Subgroups — C₂×C₃⋊C₁₂₈ #10683096

Order 768.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₃⋊C₁₂₈	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₂₈	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₃₂	C₄	1	1	yes	characteristic
5	C₃×C₆₄	C₄	1	1	yes	characteristic
6	C₃×C₆₄	C₂²	1	1	yes	characteristic
7	C₂×C₆₄	D₃	1	1	yes	characteristic
8	C₁₂₈	—	3	2	no	—
9	C₂×C₃×C₁₆	C₈	1	1	yes	characteristic
10	C₃×C₃₂	C₈	1	1	yes	characteristic
11	C₃×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃₂	Dic₃	1	1	yes	characteristic
13	C₆₄	Dic₃	1	1	yes	characteristic
14	C₆₄	C₂×D₃	1	1	yes	characteristic
15	C₂×C₃×C₈	C₁₆	1	1	yes	characteristic
16	C₃×C₁₆	C₁₆	1	1	yes	characteristic
17	C₃×C₁₆	C₂×C₈	1	1	yes	characteristic
18	C₂×C₁₆	C₃⋊C₈	1	1	yes	characteristic
19	C₃₂	C₃⋊C₈	1	1	yes	characteristic
20	C₃₂	C₂×Dic₃	1	1	yes	characteristic
21	C₂×C₃×C₄	C₃₂	1	1	yes	characteristic
22	C₃×C₈	C₃₂	1	1	yes	characteristic
23	C₃×C₈	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₈	C₃⋊C₁₆	1	1	yes	characteristic
25	C₁₆	C₃⋊C₁₆	1	1	yes	characteristic
26	C₁₆	C₂×C₃⋊C₈	1	1	yes	characteristic
27	C₂²×C₃	C₆₄	1	1	yes	characteristic
28	C₃×C₄	C₆₄	1	1	yes	characteristic
29	C₃×C₄	C₂×C₃₂	1	1	yes	characteristic
30	C₂×C₄	C₃⋊C₃₂	1	1	yes	characteristic
31	C₈	C₃⋊C₃₂	1	1	yes	characteristic
32	C₈	C₂×C₃⋊C₁₆	1	1	yes	characteristic
33	C₂×C₃	C₁₂₈	1	2	yes	complemented
34	C₂×C₃	C₂×C₆₄	1	1	yes	characteristic
35	C₂²	C₃⋊C₆₄	1	1	yes	characteristic
36	C₄	C₃⋊C₆₄	1	1	yes	characteristic
37	C₄	C₂×C₃⋊C₃₂	1	1	yes	characteristic
38	C₃	C₂×C₁₂₈	1	1	yes	characteristic, complemented, Sylow
39	C₂	C₃⋊C₁₂₈	1	2	yes	direct product factor
40	C₂	C₂×C₃⋊C₆₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₆₄	D₃
commutator, hypocenter	C₃	C₂×C₁₂₈
Frattini	C₆₄	C₂×D₃
Fitting	C₂×C₃×C₆₄	C₂
socle, prime radical	C₂²×C₃	C₆₄
cosocle	C₃×C₆₄	C₂²
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊C₁₂₈	C₂	direct (N × H)
33. C₂×C₃	C₁₂₈	semidirect
38. C₃	C₂×C₁₂₈	semidirect
39. C₂	C₃⋊C₁₂₈	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×C₆₄	2
C₃⋊C₁₂₈	2
C₂×C₁₂₈	3

Subgroups — C2×C3⋊C128 #10683096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊C₁₂₈ #10683096