Subgroups — C₇⋊D₇×D₅₇ #26014017

Order 11172.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₇⋊D₁₃₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇²×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₉×C₇⋊D₇	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	—	3	1	no	—
7	C₁₉×C₇⋊D₇	D₃	1	1	yes	characteristic, complemented
8	C₇²×D₁₉	—	3	1	no	—
9	D₇×D₅₇	—	7	8	no	maximal
10	C₇²×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃₉₉	—	7	8	no	—
12	C₇×D₅₇	D₇	1	8	yes	complemented
13	C₃×D₇×C₁₉	—	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)	—	19	1	no	—
18	D₃×C₇²	—	19	1	no	—
19	C₃×C₇⋊D₇	D₁₉	1	1	yes	characteristic, complemented
20	D₁₃₃	—	21	8	no	—
21	C₇×D₁₉	—	3	8	no	—
22	D₇×C₁₉	—	7	8	no	—
23	C₂×D₅₇	—	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	C₂×C₃×C₁₉	—	49	1	no	—
28	D₅₇	—	49	1	no	—
29	D₅₇	C₇⋊D₇	1	1	yes	characteristic, direct product factor
30	C₂×C₇²	—	57	1	no	—
31	C₇⋊D₇	—	57	1	no	—
32	C₇⋊D₇	D₅₇	1	1	yes	characteristic, direct product factor
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	C₂×D₅₇	1	1	yes	characteristic, complemented, Sylow
37	D₂₁	—	133	8	no	—
38	C₃×D₇	—	7	8	no	—
39	D₃×C₇	—	19	8	no	—
40	C₂×C₁₉	—	49	1	no	—
41	D₁₉	—	3	1	no	—
42	D₁₉	—	147	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	—	7	8	no	—
48	D₇	—	399	8	no	—
49	C₂×D₃	—	931	1	no	Hall
50	C₇	D₇×D₅₇	1	8	yes	complemented
51	C₂×C₃	—	49	1	no	—
52	D₃	—	19	1	no	—
53	D₃	—	931	1	no	—
54	C₂²	—	2793	1	no	Sylow
55	C₃	D₁₉×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	49	1	no	—
57	C₂	—	57	1	no	—
58	C₂	—	2793	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. C₃⋊(C₇⋊D₁₃₃)	C₂	semidirect
2. C₇²×D₅₇	C₂	semidirect
3. C₃×C₁₉×C₇⋊D₇	C₂	semidirect
5. C₃×C₇²×C₁₉	C₂²	semidirect
7. C₁₉×C₇⋊D₇	D₃	semidirect
10. C₇²×C₁₉	C₂×D₃	semidirect
12. C₇×D₅₇	D₇	semidirect
16. C₃×C₇×C₁₉	C₂×D₇	semidirect
19. C₃×C₇⋊D₇	D₁₉	semidirect
25. C₃×C₇²	C₂×D₁₉	semidirect
26. C₇×C₁₉	D₃×D₇	semidirect
29. D₅₇	C₇⋊D₇	direct (N × H)
32. C₇⋊D₇	D₅₇	direct (N × H)
35. C₃×C₁₉	C₂×C₇⋊D₇	semidirect
36. C₇²	C₂×D₅₇	semidirect
44. C₃×C₇	D₇×D₁₉	semidirect
45. C₁₉	D₃×C₇⋊D₇	semidirect
50. C₇	D₇×D₅₇	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
C₃⋊(C₇⋊D₁₃₃)	2
C₇²×D₅₇	2
C₃×C₁₉×C₇⋊D₇	2
D₁₉×C₇⋊D₇	3
D₇×D₅₇	7
D₃×C₇⋊D₇	19

Subgroups — C7⋊D7×D57 #26014017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊D₇×D₅₇ #26014017