Subgroups — C₂³×D₂₈ #90605

Order 448.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₇	C₂	1	2	yes	maximal, complemented
2	C₂³×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₂₈	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₇	C₂²	1	1	yes	characteristic
5	C₂³×D₇	—	2	16	no	—
6	C₂³×D₇	C₂²	1	28	yes	complemented
7	C₂²×C₄×C₇	C₂²	1	14	yes	complemented
8	C₂×D₂₈	C₂²	1	112	yes	direct product factor
9	C₂³×D₄	—	7	1	no	maximal, Sylow
10	C₂³×C₇	D₄	1	8	yes	complemented
11	C₂³×C₇	C₂³	1	7	yes	—
12	C₂²×D₇	—	2	112	no	—
13	C₂²×D₇	C₂³	1	56	yes	complemented
14	C₂×C₄×C₇	C₂³	1	28	yes	complemented
15	D₂₈	C₂³	1	64	yes	direct product factor
16	C₂⁵	—	7	2	no	—
17	C₂²×D₄	—	7	28	no	—
18	C₂³×C₄	D₇	1	1	yes	characteristic, complemented
19	C₂²×C₇	C₂×D₄	1	28	yes	complemented
20	C₂²×C₇	C₂⁴	1	7	yes	—
21	C₂×D₇	—	2	112	no	—
22	C₂×D₇	C₂⁴	1	16	yes	complemented
23	C₄×C₇	C₂⁴	1	8	yes	complemented
24	C₂⁴	—	7	28	no	—
25	C₂⁴	—	14	16	no	—
26	C₂⁴	C₂×D₇	1	1	yes	characteristic
27	C₂×D₄	—	7	112	no	—
28	C₂²×C₄	C₂×D₇	1	14	yes	complemented
29	C₂×C₇	C₂²×D₄	1	14	yes	complemented
30	C₂×C₇	C₂⁵	1	1	yes	characteristic
31	D₇	—	2	16	no	—
32	C₂³	—	7	56	no	—
33	C₂³	—	14	112	no	—
34	C₂³	D₂₈	1	8	yes	direct product factor
35	C₂³	C₂²×D₇	1	7	yes	—
36	D₄	—	7	64	no	—
37	C₂×C₄	C₂²×D₇	1	28	yes	complemented
38	C₇	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	7	16	no	—
40	C₂²	—	14	112	no	—
41	C₂²	C₂×D₂₈	1	28	yes	direct product factor
42	C₂²	C₂³×D₇	1	7	yes	—
43	C₄	C₂³×D₇	1	8	yes	complemented
44	C₂	—	14	16	no	—
45	C₂	C₂²×D₂₈	1	14	yes	direct product factor
46	C₂	C₂⁴×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₇
commutator, cosocle	C₂×C₇	C₂⁵
Frattini	C₂	C₂⁴×D₇
Fitting	C₂³×C₄×C₇	C₂
socle	C₂⁴×C₇	C₂²
hypercenter	C₂³×C₄	D₇
hypocenter	C₇	C₂³×D₄
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₇	C₂	semidirect
2. C₂³×C₄×C₇	C₂	semidirect
3. C₂²×D₂₈	C₂	direct (N × H)
6. C₂³×D₇	C₂²	semidirect
7. C₂²×C₄×C₇	C₂²	semidirect
8. C₂×D₂₈	C₂²	direct (N × H)
10. C₂³×C₇	D₄	semidirect
13. C₂²×D₇	C₂³	semidirect
14. C₂×C₄×C₇	C₂³	semidirect
15. D₂₈	C₂³	direct (N × H)
18. C₂³×C₄	D₇	semidirect
19. C₂²×C₇	C₂×D₄	semidirect
22. C₂×D₇	C₂⁴	semidirect
23. C₄×C₇	C₂⁴	semidirect
28. C₂²×C₄	C₂×D₇	semidirect
29. C₂×C₇	C₂²×D₄	semidirect
34. C₂³	D₂₈	direct (N × H)
37. C₂×C₄	C₂²×D₇	semidirect
38. C₇	C₂³×D₄	semidirect
41. C₂²	C₂×D₂₈	direct (N × H)
43. C₄	C₂³×D₇	semidirect
45. C₂	C₂²×D₂₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₇	2
C₂³×C₄×C₇	2
C₂²×D₂₈	2
C₂³×D₄	7

Subgroups — C23×D28 #90605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₂₈ #90605