Subgroups — #44535211

Order 31347.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782848	C₃	1	8	yes	maximal, complemented
2	#23782847	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782834	C₃	1	8	yes	maximal, complemented
4	#23782832	C₃	1	16	yes	maximal, complemented
5	#23782831	C₃	1	2	yes	maximal, complemented
6	#23782796	C₃	1	4	yes	maximal
7	C₄₃×#6898	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
9	C₃×#11923956	C₃²	1	4	yes	—
10	C₃×#11923956	C₃²	1	8	yes	—
11	#16812500	C₃²	1	8	yes	complemented
12	#16812499	C₃²	1	8	yes	complemented
13	(C₄₃⋊C₉)⋊C₉	C₃²	1	16	yes	complemented
14	(C₄₃⋊C₉)⋊C₉	C₃²	1	32	yes	complemented
15	C₃²⋊(C₄₃⋊C₉)	C₃²	1	8	yes	—
16	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	8	yes	—
17	(C₃×C₄₃⋊C₃)⋊C₉	C₃²	1	16	yes	—
18	C₉×C₄₃⋊C₉	C₃²	1	8	yes	complemented
19	C₄₃×C₉⋊C₉	C₃²	1	8	yes	complemented
20	C₄₃×C₃²⋊C₉	C₃²	1	4	yes	—
21	C₉²×C₄₃	C₃²	1	1	yes	characteristic, complemented
22	C₃²×C₄₃⋊C₃	—	9	4	no	—
23	C₃²×C₄₃⋊C₃	C₃³	1	2	yes	—
24	C₃²×C₄₃⋊C₃	C₃³	1	1	yes	characteristic
25	#11923956	—	9	4	no	—
26	#11923956	—	9	8	no	—
27	C₃×C₄₃⋊C₉	C₃³	1	16	yes	—
28	C₃×C₄₃⋊C₉	C₃³	1	8	yes	—
29	C₃³×C₄₃	C₃³	1	1	yes	characteristic
30	C₃×C₉×C₄₃	C₃³	1	4	yes	—
31	C₃×C₉×C₄₃	C₃³	1	8	yes	—
32	#10624912	—	43	1	no	maximal, Sylow
33	C₃²×C₄₃	—	3	4	no	—
34	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
35	C₃×C₄₃⋊C₃	—	3	4	no	—
36	C₃×C₄₃⋊C₃	—	3	8	no	—
37	C₃×C₄₃⋊C₃	—	9	9	no	—
38	C₉×C₄₃	—	3	4	no	—
39	C₉×C₄₃	—	3	8	no	—
40	C₄₃⋊C₉	—	3	16	no	—
41	C₄₃⋊C₉	—	3	8	no	—
42	#6900	—	43	8	no	—
43	#6900	—	43	1	no	—
44	#6898	—	43	8	no	—
45	#6898	C₄₃⋊C₃	1	1	yes	characteristic, complemented
46	#6897	—	43	16	no	—
47	#6897	—	43	2	no	—
48	#6891	—	43	4	no	—
49	C₃×C₄₃	—	9	1	no	—
50	C₃×C₄₃	3₋¹⁺⁴	1	4	yes	—
51	C₄₃⋊C₃	—	9	1	no	—
52	C₄₃⋊C₃	—	9	2	no	—
53	C₃⁴	—	43	1	no	—
54	C₃×3₋¹⁺²	—	43	8	no	—
55	C₃×3₋¹⁺²	—	43	4	no	—
56	C₉⋊C₉	—	43	32	no	—
57	C₉⋊C₉	—	43	16	no	—
58	C₉⋊C₉	—	43	8	no	—
59	C₉⋊C₉	—	43	8	no	—
60	C₉⋊C₉	C₃×C₄₃⋊C₃	1	8	yes	complemented
61	C₃²⋊C₉	—	43	8	no	—
62	C₃²⋊C₉	—	43	16	no	—
63	C₃²⋊C₉	—	43	8	no	—
64	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	4	yes	—
65	C₉²	—	43	8	no	—
66	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented
67	C₄₃	#10624912	1	1	yes	characteristic, complemented, Sylow
68	C₃³	—	43	2	no	—
69	C₃³	—	43	1	no	—
70	C₃³	—	387	4	no	—
71	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
72	3₋¹⁺²	—	387	8	no	—
73	3₋¹⁺²	—	387	4	no	—
74	C₃×C₉	—	43	16	no	—
75	C₃×C₉	—	43	8	no	—
76	C₃×C₉	C₃²×C₄₃⋊C₃	1	8	yes	—
77	C₃×C₉	C₃²×C₄₃⋊C₃	1	4	yes	—
78	C₃²	—	3	4	no	—
79	C₃²	—	129	4	no	—
80	C₃²	—	129	8	no	—
81	C₃²	—	387	9	no	—
82	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
83	C₉	—	3	8	no	—
84	C₉	—	3	4	no	—
85	C₉	—	129	16	no	—
86	C₉	—	129	8	no	—
87	C₃	—	9	1	no	—
88	C₃	—	387	1	no	—
89	C₃	—	387	2	no	—
90	C₃	#23782921	1	4	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₄₃⋊C₃
commutator, socle, cosocle	C₃²×C₄₃	C₃⁴
Fitting	C₄₃×#6898	C₃
prime radical	C₃³×C₄₃⋊C₃	C₃²
hypercenter	#6898	C₄₃⋊C₃
hypocenter	C₄₃	#10624912
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ #6898

Complements

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

N	H ≅ G/N	type
1. #23782848	C₃	semidirect
2. #23782847	C₃	semidirect
3. #23782834	C₃	semidirect
4. #23782832	C₃	semidirect
5. #23782831	C₃	semidirect
7. C₄₃×#6898	C₃	semidirect
11. #16812500	C₃²	semidirect
12. #16812499	C₃²	semidirect
13. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
14. (C₄₃⋊C₉)⋊C₉	C₃²	semidirect
18. C₉×C₄₃⋊C₉	C₃²	semidirect
19. C₄₃×C₉⋊C₉	C₃²	semidirect
21. C₉²×C₄₃	C₃²	semidirect
45. #6898	C₄₃⋊C₃	semidirect
60. C₉⋊C₉	C₃×C₄₃⋊C₃	semidirect
66. C₉²	C₃×C₄₃⋊C₃	semidirect
67. C₄₃	#10624912	semidirect

Maximal subgroups

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

subgroup	index
#23782848	3
#23782847	3
#23782834	3
#23782832	3
#23782831	3
#23782796	3
C₄₃×#6898	3
#10624912	43