Subgroups — C₂⁴×C₄⋊C₄ #62640

Order 256.

9871 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄	C₂	1	2	yes	maximal
2	C₂⁵×C₄	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄⋊C₄	C₂	1	60	yes	maximal, direct product factor
4	C₂⁶	C₂²	1	1	yes	characteristic
5	C₂⁴×C₄	—	2	32	no	—
6	C₂⁴×C₄	C₄	1	32	yes	complemented
7	C₂⁴×C₄	C₂²	1	60	yes	—
8	C₂⁴×C₄	C₂²	1	30	yes	—
9	C₂²×C₄⋊C₄	C₂²	1	560	yes	direct product factor
10	C₂⁵	C₂×C₄	1	16	yes	—
11	C₂⁵	D₄	1	16	yes	—
12	C₂⁵	Q₈	1	16	yes	—
13	C₂⁵	C₂³	1	15	yes	—
14	C₂³×C₄	—	2	480	no	—
15	C₂³×C₄	C₂×C₄	1	480	yes	complemented
16	C₂³×C₄	C₂³	1	280	yes	—
17	C₂³×C₄	C₂³	1	140	yes	—
18	C₂×C₄⋊C₄	C₂³	1	960	yes	direct product factor
19	C₂⁴	C₄⋊C₄	1	256	yes	direct product factor
20	C₂⁴	C₂²×C₄	1	120	yes	—
21	C₂⁴	C₂×D₄	1	120	yes	—
22	C₂⁴	C₂×Q₈	1	120	yes	—
23	C₂⁴	C₂⁴	1	35	yes	—
24	C₂²×C₄	—	2	1120	no	—
25	C₂²×C₄	C₂²×C₄	1	1120	yes	complemented
26	C₂²×C₄	C₂⁴	1	240	yes	—
27	C₂²×C₄	C₂⁴	1	120	yes	—
28	C₄⋊C₄	C₂⁴	1	256	yes	direct product factor
29	C₂³	C₂×C₄⋊C₄	1	960	yes	direct product factor
30	C₂³	C₂³×C₄	1	140	yes	—
31	C₂³	C₂²×D₄	1	140	yes	—
32	C₂³	C₂²×Q₈	1	140	yes	—
33	C₂³	C₂⁵	1	15	yes	—
34	C₂×C₄	—	2	480	no	—
35	C₂×C₄	C₂³×C₄	1	480	yes	complemented
36	C₂×C₄	C₂⁵	1	32	yes	—
37	C₂×C₄	C₂⁵	1	16	yes	—
38	C₂²	C₂²×C₄⋊C₄	1	560	yes	direct product factor
39	C₂²	C₂⁴×C₄	1	30	yes	—
40	C₂²	C₂³×D₄	1	30	yes	—
41	C₂²	C₂³×Q₈	1	30	yes	—
42	C₂²	C₂⁶	1	1	yes	characteristic
43	C₄	—	2	32	no	—
44	C₄	C₂⁴×C₄	1	32	yes	complemented
45	C₂	C₂³×C₄⋊C₄	1	60	yes	direct product factor
46	C₂	C₂⁵×C₄	1	1	yes	characteristic
47	C₂	C₂⁴×D₄	1	1	yes	characteristic
48	C₂	C₂⁴×Q₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁶	C₂²
commutator	C₂	C₂⁵×C₄
Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁶ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₂³×C₄⋊C₄	C₂	direct (N × H)
6. C₂⁴×C₄	C₄	semidirect
9. C₂²×C₄⋊C₄	C₂²	direct (N × H)
15. C₂³×C₄	C₂×C₄	semidirect
18. C₂×C₄⋊C₄	C₂³	direct (N × H)
19. C₂⁴	C₄⋊C₄	direct (N × H)
25. C₂²×C₄	C₂²×C₄	semidirect
28. C₄⋊C₄	C₂⁴	direct (N × H)
29. C₂³	C₂×C₄⋊C₄	direct (N × H)
35. C₂×C₄	C₂³×C₄	semidirect
38. C₂²	C₂²×C₄⋊C₄	direct (N × H)
44. C₄	C₂⁴×C₄	semidirect
45. C₂	C₂³×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
C₂⁵×C₄	2
C₂³×C₄⋊C₄	2

Subgroups — C24×C4⋊C4 #62640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄⋊C₄ #62640