Subgroups — C₂×C₇×C₃⋊D₁₂₃ #23780239

Order 10332.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₁₂₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₁₂₃	—	3	4	no	maximal
4	C₃²×C₇×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇×C₄₁	D₃	1	4	yes	complemented
6	C₇×D₁₂₃	—	3	8	no	—
7	C₂×C₃⋊D₁₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₄₁	—	9	1	no	Hall
9	C₃×C₇×C₄₁	C₂×D₃	1	4	yes	complemented
10	C₂×C₃²×C₄₁	C₂×C₇	1	1	yes	characteristic, complemented
11	C₃⋊D₁₂₃	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₄₁	C₃⋊D₃	1	1	yes	characteristic, complemented
13	C₇×D₄₁	—	9	2	no	—
14	C₂×D₁₂₃	—	3	4	no	—
15	C₃²×C₄₁	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₄₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₇×C₃⋊D₃	—	41	1	no	maximal, Hall
18	C₂×C₃×C₄₁	D₃×C₇	1	4	yes	complemented
19	D₁₂₃	—	3	8	no	—
20	C₂×D₄₁	—	9	1	no	Hall
21	C₂×C₃²×C₇	D₄₁	1	1	yes	characteristic, complemented
22	C₇×C₃⋊D₃	—	41	2	no	—
23	C₃×C₄₁	C₂×D₃×C₇	1	4	yes	complemented
24	C₂×D₃×C₇	—	123	4	no	—
25	C₂×C₄₁	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
26	D₄₁	—	9	2	no	—
27	C₃²×C₇	C₂×D₄₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₇	D₁₂₃	1	4	yes	complemented
29	D₃×C₇	—	123	8	no	—
30	C₄₁	C₂×C₇×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃⋊D₃	—	41	1	no	Hall
32	C₂²×C₇	—	369	1	no	Hall
33	C₃×C₇	C₂×D₁₂₃	1	4	yes	complemented
34	C₂×C₃²	C₇×D₄₁	1	1	yes	characteristic, complemented
35	C₃⋊D₃	—	41	2	no	—
36	C₂×C₇	—	369	2	no	—
37	C₂×C₇	C₃⋊D₁₂₃	1	1	yes	characteristic, direct product factor
38	C₂×D₃	—	123	4	no	—
39	C₃²	C₂×C₇×D₄₁	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×C₃⋊D₁₂₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	C₇×D₁₂₃	1	4	yes	complemented
42	D₃	—	123	8	no	—
43	C₂²	—	369	1	no	Sylow
44	C₃	C₂×C₇×D₁₂₃	1	4	yes	complemented
45	C₂	—	369	2	no	—
46	C₂	C₇×C₃⋊D₁₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	C₃⋊D₁₂₃
commutator, cosocle, hypocenter	C₃²×C₄₁	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₄₁	C₂
LCS	G ▷ C₃²×C₄₁
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×C₃⋊D₁₂₃	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₄₁	C₂	semidirect
4. C₃²×C₇×C₄₁	C₂²	semidirect
5. C₂×C₃×C₇×C₄₁	D₃	semidirect
7. C₂×C₃⋊D₁₂₃	C₇	direct (N × H)
9. C₃×C₇×C₄₁	C₂×D₃	semidirect
10. C₂×C₃²×C₄₁	C₂×C₇	semidirect
11. C₃⋊D₁₂₃	C₂×C₇	direct (N × H)
12. C₂×C₇×C₄₁	C₃⋊D₃	semidirect
15. C₃²×C₄₁	C₂²×C₇	semidirect
16. C₇×C₄₁	C₂×C₃⋊D₃	semidirect
18. C₂×C₃×C₄₁	D₃×C₇	semidirect
21. C₂×C₃²×C₇	D₄₁	semidirect
23. C₃×C₄₁	C₂×D₃×C₇	semidirect
25. C₂×C₄₁	C₇×C₃⋊D₃	semidirect
27. C₃²×C₇	C₂×D₄₁	semidirect
28. C₂×C₃×C₇	D₁₂₃	semidirect
30. C₄₁	C₂×C₇×C₃⋊D₃	semidirect
33. C₃×C₇	C₂×D₁₂₃	semidirect
34. C₂×C₃²	C₇×D₄₁	semidirect
37. C₂×C₇	C₃⋊D₁₂₃	direct (N × H)
39. C₃²	C₂×C₇×D₄₁	semidirect
40. C₇	C₂×C₃⋊D₁₂₃	direct (N × H)
41. C₂×C₃	C₇×D₁₂₃	semidirect
44. C₃	C₂×C₇×D₁₂₃	semidirect
46. C₂	C₇×C₃⋊D₁₂₃	direct (N × H)

Subgroups — C2×C7×C3⋊D123 #23780239

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₇×C₃⋊D₁₂₃ #23780239