Subgroups — C₂₃×#13050607 #44499607

Order 30636.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#66524	C₂	1	1	yes	maximal, characteristic
2	C₃×C₂₃×Dic₃₇	C₃	1	1	yes	maximal, characteristic
3	C₂₃×#66524	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, complemented, Hall
6	C₃×C₂₃×C₃₇	C₃×C₄	1	1	yes	characteristic
7	C₂×C₂₃×C₃₇	C₂×C₉	1	1	yes	characteristic
8	#13050607	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×#66524	C₂×C₂₃	1	1	yes	characteristic
12	C₃×Dic₃₇	C₃×C₂₃	1	1	yes	characteristic
13	C₂×C₉×C₂₃	—	37	1	no	—
14	#66524	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	—	37	1	no	Hall
18	Dic₃₇	C₉×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₂₃	D₃₇⋊C₃	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	Dic₃₇⋊C₃	1	1	yes	characteristic
24	C₂×C₂₃	#66524⋊C₂	1	1	yes	characteristic
25	C₃₇	C₄×C₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
26	C₄×C₉	—	37	1	no	Hall
27	C₂₃	#13050607	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	—	37	1	no	—
29	C₃×C₄	—	37	1	no	—
30	C₉	—	37	1	no	Sylow
31	C₂×C₃	C₂₃×D₃₇⋊C₃	1	1	yes	characteristic
32	C₄	—	37	1	no	Sylow
33	C₃	C₂₃×Dic₃₇⋊C₃	1	1	yes	characteristic
34	C₂	C₂₃×#66524⋊C₂	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂₃×#66524	C₄	semidirect
5. C₂₃×Dic₃₇	C₉	semidirect
8. #13050607	C₂₃	direct (N × H)
9. C₂₃×C₃₇	C₄×C₉	semidirect
14. #66524	C₄×C₂₃	semidirect
18. Dic₃₇	C₉×C₂₃	semidirect
25. C₃₇	C₄×C₉×C₂₃	semidirect
27. C₂₃	#13050607	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×C₂₃×#66524	2
C₃×C₂₃×Dic₃₇	3
#13050607	23
C₄×C₉×C₂₃	37

Subgroups — C23×#13050607 #44499607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#13050607 #44499607