Subgroups — C₂×D₁₁×C₃₂ #13070904

Order 1408.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₁×C₃₂	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₈×D₁₁	C₄	1	1	yes	characteristic
6	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₁⋊C₁₆	C₄	1	1	yes	characteristic
8	C₁₆×D₁₁	C₄	1	2	yes	—
9	C₁₆×D₁₁	C₂²	1	2	yes	—
10	C₁₁×C₃₂	C₂²	1	2	yes	complemented
11	C₁₁⋊C₃₂	C₂²	1	2	yes	complemented
12	C₂×C₄×D₁₁	C₈	1	1	yes	characteristic
13	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₁⋊C₈	C₈	1	1	yes	characteristic
15	C₈×D₁₁	C₈	1	2	yes	—
16	C₈×D₁₁	C₂×C₄	1	2	yes	—
17	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
19	C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
20	C₂²×C₃₂	—	11	1	no	maximal, Sylow
21	C₂²×D₁₁	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
23	C₂×Dic₁₁	C₁₆	1	1	yes	characteristic
24	C₄×D₁₁	C₁₆	1	2	yes	—
25	C₄×D₁₁	C₂×C₈	1	2	yes	—
26	C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
27	C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
28	C₁₁⋊C₈	C₂×C₈	1	2	yes	—
29	C₂²×C₁₆	—	11	1	no	—
30	C₂×C₃₂	—	11	1	no	—
31	C₂×C₃₂	—	11	4	no	—
32	C₂×C₃₂	D₁₁	1	1	yes	characteristic, direct product factor
33	C₂²×C₁₁	C₂×C₁₆	1	1	yes	characteristic
34	C₂×D₁₁	C₃₂	1	4	yes	direct product factor
35	C₂×D₁₁	C₂×C₁₆	1	2	yes	—
36	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
38	Dic₁₁	C₂×C₁₆	1	2	yes	—
39	C₂²×C₈	—	11	1	no	—
40	C₂×C₁₆	—	11	1	no	—
41	C₂×C₁₆	—	11	2	no	—
42	C₂×C₁₆	—	11	2	no	—
43	C₂×C₁₆	C₂×D₁₁	1	1	yes	characteristic
44	C₃₂	—	11	2	no	—
45	C₃₂	C₂×D₁₁	1	2	yes	direct product factor
46	C₂×C₁₁	C₂×C₃₂	1	2	yes	complemented
47	C₂×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
48	D₁₁	C₂×C₃₂	1	4	yes	direct product factor
49	C₂²×C₄	—	11	1	no	—
50	C₂×C₈	—	11	1	no	—
51	C₂×C₈	—	11	2	no	—
52	C₂×C₈	—	11	2	no	—
53	C₂×C₈	C₄×D₁₁	1	1	yes	characteristic
54	C₁₆	—	11	2	no	—
55	C₁₆	C₄×D₁₁	1	1	yes	characteristic
56	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
57	C₁₁	C₂²×C₃₂	1	1	yes	characteristic, complemented, Sylow
58	C₂³	—	11	1	no	—
59	C₂×C₄	—	11	1	no	—
60	C₂×C₄	—	11	2	no	—
61	C₂×C₄	—	11	2	no	—
62	C₂×C₄	C₈×D₁₁	1	1	yes	characteristic
63	C₈	—	11	2	no	—
64	C₈	C₈×D₁₁	1	1	yes	characteristic
65	C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
66	C₂²	—	11	2	no	—
67	C₂²	—	11	4	no	—
68	C₂²	C₁₆×D₁₁	1	1	yes	characteristic
69	C₄	—	11	2	no	—
70	C₄	C₁₆×D₁₁	1	1	yes	characteristic
71	C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
72	C₂	—	11	4	no	—
73	C₂	D₁₁×C₃₂	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₁₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×C₃₂	C₂	semidirect
3. C₂×C₁₁⋊C₃₂	C₂	semidirect
4. D₁₁×C₃₂	C₂	direct (N × H)
10. C₁₁×C₃₂	C₂²	semidirect
11. C₁₁⋊C₃₂	C₂²	semidirect
32. C₂×C₃₂	D₁₁	direct (N × H)
34. C₂×D₁₁	C₃₂	direct (N × H)
45. C₃₂	C₂×D₁₁	direct (N × H)
46. C₂×C₁₁	C₂×C₃₂	semidirect
48. D₁₁	C₂×C₃₂	direct (N × H)
57. C₁₁	C₂²×C₃₂	semidirect
73. C₂	D₁₁×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
C₂×C₁₆×D₁₁	2
C₂×C₁₁×C₃₂	2
C₂×C₁₁⋊C₃₂	2
D₁₁×C₃₂	2
C₂²×C₃₂	11

Subgroups — C2×D11×C32 #13070904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₁×C₃₂ #13070904