Subgroups — C₂×C₇×C₁₁×C₈₁ #72190814

Order 12474.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₈₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₁×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₁×C₂₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₁₁×C₈₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₉×C₁₁	C₉	1	1	yes	characteristic
6	C₂×C₇×C₈₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×C₈₁	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₉×C₁₁	C₂×C₉	1	1	yes	characteristic
9	C₂×C₁₁×C₂₇	C₃×C₇	1	1	yes	characteristic
10	C₇×C₈₁	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₃×C₇×C₁₁	C₂₇	1	1	yes	characteristic
12	C₂×C₇×C₂₇	C₃×C₁₁	1	1	yes	characteristic
13	C₁₁×C₂₇	C₂×C₃×C₇	1	1	yes	characteristic
14	C₃×C₇×C₁₁	C₂×C₂₇	1	1	yes	characteristic
15	C₂×C₉×C₁₁	C₇×C₉	1	1	yes	characteristic
16	C₇×C₂₇	C₂×C₃×C₁₁	1	1	yes	characteristic
17	C₂×C₈₁	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₇×C₁₁	C₈₁	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₇×C₉	C₉×C₁₁	1	1	yes	characteristic
20	C₉×C₁₁	C₂×C₇×C₉	1	1	yes	characteristic
21	C₈₁	C₂×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
22	C₇×C₁₁	C₂×C₈₁	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₁₁	C₇×C₂₇	1	1	yes	characteristic
24	C₇×C₉	C₂×C₉×C₁₁	1	1	yes	characteristic
25	C₂×C₂₇	C₃×C₇×C₁₁	1	1	yes	characteristic
26	C₂×C₃×C₇	C₁₁×C₂₇	1	1	yes	characteristic
27	C₃×C₁₁	C₂×C₇×C₂₇	1	1	yes	characteristic
28	C₂₇	C₂×C₃×C₇×C₁₁	1	1	yes	characteristic
29	C₂×C₁₁	C₇×C₈₁	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₇	C₂×C₁₁×C₂₇	1	1	yes	characteristic
31	C₂×C₉	C₇×C₉×C₁₁	1	1	yes	characteristic
32	C₂×C₇	C₁₁×C₈₁	1	1	yes	characteristic, direct product factor, Hall
33	C₁₁	C₂×C₇×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
34	C₉	C₂×C₇×C₉×C₁₁	1	1	yes	characteristic
35	C₇	C₂×C₁₁×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₃	C₇×C₁₁×C₂₇	1	1	yes	characteristic
37	C₃	C₂×C₇×C₁₁×C₂₇	1	1	yes	characteristic
38	C₂	C₇×C₁₁×C₈₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₂×C₃×C₇×C₁₁
socle, prime radical	C₂×C₃×C₇×C₁₁	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₁×C₈₁	C₂	direct (N × H)
4. C₂×C₁₁×C₈₁	C₇	direct (N × H)
6. C₂×C₇×C₈₁	C₁₁	direct (N × H)
7. C₁₁×C₈₁	C₂×C₇	direct (N × H)
10. C₇×C₈₁	C₂×C₁₁	direct (N × H)
17. C₂×C₈₁	C₇×C₁₁	direct (N × H)
18. C₂×C₇×C₁₁	C₈₁	direct (N × H)
21. C₈₁	C₂×C₇×C₁₁	direct (N × H)
22. C₇×C₁₁	C₂×C₈₁	direct (N × H)
29. C₂×C₁₁	C₇×C₈₁	direct (N × H)
32. C₂×C₇	C₁₁×C₈₁	direct (N × H)
33. C₁₁	C₂×C₇×C₈₁	direct (N × H)
35. C₇	C₂×C₁₁×C₈₁	direct (N × H)
38. C₂	C₇×C₁₁×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
C₇×C₁₁×C₈₁	2
C₂×C₇×C₁₁×C₂₇	3
C₂×C₁₁×C₈₁	7
C₂×C₇×C₈₁	11

Subgroups — C2×C7×C11×C81 #72190814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₁₁×C₈₁ #72190814