Subgroups — C₄³×D₈₃ #24909784

Order 10624.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₈₃	C₂	1	7	yes	maximal
2	C₄²×Dic₈₃	C₂	1	7	yes	maximal, complemented
3	C₄³×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₈₃	C₂²	1	7	yes	—
5	C₂×C₄×Dic₈₃	C₂²	1	21	yes	—
6	C₄²×D₈₃	C₄	1	56	yes	direct product factor
7	C₂×C₄²×C₈₃	C₂²	1	7	yes	—
8	C₂³×D₈₃	C₂³	1	1	yes	characteristic
9	C₂²×Dic₈₃	C₂³	1	7	yes	—
10	C₂×C₄×D₈₃	C₂×C₄	1	84	yes	—
11	C₄×Dic₈₃	C₂×C₄	1	84	yes	complemented
12	C₂²×C₄×C₈₃	C₂³	1	7	yes	—
13	C₄²×C₈₃	C₂×C₄	1	28	yes	complemented
14	C₂³×C₈₃	C₂⁴	1	1	yes	characteristic
15	C₂²×D₈₃	C₂²×C₄	1	14	yes	—
16	C₂×C₄×C₈₃	C₂²×C₄	1	42	yes	—
17	C₂×Dic₈₃	C₂²×C₄	1	42	yes	—
18	C₄×D₈₃	C₄²	1	112	yes	direct product factor
19	C₂²×C₈₃	C₂³×C₄	1	7	yes	—
20	C₂×D₈₃	C₂×C₄²	1	28	yes	—
21	C₄×C₈₃	C₂×C₄²	1	28	yes	complemented
22	Dic₈₃	C₂×C₄²	1	28	yes	complemented
23	C₂×C₈₃	C₂²×C₄²	1	7	yes	—
24	D₈₃	C₄³	1	8	yes	direct product factor
25	C₂×C₄³	—	83	1	no	maximal, Sylow
26	C₈₃	C₂×C₄³	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₄²	—	83	7	no	—
28	C₄³	—	83	7	no	—
29	C₄³	D₈₃	1	1	yes	characteristic, direct product factor
30	C₂³×C₄	—	83	7	no	—
31	C₂×C₄²	—	83	21	no	—
32	C₂×C₄²	—	83	56	no	—
33	C₂×C₄²	C₂×D₈₃	1	7	yes	—
34	C₂⁴	—	83	1	no	—
35	C₂²×C₄	—	83	7	no	—
36	C₂²×C₄	—	83	84	no	—
37	C₂²×C₄	C₂²×D₈₃	1	7	yes	—
38	C₄²	—	83	84	no	—
39	C₄²	C₄×D₈₃	1	28	yes	direct product factor
40	C₂³	—	83	14	no	—
41	C₂³	C₂³×D₈₃	1	1	yes	characteristic
42	C₂×C₄	—	83	42	no	—
43	C₂×C₄	—	83	112	no	—
44	C₂×C₄	C₂×C₄×D₈₃	1	42	yes	—
45	C₂²	—	83	28	no	—
46	C₂²	C₂²×C₄×D₈₃	1	7	yes	—
47	C₄	—	83	28	no	—
48	C₄	C₄²×D₈₃	1	28	yes	direct product factor
49	C₂	—	83	8	no	—
50	C₂	C₂×C₄²×D₈₃	1	7	yes	—

	subgroup	G/H
center, hypercenter	C₄³	D₈₃
commutator, hypocenter	C₈₃	C₂×C₄³
Frattini	C₂³	C₂³×D₈₃
Fitting	C₄³×C₈₃	C₂
socle, cosocle	C₂³×C₈₃	C₂⁴
prime radical	C₂³×D₈₃	C₂³
LCS	G ▷ C₈₃
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. C₄²×Dic₈₃	C₂	semidirect
3. C₄³×C₈₃	C₂	semidirect
6. C₄²×D₈₃	C₄	direct (N × H)
11. C₄×Dic₈₃	C₂×C₄	semidirect
13. C₄²×C₈₃	C₂×C₄	semidirect
18. C₄×D₈₃	C₄²	direct (N × H)
21. C₄×C₈₃	C₂×C₄²	semidirect
22. Dic₈₃	C₂×C₄²	semidirect
24. D₈₃	C₄³	direct (N × H)
26. C₈₃	C₂×C₄³	semidirect
29. C₄³	D₈₃	direct (N × H)
39. C₄²	C₄×D₈₃	direct (N × H)
48. C₄	C₄²×D₈₃	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×C₄²×D₈₃	2
C₄²×Dic₈₃	2
C₄³×C₈₃	2
C₂×C₄³	83

Subgroups — C43×D83 #24909784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×D₈₃ #24909784