Subgroups — C₂²×C₄×Dic₃ #5782

Order 192.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₃	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₃	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₄²	—	3	1	no	maximal, Sylow
5	C₂⁴×C₃	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄	C₄	1	8	yes	complemented
7	C₂²×C₃×C₄	C₂²	1	6	yes	—
8	C₂²×Dic₃	C₄	1	16	yes	direct product factor
9	C₂²×Dic₃	C₂²	1	12	yes	—
10	C₄×Dic₃	C₂²	1	16	yes	direct product factor
11	C₂³×C₄	—	3	2	no	—
12	C₂³×C₄	D₃	1	1	yes	characteristic
13	C₂×C₄²	—	3	12	no	—
14	C₂³×C₃	C₂×C₄	1	8	yes	—
15	C₂³×C₃	C₂×C₄	1	4	yes	—
16	C₂³×C₃	C₂³	1	3	yes	—
17	C₂×C₃×C₄	C₂×C₄	1	24	yes	complemented
18	C₂×C₃×C₄	C₂³	1	4	yes	—
19	C₂×Dic₃	C₂×C₄	1	48	yes	direct product factor
20	C₂×Dic₃	C₂³	1	8	yes	—
21	C₂⁴	C₂×D₃	1	1	yes	characteristic
22	C₂²×C₄	—	3	16	no	—
23	C₂²×C₄	—	3	12	no	—
24	C₂²×C₄	Dic₃	1	8	yes	direct product factor
25	C₂²×C₄	C₂×D₃	1	6	yes	—
26	C₄²	—	3	16	no	—
27	C₂²×C₃	C₄²	1	16	yes	complemented
28	C₂²×C₃	C₂²×C₄	1	12	yes	—
29	C₂²×C₃	C₂²×C₄	1	6	yes	—
30	C₂²×C₃	C₂⁴	1	1	yes	characteristic
31	C₃×C₄	C₂²×C₄	1	8	yes	complemented
32	Dic₃	C₂²×C₄	1	16	yes	direct product factor
33	C₂³	C₄×D₃	1	8	yes	—
34	C₂³	C₂×Dic₃	1	4	yes	—
35	C₂³	C₂²×D₃	1	3	yes	—
36	C₂×C₄	—	3	48	no	—
37	C₂×C₄	—	3	8	no	—
38	C₂×C₄	C₂×Dic₃	1	24	yes	direct product factor
39	C₂×C₄	C₂²×D₃	1	4	yes	—
40	C₂×C₃	C₂×C₄²	1	12	yes	complemented
41	C₂×C₃	C₂³×C₄	1	2	yes	—
42	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
43	C₂²	C₄×Dic₃	1	16	yes	direct product factor
44	C₂²	C₂×C₄×D₃	1	12	yes	—
45	C₂²	C₂²×Dic₃	1	6	yes	—
46	C₂²	C₂³×D₃	1	1	yes	characteristic
47	C₄	—	3	16	no	—
48	C₄	C₂²×Dic₃	1	8	yes	direct product factor
49	C₃	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
50	C₂	C₂×C₄×Dic₃	1	12	yes	direct product factor
51	C₂	C₂²×C₄×D₃	1	2	yes	—
52	C₂	C₂³×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	D₃
commutator, hypocenter	C₃	C₂²×C₄²
Frattini	C₂²	C₂³×D₃
Fitting	C₂³×C₃×C₄	C₂
socle, prime radical	C₂⁴×C₃	C₂²
cosocle	C₂²×C₃	C₂⁴
LCS	G ▷ C₃
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₃	C₂	direct (N × H)
6. C₂²×C₃×C₄	C₄	semidirect
8. C₂²×Dic₃	C₄	direct (N × H)
10. C₄×Dic₃	C₂²	direct (N × H)
17. C₂×C₃×C₄	C₂×C₄	semidirect
19. C₂×Dic₃	C₂×C₄	direct (N × H)
24. C₂²×C₄	Dic₃	direct (N × H)
27. C₂²×C₃	C₄²	semidirect
31. C₃×C₄	C₂²×C₄	semidirect
32. Dic₃	C₂²×C₄	direct (N × H)
38. C₂×C₄	C₂×Dic₃	direct (N × H)
40. C₂×C₃	C₂×C₄²	semidirect
43. C₂²	C₄×Dic₃	direct (N × H)
48. C₄	C₂²×Dic₃	direct (N × H)
49. C₃	C₂²×C₄²	semidirect
50. C₂	C₂×C₄×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
C₂³×C₃×C₄	2
C₂³×Dic₃	2
C₂×C₄×Dic₃	2
C₂²×C₄²	3

Subgroups — C22×C4×Dic3 #5782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×Dic₃ #5782