Subgroups — C₃×#1363 #67923

Order 384.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#499	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#334	C₂	1	1	yes	maximal, characteristic
4	#1363	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×#125	—	2	1	no	—
6	C₂×C₃×C₁₆	—	2	1	no	—
7	C₃×#107	C₄	1	1	yes	characteristic
8	C₃×#107	C₄	1	1	yes	characteristic
9	C₃×#106	—	2	1	no	—
10	C₃×C₄⋊C₈	—	2	1	no	—
11	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
12	#499	C₂×C₃	1	1	yes	characteristic
13	C₄⋊C₁₆	C₂×C₃	1	1	yes	characteristic
14	#334	C₂×C₃	1	1	yes	characteristic
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	1	no	—
19	C₃×C₄⋊C₄	—	2	1	no	—
20	C₃×C₄⋊C₄	—	4	1	no	—
21	C₃×C₄⋊C₄	—	4	1	no	—
22	C₃×C₄²	D₄	1	1	yes	characteristic
23	C₃×C₁₆	—	4	1	no	—
24	#125	—	2	1	no	—
25	C₂×C₁₆	—	2	1	no	—
26	#107	C₃×C₄	1	1	yes	characteristic
27	#107	C₃×C₄	1	1	yes	characteristic
28	#106	—	2	1	no	—
29	C₄⋊C₈	—	2	1	no	—
30	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₃×C₄	—	4	1	no	—
32	C₂×C₃×C₄	—	4	1	no	—
33	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₃×C₄	D₈	1	1	yes	characteristic
35	C₂×C₃×C₄	SD₁₆	1	1	yes	characteristic
36	C₃×C₈	—	2	1	no	—
37	C₃×C₈	—	8	1	no	—
38	C₃×C₈	SD₁₆	1	1	yes	characteristic
39	C₃×C₈	Q₁₆	1	1	yes	characteristic
40	C₂×C₈	—	4	1	no	—
41	C₂×C₈	C₂×C₃×C₄	1	1	yes	characteristic
42	C₂×C₈	C₃×D₄	1	1	yes	characteristic
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	2	1	no	—
45	C₄⋊C₄	—	4	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₄²	C₃×D₄	1	1	yes	characteristic
48	C₁₆	—	4	1	no	—
49	C₂²×C₃	#102	1	1	yes	characteristic
50	C₃×C₄	—	2	1	no	—
51	C₃×C₄	—	2	1	no	—
52	C₃×C₄	—	8	1	no	—
53	C₃×C₄	—	8	1	no	—
54	C₃×C₄	#101	1	1	yes	characteristic
55	C₃×C₄	#103	1	1	yes	characteristic
56	C₂×C₄	—	4	1	no	—
57	C₂×C₄	—	4	1	no	—
58	C₂×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₄	C₃×D₈	1	1	yes	characteristic
60	C₂×C₄	C₃×SD₁₆	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	8	1	no	—
63	C₈	C₃×SD₁₆	1	1	yes	characteristic
64	C₈	C₃×Q₁₆	1	1	yes	characteristic
65	C₂×C₃	#332	1	1	yes	characteristic
66	C₂×C₃	#359	1	1	yes	characteristic
67	C₂×C₃	#360	1	1	yes	characteristic
68	C₂²	C₃×#102	1	1	yes	characteristic
69	C₄	—	2	1	no	—
70	C₄	—	2	1	no	—
71	C₄	—	8	1	no	—
72	C₄	—	8	1	no	—
73	C₄	C₃×#101	1	1	yes	characteristic
74	C₄	C₃×#103	1	1	yes	characteristic
75	C₃	#1363	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	C₃×#332	1	1	yes	characteristic
77	C₂	C₃×#359	1	1	yes	characteristic
78	C₂	C₃×#360	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. #1363	C₃	direct (N × H)
75. C₃	#1363	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×#499	2
C₃×C₄⋊C₁₆	2
C₃×#334	2
#1363	3

Subgroups — C3×#1363 #67923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1363 #67923