Subgroups — #44534822

Order 31347.

716 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782824	C₃	1	27	yes	maximal, complemented
2	#23782822	C₃	1	6	yes	maximal, complemented
3	#23782798	C₃	1	3	yes	maximal
4	#23782782	C₃	1	3	yes	maximal, complemented
5	C₃²×3₋¹⁺²×C₄₃	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	9	yes	—
11	C₃²⋊(C₄₃⋊C₉)	C₃²	1	18	yes	—
12	C₉×C₄₃⋊C₉	C₃²	1	9	yes	complemented
13	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
14	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
15	C₃×3₋¹⁺²×C₄₃	C₃²	1	9	yes	—
16	C₃²×C₉×C₄₃	C₃²	1	2	yes	—
17	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
18	#11923958	—	9	9	no	—
19	C₃×C₄₃⋊C₉	C₃³	1	27	yes	—
20	C₃³×C₄₃	—	3	3	no	—
21	C₃³×C₄₃	—	9	3	no	—
22	C₃³×C₄₃	C₃³	1	3	yes	—
23	C₃³×C₄₃	C₃³	1	1	yes	characteristic
24	3₋¹⁺²×C₄₃	—	3	27	no	—
25	C₃×C₉×C₄₃	—	3	6	no	—
26	C₃×C₉×C₄₃	3₋¹⁺²	1	9	yes	complemented
27	C₃×C₉×C₄₃	C₃³	1	6	yes	—
28	C₃×C₉×C₄₃	C₃³	1	3	yes	—
29	#10624885	—	43	1	no	maximal, Sylow
30	C₃²×C₄₃	—	3	3	no	—
31	C₃²×C₄₃	—	3	3	no	—
32	C₃²×C₄₃	—	3	6	no	—
33	C₃²×C₄₃	—	3	3	no	—
34	C₃²×C₄₃	—	9	9	no	—
35	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
36	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
37	C₉×C₄₃	—	3	6	no	—
38	C₉×C₄₃	C₃×3₋¹⁺²	1	9	yes	—
39	C₄₃⋊C₉	—	3	27	no	—
40	C₃²×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
41	#6896	—	43	27	no	—
42	#6895	—	43	6	no	—
43	#6891	—	43	3	no	—
44	#6887	—	43	3	no	—
45	C₃×C₄₃	—	3	3	no	—
46	C₃×C₄₃	—	9	3	no	—
47	C₃×C₄₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
48	C₃×C₄₃	3₋¹⁺⁴	1	3	yes	—
49	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
50	C₃×3₋¹⁺²	—	3	9	no	—
51	C₃×3₋¹⁺²	—	43	9	no	—
52	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	9	yes	—
53	C₃²×C₉	C₃×C₄₃⋊C₃	1	2	yes	—
54	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
55	C₉⋊C₉	—	43	54	no	—
56	C₉⋊C₉	—	43	9	no	—
57	C₉⋊C₉	—	43	9	no	—
58	C₃²⋊C₉	—	43	9	no	—
59	C₃²⋊C₉	—	43	18	no	—
60	C₉²	—	43	9	no	—
61	C₄₃	#10624885	1	1	yes	characteristic, complemented, Sylow
62	C₃³	—	3	3	no	—
63	C₃³	—	9	3	no	—
64	C₃³	C₃²×C₄₃⋊C₃	1	3	yes	—
65	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
66	3₋¹⁺²	—	3	27	no	—
67	3₋¹⁺²	—	387	9	no	—
68	C₃×C₉	—	3	6	no	—
69	C₃×C₉	—	43	27	no	—
70	C₃×C₉	#11923958	1	9	yes	complemented
71	C₃×C₉	C₃²×C₄₃⋊C₃	1	6	yes	—
72	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
73	C₃²	—	3	3	no	—
74	C₃²	—	3	3	no	—
75	C₃²	—	3	3	no	—
76	C₃²	—	3	6	no	—
77	C₃²	—	9	9	no	—
78	C₃²	C₃×#11923958	1	3	yes	—
79	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
80	C₉	—	3	6	no	—
81	C₉	—	129	27	no	—
82	C₉	C₃×#11923958	1	9	yes	—
83	C₃	—	3	3	no	—
84	C₃	—	9	3	no	—
85	C₃	C₃²×#11923958	1	1	yes	characteristic
86	C₃	#23782923	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₃²×3₋¹⁺²×C₄₃	C₃
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	C₃²×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624885
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃²×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #23782824	C₃	semidirect
2. #23782822	C₃	semidirect
4. #23782782	C₃	semidirect
7. #16812500	C₃²	semidirect
8. #16812499	C₃²	semidirect
9. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
12. C₉×C₄₃⋊C₉	C₃²	semidirect
26. C₃×C₉×C₄₃	3₋¹⁺²	semidirect
61. C₄₃	#10624885	semidirect
70. C₃×C₉	#11923958	semidirect

Maximal subgroups

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

subgroup	index
#23782824	3
#23782822	3
#23782798	3
#23782782	3
C₃²×3₋¹⁺²×C₄₃	3
#10624885	43