Subgroups — C₃⋊Dic₃×C₇₁⋊C₇ #31822033

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	Dic₃×C₇₁⋊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⋊Dic₃×C₇₁	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₄×C₇₁⋊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	Dic₃×C₇₁	—	3	4	no	—
11	C₃²×C₇₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇₁⋊C₇	C₃⋊Dic₃	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₇₁	D₃×C₇	1	4	yes	—
14	C₄×C₇₁	—	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	C₇₁⋊C₇	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₇	—	639	1	no	Hall
25	C₃×C₇	—	71	4	no	—
26	C₂×C₃²	C₂×C₇₁⋊C₇	1	1	yes	characteristic
27	C₂×C₇	—	71	1	no	—
28	Dic₃	—	3	4	no	—
29	C₃²	C₄×C₇₁⋊C₇	1	1	yes	characteristic, complemented, Sylow
30	C₇	—	71	1	no	Sylow
31	C₂×C₃	D₃×C₇₁⋊C₇	1	4	yes	—
32	C₄	—	9	1	no	Sylow
33	C₃	Dic₃×C₇₁⋊C₇	1	4	yes	complemented
34	C₂	C₃⋊D₃×C₇₁⋊C₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₃×C₇₁⋊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

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₃²×C₇₁⋊C₇	C₄	semidirect
5. C₃⋊Dic₃×C₇₁	C₇	semidirect
7. C₃×C₇₁⋊C₇	Dic₃	semidirect
11. C₃²×C₇₁	C₄×C₇	semidirect
12. C₇₁⋊C₇	C₃⋊Dic₃	direct (N × H)
16. C₃×C₇₁	C₇×Dic₃	semidirect
20. C₇₁	C₇×C₃⋊Dic₃	semidirect
23. C₃⋊Dic₃	C₇₁⋊C₇	direct (N × H)
29. C₃²	C₄×C₇₁⋊C₇	semidirect
33. C₃	Dic₃×C₇₁⋊C₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃²×C₇₁⋊C₇	2
Dic₃×C₇₁⋊C₇	3
C₃⋊Dic₃×C₇₁	7
C₇×C₃⋊Dic₃	71

Subgroups — C3⋊Dic3×C71⋊C7 #31822033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊Dic₃×C₇₁⋊C₇ #31822033