Subgroups — D₇×C₂₃×D₁₇ #24926513

Order 10948.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×D₁₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₂₃×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃×D₁₇	—	7	1	no	maximal, Hall
6	C₂×C₁₇×C₂₃	—	7	1	no	—
7	C₂₃×D₁₇	—	7	1	no	—
8	C₂₃×D₁₇	D₇	1	1	yes	characteristic, direct product factor
9	C₂×D₇×C₂₃	—	17	1	no	maximal, Hall
10	D₇×D₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₇×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₇×C₂₃	—	17	1	no	—
13	D₇×C₂₃	—	17	1	no	—
14	D₇×C₂₃	D₁₇	1	1	yes	characteristic, direct product factor
15	D₁₁₉	C₂×C₂₃	1	1	yes	characteristic, complemented
16	C₇×D₁₇	C₂×C₂₃	1	1	yes	characteristic, complemented
17	D₇×C₁₇	C₂×C₂₃	1	1	yes	characteristic, complemented
18	C₇×C₂₃	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
19	C₇×C₁₇	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
20	C₂²×C₂₃	—	119	1	no	Hall
21	C₂×D₁₇	—	7	1	no	Hall
22	C₂×C₂₃	—	7	1	no	—
23	C₂×C₂₃	—	17	1	no	—
24	C₂×C₂₃	—	119	1	no	—
25	C₂×C₁₇	—	7	1	no	—
26	D₁₇	—	7	1	no	—
27	D₁₇	D₇×C₂₃	1	1	yes	characteristic, direct product factor
28	C₂×D₇	—	17	1	no	Hall
29	C₂₃	D₇×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₇	C₂×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇	—	17	1	no	—
32	D₇	—	17	1	no	—
33	D₇	C₂₃×D₁₇	1	1	yes	characteristic, direct product factor
34	C₇	C₂×C₂₃×D₁₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	119	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	17	1	no	—
38	C₂	—	119	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	D₇×D₁₇
commutator, cosocle, hypocenter	C₇×C₁₇	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₂₃	C₂²
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×D₁₁₉	C₂	semidirect
2. D₇×C₁₇×C₂₃	C₂	semidirect
3. C₇×C₂₃×D₁₇	C₂	semidirect
4. C₇×C₁₇×C₂₃	C₂²	semidirect
8. C₂₃×D₁₇	D₇	direct (N × H)
10. D₇×D₁₇	C₂₃	direct (N × H)
11. C₁₇×C₂₃	C₂×D₇	semidirect
14. D₇×C₂₃	D₁₇	direct (N × H)
15. D₁₁₉	C₂×C₂₃	semidirect
16. C₇×D₁₇	C₂×C₂₃	semidirect
17. D₇×C₁₇	C₂×C₂₃	semidirect
18. C₇×C₂₃	C₂×D₁₇	semidirect
19. C₇×C₁₇	C₂²×C₂₃	semidirect
27. D₁₇	D₇×C₂₃	direct (N × H)
29. C₂₃	D₇×D₁₇	direct (N × H)
30. C₁₇	C₂×D₇×C₂₃	semidirect
33. D₇	C₂₃×D₁₇	direct (N × H)
34. C₇	C₂×C₂₃×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×D₁₁₉	2
D₇×C₁₇×C₂₃	2
C₇×C₂₃×D₁₇	2
C₂×C₂₃×D₁₇	7
C₂×D₇×C₂₃	17
D₇×D₁₇	23

Subgroups — D7×C23×D17 #24926513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₂₃×D₁₇ #24926513