Subgroups — #15689527

Order 3008.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094023	C₂	1	2	yes	maximal
2	#13093958	C₂	1	1	yes	maximal, characteristic
3	#13093957	C₂	1	2	yes	maximal
4	C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	#107×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₄	—	2	2	no	—
7	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
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	1	yes	characteristic
17	C₂×Dic₄₇	D₄	1	1	yes	characteristic
18	Dic₉₄	—	4	4	no	—
19	C₈×C₄₇	Q₈	1	2	yes	complemented
20	C₄₇⋊C₈	Q₈	1	2	yes	complemented
21	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
22	C₄×C₄₇	—	4	2	no	—
23	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
25	Dic₄₇	—	4	2	no	—
26	Dic₄₇	D₈	1	2	yes	—
27	Dic₄₇	Q₁₆	1	2	yes	—
28	C₂×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
29	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
30	C₂×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
31	#500	—	47	1	no	maximal, Sylow
32	C₄₇	#500	1	1	yes	characteristic, complemented, Sylow
33	C₄⋊Q₈	—	47	2	no	—
34	#107	—	47	1	no	—
35	#107	—	47	2	no	—
36	#107	D₄₇	1	1	yes	characteristic
37	C₄×C₈	—	47	1	no	—
38	C₂×Q₈	—	94	2	no	—
39	C₂×C₈	—	47	1	no	—
40	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
41	C₄⋊C₄	—	47	2	no	—
42	C₄⋊C₄	—	94	2	no	—
43	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
44	C₄²	—	47	1	no	—
45	Q₈	—	188	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	47	1	no	—
48	C₂×C₄	—	47	1	no	—
49	C₂×C₄	—	94	2	no	—
50	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
51	C₈	—	47	2	no	—
52	C₈	Dic₉₄	1	2	yes	complemented
53	C₂²	D₄×D₄₇	1	1	yes	characteristic
54	C₄	—	4	2	no	—
55	C₄	—	47	2	no	—
56	C₄	—	47	2	no	—
57	C₄	—	188	2	no	—
58	C₄	C₂×Dic₉₄	1	1	yes	characteristic
59	C₄	Q₈×D₄₇	1	1	yes	characteristic
60	C₂	#13094023	1	1	yes	characteristic
61	C₂	D₈×D₄₇	1	1	yes	characteristic
62	C₂	Q₁₆×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#107×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
hypercenter	#107	D₄₇
hypocenter	C₄₇	#500
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
19. C₈×C₄₇	Q₈	semidirect
20. C₄₇⋊C₈	Q₈	semidirect
32. C₄₇	#500	semidirect
52. C₈	Dic₉₄	semidirect

Maximal subgroups

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

subgroup	index
#13094023	2
#13093958	2
#13093957	2
C₈×Dic₄₇	2
#107×C₄₇	2
#500	47