Subgroups — D₃×C₄⋊C₄ #891

Order 96.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊C₄	C₂	semidirect
4. C₄⋊Dic₃	C₂	semidirect
5. Dic₃⋊C₄	C₂	semidirect
13. C₄×D₃	C₄	semidirect
18. C₄⋊C₄	D₃	direct (N × H)
24. C₃×C₄	C₂×C₄	semidirect
26. Dic₃	C₂×C₄	semidirect
37. D₃	C₄⋊C₄	direct (N × H)
45. C₄	C₄×D₃	semidirect
46. C₃	C₂×C₄⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃	2
C₃×C₄⋊C₄	2
C₄⋊Dic₃	2
Dic₃⋊C₄	2
C₂×C₄⋊C₄	3

Subgroups — D3×C4⋊C4 #891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₄⋊C₄ #891