Subgroups — C₂×D₅₅₈₄ #36374565

Order 22336.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₇₉₂	C₂	1	2	yes	maximal, complemented
2	D₅₅₈₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₃₉₆	—	2	2	no	—
5	D₂₇₉₂	—	2	2	no	—
6	D₂₇₉₂	C₂²	1	4	yes	complemented
7	C₂×C₈×C₃₄₉	C₂²	1	1	yes	characteristic
8	C₁₆×C₃₄₉	C₂²	1	2	yes	complemented
9	C₂²×D₃₄₉	—	4	2	no	—
10	D₁₃₉₆	—	2	4	no	—
11	D₁₃₉₆	—	4	2	no	—
12	C₂×C₄×C₃₄₉	D₄	1	1	yes	characteristic
13	C₈×C₃₄₉	D₄	1	1	yes	characteristic
14	C₈×C₃₄₉	C₂³	1	1	yes	characteristic
15	C₂²×C₃₄₉	D₈	1	1	yes	characteristic
16	C₂×D₃₄₉	—	4	4	no	—
17	C₂×D₃₄₉	—	8	4	no	—
18	C₄×C₃₄₉	D₈	1	1	yes	characteristic
19	C₄×C₃₄₉	C₂×D₄	1	1	yes	characteristic
20	C₂×C₃₄₉	D₁₆	1	2	yes	complemented
21	C₂×C₃₄₉	C₂×D₈	1	1	yes	characteristic
22	D₃₄₉	—	8	4	no	—
23	C₃₄₉	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₁₆	—	349	1	no	maximal, Sylow
25	C₂×D₈	—	349	2	no	—
26	D₁₆	—	349	4	no	—
27	C₂×C₁₆	D₃₄₉	1	1	yes	characteristic, complemented
28	C₂×D₄	—	698	2	no	—
29	D₈	—	349	4	no	—
30	D₈	—	698	2	no	—
31	C₂×C₈	C₂×D₃₄₉	1	1	yes	characteristic
32	C₁₆	C₂×D₃₄₉	1	2	yes	complemented
33	C₂³	—	1396	2	no	—
34	D₄	—	1396	2	no	—
35	D₄	—	698	4	no	—
36	C₂×C₄	D₁₃₉₆	1	1	yes	characteristic
37	C₈	D₁₃₉₆	1	1	yes	characteristic
38	C₈	C₂²×D₃₄₉	1	1	yes	characteristic
39	C₂²	—	1396	4	no	—
40	C₂²	—	2792	4	no	—
41	C₂²	D₂₇₉₂	1	1	yes	characteristic
42	C₄	D₂₇₉₂	1	1	yes	characteristic
43	C₄	C₂×D₁₃₉₆	1	1	yes	characteristic
44	C₂	—	2792	4	no	—
45	C₂	D₅₅₈₄	1	2	yes	direct product factor
46	C₂	C₂×D₂₇₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₇₉₂
commutator, cosocle	C₈×C₃₄₉	C₂³
Frattini	C₈	C₂²×D₃₄₉
Fitting	C₂×C₁₆×C₃₄₉	C₂
socle	C₂²×C₃₄₉	D₈
hypercenter	C₂×C₁₆	D₃₄₉
hypocenter	C₃₄₉	C₂×D₁₆
LCS	G ▷ C₈×C₃₄₉ ▷ C₄×C₃₄₉ ▷ C₂×C₃₄₉ ▷ C₃₄₉
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×D₂₇₉₂	C₂	semidirect
2. D₅₅₈₄	C₂	direct (N × H)
3. C₂×C₁₆×C₃₄₉	C₂	semidirect
6. D₂₇₉₂	C₂²	semidirect
8. C₁₆×C₃₄₉	C₂²	semidirect
20. C₂×C₃₄₉	D₁₆	semidirect
23. C₃₄₉	C₂×D₁₆	semidirect
27. C₂×C₁₆	D₃₄₉	semidirect
32. C₁₆	C₂×D₃₄₉	semidirect
45. C₂	D₅₅₈₄	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×D₂₇₉₂	2
D₅₅₈₄	2
C₂×C₁₆×C₃₄₉	2
C₂×D₁₆	349

Subgroups — C2×D5584 #36374565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅₅₈₄ #36374565