Subgroups — C₃×#1365 #67925

Order 384.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#335	C₂	1	1	yes	maximal, characteristic
4	#1365	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₄⋊Q₈	—	2	1	no	—
6	C₂×C₃×C₁₆	—	2	1	no	—
7	C₃×#107	—	2	1	no	—
8	C₃×#107	C₄	1	2	yes	—
9	C₃×C₄⋊C₈	—	2	1	no	—
10	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
11	#500	C₂×C₃	1	1	yes	characteristic
12	C₄⋊C₁₆	C₂×C₃	1	1	yes	characteristic
13	#335	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×Q₈	—	4	1	no	—
15	C₂×C₃×C₈	—	4	1	no	—
16	C₂×C₃×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₈	D₄	1	1	yes	characteristic
18	C₃×C₄⋊C₄	—	2	2	no	—
19	C₃×C₄⋊C₄	—	4	1	no	—
20	C₃×C₄²	D₄	1	1	yes	characteristic
21	C₃×C₁₆	—	4	1	no	—
22	C₄⋊Q₈	—	2	1	no	—
23	C₂×C₁₆	—	2	1	no	—
24	#107	—	2	1	no	—
25	#107	C₃×C₄	1	2	yes	—
26	C₄⋊C₈	—	2	1	no	—
27	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
28	C₃×Q₈	—	8	2	no	—
29	C₂×C₃×C₄	—	4	2	no	—
30	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₃×C₄	D₈	1	1	yes	characteristic
32	C₂×C₃×C₄	SD₁₆	1	1	yes	characteristic
33	C₃×C₈	—	2	1	no	—
34	C₃×C₈	—	8	1	no	—
35	C₃×C₈	SD₁₆	1	1	yes	characteristic
36	C₃×C₈	Q₁₆	1	1	yes	characteristic
37	C₂×Q₈	—	4	1	no	—
38	C₂×C₈	—	4	1	no	—
39	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
40	C₂×C₈	C₃×D₄	1	1	yes	characteristic
41	C₄⋊C₄	—	2	2	no	—
42	C₄⋊C₄	—	4	1	no	—
43	C₄²	C₃×D₄	1	1	yes	characteristic
44	C₁₆	—	4	1	no	—
45	C₂²×C₃	#102	1	1	yes	characteristic
46	C₃×C₄	—	2	1	no	—
47	C₃×C₄	—	8	2	no	—
48	C₃×C₄	#101	1	1	yes	characteristic
49	C₃×C₄	#103	1	1	yes	characteristic
50	C₃×C₄	SD₃₂	1	1	yes	characteristic
51	C₃×C₄	Q₃₂	1	1	yes	characteristic
52	Q₈	—	8	2	no	—
53	C₂×C₄	—	4	2	no	—
54	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄	C₃×D₈	1	1	yes	characteristic
56	C₂×C₄	C₃×SD₁₆	1	1	yes	characteristic
57	C₈	—	2	1	no	—
58	C₈	—	8	1	no	—
59	C₈	C₃×SD₁₆	1	1	yes	characteristic
60	C₈	C₃×Q₁₆	1	1	yes	characteristic
61	C₂×C₃	#332	1	1	yes	characteristic
62	C₂×C₃	#358	1	1	yes	characteristic
63	C₂×C₃	#361	1	1	yes	characteristic
64	C₂²	C₃×#102	1	1	yes	characteristic
65	C₄	—	2	1	no	—
66	C₄	—	8	2	no	—
67	C₄	C₃×#101	1	1	yes	characteristic
68	C₄	C₃×#103	1	1	yes	characteristic
69	C₄	C₃×SD₃₂	1	1	yes	characteristic
70	C₄	C₃×Q₃₂	1	1	yes	characteristic
71	C₃	#1365	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	C₃×#332	1	1	yes	characteristic
73	C₂	C₃×#358	1	1	yes	characteristic
74	C₂	C₃×#361	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	#102
commutator	C₂×C₈	C₂×C₃×C₄
Frattini, cosocle	C₄×C₈	C₂²×C₃
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1365	C₃	direct (N × H)
71. C₃	#1365	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×#500	2
C₃×C₄⋊C₁₆	2
C₃×#335	2
#1365	3

Subgroups — C3×#1365 #67925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1365 #67925