Subgroups — D₃×C₂²⋊C₄ #880

Order 96.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₃	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#217	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₂×C₂²⋊C₄	—	3	1	no	maximal, Sylow
7	C₂³×C₃	C₂²	1	1	yes	characteristic
8	C₂²×D₃	—	2	4	no	—
9	C₂²×D₃	C₄	1	4	yes	complemented
10	C₂²×D₃	C₂²	1	1	yes	characteristic
11	C₂²×D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄	C₂²	1	2	yes	complemented
13	C₂×Dic₃	C₂²	1	2	yes	complemented
14	C₄×D₃	—	2	4	no	—
15	C₂⁴	—	3	1	no	—
16	C₂²×C₄	—	3	2	no	—
17	C₂²⋊C₄	—	3	1	no	—
18	C₂²⋊C₄	—	3	2	no	—
19	C₂²⋊C₄	D₃	1	1	yes	characteristic, direct product factor
20	C₂²×C₃	—	2	2	no	—
21	C₂²×C₃	C₂×C₄	1	2	yes	complemented
22	C₂²×C₃	C₂³	1	1	yes	characteristic
23	C₂×D₃	—	2	2	no	—
24	C₂×D₃	—	2	8	no	—
25	C₂×D₃	C₂×C₄	1	2	yes	—
26	C₂×D₃	C₂×C₄	1	2	yes	complemented
27	C₂×D₃	D₄	1	4	yes	—
28	C₃×C₄	—	2	2	no	—
29	Dic₃	—	2	2	no	—
30	C₂³	—	3	1	no	—
31	C₂³	—	3	4	no	—
32	C₂³	—	3	1	no	—
33	C₂³	—	6	4	no	—
34	C₂³	C₂×D₃	1	1	yes	characteristic
35	C₂×C₄	—	3	2	no	—
36	C₂×C₄	—	6	4	no	—
37	C₂×C₄	C₂×D₃	1	2	yes	complemented
38	C₂×C₃	—	2	2	no	—
39	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₃	C₂×D₄	1	2	yes	—
41	D₃	—	2	2	no	—
42	D₃	C₂²⋊C₄	1	4	yes	direct product factor
43	C₂²	—	2	2	no	—
44	C₂²	—	3	2	no	—
45	C₂²	—	3	4	no	—
46	C₂²	—	3	2	no	—
47	C₂²	—	6	8	no	—
48	C₂²	—	6	2	no	—
49	C₂²	C₄×D₃	1	2	yes	complemented
50	C₂²	C₂²×D₃	1	1	yes	characteristic
51	C₄	—	2	2	no	—
52	C₄	—	6	2	no	—
53	C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
54	C₂	—	2	2	no	—
55	C₂	—	3	4	no	—
56	C₂	—	6	2	no	—
57	C₂	C₂×C₄×D₃	1	1	yes	characteristic
58	C₂	D₃×D₄	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₃	C₂	semidirect
3. C₃×C₂²⋊C₄	C₂	semidirect
4. #217	C₂	semidirect
5. (C₂×D₃)⋊C₄	C₂	semidirect
9. C₂²×D₃	C₄	semidirect
12. C₂×C₃×C₄	C₂²	semidirect
13. C₂×Dic₃	C₂²	semidirect
19. C₂²⋊C₄	D₃	direct (N × H)
21. C₂²×C₃	C₂×C₄	semidirect
26. C₂×D₃	C₂×C₄	semidirect
37. C₂×C₄	C₂×D₃	semidirect
42. D₃	C₂²⋊C₄	direct (N × H)
49. C₂²	C₄×D₃	semidirect
53. C₃	C₂×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₃	2
C₂×C₄×D₃	2
C₃×C₂²⋊C₄	2
#217	2
(C₂×D₃)⋊C₄	2
C₂×C₂²⋊C₄	3

Subgroups — D3×C22⋊C4 #880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₂²⋊C₄ #880