Subgroups — SD₁₆×3₋¹⁺² #88573

Order 432.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
3	C₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×SD₁₆	C₃	1	1	yes	maximal, characteristic
5	C₉×SD₁₆	C₃	1	3	yes	maximal, complemented
6	C₂²×3₋¹⁺²	—	2	1	no	—
7	C₄×3₋¹⁺²	—	2	1	no	—
8	C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
9	C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
10	C₃²×D₄	C₂×C₃	1	1	yes	characteristic
11	C₃²×C₈	C₂×C₃	1	1	yes	characteristic
12	Q₈×C₉	C₂×C₃	1	3	yes	complemented
13	D₄×C₉	C₂×C₃	1	3	yes	—
14	C₈×C₉	C₂×C₃	1	3	yes	complemented
15	C₂×3₋¹⁺²	—	4	1	no	—
16	C₂×3₋¹⁺²	D₄	1	1	yes	characteristic
17	C₃×SD₁₆	—	3	1	no	—
18	C₃×SD₁₆	C₃²	1	1	yes	characteristic
19	C₂²×C₃²	—	2	1	no	—
20	C₃²×C₄	—	2	1	no	—
21	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
22	C₂²×C₉	—	2	3	no	—
23	C₄×C₉	—	2	3	no	—
24	C₄×C₉	C₂²×C₃	1	3	yes	—
25	3₋¹⁺²	SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
26	C₃×Q₈	—	3	1	no	—
27	C₃×Q₈	C₂×C₃²	1	1	yes	characteristic
28	C₃×D₄	—	3	1	no	—
29	C₃×D₄	C₂×C₃²	1	1	yes	characteristic
30	C₃×C₈	—	3	1	no	—
31	C₃×C₈	C₂×C₃²	1	1	yes	characteristic
32	C₂×C₃²	—	4	1	no	—
33	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
34	C₂×C₉	—	4	3	no	—
35	C₂×C₉	C₃×D₄	1	3	yes	—
36	SD₁₆	3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₃	—	2	1	no	—
38	C₂²×C₃	—	6	1	no	—
39	C₃×C₄	—	2	1	no	—
40	C₃×C₄	—	3	1	no	—
41	C₃×C₄	—	6	1	no	—
42	C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
43	C₃²	C₃×SD₁₆	1	1	yes	characteristic
44	C₉	C₃×SD₁₆	1	3	yes	complemented
45	Q₈	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
46	D₄	C₂×3₋¹⁺²	1	1	yes	characteristic
47	C₈	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
48	C₂×C₃	—	3	1	no	—
49	C₂×C₃	—	4	1	no	—
50	C₂×C₃	—	12	1	no	—
51	C₂×C₃	C₃²×D₄	1	1	yes	characteristic
52	C₂²	—	2	1	no	—
53	C₄	—	2	1	no	—
54	C₄	C₂²×3₋¹⁺²	1	1	yes	characteristic
55	C₃	—	3	1	no	—
56	C₃	C₃²×SD₁₆	1	1	yes	characteristic
57	C₂	—	4	1	no	—
58	C₂	D₄×3₋¹⁺²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₃²×D₄
commutator, Frattini, cosocle	C₃×C₄	C₂²×C₃²
prime radical	C₃²×D₄	C₂×C₃
LCS	G ▷ C₃×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₄×3₋¹⁺² ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×3₋¹⁺²	C₂	semidirect
3. C₈×3₋¹⁺²	C₂	semidirect
5. C₉×SD₁₆	C₃	semidirect
12. Q₈×C₉	C₂×C₃	semidirect
14. C₈×C₉	C₂×C₃	semidirect
25. 3₋¹⁺²	SD₁₆	direct (N × H)
36. SD₁₆	3₋¹⁺²	direct (N × H)
44. C₉	C₃×SD₁₆	semidirect
45. Q₈	C₂×3₋¹⁺²	semidirect
47. C₈	C₂×3₋¹⁺²	semidirect

Maximal subgroups

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

subgroup	index
Q₈×3₋¹⁺²	2
D₄×3₋¹⁺²	2
C₈×3₋¹⁺²	2
C₃²×SD₁₆	3
C₉×SD₁₆	3

Subgroups — SD16×3−1+2 #88573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×3₋¹⁺² #88573