Subgroups — D₇×D₂₃×C₅₃ #46802428

Order 34132.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×D₁₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₂₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₂₃×C₅₃	—	7	1	no	maximal, Hall
6	C₂×C₂₃×C₅₃	—	7	1	no	—
7	D₂₃×C₅₃	—	7	1	no	—
8	D₂₃×C₅₃	D₇	1	1	yes	characteristic, direct product factor
9	C₂×D₇×C₅₃	—	23	1	no	maximal, Hall
10	C₂₃×C₅₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×C₅₃	—	23	1	no	—
12	D₇×C₅₃	—	23	1	no	—
13	D₇×C₅₃	D₂₃	1	1	yes	characteristic, direct product factor
14	D₇×D₂₃	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₇×C₅₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
16	D₁₆₁	C₂×C₅₃	1	1	yes	characteristic, complemented
17	C₇×D₂₃	C₂×C₅₃	1	1	yes	characteristic, complemented
18	D₇×C₂₃	C₂×C₅₃	1	1	yes	characteristic, complemented
19	C₂²×C₅₃	—	161	1	no	Hall
20	C₇×C₂₃	C₂²×C₅₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅₃	—	7	1	no	—
22	C₂×C₅₃	—	23	1	no	—
23	C₂×C₅₃	—	161	1	no	—
24	C₂×D₂₃	—	7	1	no	Hall
25	C₅₃	D₇×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₂₃	—	7	1	no	—
27	D₂₃	—	7	1	no	—
28	D₂₃	D₇×C₅₃	1	1	yes	characteristic, direct product factor
29	C₂×D₇	—	23	1	no	Hall
30	C₂₃	C₂×D₇×C₅₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇	—	23	1	no	—
32	D₇	—	23	1	no	—
33	D₇	D₂₃×C₅₃	1	1	yes	characteristic, direct product factor
34	C₇	C₂×D₂₃×C₅₃	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	161	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	23	1	no	—
38	C₂	—	161	1	no	—

	subgroup	G/H
center, hypercenter	C₅₃	D₇×D₂₃
commutator, cosocle, hypocenter	C₇×C₂₃	C₂²×C₅₃
Frattini	C₁	G
Fitting, socle	C₇×C₂₃×C₅₃	C₂²
LCS	G ▷ C₇×C₂₃
UCS	C₁ ◁ C₅₃

Complements

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

N	H ≅ G/N	type
1. C₅₃×D₁₆₁	C₂	semidirect
2. D₇×C₂₃×C₅₃	C₂	semidirect
3. C₇×D₂₃×C₅₃	C₂	semidirect
4. C₇×C₂₃×C₅₃	C₂²	semidirect
8. D₂₃×C₅₃	D₇	direct (N × H)
10. C₂₃×C₅₃	C₂×D₇	semidirect
13. D₇×C₅₃	D₂₃	direct (N × H)
14. D₇×D₂₃	C₅₃	direct (N × H)
15. C₇×C₅₃	C₂×D₂₃	semidirect
16. D₁₆₁	C₂×C₅₃	semidirect
17. C₇×D₂₃	C₂×C₅₃	semidirect
18. D₇×C₂₃	C₂×C₅₃	semidirect
20. C₇×C₂₃	C₂²×C₅₃	semidirect
25. C₅₃	D₇×D₂₃	direct (N × H)
28. D₂₃	D₇×C₅₃	direct (N × H)
30. C₂₃	C₂×D₇×C₅₃	semidirect
33. D₇	D₂₃×C₅₃	direct (N × H)
34. C₇	C₂×D₂₃×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×D₁₆₁	2
D₇×C₂₃×C₅₃	2
C₇×D₂₃×C₅₃	2
C₂×D₂₃×C₅₃	7
C₂×D₇×C₅₃	23
D₇×D₂₃	53

Subgroups — D7×D23×C53 #46802428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₂₃×C₅₃ #46802428