Subgroups — C₂×C₃×D₁₆ #5379

Order 192.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₈	C₂	1	2	yes	maximal, complemented
2	C₃×D₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×D₄	—	2	2	no	—
6	C₃×D₈	—	2	2	no	—
7	C₃×D₈	C₂²	1	4	yes	complemented
8	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
9	C₃×C₁₆	C₂²	1	2	yes	complemented
10	C₂×D₈	C₂×C₃	1	2	yes	complemented
11	D₁₆	C₂×C₃	1	4	yes	direct product factor
12	C₂×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂³×C₃	—	4	2	no	—
14	C₃×D₄	—	2	4	no	—
15	C₃×D₄	—	4	2	no	—
16	C₂×C₃×C₄	D₄	1	1	yes	characteristic
17	C₃×C₈	D₄	1	1	yes	characteristic
18	C₃×C₈	C₂³	1	1	yes	characteristic
19	C₂×D₄	—	2	2	no	—
20	D₈	—	2	2	no	—
21	D₈	C₂²×C₃	1	4	yes	complemented
22	C₂×C₈	C₂²×C₃	1	1	yes	characteristic
23	C₁₆	C₂²×C₃	1	2	yes	complemented
24	C₂²×C₃	—	4	4	no	—
25	C₂²×C₃	—	8	4	no	—
26	C₂²×C₃	D₈	1	1	yes	characteristic
27	C₃×C₄	D₈	1	1	yes	characteristic
28	C₃×C₄	C₂×D₄	1	1	yes	characteristic
29	C₂³	—	4	2	no	—
30	D₄	—	2	4	no	—
31	D₄	—	4	2	no	—
32	C₂×C₄	C₃×D₄	1	1	yes	characteristic
33	C₈	C₃×D₄	1	1	yes	characteristic
34	C₈	C₂³×C₃	1	1	yes	characteristic
35	C₂×C₃	—	8	4	no	—
36	C₂×C₃	D₁₆	1	2	yes	direct product factor
37	C₂×C₃	C₂×D₈	1	1	yes	characteristic
38	C₂²	—	4	4	no	—
39	C₂²	—	8	4	no	—
40	C₂²	C₃×D₈	1	1	yes	characteristic
41	C₄	C₃×D₈	1	1	yes	characteristic
42	C₄	C₂×C₃×D₄	1	1	yes	characteristic
43	C₃	C₂×D₁₆	1	1	yes	characteristic, direct product factor, Sylow
44	C₂	—	8	4	no	—
45	C₂	C₃×D₁₆	1	2	yes	direct product factor
46	C₂	C₂×C₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₈	C₂	semidirect
2. C₃×D₁₆	C₂	direct (N × H)
3. C₂×C₃×C₁₆	C₂	semidirect
4. C₂×D₁₆	C₃	direct (N × H)
7. C₃×D₈	C₂²	semidirect
9. C₃×C₁₆	C₂²	semidirect
10. C₂×D₈	C₂×C₃	semidirect
11. D₁₆	C₂×C₃	direct (N × H)
12. C₂×C₁₆	C₂×C₃	semidirect
21. D₈	C₂²×C₃	semidirect
23. C₁₆	C₂²×C₃	semidirect
36. C₂×C₃	D₁₆	direct (N × H)
43. C₃	C₂×D₁₆	direct (N × H)
45. C₂	C₃×D₁₆	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×D₈	2
C₃×D₁₆	2
C₂×C₃×C₁₆	2
C₂×D₁₆	3

Subgroups — C2×C3×D16 #5379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₁₆ #5379