Subgroups — C₂×C₂₃×D₁₁₇ #24924503

Order 10764.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₁₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₉×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×D₃₉	—	3	1	no	maximal
4	C₉×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₂₃	D₃	1	1	yes	characteristic
6	C₂₃×D₃₉	—	3	2	no	—
7	C₂×C₂₃×D₁₃	—	9	1	no	Hall
8	C₃×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic
9	C₂×D₉×C₂₃	—	13	1	no	maximal, Hall
10	C₂×C₁₃×C₂₃	D₉	1	1	yes	characteristic, complemented
11	C₂₃×D₁₃	—	9	2	no	—
12	C₂×D₁₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₉×C₂₃	D₁₃	1	1	yes	characteristic, complemented
14	D₉×C₂₃	—	13	2	no	—
15	C₁₃×C₂₃	C₂×D₉	1	1	yes	characteristic, complemented, Hall
16	C₂×D₃×C₂₃	—	39	1	no	—
17	C₂×C₉×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
18	D₁₁₇	C₂×C₂₃	1	2	yes	direct product factor
19	C₉×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₉	—	3	1	no	—
21	C₂×C₃×C₂₃	D₃₉	1	1	yes	characteristic
22	D₃×C₂₃	—	39	2	no	—
23	C₉×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₂₃	—	117	1	no	Hall
25	C₂×C₃×C₁₃	D₃×C₂₃	1	1	yes	characteristic
26	D₃₉	—	3	2	no	—
27	C₃×C₂₃	C₂×D₃₉	1	1	yes	characteristic
28	C₂×D₁₃	—	9	1	no	Hall
29	C₂×C₂₃	—	117	2	no	—
30	C₂×C₂₃	D₁₁₇	1	1	yes	characteristic, direct product factor
31	C₃×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic
32	C₂×D₉	—	13	1	no	Hall
33	C₂×C₁₃	D₉×C₂₃	1	1	yes	characteristic, complemented
34	D₁₃	—	9	2	no	—
35	C₂₃	C₂×D₁₁₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₉	C₂₃×D₁₃	1	1	yes	characteristic, complemented
37	D₉	—	13	2	no	—
38	C₁₃	C₂×D₉×C₂₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₃	—	39	1	no	—
40	C₉	C₂×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	C₂₃×D₃₉	1	1	yes	characteristic
42	D₃	—	39	2	no	—
43	C₂²	—	117	1	no	Sylow
44	C₃	C₂×C₂₃×D₃₉	1	1	yes	characteristic
45	C₂	—	117	2	no	—
46	C₂	C₂₃×D₁₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₂₃	D₁₁₇
commutator, cosocle, hypocenter	C₉×C₁₃	C₂²×C₂₃
Frattini	C₃	C₂×C₂₃×D₃₉
Fitting	C₂×C₉×C₁₃×C₂₃	C₂
socle	C₂×C₃×C₁₃×C₂₃	D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₂×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₁₁₇	C₂	direct (N × H)
2. C₂×C₉×C₁₃×C₂₃	C₂	semidirect
4. C₉×C₁₃×C₂₃	C₂²	semidirect
10. C₂×C₁₃×C₂₃	D₉	semidirect
12. C₂×D₁₁₇	C₂₃	direct (N × H)
13. C₂×C₉×C₂₃	D₁₃	semidirect
15. C₁₃×C₂₃	C₂×D₉	semidirect
17. C₂×C₉×C₁₃	C₂×C₂₃	semidirect
18. D₁₁₇	C₂×C₂₃	direct (N × H)
19. C₉×C₂₃	C₂×D₁₃	semidirect
23. C₉×C₁₃	C₂²×C₂₃	semidirect
30. C₂×C₂₃	D₁₁₇	direct (N × H)
33. C₂×C₁₃	D₉×C₂₃	semidirect
35. C₂₃	C₂×D₁₁₇	direct (N × H)
36. C₂×C₉	C₂₃×D₁₃	semidirect
38. C₁₃	C₂×D₉×C₂₃	semidirect
40. C₉	C₂×C₂₃×D₁₃	semidirect
46. C₂	C₂₃×D₁₁₇	direct (N × H)

Subgroups — C2×C23×D117 #24924503

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₂₃×D₁₁₇ #24924503