Subgroups — C₂×#6189 #88656

Order 432.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊Dic₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₉	C₂	1	1	yes	maximal, characteristic
4	#6189	C₂	1	4	yes	maximal, direct product factor
5	C₂×#627	—	3	1	no	maximal
6	C₂×Dic₁₈	—	3	1	no	maximal
7	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
8	C₃⋊Dic₉	C₂²	1	2	yes	—
9	C₉×Dic₃	C₂²	1	2	yes	—
10	C₃×Dic₉	C₂²	1	2	yes	—
11	C₂×C₃⋊Dic₃	—	3	1	no	—
12	C₂×C₃×Dic₃	—	3	1	no	—
13	C₂×C₃×Dic₃	D₃	1	1	yes	characteristic
14	#627	—	3	4	no	—
15	C₂×C₄×C₉	—	3	1	no	—
16	C₂×Dic₉	—	3	1	no	—
17	C₂×Dic₉	—	6	1	no	—
18	C₂×Dic₉	D₃	1	1	yes	characteristic
19	Dic₁₈	—	3	4	no	—
20	C₂×C₃×C₉	Q₈	1	2	yes	complemented
21	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₆	—	9	1	no	—
23	C₂×Dic₆	—	9	1	no	—
24	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
25	C₃⋊Dic₃	—	3	2	no	—
26	C₃×Dic₃	—	3	2	no	—
27	C₃×Dic₃	C₂×D₃	1	2	yes	—
28	C₂²×C₉	—	2	1	no	—
29	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
30	C₄×C₉	—	3	2	no	—
31	Dic₉	—	3	2	no	—
32	Dic₉	—	6	2	no	—
33	Dic₉	C₂×D₃	1	2	yes	—
34	C₃×C₉	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃×C₄	—	3	1	no	—
36	C₂×C₃×C₄	—	9	1	no	—
37	C₂×Dic₃	—	3	1	no	—
38	C₂×Dic₃	—	9	1	no	—
39	C₂×Dic₃	—	9	1	no	—
40	C₂×Dic₃	—	18	1	no	—
41	C₂×Dic₃	D₉	1	1	yes	characteristic
42	Dic₆	—	9	4	no	—
43	Dic₆	—	9	4	no	—
44	C₂×C₃²	Dic₆	1	2	yes	—
45	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
46	C₂×C₉	—	2	2	no	—
47	C₂×C₉	—	2	1	no	—
48	C₂×C₉	Dic₆	1	2	yes	complemented
49	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
50	C₂×Q₈	—	27	1	no	Sylow
51	C₂²×C₃	—	2	1	no	—
52	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
53	C₂²×C₃	D₃²	1	1	yes	characteristic
54	C₃×C₄	—	3	2	no	—
55	C₃×C₄	—	9	2	no	—
56	Dic₃	—	3	2	no	—
57	Dic₃	—	9	2	no	—
58	Dic₃	—	9	2	no	—
59	Dic₃	—	18	2	no	—
60	Dic₃	C₂×D₉	1	2	yes	—
61	C₃²	C₂×Dic₆	1	1	yes	characteristic
62	C₉	—	2	1	no	—
63	C₉	C₂×Dic₆	1	1	yes	characteristic, complemented
64	Q₈	—	27	4	no	—
65	C₂×C₄	—	3	1	no	—
66	C₂×C₄	—	9	1	no	—
67	C₂×C₄	—	27	1	no	—
68	C₂×C₃	—	2	2	no	—
69	C₂×C₃	—	2	1	no	—
70	C₂×C₃	Dic₁₈	1	2	yes	complemented
71	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
72	C₂×C₃	#627	1	2	yes	—
73	C₂×C₃	C₂×D₃²	1	1	yes	characteristic
74	C₂²	D₃×D₉	1	1	yes	characteristic
75	C₄	—	3	2	no	—
76	C₄	—	9	2	no	—
77	C₄	—	27	2	no	—
78	C₃	—	2	1	no	—
79	C₃	C₂×Dic₁₈	1	1	yes	characteristic, complemented
80	C₃	C₂×#627	1	1	yes	characteristic
81	C₂	#6189	1	2	yes	direct product factor
82	C₂	C₂×D₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₉
commutator, cosocle	C₂×C₃×C₉	C₂³
Frattini	C₂×C₃	C₂×D₃²
Fitting	C₂²×C₃×C₉	C₂²
socle, prime radical	C₂²×C₃²	C₂×D₃
hypocenter	C₃×C₉	C₂×Q₈
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
4. #6189	C₂	direct (N × H)
20. C₂×C₃×C₉	Q₈	semidirect
34. C₃×C₉	C₂×Q₈	semidirect
48. C₂×C₉	Dic₆	semidirect
63. C₉	C₂×Dic₆	semidirect
70. C₂×C₃	Dic₁₈	semidirect
79. C₃	C₂×Dic₁₈	semidirect
81. C₂	#6189	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⋊Dic₉	2
C₂×C₉×Dic₃	2
C₂×C₃×Dic₉	2
#6189	2
C₂×#627	3
C₂×Dic₁₈	3

Subgroups — C2×#6189 #88656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6189 #88656