Subgroups — C₇⋊C₉×Dic₆₇ #30683045

Order 16884.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇⋊C₉×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×Dic₆₇	C₃	1	1	yes	maximal, characteristic
3	C₇⋊C₉×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₉×Dic₆₇	—	7	1	no	maximal, Hall
6	C₇×Dic₆₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₆₇	C₃×C₄	1	1	yes	characteristic
8	C₂×C₉×C₆₇	—	7	1	no	—
9	C₂×C₇×C₆₇	C₂×C₉	1	1	yes	characteristic
10	C₃×Dic₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₉×C₆₇	—	7	1	no	Hall
12	C₇×C₆₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	Dic₆₇	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₇⋊C₉	—	67	1	no	maximal, Hall
16	C₃×C₆₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₂×C₆₇	C₂×C₇⋊C₉	1	1	yes	characteristic
18	C₂×C₇⋊C₉	D₆₇	1	1	yes	characteristic
19	C₃×C₄×C₇	—	67	1	no	—
20	C₆₇	C₄×C₇⋊C₉	1	1	yes	characteristic, complemented, Sylow
21	C₇⋊C₉	Dic₆₇	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₇	C₃×D₆₇	1	1	yes	characteristic
23	C₄×C₉	—	469	1	no	Hall
24	C₄×C₇	—	67	1	no	Hall
25	C₃×C₇	C₃×Dic₆₇	1	1	yes	characteristic
26	C₂×C₉	—	7	1	no	—
27	C₂×C₇	C₉×D₆₇	1	1	yes	characteristic
28	C₃×C₄	—	67	1	no	—
29	C₉	—	7	1	no	Sylow
30	C₇	C₉×Dic₆₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	ΓL(1,𝔽₈)×D₆₇	1	1	yes	characteristic
32	C₄	—	67	1	no	Sylow
33	C₃	ΓL(1,𝔽₈)×Dic₆₇	1	1	yes	characteristic
34	C₂	C₇⋊C₉×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	ΓL(1,𝔽₈)×D₆₇
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⋊C₉×C₆₇	C₄	semidirect
6. C₇×Dic₆₇	C₉	semidirect
12. C₇×C₆₇	C₄×C₉	semidirect
14. Dic₆₇	C₇⋊C₉	direct (N × H)
20. C₆₇	C₄×C₇⋊C₉	semidirect
21. C₇⋊C₉	Dic₆₇	direct (N × H)
30. C₇	C₉×Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇⋊C₉×C₆₇	2
C₃×C₇×Dic₆₇	3
C₉×Dic₆₇	7
C₄×C₇⋊C₉	67

Subgroups — C7⋊C9×Dic67 #30683045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊C₉×Dic₆₇ #30683045