Subgroups — #10588170

Order 576.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#108	C₂	1	1	yes	maximal, characteristic
2	#63372	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#4493	—	3	1	no	maximal
5	C₉×M₁₆	—	2	1	no	—
6	C₂×C₈×C₉	C₂²	1	1	yes	characteristic
7	#3667	—	2	1	no	—
8	C₉⋊C₁₆	C₄	1	2	yes	—
9	C₃×#108	D₃	1	1	yes	characteristic
10	#819	—	3	1	no	—
11	C₂×C₃⋊C₁₆	—	3	1	no	—
12	C₂×C₄×C₉	D₄	1	1	yes	characteristic
13	C₈×C₉	—	4	1	no	—
14	C₈×C₉	C₂×C₄	1	1	yes	characteristic
15	C₈×C₉	Q₈	1	1	yes	characteristic
16	C₉⋊C₈	—	4	1	no	—
17	#368	—	9	1	no	Sylow
18	C₃×M₁₆	—	2	1	no	—
19	C₂×C₃×C₈	C₂×D₃	1	1	yes	characteristic
20	#208	—	6	1	no	—
21	C₃⋊C₁₆	—	3	2	no	—
22	C₂²×C₉	Q₁₆	1	1	yes	characteristic
23	C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
24	C₄×C₉	D₈	1	1	yes	characteristic
25	C₂×C₁₆	—	9	1	no	—
26	#108	—	9	1	no	—
27	#108	D₉	1	1	yes	characteristic
28	C₂×C₃×C₄	#67	1	1	yes	characteristic
29	C₃×C₈	—	4	1	no	—
30	C₃×C₈	Dic₆	1	1	yes	characteristic
31	C₃×C₈	C₄×D₃	1	1	yes	characteristic
32	C₃⋊C₈	—	12	1	no	—
33	C₂×C₉	—	2	1	no	—
34	C₂×C₉	#107	1	1	yes	characteristic
35	M₁₆	—	2	1	no	—
36	M₁₆	—	18	1	no	—
37	C₂×C₈	C₂×D₉	1	1	yes	characteristic
38	C₁₆	—	9	2	no	—
39	C₂²×C₃	#216	1	1	yes	characteristic
40	C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
41	C₃×C₄	#213	1	1	yes	characteristic
42	C₉	#368	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₄	#611	1	1	yes	characteristic
44	C₈	—	4	1	no	—
45	C₈	—	36	1	no	—
46	C₈	Dic₁₈	1	1	yes	characteristic
47	C₈	C₄×D₉	1	1	yes	characteristic
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	#807	1	1	yes	characteristic
50	C₂²	#3674	1	1	yes	characteristic
51	C₄	Dic₉⋊C₄	1	1	yes	characteristic
52	C₄	#3673	1	1	yes	characteristic
53	C₃	#4493	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	#63366	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#3673
commutator	C₈×C₉	C₂×C₄
Frattini	C₂×C₃×C₈	C₂×D₃
Fitting	C₉×#108	C₂
socle	C₂×C₃	#807
prime radical	C₂²×C₃	#216
cosocle	C₂×C₈×C₉	C₂²
hypercenter	#108	D₉
hypocenter	C₉	#368
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #108

Complements

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

N	H ≅ G/N	type
42. C₉	#368	semidirect

Maximal subgroups

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

subgroup	index
C₉×#108	2
#63372	2
C₂×C₉⋊C₁₆	2
#4493	3