Subgroups — C₄⋊(C₁₁⋊C₈) #66868

Order 352.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁⋊C₈	C₂	1	2	yes	maximal
3	C₂×C₄×C₁₁	C₄	1	1	yes	characteristic
4	C₂×C₄×C₁₁	C₄	1	1	yes	characteristic
5	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁⋊C₈	—	2	2	no	—
7	C₂²×C₁₁	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₁	—	2	1	no	—
9	C₄×C₁₁	C₈	1	2	yes	complemented
10	C₄×C₁₁	D₄	1	1	yes	characteristic
11	C₄×C₁₁	Q₈	1	1	yes	characteristic
12	C₄⋊C₈	—	11	1	no	maximal, Sylow
13	C₂×C₁₁	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₁₁	C₂×C₈	1	1	yes	characteristic
15	C₂×C₁₁	M₁₆	1	1	yes	characteristic
16	C₂×C₈	—	11	2	no	—
17	C₄²	D₁₁	1	1	yes	characteristic
18	C₁₁	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₄	Dic₁₁	1	1	yes	characteristic
20	C₂×C₄	Dic₁₁	1	1	yes	characteristic
21	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
22	C₈	—	22	2	no	—
23	C₂²	C₂×Dic₁₁	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	C₁₁⋊C₈	1	2	yes	complemented
26	C₄	Dic₂₂	1	1	yes	characteristic
27	C₄	D₄₄	1	1	yes	characteristic
28	C₂	C₂×C₁₁⋊C₈	1	1	yes	characteristic
29	C₂	#4318	1	1	yes	characteristic
30	C₂	C₄⋊Dic₁₁	1	1	yes	characteristic

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

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