Subgroups — C₂×C₃×C₆₄ #67987

Order 384.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₆₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₆₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₁₆	C₄	1	1	yes	characteristic
5	C₃×C₃₂	C₄	1	1	yes	characteristic
6	C₃×C₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₃₂	C₂×C₃	1	1	yes	characteristic
8	C₆₄	C₂×C₃	1	2	yes	direct product factor
9	C₂×C₃×C₈	C₈	1	1	yes	characteristic
10	C₃×C₁₆	C₈	1	1	yes	characteristic
11	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆	C₃×C₄	1	1	yes	characteristic
13	C₃₂	C₃×C₄	1	1	yes	characteristic
14	C₃₂	C₂²×C₃	1	1	yes	characteristic
15	C₂×C₃×C₄	C₁₆	1	1	yes	characteristic
16	C₃×C₈	C₁₆	1	1	yes	characteristic
17	C₃×C₈	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈	C₃×C₈	1	1	yes	characteristic
19	C₁₆	C₃×C₈	1	1	yes	characteristic
20	C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
21	C₂²×C₃	C₃₂	1	1	yes	characteristic
22	C₃×C₄	C₃₂	1	1	yes	characteristic
23	C₃×C₄	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₄	C₃×C₁₆	1	1	yes	characteristic
25	C₈	C₃×C₁₆	1	1	yes	characteristic
26	C₈	C₂×C₃×C₈	1	1	yes	characteristic
27	C₂×C₃	C₆₄	1	2	yes	direct product factor
28	C₂×C₃	C₂×C₃₂	1	1	yes	characteristic
29	C₂²	C₃×C₃₂	1	1	yes	characteristic
30	C₄	C₃×C₃₂	1	1	yes	characteristic
31	C₄	C₂×C₃×C₁₆	1	1	yes	characteristic
32	C₃	C₂×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₃×C₆₄	1	2	yes	direct product factor
34	C₂	C₂×C₃×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃₂	C₂²×C₃
socle, prime radical	C₂²×C₃	C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₆₄	C₂	direct (N × H)
3. C₂×C₆₄	C₃	direct (N × H)
8. C₆₄	C₂×C₃	direct (N × H)
27. C₂×C₃	C₆₄	direct (N × H)
32. C₃	C₂×C₆₄	direct (N × H)
33. C₂	C₃×C₆₄	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×C₃₂	2
C₃×C₆₄	2
C₂×C₆₄	3

Subgroups — C2×C3×C64 #67987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₆₄ #67987