Subgroups — #23782874

Order 10449.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812525	C₃	1	2	yes	maximal, complemented
2	C₃×C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#16812514	C₃	1	2	yes	maximal, complemented
4	#16812512	C₃	1	1	yes	maximal, characteristic, complemented
5	#16812511	C₃	1	2	yes	maximal, complemented
6	#16812509	C₃	1	1	yes	maximal, characteristic, complemented
7	#16812508	C₃	1	2	yes	maximal, complemented
8	#16812506	C₃	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#737	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
11	#11923958	C₃²	1	2	yes	—
12	#11923958	C₃²	1	2	yes	—
13	#11923957	—	3	2	no	—
14	#11923956	—	3	2	no	—
15	C₃²⋊(C₄₃⋊C₃)	C₃²	1	2	yes	—
16	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
17	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
18	C₉×C₄₃⋊C₃	—	3	2	no	—
19	C₉×C₄₃⋊C₃	—	3	1	no	—
20	C₉×C₄₃⋊C₃	—	3	2	no	—
21	3₋¹⁺²×C₄₃	—	3	2	no	—
22	3₋¹⁺²×C₄₃	C₃²	1	2	yes	—
23	H(3,𝔽₃)×C₄₃	C₃²	1	1	yes	characteristic
24	C₃×C₉×C₄₃	—	3	1	no	—
25	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
26	C₃²×C₄₃	—	3	1	no	—
27	C₃²×C₄₃	C₃³	1	1	yes	characteristic
28	C₃×C₄₃⋊C₃	—	3	1	no	—
29	C₃×C₄₃⋊C₃	—	3	3	no	—
30	C₃×C₄₃⋊C₃	—	3	2	no	—
31	C₉×C₄₃	—	3	2	no	—
32	C₉×C₄₃	H(3,𝔽₃)	1	2	yes	—
33	C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
34	C₄₃⋊C₉	—	3	1	no	—
35	C₄₃⋊C₉	—	3	1	no	—
36	C₄₃⋊C₉	—	3	2	no	—
37	C₄₃⋊C₉	—	3	2	no	—
38	#6908	—	43	1	no	maximal, Sylow
39	C₃×C₄₃	—	3	1	no	—
40	C₃×C₄₃	—	9	1	no	—
41	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₄₃⋊C₃	—	3	3	no	—
43	C₄₃⋊C₃	—	9	2	no	—
44	#737	—	43	2	no	—
45	#737	C₄₃⋊C₃	1	1	yes	characteristic, complemented
46	C₃²×C₉	—	43	1	no	—
47	#733	—	43	2	no	—
48	#732	—	43	1	no	—
49	#731	—	43	2	no	—
50	#731	—	43	1	no	—
51	AΣL(1,𝔽₂₇)	—	43	2	no	—
52	AΣL(1,𝔽₂₇)	—	43	1	no	—
53	C₄₃	#6908	1	1	yes	characteristic, complemented, Sylow
54	C₃³	—	43	1	no	—
55	3₋¹⁺²	—	3	2	no	—
56	3₋¹⁺²	—	43	2	no	—
57	3₋¹⁺²	—	43	2	no	—
58	3₋¹⁺²	—	129	2	no	—
59	3₋¹⁺²	—	129	2	no	—
60	3₋¹⁺²	C₃×C₄₃⋊C₃	1	2	yes	—
61	H(3,𝔽₃)	—	43	2	no	—
62	H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	1	yes	characteristic
63	C₃×C₉	—	3	1	no	—
64	C₃×C₉	—	43	1	no	—
65	C₃×C₉	—	43	1	no	—
66	C₃×C₉	—	129	2	no	—
67	C₃×C₉	—	129	1	no	—
68	C₃×C₉	—	129	2	no	—
69	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
70	C₃²	—	3	1	no	—
71	C₃²	—	129	3	no	—
72	C₃²	—	129	1	no	—
73	C₃²	—	129	2	no	—
74	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
75	C₉	—	3	2	no	—
76	C₉	—	129	1	no	—
77	C₉	—	129	1	no	—
78	C₉	—	129	2	no	—
79	C₉	—	129	2	no	—
80	C₉	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
81	C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
82	C₃	—	3	1	no	—
83	C₃	—	9	1	no	—
84	C₃	—	129	3	no	—
85	C₃	—	387	2	no	—
86	C₃	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#737	C₃
socle	C₃×C₄₃	C₃×H(3,𝔽₃)
hypercenter	#737	C₄₃⋊C₃
hypocenter	C₄₃	#6908
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ #737

Complements

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

N	H ≅ G/N	type
1. #16812525	C₃	semidirect
2. C₃×C₉×C₄₃⋊C₃	C₃	semidirect
3. #16812514	C₃	semidirect
4. #16812512	C₃	semidirect
5. #16812511	C₃	semidirect
6. #16812509	C₃	semidirect
7. #16812508	C₃	semidirect
8. #16812506	C₃	semidirect
9. C₄₃×#737	C₃	semidirect
45. #737	C₄₃⋊C₃	semidirect
53. C₄₃	#6908	semidirect