Subgroups — C₂³×Dic₁₁ #67044

Order 352.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₁₁	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₁₁	C₄	1	8	yes	complemented
4	C₂³×C₁₁	C₂²	1	7	yes	—
5	C₂×Dic₁₁	C₂²	1	28	yes	direct product factor
6	C₂²×C₁₁	C₂×C₄	1	28	yes	complemented
7	C₂²×C₁₁	C₂³	1	7	yes	—
8	Dic₁₁	C₂³	1	8	yes	direct product factor
9	C₂³×C₄	—	11	1	no	maximal, Sylow
10	C₂×C₁₁	C₂²×C₄	1	14	yes	complemented
11	C₂×C₁₁	C₂⁴	1	1	yes	characteristic
12	C₂⁴	D₁₁	1	1	yes	characteristic
13	C₂²×C₄	—	11	14	no	—
14	C₁₁	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₂³	Dic₁₁	1	8	yes	direct product factor
16	C₂³	C₂×D₁₁	1	7	yes	—
17	C₂×C₄	—	11	28	no	—
18	C₂²	C₂×Dic₁₁	1	28	yes	direct product factor
19	C₂²	C₂²×D₁₁	1	7	yes	—
20	C₄	—	11	8	no	—
21	C₂	C₂²×Dic₁₁	1	14	yes	direct product factor
22	C₂	C₂³×D₁₁	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.