Subgroups — C₃×#1426 #67986

Order 384.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×M₆₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#368	C₂	1	1	yes	maximal, characteristic
3	C₃×#367	C₂	1	1	yes	maximal, characteristic
4	#1426	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₃×#108	—	2	1	no	—
7	C₃×#107	—	2	1	no	—
8	C₃×C₃₂	C₄	1	2	yes	complemented
9	M₆₄	C₂×C₃	1	1	yes	characteristic
10	#368	C₂×C₃	1	1	yes	characteristic
11	#367	C₂×C₃	1	1	yes	characteristic
12	C₃×M₁₆	—	4	1	no	—
13	C₂×C₃×C₈	D₄	1	1	yes	characteristic
14	C₃×C₄⋊C₄	—	4	1	no	—
15	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₃×C₁₆	Q₈	1	1	yes	characteristic
17	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
18	#108	—	2	1	no	—
19	#107	—	2	1	no	—
20	C₃₂	C₃×C₄	1	2	yes	complemented
21	C₂×C₃×C₄	—	8	1	no	—
22	C₂×C₃×C₄	D₈	1	1	yes	characteristic
23	C₃×C₈	—	8	1	no	—
24	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
25	C₃×C₈	Q₁₆	1	1	yes	characteristic
26	M₁₆	—	4	1	no	—
27	C₂×C₈	C₃×D₄	1	1	yes	characteristic
28	C₄⋊C₄	—	4	1	no	—
29	C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
30	C₁₆	C₃×Q₈	1	1	yes	characteristic
31	C₂²×C₃	SD₃₂	1	1	yes	characteristic
32	C₃×C₄	—	16	1	no	—
33	C₃×C₄	#107	1	1	yes	characteristic
34	C₃×C₄	SD₃₂	1	1	yes	characteristic
35	C₂×C₄	—	8	1	no	—
36	C₂×C₄	C₃×D₈	1	1	yes	characteristic
37	C₈	—	8	1	no	—
38	C₈	C₃×C₄⋊C₄	1	1	yes	characteristic
39	C₈	C₃×Q₁₆	1	1	yes	characteristic
40	C₂×C₃	—	2	1	no	—
41	C₂×C₃	#367	1	1	yes	characteristic
42	C₂²	C₃×SD₃₂	1	1	yes	characteristic
43	C₄	—	16	1	no	—
44	C₄	C₃×#107	1	1	yes	characteristic
45	C₄	C₃×SD₃₂	1	1	yes	characteristic
46	C₃	#1426	1	1	yes	characteristic, direct product factor, Sylow
47	C₂	—	2	1	no	—
48	C₂	C₃×#367	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#367
commutator	C₁₆	C₂×C₃×C₄
Frattini, cosocle	C₂×C₁₆	C₂²×C₃
prime radical	C₂²×C₃	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×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
4. #1426	C₃	direct (N × H)
8. C₃×C₃₂	C₄	semidirect
20. C₃₂	C₃×C₄	semidirect
46. C₃	#1426	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×M₆₄	2
C₃×#368	2
C₃×#367	2
#1426	3

Subgroups — C3×#1426 #67986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1426 #67986