Subgroups — #44535213

Order 31347.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782845	C₃	1	9	yes	maximal, complemented
2	#23782834	C₃	1	9	yes	maximal, complemented
3	#23782829	C₃	1	18	yes	maximal, complemented
4	#23782798	C₃	1	3	yes	maximal
5	C₄₃×#6891	C₃	1	1	yes	maximal, characteristic
6	C₃×#11923958	C₃²	1	9	yes	—
7	#16812500	C₃²	1	9	yes	complemented
8	#16812499	C₃²	1	9	yes	complemented
9	(C₄₃⋊C₉)⋊C₉	C₃²	1	54	yes	complemented
10	C₃²⋊(C₄₃⋊C₉)	C₃²	1	18	yes	—
11	C₃²⋊(C₄₃⋊C₉)	C₃²	1	9	yes	—
12	C₉×C₄₃⋊C₉	C₃²	1	9	yes	complemented
13	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
14	C₃×3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
15	C₄₃×C₃²⋊C₉	C₃²	1	6	yes	—
16	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	—
17	#11923958	—	9	9	no	—
18	C₃×C₄₃⋊C₉	C₃³	1	27	yes	—
19	C₃³×C₄₃	—	9	1	no	—
20	C₃³×C₄₃	—	9	3	no	—
21	C₃³×C₄₃	C₃³	1	2	yes	—
22	C₃³×C₄₃	C₃³	1	1	yes	characteristic
23	C₃³×C₄₃	C₃³	1	1	yes	characteristic
24	3₋¹⁺²×C₄₃	—	9	3	no	—
25	C₃×C₉×C₄₃	C₃³	1	9	yes	—
26	#10624912	—	43	1	no	maximal, Sylow
27	C₃²×C₄₃	—	3	1	no	—
28	C₃²×C₄₃	—	3	6	no	—
29	C₃²×C₄₃	—	3	3	no	—
30	C₃²×C₄₃	—	3	2	no	—
31	C₃²×C₄₃	—	3	1	no	—
32	C₃²×C₄₃	—	3	3	no	—
33	C₃²×C₄₃	—	9	9	no	—
34	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
35	C₉×C₄₃	—	3	9	no	—
36	C₄₃⋊C₉	—	3	27	no	—
37	#6900	—	43	9	no	—
38	#6898	—	43	9	no	—
39	#6897	—	43	18	no	—
40	#6891	—	43	3	no	—
41	#6891	C₄₃⋊C₃	1	1	yes	characteristic
42	C₃×C₄₃	—	9	1	no	—
43	C₃×C₄₃	—	9	2	no	—
44	C₃×C₄₃	—	9	1	no	—
45	C₃×C₄₃	3₋¹⁺⁴	1	3	yes	—
46	C₃×C₄₃	3₋¹⁺⁴	1	1	yes	characteristic
47	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
48	C₃×3₋¹⁺²	—	43	9	no	—
49	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
50	C₉⋊C₉	—	43	54	no	—
51	C₉⋊C₉	—	43	9	no	—
52	C₉⋊C₉	—	43	9	no	—
53	C₃²⋊C₉	—	43	18	no	—
54	C₃²⋊C₉	—	43	9	no	—
55	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	6	yes	—
56	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
57	C₉²	—	43	9	no	—
58	C₄₃	#10624912	1	1	yes	characteristic, complemented, Sylow
59	C₃³	—	9	3	no	—
60	C₃³	—	9	1	no	—
61	C₃³	C₃²×C₄₃⋊C₃	1	2	yes	—
62	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
63	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
64	3₋¹⁺²	—	9	3	no	—
65	3₋¹⁺²	—	387	9	no	—
66	C₃×C₉	—	43	27	no	—
67	C₃×C₉	C₃²×C₄₃⋊C₃	1	9	yes	—
68	C₃²	—	3	3	no	—
69	C₃²	—	3	6	no	—
70	C₃²	—	3	3	no	—
71	C₃²	—	3	1	no	—
72	C₃²	—	3	2	no	—
73	C₃²	—	3	1	no	—
74	C₃²	—	9	9	no	—
75	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
76	C₉	—	3	9	no	—
77	C₉	—	129	27	no	—
78	C₃	—	9	1	no	—
79	C₃	—	9	2	no	—
80	C₃	—	9	1	no	—
81	C₃	#23782923	1	3	yes	—
82	C₃	#23782924	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₄₃×#6891	C₃
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	#6891	C₄₃⋊C₃
hypocenter	C₄₃	#10624912
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ #6891

Complements

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

N	H ≅ G/N	type
1. #23782845	C₃	semidirect
2. #23782834	C₃	semidirect
3. #23782829	C₃	semidirect
7. #16812500	C₃²	semidirect
8. #16812499	C₃²	semidirect
9. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
12. C₉×C₄₃⋊C₉	C₃²	semidirect
58. C₄₃	#10624912	semidirect

Maximal subgroups

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

subgroup	index
#23782845	3
#23782834	3
#23782829	3
#23782798	3
C₄₃×#6891	3
#10624912	43