Subgroups — C₂²×C₄⋊Dic₃ #5785

Order 192.

418 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×C₄⋊C₄	—	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	—	2	8	no	—
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×C₄⋊C₄	—	3	12	no	—
14	C₂³×C₃	C₂×C₄	1	4	yes	—
15	C₂³×C₃	D₄	1	4	yes	—
16	C₂³×C₃	Q₈	1	4	yes	—
17	C₂³×C₃	C₂³	1	3	yes	—
18	C₂×C₃×C₄	C₂×C₄	1	24	yes	complemented
19	C₂×C₃×C₄	C₂³	1	4	yes	—
20	C₂×Dic₃	—	2	24	no	—
21	C₂×Dic₃	C₂³	1	8	yes	—
22	C₂⁴	C₂×D₃	1	1	yes	characteristic
23	C₂²×C₄	—	3	12	no	—
24	C₂²×C₄	—	6	8	no	—
25	C₂²×C₄	Dic₃	1	8	yes	complemented
26	C₂²×C₄	C₂×D₃	1	6	yes	—
27	C₄⋊C₄	—	3	16	no	—
28	C₂²×C₃	C₄⋊C₄	1	16	yes	complemented
29	C₂²×C₃	C₂²×C₄	1	6	yes	—
30	C₂²×C₃	C₂×D₄	1	6	yes	—
31	C₂²×C₃	C₂×Q₈	1	6	yes	—
32	C₂²×C₃	C₂⁴	1	1	yes	characteristic
33	C₃×C₄	C₂²×C₄	1	8	yes	complemented
34	Dic₃	—	2	8	no	—
35	C₂³	Dic₆	1	4	yes	—
36	C₂³	D₁₂	1	4	yes	—
37	C₂³	C₂×Dic₃	1	4	yes	—
38	C₂³	C₂²×D₃	1	3	yes	—
39	C₂×C₄	—	3	8	no	—
40	C₂×C₄	—	6	24	no	—
41	C₂×C₄	C₂×Dic₃	1	24	yes	complemented
42	C₂×C₄	C₂²×D₃	1	4	yes	—
43	C₂×C₃	C₂×C₄⋊C₄	1	12	yes	complemented
44	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
45	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
46	C₂×C₃	C₂²×Q₈	1	1	yes	characteristic
47	C₂²	C₄⋊Dic₃	1	16	yes	direct product factor
48	C₂²	C₂×Dic₆	1	6	yes	—
49	C₂²	C₂×D₁₂	1	6	yes	—
50	C₂²	C₂²×Dic₃	1	6	yes	—
51	C₂²	C₂³×D₃	1	1	yes	characteristic
52	C₄	—	6	8	no	—
53	C₄	C₂²×Dic₃	1	8	yes	complemented
54	C₃	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
55	C₂	C₂×C₄⋊Dic₃	1	12	yes	direct product factor
56	C₂	C₂²×Dic₆	1	1	yes	characteristic
57	C₂	C₂²×D₁₂	1	1	yes	characteristic
58	C₂	C₂³×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃
commutator	C₂×C₃	C₂³×C₄
Frattini	C₂²	C₂³×D₃
Fitting	C₂³×C₃×C₄	C₂
socle, prime radical	C₂⁴×C₃	C₂²
cosocle	C₂²×C₃	C₂⁴
hypercenter	C₂³×C₄	D₃
hypocenter	C₃	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ 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
10. C₄⋊Dic₃	C₂²	direct (N × H)
18. C₂×C₃×C₄	C₂×C₄	semidirect
25. C₂²×C₄	Dic₃	semidirect
28. C₂²×C₃	C₄⋊C₄	semidirect
33. C₃×C₄	C₂²×C₄	semidirect
41. C₂×C₄	C₂×Dic₃	semidirect
43. C₂×C₃	C₂×C₄⋊C₄	semidirect
47. C₂²	C₄⋊Dic₃	direct (N × H)
53. C₄	C₂²×Dic₃	semidirect
54. C₃	C₂²×C₄⋊C₄	semidirect
55. 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×C₄⋊C₄	3

Subgroups — C22×C4⋊Dic3 #5785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄⋊Dic₃ #5785