Subgroups — Dic₁₃₅₈₄ #72289708

Order 54336.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₇₉₂	C₂	1	2	yes	maximal
2	Dic₃₃₉₆	—	2	2	no	—
3	Dic₁₆₉₈	—	4	2	no	—
4	C₃×C₃₂×C₂₈₃	C₂	1	1	yes	maximal, characteristic
5	C₃×C₁₆×C₂₈₃	C₂²	1	1	yes	characteristic
6	C₃×C₈×C₂₈₃	D₄	1	1	yes	characteristic
7	Dic₄₅₂₈	—	3	1	no	maximal, Hall
8	Dic₂₂₆₄	—	3	2	no	—
9	C₃₂×C₂₈₃	D₃	1	1	yes	characteristic
10	Dic₁₁₃₂	—	6	2	no	—
11	C₁₆×C₂₈₃	C₂×D₃	1	1	yes	characteristic
12	Dic₈₄₉	—	8	2	no	—
13	C₃×C₄×C₂₈₃	D₈	1	1	yes	characteristic
14	Dic₅₆₆	—	12	2	no	—
15	C₈×C₂₈₃	D₁₂	1	1	yes	characteristic
16	C₂×C₃×C₂₈₃	D₁₆	1	1	yes	characteristic
17	C₄×C₂₈₃	D₂₄	1	1	yes	characteristic
18	Dic₂₈₃	—	24	2	no	—
19	C₃×C₂₈₃	Q₆₄	1	1	yes	characteristic, complemented, Hall
20	C₂×C₂₈₃	D₄₈	1	1	yes	characteristic
21	C₂₈₃	Dic₄₈	1	1	yes	characteristic, complemented, Sylow
22	Dic₄₈	—	283	1	no	maximal, Hall
23	Dic₂₄	—	283	2	no	—
24	C₃×C₃₂	D₂₈₃	1	1	yes	characteristic
25	Q₆₄	—	849	1	no	Sylow
26	Dic₁₂	—	566	2	no	—
27	C₃×C₁₆	C₂×D₂₈₃	1	1	yes	characteristic
28	Q₃₂	—	849	2	no	—
29	C₃₂	D₈₄₉	1	1	yes	characteristic
30	Dic₆	—	1132	2	no	—
31	C₃×C₈	D₁₁₃₂	1	1	yes	characteristic
32	Q₁₆	—	1698	2	no	—
33	C₁₆	C₂×D₈₄₉	1	1	yes	characteristic
34	C₃×C₄	D₂₂₆₄	1	1	yes	characteristic
35	Dic₃	—	2264	2	no	—
36	Q₈	—	3396	2	no	—
37	C₈	D₃₃₉₆	1	1	yes	characteristic
38	C₂×C₃	D₄₅₂₈	1	1	yes	characteristic
39	C₄	—	6792	2	no	—
40	C₄	D₆₇₉₂	1	1	yes	characteristic
41	C₃	Dic₄₅₂₈	1	1	yes	characteristic, complemented, Sylow
42	C₂	D₁₃₅₈₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₃₅₈₄
commutator, cosocle	C₃×C₁₆×C₂₈₃	C₂²
Frattini	C₁₆	C₂×D₈₄₉
Fitting	C₃×C₃₂×C₂₈₃	C₂
socle, prime radical	C₂×C₃×C₂₈₃	D₁₆
hypercenter	C₃₂	D₈₄₉
hypocenter	C₃×C₂₈₃	Q₆₄
LCS	G ▷ C₃×C₁₆×C₂₈₃ ▷ C₃×C₈×C₂₈₃ ▷ C₃×C₄×C₂₈₃ ▷ C₂×C₃×C₂₈₃ ▷ C₃×C₂₈₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
19. C₃×C₂₈₃	Q₆₄	semidirect
21. C₂₈₃	Dic₄₈	semidirect
41. C₃	Dic₄₅₂₈	semidirect

Maximal subgroups

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

subgroup	index
Dic₆₇₉₂	2
C₃×C₃₂×C₂₈₃	2
Dic₄₅₂₈	3
Dic₄₈	283

Subgroups — Dic13584 #72289708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃₅₈₄ #72289708