Subgroups — C₂⁴×#41 #63097

Order 256.

32735 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41	C₂	1	120	yes	maximal, direct product factor
2	C₂⁴×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×D₄	C₂	1	3	yes	maximal, complemented
4	C₂⁵×C₄	C₂	1	3	yes	maximal, complemented
5	C₂⁶	C₂²	1	3	yes	—
6	C₂²×#41	C₂²	1	2240	yes	direct product factor
7	C₂³×Q₈	C₂²	1	60	yes	complemented
8	C₂³×D₄	C₂²	1	180	yes	complemented
9	C₂⁴×C₄	C₂²	1	3	yes	—
10	C₂⁴×C₄	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄	C₂²	1	180	yes	complemented
12	C₂⁵	—	2	48	no	—
13	C₂⁵	C₂³	1	90	yes	—
14	C₂⁵	C₂³	1	1	yes	characteristic
15	C₂×#41	C₂³	1	7680	yes	direct product factor
16	C₂²×Q₈	C₂³	1	560	yes	complemented
17	C₂²×D₄	C₂³	1	1680	yes	complemented
18	C₂³×C₄	C₂³	1	90	yes	—
19	C₂³×C₄	C₂³	1	30	yes	—
20	C₂³×C₄	C₂³	1	1680	yes	complemented
21	C₂⁴	—	2	720	no	—
22	C₂⁴	#41	1	16	yes	direct product factor
23	C₂⁴	C₂⁴	1	420	yes	—
24	C₂⁴	C₂⁴	1	15	yes	—
25	#41	C₂⁴	1	4096	yes	direct product factor
26	C₂×Q₈	C₂⁴	1	960	yes	complemented
27	C₂×D₄	C₂⁴	1	2880	yes	complemented
28	C₂²×C₄	C₂⁴	1	140	yes	—
29	C₂²×C₄	C₂⁴	1	420	yes	—
30	C₂²×C₄	C₂⁴	1	2880	yes	complemented
31	C₂³	—	2	1680	no	—
32	C₂³	C₂×#41	1	120	yes	direct product factor
33	C₂³	C₂⁵	1	360	yes	—
34	C₂³	C₂⁵	1	35	yes	—
35	Q₈	C₂⁵	1	256	yes	complemented
36	D₄	C₂⁵	1	768	yes	complemented
37	C₂×C₄	C₂⁵	1	120	yes	—
38	C₂×C₄	C₂⁵	1	360	yes	—
39	C₂×C₄	C₂⁵	1	768	yes	complemented
40	C₂²	—	2	720	no	—
41	C₂²	C₂²×#41	1	140	yes	direct product factor
42	C₂²	C₂⁶	1	48	yes	—
43	C₂²	C₂⁶	1	15	yes	—
44	C₄	C₂⁶	1	16	yes	—
45	C₄	C₂⁶	1	48	yes	—
46	C₂	—	2	48	no	—
47	C₂	C₂³×#41	1	30	yes	direct product factor
48	C₂	C₂⁷	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₄	C₂²
commutator, Frattini, cosocle	C₂	C₂⁷
socle	C₂⁵	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂³×#41	C₂	direct (N × H)
2. C₂⁴×Q₈	C₂	semidirect
3. C₂⁴×D₄	C₂	semidirect
4. C₂⁵×C₄	C₂	semidirect
6. C₂²×#41	C₂²	direct (N × H)
7. C₂³×Q₈	C₂²	semidirect
8. C₂³×D₄	C₂²	semidirect
11. C₂⁴×C₄	C₂²	semidirect
15. C₂×#41	C₂³	direct (N × H)
16. C₂²×Q₈	C₂³	semidirect
17. C₂²×D₄	C₂³	semidirect
20. C₂³×C₄	C₂³	semidirect
22. C₂⁴	#41	direct (N × H)
25. #41	C₂⁴	direct (N × H)
26. C₂×Q₈	C₂⁴	semidirect
27. C₂×D₄	C₂⁴	semidirect
30. C₂²×C₄	C₂⁴	semidirect
32. C₂³	C₂×#41	direct (N × H)
35. Q₈	C₂⁵	semidirect
36. D₄	C₂⁵	semidirect
39. C₂×C₄	C₂⁵	semidirect
41. C₂²	C₂²×#41	direct (N × H)
47. C₂	C₂³×#41	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#41	2
C₂⁴×Q₈	2
C₂⁴×D₄	2
C₂⁵×C₄	2

Subgroups — C24×#41 #63097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×#41 #63097