Subgroups — #15689523

Order 3008.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094015	C₂	1	2	yes	maximal
2	#13093957	C₂	1	2	yes	maximal
3	#13093956	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	#106×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
8	C₄⋊Dic₄₇	—	2	2	no	—
9	C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	Dic₄₇⋊C₄	—	2	2	no	—
11	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₄₇	—	2	2	no	—
14	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
15	C₂×Dic₄₇	—	2	2	no	—
16	C₂×Dic₄₇	D₄	1	2	yes	—
17	C₈×C₄₇	Q₈	1	2	yes	—
18	C₄₇⋊C₈	Q₈	1	2	yes	—
19	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
20	C₄×C₄₇	—	4	2	no	—
21	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
22	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
23	Dic₄₇	—	2	2	no	—
24	Dic₄₇	—	4	2	no	—
25	C₂×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
26	C₂×C₄₇	#135	1	2	yes	—
27	#499	—	47	1	no	maximal, Sylow
28	C₄₇	#499	1	1	yes	characteristic, complemented, Sylow
29	#125	—	47	2	no	—
30	#107	—	47	2	no	—
31	#106	—	47	1	no	—
32	#106	D₄₇	1	1	yes	characteristic
33	C₄×C₈	—	47	1	no	—
34	C₂×C₈	—	47	1	no	—
35	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
36	C₄⋊C₄	—	47	2	no	—
37	C₄⋊C₄	—	94	2	no	—
38	C₄⋊C₄	—	94	2	no	—
39	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
40	C₄²	—	47	1	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	47	2	no	—
43	C₂×C₄	—	94	2	no	—
44	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
45	C₈	—	47	2	no	—
46	C₈	Dic₉₄	1	2	yes	—
47	C₂²	D₄×D₄₇	1	1	yes	characteristic
48	C₄	—	4	2	no	—
49	C₄	—	94	2	no	—
50	C₄	—	188	2	no	—
51	C₄	C₂×Dic₉₄	1	1	yes	characteristic
52	C₄	Q₈×D₄₇	1	1	yes	characteristic
53	C₂	#13094023	1	1	yes	characteristic
54	C₂	#13094045	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#106×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
hypercenter	#106	D₄₇
hypocenter	C₄₇	#499
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
28. C₄₇	#499	semidirect

Maximal subgroups

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

subgroup	index
#13094015	2
#13093957	2
#13093956	2
C₈×Dic₄₇	2
#106×C₄₇	2
#499	47