Subgroups — #44532171

Order 31347.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
2	#23782718	C₃	1	2	yes	maximal, complemented
3	C₄₃×#6908	C₃	1	1	yes	maximal, characteristic
4	#16812505	—	3	2	no	—
5	C₃×C₄₃⋊C₂₇	—	3	3	no	—
6	C₃×C₄₃⋊C₂₇	—	3	1	no	—
7	C₄₃×#737	—	3	1	no	—
8	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
9	C₄₃×#733	C₉	1	2	yes	—
10	C₄₃×#732	C₉	1	1	yes	characteristic
11	C₄₃×#731	—	3	1	no	—
12	C₄₃×AΣL(1,𝔽₂₇)	—	3	1	no	—
13	C₄₃⋊C₂₇	—	3	3	no	—
14	C₄₃⋊C₂₇	—	9	2	no	—
15	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
16	3₋¹⁺²×C₄₃	—	3	2	no	—
17	3₋¹⁺²×C₄₃	—	9	1	no	—
18	3₋¹⁺²×C₄₃	—	9	1	no	—
19	H(3,𝔽₃)×C₄₃	—	3	1	no	—
20	C₃×C₉×C₄₃	—	3	1	no	—
21	C₃×C₉×C₄₃	—	3	1	no	—
22	C₃×C₉×C₄₃	—	3	1	no	—
23	C₃×C₉×C₄₃	—	9	1	no	—
24	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
25	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
27	#10624526	—	43	1	no	maximal, Sylow
28	C₃²×C₄₃	—	3	1	no	—
29	C₃²×C₄₃	—	3	3	no	—
30	C₃²×C₄₃	—	9	1	no	—
31	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
32	C₉×C₄₃	—	3	1	no	—
33	C₉×C₄₃	—	3	1	no	—
34	C₉×C₄₃	—	9	2	no	—
35	C₉×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
36	C₉×C₄₃	#731	1	1	yes	characteristic
37	C₉×C₄₃	#732	1	1	yes	characteristic
38	#6908	C₄₃⋊C₃	1	1	yes	characteristic
39	C₃²×C₂₇	—	43	1	no	—
40	#6869	—	43	2	no	—
41	C₃×C₄₃	—	3	3	no	—
42	C₃×C₄₃	—	3	1	no	—
43	C₃×C₄₃	—	27	1	no	—
44	C₃×C₄₃	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
45	#737	—	3	1	no	—
46	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
47	#733	C₄₃⋊C₉	1	2	yes	—
48	#732	C₄₃⋊C₉	1	1	yes	characteristic
49	#731	—	3	1	no	—
50	AΣL(1,𝔽₂₇)	—	3	1	no	—
51	C₂₇⋊C₃	—	129	2	no	—
52	C₃×C₂₇	—	129	1	no	—
53	C₃×C₂₇	—	129	3	no	—
54	C₄₃	#10624526	1	1	yes	characteristic, complemented, Sylow
55	C₃³	#11923958	1	1	yes	characteristic
56	3₋¹⁺²	—	3	2	no	—
57	3₋¹⁺²	—	9	1	no	—
58	3₋¹⁺²	—	9	1	no	—
59	H(3,𝔽₃)	—	3	1	no	—
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	—	9	1	no	—
64	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
65	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
66	C₃×C₉	#11923958	1	1	yes	characteristic
67	C₂₇	—	129	3	no	—
68	C₂₇	—	387	2	no	—
69	C₃²	—	3	3	no	—
70	C₃²	—	3	1	no	—
71	C₃²	—	9	1	no	—
72	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
73	C₉	—	3	1	no	—
74	C₉	—	3	1	no	—
75	C₉	—	9	2	no	—
76	C₉	#16812506	1	1	yes	characteristic
77	C₉	#16812509	1	1	yes	characteristic
78	C₉	#16812512	1	1	yes	characteristic
79	C₃	—	3	3	no	—
80	C₃	—	3	1	no	—
81	C₃	—	27	1	no	—
82	C₃	H(3,𝔽₃)⋊(C₄₃⋊C₉)	1	1	yes	characteristic

	subgroup	G/H
center	C₉	#16812512
commutator	C₃×C₉×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting, prime radical	C₄₃×#6908	C₃
socle	C₃×C₄₃	H(3,𝔽₃)⋊C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	#6908	C₄₃⋊C₃
hypocenter	C₄₃	#10624526
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6908

Complements

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

N	H ≅ G/N	type
1. C₃²×C₄₃⋊C₂₇	C₃	semidirect
2. #23782718	C₃	semidirect
54. C₄₃	#10624526	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄₃⋊C₂₇	3
#23782718	3
C₄₃×#6908	3
#10624526	43