Subgroups — C₂×C₄₇⋊C₆₄ #20241597

Order 6016.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇⋊C₆₄	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₄₇	C₄	1	1	yes	characteristic
4	C₃₂×C₄₇	C₄	1	1	yes	characteristic
5	C₃₂×C₄₇	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₄₇	C₈	1	1	yes	characteristic
7	C₁₆×C₄₇	C₈	1	1	yes	characteristic
8	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₄₇	C₁₆	1	1	yes	characteristic
10	C₈×C₄₇	C₁₆	1	1	yes	characteristic
11	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₄₇	C₃₂	1	1	yes	characteristic
13	C₄×C₄₇	C₃₂	1	1	yes	characteristic
14	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₆₄	—	47	1	no	maximal, Sylow
16	C₂×C₄₇	C₆₄	1	2	yes	complemented
17	C₂×C₄₇	C₂×C₃₂	1	1	yes	characteristic
18	C₂×C₃₂	D₄₇	1	1	yes	characteristic
19	C₆₄	—	47	2	no	—
20	C₄₇	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₆	Dic₄₇	1	1	yes	characteristic
22	C₃₂	Dic₄₇	1	1	yes	characteristic
23	C₃₂	C₂×D₄₇	1	1	yes	characteristic
24	C₂×C₈	C₄₇⋊C₈	1	1	yes	characteristic
25	C₁₆	C₄₇⋊C₈	1	1	yes	characteristic
26	C₁₆	C₂×Dic₄₇	1	1	yes	characteristic
27	C₂×C₄	C₄₇⋊C₁₆	1	1	yes	characteristic
28	C₈	C₄₇⋊C₁₆	1	1	yes	characteristic
29	C₈	C₂×C₄₇⋊C₈	1	1	yes	characteristic
30	C₂²	C₄₇⋊C₃₂	1	1	yes	characteristic
31	C₄	C₄₇⋊C₃₂	1	1	yes	characteristic
32	C₄	C₂×C₄₇⋊C₁₆	1	1	yes	characteristic
33	C₂	C₄₇⋊C₆₄	1	2	yes	direct product factor
34	C₂	C₂×C₄₇⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₄₇
commutator, hypocenter	C₄₇	C₂×C₆₄
Frattini	C₃₂	C₂×D₄₇
Fitting	C₂×C₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₃₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₄₇⋊C₆₄	C₂	direct (N × H)
16. C₂×C₄₇	C₆₄	semidirect
20. C₄₇	C₂×C₆₄	semidirect
33. C₂	C₄₇⋊C₆₄	direct (N × H)

Subgroups — C2×C47⋊C64 #20241597

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄₇⋊C₆₄ #20241597