Subgroups — C₂×D₅₇₄₄ #37526864

Order 22976.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₈₇₂	C₂	1	2	yes	maximal, complemented
2	D₅₇₄₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₃₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₄₃₆	—	2	2	no	—
5	D₂₈₇₂	—	2	2	no	—
6	D₂₈₇₂	C₂²	1	4	yes	complemented
7	C₂×C₈×C₃₅₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₃₅₉	C₂²	1	2	yes	complemented
9	C₂²×D₃₅₉	—	4	2	no	—
10	D₁₄₃₆	—	2	4	no	—
11	D₁₄₃₆	—	4	2	no	—
12	C₂×C₄×C₃₅₉	D₄	1	1	yes	characteristic
13	C₈×C₃₅₉	D₄	1	1	yes	characteristic
14	C₈×C₃₅₉	C₂³	1	1	yes	characteristic
15	C₂²×C₃₅₉	D₈	1	1	yes	characteristic
16	C₂×D₃₅₉	—	4	4	no	—
17	C₂×D₃₅₉	—	8	4	no	—
18	C₄×C₃₅₉	D₈	1	1	yes	characteristic
19	C₄×C₃₅₉	C₂×D₄	1	1	yes	characteristic
20	C₂×C₃₅₉	D₁₆	1	2	yes	complemented
21	C₂×C₃₅₉	C₂×D₈	1	1	yes	characteristic
22	D₃₅₉	—	8	4	no	—
23	C₃₅₉	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₆	—	359	1	no	maximal, Sylow
25	C₂×D₈	—	359	2	no	—
26	D₁₆	—	359	4	no	—
27	C₂×C₁₆	D₃₅₉	1	1	yes	characteristic, complemented
28	C₂×D₄	—	718	2	no	—
29	D₈	—	359	4	no	—
30	D₈	—	718	2	no	—
31	C₂×C₈	C₂×D₃₅₉	1	1	yes	characteristic
32	C₁₆	C₂×D₃₅₉	1	2	yes	complemented
33	C₂³	—	1436	2	no	—
34	D₄	—	1436	2	no	—
35	D₄	—	718	4	no	—
36	C₂×C₄	D₁₄₃₆	1	1	yes	characteristic
37	C₈	D₁₄₃₆	1	1	yes	characteristic
38	C₈	C₂²×D₃₅₉	1	1	yes	characteristic
39	C₂²	—	2872	4	no	—
40	C₂²	—	1436	4	no	—
41	C₂²	D₂₈₇₂	1	1	yes	characteristic
42	C₄	D₂₈₇₂	1	1	yes	characteristic
43	C₄	C₂×D₁₄₃₆	1	1	yes	characteristic
44	C₂	—	2872	4	no	—
45	C₂	D₅₇₄₄	1	2	yes	direct product factor
46	C₂	C₂×D₂₈₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₈₇₂
commutator, cosocle	C₈×C₃₅₉	C₂³
Frattini	C₈	C₂²×D₃₅₉
Fitting	C₂×C₁₆×C₃₅₉	C₂
socle	C₂²×C₃₅₉	D₈
hypercenter	C₂×C₁₆	D₃₅₉
hypocenter	C₃₅₉	C₂×D₁₆
LCS	G ▷ C₈×C₃₅₉ ▷ C₄×C₃₅₉ ▷ C₂×C₃₅₉ ▷ C₃₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₈₇₂	C₂	semidirect
2. D₅₇₄₄	C₂	direct (N × H)
3. C₂×C₁₆×C₃₅₉	C₂	semidirect
6. D₂₈₇₂	C₂²	semidirect
8. C₁₆×C₃₅₉	C₂²	semidirect
20. C₂×C₃₅₉	D₁₆	semidirect
23. C₃₅₉	C₂×D₁₆	semidirect
27. C₂×C₁₆	D₃₅₉	semidirect
32. C₁₆	C₂×D₃₅₉	semidirect
45. C₂	D₅₇₄₄	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×D₂₈₇₂	2
D₅₇₄₄	2
C₂×C₁₆×C₃₅₉	2
C₂×D₁₆	359

Subgroups — C2×D5744 #37526864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅₇₄₄ #37526864