Subgroups — C₃×#1420 #67980

Order 384.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₃×M₆₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#368	C₂	1	1	yes	maximal, characteristic
4	#1420	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₁₆	—	2	1	no	—
6	C₃×Q₃₂	—	2	1	no	—
7	C₃×Q₃₂	C₄	1	2	yes	—
8	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₃×#108	—	2	1	no	—
10	C₃×C₃₂	—	2	1	no	—
11	C₂×Q₃₂	C₂×C₃	1	1	yes	characteristic
12	M₆₄	C₂×C₃	1	1	yes	characteristic
13	#368	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×Q₈	—	4	1	no	—
15	C₃×Q₁₆	—	2	2	no	—
16	C₃×Q₁₆	—	4	1	no	—
17	C₃×M₁₆	—	4	1	no	—
18	C₂×C₃×C₈	D₄	1	1	yes	characteristic
19	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₃×C₁₆	D₄	1	1	yes	characteristic
21	C₂×Q₁₆	—	2	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	C₃×C₄	1	2	yes	—
24	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
25	#108	—	2	1	no	—
26	C₃₂	—	2	1	no	—
27	C₃×Q₈	—	4	2	no	—
28	C₃×Q₈	—	8	1	no	—
29	C₂×C₃×C₄	—	8	1	no	—
30	C₂×C₃×C₄	D₈	1	1	yes	characteristic
31	C₃×C₈	—	8	1	no	—
32	C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
33	C₃×C₈	SD₁₆	1	1	yes	characteristic
34	C₂×Q₈	—	4	1	no	—
35	Q₁₆	—	2	2	no	—
36	Q₁₆	—	4	1	no	—
37	M₁₆	—	4	1	no	—
38	C₂×C₈	C₃×D₄	1	1	yes	characteristic
39	C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
40	C₁₆	C₃×D₄	1	1	yes	characteristic
41	C₂²×C₃	SD₃₂	1	1	yes	characteristic
42	C₃×C₄	—	8	2	no	—
43	C₃×C₄	#102	1	1	yes	characteristic
44	C₃×C₄	D₁₆	1	1	yes	characteristic
45	Q₈	—	4	2	no	—
46	Q₈	—	8	1	no	—
47	C₂×C₄	—	8	1	no	—
48	C₂×C₄	C₃×D₈	1	1	yes	characteristic
49	C₈	—	8	1	no	—
50	C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
51	C₈	C₃×SD₁₆	1	1	yes	characteristic
52	C₂×C₃	—	2	1	no	—
53	C₂×C₃	#357	1	1	yes	characteristic
54	C₂²	C₃×SD₃₂	1	1	yes	characteristic
55	C₄	—	8	2	no	—
56	C₄	C₃×#102	1	1	yes	characteristic
57	C₄	C₃×D₁₆	1	1	yes	characteristic
58	C₃	#1420	1	1	yes	characteristic, direct product factor, Sylow
59	C₂	—	2	1	no	—
60	C₂	C₃×#357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#357
commutator	C₁₆	C₂×C₃×C₄
Frattini, cosocle	C₂×C₁₆	C₂²×C₃
prime radical	C₂²×C₃	SD₃₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1420	C₃	direct (N × H)
58. C₃	#1420	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×Q₃₂	2
C₃×M₆₄	2
C₃×#368	2
#1420	3

Subgroups — C3×#1420 #67980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1420 #67980