Subgroups — C₃×#2258 #72973

Order 384.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#504	C₂	1	1	yes	maximal, characteristic
2	C₃×M₆₄	C₂	1	3	yes	maximal, complemented
3	C₂×C₃×C₃₂	C₂	1	3	yes	maximal, complemented
4	#2258	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#131	C₄	1	1	yes	characteristic
6	C₃×M₃₂	C₄	1	3	yes	—
7	C₂×C₃×C₁₆	C₂²	1	3	yes	—
8	C₃×C₃₂	C₂²	1	3	yes	—
9	C₃×C₃₂	C₂²	1	1	yes	characteristic
10	#504	C₂×C₃	1	1	yes	characteristic
11	M₆₄	C₂×C₃	1	3	yes	complemented
12	C₂×C₃₂	C₂×C₃	1	3	yes	complemented
13	C₃×#41	C₈	1	1	yes	characteristic
14	C₃×M₁₆	C₈	1	3	yes	—
15	C₂×C₃×C₈	C₂×C₄	1	3	yes	—
16	C₃×C₁₆	C₂×C₄	1	3	yes	—
17	C₃×C₁₆	C₂³	1	1	yes	characteristic
18	#131	C₃×C₄	1	1	yes	characteristic
19	M₃₂	C₃×C₄	1	3	yes	—
20	C₂×C₁₆	C₂²×C₃	1	3	yes	—
21	C₃₂	C₂²×C₃	1	3	yes	—
22	C₃₂	C₂²×C₃	1	1	yes	characteristic
23	C₃×Q₈	C₁₆	1	1	yes	characteristic
24	C₃×D₄	C₁₆	1	3	yes	—
25	C₂×C₃×C₄	C₂×C₈	1	3	yes	—
26	C₃×C₈	C₂×C₈	1	3	yes	—
27	C₃×C₈	C₂²×C₄	1	1	yes	characteristic
28	#41	C₃×C₈	1	1	yes	characteristic
29	M₁₆	C₃×C₈	1	3	yes	—
30	C₂×C₈	C₂×C₃×C₄	1	3	yes	—
31	C₁₆	C₂×C₃×C₄	1	3	yes	—
32	C₁₆	C₂³×C₃	1	1	yes	characteristic
33	C₂²×C₃	C₂×C₁₆	1	3	yes	—
34	C₃×C₄	C₂×C₁₆	1	3	yes	—
35	C₃×C₄	C₂²×C₈	1	1	yes	characteristic
36	Q₈	C₃×C₁₆	1	1	yes	characteristic
37	D₄	C₃×C₁₆	1	3	yes	—
38	C₂×C₄	C₂×C₃×C₈	1	3	yes	—
39	C₈	C₂×C₃×C₈	1	3	yes	—
40	C₈	C₂²×C₃×C₄	1	1	yes	characteristic
41	C₂×C₃	—	2	3	no	—
42	C₂×C₃	C₂²×C₁₆	1	1	yes	characteristic
43	C₂²	C₂×C₃×C₁₆	1	3	yes	—
44	C₄	C₂×C₃×C₁₆	1	3	yes	—
45	C₄	C₂²×C₃×C₈	1	1	yes	characteristic
46	C₃	#2258	1	1	yes	characteristic, direct product factor, Sylow
47	C₂	—	2	3	no	—
48	C₂	C₂²×C₃×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₃₂	C₂²
commutator	C₂	C₂²×C₃×C₁₆
Frattini, cosocle	C₁₆	C₂³×C₃
socle	C₂×C₃	C₂²×C₁₆
prime radical	C₃×#41	C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×M₆₄	C₂	semidirect
3. C₂×C₃×C₃₂	C₂	semidirect
4. #2258	C₃	direct (N × H)
11. M₆₄	C₂×C₃	semidirect
12. C₂×C₃₂	C₂×C₃	semidirect
46. C₃	#2258	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×#504	2
C₃×M₆₄	2
C₂×C₃×C₃₂	2
#2258	3

Subgroups — C3×#2258 #72973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2258 #72973