Subgroups — C₇⋊D₁₇₂₉ #37564153

Order 24206.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₇₂₉	—	7	8	no	maximal
3	C₇⋊D₁₃₃	—	13	1	no	maximal, Hall
4	C₇×C₁₃×C₁₉	D₇	1	8	yes	complemented
5	C₇⋊D₉₁	—	19	1	no	maximal, Hall
6	C₇²×C₁₉	D₁₃	1	1	yes	characteristic, complemented, Hall
7	C₇²×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
8	D₂₄₇	—	49	1	no	Hall
9	D₁₃₃	—	91	8	no	—
10	C₁₃×C₁₉	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
11	D₉₁	—	133	8	no	—
12	C₇×C₁₉	D₉₁	1	8	yes	complemented
13	C₇⋊D₇	—	247	1	no	Hall
14	C₇×C₁₃	D₁₃₃	1	8	yes	complemented
15	C₇²	D₂₄₇	1	1	yes	characteristic, complemented, Sylow
16	D₁₉	—	637	1	no	Hall
17	D₁₃	—	931	1	no	Hall
18	C₁₉	C₇⋊D₉₁	1	1	yes	characteristic, complemented, Sylow
19	D₇	—	1729	8	no	—
20	C₁₃	C₇⋊D₁₃₃	1	1	yes	characteristic, complemented, Sylow
21	C₇	D₁₇₂₉	1	8	yes	complemented
22	C₂	—	12103	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₃×C₁₉	C₂
LCS	G ▷ C₇²×C₁₃×C₁₉
UCS	C₁

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.