Subgroups — C₂²×C₁₁⋊C₃₂ #13070905

Order 1408.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁⋊C₃₂	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₈×C₁₁	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₁₆	C₄	1	3	yes	—
5	C₂×C₁₁×C₁₆	C₂²	1	3	yes	—
6	C₁₁⋊C₃₂	C₂²	1	4	yes	direct product factor
7	C₂²×C₄×C₁₁	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₁	C₈	1	3	yes	—
9	C₂×C₈×C₁₁	C₂×C₄	1	3	yes	—
10	C₁₁×C₁₆	C₂×C₄	1	3	yes	—
11	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
12	C₂²×C₃₂	—	11	1	no	maximal, Sylow
13	C₂³×C₁₁	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₁₁	C₁₆	1	3	yes	—
15	C₂×C₄×C₁₁	C₂×C₈	1	3	yes	—
16	C₈×C₁₁	C₂×C₈	1	3	yes	—
17	C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₁₆	D₁₁	1	1	yes	characteristic
19	C₂×C₃₂	—	11	6	no	—
20	C₂²×C₁₁	C₃₂	1	4	yes	complemented
21	C₂²×C₁₁	C₂×C₁₆	1	3	yes	—
22	C₄×C₁₁	C₂×C₁₆	1	3	yes	—
23	C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
24	C₂²×C₈	Dic₁₁	1	1	yes	characteristic
25	C₂×C₁₆	Dic₁₁	1	3	yes	—
26	C₂×C₁₆	C₂×D₁₁	1	3	yes	—
27	C₃₂	—	11	4	no	—
28	C₂×C₁₁	C₂×C₃₂	1	6	yes	complemented
29	C₂×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
30	C₂²×C₄	C₁₁⋊C₈	1	1	yes	characteristic
31	C₂×C₈	C₁₁⋊C₈	1	3	yes	—
32	C₂×C₈	C₂×Dic₁₁	1	3	yes	—
33	C₁₆	C₂×Dic₁₁	1	3	yes	—
34	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
35	C₁₁	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
36	C₂³	C₁₁⋊C₁₆	1	1	yes	characteristic
37	C₂×C₄	C₁₁⋊C₁₆	1	3	yes	—
38	C₂×C₄	C₂×C₁₁⋊C₈	1	3	yes	—
39	C₈	C₂×C₁₁⋊C₈	1	3	yes	—
40	C₈	C₂²×Dic₁₁	1	1	yes	characteristic
41	C₂²	C₁₁⋊C₃₂	1	4	yes	direct product factor
42	C₂²	C₂×C₁₁⋊C₁₆	1	3	yes	—
43	C₄	C₂×C₁₁⋊C₁₆	1	3	yes	—
44	C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
45	C₂	C₂×C₁₁⋊C₃₂	1	6	yes	direct product factor
46	C₂	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₁₆	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₃₂
Frattini	C₁₆	C₂²×D₁₁
Fitting	C₂²×C₁₁×C₁₆	C₂
socle, prime radical	C₂³×C₁₁	C₁₆
cosocle	C₁₁×C₁₆	C₂³
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁⋊C₃₂	C₂	direct (N × H)
6. C₁₁⋊C₃₂	C₂²	direct (N × H)
20. C₂²×C₁₁	C₃₂	semidirect
28. C₂×C₁₁	C₂×C₃₂	semidirect
35. C₁₁	C₂²×C₃₂	semidirect
41. C₂²	C₁₁⋊C₃₂	direct (N × H)
45. C₂	C₂×C₁₁⋊C₃₂	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×C₁₁×C₁₆	2
C₂×C₁₁⋊C₃₂	2
C₂²×C₃₂	11

Subgroups — C22×C11⋊C32 #13070905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁⋊C₃₂ #13070905