Subgroups — C₄×C₄₃×C₈₁ #72192137

Order 13932.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×C₈₁	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₂×C₂₇×C₄₃	C₂×C₃	1	1	yes	characteristic
4	C₄₃×C₈₁	C₄	1	1	yes	characteristic, direct product factor, Hall
5	C₄×C₉×C₄₃	C₉	1	1	yes	characteristic
6	C₂₇×C₄₃	C₃×C₄	1	1	yes	characteristic
7	C₂×C₉×C₄₃	C₂×C₉	1	1	yes	characteristic
8	C₃×C₄×C₄₃	C₂₇	1	1	yes	characteristic
9	C₉×C₄₃	C₄×C₉	1	1	yes	characteristic
10	C₄×C₈₁	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₄₃	C₂×C₂₇	1	1	yes	characteristic
12	C₄×C₄₃	C₈₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₈₁	C₂×C₄₃	1	1	yes	characteristic
14	C₃×C₄₃	C₄×C₂₇	1	1	yes	characteristic
15	C₄×C₂₇	C₃×C₄₃	1	1	yes	characteristic
16	C₂×C₄₃	C₂×C₈₁	1	1	yes	characteristic
17	C₈₁	C₄×C₄₃	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₂₇	C₂×C₃×C₄₃	1	1	yes	characteristic
19	C₄₃	C₄×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₄×C₉	C₉×C₄₃	1	1	yes	characteristic
21	C₂₇	C₃×C₄×C₄₃	1	1	yes	characteristic
22	C₂×C₉	C₂×C₉×C₄₃	1	1	yes	characteristic
23	C₃×C₄	C₂₇×C₄₃	1	1	yes	characteristic
24	C₉	C₄×C₉×C₄₃	1	1	yes	characteristic
25	C₂×C₃	C₂×C₂₇×C₄₃	1	1	yes	characteristic
26	C₄	C₄₃×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₃	C₄×C₂₇×C₄₃	1	1	yes	characteristic
28	C₂	C₂×C₄₃×C₈₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₂₇	C₂×C₃×C₄₃
socle, prime radical	C₂×C₃×C₄₃	C₂×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₃×C₈₁	C₄	direct (N × H)
10. C₄×C₈₁	C₄₃	direct (N × H)
12. C₄×C₄₃	C₈₁	direct (N × H)
17. C₈₁	C₄×C₄₃	direct (N × H)
19. C₄₃	C₄×C₈₁	direct (N × H)
26. C₄	C₄₃×C₈₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×C₈₁	2
C₄×C₂₇×C₄₃	3
C₄×C₈₁	43

Subgroups — C4×C43×C81 #72192137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₃×C₈₁ #72192137