Subgroups — C₄⋊Dic₁₂₃₇ #34090113

Order 19792.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₂₃₇	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₂₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₂₃₇	C₂²	1	1	yes	characteristic
4	C₄×C₁₂₃₇	C₄	1	2	yes	complemented
5	Dic₁₂₃₇	—	2	2	no	—
6	C₂×C₁₂₃₇	C₂×C₄	1	1	yes	characteristic
7	C₂×C₁₂₃₇	D₄	1	1	yes	characteristic
8	C₂×C₁₂₃₇	Q₈	1	1	yes	characteristic
9	C₁₂₃₇	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
10	C₄⋊C₄	—	1237	1	no	maximal, Sylow
11	C₂×C₄	—	1237	2	no	—
12	C₂×C₄	D₁₂₃₇	1	1	yes	characteristic
13	C₂²	C₂×D₁₂₃₇	1	1	yes	characteristic
14	C₄	—	2474	2	no	—
15	C₄	Dic₁₂₃₇	1	2	yes	complemented
16	C₂	C₂×Dic₁₂₃₇	1	1	yes	characteristic
17	C₂	D₄₉₄₈	1	1	yes	characteristic
18	C₂	Dic₂₄₇₄	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.