Subgroups — D₇×D₁₂₁₉ #46802430

Order 34132.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₅₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₂₃×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₁₂₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₂₃×C₅₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₂₁₉	—	7	1	no	maximal, Hall
6	C₂×C₂₃×C₅₃	—	7	1	no	—
7	D₁₂₁₉	—	7	1	no	—
8	D₁₂₁₉	D₇	1	1	yes	characteristic, direct product factor
9	D₇×D₅₃	—	23	1	no	maximal, Hall
10	C₂₃×C₅₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	D₃₇₁	—	23	1	no	—
12	C₇×D₅₃	—	23	1	no	—
13	D₇×C₅₃	D₂₃	1	1	yes	characteristic, complemented
14	D₇×D₂₃	—	53	1	no	maximal, Hall
15	C₇×C₅₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
16	D₁₆₁	—	53	1	no	—
17	C₇×D₂₃	—	53	1	no	—
18	D₇×C₂₃	D₅₃	1	1	yes	characteristic, complemented
19	C₂×D₅₃	—	161	1	no	Hall
20	C₇×C₂₃	C₂×D₅₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅₃	—	7	1	no	—
22	D₅₃	—	23	1	no	—
23	D₅₃	—	161	1	no	—
24	C₂×D₂₃	—	371	1	no	Hall
25	C₅₃	D₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₂₃	—	7	1	no	—
27	D₂₃	—	53	1	no	—
28	D₂₃	—	371	1	no	—
29	C₂×D₇	—	1219	1	no	Hall
30	C₂₃	D₇×D₅₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇	—	1219	1	no	—
32	D₇	—	1219	1	no	—
33	D₇	D₁₂₁₉	1	1	yes	characteristic, direct product factor
34	C₇	C₂×D₁₂₁₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	8533	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	8533	1	no	—
38	C₂	—	1219	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. D₈₅₃₃	C₂	semidirect
2. D₇×C₂₃×C₅₃	C₂	semidirect
3. C₇×D₁₂₁₉	C₂	semidirect
4. C₇×C₂₃×C₅₃	C₂²	semidirect
8. D₁₂₁₉	D₇	direct (N × H)
10. C₂₃×C₅₃	C₂×D₇	semidirect
13. D₇×C₅₃	D₂₃	semidirect
15. C₇×C₅₃	C₂×D₂₃	semidirect
18. D₇×C₂₃	D₅₃	semidirect
20. C₇×C₂₃	C₂×D₅₃	semidirect
25. C₅₃	D₇×D₂₃	semidirect
30. C₂₃	D₇×D₅₃	semidirect
33. D₇	D₁₂₁₉	direct (N × H)
34. C₇	C₂×D₁₂₁₉	semidirect

Maximal subgroups

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

subgroup	index
D₈₅₃₃	2
D₇×C₂₃×C₅₃	2
C₇×D₁₂₁₉	2
C₂×D₁₂₁₉	7
D₇×D₅₃	23
D₇×D₂₃	53

Subgroups — D7×D1219 #46802430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×D₁₂₁₉ #46802430