Subgroups — C₃×C₄×D₄ #958

Order 96.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₃×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×D₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂³×C₃	C₂²	1	2	yes	—
8	C₃×D₄	C₄	1	4	yes	direct product factor
9	C₂×C₃×C₄	—	2	4	no	—
10	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄	C₂²	1	1	yes	characteristic
14	C₂×D₄	C₂×C₃	1	1	yes	characteristic
15	C₂²×C₄	C₂×C₃	1	2	yes	complemented
16	C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
18	C₄²	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂²×C₃	—	2	2	no	—
20	C₂²×C₃	—	2	2	no	—
21	C₂²×C₃	C₂×C₄	1	4	yes	complemented
22	C₂²×C₃	C₂³	1	1	yes	characteristic
23	C₃×C₄	—	2	2	no	—
24	C₃×C₄	—	2	1	no	—
25	C₃×C₄	C₂×C₄	1	2	yes	complemented
26	C₃×C₄	D₄	1	2	yes	direct product factor
27	C₂³	C₂²×C₃	1	2	yes	—
28	D₄	C₃×C₄	1	4	yes	direct product factor
29	C₂×C₄	—	2	4	no	—
30	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₄	C₂²×C₃	1	2	yes	—
32	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
33	C₂×C₄	C₂²×C₃	1	1	yes	characteristic
34	C₂×C₃	—	2	4	no	—
35	C₂×C₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₃	#41	1	1	yes	characteristic
38	C₂²	—	2	2	no	—
39	C₂²	—	2	2	no	—
40	C₂²	C₂×C₃×C₄	1	4	yes	complemented
41	C₂²	C₂³×C₃	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	2	1	no	—
44	C₄	C₂×C₃×C₄	1	2	yes	complemented
45	C₄	C₃×D₄	1	2	yes	direct product factor
46	C₃	C₄×D₄	1	1	yes	characteristic, direct product factor, Sylow
47	C₂	—	2	4	no	—
48	C₂	C₂²×C₃×C₄	1	1	yes	characteristic
49	C₂	C₂×C₃×D₄	1	1	yes	characteristic
50	C₂	C₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²
commutator	C₂	C₂²×C₃×C₄
Frattini, cosocle	C₂²	C₂³×C₃
socle	C₂²×C₃	C₂³
prime radical	C₂×C₃×D₄	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄	C₂	semidirect
3. C₃×C₄⋊C₄	C₂	semidirect
4. C₃×C₂²⋊C₄	C₂	semidirect
5. C₃×C₄²	C₂	semidirect
6. C₄×D₄	C₃	direct (N × H)
8. C₃×D₄	C₄	direct (N × H)
15. C₂²×C₄	C₂×C₃	semidirect
16. C₄⋊C₄	C₂×C₃	semidirect
17. C₂²⋊C₄	C₂×C₃	semidirect
18. C₄²	C₂×C₃	semidirect
21. C₂²×C₃	C₂×C₄	semidirect
25. C₃×C₄	C₂×C₄	semidirect
26. C₃×C₄	D₄	direct (N × H)
28. D₄	C₃×C₄	direct (N × H)
40. C₂²	C₂×C₃×C₄	semidirect
44. C₄	C₂×C₃×C₄	semidirect
45. C₄	C₃×D₄	direct (N × H)
46. C₃	C₄×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₄	2
C₂²×C₃×C₄	2
C₃×C₄⋊C₄	2
C₃×C₂²⋊C₄	2
C₃×C₄²	2
C₄×D₄	3

Subgroups — C3×C4×D4 #958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₄ #958