Subgroups — #15688930

Order 3008.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#13093960	C₂	1	1	yes	maximal, characteristic, complemented
3	#135×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#41×C₄₇	—	2	1	no	—
5	Q₁₆×C₄₇	C₄	1	1	yes	characteristic
6	SD₁₆×C₄₇	—	2	1	no	—
7	D₈×C₄₇	C₄	1	1	yes	characteristic
8	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	#10625329	—	2	1	no	—
10	C₄₇⋊C₁₆	—	2	1	no	—
11	Q₈×C₄₇	—	2	1	no	—
12	D₄×C₄₇	—	2	1	no	—
13	D₄×C₄₇	—	4	1	no	—
14	C₂×C₄×C₄₇	—	4	1	no	—
15	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
16	C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₄₇⋊C₈	—	4	1	no	—
19	C₂²×C₄₇	—	4	1	no	—
20	C₂²×C₄₇	SD₁₆	1	1	yes	characteristic
21	C₄×C₄₇	—	4	1	no	—
22	C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₄×C₄₇	D₈	1	1	yes	characteristic
24	C₂×C₄₇	—	2	1	no	—
25	C₂×C₄₇	—	8	1	no	—
26	C₂×C₄₇	#102	1	1	yes	characteristic
27	#359	—	47	1	no	maximal, Sylow
28	C₄₇	#359	1	1	yes	characteristic, complemented, Sylow
29	#135	D₄₇	1	1	yes	characteristic
30	C₂×C₁₆	—	47	1	no	—
31	#108	—	47	1	no	—
32	#41	—	2	1	no	—
33	Q₁₆	Dic₄₇	1	1	yes	characteristic
34	SD₁₆	—	2	1	no	—
35	D₈	Dic₄₇	1	1	yes	characteristic
36	M₁₆	—	94	1	no	—
37	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
38	C₁₆	—	94	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	2	1	no	—
41	D₄	—	4	1	no	—
42	C₂×C₄	—	4	1	no	—
43	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
44	C₈	—	188	1	no	—
45	C₈	C₂×Dic₄₇	1	1	yes	characteristic
46	C₈	C₂²⋊D₄₇	1	1	yes	characteristic
47	C₂²	—	4	1	no	—
48	C₂²	#10625335	1	1	yes	characteristic
49	C₄	—	4	1	no	—
50	C₄	#10625334	1	1	yes	characteristic
51	C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	8	1	no	—
54	C₂	#13093945	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10625334
commutator	C₈×C₄₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₇
Fitting, prime radical	#135×C₄₇	C₂
socle	C₂×C₄₇	#102
cosocle	C₂×C₈×C₄₇	C₂²
hypercenter	#135	D₄₇
hypocenter	C₄₇	#359
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇⋊C₁₆	C₂	semidirect
2. #13093960	C₂	semidirect
28. C₄₇	#359	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇⋊C₁₆	2
#13093960	2
#135×C₄₇	2
#359	47