Subgroups — (C₇₁⋊C₇)⋊#157 #31822060

Order 17892.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₇₁⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇₁⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇₁⋊C₇	—	6	2	no	—
4	C₇₁⋊#157	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	Dic₇₁⋊C₇	—	9	1	no	maximal, Hall
6	C₃×C₇₁⋊C₇	—	2	2	no	—
7	C₃⋊D₃×C₇₁	C₂×C₇	1	1	yes	characteristic
8	C₂×C₇₁⋊C₇	—	9	1	no	—
9	C₃²×C₇₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₇₁⋊C₇	#157	1	1	yes	characteristic, complemented, Hall
11	D₃×C₇₁	—	6	2	no	—
12	Dic₇₁	—	9	1	no	Hall
13	C₇×#157	—	71	1	no	maximal, Hall
14	C₃×C₇₁	—	2	2	no	—
15	C₂×C₇₁	—	9	1	no	—
16	C₇×C₃⋊D₃	—	71	1	no	—
17	C₇₁	C₇×#157	1	1	yes	characteristic, complemented, Sylow
18	C₃²×C₇	—	71	1	no	Hall
19	D₃×C₇	—	426	2	no	—
20	#157	—	497	1	no	Hall
21	C₄×C₇	—	639	1	no	Hall
22	C₃×C₇	—	142	2	no	—
23	C₃⋊D₃	D₇₁⋊C₇	1	1	yes	characteristic
24	C₂×C₇	—	639	1	no	—
25	C₃²	Dic₇₁⋊C₇	1	1	yes	characteristic, complemented, Sylow
26	C₇	—	71	1	no	Sylow
27	D₃	—	6	2	no	—
28	C₄	—	4473	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇₁	C₄×C₇
prime radical	C₃⋊D₃×C₇₁⋊C₇	C₂
cosocle	C₃⋊D₃×C₇₁	C₂×C₇
LCS	G ▷ C₃²×C₇₁
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.