Subgroups — C₂²×Dic₁₃₂₂ #35232573

Order 21152.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₂₂	C₂	1	12	yes	maximal, direct product factor
2	C₂²×Dic₆₆₁	C₂	1	2	yes	maximal
3	C₂²×C₄×C₆₆₁	C₂	1	1	yes	maximal, characteristic
4	Dic₁₃₂₂	C₂²	1	16	yes	direct product factor
5	C₂×Dic₆₆₁	C₂²	1	12	yes	—
6	C₂³×C₆₆₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₆₆₁	C₂²	1	6	yes	—
8	C₂²×C₆₆₁	Q₈	1	4	yes	complemented
9	C₂²×C₆₆₁	C₂³	1	3	yes	—
10	C₄×C₆₆₁	C₂³	1	4	yes	—
11	Dic₆₆₁	C₂³	1	8	yes	—
12	C₂×C₆₆₁	C₂×Q₈	1	6	yes	complemented
13	C₂×C₆₆₁	C₂⁴	1	1	yes	characteristic
14	C₆₆₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₂²×Q₈	—	661	1	no	maximal, Sylow
16	C₂×Q₈	—	661	12	no	—
17	C₂²×C₄	—	661	2	no	—
18	C₂²×C₄	D₆₆₁	1	1	yes	characteristic
19	C₂³	C₂×D₆₆₁	1	1	yes	characteristic
20	Q₈	—	661	16	no	—
21	C₂×C₄	—	661	12	no	—
22	C₂×C₄	C₂×D₆₆₁	1	6	yes	—
23	C₂²	Dic₁₃₂₂	1	4	yes	direct product factor
24	C₂²	C₂²×D₆₆₁	1	3	yes	—
25	C₄	—	661	8	no	—
26	C₄	C₂²×D₆₆₁	1	4	yes	—
27	C₂	C₂×Dic₁₃₂₂	1	6	yes	direct product factor
28	C₂	C₂³×D₆₆₁	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.