Subgroups — C₃×#1424 #67984

Order 384.

56 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×#366	C₂	1	2	yes	maximal
3	#1424	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₃×#107	—	2	2	no	—
6	C₃×C₃₂	C₄	1	2	yes	complemented
7	C₂×C₃₂	C₂×C₃	1	1	yes	characteristic
8	#366	C₂×C₃	1	2	yes	—
9	C₂×C₃×C₈	D₄	1	1	yes	characteristic
10	C₃×C₄⋊C₄	—	4	2	no	—
11	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₃×C₁₆	Q₈	1	1	yes	characteristic
13	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
14	#107	—	2	2	no	—
15	C₃₂	C₃×C₄	1	2	yes	complemented
16	C₂×C₃×C₄	—	8	2	no	—
17	C₂×C₃×C₄	D₈	1	1	yes	characteristic
18	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
19	C₃×C₈	Q₁₆	1	1	yes	characteristic
20	C₂×C₈	C₃×D₄	1	1	yes	characteristic
21	C₄⋊C₄	—	4	2	no	—
22	C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
23	C₁₆	C₃×Q₈	1	1	yes	characteristic
24	C₂²×C₃	D₁₆	1	1	yes	characteristic
25	C₃×C₄	—	16	2	no	—
26	C₃×C₄	#107	1	1	yes	characteristic
27	C₃×C₄	Q₃₂	1	1	yes	characteristic
28	C₂×C₄	—	8	2	no	—
29	C₂×C₄	C₃×D₈	1	1	yes	characteristic
30	C₈	C₃×C₄⋊C₄	1	1	yes	characteristic
31	C₈	C₃×Q₁₆	1	1	yes	characteristic
32	C₂×C₃	#366	1	1	yes	characteristic
33	C₂×C₃	SD₆₄	1	2	yes	—
34	C₂²	C₃×D₁₆	1	1	yes	characteristic
35	C₄	—	16	2	no	—
36	C₄	C₃×#107	1	1	yes	characteristic
37	C₄	C₃×Q₃₂	1	1	yes	characteristic
38	C₃	#1424	1	1	yes	characteristic, direct product factor, Sylow
39	C₂	C₃×#366	1	1	yes	characteristic
40	C₂	C₃×SD₆₄	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	D₁₆
commutator	C₁₆	C₂×C₃×C₄
Frattini, cosocle	C₂×C₁₆	C₂²×C₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1424	C₃	direct (N × H)
6. C₃×C₃₂	C₄	semidirect
15. C₃₂	C₃×C₄	semidirect
38. C₃	#1424	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×#366	2
#1424	3

Subgroups — C3×#1424 #67984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1424 #67984