Subgroups — C₄×C₇×C₁₁×C₁₀₃ #44540566

Order 31724.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₁₁×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₁₀₃	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₁₁×C₁₀₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₄×C₇×C₁₀₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₁₁×C₁₀₃	C₂×C₇	1	1	yes	characteristic
6	C₂×C₇×C₁₀₃	C₂×C₁₁	1	1	yes	characteristic
7	C₁₁×C₁₀₃	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₁₀₃	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₁₀₃	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
10	C₄×C₇×C₁₁	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₁₀₃	C₂×C₇×C₁₁	1	1	yes	characteristic
12	C₂×C₇×C₁₁	C₂×C₁₀₃	1	1	yes	characteristic
13	C₁₀₃	C₄×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
14	C₇×C₁₁	C₄×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₁₁	C₇×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
16	C₄×C₇	C₁₁×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₁₁	C₂×C₇×C₁₀₃	1	1	yes	characteristic
18	C₂×C₇	C₂×C₁₁×C₁₀₃	1	1	yes	characteristic
19	C₁₁	C₄×C₇×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₇	C₄×C₁₁×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₄	C₇×C₁₁×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₇×C₁₁×C₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₇×C₁₁×C₁₀₃
socle, prime radical	C₂×C₇×C₁₁×C₁₀₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×C₁₁×C₁₀₃	C₄	direct (N × H)
3. C₄×C₁₁×C₁₀₃	C₇	direct (N × H)
4. C₄×C₇×C₁₀₃	C₁₁	direct (N × H)
7. C₁₁×C₁₀₃	C₄×C₇	direct (N × H)
8. C₇×C₁₀₃	C₄×C₁₁	direct (N × H)
9. C₄×C₁₀₃	C₇×C₁₁	direct (N × H)
10. C₄×C₇×C₁₁	C₁₀₃	direct (N × H)
13. C₁₀₃	C₄×C₇×C₁₁	direct (N × H)
14. C₇×C₁₁	C₄×C₁₀₃	direct (N × H)
15. C₄×C₁₁	C₇×C₁₀₃	direct (N × H)
16. C₄×C₇	C₁₁×C₁₀₃	direct (N × H)
19. C₁₁	C₄×C₇×C₁₀₃	direct (N × H)
20. C₇	C₄×C₁₁×C₁₀₃	direct (N × H)
21. C₄	C₇×C₁₁×C₁₀₃	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×C₇×C₁₁×C₁₀₃	2
C₄×C₁₁×C₁₀₃	7
C₄×C₇×C₁₀₃	11
C₄×C₇×C₁₁	103

Subgroups — C4×C7×C11×C103 #44540566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₇×C₁₁×C₁₀₃ #44540566