Subgroups — C₂²⋊C₁₆×C₅₆₃ #49112968

Order 36032.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₅₆₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×C₅₆₃	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×C₅₆₃	C₄	1	1	yes	characteristic
4	C₂×C₈×C₅₆₃	—	2	2	no	—
5	C₂×C₈×C₅₆₃	C₄	1	1	yes	characteristic
6	C₂×C₈×C₅₆₃	C₂²	1	1	yes	characteristic
7	C₁₆×C₅₆₃	—	2	2	no	—
8	C₂³×C₅₆₃	C₈	1	1	yes	characteristic
9	C₂×C₄×C₅₆₃	—	2	1	no	—
10	C₂×C₄×C₅₆₃	—	2	1	no	—
11	C₂×C₄×C₅₆₃	C₈	1	1	yes	characteristic
12	C₂×C₄×C₅₆₃	C₂×C₄	1	1	yes	characteristic
13	C₈×C₅₆₃	—	2	1	no	—
14	C₈×C₅₆₃	D₄	1	2	yes	—
15	C₂²×C₅₆₃	—	2	1	no	—
16	C₂²×C₅₆₃	—	2	1	no	—
17	C₂²×C₅₆₃	C₁₆	1	2	yes	complemented
18	C₂²×C₅₆₃	C₂×C₈	1	1	yes	characteristic
19	C₄×C₅₆₃	—	2	1	no	—
20	C₄×C₅₆₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₅₆₃	M₁₆	1	1	yes	characteristic
22	C₂×C₅₆₃	—	2	2	no	—
23	C₂×C₅₆₃	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₅₆₃	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₅₆₃	M₃₂	1	1	yes	characteristic
26	C₅₆₃	C₂²⋊C₁₆	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²⋊C₁₆	C₅₆₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₈	C₂×C₅₆₃	1	1	yes	characteristic
29	C₂×C₁₆	C₂×C₅₆₃	1	2	yes	complemented
30	C₂²×C₄	C₄×C₅₆₃	1	1	yes	characteristic
31	C₂×C₈	—	2	2	no	—
32	C₂×C₈	C₄×C₅₆₃	1	1	yes	characteristic
33	C₂×C₈	C₂²×C₅₆₃	1	1	yes	characteristic
34	C₁₆	—	2	2	no	—
35	C₂³	C₈×C₅₆₃	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	C₈×C₅₆₃	1	1	yes	characteristic
39	C₂×C₄	C₂×C₄×C₅₆₃	1	1	yes	characteristic
40	C₈	—	2	1	no	—
41	C₈	D₄×C₅₆₃	1	2	yes	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	C₁₆×C₅₆₃	1	2	yes	complemented
45	C₂²	C₂×C₈×C₅₆₃	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	C₂²⋊C₄×C₅₆₃	1	1	yes	characteristic
48	C₄	M₁₆×C₅₆₃	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊C₈×C₅₆₃	1	1	yes	characteristic
51	C₂	C₂×C₁₆×C₅₆₃	1	1	yes	characteristic
52	C₂	M₃₂×C₅₆₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₅₆₃	C₂²
commutator	C₂	C₂×C₁₆×C₅₆₃
Frattini, cosocle	C₂×C₈	C₂²×C₅₆₃
socle	C₂²×C₅₆₃	C₂×C₈
prime radical	C₂³×C₅₆₃	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₅₆₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₆×C₅₆₃	C₂	semidirect
17. C₂²×C₅₆₃	C₁₆	semidirect
26. C₅₆₃	C₂²⋊C₁₆	direct (N × H)
27. C₂²⋊C₁₆	C₅₆₃	direct (N × H)
29. C₂×C₁₆	C₂×C₅₆₃	semidirect
44. C₂²	C₁₆×C₅₆₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×C₅₆₃	2
C₂×C₁₆×C₅₆₃	2
C₂²⋊C₁₆	563

Subgroups — C22⋊C16×C563 #49112968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊C₁₆×C₅₆₃ #49112968