Subgroups — #15689533

Order 3008.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13094024	C₂	1	1	yes	maximal, characteristic
2	#13093957	C₂	1	2	yes	maximal
3	#13093955	C₂	1	2	yes	maximal
4	#13093935	C₂	1	1	yes	maximal, characteristic
5	#125×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₄	—	2	1	no	—
7	C₄⋊C₄×C₄₇	—	2	1	no	—
8	C₄⋊C₄×C₄₇	—	2	1	no	—
9	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₇	—	2	1	no	—
13	C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₄₇	—	2	1	no	—
16	C₂×C₄×C₄₇	—	2	1	no	—
17	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
20	C₂×Dic₄₇	—	2	2	no	—
21	Dic₉₄	—	4	2	no	—
22	C₄₇⋊C₈	Q₈	1	4	yes	complemented
23	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₇	—	2	1	no	—
25	C₄×C₄₇	—	2	1	no	—
26	C₄×C₄₇	—	4	1	no	—
27	C₄×C₄₇	—	4	1	no	—
28	C₄×C₄₇	C₂×Q₈	1	2	yes	—
29	Dic₄₇	—	4	2	no	—
30	C₂×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
32	C₂×C₄₇	#137	1	1	yes	characteristic
33	#501	—	47	1	no	maximal, Sylow
34	C₄₇	#501	1	1	yes	characteristic, complemented, Sylow
35	C₄⋊Q₈	—	47	1	no	—
36	#125	D₄₇	1	1	yes	characteristic
37	#107	—	47	2	no	—
38	#106	—	47	2	no	—
39	#97	—	47	1	no	—
40	C₂×Q₈	—	94	1	no	—
41	C₂×C₈	—	47	2	no	—
42	C₄⋊C₄	—	2	1	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	47	2	no	—
45	C₄⋊C₄	—	94	1	no	—
46	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
47	C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
48	C₄²	C₂×D₄₇	1	1	yes	characteristic
49	Q₈	—	188	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	94	2	no	—
53	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
54	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
55	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
56	C₈	—	47	4	no	—
57	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	4	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	188	2	no	—
63	C₄	Q₈×D₄₇	1	2	yes	—
64	C₂	#13094022	1	1	yes	characteristic
65	C₂	#13094049	1	1	yes	characteristic
66	C₂	#13094054	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#125×C₄₇	C₂
socle, prime radical	C₂²×C₄₇	C₂×D₄
hypercenter	#125	D₄₇
hypocenter	C₄₇	#501
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
22. C₄₇⋊C₈	Q₈	semidirect
34. C₄₇	#501	semidirect

Maximal subgroups

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

subgroup	index
#13094024	2
#13093957	2
#13093955	2
#13093935	2
#125×C₄₇	2
#501	47