Subgroups — C₃⋊(C₃⋊(Dic₇₁⋊C₇)) #31822032

Order 17892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇₁⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(Dic₇₁⋊C₇)	—	3	4	no	maximal
3	C₃²×C₇₁⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇₁⋊C₇	D₃	1	4	yes	—
5	C₃⋊Dic₂₁₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	Dic₇₁⋊C₇	—	9	1	no	Hall
7	C₃×C₇₁⋊C₇	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₇₁	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇₁⋊C₇	C₃⋊D₃	1	1	yes	characteristic
10	Dic₂₁₃	—	3	4	no	—
11	C₃²×C₇₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇₁⋊C₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇₁	D₃×C₇	1	4	yes	—
14	Dic₇₁	—	9	1	no	Hall
15	C₇×C₃⋊Dic₃	—	71	1	no	maximal, Hall
16	C₃×C₇₁	C₇×Dic₃	1	4	yes	complemented
17	C₂×C₇₁	C₇×C₃⋊D₃	1	1	yes	characteristic
18	C₂×C₃²×C₇	—	71	1	no	—
19	C₇×Dic₃	—	213	4	no	—
20	C₇₁	C₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
21	C₃²×C₇	—	71	1	no	Hall
22	C₂×C₃×C₇	—	71	4	no	—
23	C₃⋊Dic₃	—	497	1	no	Hall
24	C₄×C₇	—	639	1	no	Hall
25	C₃×C₇	—	71	4	no	—
26	C₂×C₃²	D₇₁⋊C₇	1	1	yes	characteristic
27	C₂×C₇	—	71	1	no	—
28	Dic₃	—	1491	4	no	—
29	C₃²	Dic₇₁⋊C₇	1	1	yes	characteristic, complemented, Sylow
30	C₇	—	71	1	no	Sylow
31	C₂×C₃	C₃⋊(D₇₁⋊C₇)	1	4	yes	—
32	C₄	—	4473	1	no	Sylow
33	C₃	C₃⋊(Dic₇₁⋊C₇)	1	4	yes	complemented
34	C₂	C₃⋊(C₃⋊(D₇₁⋊C₇))	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(C₃⋊(D₇₁⋊C₇))
commutator, hypocenter	C₃²×C₇₁	C₄×C₇
Fitting, socle, cosocle	C₂×C₃²×C₇₁	C₂×C₇
prime radical	C₂×C₃²×C₇₁⋊C₇	C₂
LCS	G ▷ C₃²×C₇₁
UCS	C₁ ◁ C₂

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.