Subgroups — SD₁₆×D₁₁₃ #16813634

Order 3616.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#14268636	C₂	1	1	yes	maximal, characteristic, complemented
4	#14268635	C₂	1	1	yes	maximal, characteristic, complemented
5	#14268634	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₁₁₃	—	2	1	no	—
9	Q₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
10	D₄×C₁₁₃	C₂²	1	1	yes	characteristic
11	C₂²⋊D₁₁₃	—	2	1	no	—
12	D₄₅₂	C₂²	1	1	yes	characteristic
13	C₄×D₁₁₃	—	2	1	no	—
14	C₄×D₁₁₃	C₂²	1	1	yes	characteristic
15	Dic₂₂₆	—	2	1	no	—
16	Dic₂₂₆	C₂²	1	1	yes	characteristic, complemented
17	C₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
18	#11744751	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₁₁₃	—	2	1	no	—
20	C₂×D₁₁₃	—	2	1	no	—
21	C₂×D₁₁₃	—	4	2	no	—
22	C₂×D₁₁₃	D₄	1	1	yes	characteristic
23	C₄×C₁₁₃	—	2	1	no	—
24	C₄×C₁₁₃	C₂³	1	1	yes	characteristic
25	Dic₁₁₃	—	2	1	no	—
26	Dic₁₁₃	D₄	1	1	yes	characteristic
27	C₂×C₁₁₃	—	4	1	no	—
28	C₂×C₁₁₃	C₂×D₄	1	1	yes	characteristic
29	D₁₁₃	—	4	1	no	—
30	D₁₁₃	SD₁₆	1	2	yes	direct product factor
31	C₁₁₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	113	1	no	maximal, Sylow
33	C₂×Q₈	—	113	1	no	—
34	C₂×D₄	—	113	1	no	—
35	SD₁₆	—	113	1	no	—
36	SD₁₆	—	113	1	no	—
37	SD₁₆	—	113	1	no	—
38	SD₁₆	D₁₁₃	1	1	yes	characteristic, direct product factor
39	C₂×C₈	—	113	1	no	—
40	C₂³	—	226	1	no	—
41	Q₈	—	113	1	no	—
42	Q₈	—	226	1	no	—
43	Q₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
44	D₄	—	113	1	no	—
45	D₄	—	226	1	no	—
46	D₄	C₂×D₁₁₃	1	1	yes	characteristic
47	C₂×C₄	—	113	1	no	—
48	C₂×C₄	—	226	1	no	—
49	C₈	—	113	1	no	—
50	C₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
51	C₂²	—	2	1	no	—
52	C₂²	—	113	1	no	—
53	C₂²	—	452	2	no	—
54	C₂²	—	226	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	113	1	no	—
57	C₄	—	226	1	no	—
58	C₄	C₂²×D₁₁₃	1	1	yes	characteristic
59	C₂	—	4	1	no	—
60	C₂	—	113	2	no	—
61	C₂	—	452	1	no	—
62	C₂	D₄×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₁₃
commutator, cosocle	C₄×C₁₁₃	C₂³
Frattini	C₄	C₂²×D₁₁₃
Fitting	SD₁₆×C₁₁₃	C₂
socle	C₂×C₁₁₃	C₂×D₄
prime radical	D₄×D₁₁₃	C₂
hypercenter	SD₁₆	D₁₁₃
hypocenter	C₁₁₃	C₂×SD₁₆
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₁₁₃	C₂	semidirect
3. #14268636	C₂	semidirect
4. #14268635	C₂	semidirect
5. #14268634	C₂	semidirect
6. C₈×D₁₁₃	C₂	semidirect
7. SD₁₆×C₁₁₃	C₂	semidirect
9. Q₈×C₁₁₃	C₂²	semidirect
16. Dic₂₂₆	C₂²	semidirect
17. C₈×C₁₁₃	C₂²	semidirect
18. #11744751	C₂²	semidirect
30. D₁₁₃	SD₁₆	direct (N × H)
31. C₁₁₃	C₂×SD₁₆	semidirect
38. SD₁₆	D₁₁₃	direct (N × H)
43. Q₈	C₂×D₁₁₃	semidirect
50. C₈	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₁₁₃	2
D₄×D₁₁₃	2
#14268636	2
#14268635	2
#14268634	2
C₈×D₁₁₃	2
SD₁₆×C₁₁₃	2
C₂×SD₁₆	113

Subgroups — SD16×D113 #16813634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₁₁₃ #16813634