Subgroups — C₂×C₁₁×SD₁₆ #67026

Order 352.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×SD₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₁₁	—	2	1	no	—
6	Q₈×C₁₁	—	2	1	no	—
7	Q₈×C₁₁	C₂²	1	2	yes	complemented
8	D₄×C₁₁	—	2	1	no	—
9	D₄×C₁₁	C₂²	1	2	yes	—
10	C₂×C₄×C₁₁	—	2	1	no	—
11	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₈×C₁₁	C₂²	1	2	yes	complemented
13	C₂²×C₁₁	—	2	2	no	—
14	C₂²×C₁₁	—	4	2	no	—
15	C₂²×C₁₁	D₄	1	1	yes	characteristic
16	C₄×C₁₁	—	2	2	no	—
17	C₄×C₁₁	D₄	1	1	yes	characteristic
18	C₄×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×SD₁₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×C₁₁	—	4	2	no	—
21	C₂×C₁₁	SD₁₆	1	2	yes	direct product factor
22	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
23	C₂×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
24	C₂×D₄	C₂×C₁₁	1	1	yes	characteristic
25	SD₁₆	C₂×C₁₁	1	4	yes	direct product factor
26	C₂×C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
27	C₁₁	C₂×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
28	C₂³	—	2	1	no	—
29	Q₈	—	2	1	no	—
30	Q₈	C₂²×C₁₁	1	2	yes	complemented
31	D₄	—	2	1	no	—
32	D₄	C₂²×C₁₁	1	2	yes	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	C₂²×C₁₁	1	1	yes	characteristic
35	C₈	C₂²×C₁₁	1	2	yes	complemented
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	D₄×C₁₁	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	D₄×C₁₁	1	1	yes	characteristic
41	C₄	C₂³×C₁₁	1	1	yes	characteristic
42	C₂	—	4	2	no	—
43	C₂	C₁₁×SD₁₆	1	2	yes	direct product factor
44	C₂	C₂×D₄×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₁₁
prime radical	C₂×D₄×C₁₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₁₁	C₂	semidirect
3. C₁₁×SD₁₆	C₂	direct (N × H)
4. C₂×C₈×C₁₁	C₂	semidirect
7. Q₈×C₁₁	C₂²	semidirect
12. C₈×C₁₁	C₂²	semidirect
19. C₂×SD₁₆	C₁₁	direct (N × H)
21. C₂×C₁₁	SD₁₆	direct (N × H)
23. C₂×Q₈	C₂×C₁₁	semidirect
25. SD₁₆	C₂×C₁₁	direct (N × H)
26. C₂×C₈	C₂×C₁₁	semidirect
27. C₁₁	C₂×SD₁₆	direct (N × H)
30. Q₈	C₂²×C₁₁	semidirect
35. C₈	C₂²×C₁₁	semidirect
43. C₂	C₁₁×SD₁₆	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×Q₈×C₁₁	2
C₂×D₄×C₁₁	2
C₁₁×SD₁₆	2
C₂×C₈×C₁₁	2
C₂×SD₁₆	11

Subgroups — C2×C11×SD16 #67026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×SD₁₆ #67026