Subgroups — #44532218

Order 31347.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782754	C₃	1	1	yes	maximal, characteristic, complemented
2	#23782751	C₃	1	1	yes	maximal, characteristic
3	C₉×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#6880	C₃	1	1	yes	maximal, characteristic, complemented
5	#16812515	—	3	1	no	—
6	#16812513	—	3	1	no	—
7	C₃×C₄₃⋊C₂₇	—	3	1	no	—
8	C₄₃×#733	—	3	1	no	—
9	C₉²×C₄₃	C₃²	1	1	yes	characteristic
10	#11923958	—	9	1	no	—
11	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
12	C₄₃⋊C₂₇	—	3	3	no	—
13	3₋¹⁺²×C₄₃	—	9	1	no	—
14	C₃×C₉×C₄₃	—	3	1	no	—
15	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
16	#10624538	—	43	1	no	maximal, Sylow
17	C₃²×C₄₃	#732	1	1	yes	characteristic
18	C₃×C₄₃⋊C₃	—	27	1	no	—
19	C₉×C₄₃	—	3	3	no	—
20	C₉×C₄₃	—	3	1	no	—
21	C₉×C₄₃	—	27	1	no	—
22	C₄₃⋊C₉	—	27	1	no	—
23	#6880	—	43	1	no	—
24	#6880	C₄₃⋊C₃	1	1	yes	characteristic, complemented
25	#6879	—	43	1	no	—
26	C₉×C₂₇	—	43	1	no	—
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	#6879	1	1	yes	characteristic
29	C₄₃⋊C₃	—	81	1	no	—
30	#733	—	3	1	no	—
31	#733	—	129	1	no	—
32	#732	—	129	1	no	—
33	C₃×C₂₇	—	129	1	no	—
34	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
35	C₄₃	#10624538	1	1	yes	characteristic, complemented, Sylow
36	3₋¹⁺²	—	9	1	no	—
37	3₋¹⁺²	—	387	1	no	—
38	H(3,𝔽₃)	—	387	1	no	—
39	C₃×C₉	—	3	1	no	—
40	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
41	C₂₇	—	129	3	no	—
42	C₃²	—	1161	1	no	—
43	C₃²	#16812512	1	1	yes	characteristic
44	C₉	—	3	3	no	—
45	C₉	—	3	1	no	—
46	C₉	—	27	1	no	—
47	C₉	—	1161	1	no	—
48	C₃	—	3	1	no	—
49	C₃	—	3483	1	no	—
50	C₃	#23782750	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782750
commutator, cosocle	C₉²×C₄₃	C₃²
Frattini	C₉²	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6880	C₃
socle	C₃×C₄₃	#6879
prime radical	#23782751	C₃
hypercenter	#6880	C₄₃⋊C₃
hypocenter	C₄₃	#10624538
LCS	G ▷ C₉²×C₄₃ ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉² ◁ #6880

Complements

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

N	H ≅ G/N	type
1. #23782754	C₃	semidirect
3. C₉×C₄₃⋊C₂₇	C₃	semidirect
4. C₄₃×#6880	C₃	semidirect
24. #6880	C₄₃⋊C₃	semidirect
35. C₄₃	#10624538	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23782754	3
#23782751	3
C₉×C₄₃⋊C₂₇	3
C₄₃×#6880	3
#10624538	43