Subgroups — #44531886

Order 31347.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₉×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₉×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic
4	C₉×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic
5	C₃×C₄₃⋊C₂₇	C₉	1	3	yes	—
6	C₃×C₄₃⋊C₂₇	C₉	1	3	yes	—
7	C₃×C₄₃⋊C₂₇	C₉	1	3	yes	—
8	C₃×C₂₇×C₄₃	C₉	1	3	yes	—
9	C₉²×C₄₃	C₃²	1	1	yes	characteristic
10	C₄₃⋊C₂₇	—	3	3	no	—
11	C₄₃⋊C₂₇	—	3	3	no	—
12	C₄₃⋊C₂₇	C₂₇	1	9	yes	complemented
13	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
17	C₂₇×C₄₃	—	3	3	no	—
18	#10624443	—	43	1	no	maximal, Sylow
19	C₃²×C₄₃	C₉²	1	1	yes	characteristic
20	C₉×C₄₃	C₃×C₂₇	1	3	yes	—
21	C₉×C₄₃	C₂₇⋊C₃	1	3	yes	—
22	C₉×C₄₃	C₂₇⋊C₃	1	3	yes	—
23	C₉×C₄₃	C₂₇⋊C₃	1	3	yes	—
24	C₉×C₂₇	—	43	1	no	—
25	C₉×C₂₇	—	43	1	no	—
26	C₉×C₂₇	—	43	1	no	—
27	C₉×C₂₇	C₄₃⋊C₃	1	1	yes	characteristic
28	C₃×C₄₃	C₉×C₂₇	1	1	yes	characteristic
29	C₃×C₄₃	#6864	1	1	yes	characteristic
30	C₃×C₄₃	#6864	1	1	yes	characteristic
31	C₃×C₄₃	#6864	1	1	yes	characteristic
32	C₃×C₂₇	—	43	3	no	—
33	C₃×C₂₇	—	43	3	no	—
34	C₃×C₂₇	—	43	3	no	—
35	C₃×C₂₇	C₄₃⋊C₉	1	3	yes	—
36	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
37	C₄₃	#10624443	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
39	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
40	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
41	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
42	C₂₇	—	3	3	no	—
43	C₂₇	—	43	9	no	—
44	C₂₇	—	129	3	no	—
45	C₂₇	—	129	3	no	—
46	C₃²	C₉×C₄₃⋊C₉	1	1	yes	characteristic
47	C₉	C₂₇×C₄₃⋊C₃	1	3	yes	—
48	C₉	#16812503	1	3	yes	—
49	C₉	#16812504	1	3	yes	—
50	C₉	#16812505	1	3	yes	—
51	C₃	C₂₇×C₄₃⋊C₉	1	1	yes	characteristic
52	C₃	#23782706	1	1	yes	characteristic
53	C₃	#23782707	1	1	yes	characteristic
54	C₃	#23782708	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₉²	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₉×C₂₇
Fitting	C₉×C₂₇×C₄₃	C₃
socle, prime radical	C₃²×C₄₃	C₉²
cosocle	C₉²×C₄₃	C₃²
hypercenter	C₉×C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	#10624443
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉² ◁ C₉×C₂₇

Complements

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

N	H ≅ G/N	type
12. C₄₃⋊C₂₇	C₂₇	semidirect
37. C₄₃	#10624443	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₄₃⋊C₂₇	3
C₉×C₂₇×C₄₃	3
#10624443	43