Subgroups — #10589144

Order 576.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₃×#819	C₂	1	2	yes	maximal
3	#4493	—	3	2	no	maximal
4	C₂×C₃²×C₈	C₂²	1	1	yes	characteristic
5	C₃×#208	—	2	2	no	—
6	C₃⋊(C₃⋊C₁₆)	C₄	1	2	yes	—
7	C₃×#108	—	3	2	no	—
8	#819	D₃	1	2	yes	—
9	C₂×C₃⋊C₁₆	—	3	2	no	—
10	C₂×C₃⋊C₁₆	—	6	1	no	—
11	C₂×C₃²×C₄	D₄	1	1	yes	characteristic
12	C₃²×C₈	C₂×C₄	1	1	yes	characteristic
13	C₃²×C₈	Q₈	1	1	yes	characteristic
14	C₃×C₃⋊C₈	—	4	2	no	—
15	#368	—	9	1	no	Sylow
16	C₃×M₁₆	—	6	2	no	—
17	C₂×C₃×C₈	—	2	1	no	—
18	C₂×C₃×C₈	C₂×D₃	1	2	yes	—
19	#208	—	2	2	no	—
20	C₃⋊C₁₆	—	3	4	no	—
21	C₃⋊C₁₆	—	6	2	no	—
22	C₂²×C₃²	Q₁₆	1	1	yes	characteristic
23	C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
24	C₃²×C₄	D₈	1	1	yes	characteristic
25	C₂×C₁₆	—	9	1	no	—
26	#108	—	3	2	no	—
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	#67	1	2	yes	—
29	C₃×C₈	—	2	1	no	—
30	C₃×C₈	—	2	1	no	—
31	C₃×C₈	—	12	2	no	—
32	C₃×C₈	Dic₆	1	2	yes	—
33	C₃×C₈	C₄×D₃	1	2	yes	—
34	C₃⋊C₈	—	4	2	no	—
35	C₂×C₃²	—	2	1	no	—
36	C₂×C₃²	#107	1	1	yes	characteristic
37	M₁₆	—	6	2	no	—
38	C₂×C₈	D₃²	1	1	yes	characteristic
39	C₁₆	—	9	2	no	—
40	C₂²×C₃	—	2	1	no	—
41	C₂²×C₃	#216	1	2	yes	—
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	—	2	1	no	—
44	C₃×C₄	Dic₃⋊C₄	1	2	yes	—
45	C₃×C₄	#213	1	2	yes	—
46	C₃²	#368	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄	#625	1	1	yes	characteristic
48	C₈	—	12	2	no	—
49	C₈	#624	1	1	yes	characteristic
50	C₈	#627	1	1	yes	characteristic
51	C₂×C₃	—	2	2	no	—
52	C₂×C₃	—	2	2	no	—
53	C₂×C₃	—	2	1	no	—
54	C₂×C₃	#807	1	2	yes	—
55	C₂²	#3718	1	1	yes	characteristic
56	C₄	#3713	1	1	yes	characteristic
57	C₄	#3724	1	1	yes	characteristic
58	C₃	—	2	1	no	—
59	C₃	#4493	1	2	yes	complemented
60	C₂	—	2	1	no	—
61	C₂	#63576	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#3713
commutator	C₃²×C₈	C₂×C₄
Frattini, hypercenter	C₂×C₈	D₃²
Fitting, cosocle	C₂×C₃²×C₈	C₂²
socle	C₂×C₃²	#107
prime radical	C₂²×C₃²	Q₁₆
hypocenter	C₃²	#368
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
46. C₃²	#368	semidirect
59. C₃	#4493	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊(C₃⋊C₁₆)	2
C₃×#819	2
#4493	3