Subgroups — C₂²×C₁₁⋊C₈ #66973

Order 352.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁⋊C₈	C₂	1	6	yes	maximal, direct product factor
3	C₂³×C₁₁	C₄	1	1	yes	characteristic
4	C₂×C₄×C₁₁	C₄	1	3	yes	—
5	C₂×C₄×C₁₁	C₂²	1	3	yes	—
6	C₁₁⋊C₈	C₂²	1	4	yes	direct product factor
7	C₂²×C₁₁	C₈	1	4	yes	complemented
8	C₂²×C₁₁	C₂×C₄	1	3	yes	—
9	C₄×C₁₁	C₂×C₄	1	3	yes	—
10	C₄×C₁₁	C₂³	1	1	yes	characteristic
11	C₂²×C₈	—	11	1	no	maximal, Sylow
12	C₂×C₁₁	C₂×C₈	1	6	yes	complemented
13	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
14	C₂²×C₄	D₁₁	1	1	yes	characteristic
15	C₂×C₈	—	11	6	no	—
16	C₁₁	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
17	C₂³	Dic₁₁	1	1	yes	characteristic
18	C₂×C₄	Dic₁₁	1	3	yes	—
19	C₂×C₄	C₂×D₁₁	1	3	yes	—
20	C₈	—	11	4	no	—
21	C₂²	C₁₁⋊C₈	1	4	yes	direct product factor
22	C₂²	C₂×Dic₁₁	1	3	yes	—
23	C₄	C₂×Dic₁₁	1	3	yes	—
24	C₄	C₂²×D₁₁	1	1	yes	characteristic
25	C₂	C₂×C₁₁⋊C₈	1	6	yes	direct product factor
26	C₂	C₂²×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.