Subgroups — #23782858

Order 10449.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812525	C₃	1	1	yes	maximal, characteristic
2	#16812505	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812504	C₃	1	3	yes	maximal, complemented
4	#16812503	C₃	1	3	yes	maximal, complemented
5	C₃×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂₇×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
7	C₄₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
8	#11923958	C₉	1	2	yes	—
9	#11923957	C₉	1	3	yes	—
10	#11923956	C₉	1	3	yes	—
11	C₃²⋊(C₄₃⋊C₃)	C₉	1	1	yes	characteristic
12	C₉×C₄₃⋊C₃	C₃²	1	3	yes	—
13	C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
14	C₄₃⋊C₂₇	C₃²	1	3	yes	—
15	C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
16	C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
18	C₂₇×C₄₃	C₃²	1	3	yes	—
19	C₃²×C₄₃	C₃×C₉	1	1	yes	characteristic
20	C₃×C₄₃⋊C₃	C₃×C₉	1	3	yes	—
21	C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
22	C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
23	C₉×C₄₃	C₃³	1	1	yes	characteristic
24	C₄₃⋊C₉	C₃×C₉	1	6	yes	—
25	#6903	—	43	1	no	maximal, Sylow
26	C₃×C₄₃	—	3	1	no	—
27	C₃×C₄₃	C₃²×C₉	1	1	yes	characteristic
28	C₄₃⋊C₃	—	3	3	no	—
29	#737	—	43	1	no	—
30	C₂₇⋊C₃	—	43	1	no	—
31	C₂₇⋊C₃	—	43	3	no	—
32	C₂₇⋊C₃	—	43	3	no	—
33	C₂₇⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic, complemented
34	C₃×C₂₇	—	43	1	no	—
35	C₃×C₂₇	—	43	3	no	—
36	C₄₃	#6903	1	1	yes	characteristic, complemented, Sylow
37	3₋¹⁺²	—	43	2	no	—
38	3₋¹⁺²	—	43	3	no	—
39	3₋¹⁺²	—	43	3	no	—
40	H(3,𝔽₃)	—	43	1	no	—
41	C₃×C₉	—	43	3	no	—
42	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
43	C₂₇	—	43	1	no	—
44	C₂₇	—	43	1	no	—
45	C₂₇	—	43	1	no	—
46	C₂₇	—	43	3	no	—
47	C₂₇	C₃×C₄₃⋊C₃	1	3	yes	—
48	C₃²	—	43	3	no	—
49	C₃²	C₉×C₄₃⋊C₃	1	1	yes	characteristic
50	C₉	—	43	6	no	—
51	C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
52	C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
53	C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
54	C₃	—	3	1	no	—
55	C₃	—	129	3	no	—
56	C₃	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₉	C₃²×C₄₃⋊C₃
commutator, socle	C₃×C₄₃	C₃²×C₉
Fitting	C₄₃×C₂₇⋊C₃	C₃
prime radical	C₃²⋊(C₄₃⋊C₃)	C₉
cosocle	C₉×C₄₃	C₃³
hypercenter	C₂₇⋊C₃	C₄₃⋊C₃
hypocenter	C₄₃	#6903
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #16812505	C₃	semidirect
3. #16812504	C₃	semidirect
4. #16812503	C₃	semidirect
5. C₃×C₄₃⋊C₂₇	C₃	semidirect
6. C₂₇×C₄₃⋊C₃	C₃	semidirect
7. C₄₃×C₂₇⋊C₃	C₃	semidirect
33. C₂₇⋊C₃	C₄₃⋊C₃	semidirect
36. C₄₃	#6903	semidirect