Subgroups — Dic₂₂₃⋊C₁₆ #28383398

Order 14272.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₂₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₂₃⋊C₈	C₄	1	1	yes	characteristic
5	C₄×Dic₂₂₃	C₄	1	1	yes	characteristic
6	C₂₂₃⋊C₁₆	—	2	1	no	—
7	C₂×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
8	C₁₆×C₂₂₃	—	2	1	no	—
9	C₂×Dic₂₂₃	C₈	1	1	yes	characteristic
10	C₂×Dic₂₂₃	C₈	1	1	yes	characteristic
11	C₂₂₃⋊C₈	—	2	1	no	—
12	C₂×C₄×C₂₂₃	C₂×C₄	1	1	yes	characteristic
13	C₈×C₂₂₃	D₄	1	1	yes	characteristic
14	C₈×C₂₂₃	Q₈	1	1	yes	characteristic
15	C₂²×C₂₂₃	C₂×C₈	1	1	yes	characteristic
16	C₄×C₂₂₃	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₂₂₃	M₁₆	1	1	yes	characteristic
18	Dic₂₂₃	—	2	1	no	—
19	Dic₂₂₃	C₁₆	1	2	yes	complemented
20	C₂×C₂₂₃	C₄⋊C₈	1	1	yes	characteristic
21	C₂×C₂₂₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₂₂₃	M₃₂	1	1	yes	characteristic
23	C₂₂₃	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₄⋊C₁₆	—	223	1	no	maximal, Sylow
25	C₂×C₁₆	—	223	1	no	—
26	C₂×C₁₆	D₂₂₃	1	1	yes	characteristic
27	C₄×C₈	—	223	1	no	—
28	C₂×C₈	—	223	1	no	—
29	C₂×C₈	C₂×D₂₂₃	1	1	yes	characteristic
30	C₄²	—	223	1	no	—
31	C₁₆	—	2	1	no	—
32	C₁₆	—	446	1	no	—
33	C₂×C₄	—	223	1	no	—
34	C₂×C₄	—	223	1	no	—
35	C₂×C₄	C₄×D₂₂₃	1	1	yes	characteristic
36	C₈	—	446	1	no	—
37	C₈	C₂²⋊D₂₂₃	1	1	yes	characteristic
38	C₈	Dic₄₄₆	1	1	yes	characteristic
39	C₂²	C₈×D₂₂₃	1	1	yes	characteristic
40	C₄	—	446	1	no	—
41	C₄	—	223	2	no	—
42	C₄	Dic₂₂₃⋊C₄	1	1	yes	characteristic
43	C₄	#16813153	1	1	yes	characteristic
44	C₂	Dic₂₂₃⋊C₈	1	1	yes	characteristic
45	C₂	C₁₆×D₂₂₃	1	1	yes	characteristic
46	C₂	#20297243	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₂₂₃
commutator	C₂×C₂₂₃	C₂×C₁₆
Fitting	C₂×C₁₆×C₂₂₃	C₂
socle, prime radical	C₂²×C₂₂₃	C₂×C₈
cosocle	C₂×C₈×C₂₂₃	C₂²
hypercenter	C₂×C₁₆	D₂₂₃
hypocenter	C₂₂₃	C₄⋊C₁₆
LCS	G ▷ C₂×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₂₂₃	C₁₆	semidirect
23. C₂₂₃	C₄⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₂₃⋊C₁₆	2
C₈×Dic₂₂₃	2
C₂×C₁₆×C₂₂₃	2
C₄⋊C₁₆	223

Subgroups — Dic223⋊C16 #28383398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₂₂₃⋊C₁₆ #28383398