Subgroups — D₄×D₅₇ #11744986

Order 912.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅₇	C₂	1	2	yes	maximal, complemented
2	C₃×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#90718	C₂	1	2	yes	maximal, complemented
4	D₂₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₁₉	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₁₉	C₂²	1	2	yes	complemented
8	C₂×D₅₇	—	2	4	no	—
9	C₂×D₅₇	C₂²	1	1	yes	characteristic
10	C₂×D₅₇	C₂²	1	2	yes	complemented
11	C₃×C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	Dic₅₇	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₁₉	—	3	2	no	—
14	D₄×C₁₉	D₃	1	1	yes	characteristic, complemented
15	C₂²⋊D₁₉	—	3	2	no	—
16	D₇₆	—	3	1	no	—
17	C₄×D₁₉	—	3	1	no	—
18	C₂×C₃×C₁₉	—	2	2	no	—
19	C₂×C₃×C₁₉	C₂³	1	1	yes	characteristic
20	D₅₇	—	2	2	no	—
21	D₅₇	D₄	1	2	yes	direct product factor
22	C₂²×C₁₉	C₂×D₃	1	2	yes	complemented
23	C₂×D₁₉	—	3	1	no	—
24	C₂×D₁₉	—	3	2	no	—
25	C₂×D₁₉	—	6	4	no	—
26	C₄×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
27	Dic₁₉	—	3	1	no	—
28	C₃×C₁₉	C₂×D₄	1	1	yes	characteristic, complemented, Hall
29	D₃×D₄	—	19	1	no	maximal, Hall
30	C₂×C₁₉	—	2	2	no	—
31	C₂×C₁₉	C₂²×D₃	1	1	yes	characteristic
32	D₁₉	—	3	2	no	—
33	D₁₉	—	6	2	no	—
34	C₂²×D₃	—	19	2	no	—
35	C₃×D₄	D₁₉	1	1	yes	characteristic, complemented
36	#67	—	19	2	no	—
37	D₁₂	—	19	1	no	—
38	C₄×D₃	—	19	1	no	—
39	C₁₉	D₃×D₄	1	1	yes	characteristic, complemented, Sylow
40	C₂×D₄	—	57	1	no	Sylow
41	C₂²×C₃	C₂×D₁₉	1	2	yes	complemented
42	C₂×D₃	—	19	1	no	—
43	C₂×D₃	—	19	2	no	—
44	C₂×D₃	—	38	4	no	—
45	C₃×C₄	C₂×D₁₉	1	1	yes	characteristic, complemented
46	Dic₃	—	19	1	no	—
47	C₂³	—	57	2	no	—
48	D₄	—	57	2	no	—
49	D₄	—	57	1	no	—
50	D₄	D₅₇	1	1	yes	characteristic, direct product factor
51	C₂×C₄	—	57	1	no	—
52	C₂×C₃	—	2	2	no	—
53	C₂×C₃	C₂²×D₁₉	1	1	yes	characteristic
54	D₃	—	19	2	no	—
55	D₃	—	38	2	no	—
56	C₂²	—	57	1	no	—
57	C₂²	—	57	2	no	—
58	C₂²	—	114	4	no	—
59	C₂²	C₂×D₅₇	1	2	yes	complemented
60	C₄	—	57	1	no	—
61	C₄	C₂×D₅₇	1	1	yes	characteristic, complemented
62	C₃	D₄×D₁₉	1	1	yes	characteristic, complemented, Sylow
63	C₂	—	2	2	no	—
64	C₂	—	57	2	no	—
65	C₂	—	114	2	no	—
66	C₂	C₂²×D₅₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×D₅₇
commutator, socle, cosocle	C₂×C₃×C₁₉	C₂³
Fitting	C₃×D₄×C₁₉	C₂
hypercenter	D₄	D₅₇
hypocenter	C₃×C₁₉	C₂×D₄
LCS	G ▷ C₂×C₃×C₁₉ ▷ C₃×C₁₉
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₅₇	C₂	semidirect
2. C₃×D₄×C₁₉	C₂	semidirect
3. #90718	C₂	semidirect
4. D₂₂₈	C₂	semidirect
5. C₄×D₅₇	C₂	semidirect
7. C₂²×C₃×C₁₉	C₂²	semidirect
10. C₂×D₅₇	C₂²	semidirect
11. C₃×C₄×C₁₉	C₂²	semidirect
12. Dic₅₇	C₂²	semidirect
14. D₄×C₁₉	D₃	semidirect
21. D₅₇	D₄	direct (N × H)
22. C₂²×C₁₉	C₂×D₃	semidirect
26. C₄×C₁₉	C₂×D₃	semidirect
28. C₃×C₁₉	C₂×D₄	semidirect
35. C₃×D₄	D₁₉	semidirect
39. C₁₉	D₃×D₄	semidirect
41. C₂²×C₃	C₂×D₁₉	semidirect
45. C₃×C₄	C₂×D₁₉	semidirect
50. D₄	D₅₇	direct (N × H)
59. C₂²	C₂×D₅₇	semidirect
61. C₄	C₂×D₅₇	semidirect
62. C₃	D₄×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₅₇	2
C₃×D₄×C₁₉	2
#90718	2
D₂₂₈	2
C₄×D₅₇	2
D₄×D₁₉	3
D₃×D₄	19

Subgroups — D4×D57 #11744986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×D₅₇ #11744986