Subgroups — C₂×C₈×Dic₅₃ #16810568

Order 3392.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88322	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₅₃	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₅₃	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₅₃	C₂²	1	1	yes	characteristic
6	C₂²×Dic₅₃	C₄	1	2	yes	—
7	C₂×C₈×C₅₃	C₄	1	4	yes	complemented
8	C₂×C₈×C₅₃	C₂²	1	2	yes	—
9	C₄×Dic₅₃	C₄	1	2	yes	—
10	C₄×Dic₅₃	C₂²	1	2	yes	—
11	C₂×#88322	C₄	1	4	yes	complemented
12	C₂×#88322	C₂²	1	2	yes	—
13	C₂³×C₅₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₅₃	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₅₃	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₅₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₅₃	C₈	1	8	yes	direct product factor
19	C₂×Dic₅₃	C₂×C₄	1	4	yes	—
20	C₈×C₅₃	C₂×C₄	1	4	yes	complemented
21	#88322	C₂×C₄	1	4	yes	complemented
22	C₂²×C₅₃	C₄²	1	2	yes	—
23	C₂²×C₅₃	C₂×C₈	1	4	yes	—
24	C₂²×C₅₃	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₅₃	C₄²	1	2	yes	—
26	C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
28	Dic₅₃	C₂×C₈	1	8	yes	direct product factor
29	C₂×C₅₃	C₄×C₈	1	4	yes	complemented
30	C₂×C₅₃	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₅₃	C₂²×C₈	1	2	yes	—
32	C₂×C₄×C₈	—	53	1	no	maximal, Sylow
33	C₅₃	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₈	—	53	1	no	—
35	C₂²×C₈	D₅₃	1	1	yes	characteristic
36	C₂×C₄²	—	53	1	no	—
37	C₄×C₈	—	53	4	no	—
38	C₂²×C₄	—	53	2	no	—
39	C₂²×C₄	C₂×D₅₃	1	1	yes	characteristic
40	C₂×C₈	—	53	4	no	—
41	C₂×C₈	—	53	2	no	—
42	C₂×C₈	Dic₅₃	1	4	yes	direct product factor
43	C₂×C₈	C₂×D₅₃	1	2	yes	—
44	C₄²	—	53	2	no	—
45	C₄²	—	53	2	no	—
46	C₂³	C₄×D₅₃	1	1	yes	characteristic
47	C₂×C₄	—	53	4	no	—
48	C₂×C₄	—	53	8	no	—
49	C₂×C₄	C₄×D₅₃	1	2	yes	—
50	C₂×C₄	C₄×D₅₃	1	1	yes	characteristic
51	C₂×C₄	C₂×Dic₅₃	1	2	yes	—
52	C₂×C₄	C₂²×D₅₃	1	1	yes	characteristic
53	C₈	—	53	4	no	—
54	C₈	C₂×Dic₅₃	1	4	yes	direct product factor
55	C₂²	C₈×D₅₃	1	4	yes	—
56	C₂²	C₄×Dic₅₃	1	2	yes	—
57	C₂²	C₂×C₄×D₅₃	1	1	yes	characteristic
58	C₄	—	53	8	no	—
59	C₄	C₄×Dic₅₃	1	2	yes	—
60	C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
61	C₄	C₂²×Dic₅₃	1	1	yes	characteristic
62	C₂	C₈×Dic₅₃	1	4	yes	direct product factor
63	C₂	C₂×C₄×Dic₅₃	1	1	yes	characteristic
64	C₂	C₂×C₈×D₅₃	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₅₃
commutator, hypocenter	C₅₃	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×D₅₃
Fitting	C₂²×C₈×C₅₃	C₂
socle, prime radical	C₂³×C₅₃	C₂×C₄
cosocle	C₂×C₄×C₅₃	C₂³
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₈×Dic₅₃	C₂	direct (N × H)
7. C₂×C₈×C₅₃	C₄	semidirect
11. C₂×#88322	C₄	semidirect
18. C₂×Dic₅₃	C₈	direct (N × H)
20. C₈×C₅₃	C₂×C₄	semidirect
21. #88322	C₂×C₄	semidirect
28. Dic₅₃	C₂×C₈	direct (N × H)
29. C₂×C₅₃	C₄×C₈	semidirect
33. C₅₃	C₂×C₄×C₈	semidirect
42. C₂×C₈	Dic₅₃	direct (N × H)
54. C₈	C₂×Dic₅₃	direct (N × H)
62. C₂	C₈×Dic₅₃	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×#88322	2
C₂×C₄×Dic₅₃	2
C₈×Dic₅₃	2
C₂²×C₈×C₅₃	2
C₂×C₄×C₈	53

Subgroups — C2×C8×Dic53 #16810568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×Dic₅₃ #16810568