Subgroups — D₂₁₇⋊C₄ #13181908

Order 1736.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₁₇	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×C₃₁	C₂²	1	1	yes	characteristic
5	D₂₁₇	C₄	1	2	yes	complemented
6	C₄×D₃₁	—	7	1	no	maximal, Hall
7	C₇×C₃₁	C₂×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×D₃₁	—	7	1	no	—
9	C₄×C₃₁	—	7	1	no	—
10	Dic₃₁	D₇	1	1	yes	characteristic, complemented
11	C₂×C₃₁	C₂×D₇	1	1	yes	characteristic
12	D₃₁	—	7	2	no	—
13	C₄×D₇	—	31	1	no	maximal, Hall
14	C₃₁	C₄×D₇	1	1	yes	characteristic, complemented, Sylow
15	C₂×D₇	—	31	1	no	—
16	C₄×C₇	—	31	1	no	—
17	Dic₇	D₃₁	1	1	yes	characteristic, complemented
18	C₂×C₇	C₂×D₃₁	1	1	yes	characteristic
19	D₇	—	31	2	no	—
20	C₂×C₄	—	217	1	no	Sylow
21	C₇	C₄×D₃₁	1	1	yes	characteristic, complemented, Sylow
22	C₂²	—	217	1	no	—
23	C₄	—	7	1	no	—
24	C₄	—	31	1	no	—
25	C₂	—	217	2	no	—
26	C₂	D₇×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇×D₃₁
commutator, hypocenter	C₇×C₃₁	C₂×C₄
Fitting, socle, cosocle	C₂×C₇×C₃₁	C₂²
prime radical	C₂×D₂₁₇	C₂
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₂

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.