Subgroups — #44531946

Order 31347.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812505	C₃	1	3	yes	maximal
2	C₃×C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	#16812505	—	3	3	no	—
4	#16812505	—	3	3	no	—
5	#16812505	C₉	1	9	yes	complemented
6	C₃×C₄₃⋊C₂₇	—	3	3	no	—
7	C₃²×C₉×C₄₃	C₉	1	3	yes	—
8	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
9	C₉²×C₄₃	—	3	1	no	—
10	C₉²×C₄₃	—	3	2	no	—
11	C₄₃⋊C₂₇	—	3	9	no	—
12	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₄₃	—	3	3	no	—
14	C₃×C₉×C₄₃	—	3	9	no	—
15	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
16	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
17	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
18	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
19	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
20	#10624467	—	43	1	no	maximal, Sylow
21	C₃²×C₄₃	—	3	3	no	—
22	C₃²×C₄₃	C₉²	1	1	yes	characteristic
23	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
24	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
25	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
26	C₉×C₄₃	—	3	9	no	—
27	C₉×C₄₃	C₃²⋊C₉	1	3	yes	—
28	C₉×C₄₃	C₉⋊C₉	1	6	yes	—
29	C₃×C₂₇⋊C₃	—	43	3	no	—
30	C₃×C₉²	C₄₃⋊C₃	1	1	yes	characteristic
31	C₃×C₄₃	—	3	1	no	—
32	C₃×C₄₃	—	3	1	no	—
33	C₃×C₄₃	—	3	1	no	—
34	C₃×C₄₃	#6855	1	1	yes	characteristic
35	C₃×C₄₃	#6869	1	3	yes	—
36	C₃²×C₉	C₄₃⋊C₉	1	3	yes	—
37	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
38	C₂₇⋊C₃	—	43	9	no	—
39	C₂₇⋊C₃	—	129	3	no	—
40	C₂₇⋊C₃	—	129	3	no	—
41	C₃×C₂₇	—	129	3	no	—
42	C₉²	—	3	1	no	—
43	C₉²	—	3	2	no	—
44	C₄₃	#10624467	1	1	yes	characteristic, complemented, Sylow
45	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	—	3	9	no	—
48	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
49	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
50	C₃×C₉	#11923956	1	3	yes	—
51	C₃×C₉	#11923957	1	3	yes	—
52	C₃×C₉	#11923958	1	2	yes	—
53	C₂₇	—	129	9	no	—
54	C₃²	—	3	3	no	—
55	C₃²	C₉×C₄₃⋊C₉	1	1	yes	characteristic
56	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
57	C₃²	#16812499	1	1	yes	characteristic
58	C₃²	#16812500	1	1	yes	characteristic
59	C₉	—	3	9	no	—
60	C₉	(C₃×C₄₃⋊C₃)⋊C₉	1	3	yes	—
61	C₉	(C₄₃⋊C₉)⋊C₉	1	6	yes	—
62	C₃	—	3	1	no	—
63	C₃	—	3	1	no	—
64	C₃	—	3	1	no	—
65	C₃	C₄₃⋊#6855	1	1	yes	characteristic
66	C₃	#23782718	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator	C₃²×C₄₃	C₉²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₉²×C₄₃	C₃
socle	C₃²×C₄₃	C₃²⋊C₉
prime radical	C₃³×C₄₃	C₃×C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₉²	C₄₃⋊C₃
hypocenter	C₄₃	#10624467
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
5. #16812505	C₉	semidirect
44. C₄₃	#10624467	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812505	3
C₃×C₉²×C₄₃	3
#10624467	43