Subgroups — C₂²×C₂²⋊D₁₁ #67045

Order 352.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂²⋊D₁₁	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₁₁	—	2	4	no	—
6	C₂³×C₁₁	C₂²	1	1	yes	characteristic
7	C₂³×C₁₁	C₂²	1	6	yes	complemented
8	C₂²×D₁₁	—	2	4	no	—
9	C₂²×D₁₁	C₂²	1	6	yes	complemented
10	C₂²⋊D₁₁	C₂²	1	16	yes	direct product factor
11	C₂×Dic₁₁	C₂²	1	6	yes	complemented
12	C₂²×C₁₁	—	2	12	no	—
13	C₂²×C₁₁	D₄	1	4	yes	complemented
14	C₂²×C₁₁	C₂³	1	3	yes	—
15	C₂²×C₁₁	C₂³	1	4	yes	complemented
16	C₂×D₁₁	—	2	12	no	—
17	C₂×D₁₁	C₂³	1	4	yes	complemented
18	Dic₁₁	C₂³	1	4	yes	complemented
19	C₂²×D₄	—	11	1	no	maximal, Sylow
20	C₂×C₁₁	—	2	4	no	—
21	C₂×C₁₁	C₂×D₄	1	6	yes	complemented
22	C₂×C₁₁	C₂⁴	1	1	yes	characteristic
23	D₁₁	—	2	4	no	—
24	C₂⁴	—	11	1	no	—
25	C₂⁴	D₁₁	1	1	yes	characteristic, complemented
26	C₂×D₄	—	11	12	no	—
27	C₂²×C₄	—	11	1	no	—
28	C₁₁	C₂²×D₄	1	1	yes	characteristic, complemented, Sylow
29	C₂³	—	2	4	no	—
30	C₂³	—	11	6	no	—
31	C₂³	—	22	4	no	—
32	C₂³	C₂×D₁₁	1	1	yes	characteristic
33	C₂³	C₂×D₁₁	1	6	yes	complemented
34	D₄	—	11	16	no	—
35	C₂×C₄	—	11	6	no	—
36	C₂²	—	2	12	no	—
37	C₂²	—	11	4	no	—
38	C₂²	—	22	12	no	—
39	C₂²	C₂²⋊D₁₁	1	4	yes	direct product factor
40	C₂²	C₂²×D₁₁	1	3	yes	—
41	C₂²	C₂²×D₁₁	1	4	yes	complemented
42	C₄	—	11	4	no	—
43	C₂	—	2	4	no	—
44	C₂	—	22	4	no	—
45	C₂	C₂×C₂²⋊D₁₁	1	6	yes	direct product factor
46	C₂	C₂³×D₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₁
commutator, cosocle	C₂×C₁₁	C₂⁴
Frattini	C₂	C₂³×D₁₁
Fitting	C₂⁴×C₁₁	C₂
socle	C₂³×C₁₁	C₂²
hypercenter	C₂⁴	D₁₁
hypocenter	C₁₁	C₂²×D₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₁₁	C₂	semidirect
2. C₂³×D₁₁	C₂	semidirect
3. C₂×C₂²⋊D₁₁	C₂	direct (N × H)
4. C₂²×Dic₁₁	C₂	semidirect
7. C₂³×C₁₁	C₂²	semidirect
9. C₂²×D₁₁	C₂²	semidirect
10. C₂²⋊D₁₁	C₂²	direct (N × H)
11. C₂×Dic₁₁	C₂²	semidirect
13. C₂²×C₁₁	D₄	semidirect
15. C₂²×C₁₁	C₂³	semidirect
17. C₂×D₁₁	C₂³	semidirect
18. Dic₁₁	C₂³	semidirect
21. C₂×C₁₁	C₂×D₄	semidirect
25. C₂⁴	D₁₁	semidirect
28. C₁₁	C₂²×D₄	semidirect
33. C₂³	C₂×D₁₁	semidirect
39. C₂²	C₂²⋊D₁₁	direct (N × H)
41. C₂²	C₂²×D₁₁	semidirect
45. C₂	C₂×C₂²⋊D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₁₁	2
C₂³×D₁₁	2
C₂×C₂²⋊D₁₁	2
C₂²×Dic₁₁	2
C₂²×D₄	11

Subgroups — C22×C22⋊D11 #67045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₂²⋊D₁₁ #67045