Subgroups — C₂²×C₄×D₁₁ #67032

Order 352.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₄	D₁₁
commutator, hypocenter	C₁₁	C₂³×C₄
Frattini	C₂	C₂³×D₁₁
Fitting	C₂²×C₄×C₁₁	C₂
socle	C₂³×C₁₁	C₂²
prime radical	C₂³×D₁₁	C₂
cosocle	C₂×C₁₁	C₂⁴
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₁₁	C₂	semidirect
3. C₂²×Dic₁₁	C₂	semidirect
4. C₂×C₄×D₁₁	C₂	direct (N × H)
6. C₂²×D₁₁	C₄	direct (N × H)
8. C₂×C₄×C₁₁	C₂²	semidirect
9. C₂×Dic₁₁	C₂²	semidirect
10. C₄×D₁₁	C₂²	direct (N × H)
11. C₂²×C₁₁	C₂×C₄	semidirect
13. C₂×D₁₁	C₂×C₄	direct (N × H)
15. C₄×C₁₁	C₂³	semidirect
16. Dic₁₁	C₂³	semidirect
18. C₂×C₁₁	C₂²×C₄	semidirect
20. D₁₁	C₂²×C₄	direct (N × H)
24. C₂²×C₄	D₁₁	direct (N × H)
25. C₁₁	C₂³×C₄	semidirect
31. C₂×C₄	C₂×D₁₁	direct (N × H)
34. C₂²	C₄×D₁₁	direct (N × H)
37. C₄	C₂²×D₁₁	direct (N × H)
39. C₂	C₂×C₄×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
C₂³×D₁₁	2
C₂²×C₄×C₁₁	2
C₂²×Dic₁₁	2
C₂×C₄×D₁₁	2
C₂³×C₄	11

Subgroups — C22×C4×D11 #67032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×D₁₁ #67032