Subgroups — C₂×C₃×D₂₄₉₇ #44471981

Order 29964.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₄₉₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₄₉₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁×C₂₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₂₂₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₂₄₉₇	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₃×D₂₂₇	—	11	1	no	maximal, Hall
8	C₁₁×C₂₂₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₂₂₇	D₁₁	1	1	yes	characteristic, complemented
10	C₃×D₂₂₇	—	11	2	no	—
11	C₂×D₂₂₇	—	11	1	no	Hall
12	C₃×C₂₂₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₂₂₇	C₃×D₁₁	1	1	yes	characteristic, complemented
14	D₂₂₇	—	11	2	no	—
15	C₂₂₇	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃×D₁₁	—	227	1	no	maximal, Hall
17	C₂×C₃×C₁₁	D₂₂₇	1	1	yes	characteristic, complemented
18	C₃×D₁₁	—	227	2	no	—
19	C₂×D₁₁	—	227	1	no	Hall
20	C₃×C₁₁	C₂×D₂₂₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₁	C₃×D₂₂₇	1	1	yes	characteristic, complemented
22	D₁₁	—	227	2	no	—
23	C₂²×C₃	—	2497	1	no	Hall
24	C₁₁	C₂×C₃×D₂₂₇	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	2497	2	no	—
26	C₂×C₃	D₂₄₉₇	1	1	yes	characteristic, direct product factor
27	C₂²	—	2497	1	no	Sylow
28	C₃	C₂×D₂₄₉₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	—	2497	2	no	—
30	C₂	C₃×D₂₄₉₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₄₉₇
commutator, cosocle, hypocenter	C₁₁×C₂₂₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁×C₂₂₇	C₂
LCS	G ▷ C₁₁×C₂₂₇
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₂₄₉₇	C₂	direct (N × H)
2. C₂×C₃×C₁₁×C₂₂₇	C₂	semidirect
3. C₂×D₂₄₉₇	C₃	direct (N × H)
4. C₃×C₁₁×C₂₂₇	C₂²	semidirect
5. C₂×C₁₁×C₂₂₇	C₂×C₃	semidirect
6. D₂₄₉₇	C₂×C₃	direct (N × H)
8. C₁₁×C₂₂₇	C₂²×C₃	semidirect
9. C₂×C₃×C₂₂₇	D₁₁	semidirect
12. C₃×C₂₂₇	C₂×D₁₁	semidirect
13. C₂×C₂₂₇	C₃×D₁₁	semidirect
15. C₂₂₇	C₂×C₃×D₁₁	semidirect
17. C₂×C₃×C₁₁	D₂₂₇	semidirect
20. C₃×C₁₁	C₂×D₂₂₇	semidirect
21. C₂×C₁₁	C₃×D₂₂₇	semidirect
24. C₁₁	C₂×C₃×D₂₂₇	semidirect
26. C₂×C₃	D₂₄₉₇	direct (N × H)
28. C₃	C₂×D₂₄₉₇	direct (N × H)
30. C₂	C₃×D₂₄₉₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₂₄₉₇	2
C₂×C₃×C₁₁×C₂₂₇	2
C₂×D₂₄₉₇	3
C₂×C₃×D₂₂₇	11
C₂×C₃×D₁₁	227

Subgroups — C2×C3×D2497 #44471981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₂₄₉₇ #44471981