Subgroups — #10588164

Order 576.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#106	C₂	1	1	yes	maximal, characteristic
2	#63372	C₂	1	1	yes	maximal, characteristic
3	#63371	C₂	1	1	yes	maximal, characteristic
4	#4487	—	3	1	no	maximal
5	C₂×C₈×C₉	C₂²	1	1	yes	characteristic
6	C₉×C₄⋊C₄	—	2	1	no	—
7	#3667	—	2	1	no	—
8	C₉⋊C₁₆	C₄	1	2	yes	complemented
9	C₃×#106	D₃	1	1	yes	characteristic
10	#819	—	3	1	no	—
11	#812	—	3	1	no	—
12	C₂×C₄×C₉	—	4	1	no	—
13	C₂×C₄×C₉	D₄	1	1	yes	characteristic
14	C₈×C₉	C₂×C₄	1	1	yes	characteristic
15	C₈×C₉	Q₈	1	1	yes	characteristic
16	C₉⋊C₈	—	4	1	no	—
17	#365	—	9	1	no	Sylow
18	C₂×C₃×C₈	C₂×D₃	1	1	yes	characteristic
19	C₃×C₄⋊C₄	—	2	1	no	—
20	#208	—	6	1	no	—
21	C₃⋊C₁₆	—	3	2	no	—
22	C₂²×C₉	SD₁₆	1	1	yes	characteristic
23	C₄×C₉	—	8	1	no	—
24	C₄×C₉	C₄⋊C₄	1	1	yes	characteristic
25	C₄×C₉	SD₁₆	1	1	yes	characteristic
26	M₃₂	—	9	1	no	—
27	#108	—	9	1	no	—
28	#106	D₉	1	1	yes	characteristic
29	C₂×C₃×C₄	—	4	1	no	—
30	C₂×C₃×C₄	#67	1	1	yes	characteristic
31	C₃×C₈	Dic₆	1	1	yes	characteristic
32	C₃×C₈	C₄×D₃	1	1	yes	characteristic
33	C₃⋊C₈	—	12	1	no	—
34	C₂×C₉	—	2	1	no	—
35	C₂×C₉	#106	1	1	yes	characteristic
36	M₁₆	—	18	1	no	—
37	C₂×C₈	C₂×D₉	1	1	yes	characteristic
38	C₄⋊C₄	—	2	1	no	—
39	C₁₆	—	9	2	no	—
40	C₂²×C₃	#214	1	1	yes	characteristic
41	C₃×C₄	—	8	1	no	—
42	C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
43	C₃×C₄	#215	1	1	yes	characteristic
44	C₉	#365	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₄	—	4	1	no	—
46	C₂×C₄	#611	1	1	yes	characteristic
47	C₈	—	36	1	no	—
48	C₈	Dic₁₈	1	1	yes	characteristic
49	C₈	C₄×D₉	1	1	yes	characteristic
50	C₂×C₃	—	2	1	no	—
51	C₂×C₃	#808	1	1	yes	characteristic
52	C₂²	#3672	1	1	yes	characteristic
53	C₄	—	8	1	no	—
54	C₄	Dic₉⋊C₄	1	1	yes	characteristic
55	C₄	#3675	1	1	yes	characteristic
56	C₃	#4487	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#63367	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#63367
commutator	C₈×C₉	C₂×C₄
Frattini	C₂×C₃×C₈	C₂×D₃
Fitting	C₉×#106	C₂
socle	C₂×C₃	#808
prime radical	C₂²×C₃	#214
cosocle	C₂×C₈×C₉	C₂²
hypercenter	#106	D₉
hypocenter	C₉	#365
LCS	G ▷ C₈×C₉ ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
8. C₉⋊C₁₆	C₄	semidirect
44. C₉	#365	semidirect

Maximal subgroups

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

subgroup	index
C₉×#106	2
#63372	2
#63371	2
#4487	3