Subgroups — #23782726

Order 10449.

52 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	C₃×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	#11923958	C₉	1	2	yes	—
6	#11923957	—	3	1	no	—
7	#11923956	—	3	1	no	—
8	C₃²⋊(C₄₃⋊C₃)	C₉	1	1	yes	characteristic
9	C₉×C₄₃⋊C₃	—	3	1	no	—
10	C₄₃⋊C₂₇	—	3	1	no	—
11	C₄₃⋊C₂₇	—	3	1	no	—
12	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
13	C₂₇×C₄₃	—	3	1	no	—
14	C₃²×C₄₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₄₃⋊C₃	—	3	1	no	—
16	C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
17	C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
18	C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
19	C₄₃⋊C₉	—	3	2	no	—
20	#6872	—	43	1	no	maximal, Sylow
21	C₃×C₄₃	—	3	1	no	—
22	C₃×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
23	C₄₃⋊C₃	—	9	1	no	—
24	#737	—	43	1	no	—
25	C₂₇⋊C₃	—	43	1	no	—
26	C₂₇⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic, complemented
27	C₃×C₂₇	—	43	1	no	—
28	C₄₃	#6872	1	1	yes	characteristic, complemented, Sylow
29	3₋¹⁺²	—	43	2	no	—
30	3₋¹⁺²	—	129	1	no	—
31	3₋¹⁺²	—	129	1	no	—
32	H(3,𝔽₃)	—	43	1	no	—
33	C₃×C₉	—	129	1	no	—
34	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
35	C₂₇	—	3	1	no	—
36	C₂₇	—	129	1	no	—
37	C₂₇	—	129	1	no	—
38	C₃²	—	129	1	no	—
39	C₃²	C₉×C₄₃⋊C₃	1	1	yes	characteristic
40	C₉	—	129	2	no	—
41	C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
42	C₉	#11923956	1	1	yes	characteristic
43	C₉	#11923957	1	1	yes	characteristic
44	C₃	—	3	1	no	—
45	C₃	—	387	1	no	—
46	C₃	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊(C₄₃⋊C₃)
commutator	C₃²×C₄₃	C₃×C₉
Frattini	C₃×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×C₂₇⋊C₃	C₃
socle	C₃×C₄₃	C₃²⋊C₉
prime radical	C₃²⋊(C₄₃⋊C₃)	C₉
cosocle	C₃×C₉×C₄₃	C₃²
hypercenter	C₂₇⋊C₃	C₄₃⋊C₃
hypocenter	C₄₃	#6872
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #16812505	C₃	semidirect
3. C₃×C₄₃⋊C₂₇	C₃	semidirect
4. C₄₃×C₂₇⋊C₃	C₃	semidirect
26. C₂₇⋊C₃	C₄₃⋊C₃	semidirect
28. C₄₃	#6872	semidirect