Subgroups — C₂×Dic₁₀₉₆ #22577831

Order 8768.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₄₈	C₂	1	2	yes	maximal
2	Dic₁₀₉₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₁₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₇₄	—	2	2	no	—
5	Dic₅₄₈	—	2	2	no	—
6	Dic₅₄₈	C₂²	1	4	yes	—
7	C₂×C₈×C₁₃₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₃₇	C₂²	1	2	yes	—
9	Dic₂₇₄	—	2	4	no	—
10	Dic₂₇₄	—	4	2	no	—
11	C₂×Dic₁₃₇	—	4	2	no	—
12	C₂×C₄×C₁₃₇	D₄	1	1	yes	characteristic
13	C₈×C₁₃₇	D₄	1	1	yes	characteristic
14	C₈×C₁₃₇	C₂³	1	1	yes	characteristic
15	C₂²×C₁₃₇	D₈	1	1	yes	characteristic
16	C₄×C₁₃₇	D₈	1	1	yes	characteristic
17	C₄×C₁₃₇	C₂×D₄	1	1	yes	characteristic
18	Dic₁₃₇	—	4	4	no	—
19	C₂×C₁₃₇	Q₃₂	1	2	yes	complemented
20	C₂×C₁₃₇	C₂×D₈	1	1	yes	characteristic
21	C₁₃₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
22	C₂×Q₃₂	—	137	1	no	maximal, Sylow
23	C₂×Q₁₆	—	137	2	no	—
24	Q₃₂	—	137	4	no	—
25	C₂×C₁₆	D₁₃₇	1	1	yes	characteristic
26	C₂×Q₈	—	274	2	no	—
27	Q₁₆	—	274	2	no	—
28	Q₁₆	—	137	4	no	—
29	C₂×C₈	C₂×D₁₃₇	1	1	yes	characteristic
30	C₁₆	C₂×D₁₃₇	1	2	yes	—
31	Q₈	—	274	4	no	—
32	Q₈	—	548	2	no	—
33	C₂×C₄	—	548	2	no	—
34	C₂×C₄	D₅₄₈	1	1	yes	characteristic
35	C₈	D₅₄₈	1	1	yes	characteristic
36	C₈	C₂²×D₁₃₇	1	1	yes	characteristic
37	C₂²	D₁₀₉₆	1	1	yes	characteristic
38	C₄	—	548	4	no	—
39	C₄	D₁₀₉₆	1	1	yes	characteristic
40	C₄	C₂×D₅₄₈	1	1	yes	characteristic
41	C₂	Dic₁₀₉₆	1	2	yes	direct product factor
42	C₂	C₂×D₁₀₉₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₀₉₆
commutator	C₈×C₁₃₇	C₂³
Frattini	C₈	C₂²×D₁₃₇
Fitting	C₂×C₁₆×C₁₃₇	C₂
socle	C₂²×C₁₃₇	D₈
hypercenter	C₂×C₁₆	D₁₃₇
hypocenter	C₁₃₇	C₂×Q₃₂
LCS	G ▷ C₈×C₁₃₇ ▷ C₄×C₁₃₇ ▷ C₂×C₁₃₇ ▷ C₁₃₇
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
2. Dic₁₀₉₆	C₂	direct (N × H)
19. C₂×C₁₃₇	Q₃₂	semidirect
21. C₁₃₇	C₂×Q₃₂	semidirect
41. C₂	Dic₁₀₉₆	direct (N × H)

Subgroups — C2×Dic1096 #22577831

Conjugacy classes of subgroups

Complements

Subgroups — C₂×Dic₁₀₉₆ #22577831