Subgroups — #20258100

Order 6016.

1424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689890	C₂	1	15	yes	maximal, complemented
2	C₂×#13094031	C₂	1	15	yes	maximal, complemented
3	C₄₇×#585	C₂	1	1	yes	maximal, characteristic
4	#13094031	C₂²	1	20	yes	complemented
5	#13094031	C₂²	1	60	yes	complemented
6	C₂×#10625329	C₂²	1	45	yes	complemented
7	C₂²×C₄₇⋊C₈	C₂²	1	15	yes	complemented
8	2₋¹⁺⁴×C₄₇	C₄	1	6	yes	—
9	H(5,𝔽₂)×C₄₇	C₄	1	10	yes	—
10	C₂×#41×C₄₇	C₂²	1	15	yes	—
11	#41×C₄₇	C₂×C₄	1	60	yes	—
12	#41×C₄₇	C₂³	1	20	yes	—
13	C₂×Q₈×C₄₇	C₂×C₄	1	15	yes	—
14	C₂×D₄×C₄₇	C₂×C₄	1	45	yes	—
15	C₂²×C₄×C₄₇	C₂³	1	15	yes	—
16	#10625329	C₂³	1	60	yes	—
17	C₂×C₄₇⋊C₈	C₂³	1	15	yes	—
18	C₂×C₄₇⋊C₈	C₂³	1	45	yes	—
19	C₂³×C₄₇	C₂²×C₄	1	15	yes	—
20	Q₈×C₄₇	C₂²×C₄	1	20	yes	—
21	D₄×C₄₇	C₂²×C₄	1	60	yes	—
22	C₂×C₄×C₄₇	C₂²×C₄	1	45	yes	—
23	C₂×C₄×C₄₇	C₂⁴	1	15	yes	—
24	C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
25	C₄₇⋊C₈	C₂⁴	1	15	yes	—
26	C₂²×C₄₇	—	4	15	no	—
27	C₂²×C₄₇	C₂³×C₄	1	15	yes	—
28	C₄×C₄₇	C₂³×C₄	1	15	yes	—
29	C₄×C₄₇	C₂⁵	1	1	yes	characteristic
30	#3573	—	47	1	no	maximal, Sylow
31	C₂×C₄₇	—	2	15	no	—
32	C₂×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
33	#585	D₄₇	1	1	yes	characteristic
34	#568	—	47	15	no	—
35	C₂×#131	—	47	15	no	—
36	C₄₇	#3573	1	1	yes	characteristic, complemented, Sylow
37	2₋¹⁺⁴	Dic₄₇	1	6	yes	—
38	H(5,𝔽₂)	Dic₄₇	1	10	yes	—
39	C₂×#41	C₂×D₄₇	1	15	yes	—
40	#131	—	47	20	no	—
41	#131	—	47	60	no	—
42	C₂×M₁₆	—	47	45	no	—
43	C₂²×C₈	—	47	15	no	—
44	#41	C₂×Dic₄₇	1	60	yes	—
45	#41	C₂²×D₄₇	1	20	yes	—
46	C₂×Q₈	C₂×Dic₄₇	1	15	yes	—
47	C₂×D₄	C₂×Dic₄₇	1	45	yes	—
48	C₂²×C₄	C₂²×D₄₇	1	15	yes	—
49	M₁₆	—	47	60	no	—
50	C₂×C₈	—	47	15	no	—
51	C₂×C₈	—	47	45	no	—
52	C₂³	C₂²×Dic₄₇	1	15	yes	—
53	Q₈	C₂²×Dic₄₇	1	20	yes	—
54	D₄	C₂²×Dic₄₇	1	60	yes	—
55	C₂×C₄	C₂²×Dic₄₇	1	45	yes	—
56	C₂×C₄	C₂³×D₄₇	1	15	yes	—
57	C₈	—	47	1	no	—
58	C₈	—	47	15	no	—
59	C₂²	—	4	15	no	—
60	C₂²	C₂³×Dic₄₇	1	15	yes	—
61	C₄	C₂³×Dic₄₇	1	15	yes	—
62	C₄	C₂⁴×D₄₇	1	1	yes	characteristic
63	C₂	—	2	15	no	—
64	C₂	C₂⁴×Dic₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂⁴×D₄₇
commutator, socle	C₂×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#585	C₂
hypercenter	#585	D₄₇
hypocenter	C₄₇	#3573
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ #585

Complements

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

N	H ≅ G/N	type
1. #15689890	C₂	semidirect
2. C₂×#13094031	C₂	semidirect
4. #13094031	C₂²	semidirect
5. #13094031	C₂²	semidirect
6. C₂×#10625329	C₂²	semidirect
7. C₂²×C₄₇⋊C₈	C₂²	semidirect
36. C₄₇	#3573	semidirect