Subgroups — #15689520

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	#13093956	C₂	1	1	yes	maximal, characteristic
3	#13093955	C₂	1	2	yes	maximal
4	C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	#106×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	2	yes	—
17	Dic₉₄	—	4	4	no	—
18	C₈×C₄₇	Q₈	1	2	yes	complemented
19	C₄₇⋊C₈	Q₈	1	2	yes	complemented
20	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
21	C₄×C₄₇	—	4	2	no	—
22	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
23	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
24	Dic₄₇	—	4	2	no	—
25	Dic₄₇	SD₁₆	1	4	yes	—
26	C₂×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
27	C₂×C₄₇	C₂×SD₁₆	1	2	yes	—
28	#498	—	47	1	no	maximal, Sylow
29	C₄₇	#498	1	1	yes	characteristic, complemented, Sylow
30	C₄⋊Q₈	—	47	2	no	—
31	#106	—	47	1	no	—
32	#106	—	47	2	no	—
33	#106	D₄₇	1	1	yes	characteristic
34	C₄×C₈	—	47	1	no	—
35	C₂×Q₈	—	94	2	no	—
36	C₂×C₈	—	47	1	no	—
37	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
38	C₄⋊C₄	—	47	2	no	—
39	C₄⋊C₄	—	94	2	no	—
40	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
41	C₄²	—	47	1	no	—
42	Q₈	—	188	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	47	2	no	—
45	C₂×C₄	—	94	2	no	—
46	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
47	C₈	—	47	2	no	—
48	C₈	Dic₉₄	1	2	yes	complemented
49	C₂²	D₄×D₄₇	1	1	yes	characteristic
50	C₄	—	4	2	no	—
51	C₄	—	47	4	no	—
52	C₄	—	188	2	no	—
53	C₄	C₂×Dic₉₄	1	1	yes	characteristic
54	C₄	Q₈×D₄₇	1	1	yes	characteristic
55	C₂	#13094023	1	1	yes	characteristic
56	C₂	SD₁₆×D₄₇	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	#498
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
18. C₈×C₄₇	Q₈	semidirect
19. C₄₇⋊C₈	Q₈	semidirect
29. C₄₇	#498	semidirect
48. 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
#13093956	2
#13093955	2
C₈×Dic₄₇	2
#106×C₄₇	2
#498	47