Subgroups — C₄²×D₁₁ #66924

Order 352.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₁₁	C₂	1	3	yes	maximal
2	C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₁₁	C₂	1	3	yes	maximal, complemented
4	C₂²×D₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₁	C₂²	1	3	yes	—
6	C₂×Dic₁₁	C₂²	1	3	yes	—
7	C₄×D₁₁	C₄	1	12	yes	direct product factor
8	C₂²×C₁₁	C₂³	1	1	yes	characteristic
9	C₂×D₁₁	C₂×C₄	1	6	yes	—
10	C₄×C₁₁	C₂×C₄	1	6	yes	complemented
11	Dic₁₁	C₂×C₄	1	6	yes	complemented
12	C₂×C₄²	—	11	1	no	maximal, Sylow
13	C₂×C₁₁	C₂²×C₄	1	3	yes	—
14	D₁₁	C₄²	1	4	yes	direct product factor
15	C₂²×C₄	—	11	3	no	—
16	C₄²	—	11	3	no	—
17	C₄²	D₁₁	1	1	yes	characteristic, direct product factor
18	C₁₁	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
19	C₂³	—	11	1	no	—
20	C₂×C₄	—	11	3	no	—
21	C₂×C₄	—	11	12	no	—
22	C₂×C₄	C₂×D₁₁	1	3	yes	—
23	C₂²	—	11	6	no	—
24	C₂²	C₂²×D₁₁	1	1	yes	characteristic
25	C₄	—	11	6	no	—
26	C₄	C₄×D₁₁	1	6	yes	direct product factor
27	C₂	—	11	4	no	—
28	C₂	C₂×C₄×D₁₁	1	3	yes	—

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.