Subgroups — #44534457

Order 31347.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782735	C₃	1	9	yes	maximal, complemented
2	#23782718	C₃	1	3	yes	maximal
3	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic
4	#16812505	C₃²	1	9	yes	—
5	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
6	C₄₃×C₉⋊C₉	—	3	1	no	—
7	C₄₃×C₉⋊C₉	C₃²	1	3	yes	—
8	C₄₃×C₃²⋊C₉	—	3	1	no	—
9	C₉²×C₄₃	—	3	1	no	—
10	C₄₃⋊C₂₇	—	3	9	no	—
11	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
12	C₃×C₉×C₄₃	—	3	3	no	—
13	C₃×C₉×C₄₃	—	3	3	no	—
14	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
15	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
16	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
17	#10624830	—	43	1	no	maximal, Sylow
18	C₃²×C₄₃	—	3	1	no	—
19	C₃²×C₄₃	—	9	1	no	—
20	C₃²×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
21	C₉×C₄₃	—	3	1	no	—
22	C₉×C₄₃	—	3	1	no	—
23	C₉×C₄₃	—	9	3	no	—
24	C₉×C₄₃	#737	1	3	yes	—
25	#6887	C₄₃⋊C₃	1	1	yes	characteristic
26	#6875	—	43	9	no	—
27	#6869	—	43	3	no	—
28	C₃×C₄₃	—	3	1	no	—
29	C₃×C₄₃	—	9	1	no	—
30	C₃×C₄₃	#6895	1	1	yes	characteristic
31	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
32	C₂₇⋊C₃	—	43	9	no	—
33	C₉⋊C₉	—	3	1	no	—
34	C₉⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
35	C₃²⋊C₉	—	3	1	no	—
36	C₉²	—	3	1	no	—
37	C₄₃	#10624830	1	1	yes	characteristic, complemented, Sylow
38	C₃³	#11923958	1	1	yes	characteristic
39	C₃×C₉	—	3	3	no	—
40	C₃×C₉	—	3	3	no	—
41	C₃×C₉	#11923958	1	1	yes	characteristic
42	C₃×C₉	#11923958	1	1	yes	characteristic
43	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
44	C₂₇	—	129	9	no	—
45	C₃²	—	3	1	no	—
46	C₃²	—	9	1	no	—
47	C₃²	C₃×#11923958	1	1	yes	characteristic
48	C₉	—	3	1	no	—
49	C₉	—	3	1	no	—
50	C₉	—	9	3	no	—
51	C₉	#16812525	1	3	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	9	1	no	—
54	C₃	#23782822	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782822
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃×C₄₃	#6895
prime radical	C₃³×C₄₃	3₋¹⁺²
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624830
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
1. #23782735	C₃	semidirect
37. C₄₃	#10624830	semidirect

Maximal subgroups

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

subgroup	index
#23782735	3
#23782718	3
C₄₃×#6887	3
#10624830	43