Subgroups — C₂×C₁₁⋊C₆₄ #13066825

Order 1408.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊C₆₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₁×C₁₆	C₄	1	1	yes	characteristic
4	C₁₁×C₃₂	C₄	1	1	yes	characteristic
5	C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₁	C₈	1	1	yes	characteristic
7	C₁₁×C₁₆	C₈	1	1	yes	characteristic
8	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₂×C₆₄	—	11	1	no	maximal, Sylow
10	C₂×C₄×C₁₁	C₁₆	1	1	yes	characteristic
11	C₈×C₁₁	C₁₆	1	1	yes	characteristic
12	C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
13	C₂×C₃₂	D₁₁	1	1	yes	characteristic
14	C₆₄	—	11	2	no	—
15	C₂²×C₁₁	C₃₂	1	1	yes	characteristic
16	C₄×C₁₁	C₃₂	1	1	yes	characteristic
17	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
18	C₂×C₁₆	Dic₁₁	1	1	yes	characteristic
19	C₃₂	Dic₁₁	1	1	yes	characteristic
20	C₃₂	C₂×D₁₁	1	1	yes	characteristic
21	C₂×C₁₁	C₆₄	1	2	yes	complemented
22	C₂×C₁₁	C₂×C₃₂	1	1	yes	characteristic
23	C₂×C₈	C₁₁⋊C₈	1	1	yes	characteristic
24	C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
25	C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
26	C₁₁	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄	C₁₁⋊C₁₆	1	1	yes	characteristic
28	C₈	C₁₁⋊C₁₆	1	1	yes	characteristic
29	C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
30	C₂²	C₁₁⋊C₃₂	1	1	yes	characteristic
31	C₄	C₁₁⋊C₃₂	1	1	yes	characteristic
32	C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
33	C₂	C₁₁⋊C₆₄	1	2	yes	direct product factor
34	C₂	C₂×C₁₁⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₁₁
commutator, hypocenter	C₁₁	C₂×C₆₄
Frattini	C₃₂	C₂×D₁₁
Fitting	C₂×C₁₁×C₃₂	C₂
socle, prime radical	C₂²×C₁₁	C₃₂
cosocle	C₁₁×C₃₂	C₂²
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₁₁⋊C₆₄	C₂	direct (N × H)
21. C₂×C₁₁	C₆₄	semidirect
26. C₁₁	C₂×C₆₄	semidirect
33. C₂	C₁₁⋊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×C₁₁×C₃₂	2
C₁₁⋊C₆₄	2
C₂×C₆₄	11

Subgroups — C2×C11⋊C64 #13066825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁⋊C₆₄ #13066825