Subgroups — #20257250

Order 6016.

1012 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689859	C₂	1	2	yes	maximal, complemented
2	#15689848	C₂	1	2	yes	maximal, complemented
3	#15689843	C₂	1	2	yes	maximal, complemented
4	#15689842	C₂	1	4	yes	maximal, complemented
5	#15689830	C₂	1	2	yes	maximal, complemented
6	#15689813	C₂	1	4	yes	maximal, complemented
7	#15689718	C₂	1	4	yes	maximal, complemented
8	#15689694	C₂	1	2	yes	maximal, complemented
9	#15689680	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689654	C₂	1	4	yes	maximal, complemented
11	#15689606	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₇×#532	C₂	1	1	yes	maximal, characteristic
14	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
15	#13094024	C₂²	1	1	yes	characteristic
16	#13094024	C₂²	1	1	yes	characteristic
17	#13094022	C₂²	1	4	yes	—
18	#13094017	C₂²	1	8	yes	—
19	#13094017	C₂²	1	8	yes	—
20	#13094016	C₂²	1	2	yes	—
21	#13094015	C₂²	1	4	yes	—
22	#13094014	C₂²	1	8	yes	—
23	#13094011	C₂²	1	4	yes	—
24	#13094011	C₂²	1	4	yes	—
25	#13094005	C₂²	1	8	yes	—
26	#13094005	C₂²	1	8	yes	—
27	#13094003	C₂²	1	4	yes	—
28	#13094003	C₂²	1	4	yes	—
29	#13094003	C₂²	1	2	yes	—
30	#13094003	C₂²	1	2	yes	—
31	#13094001	C₂²	1	8	yes	—
32	Q₈×Dic₄₇	C₂²	1	4	yes	—
33	C₄×Dic₉₄	C₂²	1	2	yes	—
34	C₄×Dic₉₄	C₂²	1	2	yes	—
35	C₄×Dic₉₄	C₂²	1	2	yes	—
36	C₄×Dic₉₄	C₂²	1	2	yes	—
37	C₄×Dic₉₄	C₂²	1	2	yes	—
38	C₄×Dic₉₄	C₂²	1	2	yes	—
39	#13093989	C₂²	1	4	yes	—
40	D₄×Dic₄₇	C₂²	1	4	yes	—
41	D₄×Dic₄₇	C₂²	1	4	yes	—
42	D₄×Dic₄₇	C₂²	1	8	yes	—
43	#13093983	C₂²	1	4	yes	—
44	#13093983	C₂²	1	2	yes	—
45	#13093980	C₂²	1	8	yes	—
46	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
47	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
48	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
49	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
50	C₂×#41×C₄₇	C₂²	1	2	yes	—
51	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
52	#127×C₄₇	C₂²	1	1	yes	characteristic
53	#124×C₄₇	C₂²	1	2	yes	—
54	#121×C₄₇	C₂²	1	2	yes	—
55	#121×C₄₇	C₂²	1	2	yes	—
56	C₄×D₄×C₄₇	C₂²	1	2	yes	—
57	C₄×D₄×C₄₇	C₂²	1	2	yes	—
58	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
59	#41×C₄₇	—	2	8	no	—
60	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
61	C₂×D₄×C₄₇	C₂³	1	2	yes	—
62	C₂×D₄×C₄₇	C₂³	1	4	yes	—
63	C₂×D₄×C₄₇	C₂³	1	2	yes	—
64	C₂×D₄×C₄₇	C₂³	1	2	yes	—
65	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
67	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂²×Dic₄₇	C₂³	1	2	yes	—
70	C₂²×Dic₄₇	C₂³	1	2	yes	—
71	C₂²×Dic₄₇	C₂³	1	8	yes	—
72	C₂×Dic₉₄	—	2	4	no	—
73	C₂×Dic₉₄	C₂³	1	2	yes	—
74	C₂×Dic₉₄	C₂³	1	2	yes	—
75	C₂×Dic₉₄	C₂³	1	2	yes	—
76	C₂×Dic₉₄	C₂³	1	2	yes	—
77	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
79	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
80	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
81	C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²⋊Dic₄₇	C₂³	1	8	yes	—
86	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
87	C₂²⋊Dic₄₇	C₂³	1	8	yes	—
88	C₂²⋊Dic₄₇	C₂³	1	8	yes	—
89	C₄⋊Dic₄₇	C₂³	1	2	yes	—
90	C₄⋊Dic₄₇	C₂³	1	2	yes	—
91	C₄⋊Dic₄₇	C₂³	1	2	yes	—
92	C₄⋊Dic₄₇	C₂³	1	8	yes	—
93	C₄⋊Dic₄₇	C₂³	1	2	yes	—
94	C₄⋊Dic₄₇	C₂³	1	2	yes	—
95	C₄⋊Dic₄₇	C₂³	1	2	yes	—
96	Dic₄₇⋊C₄	C₂³	1	4	yes	—
97	Dic₄₇⋊C₄	C₂³	1	4	yes	—
98	Dic₄₇⋊C₄	C₂³	1	4	yes	—
99	Dic₄₇⋊C₄	C₂³	1	8	yes	—
100	Dic₄₇⋊C₄	C₂³	1	8	yes	—
101	Dic₄₇⋊C₄	C₂³	1	4	yes	—
102	C₄×Dic₄₇	C₂³	1	4	yes	—
103	C₄×Dic₄₇	C₂³	1	4	yes	—
104	C₄×Dic₄₇	C₂³	1	8	yes	—
105	C₄×Dic₄₇	C₂³	1	4	yes	—
106	C₂³×C₄₇	C₂⁴	1	4	yes	—
107	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
108	Q₈×C₄₇	—	2	4	no	—
109	D₄×C₄₇	—	2	8	no	—
110	D₄×C₄₇	—	2	4	no	—
111	D₄×C₄₇	—	2	4	no	—
112	D₄×C₄₇	—	4	2	no	—
113	C₂×C₄×C₄₇	—	2	8	no	—
114	C₂×C₄×C₄₇	—	2	2	no	—
115	C₂×C₄×C₄₇	—	4	1	no	—
116	C₂×C₄×C₄₇	#41	1	4	yes	—
117	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
118	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
119	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
123	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₂×Dic₄₇	—	2	4	no	—
125	C₂×Dic₄₇	—	4	8	no	—
126	C₂×Dic₄₇	—	4	2	no	—
127	C₂×Dic₄₇	C₂⁴	1	4	yes	—
128	C₂×Dic₄₇	C₂⁴	1	4	yes	—
129	C₂×Dic₄₇	C₂⁴	1	4	yes	—
130	C₂×Dic₄₇	C₂⁴	1	4	yes	—
131	Dic₉₄	—	2	4	no	—
132	Dic₉₄	—	2	4	no	—
133	Dic₉₄	—	2	4	no	—
134	Dic₉₄	—	4	2	no	—
135	C₂²×C₄₇	—	2	1	no	—
136	C₂²×C₄₇	—	2	1	no	—
137	C₂²×C₄₇	—	2	4	no	—
138	C₂²×C₄₇	—	2	4	no	—
139	C₂²×C₄₇	—	2	4	no	—
140	C₂²×C₄₇	C₂×#41	1	2	yes	—
141	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
142	C₄×C₄₇	—	2	4	no	—
143	C₄×C₄₇	—	2	1	no	—
144	C₄×C₄₇	—	2	1	no	—
145	C₄×C₄₇	—	2	1	no	—
146	C₄×C₄₇	C₂×#41	1	2	yes	—
147	C₄×C₄₇	C₂×#41	1	2	yes	—
148	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
149	Dic₄₇	—	2	4	no	—
150	Dic₄₇	—	2	4	no	—
151	Dic₄₇	—	2	4	no	—
152	Dic₄₇	—	2	4	no	—
153	#3507	—	47	1	no	maximal, Sylow
154	C₂×C₄₇	—	2	2	no	—
155	C₂×C₄₇	—	4	4	no	—
156	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
157	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×C₄₇	#585	1	1	yes	characteristic
159	#559	—	47	2	no	—
160	#557	—	47	2	no	—
161	#556	—	47	4	no	—
162	#556	—	47	2	no	—
163	#554	—	47	2	no	—
164	#552	—	47	4	no	—
165	#539	—	47	4	no	—
166	#536	—	47	2	no	—
167	#533	—	47	1	no	—
168	#532	D₄₇	1	1	yes	characteristic
169	#529	—	47	4	no	—
170	#520	—	47	2	no	—
171	C₂×C₄×Q₈	—	47	1	no	—
172	C₄₇	#3507	1	1	yes	characteristic, complemented, Sylow
173	C₂×#41	C₂×D₄₇	1	2	yes	—
174	C₂²×Q₈	—	47	1	no	—
175	C₄⋊Q₈	—	47	4	no	—
176	C₄⋊Q₈	—	47	1	no	—
177	C₄⋊Q₈	—	47	1	no	—
178	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
179	#127	C₂×D₄₇	1	1	yes	characteristic
180	#126	—	47	8	no	—
181	#126	—	47	8	no	—
182	#125	—	47	4	no	—
183	#125	—	47	8	no	—
184	#125	—	47	2	no	—
185	#124	—	47	4	no	—
186	#124	—	47	4	no	—
187	#124	C₂×D₄₇	1	2	yes	—
188	#123	—	47	8	no	—
189	#123	—	47	8	no	—
190	C₂²⋊Q₈	—	47	2	no	—
191	C₂²⋊Q₈	—	47	2	no	—
192	C₂²⋊Q₈	—	47	4	no	—
193	C₂²⋊Q₈	—	47	4	no	—
194	C₂²⋊Q₈	—	47	8	no	—
195	#121	C₂×D₄₇	1	2	yes	—
196	#121	C₂×D₄₇	1	2	yes	—
197	C₄×Q₈	—	47	4	no	—
198	C₄×Q₈	—	47	4	no	—
199	C₄×Q₈	—	47	2	no	—
200	C₄×Q₈	—	47	2	no	—
201	C₄×Q₈	—	47	2	no	—
202	C₄×Q₈	—	47	2	no	—
203	C₄×Q₈	—	47	2	no	—
204	C₄×Q₈	—	47	2	no	—
205	C₄×D₄	—	47	8	no	—
206	C₄×D₄	—	47	4	no	—
207	C₄×D₄	—	47	4	no	—
208	C₄×D₄	C₂×D₄₇	1	2	yes	—
209	C₄×D₄	C₂×D₄₇	1	2	yes	—
210	#117	—	47	2	no	—
211	#117	—	47	4	no	—
212	#117	—	47	8	no	—
213	C₂×C₄⋊C₄	—	47	1	no	—
214	C₂×C₄⋊C₄	—	47	2	no	—
215	C₂×C₄⋊C₄	—	47	4	no	—
216	C₂×C₄²	—	47	2	no	—
217	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
218	#41	—	2	8	no	—
219	C₂×Q₈	—	47	2	no	—
220	C₂×Q₈	—	47	2	no	—
221	C₂×Q₈	—	47	2	no	—
222	C₂×Q₈	—	47	2	no	—
223	C₂×Q₈	—	94	4	no	—
224	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
225	C₂×D₄	C₂²×D₄₇	1	2	yes	—
226	C₂×D₄	C₂²×D₄₇	1	4	yes	—
227	C₂×D₄	C₂²×D₄₇	1	2	yes	—
228	C₂×D₄	C₂²×D₄₇	1	2	yes	—
229	C₂²×C₄	—	47	2	no	—
230	C₂²×C₄	—	47	2	no	—
231	C₂²×C₄	—	47	8	no	—
232	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
233	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
234	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
235	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
236	C₄⋊C₄	—	47	4	no	—
237	C₄⋊C₄	—	47	4	no	—
238	C₄⋊C₄	—	47	4	no	—
239	C₄⋊C₄	—	47	8	no	—
240	C₄⋊C₄	—	47	4	no	—
241	C₄⋊C₄	—	47	8	no	—
242	C₄⋊C₄	—	47	2	no	—
243	C₄⋊C₄	—	47	2	no	—
244	C₄⋊C₄	—	47	2	no	—
245	C₄⋊C₄	—	47	8	no	—
246	C₄⋊C₄	—	47	2	no	—
247	C₄⋊C₄	—	47	2	no	—
248	C₄⋊C₄	—	47	2	no	—
249	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
250	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
251	C₂²⋊C₄	—	47	4	no	—
252	C₂²⋊C₄	—	47	8	no	—
253	C₂²⋊C₄	—	47	8	no	—
254	C₂²⋊C₄	—	47	8	no	—
255	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
256	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
257	C₄²	—	47	4	no	—
258	C₄²	—	47	4	no	—
259	C₄²	—	47	8	no	—
260	C₄²	—	47	4	no	—
261	C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	C₄²	C₂²×D₄₇	1	1	yes	characteristic
264	C₄²	C₂²×D₄₇	1	1	yes	characteristic
265	C₂³	C₂³×D₄₇	1	4	yes	—
266	C₂³	C₂³×D₄₇	1	1	yes	characteristic
267	Q₈	—	2	4	no	—
268	Q₈	—	94	4	no	—
269	Q₈	—	94	4	no	—
270	Q₈	—	94	4	no	—
271	Q₈	—	188	2	no	—
272	D₄	—	2	8	no	—
273	D₄	—	2	4	no	—
274	D₄	—	2	4	no	—
275	D₄	—	4	2	no	—
276	C₂×C₄	—	2	8	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	47	4	no	—
280	C₂×C₄	—	47	4	no	—
281	C₂×C₄	—	47	4	no	—
282	C₂×C₄	—	47	4	no	—
283	C₂×C₄	—	94	4	no	—
284	C₂×C₄	—	188	2	no	—
285	C₂×C₄	—	188	8	no	—
286	C₂×C₄	#10625352	1	4	yes	—
287	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
288	C₂×C₄	C₂³×D₄₇	1	4	yes	—
289	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
290	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
291	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
292	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
293	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
294	C₂²	—	2	1	no	—
295	C₂²	—	2	1	no	—
296	C₂²	—	2	4	no	—
297	C₂²	—	2	4	no	—
298	C₂²	—	2	4	no	—
299	C₂²	C₂×#10625352	1	2	yes	—
300	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
301	C₄	—	2	4	no	—
302	C₄	—	2	1	no	—
303	C₄	—	2	1	no	—
304	C₄	—	2	1	no	—
305	C₄	—	94	4	no	—
306	C₄	—	94	4	no	—
307	C₄	—	94	4	no	—
308	C₄	—	94	4	no	—
309	C₄	C₂×#10625352	1	2	yes	—
310	C₄	C₂×#10625352	1	2	yes	—
311	C₄	#13094071	1	2	yes	—
312	C₂	—	2	2	no	—
313	C₂	—	4	4	no	—
314	C₂	C₂²×#10625352	1	1	yes	characteristic
315	C₂	C₂×#13094071	1	1	yes	characteristic
316	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#532	C₂
hypercenter	#532	D₄₇
hypocenter	C₄₇	#3507
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #15689859	C₂	semidirect
2. #15689848	C₂	semidirect
3. #15689843	C₂	semidirect
4. #15689842	C₂	semidirect
5. #15689830	C₂	semidirect
6. #15689813	C₂	semidirect
7. #15689718	C₂	semidirect
8. #15689694	C₂	semidirect
9. #15689680	C₂	semidirect
10. #15689654	C₂	semidirect
11. #15689606	C₂	semidirect
12. C₂×C₄×Dic₉₄	C₂	semidirect
172. C₄₇	#3507	semidirect