Subgroups — #20257108

Order 6016.

1040 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689841	C₂	1	4	yes	maximal, complemented
2	#15689836	C₂	1	4	yes	maximal, complemented
3	#15689817	C₂	1	4	yes	maximal, complemented
4	#15689812	C₂	1	4	yes	maximal, complemented
5	#15689754	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689711	C₂	1	4	yes	maximal, complemented
7	#15689704	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689657	C₂	1	4	yes	maximal, complemented
9	#15689634	C₂	1	2	yes	maximal, complemented
10	#15689604	C₂	1	2	yes	maximal, complemented
11	C₂×#117×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625350	C₂²	1	2	yes	—
13	#13094023	C₂²	1	4	yes	complemented
14	#13094018	C₂²	1	8	yes	complemented
15	#13094017	C₂²	1	8	yes	—
16	#13094016	C₂²	1	4	yes	complemented
17	#13094015	C₂²	1	4	yes	complemented
18	#13094012	C₂²	1	4	yes	complemented
19	#13094010	C₂²	1	8	yes	—
20	#13094007	C₂²	1	4	yes	—
21	#13094006	C₂²	1	8	yes	—
22	#13094004	C₂²	1	4	yes	complemented
23	#13094003	C₂²	1	4	yes	—
24	#13094003	C₂²	1	2	yes	—
25	#13094003	C₂²	1	2	yes	—
26	#13093999	C₂²	1	4	yes	complemented
27	#13093998	C₂²	1	2	yes	—
28	#13093998	C₂²	1	2	yes	—
29	#13093998	C₂²	1	4	yes	—
30	#13093997	C₂²	1	8	yes	—
31	#13093993	C₂²	1	4	yes	—
32	C₄×Dic₉₄	C₂²	1	4	yes	complemented
33	#13093989	C₂²	1	4	yes	complemented
34	C₄×D₁₈₈	C₂²	1	4	yes	complemented
35	#13093986	C₂²	1	4	yes	complemented
36	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
37	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	—
38	C₄×C₂²⋊D₄₇	C₂²	1	8	yes	—
39	#13093983	C₂²	1	2	yes	—
40	#13093982	C₂²	1	4	yes	complemented
41	#13093981	C₂²	1	8	yes	complemented
42	C₄⋊C₄×D₄₇	C₂²	1	4	yes	complemented
43	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
44	#117×C₄₇	C₂²	1	4	yes	—
45	#117×C₄₇	C₂²	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
49	C₂×C₄²×C₄₇	C₂²	1	2	yes	—
50	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	—	2	4	no	—
52	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
54	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
55	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
56	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
57	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
59	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
60	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
61	#10625350	—	2	8	no	—
62	C₂×D₁₈₈	C₂³	1	2	yes	—
63	C₂×D₁₈₈	C₂³	1	4	yes	—
64	C₂×C₄×D₄₇	C₂³	1	4	yes	—
65	C₂×C₄×D₄₇	C₂³	1	8	yes	—
66	C₂×Dic₉₄	C₂³	1	2	yes	—
67	C₂×Dic₉₄	C₂³	1	4	yes	—
68	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
69	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
70	C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
71	C₄²×C₄₇	C₂³	1	4	yes	—
72	C₄²×C₄₇	C₂³	1	4	yes	—
73	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
74	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
75	C₂²⋊Dic₄₇	C₂³	1	4	yes	—
76	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
77	(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
78	(C₂×D₄₇)⋊C₄	C₂³	1	8	yes	—
79	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
80	C₄⋊Dic₄₇	C₂³	1	2	yes	—
81	C₄⋊Dic₄₇	C₂³	1	2	yes	—
82	C₄⋊Dic₄₇	C₂³	1	4	yes	—
83	C₄⋊Dic₄₇	C₂³	1	4	yes	—
84	Dic₄₇⋊C₄	C₂³	1	8	yes	—
85	Dic₄₇⋊C₄	C₂³	1	4	yes	—
86	Dic₄₇⋊C₄	C₂³	1	8	yes	—
87	Dic₄₇⋊C₄	C₂³	1	4	yes	—
88	C₄×Dic₄₇	C₂³	1	8	yes	—
89	C₄×Dic₄₇	C₂³	1	4	yes	—
90	C₂³×C₄₇	—	2	2	no	—
91	C₂³×C₄₇	—	4	1	no	—
92	C₂³×C₄₇	—	4	1	no	—
93	C₂³×C₄₇	C₂⁴	1	2	yes	—
94	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×D₄₇	C₂⁴	1	4	yes	—
96	C₂×C₄×C₄₇	—	2	2	no	—
97	C₂×C₄×C₄₇	—	2	4	no	—
98	C₂×C₄×C₄₇	—	2	4	no	—
99	C₂×C₄×C₄₇	—	4	2	no	—
100	C₂×C₄×C₄₇	—	4	2	no	—
101	C₂×C₄×C₄₇	#41	1	4	yes	—
102	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
103	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
106	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
107	C₂²⋊D₄₇	—	2	8	no	—
108	C₂²⋊D₄₇	—	4	4	no	—
109	C₂²⋊D₄₇	—	4	4	no	—
110	C₂×Dic₄₇	C₂⁴	1	4	yes	—
111	C₂×Dic₄₇	C₂⁴	1	4	yes	—
112	C₂×Dic₄₇	C₂⁴	1	4	yes	—
113	D₁₈₈	—	2	4	no	—
114	D₁₈₈	—	4	4	no	—
115	C₄×D₄₇	—	2	8	no	—
116	C₄×D₄₇	—	4	8	no	—
117	Dic₉₄	—	2	4	no	—
118	Dic₉₄	—	4	4	no	—
119	C₂²×C₄₇	—	2	1	no	—
120	C₂²×C₄₇	—	2	1	no	—
121	C₂²×C₄₇	—	2	2	no	—
122	C₂²×C₄₇	—	2	2	no	—
123	C₂²×C₄₇	—	2	2	no	—
124	C₂²×C₄₇	—	4	4	no	—
125	C₂²×C₄₇	C₂×#41	1	2	yes	—
126	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
127	C₂×D₄₇	—	2	4	no	—
128	C₂×D₄₇	—	2	4	no	—
129	C₂×D₄₇	—	2	4	no	—
130	C₄×C₄₇	—	2	1	no	—
131	C₄×C₄₇	—	2	1	no	—
132	C₄×C₄₇	—	2	4	no	—
133	C₄×C₄₇	—	2	4	no	—
134	C₄×C₄₇	C₂×#41	1	4	yes	—
135	Dic₄₇	—	2	4	no	—
136	Dic₄₇	—	2	4	no	—
137	Dic₄₇	—	2	4	no	—
138	#3493	—	47	1	no	maximal, Sylow
139	C₂×C₄₇	—	2	2	no	—
140	C₂×C₄₇	—	4	2	no	—
141	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
142	C₂×C₄₇	#585	1	1	yes	characteristic
143	C₂×C₄₇	#585	1	1	yes	characteristic
144	D₄₇	—	4	4	no	—
145	#556	—	47	4	no	—
146	#555	—	47	4	no	—
147	#553	—	47	4	no	—
148	#552	—	47	4	no	—
149	#544	—	47	1	no	—
150	#538	—	47	4	no	—
151	#537	—	47	1	no	—
152	#529	—	47	4	no	—
153	#525	—	47	2	no	—
154	#520	—	47	2	no	—
155	C₂×#117	D₄₇	1	1	yes	characteristic, complemented
156	C₄₇	#3493	1	1	yes	characteristic, complemented, Sylow
157	C₂×#41	—	47	2	no	—
158	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
159	C₄⋊Q₈	—	47	4	no	—
160	#126	—	47	8	no	—
161	#126	—	47	8	no	—
162	#125	—	47	4	no	—
163	#125	—	47	4	no	—
164	#124	—	47	8	no	—
165	#124	—	47	4	no	—
166	#123	—	47	4	no	—
167	#123	—	47	8	no	—
168	C₂²⋊Q₈	—	47	2	no	—
169	C₂²⋊Q₈	—	47	2	no	—
170	C₂²⋊Q₈	—	47	4	no	—
171	C₂²⋊Q₈	—	47	4	no	—
172	#121	—	47	2	no	—
173	#121	—	47	2	no	—
174	#121	—	47	4	no	—
175	#121	—	47	4	no	—
176	#121	—	47	8	no	—
177	#120	—	47	4	no	—
178	C₄×Q₈	—	47	4	no	—
179	C₄×Q₈	—	47	4	no	—
180	C₄×D₄	—	47	8	no	—
181	C₄×D₄	—	47	4	no	—
182	C₄×D₄	—	47	4	no	—
183	C₄×D₄	—	47	4	no	—
184	C₄×D₄	—	47	4	no	—
185	#117	—	47	2	no	—
186	#117	—	47	4	no	—
187	#117	—	47	8	no	—
188	#117	C₂×D₄₇	1	4	yes	—
189	#117	C₂×D₄₇	1	4	yes	—
190	C₂×C₄⋊C₄	—	47	4	no	—
191	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
192	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
193	C₂×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
194	C₂×C₄²	C₂×D₄₇	1	2	yes	—
195	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
196	#41	—	94	8	no	—
197	C₂×Q₈	—	47	2	no	—
198	C₂×Q₈	—	47	4	no	—
199	C₂×D₄	—	47	4	no	—
200	C₂×D₄	—	47	4	no	—
201	C₂×D₄	—	47	4	no	—
202	C₂×D₄	—	47	2	no	—
203	C₂×D₄	—	47	4	no	—
204	C₂²×C₄	—	2	4	no	—
205	C₂²×C₄	—	47	4	no	—
206	C₂²×C₄	—	47	8	no	—
207	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
208	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
209	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
210	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
211	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
212	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
213	C₄⋊C₄	—	47	8	no	—
214	C₄⋊C₄	—	47	4	no	—
215	C₄⋊C₄	—	47	8	no	—
216	C₄⋊C₄	—	47	4	no	—
217	C₄⋊C₄	—	47	2	no	—
218	C₄⋊C₄	—	47	2	no	—
219	C₄⋊C₄	—	47	4	no	—
220	C₄⋊C₄	—	47	4	no	—
221	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
222	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
223	C₂²⋊C₄	—	47	4	no	—
224	C₂²⋊C₄	—	47	4	no	—
225	C₂²⋊C₄	—	47	4	no	—
226	C₂²⋊C₄	—	47	4	no	—
227	C₂²⋊C₄	—	47	8	no	—
228	C₂²⋊C₄	—	47	8	no	—
229	C₂²⋊C₄	—	47	4	no	—
230	C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
231	C₄²	—	47	8	no	—
232	C₄²	—	47	4	no	—
233	C₄²	C₂²×D₄₇	1	4	yes	—
234	C₄²	C₂²×D₄₇	1	4	yes	—
235	C₂³	—	2	2	no	—
236	C₂³	—	4	1	no	—
237	C₂³	—	4	1	no	—
238	C₂³	—	47	4	no	—
239	C₂³	C₂³×D₄₇	1	2	yes	—
240	C₂³	C₂³×D₄₇	1	1	yes	characteristic
241	Q₈	—	94	4	no	—
242	Q₈	—	188	4	no	—
243	D₄	—	94	8	no	—
244	D₄	—	94	4	no	—
245	D₄	—	188	4	no	—
246	D₄	—	188	4	no	—
247	D₄	—	188	4	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	4	no	—
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	4	2	no	—
252	C₂×C₄	—	4	2	no	—
253	C₂×C₄	—	47	4	no	—
254	C₂×C₄	—	47	4	no	—
255	C₂×C₄	—	47	4	no	—
256	C₂×C₄	—	94	8	no	—
257	C₂×C₄	—	188	8	no	—
258	C₂×C₄	#10625350	1	4	yes	—
259	C₂×C₄	C₂³×D₄₇	1	4	yes	—
260	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
261	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
262	C₂×C₄	C₂³×D₄₇	1	4	yes	—
263	C₂×C₄	C₂³×D₄₇	1	2	yes	—
264	C₂²	—	2	1	no	—
265	C₂²	—	2	1	no	—
266	C₂²	—	2	2	no	—
267	C₂²	—	2	2	no	—
268	C₂²	—	2	2	no	—
269	C₂²	—	4	4	no	—
270	C₂²	—	94	4	no	—
271	C₂²	—	94	4	no	—
272	C₂²	—	94	4	no	—
273	C₂²	C₂×#10625350	1	2	yes	—
274	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
275	C₄	—	2	1	no	—
276	C₄	—	2	1	no	—
277	C₄	—	2	4	no	—
278	C₄	—	2	4	no	—
279	C₄	—	94	4	no	—
280	C₄	—	94	4	no	—
281	C₄	—	94	4	no	—
282	C₄	C₂×#10625350	1	4	yes	—
283	C₂	—	2	2	no	—
284	C₂	—	4	2	no	—
285	C₂	—	188	4	no	—
286	C₂	C₂²×#10625350	1	1	yes	characteristic
287	C₂	#15689959	1	1	yes	characteristic
288	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₂×#117×C₄₇	C₂
hypercenter	C₂×#117	D₄₇
hypocenter	C₄₇	#3493
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. #15689841	C₂	semidirect
2. #15689836	C₂	semidirect
3. #15689817	C₂	semidirect
4. #15689812	C₂	semidirect
5. #15689754	C₂	semidirect
6. #15689711	C₂	semidirect
7. #15689704	C₂	semidirect
8. #15689657	C₂	semidirect
9. #15689634	C₂	semidirect
10. #15689604	C₂	semidirect
11. C₂×#117×C₄₇	C₂	semidirect
13. #13094023	C₂²	semidirect
14. #13094018	C₂²	semidirect
16. #13094016	C₂²	semidirect
17. #13094015	C₂²	semidirect
18. #13094012	C₂²	semidirect
22. #13094004	C₂²	semidirect
26. #13093999	C₂²	semidirect
32. C₄×Dic₉₄	C₂²	semidirect
33. #13093989	C₂²	semidirect
34. C₄×D₁₈₈	C₂²	semidirect
35. #13093986	C₂²	semidirect
40. #13093982	C₂²	semidirect
41. #13093981	C₂²	semidirect
42. C₄⋊C₄×D₄₇	C₂²	semidirect
155. C₂×#117	D₄₇	semidirect
156. C₄₇	#3493	semidirect