Subgroups — #44535349

Order 31347.

978 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782924	C₃	1	1	yes	maximal, characteristic, complemented
2	C₄₃⋊H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃×#16812524	C₃	1	1	yes	maximal, characteristic, complemented
4	#23782888	C₃	1	24	yes	maximal, complemented
5	C₃×#16812511	C₃	1	12	yes	maximal, complemented
6	C₄₃×3₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic, complemented
7	#16812524	—	3	9	no	—
8	#16812524	—	3	9	no	—
9	C₃×#11923958	C₃²	1	12	yes	complemented
10	C₃×#11923958	C₃²	1	8	yes	complemented
11	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	12	yes	—
12	H(3,𝔽₃)×C₄₃⋊C₃	—	3	9	no	—
13	C₃²×C₄₃⋊C₉	C₃²	1	4	yes	complemented
14	#16812511	C₃²	1	9	yes	complemented
15	#16812511	C₃²	1	72	yes	complemented
16	C₄₃×#737	—	3	9	no	—
17	C₃×3₋¹⁺²×C₄₃	C₃²	1	12	yes	complemented
18	C₃×H(3,𝔽₃)×C₄₃	C₃²	1	1	yes	characteristic
19	C₃²×C₄₃⋊C₃	—	3	12	no	—
20	#11923958	—	3	24	no	—
21	#11923958	—	3	24	no	—
22	#11923958	C₃³	1	9	yes	—
23	C₃²⋊(C₄₃⋊C₃)	—	3	24	no	—
24	C₃²⋊(C₄₃⋊C₃)	C₃³	1	9	yes	—
25	C₃×C₄₃⋊C₉	—	3	12	no	—
26	C₃×C₄₃⋊C₉	—	3	12	no	—
27	C₃×C₄₃⋊C₉	C₃³	1	1	yes	characteristic
28	C₃×C₄₃⋊C₉	C₃³	1	8	yes	—
29	C₃³×C₄₃	C₃³	1	4	yes	—
30	3₋¹⁺²×C₄₃	—	3	24	no	—
31	3₋¹⁺²×C₄₃	C₃³	1	9	yes	—
32	H(3,𝔽₃)×C₄₃	H(3,𝔽₃)	1	9	yes	—
33	C₃×C₉×C₄₃	—	3	12	no	—
34	#10624931	—	43	1	no	maximal, Sylow
35	C₃²×C₄₃	—	9	4	no	—
36	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	12	yes	—
37	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
38	C₃×C₄₃⋊C₃	—	3	9	no	—
39	C₃×C₄₃⋊C₃	—	27	12	no	—
40	C₉×C₄₃	—	3	9	no	—
41	C₄₃⋊C₉	—	3	1	no	—
42	C₄₃⋊C₉	—	3	9	no	—
43	C₄₃⋊C₉	—	3	8	no	—
44	3₋¹⁺⁴	—	43	1	no	—
45	3₋¹⁺⁴	C₄₃⋊C₃	1	1	yes	characteristic, complemented
46	H(5,𝔽₃)	—	43	1	no	—
47	C₃×#737	—	43	1	no	—
48	#6910	—	43	24	no	—
49	C₃×#731	—	43	12	no	—
50	C₃×C₄₃	—	3	12	no	—
51	C₃×C₄₃	—	3	1	no	—
52	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
53	C₄₃⋊C₃	—	9	9	no	—
54	#737	—	3	9	no	—
55	#737	—	129	9	no	—
56	#737	—	129	9	no	—
57	C₃×3₋¹⁺²	—	43	8	no	—
58	C₃×3₋¹⁺²	—	43	12	no	—
59	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	12	yes	complemented
60	C₃×H(3,𝔽₃)	—	43	12	no	—
61	C₃×H(3,𝔽₃)	—	129	9	no	—
62	C₃×H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	1	yes	characteristic
63	C₃²×C₉	—	43	4	no	—
64	#731	—	43	9	no	—
65	#731	—	43	72	no	—
66	C₄₃	#10624931	1	1	yes	characteristic, complemented, Sylow
67	C₃³	—	129	12	no	—
68	C₃³	C₃²×C₄₃⋊C₃	1	4	yes	—
69	3₋¹⁺²	—	3	24	no	—
70	3₋¹⁺²	—	43	9	no	—
71	3₋¹⁺²	—	129	24	no	—
72	3₋¹⁺²	—	129	24	no	—
73	3₋¹⁺²	C₃²×C₄₃⋊C₃	1	9	yes	—
74	H(3,𝔽₃)	—	43	9	no	—
75	H(3,𝔽₃)	—	129	24	no	—
76	H(3,𝔽₃)	C₃²⋊(C₄₃⋊C₃)	1	9	yes	—
77	C₃×C₉	—	3	12	no	—
78	C₃×C₉	—	43	1	no	—
79	C₃×C₉	—	43	8	no	—
80	C₃×C₉	—	129	12	no	—
81	C₃×C₉	—	129	12	no	—
82	C₃²	—	9	4	no	—
83	C₃²	—	129	9	no	—
84	C₃²	—	1161	12	no	—
85	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	12	yes	—
86	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
87	C₉	—	3	9	no	—
88	C₉	—	129	1	no	—
89	C₉	—	129	8	no	—
90	C₉	—	129	9	no	—
91	C₃	—	3	1	no	—
92	C₃	—	3	12	no	—
93	C₃	—	387	9	no	—
94	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃⁴
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting	C₄₃×3₋¹⁺⁴	C₃
socle	C₃×C₄₃	C₃²×H(3,𝔽₃)
prime radical	C₄₃⋊H(5,𝔽₃)	C₃
hypercenter	3₋¹⁺⁴	C₄₃⋊C₃
hypocenter	C₄₃	#10624931
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃×H(3,𝔽₃) ◁ 3₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. #23782924	C₃	semidirect
3. C₃×#16812524	C₃	semidirect
4. #23782888	C₃	semidirect
5. C₃×#16812511	C₃	semidirect
6. C₄₃×3₋¹⁺⁴	C₃	semidirect
9. C₃×#11923958	C₃²	semidirect
10. C₃×#11923958	C₃²	semidirect
13. C₃²×C₄₃⋊C₉	C₃²	semidirect
14. #16812511	C₃²	semidirect
15. #16812511	C₃²	semidirect
17. C₃×3₋¹⁺²×C₄₃	C₃²	semidirect
45. 3₋¹⁺⁴	C₄₃⋊C₃	semidirect
59. C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	semidirect
66. C₄₃	#10624931	semidirect

Maximal subgroups

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

subgroup	index
#23782924	3
C₄₃⋊H(5,𝔽₃)	3
C₃×#16812524	3
#23782888	3
C₃×#16812511	3
C₄₃×3₋¹⁺⁴	3
#10624931	43