Subgroups — D₅₇⋊(C₇⋊D₇) #26014019

Order 11172.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇⋊D₁₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×C₇⋊D₇	—	3	1	no	maximal, Hall
5	C₃×C₇²×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₁₃₃	D₃	1	1	yes	characteristic, complemented
7	C₁₉×C₇⋊D₇	—	3	1	no	—
8	C₇²×D₁₉	—	3	1	no	—
9	D₂₁⋊D₁₉	—	7	8	no	maximal
10	C₇²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₁₉×D₂₁	—	7	8	no	—
12	C₇×D₅₇	D₇	1	8	yes	complemented
13	C₃×D₁₃₃	—	7	8	no	—
14	D₃×C₇⋊D₇	—	19	1	no	maximal, Hall
15	D₇×D₁₉	—	21	8	no	—
16	C₃×C₇×C₁₉	C₂×D₇	1	8	yes	complemented
17	C₃⋊(C₇⋊D₇)	D₁₉	1	1	yes	characteristic, complemented
18	D₃×C₇²	—	19	1	no	—
19	C₃×C₇⋊D₇	—	19	1	no	—
20	D₁₃₃	—	7	8	no	—
21	C₇×D₁₉	—	3	8	no	—
22	D₇×C₁₉	—	21	8	no	—
23	D₃×D₁₉	—	49	1	no	Hall
24	C₂×C₇⋊D₇	—	57	1	no	Hall
25	C₃×C₇²	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
26	C₇×C₁₉	D₃×D₇	1	8	yes	complemented
27	D₅₇	C₇⋊D₇	1	1	yes	characteristic, complemented
28	C₃×D₁₉	—	49	1	no	—
29	D₃×C₁₉	—	49	1	no	—
30	C₂×C₇²	—	57	1	no	—
31	C₇⋊D₇	—	3	1	no	—
32	C₇⋊D₇	—	19	1	no	—
33	D₃×D₇	—	133	8	no	—
34	C₂×D₁₉	—	147	1	no	Hall
35	C₃×C₁₉	C₂×C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
36	C₇²	D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
37	D₂₁	—	7	8	no	—
38	C₃×D₇	—	133	8	no	—
39	D₃×C₇	—	19	8	no	—
40	C₂×C₁₉	—	147	1	no	—
41	D₁₉	—	3	1	no	—
42	D₁₉	—	49	1	no	—
43	C₂×D₇	—	399	8	no	—
44	C₃×C₇	D₇×D₁₉	1	8	yes	complemented
45	C₁₉	D₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₇	—	57	8	no	—
47	D₇	—	21	8	no	—
48	D₇	—	133	8	no	—
49	C₂×D₃	—	931	1	no	Hall
50	C₇	D₂₁⋊D₁₉	1	8	yes	complemented
51	C₂×C₃	—	931	1	no	—
52	D₃	—	19	1	no	—
53	D₃	—	49	1	no	—
54	C₂²	—	2793	1	no	Sylow
55	C₃	D₁₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	57	1	no	—
57	C₂	—	147	1	no	—
58	C₂	—	931	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₁₉	C₂²
LCS	G ▷ C₃×C₇²×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₃⋊(C₇⋊D₇)	C₂	semidirect
2. C₇²×D₅₇	C₂	semidirect
3. C₃×C₇⋊D₁₃₃	C₂	semidirect
5. C₃×C₇²×C₁₉	C₂²	semidirect
6. C₇⋊D₁₃₃	D₃	semidirect
10. C₇²×C₁₉	C₂×D₃	semidirect
12. C₇×D₅₇	D₇	semidirect
16. C₃×C₇×C₁₉	C₂×D₇	semidirect
17. C₃⋊(C₇⋊D₇)	D₁₉	semidirect
25. C₃×C₇²	C₂×D₁₉	semidirect
26. C₇×C₁₉	D₃×D₇	semidirect
27. D₅₇	C₇⋊D₇	semidirect
35. C₃×C₁₉	C₂×C₇⋊D₇	semidirect
36. C₇²	D₃×D₁₉	semidirect
44. C₃×C₇	D₇×D₁₉	semidirect
45. C₁₉	D₃×C₇⋊D₇	semidirect
50. C₇	D₂₁⋊D₁₉	semidirect
55. C₃	D₁₉×C₇⋊D₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₃⋊(C₇⋊D₇)	2
C₇²×D₅₇	2
C₃×C₇⋊D₁₃₃	2
D₁₉×C₇⋊D₇	3
D₂₁⋊D₁₉	7
D₃×C₇⋊D₇	19

Subgroups — D57⋊(C7⋊D7) #26014019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₇⋊(C₇⋊D₇) #26014019