Subgroups — #63396

Order 288.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#41	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#3667	C₂	1	1	yes	maximal, characteristic, complemented
4	#837	—	3	1	no	maximal
5	Q₈×C₉	C₄	1	1	yes	characteristic, complemented
6	D₄×C₉	—	2	1	no	—
7	D₄×C₉	C₄	1	1	yes	characteristic, complemented
8	C₂×C₄×C₉	—	2	1	no	—
9	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₉	—	2	1	no	—
11	C₉⋊C₈	—	2	1	no	—
12	C₃×#41	D₃	1	1	yes	characteristic
13	C₄×Dic₃	—	3	1	no	—
14	#208	—	3	1	no	—
15	C₂²×C₉	—	2	1	no	—
16	C₂²×C₉	D₄	1	1	yes	characteristic
17	C₄×C₉	—	2	1	no	—
18	C₄×C₉	C₂×C₄	1	1	yes	characteristic
19	C₄×C₉	D₄	1	1	yes	characteristic
20	Dic₉	—	2	2	no	—
21	#104	—	9	1	no	Sylow
22	C₃×Q₈	Dic₃	1	1	yes	characteristic
23	C₃×D₄	—	2	1	no	—
24	C₃×D₄	Dic₃	1	1	yes	characteristic
25	C₂×C₃×C₄	—	2	1	no	—
26	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
27	C₂×Dic₃	—	6	1	no	—
28	C₃⋊C₈	—	6	1	no	—
29	C₂×C₉	—	2	1	no	—
30	C₂×C₉	—	4	1	no	—
31	C₂×C₉	C₂²⋊C₄	1	1	yes	characteristic
32	#41	D₉	1	1	yes	characteristic
33	M₁₆	—	9	1	no	—
34	C₄²	—	9	1	no	—
35	C₂²×C₃	—	2	1	no	—
36	C₂²×C₃	#67	1	1	yes	characteristic
37	C₃×C₄	—	2	1	no	—
38	C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
39	C₃×C₄	#67	1	1	yes	characteristic
40	Dic₃	—	6	2	no	—
41	C₉	#104	1	1	yes	characteristic, complemented, Sylow
42	Q₈	Dic₉	1	1	yes	characteristic, complemented
43	D₄	—	2	1	no	—
44	D₄	Dic₉	1	1	yes	characteristic, complemented
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	18	1	no	—
47	C₂×C₄	C₂×D₉	1	1	yes	characteristic
48	C₈	—	18	1	no	—
49	C₂×C₃	—	2	1	no	—
50	C₂×C₃	—	4	1	no	—
51	C₂×C₃	#217	1	1	yes	characteristic
52	C₂²	—	2	1	no	—
53	C₂²	#611	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	18	2	no	—
56	C₄	C₂×Dic₉	1	1	yes	characteristic
57	C₄	#611	1	1	yes	characteristic
58	C₃	#837	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	—	4	1	no	—
61	C₂	#3676	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#611
commutator	C₄×C₉	C₂×C₄
Frattini	C₂×C₃×C₄	C₂×D₃
Fitting	C₉×#41	C₂
socle	C₂×C₃	#217
prime radical	C₃×#41	D₃
cosocle	C₂×C₄×C₉	C₂²
hypercenter	#41	D₉
hypocenter	C₉	#104
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
2. C₄×Dic₉	C₂	semidirect
3. #3667	C₂	semidirect
5. Q₈×C₉	C₄	semidirect
7. D₄×C₉	C₄	semidirect
41. C₉	#104	semidirect
42. Q₈	Dic₉	semidirect
44. D₄	Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×#41	2
C₄×Dic₉	2
#3667	2
#837	3