Subgroups — C₉×C₂₃×Dic₃₇ #44499600

Order 30636.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂₃×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃×Dic₃₇	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₃×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₂₃×C₃₇	C₂×C₃	1	1	yes	characteristic
5	C₂₃×Dic₃₇	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₃×C₃₇	C₃×C₄	1	1	yes	characteristic
7	C₂×C₂₃×C₃₇	C₂×C₉	1	1	yes	characteristic
8	C₉×Dic₃₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂₃×C₃₇	C₄×C₉	1	1	yes	characteristic, complemented, Hall
10	C₄×C₉×C₂₃	—	37	1	no	maximal, Hall
11	C₂×C₉×C₃₇	C₂×C₂₃	1	1	yes	characteristic
12	C₃×Dic₃₇	C₃×C₂₃	1	1	yes	characteristic
13	C₂×C₉×C₂₃	D₃₇	1	1	yes	characteristic
14	C₉×C₃₇	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
15	C₃×C₄×C₂₃	—	37	1	no	—
16	C₂×C₃×C₃₇	C₂×C₃×C₂₃	1	1	yes	characteristic
17	C₉×C₂₃	Dic₃₇	1	1	yes	characteristic, direct product factor, Hall
18	Dic₃₇	C₉×C₂₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₂₃	C₃×D₃₇	1	1	yes	characteristic
20	C₃×C₃₇	C₃×C₄×C₂₃	1	1	yes	characteristic
21	C₄×C₂₃	—	37	1	no	Hall
22	C₂×C₃₇	C₂×C₉×C₂₃	1	1	yes	characteristic
23	C₃×C₂₃	C₃×Dic₃₇	1	1	yes	characteristic
24	C₂×C₂₃	C₉×D₃₇	1	1	yes	characteristic
25	C₃₇	C₄×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
26	C₄×C₉	—	37	1	no	Hall
27	C₂₃	C₉×Dic₃₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	C₂₃×D₃₇	1	1	yes	characteristic
29	C₃×C₄	—	37	1	no	—
30	C₉	C₂₃×Dic₃₇	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₃×C₂₃×D₃₇	1	1	yes	characteristic
32	C₄	—	37	1	no	Sylow
33	C₃	C₃×C₂₃×Dic₃₇	1	1	yes	characteristic
34	C₂	C₉×C₂₃×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉×C₂₃	D₃₇
commutator, hypocenter	C₃₇	C₄×C₉×C₂₃
Frattini	C₂×C₃	C₃×C₂₃×D₃₇
Fitting	C₂×C₉×C₂₃×C₃₇	C₂
socle, prime radical	C₂×C₃×C₂₃×C₃₇	C₂×C₃
cosocle	C₂×C₃×C₃₇	C₂×C₃×C₂₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₉×C₂₃

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₃×C₃₇	C₄	semidirect
5. C₂₃×Dic₃₇	C₉	direct (N × H)
8. C₉×Dic₃₇	C₂₃	direct (N × H)
9. C₂₃×C₃₇	C₄×C₉	semidirect
14. C₉×C₃₇	C₄×C₂₃	semidirect
17. C₉×C₂₃	Dic₃₇	direct (N × H)
18. Dic₃₇	C₉×C₂₃	direct (N × H)
25. C₃₇	C₄×C₉×C₂₃	semidirect
27. C₂₃	C₉×Dic₃₇	direct (N × H)
30. C₉	C₂₃×Dic₃₇	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×C₉×C₂₃×C₃₇	2
C₃×C₂₃×Dic₃₇	3
C₉×Dic₃₇	23
C₄×C₉×C₂₃	37

Subgroups — C9×C23×Dic37 #44499600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₂₃×Dic₃₇ #44499600