Subgroups — #20243000

Order 6016.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689474	C₂	1	3	yes	maximal, complemented
2	#15689470	C₂	1	3	yes	maximal
3	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#13094024	C₂²	1	3	yes	—
5	#13094021	C₂²	1	1	yes	characteristic
6	#13093949	—	2	6	no	—
7	#13093946	—	2	6	no	—
8	C₄×C₈×C₄₇	C₂²	1	3	yes	—
9	C₂×D₁₈₈	—	2	3	no	—
10	C₂×Dic₉₄	—	2	3	no	—
11	C₂×C₈×C₄₇	D₄	1	6	yes	—
12	C₄²×C₄₇	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₄₇	—	2	3	no	—
14	C₄⋊Dic₄₇	—	2	3	no	—
15	C₂²×D₄₇	—	4	1	no	—
16	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
17	C₂×Dic₄₇	—	4	3	no	—
18	D₁₈₈	—	4	6	no	—
19	Dic₉₄	—	4	6	no	—
20	C₈×C₄₇	—	2	6	no	—
21	C₂²×C₄₇	#127	1	1	yes	characteristic
22	C₂×D₄₇	—	8	3	no	—
23	C₄×C₄₇	#135	1	6	yes	—
24	Dic₄₇	—	8	3	no	—
25	#1711	—	47	1	no	maximal, Sylow
26	C₂×C₄₇	#495	1	3	yes	—
27	D₄₇	—	16	1	no	—
28	#487	—	47	3	no	—
29	#486	—	47	3	no	—
30	C₈²	D₄₇	1	1	yes	characteristic, complemented
31	C₄₇	#1711	1	1	yes	characteristic, complemented, Sylow
32	C₄⋊Q₈	—	47	3	no	—
33	#127	—	47	1	no	—
34	#103	—	94	6	no	—
35	#102	—	94	6	no	—
36	C₄×C₈	C₂×D₄₇	1	3	yes	—
37	C₂×Q₈	—	94	3	no	—
38	C₂×D₄	—	94	3	no	—
39	C₂×C₈	D₁₈₈	1	6	yes	—
40	C₄⋊C₄	—	94	3	no	—
41	C₄⋊C₄	—	94	3	no	—
42	C₄²	C₂²×D₄₇	1	1	yes	characteristic
43	C₂³	—	188	1	no	—
44	Q₈	—	188	6	no	—
45	D₄	—	188	6	no	—
46	C₂×C₄	—	188	3	no	—
47	C₂×C₄	C₂×D₁₈₈	1	3	yes	—
48	C₈	—	2	6	no	—
49	C₂²	—	376	3	no	—
50	C₂²	#13094021	1	1	yes	characteristic
51	C₄	—	376	3	no	—
52	C₄	#13094046	1	6	yes	—
53	C₂	—	752	1	no	—
54	C₂	#15689507	1	3	yes	—

	subgroup	G/H
center	C₂²	#13094021
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₈²×C₄₇	C₂
socle	C₂²×C₄₇	#127
hypercenter	C₈²	D₄₇
hypocenter	C₄₇	#1711
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #15689474	C₂	semidirect
3. C₈²×C₄₇	C₂	semidirect
30. C₈²	D₄₇	semidirect
31. C₄₇	#1711	semidirect