Subgroups — C₇×C₃⋊Dic₂₁₃ #31822051

Order 17892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₂₁₃	—	3	4	no	maximal
3	C₃²×C₇×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₇₁	D₃	1	4	yes	—
5	C₃⋊Dic₂₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×Dic₇₁	—	9	1	no	Hall
7	C₃×C₇×C₇₁	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₇₁	C₂×C₇	1	1	yes	characteristic
9	C₂×C₇×C₇₁	C₃⋊D₃	1	1	yes	characteristic
10	Dic₂₁₃	—	3	4	no	—
11	C₃²×C₇₁	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₇₁	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	D₇₁	1	1	yes	characteristic
19	C₇×Dic₃	—	213	4	no	—
20	C₇₁	C₇×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
21	C₃²×C₇	Dic₇₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₂₁₃	1	4	yes	—
23	C₃⋊Dic₃	—	71	1	no	Hall
24	C₄×C₇	—	639	1	no	Hall
25	C₃×C₇	Dic₂₁₃	1	4	yes	complemented
26	C₂×C₃²	C₇×D₇₁	1	1	yes	characteristic
27	C₂×C₇	C₃⋊D₂₁₃	1	1	yes	characteristic
28	Dic₃	—	213	4	no	—
29	C₃²	C₇×Dic₇₁	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊Dic₂₁₃	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₇×D₂₁₃	1	4	yes	—
32	C₄	—	639	1	no	Sylow
33	C₃	C₇×Dic₂₁₃	1	4	yes	complemented
34	C₂	C₇×C₃⋊D₂₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₇	C₃⋊D₂₁₃
commutator, hypocenter	C₃²×C₇₁	C₄×C₇
Frattini	C₂	C₇×C₃⋊D₂₁₃
Fitting, socle, prime radical	C₂×C₃²×C₇×C₇₁	C₂
cosocle	C₂×C₃²×C₇₁	C₂×C₇
LCS	G ▷ C₃²×C₇₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇×C₇₁	C₄	semidirect
5. C₃⋊Dic₂₁₃	C₇	direct (N × H)
7. C₃×C₇×C₇₁	Dic₃	semidirect
11. C₃²×C₇₁	C₄×C₇	semidirect
12. C₇×C₇₁	C₃⋊Dic₃	semidirect
16. C₃×C₇₁	C₇×Dic₃	semidirect
20. C₇₁	C₇×C₃⋊Dic₃	semidirect
21. C₃²×C₇	Dic₇₁	semidirect
25. C₃×C₇	Dic₂₁₃	semidirect
29. C₃²	C₇×Dic₇₁	semidirect
30. C₇	C₃⋊Dic₂₁₃	direct (N × H)
33. C₃	C₇×Dic₂₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇×C₇₁	2
C₇×Dic₂₁₃	3
C₃⋊Dic₂₁₃	7
C₇×C₃⋊Dic₃	71

Subgroups — C7×C3⋊Dic213 #31822051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊Dic₂₁₃ #31822051