Subgroups — C₇×D₁₄₁₃ #34089939

Order 19782.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₄₇₁	—	3	1	no	maximal
3	C₃×C₇×C₁₅₇	D₃	1	1	yes	characteristic
4	D₁₄₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×D₁₅₇	—	9	1	no	Hall
6	C₉×C₁₅₇	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₅₇	D₉	1	1	yes	characteristic, complemented, Hall
8	D₄₇₁	—	3	1	no	—
9	C₃×C₁₅₇	D₃×C₇	1	1	yes	characteristic
10	D₁₅₇	—	9	1	no	Hall
11	C₁₅₇	C₇×D₉	1	1	yes	characteristic, complemented, Sylow
12	C₇×D₉	—	157	1	no	maximal, Hall
13	C₇×C₉	D₁₅₇	1	1	yes	characteristic, complemented, Hall
14	D₃×C₇	—	471	1	no	—
15	C₃×C₇	D₄₇₁	1	1	yes	characteristic
16	D₉	—	157	1	no	Hall
17	C₂×C₇	—	1413	1	no	Hall
18	C₉	C₇×D₁₅₇	1	1	yes	characteristic, complemented, Sylow
19	C₇	D₁₄₁₃	1	1	yes	characteristic, direct product factor, Sylow
20	D₃	—	471	1	no	—
21	C₃	C₇×D₄₇₁	1	1	yes	characteristic
22	C₂	—	1413	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₁₄₁₃
commutator, cosocle, hypocenter	C₉×C₁₅₇	C₂×C₇
Frattini	C₃	C₇×D₄₇₁
Fitting	C₇×C₉×C₁₅₇	C₂
socle	C₃×C₇×C₁₅₇	D₃
LCS	G ▷ C₉×C₁₅₇
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.