Subgroups — #63421

Order 288.

45 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic
2	#835	—	3	1	no	maximal
3	C₂×Dic₉	—	4	1	no	maximal
4	Q₈⋊C₉	C₄	1	1	yes	characteristic, complemented
5	C₂×C₃×Q₈	D₃	1	1	yes	characteristic
6	C₄⋊Dic₃	—	3	1	no	—
7	C₂×C₃⋊C₈	—	3	1	no	—
8	C₂²×C₉	—	4	1	no	—
9	Dic₉	—	4	2	no	—
10	#103	—	9	1	no	Sylow
11	C₃×Q₈	—	3	1	no	—
12	C₃×Q₈	Dic₃	1	1	yes	characteristic
13	C₂×C₃×C₄	—	3	1	no	—
14	C₂×Dic₃	—	6	1	no	—
15	C₃⋊C₈	—	6	1	no	—
16	C₂×C₉	—	4	1	no	—
17	C₂×C₉	—	4	1	no	—
18	C₂×C₉	—	4	1	no	—
19	C₂×Q₈	D₉	1	1	yes	characteristic
20	C₂×C₈	—	9	1	no	—
21	C₄⋊C₄	—	9	1	no	—
22	C₂²×C₃	S₄	1	1	yes	characteristic
23	C₃×C₄	—	3	1	no	—
24	C₃×C₄	—	3	1	no	—
25	Dic₃	—	12	1	no	—
26	C₉	—	4	1	no	Sylow
27	Q₈	—	3	1	no	—
28	Q₈	Dic₉	1	1	yes	characteristic, complemented
29	C₂×C₄	—	3	1	no	—
30	C₂×C₄	—	18	1	no	—
31	C₈	—	18	1	no	—
32	C₂×C₃	#226	1	1	yes	characteristic
33	C₂×C₃	GL(2,𝔽₃)	1	1	yes	characteristic
34	C₂×C₃	SL(2,ℤ/4)	1	1	yes	characteristic
35	C₂²	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
36	C₄	—	3	1	no	—
37	C₄	—	3	1	no	—
38	C₄	—	36	1	no	—
39	C₃	#859	1	1	yes	characteristic
40	C₂	#3688	1	1	yes	characteristic
41	C₂	#3689	1	1	yes	characteristic
42	C₂	(C₂²⋊C₉)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	(C₂²⋊C₉)⋊C₂
commutator, hypocenter	Q₈⋊C₉	C₄
Frattini, socle, prime radical	C₂²×C₃	S₄
Fitting	C₂×C₃×Q₈	D₃
cosocle	C₂×Q₈⋊C₉	C₂
LCS	G ▷ Q₈⋊C₉
UCS	C₁ ◁ C₂²

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

N	H ≅ G/N	type
4. Q₈⋊C₉	C₄	semidirect
28. Q₈	Dic₉	semidirect

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