Subgroups — C₃×#2070 #72785

Order 384.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#430	C₂	1	3	yes	maximal
2	C₂×C₃×#101	C₂	1	3	yes	maximal
3	C₃×#338	C₂	1	1	yes	maximal, characteristic
4	#2070	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic
6	C₂×C₃×M₁₆	C₂²	1	3	yes	—
7	C₂×C₃×M₁₆	C₂²	1	3	yes	—
8	C₃×#108	—	2	6	no	—
9	C₃×#101	—	2	6	no	—
10	#430	C₂×C₃	1	3	yes	—
11	C₂×#101	C₂×C₃	1	3	yes	—
12	#338	C₂×C₃	1	1	yes	characteristic
13	C₂×C₃×Q₈	—	2	3	no	—
14	C₂×C₃×Q₈	—	2	3	no	—
15	C₂²×C₃×C₄	Q₈	1	2	yes	—
16	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
17	C₃×M₁₆	—	2	3	no	—
18	C₃×M₁₆	—	2	3	no	—
19	C₃×M₁₆	—	2	3	no	—
20	C₃×M₁₆	D₄	1	6	yes	—
21	C₂×C₃×C₈	—	2	3	no	—
22	C₂×C₃×C₈	—	2	3	no	—
23	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic
24	C₂×M₁₆	C₂²×C₃	1	3	yes	—
25	C₂×M₁₆	C₂²×C₃	1	3	yes	—
26	#108	—	2	6	no	—
27	#101	—	2	6	no	—
28	C₂³×C₃	C₂×Q₈	1	1	yes	characteristic
29	C₃×Q₈	—	4	3	no	—
30	C₃×Q₈	—	4	1	no	—
31	C₂×C₃×C₄	—	2	6	no	—
32	C₂×C₃×C₄	C₂×D₄	1	3	yes	—
33	C₂×C₃×C₄	#41	1	3	yes	—
34	C₃×C₈	—	2	6	no	—
35	C₃×C₈	—	4	3	no	—
36	C₂×Q₈	—	2	3	no	—
37	C₂×Q₈	—	2	3	no	—
38	C₂²×C₄	C₃×Q₈	1	2	yes	—
39	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
40	M₁₆	—	2	3	no	—
41	M₁₆	—	2	3	no	—
42	M₁₆	—	2	3	no	—
43	M₁₆	C₃×D₄	1	6	yes	—
44	C₂×C₈	—	2	3	no	—
45	C₂×C₈	—	2	3	no	—
46	C₂²×C₃	—	4	1	no	—
47	C₂²×C₃	C₂²⋊Q₈	1	3	yes	—
48	C₃×C₄	—	4	2	no	—
49	C₃×C₄	#121	1	3	yes	—
50	C₃×C₄	#126	1	1	yes	characteristic
51	C₂³	C₂×C₃×Q₈	1	1	yes	characteristic
52	Q₈	—	4	3	no	—
53	Q₈	—	4	1	no	—
54	C₂×C₄	—	2	6	no	—
55	C₂×C₄	C₂×C₃×D₄	1	3	yes	—
56	C₂×C₄	C₃×#41	1	3	yes	—
57	C₈	—	2	6	no	—
58	C₈	—	4	3	no	—
59	C₂×C₃	—	2	3	no	—
60	C₂×C₃	#396	1	1	yes	characteristic
61	C₂²	—	4	1	no	—
62	C₂²	C₃×C₂²⋊Q₈	1	3	yes	—
63	C₄	—	4	2	no	—
64	C₄	C₃×#121	1	3	yes	—
65	C₄	C₃×#126	1	1	yes	characteristic
66	C₃	#2070	1	1	yes	characteristic, direct product factor, Sylow
67	C₂	—	2	3	no	—
68	C₂	C₃×#396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#396
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃
prime radical	C₂³×C₃	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
4. #2070	C₃	direct (N × H)
66. C₃	#2070	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×#430	2
C₂×C₃×#101	2
C₃×#338	2
#2070	3

Subgroups — C3×#2070 #72785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2070 #72785