Subgroups — C₆₁×Dic₇⋊C₉ #29506708

Order 15372.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×C₇⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₇×C₆₁	C₃	1	1	yes	maximal, characteristic
3	C₆₁×C₇⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₆₁	C₂×C₃	1	1	yes	characteristic
5	C₄×C₉×C₆₁	—	7	1	no	maximal, Hall
6	Dic₇×C₆₁	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇×C₆₁	C₃×C₄	1	1	yes	characteristic
8	C₂×C₉×C₆₁	—	7	1	no	—
9	C₂×C₇×C₆₁	C₂×C₉	1	1	yes	characteristic
10	C₃×C₄×C₆₁	—	7	1	no	—
11	C₉×C₆₁	—	7	1	no	Hall
12	C₇×C₆₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₆₁	AGL(1,𝔽₇)	1	1	yes	characteristic
14	Dic₇⋊C₉	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₄×C₆₁	—	7	1	no	Hall
16	C₃×C₆₁	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
17	C₂×C₇⋊C₉	C₂×C₆₁	1	1	yes	characteristic
18	C₂×C₆₁	D₇⋊C₉	1	1	yes	characteristic
19	C₃×Dic₇	C₃×C₆₁	1	1	yes	characteristic
20	C₇⋊C₉	C₄×C₆₁	1	1	yes	characteristic, complemented, Hall
21	C₆₁	Dic₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂×C₃×C₇	C₂×C₃×C₆₁	1	1	yes	characteristic
23	C₄×C₉	—	7	1	no	Hall
24	Dic₇	C₉×C₆₁	1	1	yes	characteristic, complemented, Hall
25	C₃×C₇	C₃×C₄×C₆₁	1	1	yes	characteristic
26	C₂×C₉	—	7	1	no	—
27	C₂×C₇	C₂×C₉×C₆₁	1	1	yes	characteristic
28	C₃×C₄	—	7	1	no	—
29	C₉	—	7	1	no	Sylow
30	C₇	C₄×C₉×C₆₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	AGL(1,𝔽₇)×C₆₁	1	1	yes	characteristic
32	C₄	—	7	1	no	Sylow
33	C₃	C₆₁×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic
34	C₂	C₆₁×D₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₆₁	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₄×C₉×C₆₁
Frattini	C₂×C₃	AGL(1,𝔽₇)×C₆₁
Fitting, socle, prime radical	C₂×C₃×C₇×C₆₁	C₂×C₃
cosocle	C₂×C₃×C₇	C₂×C₃×C₆₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₆₁

Complements

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

N	H ≅ G/N	type
3. C₆₁×C₇⋊C₉	C₄	semidirect
6. Dic₇×C₆₁	C₉	semidirect
12. C₇×C₆₁	C₄×C₉	semidirect
14. Dic₇⋊C₉	C₆₁	direct (N × H)
20. C₇⋊C₉	C₄×C₆₁	semidirect
21. C₆₁	Dic₇⋊C₉	direct (N × H)
24. Dic₇	C₉×C₆₁	semidirect
30. C₇	C₄×C₉×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×C₇⋊C₉	2
C₃×Dic₇×C₆₁	3
C₄×C₉×C₆₁	7
Dic₇⋊C₉	61

Subgroups — C61×Dic7⋊C9 #29506708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×Dic₇⋊C₉ #29506708