Subgroups — #44531911

Order 31347.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812505	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃²⋊(C₄₃⋊C₂₇)	C₃	1	2	yes	maximal, complemented
3	C₉×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic
4	#16812505	—	3	3	no	—
5	C₃×C₄₃⋊C₂₇	—	3	1	no	—
6	C₃×C₄₃⋊C₂₇	—	3	2	no	—
7	C₃×H(3,𝔽₃)×C₄₃	C₉	1	1	yes	characteristic
8	C₃²×C₉×C₄₃	—	3	1	no	—
9	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
10	C₄₃×C₃²⋊C₉	—	3	2	no	—
11	C₄₃×C₃²⋊C₉	C₉	1	2	yes	—
12	C₄₃⋊C₂₇	—	3	3	no	—
13	C₄₃⋊C₂₇	—	9	2	no	—
14	C₃³×C₄₃	—	3	1	no	—
15	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
16	H(3,𝔽₃)×C₄₃	—	3	3	no	—
17	C₃×C₉×C₄₃	—	3	1	no	—
18	C₃×C₉×C₄₃	—	3	1	no	—
19	C₃×C₉×C₄₃	—	3	1	no	—
20	C₃×C₉×C₄₃	—	3	2	no	—
21	C₃×C₉×C₄₃	—	9	1	no	—
22	C₃×C₉×C₄₃	—	9	1	no	—
23	C₃×C₉×C₄₃	—	9	1	no	—
24	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
26	#10624453	—	43	1	no	maximal, Sylow
27	C₃²×C₄₃	—	3	1	no	—
28	C₃²×C₄₃	—	3	3	no	—
29	C₃²×C₄₃	—	3	1	no	—
30	C₃²×C₄₃	—	3	1	no	—
31	C₃²×C₄₃	—	3	1	no	—
32	C₃²×C₄₃	—	9	1	no	—
33	C₃²×C₄₃	—	9	1	no	—
34	C₃²×C₄₃	—	9	1	no	—
35	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
36	C₉×C₄₃	—	3	2	no	—
37	C₉×C₄₃	—	9	2	no	—
38	C₉×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
39	C₉×C₄₃	#731	1	1	yes	characteristic
40	C₉×C₄₃	#732	1	1	yes	characteristic
41	C₃×C₂₇⋊C₃	—	43	1	no	—
42	C₉×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic
43	C₃²⋊C₂₇	—	43	2	no	—
44	C₃×C₄₃	—	9	1	no	—
45	C₃×C₄₃	—	9	3	no	—
46	C₃×C₄₃	#6869	1	1	yes	characteristic
47	C₃×C₄₃	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
48	C₃×C₄₃	#6872	1	1	yes	characteristic
49	C₃×C₄₃	#6873	1	1	yes	characteristic
50	C₃×H(3,𝔽₃)	C₄₃⋊C₉	1	1	yes	characteristic
51	C₃²×C₉	—	3	1	no	—
52	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
53	C₂₇⋊C₃	—	129	3	no	—
54	C₃×C₂₇	—	129	1	no	—
55	C₃×C₂₇	—	129	2	no	—
56	C₃²⋊C₉	—	3	2	no	—
57	C₃²⋊C₉	C₄₃⋊C₉	1	2	yes	—
58	C₄₃	#10624453	1	1	yes	characteristic, complemented, Sylow
59	C₃³	—	3	1	no	—
60	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
61	H(3,𝔽₃)	—	3	3	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	—	3	1	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	3	2	no	—
66	C₃×C₉	—	9	1	no	—
67	C₃×C₉	—	9	1	no	—
68	C₃×C₉	—	9	1	no	—
69	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
70	C₃×C₉	#11923958	1	2	yes	—
71	C₂₇	—	129	3	no	—
72	C₂₇	—	387	2	no	—
73	C₃²	—	3	1	no	—
74	C₃²	—	3	3	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	3	1	no	—
78	C₃²	—	9	1	no	—
79	C₃²	—	9	1	no	—
80	C₃²	—	9	1	no	—
81	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
82	C₉	—	3	2	no	—
83	C₉	—	9	2	no	—
84	C₉	#16812506	1	1	yes	characteristic
85	C₉	#16812509	1	1	yes	characteristic
86	C₉	#16812512	1	1	yes	characteristic
87	C₃	—	9	1	no	—
88	C₃	—	9	3	no	—
89	C₃	#23782718	1	1	yes	characteristic
90	C₃	H(3,𝔽₃)⋊(C₄₃⋊C₉)	1	1	yes	characteristic
91	C₃	#23782727	1	1	yes	characteristic
92	C₃	#23782730	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator	C₃³×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₉×H(3,𝔽₃)×C₄₃	C₃
socle	C₃²×C₄₃	C₃²⋊C₉
prime radical	C₃×H(3,𝔽₃)×C₄₃	C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₉×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	#10624453
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₉×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#16812505	C₃	semidirect
2. C₃²⋊(C₄₃⋊C₂₇)	C₃	semidirect
58. C₄₃	#10624453	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812505	3
C₃²⋊(C₄₃⋊C₂₇)	3
C₉×H(3,𝔽₃)×C₄₃	3
#10624453	43