Subgroups — C₂×Dic₁₁⋊C₄ #66976

Order 352.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	Dic₁₁⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₁	—	2	2	no	—
7	C₂×C₄×C₁₁	C₂²	1	2	yes	—
8	C₂×Dic₁₁	—	2	2	no	—
9	C₂×Dic₁₁	C₄	1	4	yes	complemented
10	C₂×Dic₁₁	C₂²	1	2	yes	—
11	C₂×Dic₁₁	C₂²	1	2	yes	—
12	C₂²×C₁₁	C₂×C₄	1	2	yes	—
13	C₂²×C₁₁	D₄	1	2	yes	—
14	C₂²×C₁₁	Q₈	1	2	yes	—
15	C₂²×C₁₁	C₂³	1	1	yes	characteristic
16	C₄×C₁₁	—	2	2	no	—
17	Dic₁₁	—	2	2	no	—
18	Dic₁₁	C₂×C₄	1	4	yes	complemented
19	C₂×C₄⋊C₄	—	11	1	no	maximal, Sylow
20	C₂×C₁₁	C₄⋊C₄	1	4	yes	complemented
21	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
23	C₂×C₁₁	C₂×Q₈	1	1	yes	characteristic
24	C₂²×C₄	—	11	1	no	—
25	C₂²×C₄	—	11	1	no	—
26	C₂²×C₄	D₁₁	1	1	yes	characteristic
27	C₄⋊C₄	—	11	4	no	—
28	C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
29	C₂³	C₂×D₁₁	1	1	yes	characteristic
30	C₂×C₄	—	2	2	no	—
31	C₂×C₄	—	11	2	no	—
32	C₂×C₄	—	11	4	no	—
33	C₂×C₄	—	11	2	no	—
34	C₂×C₄	—	22	2	no	—
35	C₂×C₄	C₂×D₁₁	1	2	yes	—
36	C₂²	Dic₂₂	1	2	yes	—
37	C₂²	C₄×D₁₁	1	2	yes	—
38	C₂²	C₂²⋊D₁₁	1	2	yes	—
39	C₂²	C₂²×D₁₁	1	1	yes	characteristic
40	C₄	—	2	2	no	—
41	C₄	—	11	4	no	—
42	C₄	—	22	2	no	—
43	C₂	Dic₁₁⋊C₄	1	4	yes	direct product factor
44	C₂	C₂×Dic₂₂	1	1	yes	characteristic
45	C₂	C₂×C₄×D₁₁	1	1	yes	characteristic
46	C₂	C₂×C₂²⋊D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₁
commutator	C₂×C₁₁	C₂²×C₄
Frattini	C₂²	C₂²×D₁₁
Fitting	C₂²×C₄×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂²
cosocle	C₂²×C₁₁	C₂³
hypercenter	C₂²×C₄	D₁₁
hypocenter	C₁₁	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
4. Dic₁₁⋊C₄	C₂	direct (N × H)
9. C₂×Dic₁₁	C₄	semidirect
18. Dic₁₁	C₂×C₄	semidirect
20. C₂×C₁₁	C₄⋊C₄	semidirect
28. C₁₁	C₂×C₄⋊C₄	semidirect
43. C₂	Dic₁₁⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₁₁	2
C₂²×Dic₁₁	2
Dic₁₁⋊C₄	2
C₂×C₄⋊C₄	11

Subgroups — C2×Dic11⋊C4 #66976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₁₁⋊C₄ #66976