Subgroups — C₃×#1454 #72169

Order 384.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#431	C₂	1	3	yes	maximal
2	C₃×#322	C₂	1	3	yes	maximal, complemented
3	C₃×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
4	#1454	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
6	C₃×C₄⋊C₈	C₄	1	6	yes	—
7	C₃×C₂²⋊C₈	C₄	1	6	yes	—
8	C₃×C₄×C₈	C₂²	1	3	yes	—
9	C₃×C₄×C₈	C₂²	1	3	yes	—
10	#431	C₂×C₃	1	3	yes	—
11	#322	C₂×C₃	1	3	yes	complemented
12	C₈²	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
14	C₂×C₃×C₈	C₂×C₄	1	6	yes	—
15	C₂×C₃×C₈	C₂×C₄	1	6	yes	—
16	C₃×C₄²	C₂×C₄	1	3	yes	—
17	C₃×C₄²	C₂³	1	1	yes	characteristic
18	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
19	C₄⋊C₈	C₃×C₄	1	6	yes	—
20	C₂²⋊C₈	C₃×C₄	1	6	yes	—
21	C₄×C₈	C₂²×C₃	1	3	yes	—
22	C₄×C₈	C₂²×C₃	1	3	yes	—
23	C₂³×C₃	C₄²	1	1	yes	characteristic
24	C₂×C₃×C₄	—	2	6	no	—
25	C₂×C₃×C₄	C₄²	1	3	yes	—
26	C₂×C₃×C₄	C₂²×C₄	1	3	yes	—
27	C₃×C₈	—	2	6	no	—
28	C₃×C₈	—	2	6	no	—
29	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
30	C₂×C₈	C₂×C₃×C₄	1	6	yes	—
31	C₂×C₈	C₂×C₃×C₄	1	6	yes	—
32	C₄²	C₂×C₃×C₄	1	3	yes	—
33	C₄²	C₂³×C₃	1	1	yes	characteristic
34	C₂²×C₃	—	2	3	no	—
35	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
36	C₃×C₄	—	2	3	no	—
37	C₃×C₄	#131	1	6	yes	—
38	C₂³	C₃×C₄²	1	1	yes	characteristic
39	C₂×C₄	—	2	6	no	—
40	C₂×C₄	C₃×C₄²	1	3	yes	—
41	C₂×C₄	C₂²×C₃×C₄	1	3	yes	—
42	C₈	—	2	6	no	—
43	C₈	—	2	6	no	—
44	C₂×C₃	—	4	1	no	—
45	C₂×C₃	#405	1	3	yes	—
46	C₂²	—	2	3	no	—
47	C₂²	C₂×C₃×C₄²	1	1	yes	characteristic
48	C₄	—	2	3	no	—
49	C₄	C₃×#131	1	6	yes	—
50	C₃	#1454	1	1	yes	characteristic, direct product factor, Sylow
51	C₂	—	4	1	no	—
52	C₂	C₃×#405	1	3	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂³
commutator	C₂²	C₂×C₃×C₄²
Frattini, cosocle	C₄²	C₂³×C₃
socle	C₂²×C₃	C₂×C₄²
prime radical	C₂³×C₃	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#322	C₂	semidirect
3. C₃×C₈²	C₂	semidirect
4. #1454	C₃	direct (N × H)
11. #322	C₂×C₃	semidirect
12. C₈²	C₂×C₃	semidirect
50. C₃	#1454	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×#431	2
C₃×#322	2
C₃×C₈²	2
#1454	3

Subgroups — C3×#1454 #72169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1454 #72169