Subgroups — #23782897

Order 10449.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812526	C₃	1	2	yes	maximal, complemented
2	#16812524	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#11923958	C₃	1	1	yes	maximal, characteristic, complemented
4	#16812514	C₃	1	2	yes	maximal, complemented
5	#16812512	C₃	1	1	yes	maximal, characteristic, complemented
6	#16812511	C₃	1	2	yes	maximal, complemented
7	#16812509	C₃	1	1	yes	maximal, characteristic, complemented
8	#16812507	C₃	1	2	yes	maximal, complemented
9	C₄₃×AΣL(1,𝔽₂₇)	C₃	1	1	yes	maximal, characteristic, complemented
10	#11923958	—	3	2	no	—
11	#11923958	—	3	1	no	—
12	#11923958	—	3	2	no	—
13	#11923958	C₃²	1	2	yes	—
14	#11923958	C₃²	1	2	yes	—
15	#11923957	—	3	2	no	—
16	#11923956	—	3	2	no	—
17	C₃²⋊(C₄₃⋊C₃)	C₃²	1	2	yes	—
18	C₃×C₄₃⋊C₉	—	3	1	no	—
19	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
20	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
21	C₃×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
22	C₉×C₄₃⋊C₃	—	3	2	no	—
23	C₃³×C₄₃	C₃²	1	1	yes	characteristic
24	3₋¹⁺²×C₄₃	C₃²	1	2	yes	—
25	H(3,𝔽₃)×C₄₃	C₃²	1	1	yes	characteristic
26	C₃²×C₄₃	—	3	1	no	—
27	C₃²×C₄₃	—	3	1	no	—
28	C₃²×C₄₃	—	9	1	no	—
29	C₃²×C₄₃	C₃³	1	1	yes	characteristic
30	C₃×C₄₃⋊C₃	—	3	2	no	—
31	C₉×C₄₃	—	3	2	no	—
32	C₄₃⋊C₉	—	3	2	no	—
33	C₄₃⋊C₉	—	3	2	no	—
34	C₄₃⋊C₉	—	3	1	no	—
35	C₄₃⋊C₉	—	3	1	no	—
36	C₄₃⋊C₉	H(3,𝔽₃)	1	2	yes	—
37	C₄₃⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
38	#6913	—	43	1	no	maximal, Sylow
39	C₃×C₄₃	—	3	1	no	—
40	C₃×C₄₃	—	9	1	no	—
41	C₃×C₄₃	—	9	1	no	—
42	C₃×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
43	C₄₃⋊C₃	—	9	2	no	—
44	#737	—	43	2	no	—
45	#737	—	43	1	no	—
46	C₃×3₋¹⁺²	—	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)	C₄₃⋊C₃	1	1	yes	characteristic, complemented
53	C₄₃	#6913	1	1	yes	characteristic, complemented, Sylow
54	C₃³	C₃×C₄₃⋊C₃	1	1	yes	characteristic
55	3₋¹⁺²	—	43	2	no	—
56	3₋¹⁺²	—	43	2	no	—
57	3₋¹⁺²	—	129	2	no	—
58	3₋¹⁺²	—	129	2	no	—
59	3₋¹⁺²	—	129	2	no	—
60	3₋¹⁺²	—	129	1	no	—
61	3₋¹⁺²	—	129	2	no	—
62	3₋¹⁺²	C₃×C₄₃⋊C₃	1	2	yes	—
63	H(3,𝔽₃)	—	43	2	no	—
64	H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	1	yes	characteristic
65	C₃×C₉	—	43	1	no	—
66	C₃×C₉	—	43	1	no	—
67	C₃×C₉	—	43	1	no	—
68	C₃×C₉	—	129	2	no	—
69	C₃×C₉	—	129	1	no	—
70	C₃²	—	3	1	no	—
71	C₃²	—	3	1	no	—
72	C₃²	—	9	1	no	—
73	C₃²	—	129	2	no	—
74	C₃²	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
75	C₉	—	3	2	no	—
76	C₉	—	43	2	no	—
77	C₉	—	43	1	no	—
78	C₉	—	129	1	no	—
79	C₉	—	129	1	no	—
80	C₉	—	129	2	no	—
81	C₉	—	129	2	no	—
82	C₃	—	3	1	no	—
83	C₃	—	9	1	no	—
84	C₃	—	9	1	no	—
85	C₃	—	387	2	no	—
86	C₃	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₄₃⋊C₃
commutator, cosocle	C₃²×C₄₃	C₃³
Frattini	C₃²	C₃²×C₄₃⋊C₃
Fitting	C₄₃×AΣL(1,𝔽₂₇)	C₃
socle	C₃×C₄₃	C₃×H(3,𝔽₃)
hypercenter	AΣL(1,𝔽₂₇)	C₄₃⋊C₃
hypocenter	C₄₃	#6913
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ AΣL(1,𝔽₂₇)

Complements

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

N	H ≅ G/N	type
1. #16812526	C₃	semidirect
2. #16812524	C₃	semidirect
3. C₃×#11923958	C₃	semidirect
4. #16812514	C₃	semidirect
5. #16812512	C₃	semidirect
6. #16812511	C₃	semidirect
7. #16812509	C₃	semidirect
8. #16812507	C₃	semidirect
9. C₄₃×AΣL(1,𝔽₂₇)	C₃	semidirect
52. AΣL(1,𝔽₂₇)	C₄₃⋊C₃	semidirect
53. C₄₃	#6913	semidirect