Subgroups — Dic₇×C₆₇⋊C₉ #30683048

Order 16884.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₆₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₇×C₆₇	C₃	1	1	yes	maximal, characteristic
3	C₇×C₆₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₄×C₆₇⋊C₉	—	7	1	no	maximal, Hall
6	Dic₇×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₆₇	C₃×C₄	1	1	yes	characteristic
8	C₂×C₆₇⋊C₉	D₇	1	1	yes	characteristic
9	C₂×C₇×C₆₇	C₂×C₉	1	1	yes	characteristic
10	C₃×C₄×C₆₇	—	7	1	no	—
11	C₆₇⋊C₉	Dic₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇×C₆₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₆₇	C₃×D₇	1	1	yes	characteristic
14	C₄×C₆₇	—	7	1	no	Hall
15	C₉×Dic₇	—	67	1	no	maximal, Hall
16	C₃×C₆₇	C₃×Dic₇	1	1	yes	characteristic
17	C₂×C₆₇	C₉×D₇	1	1	yes	characteristic
18	C₂×C₇×C₉	—	67	1	no	—
19	C₃×Dic₇	C₆₇⋊C₃	1	1	yes	characteristic
20	C₆₇	C₉×Dic₇	1	1	yes	characteristic, complemented, Sylow
21	C₇×C₉	—	67	1	no	Hall
22	C₂×C₃×C₇	C₂×C₆₇⋊C₃	1	1	yes	characteristic
23	C₄×C₉	—	469	1	no	Hall
24	Dic₇	C₆₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₇	C₄×C₆₇⋊C₃	1	1	yes	characteristic
26	C₂×C₉	—	67	1	no	—
27	C₂×C₇	C₂×C₆₇⋊C₉	1	1	yes	characteristic
28	C₃×C₄	—	7	1	no	—
29	C₉	—	67	1	no	Sylow
30	C₇	C₄×C₆₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₇×C₆₇⋊C₃	1	1	yes	characteristic
32	C₄	—	7	1	no	Sylow
33	C₃	Dic₇×C₆₇⋊C₃	1	1	yes	characteristic
34	C₂	D₇×C₆₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₇×C₆₇⋊C₃
commutator, hypocenter	C₇×C₆₇	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇×C₆₇	C₂×C₃
LCS	G ▷ C₇×C₆₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₇×C₆₇⋊C₉	C₄	semidirect
6. Dic₇×C₆₇	C₉	semidirect
11. C₆₇⋊C₉	Dic₇	direct (N × H)
12. C₇×C₆₇	C₄×C₉	semidirect
20. C₆₇	C₉×Dic₇	semidirect
24. Dic₇	C₆₇⋊C₉	direct (N × H)
30. C₇	C₄×C₆₇⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×C₆₇⋊C₉	2
C₃×Dic₇×C₆₇	3
C₄×C₆₇⋊C₉	7
C₉×Dic₇	67

Subgroups — Dic7×C67⋊C9 #30683048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₇×C₆₇⋊C₉ #30683048