Subgroups — C₆₇×C₃⋊Dic₂₁ #30683142

Order 16884.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×Dic₂₁	—	3	4	no	maximal
3	C₃²×C₇×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₆₇	D₃	1	4	yes	—
5	C₃⋊Dic₃×C₆₇	—	7	1	no	maximal, Hall
6	Dic₇×C₆₇	—	9	1	no	Hall
7	C₃×C₇×C₆₇	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₆₇	D₇	1	1	yes	characteristic
9	C₂×C₇×C₆₇	C₃⋊D₃	1	1	yes	characteristic
10	Dic₃×C₆₇	—	21	4	no	—
11	C₃²×C₆₇	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₆₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₆₇	D₂₁	1	4	yes	—
14	C₄×C₆₇	—	63	1	no	Hall
15	C₃⋊Dic₂₁	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₆₇	Dic₂₁	1	4	yes	complemented
17	C₂×C₆₇	C₃⋊D₂₁	1	1	yes	characteristic
18	C₂×C₃²×C₇	C₂×C₆₇	1	1	yes	characteristic
19	Dic₂₁	—	3	4	no	—
20	C₆₇	C₃⋊Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃²×C₇	C₄×C₆₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₃×C₆₇	1	4	yes	—
23	C₃⋊Dic₃	—	7	1	no	Hall
24	Dic₇	—	9	1	no	Hall
25	C₃×C₇	Dic₃×C₆₇	1	4	yes	complemented
26	C₂×C₃²	D₇×C₆₇	1	1	yes	characteristic
27	C₂×C₇	C₃⋊D₃×C₆₇	1	1	yes	characteristic
28	Dic₃	—	21	4	no	—
29	C₃²	Dic₇×C₆₇	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊Dic₃×C₆₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₂₁×C₆₇	1	4	yes	—
32	C₄	—	63	1	no	Sylow
33	C₃	C₆₇×Dic₂₁	1	4	yes	complemented
34	C₂	C₆₇×C₃⋊D₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₆₇	C₃⋊D₂₁
commutator, hypocenter	C₃²×C₇	C₄×C₆₇
Frattini	C₂	C₆₇×C₃⋊D₂₁
Fitting, socle, prime radical	C₂×C₃²×C₇×C₆₇	C₂
cosocle	C₂×C₃²×C₇	C₂×C₆₇
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₆₇

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇×C₆₇	C₄	semidirect
7. C₃×C₇×C₆₇	Dic₃	semidirect
11. C₃²×C₆₇	Dic₇	semidirect
12. C₇×C₆₇	C₃⋊Dic₃	semidirect
15. C₃⋊Dic₂₁	C₆₇	direct (N × H)
16. C₃×C₆₇	Dic₂₁	semidirect
20. C₆₇	C₃⋊Dic₂₁	direct (N × H)
21. C₃²×C₇	C₄×C₆₇	semidirect
25. C₃×C₇	Dic₃×C₆₇	semidirect
29. C₃²	Dic₇×C₆₇	semidirect
30. C₇	C₃⋊Dic₃×C₆₇	semidirect
33. C₃	C₆₇×Dic₂₁	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×C₆₇	2
C₆₇×Dic₂₁	3
C₃⋊Dic₃×C₆₇	7
C₃⋊Dic₂₁	67

Subgroups — C67×C3⋊Dic21 #30683142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×C₃⋊Dic₂₁ #30683142