	—	94	8	no	—
593	SD₁₆	—	94	8	no	—
594	D₈	—	2	4	no	—
595	D₈	—	2	4	no	—
596	M₁₆	—	2	2	no	—
597	M₁₆	—	94	2	no	—
598	M₁₆	—	94	2	no	—
599	M₁₆	—	94	2	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	47	1	no	—
602	C₂×C₈	—	47	1	no	—
603	C₂×C₈	—	47	4	no	—
604	C₂×C₈	—	47	4	no	—
605	C₂×C₈	—	47	1	no	—
606	C₂×C₈	—	47	1	no	—
607	C₂×C₈	—	94	2	no	—
608	C₂×C₈	—	94	2	no	—
609	C₂×C₈	—	94	2	no	—
610	C₂×C₈	—	94	2	no	—
611	C₂×C₈	—	94	2	no	—
612	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
613	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
614	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
615	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	47	2	no	—
618	C₄⋊C₄	—	47	2	no	—
619	C₄⋊C₄	—	47	2	no	—
620	C₄⋊C₄	—	47	4	no	—
621	C₄⋊C₄	—	94	4	no	—
622	C₄⋊C₄	—	94	4	no	—
623	C₄⋊C₄	—	94	4	no	—
624	C₄⋊C₄	—	94	4	no	—
625	C₄⋊C₄	—	94	4	no	—
626	C₄⋊C₄	—	94	4	no	—
627	C₄⋊C₄	—	94	4	no	—
628	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
629	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	47	2	no	—
633	C₂²⋊C₄	—	47	2	no	—
634	C₂²⋊C₄	—	47	2	no	—
635	C₂²⋊C₄	—	94	4	no	—
636	C₂²⋊C₄	—	94	4	no	—
637	C₂²⋊C₄	—	94	4	no	—
638	C₂²⋊C₄	—	94	4	no	—
639	C₂²⋊C₄	—	94	4	no	—
640	C₂²⋊C₄	—	94	4	no	—
641	C₂²⋊C₄	—	94	4	no	—
642	C₂²⋊C₄	D₄×D₄₇	1	2	yes	—
643	C₄²	—	47	2	no	—
644	C₄²	—	47	2	no	—
645	C₄²	—	47	1	no	—
646	C₄²	—	47	1	no	—
647	C₄²	—	94	4	no	—
648	C₄²	—	94	4	no	—
649	C₄²	—	94	4	no	—
650	C₄²	C₂³×D₄₇	1	1	yes	characteristic
651	C₄²	C₂³×D₄₇	1	1	yes	characteristic
652	C₂³	—	2	4	no	—
653	C₂³	—	47	1	no	—
654	C₂³	—	47	1	no	—
655	C₂³	—	94	2	no	—
656	C₂³	—	188	2	no	—
657	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
658	Q₈	—	94	4	no	—
659	Q₈	—	94	4	no	—
660	Q₈	—	376	4	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	4	no	—
663	D₄	—	8	4	no	—
664	D₄	—	8	4	no	—
665	D₄	—	376	4	no	—
666	D₄	—	188	8	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	8	4	no	—
671	C₂×C₄	—	47	1	no	—
672	C₂×C₄	—	47	2	no	—
673	C₂×C₄	—	47	2	no	—
674	C₂×C₄	—	47	2	no	—
675	C₂×C₄	—	47	2	no	—
676	C₂×C₄	—	47	1	no	—
677	C₂×C₄	—	94	2	no	—
678	C₂×C₄	—	94	2	no	—
679	C₂×C₄	—	94	2	no	—
680	C₂×C₄	—	94	1	no	—
681	C₂×C₄	—	94	1	no	—
682	C₂×C₄	—	94	4	no	—
683	C₂×C₄	—	94	4	no	—
684	C₂×C₄	—	376	4	no	—
685	C₂×C₄	—	188	2	no	—
686	C₂×C₄	—	188	2	no	—
687	C₂×C₄	—	188	8	no	—
688	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
689	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
690	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
691	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
692	C₈	—	2	1	no	—
693	C₈	—	2	1	no	—
694	C₈	—	47	2	no	—
695	C₈	—	47	2	no	—
696	C₈	—	94	1	no	—
697	C₈	—	94	1	no	—
698	C₈	#41×D₄₇	1	2	yes	—
699	C₈	#41×D₄₇	1	2	yes	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	47	2	no	—
706	C₂²	—	94	2	no	—
707	C₂²	—	94	2	no	—
708	C₂²	—	94	1	no	—
709	C₂²	—	188	4	no	—
710	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	1	no	—
714	C₄	—	4	4	no	—
715	C₄	—	47	2	no	—
716	C₄	—	94	2	no	—
717	C₄	—	94	2	no	—
718	C₄	—	94	1	no	—
719	C₄	—	188	4	no	—
720	C₄	—	188	4	no	—
721	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
722	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
723	C₂	—	4	1	no	—
724	C₂	—	8	4	no	—
725	C₂	—	94	2	no	—
726	C₂	—	188	1	no	—
727	C₂	#532×D₄₇	1	1	yes	characteristic
728	C₂	#20258156	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3176	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3176	D₄₇
hypocenter	C₄₇	#60682
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3176

Complements

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

N	H ≅ G/N	type
1. #20256772	C₂	semidirect
2. #20254048	C₂	semidirect
3. #20254047	C₂	semidirect
4. #20254035	C₂	semidirect
5. #20254023	C₂	semidirect
6. #20254020	C₂	semidirect
7. #20254015	C₂	semidirect
8. #20254010	C₂	semidirect
9. #20254003	C₂	semidirect
10. #20254000	C₂	semidirect
11. #20253901	C₂	semidirect
12. #20253815	C₂	semidirect
13. #20253732	C₂	semidirect
14. #20252995	C₂	semidirect
15. #20252967	C₂	semidirect
16. #20252185	C₂	semidirect
17. C₄×#13094043	C₂	semidirect
18. #405×D₄₇	C₂	semidirect
19. C₄₇×#3176	C₂	semidirect
38. #15689527	C₂²	semidirect
39. #15689525	C₂²	semidirect
40. #15689522	C₂²	semidirect
41. #15689520	C₂²	semidirect
42. #15689506	C₂²	semidirect
43. #15689506	C₂²	semidirect
44. #15689503	C₂²	semidirect
45. #15689495	C₂²	semidirect
46. #15689493	C₂²	semidirect
47. #15689492	C₂²	semidirect
48. #15689487	C₂²	semidirect
49. #15689481	C₂²	semidirect
50. #15689481	C₂²	semidirect
61. #15689235	C₂²	semidirect
62. #15689231	C₂²	semidirect
63. #15689229	C₂²	semidirect
64. #15689223	C₂²	semidirect
65. #15689220	C₂²	semidirect
66. C₄×Dic₁₈₈	C₂²	semidirect
67. #15689217	C₂²	semidirect
68. #15689214	C₂²	semidirect
69. C₄×#10625335	C₂²	semidirect
70. D₈×Dic₄₇	C₂²	semidirect
87. C₄₇×#499	C₂²	semidirect
88. C₄₇×#493	C₂²	semidirect
89. C₄₇×#490	C₂²	semidirect
92. C₄₇×#442	C₂²	semidirect
93. C₄×D₈×C₄₇	C₂²	semidirect
363. #3176	D₄₇	semidirect
406. #499	C₂×D₄₇	semidirect
411. #493	C₂×D₄₇	semidirect
416. #490	C₂×D₄₇	semidirect
432. #442	C₂×D₄₇	semidirect
442. C₄×D₈	C₂×D₄₇	semidirect
459. C₄₇	#60682	semidirect

Maximal subgroups

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

subgroup	index
#20256772	2
#20254048	2
#20254047	2
#20254035	2
#20254023	2
#20254020	2
#20254015	2
#20254010	2
#20254003	2
#20254000	2
#20253901	2
#20253815	2
#20253732	2
#20252995	2
#20252967	2
#20252185	2
C₄×#13094043	2
#405×D₄₇	2
C₄₇×#3176	2
#60682	47