Subgroups — Dic₇₉₁₇ #44539727

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	Dic₂₆₃₉	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₃×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₃×C₂₉	D₃	1	1	yes	characteristic
5	Dic₁₁₃₁	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
7	Dic₆₀₉	—	13	1	no	maximal, Hall
8	C₂×C₃×C₁₃×C₂₉	D₇	1	1	yes	characteristic
9	Dic₃₇₇	—	21	1	no	Hall
10	C₂×C₃×C₇×C₂₉	D₁₃	1	1	yes	characteristic
11	C₃×C₁₃×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
12	Dic₂₇₃	—	29	1	no	maximal, Hall
13	Dic₂₀₃	—	39	1	no	Hall
14	C₂×C₁₃×C₂₉	D₂₁	1	1	yes	characteristic
15	C₃×C₇×C₂₉	Dic₁₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₇×C₁₃	D₂₉	1	1	yes	characteristic
17	C₂×C₇×C₂₉	D₃₉	1	1	yes	characteristic
18	C₁₃×C₂₉	Dic₂₁	1	1	yes	characteristic, complemented, Hall
19	Dic₉₁	—	87	1	no	Hall
20	Dic₈₇	—	91	1	no	Hall
21	C₃×C₇×C₁₃	Dic₂₉	1	1	yes	characteristic, complemented, Hall
22	C₇×C₂₉	Dic₃₉	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	D₈₇	1	1	yes	characteristic
24	C₂×C₃×C₂₉	D₉₁	1	1	yes	characteristic
25	Dic₃₉	—	203	1	no	Hall
26	Dic₂₉	—	273	1	no	Hall
27	C₇×C₁₃	Dic₈₇	1	1	yes	characteristic, complemented, Hall
28	C₃×C₂₉	Dic₉₁	1	1	yes	characteristic, complemented, Hall
29	Dic₂₁	—	377	1	no	Hall
30	C₂×C₃×C₁₃	D₂₀₃	1	1	yes	characteristic
31	C₂×C₂₉	D₂₇₃	1	1	yes	characteristic
32	Dic₁₃	—	609	1	no	Hall
33	C₂×C₃×C₇	D₃₇₇	1	1	yes	characteristic
34	C₃×C₁₃	Dic₂₀₃	1	1	yes	characteristic, complemented, Hall
35	C₂₉	Dic₂₇₃	1	1	yes	characteristic, complemented, Sylow
36	Dic₇	—	1131	1	no	Hall
37	C₂×C₁₃	D₆₀₉	1	1	yes	characteristic
38	C₃×C₇	Dic₃₇₇	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	D₁₁₃₁	1	1	yes	characteristic
40	C₁₃	Dic₆₀₉	1	1	yes	characteristic, complemented, Sylow
41	Dic₃	—	2639	1	no	Hall
42	C₇	Dic₁₁₃₁	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	D₂₆₃₉	1	1	yes	characteristic
44	C₄	—	7917	1	no	Sylow
45	C₃	Dic₂₆₃₉	1	1	yes	characteristic, complemented, Sylow
46	C₂	D₇₉₁₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₉₁₇
commutator, hypocenter	C₃×C₇×C₁₃×C₂₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇×C₁₃×C₂₉	C₂
LCS	G ▷ C₃×C₇×C₁₃×C₂₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₃×C₇×C₁₃×C₂₉	C₄	semidirect
6. C₇×C₁₃×C₂₉	Dic₃	semidirect
11. C₃×C₁₃×C₂₉	Dic₇	semidirect
15. C₃×C₇×C₂₉	Dic₁₃	semidirect
18. C₁₃×C₂₉	Dic₂₁	semidirect
21. C₃×C₇×C₁₃	Dic₂₉	semidirect
22. C₇×C₂₉	Dic₃₉	semidirect
27. C₇×C₁₃	Dic₈₇	semidirect
28. C₃×C₂₉	Dic₉₁	semidirect
34. C₃×C₁₃	Dic₂₀₃	semidirect
35. C₂₉	Dic₂₇₃	semidirect
38. C₃×C₇	Dic₃₇₇	semidirect
40. C₁₃	Dic₆₀₉	semidirect
42. C₇	Dic₁₁₃₁	semidirect
45. C₃	Dic₂₆₃₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₃×C₂₉	2
Dic₂₆₃₉	3
Dic₁₁₃₁	7
Dic₆₀₉	13
Dic₂₇₃	29

Subgroups — Dic7917 #44539727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₇₉₁₇ #44539727