Subgroups — C₂×C₄⋊(C₃⋊Dic₃) #64134

Order 288.

276 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊Dic₃	C₂	1	2	yes	maximal
3	C₄⋊(C₃⋊Dic₃)	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊Dic₃	—	3	4	no	maximal
5	C₂³×C₃²	C₂²	1	1	yes	characteristic
6	C₂×C₃²×C₄	C₄	1	4	yes	complemented
7	C₂×C₃²×C₄	C₂²	1	2	yes	—
8	C₂×C₃⋊Dic₃	—	2	4	no	—
9	C₂×C₃⋊Dic₃	C₂²	1	4	yes	—
10	C₂²×C₃×C₄	D₃	1	4	yes	—
11	C₂²×Dic₃	—	3	8	no	—
12	C₄⋊Dic₃	—	3	16	no	—
13	C₂²×C₃²	C₂×C₄	1	2	yes	—
14	C₂²×C₃²	D₄	1	2	yes	—
15	C₂²×C₃²	Q₈	1	2	yes	—
16	C₂²×C₃²	C₂³	1	1	yes	characteristic
17	C₃²×C₄	C₂×C₄	1	4	yes	complemented
18	C₃⋊Dic₃	—	2	4	no	—
19	C₂×C₄⋊C₄	—	9	1	no	Sylow
20	C₂³×C₃	C₂×D₃	1	4	yes	—
21	C₂×C₃×C₄	Dic₃	1	16	yes	complemented
22	C₂×C₃×C₄	C₂×D₃	1	8	yes	—
23	C₂×Dic₃	—	3	16	no	—
24	C₂×Dic₃	—	6	16	no	—
25	C₂×C₃²	C₄⋊C₄	1	4	yes	complemented
26	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₄	—	9	2	no	—
30	C₂²×C₄	C₃⋊D₃	1	1	yes	characteristic
31	C₄⋊C₄	—	9	4	no	—
32	C₂²×C₃	Dic₆	1	8	yes	—
33	C₂²×C₃	D₁₂	1	8	yes	—
34	C₂²×C₃	C₂×Dic₃	1	8	yes	—
35	C₂²×C₃	C₂²×D₃	1	4	yes	—
36	C₃×C₄	C₂×Dic₃	1	16	yes	complemented
37	Dic₃	—	6	16	no	—
38	C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
39	C₂³	C₂×C₃⋊D₃	1	1	yes	characteristic
40	C₂×C₄	—	9	4	no	—
41	C₂×C₄	—	18	4	no	—
42	C₂×C₄	C₃⋊Dic₃	1	4	yes	complemented
43	C₂×C₄	C₂×C₃⋊D₃	1	2	yes	—
44	C₂×C₃	C₄⋊Dic₃	1	16	yes	complemented
45	C₂×C₃	C₂×Dic₆	1	4	yes	—
46	C₂×C₃	C₂×D₁₂	1	4	yes	—
47	C₂×C₃	C₂²×Dic₃	1	4	yes	—
48	C₂²	#634	1	2	yes	—
49	C₂²	C₄⋊(C₃⋊D₃)	1	2	yes	—
50	C₂²	C₂×C₃⋊Dic₃	1	2	yes	—
51	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
52	C₄	—	18	4	no	—
53	C₄	C₂×C₃⋊Dic₃	1	4	yes	complemented
54	C₃	C₂×C₄⋊Dic₃	1	4	yes	complemented
55	C₂	C₄⋊(C₃⋊Dic₃)	1	4	yes	direct product factor
56	C₂	C₂×#634	1	1	yes	characteristic
57	C₂	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
58	C₂	C₂²×C₃⋊Dic₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄⋊(C₃⋊Dic₃)	C₂	direct (N × H)
6. C₂×C₃²×C₄	C₄	semidirect
17. C₃²×C₄	C₂×C₄	semidirect
21. C₂×C₃×C₄	Dic₃	semidirect
25. C₂×C₃²	C₄⋊C₄	semidirect
36. C₃×C₄	C₂×Dic₃	semidirect
38. C₃²	C₂×C₄⋊C₄	semidirect
42. C₂×C₄	C₃⋊Dic₃	semidirect
44. C₂×C₃	C₄⋊Dic₃	semidirect
53. C₄	C₂×C₃⋊Dic₃	semidirect
54. C₃	C₂×C₄⋊Dic₃	semidirect
55. C₂	C₄⋊(C₃⋊Dic₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₄	2
C₂²×C₃⋊Dic₃	2
C₄⋊(C₃⋊Dic₃)	2
C₂×C₄⋊Dic₃	3

Subgroups — C2×C4⋊(C3⋊Dic3) #64134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊(C₃⋊Dic₃) #64134