Subgroups — C₂×C₇⋊D₁₁₉ #16809727

Order 3332.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇⋊D₁₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₇²×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁₉	—	7	8	no	maximal
5	C₂×C₇×C₁₇	D₇	1	8	yes	complemented
6	D₁₁₉	—	7	16	no	—
7	C₂×C₇⋊D₇	—	17	1	no	maximal, Hall
8	C₇×C₁₇	C₂×D₇	1	8	yes	complemented
9	C₂×C₇²	D₁₇	1	1	yes	characteristic, complemented
10	C₇⋊D₇	—	17	2	no	—
11	C₂×D₁₇	—	49	1	no	Hall
12	C₇²	C₂×D₁₇	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₇	C₇⋊D₇	1	1	yes	characteristic, complemented
14	D₁₇	—	49	2	no	—
15	C₂×D₇	—	119	8	no	—
16	C₁₇	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₇	D₁₁₉	1	8	yes	complemented
18	D₇	—	119	16	no	—
19	C₇	C₂×D₁₁₉	1	8	yes	complemented
20	C₂²	—	833	1	no	Sylow
21	C₂	—	833	2	no	—
22	C₂	C₇⋊D₁₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₇⋊D₁₁₉
commutator, cosocle, hypocenter	C₇²×C₁₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₇	C₂
LCS	G ▷ C₇²×C₁₇
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.