Subgroups — C₃⋊((C₁₅₇⋊C₃)⋊D₇) #34089985

Order 19782.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₅₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₅₇⋊C₃)⋊D₇	—	3	1	no	maximal
3	D₃₂₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₁₅₇⋊C₃	—	2	1	no	—
6	C₇×C₁₅₇⋊C₃	D₃	1	1	yes	characteristic, complemented
7	C₃⋊(D₁₅₇⋊C₃)	—	7	1	no	maximal, Hall
8	D₁₀₉₉	—	3	1	no	Hall
9	C₃×C₁₅₇⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₅₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₄₇₁	—	7	1	no	—
12	D₁₅₇⋊C₃	—	21	1	no	—
13	C₃×C₁₅₇	C₃×D₇	1	1	yes	characteristic, complemented
14	C₁₅₇⋊C₃	—	2	1	no	—
15	C₁₅₇⋊C₃	D₂₁	1	1	yes	characteristic, complemented
16	D₁₅₇	—	21	1	no	Hall
17	C₁₅₇	C₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₂₁	—	157	1	no	maximal, Hall
19	C₃²×C₇	—	314	1	no	Hall
20	D₂₁	—	157	1	no	—
21	C₃×D₇	—	471	1	no	—
22	C₃×C₇	—	314	1	no	—
23	C₃×C₇	—	314	1	no	—
24	C₃×C₇	D₁₅₇⋊C₃	1	1	yes	characteristic, complemented
25	C₃×D₃	—	1099	1	no	Hall
26	D₇	—	471	1	no	Hall
27	C₃²	—	314	1	no	Sylow
28	C₇	C₃⋊(D₁₅₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3297	1	no	—
30	D₃	—	1099	1	no	—
31	C₃	—	314	1	no	—
32	C₃	—	314	1	no	—
33	C₃	(C₁₅₇⋊C₃)⋊D₇	1	1	yes	characteristic, complemented
34	C₂	—	3297	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₅₇	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₅₇
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.