Subgroups — #44532362

Order 31347.

524 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11923958	C₃	1	1	yes	maximal, characteristic
2	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	2	yes	maximal
3	C₄₃⋊#6855	C₃	1	9	yes	maximal, complemented
4	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
5	C₃×#11923958	—	3	9	no	—
6	C₃×#11923958	—	3	3	no	—
7	C₃²×C₄₃⋊C₉	C₃²	1	6	yes	—
8	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
9	C₃²⋊(C₄₃⋊C₉)	—	3	6	no	—
10	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
11	C₃×3₋¹⁺²×C₄₃	—	3	3	no	—
12	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
13	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
14	#11923958	—	3	27	no	—
15	C₃×C₄₃⋊C₉	—	3	3	no	—
16	C₃×C₄₃⋊C₉	—	3	6	no	—
17	C₃×C₄₃⋊C₉	—	3	6	no	—
18	C₃×C₄₃⋊C₉	—	3	18	no	—
19	C₃×C₄₃⋊C₉	3₋¹⁺²	1	9	yes	complemented
20	C₃³×C₄₃	—	3	3	no	—
21	C₃³×C₄₃	—	3	3	no	—
22	C₃³×C₄₃	—	3	6	no	—
23	C₃³×C₄₃	H(3,𝔽₃)	1	3	yes	—
24	C₃³×C₄₃	C₃³	1	1	yes	characteristic
25	3₋¹⁺²×C₄₃	—	3	27	no	—
26	C₃×C₉×C₄₃	—	3	3	no	—
27	C₃×C₉×C₄₃	—	3	6	no	—
28	C₃×C₉×C₄₃	3₋¹⁺²	1	9	yes	complemented
29	#10624567	—	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	—	9	9	no	—
34	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
36	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
37	C₃²×C₄₃	#737	1	6	yes	—
38	C₉×C₄₃	—	3	9	no	—
39	C₄₃⋊C₉	—	3	9	no	—
40	C₄₃⋊C₉	—	9	6	no	—
41	C₃²×3₋¹⁺²	—	43	1	no	—
42	C₃²×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
43	C₃×C₃²⋊C₉	—	43	2	no	—
44	#6855	—	43	9	no	—
45	C₃×C₄₃	—	9	3	no	—
46	C₃×C₄₃	#6891	1	1	yes	characteristic
47	C₃×C₄₃	#6891	1	1	yes	characteristic
48	C₃×C₄₃	#6893	1	2	yes	—
49	C₃×C₄₃	#6896	1	9	yes	—
50	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	C₃×3₋¹⁺²	—	3	3	no	—
52	C₃×3₋¹⁺²	—	3	9	no	—
53	C₃×3₋¹⁺²	—	129	9	no	—
54	C₃×3₋¹⁺²	—	129	3	no	—
55	C₃²×C₉	—	43	3	no	—
56	C₃²×C₉	—	43	6	no	—
57	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
58	C₃²⋊C₉	—	129	6	no	—
59	C₄₃	#10624567	1	1	yes	characteristic, complemented, Sylow
60	C₃³	—	3	3	no	—
61	C₃³	—	3	3	no	—
62	C₃³	—	3	6	no	—
63	C₃³	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
64	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
65	3₋¹⁺²	—	3	27	no	—
66	3₋¹⁺²	—	129	27	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	3	6	no	—
69	C₃×C₉	—	43	9	no	—
70	C₃×C₉	—	129	3	no	—
71	C₃×C₉	—	129	6	no	—
72	C₃×C₉	—	129	6	no	—
73	C₃×C₉	—	129	18	no	—
74	C₃×C₉	#11923958	1	9	yes	complemented
75	C₃²	—	3	3	no	—
76	C₃²	—	3	3	no	—
77	C₃²	—	3	6	no	—
78	C₃²	—	9	9	no	—
79	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
80	C₃²	3₋¹⁺²×C₄₃⋊C₃	1	3	yes	—
81	C₃²	C₃×#11923958	1	3	yes	—
82	C₃²	#16812526	1	6	yes	—
83	C₉	—	3	9	no	—
84	C₉	—	129	9	no	—
85	C₉	—	387	6	no	—
86	C₃	—	9	3	no	—
87	C₃	#23782795	1	1	yes	characteristic
88	C₃	#23782798	1	1	yes	characteristic
89	C₃	#23782809	1	2	yes	—
90	C₃	#23782824	1	9	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator, socle, cosocle	C₃³×C₄₃	C₃³
Fitting	C₃²×3₋¹⁺²×C₄₃	C₃
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	C₃²×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624567
LCS	G ▷ C₃³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃²×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
3. C₄₃⋊#6855	C₃	semidirect
19. C₃×C₄₃⋊C₉	3₋¹⁺²	semidirect
28. C₃×C₉×C₄₃	3₋¹⁺²	semidirect
59. C₄₃	#10624567	semidirect
74. 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
C₃²×#11923958	3
C₃×C₃²⋊(C₄₃⋊C₉)	3
C₄₃⋊#6855	3
C₃²×3₋¹⁺²×C₄₃	3
#10624567	43