Subgroups — C₄⋊#22550864 #45656158

Order 32576.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22550864	C₂	1	2	yes	maximal
2	C₄×#16861325	C₂	1	1	yes	maximal, characteristic
3	#22550864	—	2	2	no	—
4	C₂×#16861325	C₄	1	1	yes	characteristic
5	C₂×#16861325	C₂²	1	1	yes	characteristic
6	C₄²×C₅₀₉	C₄	1	1	yes	characteristic
7	#16861325	—	2	1	no	—
8	#16861325	D₄	1	1	yes	characteristic
9	#16861325	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₅₀₉	C₈	1	1	yes	characteristic
11	C₂×C₄×C₅₀₉	C₈	1	1	yes	characteristic
12	C₂×C₄×C₅₀₉	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₅₀₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₅₀₉	—	2	1	no	—
15	C₄×C₅₀₉	C₁₆	1	2	yes	complemented
16	C₄×C₅₀₉	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₅₀₉	M₁₆	1	1	yes	characteristic
18	C₂×C₅₀₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₅₀₉	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₅₀₉	M₃₂	1	1	yes	characteristic
21	C₅₀₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	509	1	no	maximal, Sylow
23	C₂×C₁₆	—	509	2	no	—
24	C₄×C₈	—	509	1	no	—
25	C₂×C₈	—	509	1	no	—
26	C₂×C₈	—	509	1	no	—
27	C₄²	#14523266	1	1	yes	characteristic
28	C₁₆	—	1018	2	no	—
29	C₂×C₄	#16861332	1	1	yes	characteristic
30	C₂×C₄	#16861332	1	1	yes	characteristic
31	C₂×C₄	C₂×#14523266	1	1	yes	characteristic
32	C₈	—	1018	1	no	—
33	C₈	—	509	1	no	—
34	C₈	—	509	1	no	—
35	C₂²	C₂×#16861332	1	1	yes	characteristic
36	C₄	—	2	1	no	—
37	C₄	#22550864	1	2	yes	complemented
38	C₄	C₄⋊#14523266	1	1	yes	characteristic
39	C₄	#22550871	1	1	yes	characteristic
40	C₂	C₄⋊#16861332	1	1	yes	characteristic
41	C₂	C₂×#22550864	1	1	yes	characteristic
42	C₂	#30654289	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#14523266
commutator	C₂×C₅₀₉	C₂×C₁₆
Fitting	C₄²×C₅₀₉	C₄
socle, prime radical	C₂²×C₅₀₉	C₂×C₈
cosocle	C₂×#16861325	C₂²
hypercenter	C₄²	#14523266
hypocenter	C₅₀₉	C₄⋊C₁₆
LCS	G ▷ C₂×C₅₀₉ ▷ C₅₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
15. C₄×C₅₀₉	C₁₆	semidirect
21. C₅₀₉	C₄⋊C₁₆	semidirect
37. C₄	#22550864	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22550864	2
C₄×#16861325	2
C₄⋊C₁₆	509

Subgroups — C4⋊#22550864 #45656158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊#22550864 #45656158