Subgroups — #63366

Order 288.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²	#611
commutator	C₄×C₉	C₂×C₄
Frattini	C₂×C₃×C₄	C₂×D₃
Fitting	C₉×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃	#67
cosocle	C₂×C₄×C₉	C₂²
hypercenter	C₄⋊C₄	D₉
hypocenter	C₉	#107
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
8. C₉⋊C₈	C₄	semidirect
33. C₉	#107	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₄⋊C₄	2
C₄⋊Dic₉	2
C₂×C₉⋊C₈	2
#807	3