Subgroups — #44532152

Order 31347.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782716	C₃	1	2	yes	maximal
2	#23782716	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
5	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
6	C₃²×C₉×C₄₃	—	3	1	no	—
7	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₉⋊C₉	—	3	2	no	—
9	C₄₃×C₉⋊C₉	C₉	1	3	yes	complemented
10	C₃×C₄₃⋊C₉	—	9	2	no	—
11	C₃×C₄₃⋊C₉	—	9	1	no	—
12	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₉×C₄₃	—	3	1	no	—
14	C₃×C₉×C₄₃	—	3	2	no	—
15	C₃×C₉×C₄₃	—	3	3	no	—
16	C₃×C₉×C₄₃	—	9	1	no	—
17	C₃×C₉×C₄₃	—	9	1	no	—
18	C₃×C₉×C₄₃	—	9	1	no	—
19	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
20	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
21	#10624521	—	43	1	no	maximal, Sylow
22	C₃²×C₄₃	—	3	1	no	—
23	C₃²×C₄₃	—	3	1	no	—
24	C₃²×C₄₃	—	3	1	no	—
25	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
26	C₃²×C₄₃	#732	1	1	yes	characteristic
27	C₃²×C₄₃	#733	1	2	yes	—
28	C₉×C₄₃	—	3	1	no	—
29	C₉×C₄₃	—	3	2	no	—
30	C₉×C₄₃	—	9	3	no	—
31	C₄₃⋊C₉	—	27	2	no	—
32	C₄₃⋊C₉	—	27	1	no	—
33	C₃×C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
34	#6868	—	43	2	no	—
35	#6868	—	43	1	no	—
36	C₃×C₄₃	—	3	1	no	—
37	C₃×C₄₃	—	3	2	no	—
38	C₃×C₄₃	#6868	1	1	yes	characteristic
39	C₃×C₄₃	#6881	1	1	yes	characteristic
40	C₃×C₄₃	#6882	1	1	yes	characteristic
41	C₃×C₄₃	#6883	1	1	yes	characteristic
42	C₃²×C₉	—	3	1	no	—
43	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
44	C₉⋊C₉	—	3	2	no	—
45	C₉⋊C₉	C₄₃⋊C₉	1	3	yes	complemented
46	C₃²⋊C₉	—	129	2	no	—
47	C₃²⋊C₉	—	129	1	no	—
48	C₄₃	#10624521	1	1	yes	characteristic, complemented, Sylow
49	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
50	C₃×C₉	—	3	1	no	—
51	C₃×C₉	—	3	2	no	—
52	C₃×C₉	—	3	3	no	—
53	C₃×C₉	—	9	1	no	—
54	C₃×C₉	—	9	1	no	—
55	C₃×C₉	—	9	1	no	—
56	C₃×C₉	—	387	2	no	—
57	C₃×C₉	—	387	1	no	—
58	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
59	C₃×C₉	#11923958	1	2	yes	—
60	C₃²	—	3	1	no	—
61	C₃²	—	3	1	no	—
62	C₃²	—	3	1	no	—
63	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
64	C₃²	#16812513	1	1	yes	characteristic
65	C₃²	#16812515	1	2	yes	—
66	C₉	—	3	1	no	—
67	C₉	—	3	2	no	—
68	C₉	—	9	3	no	—
69	C₉	—	1161	2	no	—
70	C₉	—	1161	1	no	—
71	C₃	—	3	1	no	—
72	C₃	—	3	2	no	—
73	C₃	#23782716	1	1	yes	characteristic
74	C₃	#23782757	1	1	yes	characteristic
75	C₃	#23782762	1	1	yes	characteristic
76	C₃	#23782767	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#16812513
commutator	C₃×C₉×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₉⋊C₉	C₃
socle	C₃²×C₄₃	#732
prime radical	C₃³×C₄₃	H(3,𝔽₃)
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#10624521
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
9. C₄₃×C₉⋊C₉	C₉	semidirect
45. C₉⋊C₉	C₄₃⋊C₉	semidirect
48. C₄₃	#10624521	semidirect

Maximal subgroups

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

subgroup	index
#23782716	3
C₃×C₄₃×C₉⋊C₉	3
#10624521	43