Subgroups — #44533578

Order 31347.

250 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₄₃⋊C₉	C₃	1	3	yes	maximal
2	C₃×#16812500	C₃	1	1	yes	maximal, characteristic
3	3₋¹⁺²⋊(C₄₃⋊C₉)	C₃	1	6	yes	maximal
4	#23782716	C₃	1	2	yes	maximal
5	C₃×C₄₃×#733	C₃	1	1	yes	maximal, characteristic
6	C₃²×C₄₃⋊C₉	C₃²	1	2	yes	—
7	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
8	#16812500	—	3	3	no	—
9	#16812500	—	3	3	no	—
10	#16812499	—	3	3	no	—
11	C₃²⋊(C₄₃⋊C₉)	C₃²	1	6	yes	—
12	C₉×C₄₃⋊C₉	—	3	3	no	—
13	C₃×3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
14	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
15	C₄₃×#733	C₉	1	9	yes	complemented
16	C₃×C₄₃⋊C₉	—	3	6	no	—
17	C₃×C₄₃⋊C₉	—	3	2	no	—
18	C₃×C₄₃⋊C₉	—	9	1	no	—
19	C₃×C₄₃⋊C₉	—	9	2	no	—
20	C₃×C₄₃⋊C₉	H(3,𝔽₃)	1	3	yes	—
21	C₃³×C₄₃	C₃³	1	1	yes	characteristic
22	3₋¹⁺²×C₄₃	—	3	6	no	—
23	3₋¹⁺²×C₄₃	C₃×C₉	1	9	yes	—
24	C₃×C₉×C₄₃	—	3	1	no	—
25	C₃×C₉×C₄₃	—	3	3	no	—
26	C₃×C₉×C₄₃	—	3	2	no	—
27	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
28	#10624723	—	43	1	no	maximal, Sylow
29	C₃²×C₄₃	—	3	1	no	—
30	C₃²×C₄₃	—	3	2	no	—
31	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
32	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃²×C₄₃	#737	1	2	yes	—
34	C₉×C₄₃	—	3	3	no	—
35	C₉×C₄₃	—	3	9	no	—
36	C₄₃⋊C₉	—	3	3	no	—
37	C₄₃⋊C₉	—	9	6	no	—
38	C₄₃⋊C₉	—	9	2	no	—
39	C₃×#733	C₄₃⋊C₃	1	1	yes	characteristic
40	C₉×3₋¹⁺²	—	43	3	no	—
41	C₃×C₉⋊C₉	—	43	1	no	—
42	3₋¹⁺²⋊C₉	—	43	6	no	—
43	#6868	—	43	2	no	—
44	C₃×C₄₃	—	3	1	no	—
45	C₃×C₄₃	—	3	2	no	—
46	C₃×C₄₃	C₉×H(3,𝔽₃)	1	1	yes	characteristic
47	C₃×C₄₃	#6912	1	1	yes	characteristic
48	C₃×C₄₃	#6913	1	2	yes	—
49	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
50	C₃²×C₉	—	43	1	no	—
51	C₃²×C₉	—	43	2	no	—
52	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
53	#733	C₄₃⋊C₉	1	9	yes	complemented
54	C₉⋊C₉	—	129	3	no	—
55	C₉⋊C₉	—	129	3	no	—
56	C₉⋊C₉	—	129	3	no	—
57	C₃²⋊C₉	—	43	6	no	—
58	C₉²	—	129	3	no	—
59	C₄₃	#10624723	1	1	yes	characteristic, complemented, Sylow
60	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
61	3₋¹⁺²	—	3	6	no	—
62	3₋¹⁺²	C₃×C₄₃⋊C₉	1	9	yes	—
63	C₃×C₉	—	3	3	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	3	2	no	—
66	C₃×C₉	—	43	3	no	—
67	C₃×C₉	—	129	6	no	—
68	C₃×C₉	—	129	2	no	—
69	C₃×C₉	—	387	1	no	—
70	C₃×C₉	—	387	2	no	—
71	C₃×C₉	C₃×C₄₃⋊C₉	1	3	yes	—
72	C₃²	—	3	1	no	—
73	C₃²	—	3	2	no	—
74	C₃²	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
75	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
76	C₃²	#16812524	1	2	yes	—
77	C₉	—	3	3	no	—
78	C₉	—	3	9	no	—
79	C₉	—	129	3	no	—
80	C₉	—	387	6	no	—
81	C₉	—	387	2	no	—
82	C₃	—	3	1	no	—
83	C₃	—	3	2	no	—
84	C₃	H(3,𝔽₃)×C₄₃⋊C₉	1	1	yes	characteristic
85	C₃	#23782894	1	1	yes	characteristic
86	C₃	#23782907	1	2	yes	—

	subgroup	G/H
center	C₃²	H(3,𝔽₃)×C₄₃⋊C₃
commutator	C₃²×C₄₃	C₃²×C₉
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₃×C₄₃×#733	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical, cosocle	C₃³×C₄₃	C₃³
hypercenter	C₃×#733	C₄₃⋊C₃
hypocenter	C₄₃	#10624723
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
15. C₄₃×#733	C₉	semidirect
53. #733	C₄₃⋊C₉	semidirect
59. C₄₃	#10624723	semidirect

Maximal subgroups

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

subgroup	index
3₋¹⁺²×C₄₃⋊C₉	3
C₃×#16812500	3
3₋¹⁺²⋊(C₄₃⋊C₉)	3
#23782716	3
C₃×C₄₃×#733	3
#10624723	43