Subgroups — C₃×#1450 #72165

Order 384.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#431	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#322	C₂	1	2	yes	maximal, complemented
4	C₃×C₈²	C₂	1	2	yes	maximal, complemented
5	#1450	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂²×C₃×C₈	C₄	1	2	yes	—
7	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₃×C₄⋊C₈	C₄	1	4	yes	—
9	C₃×C₂²⋊C₈	C₄	1	4	yes	—
10	C₃×C₄×C₈	C₄	1	2	yes	—
11	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄×C₈	C₂²	1	4	yes	—
13	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
14	#431	C₂×C₃	1	2	yes	—
15	C₂×C₄×C₈	C₂×C₃	1	1	yes	characteristic
16	#322	C₂×C₃	1	2	yes	complemented
17	C₈²	C₂×C₃	1	2	yes	complemented
18	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
19	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃×C₈	C₈	1	8	yes	complemented
21	C₂×C₃×C₈	C₂×C₄	1	8	yes	—
22	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
23	C₂×C₃×C₈	C₂×C₄	1	2	yes	—
24	C₃×C₄²	C₂×C₄	1	1	yes	characteristic
25	C₃×C₄²	C₂×C₄	1	2	yes	—
26	C₃×C₄²	C₂³	1	1	yes	characteristic
27	C₂²×C₈	C₃×C₄	1	2	yes	—
28	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
29	C₄⋊C₈	C₃×C₄	1	4	yes	—
30	C₂²⋊C₈	C₃×C₄	1	4	yes	—
31	C₄×C₈	C₃×C₄	1	2	yes	—
32	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
33	C₄×C₈	C₂²×C₃	1	4	yes	—
34	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
35	C₂³×C₃	C₄²	1	1	yes	characteristic
36	C₂×C₃×C₄	—	2	4	no	—
37	C₂×C₃×C₄	C₄²	1	2	yes	—
38	C₂×C₃×C₄	C₄²	1	1	yes	characteristic
39	C₂×C₃×C₄	C₂×C₈	1	4	yes	—
40	C₂×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄	C₂²×C₄	1	2	yes	—
42	C₃×C₈	—	2	8	no	—
43	C₃×C₈	C₂×C₈	1	4	yes	—
44	C₃×C₈	C₂×C₈	1	4	yes	—
45	C₂²×C₄	C₂×C₃×C₄	1	2	yes	—
46	C₂²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
47	C₂×C₈	C₃×C₈	1	8	yes	complemented
48	C₂×C₈	C₂×C₃×C₄	1	8	yes	—
49	C₂×C₈	C₂×C₃×C₄	1	2	yes	—
50	C₂×C₈	C₂×C₃×C₄	1	2	yes	—
51	C₄²	C₂×C₃×C₄	1	1	yes	characteristic
52	C₄²	C₂×C₃×C₄	1	2	yes	—
53	C₄²	C₂³×C₃	1	1	yes	characteristic
54	C₂²×C₃	—	2	2	no	—
55	C₂²×C₃	C₄×C₈	1	2	yes	—
56	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
57	C₃×C₄	—	2	2	no	—
58	C₃×C₄	C₄×C₈	1	2	yes	—
59	C₃×C₄	C₂²×C₈	1	2	yes	—
60	C₃×C₄	#131	1	4	yes	—
61	C₂³	C₃×C₄²	1	1	yes	characteristic
62	C₂×C₄	—	2	4	no	—
63	C₂×C₄	C₃×C₄²	1	2	yes	—
64	C₂×C₄	C₃×C₄²	1	1	yes	characteristic
65	C₂×C₄	C₂×C₃×C₈	1	4	yes	—
66	C₂×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
67	C₂×C₄	C₂²×C₃×C₄	1	2	yes	—
68	C₈	—	2	8	no	—
69	C₈	C₂×C₃×C₈	1	4	yes	—
70	C₈	C₂×C₃×C₈	1	4	yes	—
71	C₂×C₃	—	2	2	no	—
72	C₂×C₃	C₂×C₄×C₈	1	1	yes	characteristic
73	C₂×C₃	#405	1	2	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	C₃×C₄×C₈	1	2	yes	—
76	C₂²	C₂×C₃×C₄²	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	C₃×C₄×C₈	1	2	yes	—
79	C₄	C₂²×C₃×C₈	1	2	yes	—
80	C₄	C₃×#131	1	4	yes	—
81	C₃	#1450	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	—	2	2	no	—
83	C₂	C₂×C₃×C₄×C₈	1	1	yes	characteristic
84	C₂	C₃×#405	1	2	yes	—

	subgroup	G/H
center	C₃×C₄×C₈	C₂²
commutator	C₂	C₂×C₃×C₄×C₈
Frattini, cosocle	C₄²	C₂³×C₃
socle	C₂²×C₃	C₂×C₄²
prime radical	C₂³×C₃	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×#322	C₂	semidirect
4. C₃×C₈²	C₂	semidirect
5. #1450	C₃	direct (N × H)
16. #322	C₂×C₃	semidirect
17. C₈²	C₂×C₃	semidirect
20. C₂×C₃×C₈	C₈	semidirect
47. C₂×C₈	C₃×C₈	semidirect
81. C₃	#1450	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
C₂×C₃×C₄×C₈	2
C₃×#322	2
C₃×C₈²	2
#1450	3

Subgroups — C3×#1450 #72165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1450 #72165