Subgroups — C₂²×Dic₁₂ #5742

Order 192.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆	C₂	1	2	yes	maximal
2	C₂²×C₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₂	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Q₁₆	—	3	1	no	maximal, Sylow
5	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂²×Dic₃	—	2	2	no	—
7	C₂×Dic₆	—	2	6	no	—
8	C₂×Dic₆	C₂²	1	12	yes	—
9	C₂×C₃×C₈	C₂²	1	6	yes	—
10	Dic₁₂	C₂²	1	16	yes	direct product factor
11	C₂²×Q₈	—	3	2	no	—
12	C₂×Q₁₆	—	3	12	no	—
13	C₂²×C₈	D₃	1	1	yes	characteristic
14	C₂³×C₃	D₄	1	1	yes	characteristic
15	C₂×C₃×C₄	D₄	1	3	yes	—
16	C₂×C₃×C₄	C₂³	1	3	yes	—
17	C₂×Dic₃	—	2	12	no	—
18	Dic₆	—	2	12	no	—
19	Dic₆	C₂³	1	8	yes	—
20	C₃×C₈	C₂³	1	4	yes	—
21	C₂×Q₈	—	3	12	no	—
22	C₂×Q₈	—	6	6	no	—
23	C₂²×C₄	—	6	2	no	—
24	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
25	Q₁₆	—	3	16	no	—
26	C₂×C₈	C₂×D₃	1	6	yes	—
27	C₂²×C₃	Q₁₆	1	4	yes	complemented
28	C₂²×C₃	C₂×D₄	1	3	yes	—
29	C₃×C₄	C₂×D₄	1	3	yes	—
30	C₃×C₄	C₂⁴	1	1	yes	characteristic
31	Dic₃	—	2	8	no	—
32	C₂³	D₁₂	1	1	yes	characteristic
33	Q₈	—	3	8	no	—
34	Q₈	—	6	12	no	—
35	C₂×C₄	—	6	12	no	—
36	C₂×C₄	D₁₂	1	3	yes	—
37	C₂×C₄	C₂²×D₃	1	3	yes	—
38	C₈	C₂²×D₃	1	4	yes	—
39	C₂×C₃	C₂×Q₁₆	1	6	yes	complemented
40	C₂×C₃	C₂²×D₄	1	1	yes	characteristic
41	C₂²	Dic₁₂	1	4	yes	direct product factor
42	C₂²	C₂×D₁₂	1	3	yes	—
43	C₄	—	6	8	no	—
44	C₄	C₂×D₁₂	1	3	yes	—
45	C₄	C₂³×D₃	1	1	yes	characteristic
46	C₃	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₂	C₂×Dic₁₂	1	6	yes	direct product factor
48	C₂	C₂²×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₂
commutator, cosocle	C₃×C₄	C₂⁴
Frattini	C₄	C₂³×D₃
Fitting	C₂²×C₃×C₈	C₂
socle, prime radical	C₂³×C₃	D₄
hypercenter	C₂²×C₈	D₃
hypocenter	C₃	C₂²×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₁₂	C₂	direct (N × H)
10. Dic₁₂	C₂²	direct (N × H)
27. C₂²×C₃	Q₁₆	semidirect
39. C₂×C₃	C₂×Q₁₆	semidirect
41. C₂²	Dic₁₂	direct (N × H)
46. C₃	C₂²×Q₁₆	semidirect
47. C₂	C₂×Dic₁₂	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×Dic₆	2
C₂²×C₃×C₈	2
C₂×Dic₁₂	2
C₂²×Q₁₆	3

Subgroups — C22×Dic12 #5742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₁₂ #5742