Finite Group Databasebeta

← SD₁₆×C₉₈₃ #30628443

Subgroups — SD₁₆×C₉₈₃ #30628443

Order 15728.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₉₈₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₉₈₃	C₂	1	1	yes	maximal, characteristic
3	C₈×C₉₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₉₈₃	—	2	1	no	—
5	C₄×C₉₈₃	—	2	1	no	—
6	C₄×C₉₈₃	C₂²	1	1	yes	characteristic
7	C₂×C₉₈₃	—	4	1	no	—
8	C₂×C₉₈₃	D₄	1	1	yes	characteristic
9	C₉₈₃	SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
10	SD₁₆	C₉₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	Q₈	C₂×C₉₈₃	1	1	yes	characteristic, complemented
12	D₄	C₂×C₉₈₃	1	1	yes	characteristic
13	C₈	C₂×C₉₈₃	1	1	yes	characteristic, complemented
14	C₂²	—	2	1	no	—
15	C₄	—	2	1	no	—
16	C₄	C₂²×C₉₈₃	1	1	yes	characteristic
17	C₂	—	4	1	no	—
18	C₂	D₄×C₉₈₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₉₈₃	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₉₈₃
prime radical	D₄×C₉₈₃	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉₈₃ ◁ C₄×C₉₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₉₈₃	C₂	semidirect
3. C₈×C₉₈₃	C₂	semidirect
9. C₉₈₃	SD₁₆	direct (N × H)
10. SD₁₆	C₉₈₃	direct (N × H)
11. Q₈	C₂×C₉₈₃	semidirect
13. C₈	C₂×C₉₈₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₉₈₃	2
D₄×C₉₈₃	2
C₈×C₉₈₃	2
SD₁₆	983