Subgroups — C₂×C₁₁×D₃₂ #13065097

Order 1408.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₁₆	C₂	1	2	yes	maximal, complemented
2	C₁₁×D₃₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×D₈	—	2	2	no	—
5	C₁₁×D₁₆	—	2	2	no	—
6	C₁₁×D₁₆	C₂²	1	4	yes	complemented
7	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₁×C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₄×C₁₁	—	4	2	no	—
10	C₁₁×D₈	—	2	4	no	—
11	C₁₁×D₈	—	4	2	no	—
12	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
13	C₁₁×C₁₆	D₄	1	1	yes	characteristic
14	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
15	C₂×D₃₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₁₁	—	8	2	no	—
17	D₄×C₁₁	—	4	4	no	—
18	D₄×C₁₁	—	8	2	no	—
19	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
20	C₈×C₁₁	D₈	1	1	yes	characteristic
21	C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
22	C₂×D₁₆	C₂×C₁₁	1	2	yes	complemented
23	D₃₂	C₂×C₁₁	1	4	yes	direct product factor
24	C₂×C₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
25	C₂²×C₁₁	—	8	4	no	—
26	C₂²×C₁₁	—	16	4	no	—
27	C₂²×C₁₁	D₁₆	1	1	yes	characteristic
28	C₄×C₁₁	D₁₆	1	1	yes	characteristic
29	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
30	C₂×D₈	—	2	2	no	—
31	D₁₆	—	2	2	no	—
32	D₁₆	C₂²×C₁₁	1	4	yes	complemented
33	C₂×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
34	C₃₂	C₂²×C₁₁	1	2	yes	complemented
35	C₂×C₁₁	—	16	4	no	—
36	C₂×C₁₁	D₃₂	1	2	yes	direct product factor
37	C₂×C₁₁	C₂×D₁₆	1	1	yes	characteristic
38	C₂×D₄	—	4	2	no	—
39	D₈	—	2	4	no	—
40	D₈	—	4	2	no	—
41	C₂×C₈	D₄×C₁₁	1	1	yes	characteristic
42	C₁₆	D₄×C₁₁	1	1	yes	characteristic
43	C₁₆	C₂³×C₁₁	1	1	yes	characteristic
44	C₁₁	C₂×D₃₂	1	1	yes	characteristic, direct product factor, Sylow
45	C₂³	—	8	2	no	—
46	D₄	—	4	4	no	—
47	D₄	—	8	2	no	—
48	C₂×C₄	C₁₁×D₈	1	1	yes	characteristic
49	C₈	C₁₁×D₈	1	1	yes	characteristic
50	C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
51	C₂²	—	8	4	no	—
52	C₂²	—	16	4	no	—
53	C₂²	C₁₁×D₁₆	1	1	yes	characteristic
54	C₄	C₁₁×D₁₆	1	1	yes	characteristic
55	C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
56	C₂	—	16	4	no	—
57	C₂	C₁₁×D₃₂	1	2	yes	direct product factor
58	C₂	C₂×C₁₁×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₁₁
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×D₁₆	C₂	semidirect
2. C₁₁×D₃₂	C₂	direct (N × H)
3. C₂×C₁₁×C₃₂	C₂	semidirect
6. C₁₁×D₁₆	C₂²	semidirect
8. C₁₁×C₃₂	C₂²	semidirect
15. C₂×D₃₂	C₁₁	direct (N × H)
22. C₂×D₁₆	C₂×C₁₁	semidirect
23. D₃₂	C₂×C₁₁	direct (N × H)
24. C₂×C₃₂	C₂×C₁₁	semidirect
32. D₁₆	C₂²×C₁₁	semidirect
34. C₃₂	C₂²×C₁₁	semidirect
36. C₂×C₁₁	D₃₂	direct (N × H)
44. C₁₁	C₂×D₃₂	direct (N × H)
57. C₂	C₁₁×D₃₂	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×D₁₆	2
C₁₁×D₃₂	2
C₂×C₁₁×C₃₂	2
C₂×D₃₂	11

Subgroups — C2×C11×D32 #13065097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₃₂ #13065097