Subgroups — C₂×C₃×SD₁₆ #973

Order 96.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×SD₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×SD₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂³×C₃	—	2	1	no	—
7	C₃×Q₈	—	2	1	no	—
8	C₃×Q₈	C₂²	1	2	yes	complemented
9	C₃×D₄	—	2	1	no	—
10	C₃×D₄	C₂²	1	2	yes	—
11	C₂×C₃×C₄	—	2	1	no	—
12	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₃×C₈	C₂²	1	2	yes	complemented
14	C₂×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×D₄	C₂×C₃	1	1	yes	characteristic
16	SD₁₆	C₂×C₃	1	4	yes	direct product factor
17	C₂×C₈	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃	—	2	2	no	—
19	C₂²×C₃	—	4	2	no	—
20	C₂²×C₃	D₄	1	1	yes	characteristic
21	C₃×C₄	—	2	2	no	—
22	C₃×C₄	D₄	1	1	yes	characteristic
23	C₃×C₄	C₂³	1	1	yes	characteristic
24	C₂³	—	2	1	no	—
25	Q₈	—	2	1	no	—
26	Q₈	C₂²×C₃	1	2	yes	complemented
27	D₄	—	2	1	no	—
28	D₄	C₂²×C₃	1	2	yes	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
31	C₈	C₂²×C₃	1	2	yes	complemented
32	C₂×C₃	—	4	2	no	—
33	C₂×C₃	SD₁₆	1	2	yes	direct product factor
34	C₂×C₃	C₂×D₄	1	1	yes	characteristic
35	C₂²	—	2	2	no	—
36	C₂²	—	4	2	no	—
37	C₂²	C₃×D₄	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	C₃×D₄	1	1	yes	characteristic
40	C₄	C₂³×C₃	1	1	yes	characteristic
41	C₃	C₂×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
42	C₂	—	4	2	no	—
43	C₂	C₃×SD₁₆	1	2	yes	direct product factor
44	C₂	C₂×C₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃
prime radical	C₂×C₃×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈	C₂	semidirect
3. C₃×SD₁₆	C₂	direct (N × H)
4. C₂×C₃×C₈	C₂	semidirect
5. C₂×SD₁₆	C₃	direct (N × H)
8. C₃×Q₈	C₂²	semidirect
13. C₃×C₈	C₂²	semidirect
14. C₂×Q₈	C₂×C₃	semidirect
16. SD₁₆	C₂×C₃	direct (N × H)
17. C₂×C₈	C₂×C₃	semidirect
26. Q₈	C₂²×C₃	semidirect
31. C₈	C₂²×C₃	semidirect
33. C₂×C₃	SD₁₆	direct (N × H)
41. C₃	C₂×SD₁₆	direct (N × H)
43. C₂	C₃×SD₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈	2
C₂×C₃×D₄	2
C₃×SD₁₆	2
C₂×C₃×C₈	2
C₂×SD₁₆	3

Subgroups — C2×C3×SD16 #973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×SD₁₆ #973