Subgroups — #44532225

Order 31347.

58 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, complemented
3	#23782708	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#6879	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×#732	—	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	H(3,𝔽₃)×C₄₃	—	9	1	no	—
14	C₃×C₉×C₄₃	—	3	1	no	—
15	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
16	#10624540	—	43	1	no	maximal, Sylow
17	C₃²×C₄₃	—	27	1	no	—
18	C₃²×C₄₃	#732	1	1	yes	characteristic
19	C₃×C₄₃⋊C₃	—	27	1	no	—
20	C₉×C₄₃	—	3	1	no	—
21	C₉×C₄₃	—	9	1	no	—
22	C₄₃⋊C₉	—	27	1	no	—
23	#6880	—	43	1	no	—
24	#6879	—	43	1	no	—
25	#6879	C₄₃⋊C₃	1	1	yes	characteristic, complemented
26	#6864	—	43	1	no	—
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	—	81	1	no	—
29	C₃×C₄₃	#6879	1	1	yes	characteristic
30	C₄₃⋊C₃	—	81	1	no	—
31	#733	—	129	1	no	—
32	#732	—	3	1	no	—
33	#732	—	129	1	no	—
34	C₃×C₂₇	—	129	1	no	—
35	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
36	C₄₃	#10624540	1	1	yes	characteristic, complemented, Sylow
37	3₋¹⁺²	—	387	1	no	—
38	H(3,𝔽₃)	—	9	1	no	—
39	H(3,𝔽₃)	—	387	1	no	—
40	C₃×C₉	—	3	1	no	—
41	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
42	C₂₇	—	129	3	no	—
43	C₃²	—	27	1	no	—
44	C₃²	—	1161	1	no	—
45	C₃²	#16812512	1	1	yes	characteristic
46	C₉	—	3	1	no	—
47	C₉	—	9	1	no	—
48	C₉	—	1161	1	no	—
49	C₃	—	3	1	no	—
50	C₃	—	81	1	no	—
51	C₃	—	3483	1	no	—
52	C₃	#23782750	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782750
commutator, cosocle	C₉²×C₄₃	C₃²
Frattini	C₉²	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6879	C₃
socle	C₃×C₄₃	#6879
hypercenter	#6879	C₄₃⋊C₃
hypocenter	C₄₃	#10624540
LCS	G ▷ C₉²×C₄₃ ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ C₉² ◁ #6879

Complements

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

N	H ≅ G/N	type
1. #23782754	C₃	semidirect
2. #23782751	C₃	semidirect
3. #23782708	C₃	semidirect
4. C₄₃×#6879	C₃	semidirect
25. #6879	C₄₃⋊C₃	semidirect
36. C₄₃	#10624540	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
#23782708	3
C₄₃×#6879	3
#10624540	43