Subgroups — C₃×#1373 #67933

Order 384.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#364	C₂	1	2	yes	maximal
2	C₃×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
3	#1373	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃×M₃₂	—	2	2	no	—
5	C₂×C₃×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₃×C₁₆	C₄	1	1	yes	characteristic
7	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
8	#364	C₂×C₃	1	2	yes	—
9	C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
11	C₂×C₃×C₈	D₄	1	1	yes	characteristic
12	C₃×C₄²	Q₈	1	1	yes	characteristic
13	C₃×C₁₆	—	2	1	no	—
14	C₃×C₁₆	—	4	2	no	—
15	C₃×C₁₆	C₈	1	2	yes	—
16	M₃₂	—	2	2	no	—
17	C₂×C₁₆	C₃×C₄	1	1	yes	characteristic
18	C₂×C₁₆	C₃×C₄	1	1	yes	characteristic
19	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₃×C₄	—	2	1	no	—
21	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
22	C₃×C₈	C₂×C₈	1	1	yes	characteristic
23	C₃×C₈	M₁₆	1	1	yes	characteristic
24	C₃×C₈	D₈	1	1	yes	characteristic
25	C₃×C₈	Q₁₆	1	1	yes	characteristic
26	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
27	C₂×C₈	C₃×D₄	1	1	yes	characteristic
28	C₄²	C₃×Q₈	1	1	yes	characteristic
29	C₁₆	—	2	1	no	—
30	C₁₆	—	4	2	no	—
31	C₁₆	C₃×C₈	1	2	yes	—
32	C₂²×C₃	#108	1	1	yes	characteristic
33	C₃×C₄	—	2	2	no	—
34	C₃×C₄	C₄⋊C₈	1	1	yes	characteristic
35	C₃×C₄	#107	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₃×C₄⋊C₄	1	1	yes	characteristic
38	C₈	C₂×C₃×C₈	1	1	yes	characteristic
39	C₈	C₃×M₁₆	1	1	yes	characteristic
40	C₈	C₃×D₈	1	1	yes	characteristic
41	C₈	C₃×Q₁₆	1	1	yes	characteristic
42	C₂×C₃	—	2	1	no	—
43	C₂×C₃	#335	1	1	yes	characteristic
44	C₂²	C₃×#108	1	1	yes	characteristic
45	C₄	—	2	2	no	—
46	C₄	C₃×C₄⋊C₈	1	1	yes	characteristic
47	C₄	C₃×#107	1	1	yes	characteristic
48	C₃	#1373	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	2	1	no	—
50	C₂	C₃×#335	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₈	D₈
commutator	C₈	C₂×C₃×C₈
Frattini, cosocle	C₄×C₈	C₂²×C₃
socle	C₂×C₃	#335
prime radical	C₂²×C₃	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₈ ◁ C₂×C₃×C₈ ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. #1373	C₃	direct (N × H)
48. C₃	#1373	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×#364	2
C₃×C₄×C₁₆	2
#1373	3

Subgroups — C3×#1373 #67933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1373 #67933