Subgroups — C₂²×Dic₂₂ #67031

Order 352.

156 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	C₂²×Dic₁₁	C₂	1	2	yes	maximal
3	C₂×Dic₂₂	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₁	C₂²	1	6	yes	—
6	C₂×Dic₁₁	C₂²	1	12	yes	—
7	Dic₂₂	C₂²	1	16	yes	direct product factor
8	C₂²×C₁₁	Q₈	1	4	yes	complemented
9	C₂²×C₁₁	C₂³	1	3	yes	—
10	C₄×C₁₁	C₂³	1	4	yes	—
11	Dic₁₁	C₂³	1	8	yes	—
12	C₂²×Q₈	—	11	1	no	maximal, Sylow
13	C₂×C₁₁	C₂×Q₈	1	6	yes	complemented
14	C₂×C₁₁	C₂⁴	1	1	yes	characteristic
15	C₂×Q₈	—	11	12	no	—
16	C₂²×C₄	—	11	2	no	—
17	C₂²×C₄	D₁₁	1	1	yes	characteristic
18	C₁₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³	C₂×D₁₁	1	1	yes	characteristic
20	Q₈	—	11	16	no	—
21	C₂×C₄	—	11	12	no	—
22	C₂×C₄	C₂×D₁₁	1	6	yes	—
23	C₂²	Dic₂₂	1	4	yes	direct product factor
24	C₂²	C₂²×D₁₁	1	3	yes	—
25	C₄	—	11	8	no	—
26	C₄	C₂²×D₁₁	1	4	yes	—
27	C₂	C₂×Dic₂₂	1	6	yes	direct product factor
28	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.