Subgroups — C₂×C₁₁×D₃₉₉ #31798337

Order 17556.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₃₉₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×D₁₃₃	—	3	1	no	maximal, Hall
4	C₃×C₇×C₁₁×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×D₁₃₃	—	3	2	no	—
6	C₂×C₇×C₁₁×C₁₉	D₃	1	1	yes	characteristic, complemented
7	C₂×C₁₁×D₅₇	—	7	1	no	maximal, Hall
8	C₂×D₃₉₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₁₁×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₁×C₁₉	D₇	1	1	yes	characteristic, complemented
11	C₁₁×D₅₇	—	7	2	no	—
12	C₂×C₁₁×D₂₁	—	19	1	no	maximal, Hall
13	C₂×C₁₁×D₁₉	—	21	1	no	Hall
14	C₂×C₃×C₇×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented
15	D₃₉₉	C₂×C₁₁	1	2	yes	direct product factor
16	C₃×C₁₁×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
17	C₂×D₁₃₃	—	3	1	no	Hall
18	C₂×C₃×C₇×C₁₁	D₁₉	1	1	yes	characteristic, complemented
19	C₁₁×D₂₁	—	19	2	no	—
20	C₂×C₁₁×C₁₉	D₂₁	1	1	yes	characteristic, complemented
21	C₁₁×D₁₉	—	21	2	no	—
22	C₃×C₇×C₁₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
23	C₂×C₁₁×D₇	—	57	1	no	Hall
24	C₂×C₇×C₁₉	D₃×C₁₁	1	1	yes	characteristic, complemented
25	D₁₃₃	—	3	2	no	—
26	C₃×C₇×C₁₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×D₅₇	—	7	1	no	Hall
28	C₁₁×C₁₉	C₂×D₂₁	1	1	yes	characteristic, complemented, Hall
29	C₂×C₇×C₁₁	D₅₇	1	1	yes	characteristic, complemented
30	C₁₁×D₇	—	57	2	no	—
31	C₇×C₁₉	C₂×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
32	C₂×D₃×C₁₁	—	133	1	no	Hall
33	C₂×C₃×C₁₉	C₁₁×D₇	1	1	yes	characteristic, complemented
34	D₅₇	—	7	2	no	—
35	C₂×D₂₁	—	19	1	no	Hall
36	C₇×C₁₁	C₂×D₅₇	1	1	yes	characteristic, complemented, Hall
37	C₂×D₁₉	—	21	1	no	Hall
38	C₂×C₃×C₁₁	D₁₃₃	1	1	yes	characteristic, complemented
39	D₃×C₁₁	—	133	2	no	—
40	C₃×C₁₉	C₂×C₁₁×D₇	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	399	1	no	Hall
42	C₂×C₃×C₇	C₁₁×D₁₉	1	1	yes	characteristic, complemented
43	D₂₁	—	19	2	no	—
44	C₂×C₁₉	C₁₁×D₂₁	1	1	yes	characteristic, complemented
45	D₁₉	—	21	2	no	—
46	C₃×C₁₁	C₂×D₁₃₃	1	1	yes	characteristic, complemented, Hall
47	C₂×D₇	—	57	1	no	Hall
48	C₂×C₁₁	—	399	2	no	—
49	C₂×C₁₁	D₃₉₉	1	1	yes	characteristic, direct product factor
50	C₃×C₇	C₂×C₁₁×D₁₉	1	1	yes	characteristic, complemented, Hall
51	C₁₉	C₂×C₁₁×D₂₁	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₇	C₁₁×D₅₇	1	1	yes	characteristic, complemented
53	D₇	—	57	2	no	—
54	C₂×D₃	—	133	1	no	Hall
55	C₁₁	C₂×D₃₉₉	1	1	yes	characteristic, direct product factor, Sylow
56	C₇	C₂×C₁₁×D₅₇	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₃	C₁₁×D₁₃₃	1	1	yes	characteristic, complemented
58	D₃	—	133	2	no	—
59	C₂²	—	399	1	no	Sylow
60	C₃	C₂×C₁₁×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	399	2	no	—
62	C₂	C₁₁×D₃₉₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₃₉₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₉	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₁×C₁₉	C₂
LCS	G ▷ C₃×C₇×C₁₉
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×D₃₉₉	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₁×C₁₉	C₂	semidirect
4. C₃×C₇×C₁₁×C₁₉	C₂²	semidirect
6. C₂×C₇×C₁₁×C₁₉	D₃	semidirect
8. C₂×D₃₉₉	C₁₁	direct (N × H)
9. C₇×C₁₁×C₁₉	C₂×D₃	semidirect
10. C₂×C₃×C₁₁×C₁₉	D₇	semidirect
14. C₂×C₃×C₇×C₁₉	C₂×C₁₁	semidirect
15. D₃₉₉	C₂×C₁₁	direct (N × H)
16. C₃×C₁₁×C₁₉	C₂×D₇	semidirect
18. C₂×C₃×C₇×C₁₁	D₁₉	semidirect
20. C₂×C₁₁×C₁₉	D₂₁	semidirect
22. C₃×C₇×C₁₉	C₂²×C₁₁	semidirect
24. C₂×C₇×C₁₉	D₃×C₁₁	semidirect
26. C₃×C₇×C₁₁	C₂×D₁₉	semidirect
28. C₁₁×C₁₉	C₂×D₂₁	semidirect
29. C₂×C₇×C₁₁	D₅₇	semidirect
31. C₇×C₁₉	C₂×D₃×C₁₁	semidirect
33. C₂×C₃×C₁₉	C₁₁×D₇	semidirect
36. C₇×C₁₁	C₂×D₅₇	semidirect
38. C₂×C₃×C₁₁	D₁₃₃	semidirect
40. C₃×C₁₉	C₂×C₁₁×D₇	semidirect
42. C₂×C₃×C₇	C₁₁×D₁₉	semidirect
44. C₂×C₁₉	C₁₁×D₂₁	semidirect
46. C₃×C₁₁	C₂×D₁₃₃	semidirect
49. C₂×C₁₁	D₃₉₉	direct (N × H)
50. C₃×C₇	C₂×C₁₁×D₁₉	semidirect
51. C₁₉	C₂×C₁₁×D₂₁	semidirect
52. C₂×C₇	C₁₁×D₅₇	semidirect
55. C₁₁	C₂×D₃₉₉	direct (N × H)
56. C₇	C₂×C₁₁×D₅₇	semidirect
57. C₂×C₃	C₁₁×D₁₃₃	semidirect
60. C₃	C₂×C₁₁×D₁₃₃	semidirect
62. C₂	C₁₁×D₃₉₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×D₃₉₉	2
C₂×C₃×C₇×C₁₁×C₁₉	2
C₂×C₁₁×D₁₃₃	3
C₂×C₁₁×D₅₇	7
C₂×D₃₉₉	11
C₂×C₁₁×D₂₁	19

Subgroups — C2×C11×D399 #31798337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×D₃₉₉ #31798337