Subgroups — C₂×C₃²×C₁₆ #63679

Order 288.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₆	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₄	C₄	1	1	yes	characteristic
5	C₃²×C₈	C₄	1	1	yes	characteristic
6	C₃²×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₈	C₂×C₃	1	4	yes	—
8	C₃×C₁₆	C₂×C₃	1	8	yes	direct product factor
9	C₂²×C₃²	C₈	1	1	yes	characteristic
10	C₃²×C₄	C₈	1	1	yes	characteristic
11	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆	C₃²	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₄	C₃×C₄	1	4	yes	—
14	C₃×C₈	C₃×C₄	1	4	yes	—
15	C₃×C₈	C₂²×C₃	1	4	yes	—
16	C₂×C₃²	C₁₆	1	2	yes	direct product factor
17	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈	C₂×C₃²	1	1	yes	characteristic
19	C₁₆	C₂×C₃²	1	2	yes	direct product factor
20	C₂²×C₃	C₃×C₈	1	4	yes	—
21	C₃×C₄	C₃×C₈	1	4	yes	—
22	C₃×C₄	C₂×C₃×C₄	1	4	yes	—
23	C₃²	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₄	C₃²×C₄	1	1	yes	characteristic
25	C₈	C₃²×C₄	1	1	yes	characteristic
26	C₈	C₂²×C₃²	1	1	yes	characteristic
27	C₂×C₃	C₃×C₁₆	1	8	yes	direct product factor
28	C₂×C₃	C₂×C₃×C₈	1	4	yes	—
29	C₂²	C₃²×C₈	1	1	yes	characteristic
30	C₄	C₃²×C₈	1	1	yes	characteristic
31	C₄	C₂×C₃²×C₄	1	1	yes	characteristic
32	C₃	C₂×C₃×C₁₆	1	4	yes	direct product factor
33	C₂	C₃²×C₁₆	1	2	yes	direct product factor
34	C₂	C₂×C₃²×C₈	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₃²
socle, prime radical	C₂²×C₃²	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₆	C₂	direct (N × H)
3. C₂×C₃×C₁₆	C₃	direct (N × H)
8. C₃×C₁₆	C₂×C₃	direct (N × H)
12. C₂×C₁₆	C₃²	direct (N × H)
16. C₂×C₃²	C₁₆	direct (N × H)
19. C₁₆	C₂×C₃²	direct (N × H)
23. C₃²	C₂×C₁₆	direct (N × H)
27. C₂×C₃	C₃×C₁₆	direct (N × H)
32. C₃	C₂×C₃×C₁₆	direct (N × H)
33. C₂	C₃²×C₁₆	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×C₃²×C₈	2
C₃²×C₁₆	2
C₂×C₃×C₁₆	3

Subgroups — C2×C32×C16 #63679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₆ #63679