Subgroups — Dic₆₁₆₂ #72224326

Order 24648.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₀₅₄	—	3	1	no	maximal, Hall
2	Dic₃₀₈₁	C₂	1	2	yes	maximal
3	C₃×C₄×C₁₃×C₇₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₁₃×C₇₉	C₂²	1	1	yes	characteristic
5	Dic₁₀₂₇	—	3	2	no	—
6	C₄×C₁₃×C₇₉	D₃	1	1	yes	characteristic
7	C₃×C₁₃×C₇₉	Q₈	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₃×C₇₉	C₂×D₃	1	1	yes	characteristic
9	Dic₄₇₄	—	13	1	no	maximal, Hall
10	C₁₃×C₇₉	Dic₆	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄×C₇₉	D₁₃	1	1	yes	characteristic
12	Dic₂₃₇	—	13	2	no	—
13	Dic₁₅₈	—	39	1	no	Hall
14	C₂×C₃×C₇₉	C₂×D₁₃	1	1	yes	characteristic
15	C₄×C₇₉	D₃₉	1	1	yes	characteristic
16	Dic₇₉	—	39	2	no	—
17	Dic₇₈	—	79	1	no	maximal, Hall
18	C₃×C₇₉	Dic₂₆	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇₉	C₂×D₃₉	1	1	yes	characteristic
20	C₃×C₄×C₁₃	D₇₉	1	1	yes	characteristic
21	Dic₃₉	—	79	2	no	—
22	Dic₂₆	—	237	1	no	Hall
23	C₇₉	Dic₇₈	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃×C₁₃	C₂×D₇₉	1	1	yes	characteristic
25	C₄×C₁₃	D₂₃₇	1	1	yes	characteristic
26	Dic₁₃	—	237	2	no	—
27	C₃×C₁₃	Dic₁₅₈	1	1	yes	characteristic, complemented, Hall
28	C₂×C₁₃	C₂×D₂₃₇	1	1	yes	characteristic
29	Dic₆	—	1027	1	no	Hall
30	C₁₃	Dic₄₇₄	1	1	yes	characteristic, complemented, Sylow
31	C₃×C₄	D₁₀₂₇	1	1	yes	characteristic
32	Dic₃	—	1027	2	no	—
33	Q₈	—	3081	1	no	Sylow
34	C₂×C₃	C₂×D₁₀₂₇	1	1	yes	characteristic
35	C₄	—	3081	2	no	—
36	C₄	D₃₀₈₁	1	1	yes	characteristic
37	C₃	Dic₂₀₅₄	1	1	yes	characteristic, complemented, Sylow
38	C₂	C₂×D₃₀₈₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃₀₈₁
commutator, socle, prime radical, cosocle	C₂×C₃×C₁₃×C₇₉	C₂²
Fitting	C₃×C₄×C₁₃×C₇₉	C₂
hypercenter	C₄	D₃₀₈₁
hypocenter	C₃×C₁₃×C₇₉	Q₈
LCS	G ▷ C₂×C₃×C₁₃×C₇₉ ▷ C₃×C₁₃×C₇₉
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
7. C₃×C₁₃×C₇₉	Q₈	semidirect
10. C₁₃×C₇₉	Dic₆	semidirect
18. C₃×C₇₉	Dic₂₆	semidirect
23. C₇₉	Dic₇₈	semidirect
27. C₃×C₁₃	Dic₁₅₈	semidirect
30. C₁₃	Dic₄₇₄	semidirect
37. C₃	Dic₂₀₅₄	semidirect

Maximal subgroups

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

subgroup	index
Dic₂₀₅₄	3
Dic₃₀₈₁	2
C₃×C₄×C₁₃×C₇₉	2
Dic₄₇₄	13
Dic₇₈	79

Subgroups — Dic6162 #72224326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₆₁₆₂ #72224326