Subgroups — #23782781

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	#16812500	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812499	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₄₃⋊C₉)⋊C₉	C₃	1	3	yes	maximal, complemented
5	(C₃×C₄₃⋊C₃)⋊C₉	C₃	1	3	yes	maximal
6	C₉×C₄₃⋊C₉	C₃	1	3	yes	maximal, complemented
7	C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
9	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
10	C₃×C₄₃⋊C₉	C₃²	1	3	yes	—
11	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
12	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
13	C₉×C₄₃⋊C₃	C₉	1	9	yes	complemented
14	C₃×C₉×C₄₃	C₃²	1	3	yes	—
15	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
16	C₃²×C₄₃	C₃³	1	1	yes	characteristic
17	C₃×C₄₃⋊C₃	—	3	3	no	—
18	C₃×C₄₃⋊C₃	C₃×C₉	1	3	yes	—
19	C₉×C₄₃	—	3	3	no	—
20	C₉×C₄₃	C₃×C₉	1	3	yes	—
21	C₄₃⋊C₉	—	3	3	no	—
22	C₄₃⋊C₉	—	3	3	no	—
23	C₄₃⋊C₉	C₃×C₉	1	3	yes	—
24	C₄₃⋊C₉	C₃×C₉	1	3	yes	—
25	#6887	—	43	1	no	maximal, Sylow
26	C₃×C₄₃	C₃²×C₉	1	1	yes	characteristic
27	C₃×C₄₃	#737	1	3	yes	—
28	C₄₃⋊C₃	—	3	3	no	—
29	C₃²×C₉	—	43	1	no	—
30	C₉⋊C₉	—	43	3	no	—
31	C₉⋊C₉	—	43	1	no	—
32	C₉⋊C₉	—	43	1	no	—
33	C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
34	C₃²⋊C₉	—	43	3	no	—
35	C₉²	—	43	3	no	—
36	C₄₃	#6887	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	43	1	no	—
38	C₃×C₉	—	43	1	no	—
39	C₃×C₉	—	43	1	no	—
40	C₃×C₉	—	43	9	no	—
41	C₃×C₉	—	43	3	no	—
42	C₃×C₉	—	43	3	no	—
43	C₃×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
44	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
45	C₃²	—	43	3	no	—
46	C₃²	—	129	3	no	—
47	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	43	3	no	—
50	C₉	—	43	3	no	—
51	C₉	—	129	3	no	—
52	C₉	—	129	3	no	—
53	C₉	C₉×C₄₃⋊C₃	1	3	yes	—
54	C₃	—	129	3	no	—
55	C₃	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
56	C₃	#16812526	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. #16812500	C₃	semidirect
3. #16812499	C₃	semidirect
4. (C₄₃⋊C₉)⋊C₉	C₃	semidirect
6. C₉×C₄₃⋊C₉	C₃	semidirect
7. C₄₃×C₉⋊C₉	C₃	semidirect
13. C₉×C₄₃⋊C₃	C₉	semidirect
33. C₉⋊C₉	C₄₃⋊C₃	semidirect
36. C₄₃	#6887	semidirect