Subgroups — C₄²×D₅₇ #14269709

Order 1824.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅₇	C₂	1	3	yes	maximal
2	C₃×C₄²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₅₇	C₂	1	3	yes	maximal, complemented
4	C₄²×D₁₉	—	3	1	no	maximal, Hall
5	C₂²×D₅₇	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₉	C₂²	1	3	yes	—
7	C₂×Dic₅₇	C₂²	1	3	yes	—
8	C₄×D₅₇	C₄	1	12	yes	direct product factor
9	C₂×C₄×D₁₉	—	3	3	no	—
10	C₄²×C₁₉	D₃	1	1	yes	characteristic, complemented
11	C₄×Dic₁₉	—	3	3	no	—
12	C₂²×C₃×C₁₉	C₂³	1	1	yes	characteristic
13	C₂×D₅₇	C₂×C₄	1	6	yes	—
14	C₃×C₄×C₁₉	C₂×C₄	1	6	yes	complemented
15	Dic₅₇	C₂×C₄	1	6	yes	complemented
16	C₂²×D₁₉	—	3	1	no	—
17	C₂×C₄×C₁₉	C₂×D₃	1	3	yes	—
18	C₂×Dic₁₉	—	3	3	no	—
19	C₄×D₁₉	—	3	12	no	—
20	C₂×C₃×C₁₉	C₂²×C₄	1	3	yes	—
21	D₅₇	C₄²	1	4	yes	direct product factor
22	C₄²×D₃	—	19	1	no	maximal, Hall
23	C₂²×C₁₉	C₂²×D₃	1	1	yes	characteristic
24	C₂×D₁₉	—	3	6	no	—
25	C₄×C₁₉	C₄×D₃	1	6	yes	complemented
26	Dic₁₉	—	3	6	no	—
27	C₃×C₁₉	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄×D₃	—	19	3	no	—
29	C₃×C₄²	D₁₉	1	1	yes	characteristic, complemented
30	C₄×Dic₃	—	19	3	no	—
31	C₂×C₁₉	C₂×C₄×D₃	1	3	yes	—
32	D₁₉	—	3	4	no	—
33	C₂×C₄²	—	57	1	no	Sylow
34	C₂²×D₃	—	19	1	no	—
35	C₂×C₃×C₄	C₂×D₁₉	1	3	yes	—
36	C₂×Dic₃	—	19	3	no	—
37	C₄×D₃	—	19	12	no	—
38	C₁₉	C₄²×D₃	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₄	—	57	3	no	—
40	C₄²	—	57	3	no	—
41	C₄²	D₅₇	1	1	yes	characteristic, direct product factor
42	C₂²×C₃	C₂²×D₁₉	1	1	yes	characteristic
43	C₂×D₃	—	19	6	no	—
44	C₃×C₄	C₄×D₁₉	1	6	yes	complemented
45	Dic₃	—	19	6	no	—
46	C₂³	—	57	1	no	—
47	C₂×C₄	—	57	3	no	—
48	C₂×C₄	—	57	12	no	—
49	C₂×C₄	C₂×D₅₇	1	3	yes	—
50	C₂×C₃	C₂×C₄×D₁₉	1	3	yes	—
51	D₃	—	19	4	no	—
52	C₂²	—	57	6	no	—
53	C₂²	C₂²×D₅₇	1	1	yes	characteristic
54	C₄	—	57	6	no	—
55	C₄	C₄×D₅₇	1	6	yes	direct product factor
56	C₃	C₄²×D₁₉	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	57	4	no	—
58	C₂	C₂×C₄×D₅₇	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²	D₅₇
commutator, hypocenter	C₃×C₁₉	C₂×C₄²
Frattini	C₂²	C₂²×D₅₇
Fitting	C₃×C₄²×C₁₉	C₂
socle, cosocle	C₂²×C₃×C₁₉	C₂³
prime radical	C₂²×D₅₇	C₂²
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₁₉	C₂	semidirect
3. C₄×Dic₅₇	C₂	semidirect
8. C₄×D₅₇	C₄	direct (N × H)
10. C₄²×C₁₉	D₃	semidirect
14. C₃×C₄×C₁₉	C₂×C₄	semidirect
15. Dic₅₇	C₂×C₄	semidirect
21. D₅₇	C₄²	direct (N × H)
25. C₄×C₁₉	C₄×D₃	semidirect
27. C₃×C₁₉	C₂×C₄²	semidirect
29. C₃×C₄²	D₁₉	semidirect
38. C₁₉	C₄²×D₃	semidirect
41. C₄²	D₅₇	direct (N × H)
44. C₃×C₄	C₄×D₁₉	semidirect
55. C₄	C₄×D₅₇	direct (N × H)
56. C₃	C₄²×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₅₇	2
C₃×C₄²×C₁₉	2
C₄×Dic₅₇	2
C₄²×D₁₉	3
C₄²×D₃	19

Subgroups — C42×D57 #14269709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×D₅₇ #14269709