Subgroups — C₂×#6226 #88733

Order 432.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊Dic₉	C₂	1	2	yes	maximal
3	#6226	C₂	1	4	yes	maximal, direct product factor
4	C₂×#634	—	3	1	no	maximal
5	C₂×Dic₁₈	—	3	3	no	maximal
6	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₃×C₄×C₉	C₂²	1	2	yes	—
8	C₃⋊Dic₉	C₂²	1	4	yes	—
9	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
10	C₂×C₃⋊Dic₃	—	3	2	no	—
11	#634	—	3	4	no	—
12	C₂×C₄×C₉	D₃	1	3	yes	—
13	C₂×Dic₉	—	3	6	no	—
14	Dic₁₈	—	3	12	no	—
15	C₂×C₃×C₉	Q₈	1	2	yes	complemented
16	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₆	—	9	3	no	—
18	C₂×Dic₆	—	9	1	no	—
19	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
20	C₃²×C₄	C₂×D₃	1	2	yes	—
21	C₃⋊Dic₃	—	3	4	no	—
22	C₂²×C₉	C₂×D₃	1	3	yes	—
23	C₄×C₉	C₂×D₃	1	6	yes	—
24	Dic₉	—	3	12	no	—
25	C₃×C₉	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃×C₄	D₉	1	3	yes	—
27	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
28	C₂×Dic₃	—	9	6	no	—
29	C₂×Dic₃	—	9	2	no	—
30	Dic₆	—	9	12	no	—
31	Dic₆	—	9	4	no	—
32	C₂×C₃²	Dic₆	1	2	yes	—
33	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
34	C₂×C₉	Dic₆	1	6	yes	complemented
35	C₂×C₉	C₂²×D₃	1	3	yes	—
36	C₂×Q₈	—	27	1	no	Sylow
37	C₂²×C₃	C₂×D₉	1	3	yes	—
38	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
39	C₃×C₄	C₂×D₉	1	6	yes	—
40	C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
41	Dic₃	—	9	12	no	—
42	Dic₃	—	9	4	no	—
43	C₃²	C₂×Dic₆	1	1	yes	characteristic
44	C₉	C₂×Dic₆	1	3	yes	complemented
45	Q₈	—	27	4	no	—
46	C₂×C₄	—	27	2	no	—
47	C₂×C₄	C₃⋊D₉	1	1	yes	characteristic
48	C₂×C₃	Dic₁₈	1	6	yes	complemented
49	C₂×C₃	C₂²×D₉	1	3	yes	—
50	C₂×C₃	#634	1	2	yes	—
51	C₂×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
52	C₂²	C₂×C₃⋊D₉	1	1	yes	characteristic
53	C₄	—	27	4	no	—
54	C₄	C₂×C₃⋊D₉	1	2	yes	—
55	C₃	C₂×Dic₁₈	1	3	yes	complemented
56	C₃	C₂×#634	1	1	yes	characteristic
57	C₂	#6226	1	2	yes	direct product factor
58	C₂	C₂²×C₃⋊D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₃⋊D₉
commutator, cosocle	C₂×C₃×C₉	C₂³
Frattini	C₂×C₃	C₂²×C₃⋊D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle, prime radical	C₂²×C₃²	C₂×D₃
hypercenter	C₂×C₄	C₃⋊D₉
hypocenter	C₃×C₉	C₂×Q₈
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. #6226	C₂	direct (N × H)
15. C₂×C₃×C₉	Q₈	semidirect
25. C₃×C₉	C₂×Q₈	semidirect
34. C₂×C₉	Dic₆	semidirect
44. C₉	C₂×Dic₆	semidirect
48. C₂×C₃	Dic₁₈	semidirect
55. C₃	C₂×Dic₁₈	semidirect
57. C₂	#6226	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₉	2
C₂×C₃⋊Dic₉	2
#6226	2
C₂×#634	3
C₂×Dic₁₈	3

Subgroups — C2×#6226 #88733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6226 #88733