Subgroups — C₈₁×C₄₃⋊C₉ #44532084

Order 31347.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃⋊C₈₁	C₃	1	2	yes	maximal
2	C₂₇×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₃×C₈₁	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃⋊C₂₇	C₉	1	2	yes	—
5	C₉×C₄₃⋊C₉	C₉	1	1	yes	characteristic
6	C₄₃⋊C₈₁	C₉	1	6	yes	complemented
7	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₈₁	C₉	1	3	yes	complemented
9	C₃×C₄₃⋊C₉	C₂₇	1	3	yes	—
10	C₄₃⋊C₂₇	C₂₇	1	6	yes	—
11	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
12	C₂₇×C₄₃	C₃×C₉	1	2	yes	—
13	C₂₇×C₄₃	C₃×C₉	1	1	yes	characteristic
14	C₉×C₈₁	—	43	1	no	maximal, Sylow
15	C₃²×C₄₃	C₃×C₂₇	1	1	yes	characteristic
16	C₉×C₄₃	C₉²	1	1	yes	characteristic
17	C₉×C₄₃	C₃×C₂₇	1	2	yes	—
18	C₄₃⋊C₉	C₈₁	1	9	yes	direct product factor
19	C₃×C₈₁	—	43	2	no	—
20	C₃×C₈₁	C₄₃⋊C₃	1	1	yes	characteristic
21	C₉×C₂₇	—	43	1	no	—
22	C₃×C₄₃	C₉×C₂₇	1	1	yes	characteristic
23	C₃×C₄₃	C₃×C₈₁	1	3	yes	—
24	C₃×C₂₇	—	43	2	no	—
25	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
26	C₉²	—	43	1	no	—
27	C₈₁	—	43	6	no	—
28	C₈₁	C₄₃⋊C₉	1	3	yes	direct product factor
29	C₄₃	C₉×C₈₁	1	1	yes	characteristic, complemented, Sylow
30	C₃×C₉	—	43	3	no	—
31	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
32	C₂₇	—	43	6	no	—
33	C₂₇	C₉×C₄₃⋊C₃	1	2	yes	—
34	C₂₇	C₃×C₄₃⋊C₉	1	1	yes	characteristic
35	C₃²	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
36	C₉	—	43	9	no	—
37	C₉	C₉×C₄₃⋊C₉	1	1	yes	characteristic
38	C₉	C₂₇×C₄₃⋊C₃	1	2	yes	—
39	C₃	C₂₇×C₄₃⋊C₉	1	1	yes	characteristic
40	C₃	C₈₁×C₄₃⋊C₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₃×C₈₁	C₄₃⋊C₃
commutator, hypocenter	C₄₃	C₉×C₈₁
Frattini	C₃×C₂₇	C₃×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₈₁	C₃
socle, prime radical	C₃²×C₄₃	C₃×C₂₇
cosocle	C₃×C₂₇×C₄₃	C₃²
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₃×C₈₁

Complements

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

N	H ≅ G/N	type
6. C₄₃⋊C₈₁	C₉	semidirect
8. C₄₃×C₈₁	C₉	semidirect
18. C₄₃⋊C₉	C₈₁	direct (N × H)
28. C₈₁	C₄₃⋊C₉	direct (N × H)
29. C₄₃	C₉×C₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄₃⋊C₈₁	3
C₂₇×C₄₃⋊C₉	3
C₃×C₄₃×C₈₁	3
C₉×C₈₁	43

Subgroups — C81×C43⋊C9 #44532084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₁×C₄₃⋊C₉ #44532084