Subgroups — D₁₁₃₅₆ #72223893

Order 22712.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₈₃₉	C₂	1	2	yes	maximal, complemented
2	C₄×C₁₇×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×C₁₆₇	C₂²	1	1	yes	characteristic
4	D₂₈₃₉	—	2	2	no	—
5	C₁₇×C₁₆₇	D₄	1	1	yes	characteristic, complemented, Hall
6	D₆₆₈	—	17	1	no	maximal, Hall
7	C₂×D₁₆₇	—	17	2	no	—
8	C₄×C₁₆₇	D₁₇	1	1	yes	characteristic, complemented
9	C₂×C₁₆₇	C₂×D₁₇	1	1	yes	characteristic
10	D₁₆₇	—	34	2	no	—
11	C₁₆₇	D₆₈	1	1	yes	characteristic, complemented, Sylow
12	D₆₈	—	167	1	no	maximal, Hall
13	C₂×D₁₇	—	167	2	no	—
14	C₄×C₁₇	D₁₆₇	1	1	yes	characteristic, complemented
15	C₂×C₁₇	C₂×D₁₆₇	1	1	yes	characteristic
16	D₁₇	—	334	2	no	—
17	C₁₇	D₆₆₈	1	1	yes	characteristic, complemented, Sylow
18	D₄	—	2839	1	no	Sylow
19	C₂²	—	2839	2	no	—
20	C₄	D₂₈₃₉	1	1	yes	characteristic, complemented
21	C₂	—	5678	2	no	—
22	C₂	C₂×D₂₈₃₉	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.