Subgroups — C₇×D₂₃₁₃ #44569205

Order 32382.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₂₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇₇₁	—	3	1	no	maximal
3	C₃×C₇×C₂₅₇	D₃	1	1	yes	characteristic
4	D₂₃₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₂₅₇	—	9	1	no	Hall
6	C₉×C₂₅₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₂₅₇	D₉	1	1	yes	characteristic, complemented, Hall
8	D₇₇₁	—	3	1	no	—
9	C₃×C₂₅₇	D₃×C₇	1	1	yes	characteristic
10	D₂₅₇	—	9	1	no	Hall
11	C₂₅₇	C₇×D₉	1	1	yes	characteristic, complemented, Sylow
12	C₇×D₉	—	257	1	no	maximal, Hall
13	C₇×C₉	D₂₅₇	1	1	yes	characteristic, complemented, Hall
14	D₃×C₇	—	771	1	no	—
15	C₃×C₇	D₇₇₁	1	1	yes	characteristic
16	D₉	—	257	1	no	Hall
17	C₂×C₇	—	2313	1	no	Hall
18	C₉	C₇×D₂₅₇	1	1	yes	characteristic, complemented, Sylow
19	C₇	D₂₃₁₃	1	1	yes	characteristic, direct product factor, Sylow
20	D₃	—	771	1	no	—
21	C₃	C₇×D₇₇₁	1	1	yes	characteristic
22	C₂	—	2313	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₂₃₁₃
commutator, cosocle, hypocenter	C₉×C₂₅₇	C₂×C₇
Frattini	C₃	C₇×D₇₇₁
Fitting	C₇×C₉×C₂₅₇	C₂
socle	C₃×C₇×C₂₅₇	D₃
LCS	G ▷ C₉×C₂₅₇
UCS	C₁ ◁ C₇

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.