Subgroups — C₃×#5403 #10593589

Order 576.

125 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#984	C₂	1	2	yes	maximal
2	C₃×#131⋊C₃	C₂	1	1	yes	maximal, characteristic
3	#5403	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×#473	—	3	1	no	maximal
5	C₃×#41⋊C₃	C₂²	1	1	yes	characteristic
6	C₃×#226	—	2	2	no	—
7	C₃×Dic₁₂	—	4	1	no	maximal
8	#984	C₂×C₃	1	2	yes	—
9	C₃×#137	—	3	2	no	—
10	C₂×C₃×Q₁₆	—	3	1	no	—
11	C₃×#131	D₃	1	1	yes	characteristic
12	#131⋊C₃	—	2	1	no	—
13	#131⋊C₃	C₂×C₃	1	1	yes	characteristic
14	C₃×#108	—	3	1	no	—
15	C₃×#101	—	3	2	no	—
16	C₃×Dic₆	—	4	2	no	—
17	C₃×SL(2,𝔽₃)	D₄	1	1	yes	characteristic
18	C₃²×C₈	—	4	1	no	—
19	#473	—	3	1	no	Sylow
20	C₃×#41	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃×Q₈	—	3	2	no	—
22	#41⋊C₃	—	2	1	no	—
23	#41⋊C₃	C₂²×C₃	1	1	yes	characteristic
24	#226	—	2	2	no	—
25	C₃×Q₁₆	—	6	1	no	—
26	C₃×Q₁₆	—	6	2	no	—
27	C₃×Q₁₆	—	6	1	no	—
28	C₃×SD₁₆	—	6	2	no	—
29	C₃×M₁₆	—	3	1	no	—
30	C₃×M₁₆	—	3	2	no	—
31	C₂×C₃×C₈	—	3	1	no	—
32	Dic₁₂	—	4	1	no	—
33	C₃²×C₄	—	4	1	no	—
34	C₃×Dic₃	—	8	2	no	—
35	#137	—	3	2	no	—
36	C₂×Q₁₆	—	3	1	no	—
37	#131	C₃×D₃	1	1	yes	characteristic
38	#108	—	3	1	no	—
39	#101	—	3	2	no	—
40	C₃×Q₈	—	6	2	no	—
41	C₃×Q₈	—	6	2	no	—
42	C₃×Q₈	D₁₂	1	1	yes	characteristic
43	C₃×D₄	—	3	1	no	—
44	C₂×C₃×C₄	—	3	1	no	—
45	C₂×C₃×C₄	—	6	2	no	—
46	Dic₆	—	4	2	no	—
47	SL(2,𝔽₃)	—	2	1	no	—
48	SL(2,𝔽₃)	C₃×D₄	1	1	yes	characteristic
49	C₃×C₈	—	3	1	no	—
50	C₃×C₈	—	4	1	no	—
51	C₃×C₈	—	6	2	no	—
52	C₃×C₈	—	8	1	no	—
53	C₃×C₈	S₄	1	1	yes	characteristic
54	C₂×C₃²	—	4	1	no	—
55	#41	C₂×C₃×D₃	1	1	yes	characteristic
56	C₂×Q₈	—	3	2	no	—
57	Q₁₆	—	6	1	no	—
58	Q₁₆	—	6	2	no	—
59	Q₁₆	—	6	1	no	—
60	SD₁₆	—	6	2	no	—
61	M₁₆	—	3	1	no	—
62	M₁₆	—	3	2	no	—
63	C₂×C₈	—	3	1	no	—
64	C₂²×C₃	—	3	1	no	—
65	C₃×C₄	—	3	1	no	—
66	C₃×C₄	—	4	1	no	—
67	C₃×C₄	—	8	1	no	—
68	C₃×C₄	—	12	2	no	—
69	C₃×C₄	C₂×S₄	1	1	yes	characteristic
70	Dic₃	—	8	2	no	—
71	C₃²	—	4	1	no	Sylow
72	Q₈	—	6	2	no	—
73	Q₈	—	6	2	no	—
74	Q₈	C₃×D₁₂	1	1	yes	characteristic
75	D₄	—	3	1	no	—
76	C₂×C₄	—	3	1	no	—
77	C₂×C₄	—	6	2	no	—
78	C₈	—	3	1	no	—
79	C₈	—	6	2	no	—
80	C₈	C₃×S₄	1	1	yes	characteristic
81	C₂×C₃	—	4	1	no	—
82	C₂×C₃	—	6	1	no	—
83	C₂×C₃	—	8	1	no	—
84	C₂×C₃	C₄⋊S₄	1	1	yes	characteristic
85	C₂²	—	3	1	no	—
86	C₄	—	3	1	no	—
87	C₄	—	12	2	no	—
88	C₄	C₂×C₃×S₄	1	1	yes	characteristic
89	C₃	—	4	1	no	—
90	C₃	—	8	1	no	—
91	C₃	#5403	1	1	yes	characteristic, direct product factor
92	C₂	—	6	1	no	—
93	C₂	C₃×C₄⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₄⋊S₄
commutator, cosocle	#41⋊C₃	C₂²×C₃
Frattini	C₄	C₂×C₃×S₄
Fitting	C₃×#131	D₃
prime radical	C₃×#41⋊C₃	C₂²
hypercenter	C₃×C₈	S₄
hypocenter	SL(2,𝔽₃)	C₃×D₄
LCS	G ▷ #41⋊C₃ ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
3. #5403	C₃	direct (N × H)
91. C₃	#5403	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×#984	2
C₃×#131⋊C₃	2
#5403	3
C₃×#473	3
C₃×Dic₁₂	4

Subgroups — C3×#5403 #10593589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#5403 #10593589