Subgroups — C₄₇⋊#564 #15689878

Order 3008.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094016	C₂	1	2	yes	maximal
2	#13094015	C₂	1	4	yes	maximal
3	#13094014	C₂	1	4	yes	maximal
4	#13094014	C₂	1	4	yes	maximal
5	#125×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
7	C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
8	C₄²×C₄₇	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₄⋊Dic₄₇	C₂²	1	4	yes	—
11	C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	Dic₄₇⋊C₄	C₂²	1	4	yes	—
13	Dic₄₇⋊C₄	C₂²	1	4	yes	—
14	Dic₄₇⋊C₄	C₂²	1	4	yes	—
15	Dic₄₇⋊C₄	C₂²	1	4	yes	—
16	C₄×Dic₄₇	C₂²	1	4	yes	—
17	C₂×C₄×C₄₇	C₂³	1	4	yes	—
18	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₄₇	C₂³	1	2	yes	—
20	C₂×Dic₄₇	C₂³	1	4	yes	—
21	C₂×Dic₄₇	C₂³	1	4	yes	—
22	C₂²×C₄₇	C₂⁴	1	1	yes	characteristic
23	C₄×C₄₇	—	2	4	no	—
24	C₄×C₄₇	—	2	2	no	—
25	C₄×C₄₇	—	2	1	no	—
26	Dic₄₇	—	2	4	no	—
27	Dic₄₇	—	2	4	no	—
28	C₂×C₄₇	2₋¹⁺⁴	1	2	yes	—
29	C₂×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
30	#564	—	47	1	no	maximal, Sylow
31	C₄₇	#564	1	1	yes	characteristic, complemented, Sylow
32	#125	—	47	4	no	—
33	#125	—	47	4	no	—
34	#125	—	47	4	no	—
35	#125	—	47	2	no	—
36	#125	D₄₇	1	1	yes	characteristic
37	C₄⋊C₄	—	47	4	no	—
38	C₄⋊C₄	—	47	4	no	—
39	C₄⋊C₄	—	47	4	no	—
40	C₄⋊C₄	—	47	4	no	—
41	C₄⋊C₄	—	47	4	no	—
42	C₄⋊C₄	—	47	2	no	—
43	C₄⋊C₄	—	47	2	no	—
44	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
45	C₄⋊C₄	C₂×D₄₇	1	4	yes	—
46	C₄²	—	47	4	no	—
47	C₄²	C₂×D₄₇	1	1	yes	characteristic
48	C₂×C₄	—	47	4	no	—
49	C₂×C₄	—	47	4	no	—
50	C₂×C₄	C₂²×D₄₇	1	4	yes	—
51	C₂×C₄	C₂²×D₄₇	1	2	yes	—
52	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
53	C₂²	C₂³×D₄₇	1	1	yes	characteristic
54	C₄	—	2	4	no	—
55	C₄	—	2	2	no	—
56	C₄	—	2	1	no	—
57	C₄	—	94	4	no	—
58	C₄	—	94	4	no	—
59	C₂	#13094071	1	2	yes	—
60	C₂	#13094072	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₇
commutator, socle, prime radical, cosocle	C₂²×C₄₇	C₂⁴
Fitting	#125×C₄₇	C₂
hypercenter	#125	D₄₇
hypocenter	C₄₇	#564
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
31. C₄₇	#564	semidirect

Maximal subgroups

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

subgroup	index
#13094016	2
#13094015	2
#13094014	2
#125×C₄₇	2
#564	47

Subgroups — C47⋊#564 #15689878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇⋊#564 #15689878