Subgroups — C₄×C₉×C₁₁₃⋊C₇ #43249751

Order 28476.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁₃⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₁₁₃⋊C₇	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₁₃⋊C₇	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₁₁₃⋊C₇	C₂×C₃	1	1	yes	characteristic
5	C₄×C₉×C₁₁₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₄×C₁₁₃⋊C₇	C₉	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₁₁₃⋊C₇	C₃×C₄	1	1	yes	characteristic
8	C₂×C₉×C₁₁₃	C₂×C₇	1	1	yes	characteristic
9	C₂×C₁₁₃⋊C₇	C₂×C₉	1	1	yes	characteristic
10	C₃×C₄×C₁₁₃	C₃×C₇	1	1	yes	characteristic
11	C₉×C₁₁₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₁₁₃⋊C₇	C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₁₁₃	C₂×C₃×C₇	1	1	yes	characteristic
14	C₄×C₁₁₃	C₇×C₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁₃	C₃×C₄×C₇	1	1	yes	characteristic
16	C₄×C₇×C₉	—	113	1	no	maximal, Hall
17	C₂×C₁₁₃	C₂×C₇×C₉	1	1	yes	characteristic
18	C₂×C₇×C₉	—	113	1	no	—
19	C₁₁₃	C₄×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
20	C₃×C₄×C₇	—	113	1	no	—
21	C₇×C₉	—	113	1	no	Hall
22	C₂×C₃×C₇	—	113	1	no	—
23	C₄×C₉	C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₇	—	113	1	no	Hall
25	C₃×C₇	—	113	1	no	—
26	C₂×C₉	C₂×C₁₁₃⋊C₇	1	1	yes	characteristic
27	C₂×C₇	—	113	1	no	—
28	C₃×C₄	C₃×C₁₁₃⋊C₇	1	1	yes	characteristic
29	C₉	C₄×C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₇	—	113	1	no	Sylow
31	C₂×C₃	C₂×C₃×C₁₁₃⋊C₇	1	1	yes	characteristic
32	C₄	C₉×C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₁₁₃⋊C₇	1	1	yes	characteristic
34	C₂	C₂×C₉×C₁₁₃⋊C₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₉	C₁₁₃⋊C₇
commutator, hypocenter	C₁₁₃	C₄×C₇×C₉
Frattini	C₂×C₃	C₂×C₃×C₁₁₃⋊C₇
Fitting	C₄×C₉×C₁₁₃	C₇
socle, cosocle	C₂×C₃×C₁₁₃	C₂×C₃×C₇
prime radical	C₂×C₃×C₁₁₃⋊C₇	C₂×C₃
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
3. C₉×C₁₁₃⋊C₇	C₄	direct (N × H)
5. C₄×C₉×C₁₁₃	C₇	semidirect
6. C₄×C₁₁₃⋊C₇	C₉	direct (N × H)
11. C₉×C₁₁₃	C₄×C₇	semidirect
12. C₁₁₃⋊C₇	C₄×C₉	direct (N × H)
14. C₄×C₁₁₃	C₇×C₉	semidirect
19. C₁₁₃	C₄×C₇×C₉	semidirect
23. C₄×C₉	C₁₁₃⋊C₇	direct (N × H)
29. C₉	C₄×C₁₁₃⋊C₇	direct (N × H)
32. C₄	C₉×C₁₁₃⋊C₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×C₁₁₃⋊C₇	2
C₃×C₄×C₁₁₃⋊C₇	3
C₄×C₉×C₁₁₃	7
C₄×C₇×C₉	113

Subgroups — C4×C9×C113⋊C7 #43249751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×C₁₁₃⋊C₇ #43249751