Subgroups — C₂×D₅₉₂ #14557954

Order 2368.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₉₆	C₂	1	2	yes	maximal, complemented
2	D₅₉₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₄₈	—	2	2	no	—
5	C₂×C₈×C₃₇	C₂²	1	1	yes	characteristic
6	D₂₉₆	—	2	2	no	—
7	D₂₉₆	C₂²	1	4	yes	complemented
8	C₁₆×C₃₇	C₂²	1	2	yes	complemented
9	C₂²×D₃₇	—	4	2	no	—
10	C₂×C₄×C₃₇	D₄	1	1	yes	characteristic
11	D₁₄₈	—	2	4	no	—
12	D₁₄₈	—	4	2	no	—
13	C₈×C₃₇	D₄	1	1	yes	characteristic
14	C₈×C₃₇	C₂³	1	1	yes	characteristic
15	C₂²×C₃₇	D₈	1	1	yes	characteristic
16	C₂×D₃₇	—	4	4	no	—
17	C₂×D₃₇	—	8	4	no	—
18	C₄×C₃₇	D₈	1	1	yes	characteristic
19	C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
20	C₂×C₃₇	D₁₆	1	2	yes	complemented
21	C₂×C₃₇	C₂×D₈	1	1	yes	characteristic
22	D₃₇	—	8	4	no	—
23	C₂×D₁₆	—	37	1	no	maximal, Sylow
24	C₃₇	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₈	—	37	2	no	—
26	D₁₆	—	37	4	no	—
27	C₂×C₁₆	D₃₇	1	1	yes	characteristic, complemented
28	C₂×D₄	—	74	2	no	—
29	D₈	—	37	4	no	—
30	D₈	—	74	2	no	—
31	C₂×C₈	C₂×D₃₇	1	1	yes	characteristic
32	C₁₆	C₂×D₃₇	1	2	yes	complemented
33	C₂³	—	148	2	no	—
34	D₄	—	74	4	no	—
35	D₄	—	148	2	no	—
36	C₂×C₄	D₁₄₈	1	1	yes	characteristic
37	C₈	D₁₄₈	1	1	yes	characteristic
38	C₈	C₂²×D₃₇	1	1	yes	characteristic
39	C₂²	—	296	4	no	—
40	C₂²	—	148	4	no	—
41	C₂²	D₂₉₆	1	1	yes	characteristic
42	C₄	D₂₉₆	1	1	yes	characteristic
43	C₄	C₂×D₁₄₈	1	1	yes	characteristic
44	C₂	—	296	4	no	—
45	C₂	D₅₉₂	1	2	yes	direct product factor
46	C₂	C₂×D₂₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₉₆
commutator, cosocle	C₈×C₃₇	C₂³
Frattini	C₈	C₂²×D₃₇
Fitting	C₂×C₁₆×C₃₇	C₂
socle	C₂²×C₃₇	D₈
hypercenter	C₂×C₁₆	D₃₇
hypocenter	C₃₇	C₂×D₁₆
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
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×D₂₉₆	C₂	semidirect
2. D₅₉₂	C₂	direct (N × H)
3. C₂×C₁₆×C₃₇	C₂	semidirect
7. D₂₉₆	C₂²	semidirect
8. C₁₆×C₃₇	C₂²	semidirect
20. C₂×C₃₇	D₁₆	semidirect
24. C₃₇	C₂×D₁₆	semidirect
27. C₂×C₁₆	D₃₇	semidirect
32. C₁₆	C₂×D₃₇	semidirect
45. C₂	D₅₉₂	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×D₂₉₆	2
D₅₉₂	2
C₂×C₁₆×C₃₇	2
C₂×D₁₆	37

Subgroups — C2×D592 #14557954

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅₉₂ #14557954