Subgroups — (C₄₃⋊C₉)⋊C₂₇ #23782732

Order 10449.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₃×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₉×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic
5	C₃×C₄₃⋊C₉	C₉	1	1	yes	characteristic
6	C₃×C₄₃⋊C₉	C₉	1	1	yes	characteristic
7	C₃×C₄₃⋊C₉	C₉	1	1	yes	characteristic
8	C₄₃⋊C₂₇	—	3	1	no	—
9	C₄₃⋊C₂₇	—	3	1	no	—
10	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
11	C₂₇×C₄₃	—	3	1	no	—
12	C₃²×C₄₃	C₃×C₉	1	1	yes	characteristic
13	C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
14	C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
15	C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
16	C₄₃⋊C₉	—	3	1	no	—
17	C₄₃⋊C₉	—	3	1	no	—
18	C₄₃⋊C₉	C₂₇	1	3	yes	complemented
19	C₉⋊C₂₇	—	43	1	no	maximal, Sylow
20	C₃×C₄₃	C₉⋊C₉	1	1	yes	characteristic
21	C₃×C₄₃	C₃×C₂₇	1	1	yes	characteristic
22	C₃×C₄₃	C₂₇⋊C₃	1	1	yes	characteristic
23	C₃×C₄₃	C₂₇⋊C₃	1	1	yes	characteristic
24	C₃×C₂₇	—	43	1	no	—
25	C₃×C₂₇	—	43	1	no	—
26	C₃×C₂₇	C₄₃⋊C₃	1	1	yes	characteristic
27	C₉²	—	43	1	no	—
28	C₄₃	C₉⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₉	—	43	1	no	—
30	C₃×C₉	—	43	1	no	—
31	C₃×C₉	—	43	1	no	—
32	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
33	C₂₇	—	3	1	no	—
34	C₂₇	—	129	1	no	—
35	C₂₇	—	129	1	no	—
36	C₃²	C₉×C₄₃⋊C₃	1	1	yes	characteristic
37	C₉	—	43	3	no	—
38	C₉	—	129	1	no	—
39	C₉	—	129	1	no	—
40	C₉	#11923956	1	1	yes	characteristic
41	C₉	#11923957	1	1	yes	characteristic
42	C₉	#11923958	1	1	yes	characteristic
43	C₃	(C₄₃⋊C₉)⋊C₉	1	1	yes	characteristic
44	C₃	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
45	C₃	#16812503	1	1	yes	characteristic
46	C₃	#16812504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃×C₉	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃×C₂₇
Fitting	C₃×C₂₇×C₄₃	C₃
socle, prime radical	C₃²×C₄₃	C₃×C₉
cosocle	C₃×C₉×C₄₃	C₃²
hypercenter	C₃×C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	C₉⋊C₂₇
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
18. C₄₃⋊C₉	C₂₇	semidirect
28. C₄₃	C₉⋊C₂₇	semidirect

Subgroups — (C43⋊C9)⋊C27 #23782732

Conjugacy classes of subgroups

Complements

Subgroups — (C₄₃⋊C₉)⋊C₂₇ #23782732