Subgroups — C₂×Dic₂₆₄₄ #35232551

Order 21152.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₂₂	C₂	1	2	yes	maximal
2	Dic₂₆₄₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₆₆₁	C₂	1	1	yes	maximal, characteristic
4	Dic₁₃₂₂	—	2	2	no	—
5	Dic₁₃₂₂	C₂²	1	4	yes	—
6	C₂×Dic₆₆₁	—	2	2	no	—
7	C₂×C₄×C₆₆₁	C₂²	1	1	yes	characteristic
8	C₈×C₆₆₁	C₂²	1	2	yes	—
9	C₂²×C₆₆₁	D₄	1	1	yes	characteristic
10	C₄×C₆₆₁	D₄	1	1	yes	characteristic
11	C₄×C₆₆₁	C₂³	1	1	yes	characteristic
12	Dic₆₆₁	—	2	4	no	—
13	C₂×C₆₆₁	Q₁₆	1	2	yes	complemented
14	C₂×C₆₆₁	C₂×D₄	1	1	yes	characteristic
15	C₆₆₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
16	C₂×Q₁₆	—	661	1	no	maximal, Sylow
17	C₂×Q₈	—	661	2	no	—
18	Q₁₆	—	661	4	no	—
19	C₂×C₈	D₆₆₁	1	1	yes	characteristic
20	Q₈	—	1322	2	no	—
21	Q₈	—	661	4	no	—
22	C₂×C₄	—	1322	2	no	—
23	C₂×C₄	C₂×D₆₆₁	1	1	yes	characteristic
24	C₈	C₂×D₆₆₁	1	2	yes	—
25	C₂²	D₂₆₄₄	1	1	yes	characteristic
26	C₄	—	1322	4	no	—
27	C₄	D₂₆₄₄	1	1	yes	characteristic
28	C₄	C₂²×D₆₆₁	1	1	yes	characteristic
29	C₂	Dic₂₆₄₄	1	2	yes	direct product factor
30	C₂	C₂×D₂₆₄₄	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.