Subgroups — C₂×C₃×C₄⋊C₄ #956

Order 96.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊C₄	C₂	direct (N × H)
4. C₂×C₄⋊C₄	C₃	direct (N × H)
7. C₂×C₃×C₄	C₄	semidirect
12. C₄⋊C₄	C₂×C₃	direct (N × H)
18. C₃×C₄	C₂×C₄	semidirect
21. C₂×C₄	C₃×C₄	semidirect
24. C₂×C₃	C₄⋊C₄	direct (N × H)
33. C₄	C₂×C₃×C₄	semidirect
34. C₃	C₂×C₄⋊C₄	direct (N × H)
35. C₂	C₃×C₄⋊C₄	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×C₃×C₄	2
C₃×C₄⋊C₄	2
C₂×C₄⋊C₄	3

Subgroups — C2×C3×C4⋊C4 #956

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄⋊C₄ #956