Subgroups — #44531932

Order 31347.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782782	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊(C₄₃⋊C₂₇)	C₃	1	2	yes	maximal
3	C₄₃×C₃²⋊C₂₇	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃⋊C₂₇	—	3	2	no	—
5	#16812500	—	3	1	no	—
6	#16812499	—	3	1	no	—
7	C₃²⋊(C₄₃⋊C₉)	C₉	1	2	yes	—
8	C₃²⋊(C₄₃⋊C₉)	C₉	1	1	yes	characteristic
9	C₉×C₄₃⋊C₉	—	3	1	no	—
10	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
11	C₃×C₂₇×C₄₃	—	3	1	no	—
12	C₃×C₄₃⋊C₉	—	3	2	no	—
13	C₃×C₄₃⋊C₉	—	3	1	no	—
14	C₄₃⋊C₂₇	—	9	2	no	—
15	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₄₃	—	3	1	no	—
17	C₃×C₉×C₄₃	—	3	2	no	—
18	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
20	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
21	C₂₇×C₄₃	—	9	1	no	—
22	#10624461	—	43	1	no	maximal, Sylow
23	C₃²×C₄₃	—	3	1	no	—
24	C₃²×C₄₃	—	3	2	no	—
25	C₃²×C₄₃	—	3	1	no	—
26	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
27	C₉×C₄₃	—	3	1	no	—
28	C₉×C₄₃	—	3	1	no	—
29	C₉×C₄₃	#732	1	1	yes	characteristic
30	C₉×C₄₃	#733	1	2	yes	—
31	C₄₃⋊C₉	—	9	2	no	—
32	C₄₃⋊C₉	—	9	1	no	—
33	#6887	—	43	1	no	—
34	C₃²⋊C₂₇	—	43	2	no	—
35	C₃²⋊C₂₇	C₄₃⋊C₃	1	1	yes	characteristic
36	C₃×C₄₃	—	9	1	no	—
37	C₃×C₄₃	#6868	1	1	yes	characteristic
38	C₃×C₄₃	#6873	1	2	yes	—
39	C₃×C₄₃	#6873	1	1	yes	characteristic
40	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
41	C₃×C₂₇	—	3	1	no	—
42	C₃×C₂₇	—	129	2	no	—
43	C₉⋊C₉	—	129	1	no	—
44	C₉⋊C₉	—	129	1	no	—
45	C₃²⋊C₉	—	43	2	no	—
46	C₃²⋊C₉	—	43	1	no	—
47	C₉²	—	129	1	no	—
48	C₄₃	#10624461	1	1	yes	characteristic, complemented, Sylow
49	C₃³	C₉×C₄₃⋊C₃	1	1	yes	characteristic
50	C₃×C₉	—	3	1	no	—
51	C₃×C₉	—	3	2	no	—
52	C₃×C₉	—	129	2	no	—
53	C₃×C₉	—	129	1	no	—
54	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
55	C₃×C₉	#11923956	1	1	yes	characteristic
56	C₃×C₉	#11923957	1	1	yes	characteristic
57	C₂₇	—	9	1	no	—
58	C₂₇	—	387	2	no	—
59	C₃²	—	3	1	no	—
60	C₃²	—	3	2	no	—
61	C₃²	—	3	1	no	—
62	C₃²	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
63	C₉	—	3	1	no	—
64	C₉	—	3	1	no	—
65	C₉	—	387	2	no	—
66	C₉	—	387	1	no	—
67	C₉	#16812512	1	1	yes	characteristic
68	C₉	#16812514	1	2	yes	—
69	C₃	—	9	1	no	—
70	C₃	#23782715	1	1	yes	characteristic
71	C₃	#23782729	1	2	yes	—
72	C₃	#23782731	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator, prime radical	C₃³×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×C₃²⋊C₂₇	C₃
socle	C₃²×C₄₃	C₃²⋊C₉
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃²⋊C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	#10624461
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃²⋊C₂₇

Complements

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

N	H ≅ G/N	type
48. C₄₃	#10624461	semidirect

Maximal subgroups

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

subgroup	index
#23782782	3
C₃²⋊(C₄₃⋊C₂₇)	3
C₄₃×C₃²⋊C₂₇	3
#10624461	43