Subgroups — C₂×Dic₁₃₃₆ #24923697

Order 10688.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₆₈	C₂	1	2	yes	maximal
2	Dic₁₃₃₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₁₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₃₄	—	2	2	no	—
5	Dic₆₆₈	—	2	2	no	—
6	Dic₆₆₈	C₂²	1	4	yes	—
7	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₁₆₇	C₂²	1	2	yes	—
9	Dic₃₃₄	—	2	4	no	—
10	Dic₃₃₄	—	4	2	no	—
11	C₂×Dic₁₆₇	—	4	2	no	—
12	C₂×C₄×C₁₆₇	D₄	1	1	yes	characteristic
13	C₈×C₁₆₇	D₄	1	1	yes	characteristic
14	C₈×C₁₆₇	C₂³	1	1	yes	characteristic
15	C₂²×C₁₆₇	D₈	1	1	yes	characteristic
16	C₄×C₁₆₇	D₈	1	1	yes	characteristic
17	C₄×C₁₆₇	C₂×D₄	1	1	yes	characteristic
18	Dic₁₆₇	—	4	4	no	—
19	C₂×C₁₆₇	Q₃₂	1	2	yes	complemented
20	C₂×C₁₆₇	C₂×D₈	1	1	yes	characteristic
21	C₁₆₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
22	C₂×Q₃₂	—	167	1	no	maximal, Sylow
23	C₂×Q₁₆	—	167	2	no	—
24	Q₃₂	—	167	4	no	—
25	C₂×C₁₆	D₁₆₇	1	1	yes	characteristic
26	C₂×Q₈	—	334	2	no	—
27	Q₁₆	—	334	2	no	—
28	Q₁₆	—	167	4	no	—
29	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
30	C₁₆	C₂×D₁₆₇	1	2	yes	—
31	Q₈	—	334	4	no	—
32	Q₈	—	668	2	no	—
33	C₂×C₄	—	668	2	no	—
34	C₂×C₄	D₆₆₈	1	1	yes	characteristic
35	C₈	D₆₆₈	1	1	yes	characteristic
36	C₈	C₂²×D₁₆₇	1	1	yes	characteristic
37	C₂²	D₁₃₃₆	1	1	yes	characteristic
38	C₄	—	668	4	no	—
39	C₄	D₁₃₃₆	1	1	yes	characteristic
40	C₄	C₂×D₆₆₈	1	1	yes	characteristic
41	C₂	Dic₁₃₃₆	1	2	yes	direct product factor
42	C₂	C₂×D₁₃₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₃₃₆
commutator, cosocle	C₈×C₁₆₇	C₂³
Frattini	C₈	C₂²×D₁₆₇
Fitting	C₂×C₁₆×C₁₆₇	C₂
socle, prime radical	C₂²×C₁₆₇	D₈
hypercenter	C₂×C₁₆	D₁₆₇
hypocenter	C₁₆₇	C₂×Q₃₂
LCS	G ▷ C₈×C₁₆₇ ▷ C₄×C₁₆₇ ▷ C₂×C₁₆₇ ▷ C₁₆₇
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. Dic₁₃₃₆	C₂	direct (N × H)
19. C₂×C₁₆₇	Q₃₂	semidirect
21. C₁₆₇	C₂×Q₃₂	semidirect
41. C₂	Dic₁₃₃₆	direct (N × H)

Subgroups — C2×Dic1336 #24923697

Conjugacy classes of subgroups

Complements

Subgroups — C₂×Dic₁₃₃₆ #24923697