Subgroups — C₂²⋊Dic₂₂₉₇ #49145145

Order 36752.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₂₉₇	C₂	1	2	yes	maximal, complemented
2	C₂³×C₂₂₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₂₉₇	—	2	2	no	—
4	C₂²×C₂₂₉₇	C₄	1	2	yes	complemented
5	C₂²×C₂₂₉₇	C₂²	1	1	yes	characteristic
6	Dic₂₂₉₇	—	2	2	no	—
7	C₂×C₂₂₉₇	—	2	2	no	—
8	C₂×C₂₂₉₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₂₂₉₇	D₄	1	2	yes	—
10	C₂₂₉₇	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
11	C₂²⋊C₄	—	2297	1	no	maximal, Sylow
12	C₂³	D₂₂₉₇	1	1	yes	characteristic
13	C₂×C₄	—	2297	2	no	—
14	C₂²	—	2	2	no	—
15	C₂²	Dic₂₂₉₇	1	2	yes	complemented
16	C₂²	C₂×D₂₂₉₇	1	1	yes	characteristic
17	C₄	—	4594	2	no	—
18	C₂	—	2	2	no	—
19	C₂	C₂×Dic₂₂₉₇	1	1	yes	characteristic
20	C₂	C₂²⋊D₂₂₉₇	1	2	yes	—

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.