Subgroups — C₂²×C₄₇⋊C₆₄ #26137312

Order 12032.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₆₄	C₂	1	6	yes	maximal, direct product factor
2	C₂²×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇⋊C₆₄	C₂²	1	4	yes	direct product factor
4	C₂²×C₁₆×C₄₇	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₄₇	C₄	1	3	yes	—
6	C₂×C₃₂×C₄₇	C₂²	1	3	yes	—
7	C₂²×C₈×C₄₇	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₄₇	C₈	1	3	yes	—
9	C₂×C₁₆×C₄₇	C₂×C₄	1	3	yes	—
10	C₃₂×C₄₇	C₂×C₄	1	3	yes	—
11	C₃₂×C₄₇	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₄₇	C₁₆	1	3	yes	—
14	C₂×C₈×C₄₇	C₂×C₈	1	3	yes	—
15	C₁₆×C₄₇	C₂×C₈	1	3	yes	—
16	C₁₆×C₄₇	C₂²×C₄	1	1	yes	characteristic
17	C₂³×C₄₇	C₃₂	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₃₂	1	3	yes	—
19	C₂×C₄×C₄₇	C₂×C₁₆	1	3	yes	—
20	C₈×C₄₇	C₂×C₁₆	1	3	yes	—
21	C₈×C₄₇	C₂²×C₈	1	1	yes	characteristic
22	C₂²×C₆₄	—	47	1	no	maximal, Sylow
23	C₂²×C₄₇	C₆₄	1	4	yes	complemented
24	C₂²×C₄₇	C₂×C₃₂	1	3	yes	—
25	C₄×C₄₇	C₂×C₃₂	1	3	yes	—
26	C₄×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
27	C₂²×C₃₂	D₄₇	1	1	yes	characteristic
28	C₂×C₆₄	—	47	6	no	—
29	C₂×C₄₇	C₂×C₆₄	1	6	yes	complemented
30	C₂×C₄₇	C₂²×C₃₂	1	1	yes	characteristic
31	C₂²×C₁₆	Dic₄₇	1	1	yes	characteristic
32	C₂×C₃₂	Dic₄₇	1	3	yes	—
33	C₂×C₃₂	C₂×D₄₇	1	3	yes	—
34	C₆₄	—	47	4	no	—
35	C₄₇	C₂²×C₆₄	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	C₄₇⋊C₈	1	1	yes	characteristic
37	C₂×C₁₆	C₄₇⋊C₈	1	3	yes	—
38	C₂×C₁₆	C₂×Dic₄₇	1	3	yes	—
39	C₃₂	C₂×Dic₄₇	1	3	yes	—
40	C₃₂	C₂²×D₄₇	1	1	yes	characteristic
41	C₂²×C₄	C₄₇⋊C₁₆	1	1	yes	characteristic
42	C₂×C₈	C₄₇⋊C₁₆	1	3	yes	—
43	C₂×C₈	C₂×C₄₇⋊C₈	1	3	yes	—
44	C₁₆	C₂×C₄₇⋊C₈	1	3	yes	—
45	C₁₆	C₂²×Dic₄₇	1	1	yes	characteristic
46	C₂³	C₄₇⋊C₃₂	1	1	yes	characteristic
47	C₂×C₄	C₄₇⋊C₃₂	1	3	yes	—
48	C₂×C₄	C₂×C₄₇⋊C₁₆	1	3	yes	—
49	C₈	C₂×C₄₇⋊C₁₆	1	3	yes	—
50	C₈	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
51	C₂²	C₄₇⋊C₆₄	1	4	yes	direct product factor
52	C₂²	C₂×C₄₇⋊C₃₂	1	3	yes	—
53	C₄	C₂×C₄₇⋊C₃₂	1	3	yes	—
54	C₄	C₂²×C₄₇⋊C₁₆	1	1	yes	characteristic
55	C₂	C₂×C₄₇⋊C₆₄	1	6	yes	direct product factor
56	C₂	C₂²×C₄₇⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃₂	D₄₇
commutator, hypocenter	C₄₇	C₂²×C₆₄
Frattini	C₃₂	C₂²×D₄₇
Fitting	C₂²×C₃₂×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₃₂
cosocle	C₃₂×C₄₇	C₂³
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇⋊C₆₄	C₂	direct (N × H)
3. C₄₇⋊C₆₄	C₂²	direct (N × H)
23. C₂²×C₄₇	C₆₄	semidirect
29. C₂×C₄₇	C₂×C₆₄	semidirect
35. C₄₇	C₂²×C₆₄	semidirect
51. C₂²	C₄₇⋊C₆₄	direct (N × H)
55. C₂	C₂×C₄₇⋊C₆₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇⋊C₆₄	2
C₂²×C₃₂×C₄₇	2
C₂²×C₆₄	47

Subgroups — C22×C47⋊C64 #26137312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄₇⋊C₆₄ #26137312