Subgroups — SD₁₆×D₃₅₃ #26015004

Order 11296.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₃₅₃	C₂	1	1	yes	maximal, characteristic
3	#19150726	C₂	1	1	yes	maximal, characteristic, complemented
4	#19150725	C₂	1	1	yes	maximal, characteristic, complemented
5	#19150724	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₃₅₃	—	2	1	no	—
9	Dic₇₀₆	—	2	1	no	—
10	Dic₇₀₆	C₂²	1	1	yes	characteristic, complemented
11	D₁₄₁₂	C₂²	1	1	yes	characteristic
12	C₂²⋊D₃₅₃	—	2	1	no	—
13	C₄×D₃₅₃	—	2	1	no	—
14	C₄×D₃₅₃	C₂²	1	1	yes	characteristic
15	#15667725	C₂²	1	1	yes	characteristic, complemented
16	Q₈×C₃₅₃	C₂²	1	1	yes	characteristic, complemented
17	D₄×C₃₅₃	C₂²	1	1	yes	characteristic
18	C₈×C₃₅₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃₅₃	—	2	1	no	—
20	C₂×D₃₅₃	—	2	1	no	—
21	C₂×D₃₅₃	—	4	2	no	—
22	C₂×D₃₅₃	D₄	1	1	yes	characteristic
23	C₄×C₃₅₃	—	2	1	no	—
24	C₄×C₃₅₃	C₂³	1	1	yes	characteristic
25	Dic₃₅₃	—	2	1	no	—
26	Dic₃₅₃	D₄	1	1	yes	characteristic
27	C₂×C₃₅₃	—	4	1	no	—
28	C₂×C₃₅₃	C₂×D₄	1	1	yes	characteristic
29	D₃₅₃	—	4	1	no	—
30	D₃₅₃	SD₁₆	1	2	yes	direct product factor
31	C₃₅₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	353	1	no	maximal, Sylow
33	C₂×Q₈	—	353	1	no	—
34	C₂×D₄	—	353	1	no	—
35	SD₁₆	—	353	1	no	—
36	SD₁₆	—	353	1	no	—
37	SD₁₆	—	353	1	no	—
38	SD₁₆	D₃₅₃	1	1	yes	characteristic, direct product factor
39	C₂×C₈	—	353	1	no	—
40	C₂³	—	706	1	no	—
41	Q₈	—	353	1	no	—
42	Q₈	—	706	1	no	—
43	Q₈	C₂×D₃₅₃	1	1	yes	characteristic, complemented
44	D₄	—	353	1	no	—
45	D₄	—	706	1	no	—
46	D₄	C₂×D₃₅₃	1	1	yes	characteristic
47	C₂×C₄	—	353	1	no	—
48	C₂×C₄	—	706	1	no	—
49	C₈	—	353	1	no	—
50	C₈	C₂×D₃₅₃	1	1	yes	characteristic, complemented
51	C₂²	—	2	1	no	—
52	C₂²	—	353	1	no	—
53	C₂²	—	1412	2	no	—
54	C₂²	—	706	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	353	1	no	—
57	C₄	—	706	1	no	—
58	C₄	C₂²×D₃₅₃	1	1	yes	characteristic
59	C₂	—	4	1	no	—
60	C₂	—	353	2	no	—
61	C₂	—	1412	1	no	—
62	C₂	D₄×D₃₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₃₅₃
commutator, cosocle	C₄×C₃₅₃	C₂³
Frattini	C₄	C₂²×D₃₅₃
Fitting	SD₁₆×C₃₅₃	C₂
socle	C₂×C₃₅₃	C₂×D₄
prime radical	D₄×D₃₅₃	C₂
hypercenter	SD₁₆	D₃₅₃
hypocenter	C₃₅₃	C₂×SD₁₆
LCS	G ▷ C₄×C₃₅₃ ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₃₅₃	C₂	semidirect
3. #19150726	C₂	semidirect
4. #19150725	C₂	semidirect
5. #19150724	C₂	semidirect
6. C₈×D₃₅₃	C₂	semidirect
7. SD₁₆×C₃₅₃	C₂	semidirect
10. Dic₇₀₆	C₂²	semidirect
15. #15667725	C₂²	semidirect
16. Q₈×C₃₅₃	C₂²	semidirect
18. C₈×C₃₅₃	C₂²	semidirect
30. D₃₅₃	SD₁₆	direct (N × H)
31. C₃₅₃	C₂×SD₁₆	semidirect
38. SD₁₆	D₃₅₃	direct (N × H)
43. Q₈	C₂×D₃₅₃	semidirect
50. C₈	C₂×D₃₅₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₃₅₃	2
D₄×D₃₅₃	2
#19150726	2
#19150725	2
#19150724	2
C₈×D₃₅₃	2
SD₁₆×C₃₅₃	2
C₂×SD₁₆	353

Subgroups — SD16×D353 #26015004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₃₅₃ #26015004