Subgroups — Dic₁₁⋊C₈ #66878

Order 352.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×Dic₁₁	C₄	1	1	yes	characteristic
6	C₂×Dic₁₁	C₄	1	1	yes	characteristic
7	C₈×C₁₁	—	2	1	no	—
8	C₁₁⋊C₈	—	2	1	no	—
9	C₂²×C₁₁	C₂×C₄	1	1	yes	characteristic
10	C₄×C₁₁	D₄	1	1	yes	characteristic
11	C₄×C₁₁	Q₈	1	1	yes	characteristic
12	Dic₁₁	—	2	1	no	—
13	Dic₁₁	C₈	1	2	yes	complemented
14	C₄⋊C₈	—	11	1	no	maximal, Sylow
15	C₂×C₁₁	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₁₁	C₂×C₈	1	1	yes	characteristic
17	C₂×C₁₁	M₁₆	1	1	yes	characteristic
18	C₂×C₈	—	11	1	no	—
19	C₂×C₈	D₁₁	1	1	yes	characteristic
20	C₄²	—	11	1	no	—
21	C₁₁	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₄	—	11	1	no	—
23	C₂×C₄	—	11	1	no	—
24	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
25	C₈	—	2	1	no	—
26	C₈	—	22	1	no	—
27	C₂²	C₄×D₁₁	1	1	yes	characteristic
28	C₄	—	11	2	no	—
29	C₄	—	22	1	no	—
30	C₄	Dic₂₂	1	1	yes	characteristic
31	C₄	C₂²⋊D₁₁	1	1	yes	characteristic
32	C₂	C₈×D₁₁	1	1	yes	characteristic
33	C₂	#4313	1	1	yes	characteristic
34	C₂	Dic₁₁⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. Dic₁₁	C₈	semidirect
21. C₁₁	C₄⋊C₈	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.