Subgroups — C₂×C₇×D₁₂₃₃ #46828593

Order 34524.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₁₂₃₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇×C₉×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×D₄₁₁	—	3	1	no	maximal
4	C₇×C₉×C₁₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×D₄₁₁	—	3	2	no	—
6	C₂×C₃×C₇×C₁₃₇	D₃	1	1	yes	characteristic
7	C₂×D₁₂₃₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×D₁₃₇	—	9	1	no	Hall
9	C₃×C₇×C₁₃₇	C₂×D₃	1	1	yes	characteristic
10	D₁₂₃₃	C₂×C₇	1	2	yes	direct product factor
11	C₂×C₉×C₁₃₇	C₂×C₇	1	1	yes	characteristic, complemented
12	C₂×C₇×C₁₃₇	D₉	1	1	yes	characteristic, complemented
13	C₇×D₁₃₇	—	9	2	no	—
14	C₂×D₄₁₁	—	3	1	no	—
15	C₉×C₁₃₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
16	C₇×C₁₃₇	C₂×D₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₁₃₇	D₃×C₇	1	1	yes	characteristic
18	D₄₁₁	—	3	2	no	—
19	C₂×D₁₃₇	—	9	1	no	Hall
20	C₃×C₁₃₇	C₂×D₃×C₇	1	1	yes	characteristic
21	C₂×C₁₃₇	C₇×D₉	1	1	yes	characteristic, complemented
22	D₁₃₇	—	9	2	no	—
23	C₂×C₇×D₉	—	137	1	no	maximal, Hall
24	C₁₃₇	C₂×C₇×D₉	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇×C₉	D₁₃₇	1	1	yes	characteristic, complemented
26	C₇×D₉	—	137	2	no	—
27	C₂×D₃×C₇	—	411	1	no	—
28	C₇×C₉	C₂×D₁₃₇	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₇	D₄₁₁	1	1	yes	characteristic
30	D₃×C₇	—	411	2	no	—
31	C₂×D₉	—	137	1	no	Hall
32	C₂²×C₇	—	1233	1	no	Hall
33	C₃×C₇	C₂×D₄₁₁	1	1	yes	characteristic
34	C₂×C₉	C₇×D₁₃₇	1	1	yes	characteristic, complemented
35	D₉	—	137	2	no	—
36	C₂×C₇	—	1233	2	no	—
37	C₂×C₇	D₁₂₃₃	1	1	yes	characteristic, direct product factor
38	C₂×D₃	—	411	1	no	—
39	C₉	C₂×C₇×D₁₃₇	1	1	yes	characteristic, complemented, Sylow
40	C₇	C₂×D₁₂₃₃	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×C₃	C₇×D₄₁₁	1	1	yes	characteristic
42	D₃	—	411	2	no	—
43	C₂²	—	1233	1	no	Sylow
44	C₃	C₂×C₇×D₄₁₁	1	1	yes	characteristic
45	C₂	—	1233	2	no	—
46	C₂	C₇×D₁₂₃₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₂₃₃
commutator, cosocle, hypocenter	C₉×C₁₃₇	C₂²×C₇
Frattini	C₃	C₂×C₇×D₄₁₁
Fitting	C₂×C₇×C₉×C₁₃₇	C₂
socle	C₂×C₃×C₇×C₁₃₇	D₃
LCS	G ▷ C₉×C₁₃₇
UCS	C₁ ◁ C₂×C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₁₂₃₃	C₂	direct (N × H)
2. C₂×C₇×C₉×C₁₃₇	C₂	semidirect
4. C₇×C₉×C₁₃₇	C₂²	semidirect
7. C₂×D₁₂₃₃	C₇	direct (N × H)
10. D₁₂₃₃	C₂×C₇	direct (N × H)
11. C₂×C₉×C₁₃₇	C₂×C₇	semidirect
12. C₂×C₇×C₁₃₇	D₉	semidirect
15. C₉×C₁₃₇	C₂²×C₇	semidirect
16. C₇×C₁₃₇	C₂×D₉	semidirect
21. C₂×C₁₃₇	C₇×D₉	semidirect
24. C₁₃₇	C₂×C₇×D₉	semidirect
25. C₂×C₇×C₉	D₁₃₇	semidirect
28. C₇×C₉	C₂×D₁₃₇	semidirect
34. C₂×C₉	C₇×D₁₃₇	semidirect
37. C₂×C₇	D₁₂₃₃	direct (N × H)
39. C₉	C₂×C₇×D₁₃₇	semidirect
40. C₇	C₂×D₁₂₃₃	direct (N × H)
46. C₂	C₇×D₁₂₃₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×D₁₂₃₃	2
C₂×C₇×C₉×C₁₃₇	2
C₂×C₇×D₄₁₁	3
C₂×D₁₂₃₃	7
C₂×C₇×D₉	137

Subgroups — C2×C7×D1233 #46828593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₁₂₃₃ #46828593