Subgroups — D₁₆×D₂₂₃ #28383999

Order 14272.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₂₂₃	C₂	1	2	yes	maximal, complemented
2	D₃₅₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20297245	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₂₂₃	—	2	2	no	—
7	D₁₇₈₄	C₂²	1	2	yes	complemented
8	#16813155	—	2	2	no	—
9	C₈×D₂₂₃	C₂²	1	1	yes	characteristic
10	C₂₂₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₂₂₃	C₂²	1	2	yes	complemented
12	C₁₆×C₂₂₃	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₂₂₃	—	4	2	no	—
14	D₈₉₂	—	2	2	no	—
15	C₂²⋊D₂₂₃	—	4	2	no	—
16	C₄×D₂₂₃	D₄	1	1	yes	characteristic
17	C₂₂₃⋊C₈	D₄	1	1	yes	characteristic
18	D₄×C₂₂₃	—	2	2	no	—
19	C₈×C₂₂₃	C₂³	1	1	yes	characteristic
20	C₂²×C₂₂₃	—	4	2	no	—
21	C₂×D₂₂₃	—	4	2	no	—
22	C₂×D₂₂₃	—	8	4	no	—
23	C₂×D₂₂₃	D₈	1	1	yes	characteristic
24	C₄×C₂₂₃	C₂×D₄	1	1	yes	characteristic
25	Dic₂₂₃	D₈	1	1	yes	characteristic
26	C₂×C₂₂₃	—	8	2	no	—
27	C₂×C₂₂₃	C₂×D₈	1	1	yes	characteristic
28	D₂₂₃	—	8	2	no	—
29	D₂₂₃	D₁₆	1	2	yes	direct product factor
30	C₂₂₃	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	223	1	no	maximal, Sylow
32	C₂×D₈	—	223	2	no	—
33	D₁₆	—	223	2	no	—
34	D₁₆	—	223	1	no	—
35	D₁₆	D₂₂₃	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	223	1	no	—
37	C₂×D₄	—	446	2	no	—
38	D₈	—	446	2	no	—
39	D₈	—	223	2	no	—
40	D₈	C₂×D₂₂₃	1	2	yes	complemented
41	C₂×C₈	—	223	1	no	—
42	C₁₆	—	223	1	no	—
43	C₁₆	C₂×D₂₂₃	1	1	yes	characteristic, complemented
44	C₂³	—	892	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	892	2	no	—
47	D₄	—	446	2	no	—
48	C₂×C₄	—	223	1	no	—
49	C₈	—	223	1	no	—
50	C₈	C₂²×D₂₂₃	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	892	2	no	—
53	C₂²	—	223	1	no	—
54	C₂²	—	1784	4	no	—
55	C₄	—	223	1	no	—
56	C₄	D₄×D₂₂₃	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	223	2	no	—
59	C₂	—	1784	2	no	—
60	C₂	D₈×D₂₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₂₂₃
commutator, cosocle	C₈×C₂₂₃	C₂³
Frattini	C₈	C₂²×D₂₂₃
Fitting	D₁₆×C₂₂₃	C₂
socle	C₂×C₂₂₃	C₂×D₈
hypercenter	D₁₆	D₂₂₃
hypocenter	C₂₂₃	C₂×D₁₆
LCS	G ▷ C₈×C₂₂₃ ▷ C₄×C₂₂₃ ▷ C₂×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₂₂₃	C₂	semidirect
2. D₃₅₆₈	C₂	semidirect
3. #20297245	C₂	semidirect
4. C₁₆×D₂₂₃	C₂	semidirect
5. D₁₆×C₂₂₃	C₂	semidirect
7. D₁₇₈₄	C₂²	semidirect
10. C₂₂₃⋊C₁₆	C₂²	semidirect
11. D₈×C₂₂₃	C₂²	semidirect
12. C₁₆×C₂₂₃	C₂²	semidirect
29. D₂₂₃	D₁₆	direct (N × H)
30. C₂₂₃	C₂×D₁₆	semidirect
35. D₁₆	D₂₂₃	direct (N × H)
40. D₈	C₂×D₂₂₃	semidirect
43. C₁₆	C₂×D₂₂₃	semidirect

Maximal subgroups

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

subgroup	index
D₈×D₂₂₃	2
D₃₅₆₈	2
#20297245	2
C₁₆×D₂₂₃	2
D₁₆×C₂₂₃	2
C₂×D₁₆	223

Subgroups — D16×D223 #28383999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆×D₂₂₃ #28383999