Subgroups — #23782780

Order 10449.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	(C₄₃⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
3	(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	3	yes	maximal
4	C₉×C₄₃⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×C₄₃⋊C₉	C₃²	1	6	yes	—
8	C₃×C₄₃⋊C₉	C₃²	1	2	yes	—
9	C₉×C₄₃⋊C₃	C₉	1	9	yes	complemented
10	C₃×C₉×C₄₃	C₃²	1	3	yes	—
11	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₃²×C₄₃	C₃³	1	1	yes	characteristic
13	C₃×C₄₃⋊C₃	—	3	3	no	—
14	C₃×C₄₃⋊C₃	C₃×C₉	1	3	yes	—
15	C₉×C₄₃	—	3	3	no	—
16	C₉×C₄₃	C₃×C₉	1	3	yes	—
17	C₄₃⋊C₉	—	3	6	no	—
18	C₄₃⋊C₉	C₃×C₉	1	6	yes	—
19	#6887	—	43	1	no	maximal, Sylow
20	C₃×C₄₃	C₃²×C₉	1	1	yes	characteristic
21	C₃×C₄₃	#737	1	3	yes	—
22	C₄₃⋊C₃	—	3	3	no	—
23	C₃²×C₉	—	43	1	no	—
24	C₉⋊C₉	—	43	6	no	—
25	C₃²⋊C₉	—	43	3	no	—
26	C₉²	—	43	2	no	—
27	C₉²	C₄₃⋊C₃	1	1	yes	characteristic, complemented
28	C₄₃	#6887	1	1	yes	characteristic, complemented, Sylow
29	C₃³	—	43	1	no	—
30	C₃×C₉	—	43	2	no	—
31	C₃×C₉	—	43	9	no	—
32	C₃×C₉	—	43	6	no	—
33	C₃×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
34	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
35	C₃²	—	43	3	no	—
36	C₃²	—	129	3	no	—
37	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
38	C₉	—	3	3	no	—
39	C₉	—	43	6	no	—
40	C₉	—	129	6	no	—
41	C₉	C₉×C₄₃⋊C₃	1	3	yes	—
42	C₃	—	129	3	no	—
43	C₃	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
44	C₃	#16812525	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃²×C₉
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₉²×C₄₃	C₃
socle, cosocle	C₃²×C₄₃	C₃³
prime radical	C₃²×C₄₃⋊C₃	C₃²
hypercenter	C₉²	C₄₃⋊C₃
hypocenter	C₄₃	#6887
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₉²

Complements

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

N	H ≅ G/N	type
2. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
4. C₉×C₄₃⋊C₉	C₃	semidirect
5. C₉²×C₄₃	C₃	semidirect
9. C₉×C₄₃⋊C₃	C₉	semidirect
27. C₉²	C₄₃⋊C₃	semidirect
28. C₄₃	#6887	semidirect