Subgroups — #10593637

Order 576.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64265	C₂	1	2	yes	maximal
2	C₃×#131⋊C₃	C₂	1	1	yes	maximal, characteristic
3	#5403	—	3	3	no	maximal
4	#5143	—	3	1	no	maximal
5	C₃×#41⋊C₃	C₂²	1	1	yes	characteristic
6	C₃⋊#226	—	2	2	no	—
7	#3746	—	4	1	no	maximal
8	#984	—	3	6	no	—
9	C₃×#131	D₃	1	1	yes	characteristic
10	#951	—	3	2	no	—
11	C₂×Dic₁₂	—	3	1	no	—
12	#131⋊C₃	D₃	1	3	yes	—
13	#824	—	3	2	no	—
14	#819	—	3	1	no	—
15	#634	—	4	2	no	—
16	C₃×SL(2,𝔽₃)	D₄	1	1	yes	characteristic
17	C₃²×C₈	—	4	1	no	—
18	#473	—	9	1	no	Sylow
19	C₃×#41	C₂×D₃	1	1	yes	characteristic
20	C₂×Dic₆	—	3	2	no	—
21	#41⋊C₃	C₂×D₃	1	3	yes	—
22	#226	—	6	6	no	—
23	C₃×M₁₆	—	3	1	no	—
24	C₂×C₃×C₈	—	3	1	no	—
25	#216	—	6	2	no	—
26	#214	—	6	2	no	—
27	#208	—	3	2	no	—
28	Dic₁₂	—	6	1	no	—
29	Dic₁₂	—	6	1	no	—
30	Dic₁₂	—	12	3	no	—
31	C₃²×C₄	—	4	1	no	—
32	C₃⋊Dic₃	—	8	2	no	—
33	#137	—	9	2	no	—
34	C₂×Q₁₆	—	9	1	no	—
35	#131	C₃⋊D₃	1	1	yes	characteristic
36	#108	—	9	1	no	—
37	#101	—	9	2	no	—
38	C₃×Q₈	D₁₂	1	1	yes	characteristic
39	C₃×D₄	—	3	1	no	—
40	C₂×C₃×C₄	—	3	1	no	—
41	C₂×Dic₃	—	6	2	no	—
42	Dic₆	—	6	2	no	—
43	Dic₆	—	6	2	no	—
44	Dic₆	—	12	6	no	—
45	SL(2,𝔽₃)	D₁₂	1	3	yes	—
46	C₃×C₈	—	3	1	no	—
47	C₃×C₈	—	4	3	no	—
48	C₃×C₈	S₄	1	1	yes	characteristic
49	C₃⋊C₈	—	6	2	no	—
50	C₂×C₃²	—	4	1	no	—
51	#41	C₂×C₃⋊D₃	1	1	yes	characteristic
52	C₂×Q₈	—	9	2	no	—
53	Q₁₆	—	18	1	no	—
54	Q₁₆	—	18	2	no	—
55	Q₁₆	—	18	1	no	—
56	SD₁₆	—	18	2	no	—
57	M₁₆	—	3	1	no	—
58	M₁₆	—	9	2	no	—
59	C₂×C₈	—	3	1	no	—
60	C₂²×C₃	—	3	1	no	—
61	C₃×C₄	—	3	1	no	—
62	C₃×C₄	—	4	3	no	—
63	C₃×C₄	C₂×S₄	1	1	yes	characteristic
64	Dic₃	—	12	2	no	—
65	Dic₃	—	24	6	no	—
66	C₃²	—	4	1	no	Sylow
67	Q₈	—	18	2	no	—
68	Q₈	—	18	2	no	—
69	Q₈	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
70	D₄	—	3	1	no	—
71	C₂×C₄	—	3	1	no	—
72	C₂×C₄	—	18	2	no	—
73	C₈	—	3	1	no	—
74	C₈	—	18	2	no	—
75	C₈	C₃⋊S₄	1	1	yes	characteristic
76	C₂×C₃	—	4	3	no	—
77	C₂×C₃	—	6	1	no	—
78	C₂×C₃	C₄⋊S₄	1	1	yes	characteristic
79	C₂²	—	3	1	no	—
80	C₄	—	3	1	no	—
81	C₄	—	36	2	no	—
82	C₄	C₂×C₃⋊S₄	1	1	yes	characteristic
83	C₃	—	4	3	no	—
84	C₃	#5403	1	1	yes	characteristic, complemented
85	C₂	—	6	1	no	—
86	C₂	C₄⋊(C₃⋊S₄)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
84. C₃	#5403	semidirect

Maximal subgroups

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

subgroup	index
#64265	2
C₃×#131⋊C₃	2
#5403	3
#5143	3
#3746	4