Subgroups — C₇×D₂₅₂₃ #47977310

Order 35322.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₈₄₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₈₄₁	—	3	1	no	maximal, Hall
3	C₇×C₈₄₁	D₃	1	1	yes	characteristic, complemented, Hall
4	D₂₅₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₈₄₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
6	D₈₄₁	—	3	1	no	Hall
7	C₇×D₈₇	—	29	1	no	maximal
8	C₈₄₁	D₃×C₇	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₇×C₂₉	D₂₉	1	1	yes	characteristic
10	C₇×D₂₉	—	87	1	no	—
11	C₇×C₂₉	D₈₇	1	1	yes	characteristic
12	D₈₇	—	29	1	no	—
13	C₃×C₂₉	C₇×D₂₉	1	1	yes	characteristic
14	D₂₉	—	87	1	no	—
15	D₃×C₇	—	841	1	no	Hall
16	C₂₉	C₇×D₈₇	1	1	yes	characteristic
17	C₃×C₇	D₈₄₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₇	—	2523	1	no	Hall
19	C₇	D₂₅₂₃	1	1	yes	characteristic, direct product factor, Sylow
20	D₃	—	841	1	no	Hall
21	C₃	C₇×D₈₄₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	2523	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₂₅₂₃
commutator, cosocle, hypocenter	C₃×C₈₄₁	C₂×C₇
Frattini	C₂₉	C₇×D₈₇
Fitting	C₃×C₇×C₈₄₁	C₂
socle	C₃×C₇×C₂₉	D₂₉
LCS	G ▷ C₃×C₈₄₁
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.