Subgroups — #44531942

Order 31347.

156 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	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic
3	#16812505	—	3	3	no	—
4	#16812505	—	3	3	no	—
5	#16812505	—	3	3	no	—
6	C₃×C₄₃⋊C₂₇	C₉	1	9	yes	complemented
7	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₉⋊C₉	—	3	1	no	—
9	C₄₃×C₉⋊C₉	—	3	1	no	—
10	C₄₃×C₃²⋊C₉	—	3	1	no	—
11	C₉²×C₄₃	C₉	1	3	yes	—
12	C₄₃⋊C₂₇	—	3	9	no	—
13	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
14	C₃×C₉×C₄₃	—	3	3	no	—
15	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
16	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
19	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
20	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
21	#10624465	—	43	1	no	maximal, Sylow
22	C₃²×C₄₃	—	9	1	no	—
23	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
24	C₃²×C₄₃	C₉⋊C₉	1	3	yes	—
25	C₉×C₄₃	—	9	3	no	—
26	C₉×C₄₃	C₉²	1	1	yes	characteristic
27	C₉×C₄₃	C₃²⋊C₉	1	3	yes	—
28	C₉×C₄₃	C₉⋊C₉	1	3	yes	—
29	C₉×C₄₃	C₉⋊C₉	1	1	yes	characteristic
30	C₉×C₄₃	C₉⋊C₉	1	1	yes	characteristic
31	C₃×C₂₇⋊C₃	—	43	3	no	—
32	#6887	C₄₃⋊C₃	1	1	yes	characteristic
33	C₃×C₄₃	—	3	1	no	—
34	C₃×C₄₃	—	3	3	no	—
35	C₃×C₄₃	#6855	1	1	yes	characteristic
36	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
37	C₂₇⋊C₃	—	129	3	no	—
38	C₂₇⋊C₃	—	129	3	no	—
39	C₂₇⋊C₃	—	129	3	no	—
40	C₃×C₂₇	—	43	9	no	—
41	C₉⋊C₉	—	3	1	no	—
42	C₉⋊C₉	—	3	1	no	—
43	C₃²⋊C₉	—	3	1	no	—
44	C₉²	C₄₃⋊C₉	1	3	yes	—
45	C₄₃	#10624465	1	1	yes	characteristic, complemented, Sylow
46	C₃³	#11923958	1	1	yes	characteristic
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
49	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
50	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
51	C₃×C₉	#11923956	1	3	yes	—
52	C₃×C₉	#11923957	1	3	yes	—
53	C₃×C₉	#11923958	1	1	yes	characteristic
54	C₂₇	—	129	9	no	—
55	C₃²	—	9	1	no	—
56	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
57	C₃²	(C₄₃⋊C₉)⋊C₉	1	3	yes	—
58	C₉	—	9	3	no	—
59	C₉	C₉×C₄₃⋊C₉	1	1	yes	characteristic
60	C₉	(C₃×C₄₃⋊C₃)⋊C₉	1	3	yes	—
61	C₉	(C₄₃⋊C₉)⋊C₉	1	3	yes	—
62	C₉	#16812499	1	1	yes	characteristic
63	C₉	#16812500	1	1	yes	characteristic
64	C₃	—	3	1	no	—
65	C₃	—	3	3	no	—
66	C₃	C₄₃⋊#6855	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₉×C₄₃⋊C₉
commutator	C₉×C₄₃	C₉²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃×C₄₃	#6855
prime radical	C₃³×C₄₃	3₋¹⁺²
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624465
LCS	G ▷ C₉×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
6. C₃×C₄₃⋊C₂₇	C₉	semidirect
45. C₄₃	#10624465	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
C₄₃×#6887	3
#10624465	43