Subgroups — C₃×#1422 #67982

Order 384.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×M₆₄	C₂	1	2	yes	maximal
2	C₃×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#1422	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₈	C₄	1	1	yes	characteristic
7	C₃×C₃₂	—	2	2	no	—
8	M₆₄	C₂×C₃	1	2	yes	—
9	C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×C₈	C₈	1	1	yes	characteristic
11	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
12	C₃×C₄²	C₈	1	1	yes	characteristic
13	C₃×C₁₆	—	2	1	no	—
14	C₃×C₁₆	D₄	1	1	yes	characteristic
15	C₃×C₁₆	Q₈	1	1	yes	characteristic
16	C₂×C₁₆	C₃×C₄	1	1	yes	characteristic
17	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
18	C₄×C₈	C₃×C₄	1	1	yes	characteristic
19	C₃₂	—	2	2	no	—
20	C₂×C₃×C₄	—	2	1	no	—
21	C₂×C₃×C₄	C₂×C₈	1	1	yes	characteristic
22	C₃×C₈	C₁₆	1	2	yes	—
23	C₃×C₈	C₄⋊C₄	1	1	yes	characteristic
24	C₃×C₈	M₁₆	1	1	yes	characteristic
25	C₂×C₈	C₃×C₈	1	1	yes	characteristic
26	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
27	C₄²	C₃×C₈	1	1	yes	characteristic
28	C₁₆	—	2	1	no	—
29	C₁₆	C₃×D₄	1	1	yes	characteristic
30	C₁₆	C₃×Q₈	1	1	yes	characteristic
31	C₂²×C₃	M₃₂	1	1	yes	characteristic
32	C₃×C₄	—	2	2	no	—
33	C₃×C₄	C₄⋊C₈	1	1	yes	characteristic
34	C₃×C₄	C₂×C₁₆	1	1	yes	characteristic
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₂×C₃×C₈	1	1	yes	characteristic
37	C₈	C₃×C₁₆	1	2	yes	—
38	C₈	C₃×C₄⋊C₄	1	1	yes	characteristic
39	C₈	C₃×M₁₆	1	1	yes	characteristic
40	C₂×C₃	—	2	1	no	—
41	C₂×C₃	C₄⋊C₁₆	1	1	yes	characteristic
42	C₂²	C₃×M₃₂	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	C₃×C₄⋊C₈	1	1	yes	characteristic
45	C₄	C₂×C₃×C₁₆	1	1	yes	characteristic
46	C₃	#1422	1	1	yes	characteristic, direct product factor, Sylow
47	C₂	—	2	1	no	—
48	C₂	C₃×C₄⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₁₆	D₄
commutator	C₄	C₂×C₃×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂²×C₃
socle	C₂×C₃	C₄⋊C₁₆
prime radical	C₂²×C₃	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₁₆ ◁ C₂×C₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1422	C₃	direct (N × H)
46. C₃	#1422	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×C₄×C₁₆	2
#1422	3

Subgroups — C3×#1422 #67982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1422 #67982