Subgroups — C₄×C₄₇⋊C₃₂ #20241520

Order 6016.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₃₂	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇⋊C₃₂	C₄	1	4	yes	direct product factor
4	C₂×C₁₆×C₄₇	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
6	C₄×C₈×C₄₇	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₄₇	C₈	1	1	yes	characteristic
10	C₁₆×C₄₇	C₈	1	2	yes	—
11	C₁₆×C₄₇	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₄₇	C₁₆	1	2	yes	—
13	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
14	C₈×C₄₇	C₁₆	1	2	yes	—
15	C₈×C₄₇	C₄²	1	1	yes	characteristic
16	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
17	C₂²×C₄₇	C₂×C₁₆	1	1	yes	characteristic
18	C₄×C₄₇	C₃₂	1	4	yes	complemented
19	C₄×C₄₇	C₄×C₈	1	1	yes	characteristic
20	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₃₂	—	47	1	no	maximal, Sylow
22	C₂×C₄₇	C₄×C₁₆	1	1	yes	characteristic
23	C₂×C₄₇	C₂×C₃₂	1	2	yes	—
24	C₂×C₃₂	—	47	2	no	—
25	C₄×C₁₆	D₄₇	1	1	yes	characteristic
26	C₄₇	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₁₆	Dic₄₇	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
29	C₄×C₈	Dic₄₇	1	1	yes	characteristic
30	C₃₂	—	47	4	no	—
31	C₂×C₈	C₄₇⋊C₈	1	1	yes	characteristic
32	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
33	C₄²	C₄₇⋊C₈	1	1	yes	characteristic
34	C₁₆	C₄₇⋊C₈	1	2	yes	—
35	C₁₆	C₄×D₄₇	1	2	yes	—
36	C₂×C₄	C₄₇⋊C₁₆	1	2	yes	—
37	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
38	C₈	C₄₇⋊C₁₆	1	2	yes	—
39	C₈	C₂×C₄₇⋊C₈	1	1	yes	characteristic
40	C₈	C₄×Dic₄₇	1	1	yes	characteristic
41	C₂²	C₂×C₄₇⋊C₁₆	1	1	yes	characteristic
42	C₄	C₄₇⋊C₃₂	1	4	yes	direct product factor
43	C₄	C₄×C₄₇⋊C₈	1	1	yes	characteristic
44	C₄	C₂×C₄₇⋊C₁₆	1	1	yes	characteristic
45	C₂	C₄×C₄₇⋊C₁₆	1	1	yes	characteristic
46	C₂	C₂×C₄₇⋊C₃₂	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₁₆	D₄₇
commutator, hypocenter	C₄₇	C₄×C₃₂
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₄×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₁₆
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₄₇⋊C₃₂	C₄	direct (N × H)
18. C₄×C₄₇	C₃₂	semidirect
26. C₄₇	C₄×C₃₂	semidirect
42. C₄	C₄₇⋊C₃₂	direct (N × H)

Subgroups — C4×C47⋊C32 #20241520

Conjugacy classes of subgroups

Complements

Subgroups — C₄×C₄₇⋊C₃₂ #20241520