Subgroups — C₃×#1710 #72425

Order 384.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#500	C₂	1	2	yes	maximal
2	C₃×#487	C₂	1	4	yes	maximal
3	C₃×C₈²	C₂	1	1	yes	maximal, characteristic
4	#1710	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₄⋊Q₈	C₂²	1	4	yes	—
6	C₃×#107	—	2	4	no	—
7	C₃×#103	—	2	8	no	—
8	C₃×C₄×C₈	C₂²	1	2	yes	—
9	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
10	#500	C₂×C₃	1	2	yes	—
11	#487	C₂×C₃	1	4	yes	—
12	C₈²	C₂×C₃	1	1	yes	characteristic
13	C₂×C₃×Q₈	—	2	4	no	—
14	C₂×C₃×C₈	D₄	1	4	yes	—
15	C₂×C₃×C₈	D₄	1	2	yes	—
16	C₃×C₄⋊C₄	—	2	4	no	—
17	C₃×C₄⋊C₄	—	2	4	no	—
18	C₃×C₄²	C₂³	1	1	yes	characteristic
19	C₄⋊Q₈	C₂²×C₃	1	4	yes	—
20	#107	—	2	4	no	—
21	#103	—	2	8	no	—
22	C₄×C₈	C₂²×C₃	1	2	yes	—
23	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
24	C₃×Q₈	—	4	8	no	—
25	C₂×C₃×C₄	—	4	4	no	—
26	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
27	C₂×C₃×C₄	C₂×D₄	1	2	yes	—
28	C₃×C₈	—	2	4	no	—
29	C₃×C₈	Q₁₆	1	4	yes	—
30	C₂×Q₈	—	2	4	no	—
31	C₂×C₈	C₃×D₄	1	4	yes	—
32	C₂×C₈	C₃×D₄	1	2	yes	—
33	C₄⋊C₄	—	2	4	no	—
34	C₄⋊C₄	—	2	4	no	—
35	C₄²	C₂³×C₃	1	1	yes	characteristic
36	C₂²×C₃	#127	1	1	yes	characteristic
37	C₃×C₄	—	8	4	no	—
38	C₃×C₄	C₂×Q₁₆	1	2	yes	—
39	C₃×C₄	#135	1	4	yes	—
40	Q₈	—	4	8	no	—
41	C₂×C₄	—	4	4	no	—
42	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
43	C₂×C₄	C₂×C₃×D₄	1	2	yes	—
44	C₈	—	2	4	no	—
45	C₈	C₃×Q₁₆	1	4	yes	—
46	C₂×C₃	#494	1	1	yes	characteristic
47	C₂×C₃	#495	1	2	yes	—
48	C₂²	C₃×#127	1	1	yes	characteristic
49	C₄	—	8	4	no	—
50	C₄	C₂×C₃×Q₁₆	1	2	yes	—
51	C₄	C₃×#135	1	4	yes	—
52	C₃	#1710	1	1	yes	characteristic, direct product factor, Sylow
53	C₂	C₃×#494	1	1	yes	characteristic
54	C₂	C₃×#495	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
4. #1710	C₃	direct (N × H)
52. C₃	#1710	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×#500	2
C₃×#487	2
C₃×C₈²	2
#1710	3

Subgroups — C3×#1710 #72425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1710 #72425