Subgroups — C₂×C₂₃×D₃₄₁ #44535893

Order 31372.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₃₄₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁×C₂₃×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×C₂₃×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₂₃×D₃₁	—	11	1	no	maximal, Hall
5	C₂×C₂₃×C₃₁	D₁₁	1	1	yes	characteristic, complemented
6	C₂₃×D₃₁	—	11	2	no	—
7	C₂×D₃₄₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×D₁₁×C₂₃	—	31	1	no	maximal, Hall
9	C₂₃×C₃₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁×C₃₁	C₂×C₂₃	1	1	yes	characteristic, complemented
11	D₃₄₁	C₂×C₂₃	1	2	yes	direct product factor
12	C₂×C₁₁×C₂₃	D₃₁	1	1	yes	characteristic, complemented
13	D₁₁×C₂₃	—	31	2	no	—
14	C₁₁×C₃₁	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₂₃	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃₁	—	11	1	no	Hall
17	C₂²×C₂₃	—	341	1	no	Hall
18	C₂×C₃₁	D₁₁×C₂₃	1	1	yes	characteristic, complemented
19	D₃₁	—	11	2	no	—
20	C₂×C₂₃	—	341	2	no	—
21	C₂×C₂₃	D₃₄₁	1	1	yes	characteristic, direct product factor
22	C₂×D₁₁	—	31	1	no	Hall
23	C₃₁	C₂×D₁₁×C₂₃	1	1	yes	characteristic, complemented, Sylow
24	C₂₃	C₂×D₃₄₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₁₁	C₂₃×D₃₁	1	1	yes	characteristic, complemented
26	D₁₁	—	31	2	no	—
27	C₁₁	C₂×C₂₃×D₃₁	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	341	1	no	Sylow
29	C₂	—	341	2	no	—
30	C₂	C₂₃×D₃₄₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₃₄₁
commutator, cosocle, hypocenter	C₁₁×C₃₁	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₂₃×C₃₁	C₂
LCS	G ▷ C₁₁×C₃₁
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₃₄₁	C₂	direct (N × H)
2. C₂×C₁₁×C₂₃×C₃₁	C₂	semidirect
3. C₁₁×C₂₃×C₃₁	C₂²	semidirect
5. C₂×C₂₃×C₃₁	D₁₁	semidirect
7. C₂×D₃₄₁	C₂₃	direct (N × H)
9. C₂₃×C₃₁	C₂×D₁₁	semidirect
10. C₂×C₁₁×C₃₁	C₂×C₂₃	semidirect
11. D₃₄₁	C₂×C₂₃	direct (N × H)
12. C₂×C₁₁×C₂₃	D₃₁	semidirect
14. C₁₁×C₃₁	C₂²×C₂₃	semidirect
15. C₁₁×C₂₃	C₂×D₃₁	semidirect
18. C₂×C₃₁	D₁₁×C₂₃	semidirect
21. C₂×C₂₃	D₃₄₁	direct (N × H)
23. C₃₁	C₂×D₁₁×C₂₃	semidirect
24. C₂₃	C₂×D₃₄₁	direct (N × H)
25. C₂×C₁₁	C₂₃×D₃₁	semidirect
27. C₁₁	C₂×C₂₃×D₃₁	semidirect
30. C₂	C₂₃×D₃₄₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×D₃₄₁	2
C₂×C₁₁×C₂₃×C₃₁	2
C₂×C₂₃×D₃₁	11
C₂×D₃₄₁	23
C₂×D₁₁×C₂₃	31

Subgroups — C2×C23×D341 #44535893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×D₃₄₁ #44535893