Subgroups — C₃×#3688 #88597

Order 432.

49 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#216	—	3	1	no	maximal
3	#3688	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×Dic₉	—	4	1	no	maximal
5	C₃²×Q₈	D₃	1	1	yes	characteristic
6	C₃×Dic₆	—	3	1	no	—
7	C₃×C₃⋊C₈	—	3	1	no	—
8	Q₈⋊C₉	—	2	1	no	—
9	Q₈⋊C₉	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×C₉	—	4	1	no	—
11	C₃×Q₁₆	—	9	1	no	—
12	#216	—	3	1	no	—
13	C₃²×C₄	—	3	1	no	—
14	C₃×Dic₃	—	6	1	no	—
15	Dic₉	—	4	1	no	—
16	C₃×C₉	—	4	1	no	Sylow
17	C₃×Q₈	—	2	1	no	—
18	C₃×Q₈	—	9	1	no	—
19	C₃×Q₈	D₉	1	1	yes	characteristic
20	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
21	Dic₆	—	3	1	no	—
22	C₃×C₈	—	9	1	no	—
23	C₃⋊C₈	—	3	1	no	—
24	C₂×C₃²	S₄	1	1	yes	characteristic
25	C₂×C₉	—	4	1	no	—
26	C₂×C₉	—	8	1	no	—
27	Q₁₆	—	9	1	no	Sylow
28	C₃×C₄	—	3	1	no	—
29	C₃×C₄	—	3	1	no	—
30	C₃×C₄	—	6	1	no	—
31	C₃×C₄	—	18	1	no	—
32	Dic₃	—	6	1	no	—
33	C₃²	#226	1	1	yes	characteristic
34	C₉	—	4	1	no	—
35	C₉	—	8	1	no	—
36	Q₈	—	9	1	no	—
37	Q₈	C₃×D₉	1	1	yes	characteristic
38	C₈	—	9	1	no	—
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
41	C₂×C₃	C₃×S₄	1	1	yes	characteristic
42	C₄	—	3	1	no	—
43	C₄	—	18	1	no	—
44	C₃	—	2	1	no	—
45	C₃	#3688	1	1	yes	characteristic, direct product factor
46	C₃	C₃×#226	1	1	yes	characteristic
47	C₂	C₃×(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₂²⋊C₉)⋊C₂
commutator, cosocle, hypocenter	Q₈⋊C₉	C₂×C₃
Frattini	C₂×C₃	C₃×S₄
Fitting	C₃²×Q₈	D₃
socle, prime radical	C₂×C₃²	S₄
LCS	G ▷ Q₈⋊C₉
UCS	C₁ ◁ C₂×C₃

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

N	H ≅ G/N	type
3. #3688	C₃	direct (N × H)
45. C₃	#3688	direct (N × H)

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