Subgroups — C₂²×D₁₃₃₆ #24924039

Order 10688.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₆₆₈	C₂	1	2	yes	maximal, complemented
2	C₂×D₁₃₃₆	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×C₁₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₁₆₇	—	2	2	no	—
5	C₂×D₆₆₈	—	2	6	no	—
6	C₂×D₆₆₈	C₂²	1	12	yes	complemented
7	D₁₃₃₆	C₂²	1	16	yes	direct product factor
8	C₂²×C₄×C₁₆₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₁₆₇	C₂²	1	6	yes	complemented
10	C₂²×D₁₆₇	—	2	12	no	—
11	C₂²×D₁₆₇	—	4	8	no	—
12	D₆₆₈	—	2	12	no	—
13	D₆₆₈	C₂³	1	8	yes	complemented
14	C₂³×C₁₆₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₆₇	D₄	1	3	yes	—
16	C₂×C₄×C₁₆₇	C₂³	1	3	yes	—
17	C₈×C₁₆₇	C₂³	1	4	yes	complemented
18	C₂²×C₁₆₇	D₈	1	4	yes	complemented
19	C₂²×C₁₆₇	C₂×D₄	1	3	yes	—
20	C₂×D₁₆₇	—	2	8	no	—
21	C₂×D₁₆₇	—	4	24	no	—
22	C₄×C₁₆₇	C₂×D₄	1	3	yes	—
23	C₄×C₁₆₇	C₂⁴	1	1	yes	characteristic
24	C₂×C₁₆₇	C₂×D₈	1	6	yes	complemented
25	C₂×C₁₆₇	C₂²×D₄	1	1	yes	characteristic
26	D₁₆₇	—	4	8	no	—
27	C₁₆₇	C₂²×D₈	1	1	yes	characteristic, complemented, Sylow
28	C₂²×D₈	—	167	1	no	maximal, Sylow
29	C₂²×D₄	—	167	2	no	—
30	C₂×D₈	—	167	12	no	—
31	C₂²×C₈	D₁₆₇	1	1	yes	characteristic, complemented
32	C₂⁴	—	334	2	no	—
33	C₂×D₄	—	334	6	no	—
34	C₂×D₄	—	167	12	no	—
35	C₂²×C₄	C₂×D₁₆₇	1	1	yes	characteristic
36	D₈	—	167	16	no	—
37	C₂×C₈	C₂×D₁₆₇	1	6	yes	complemented
38	C₂³	—	334	12	no	—
39	C₂³	—	668	8	no	—
40	C₂³	D₆₆₈	1	1	yes	characteristic
41	D₄	—	334	12	no	—
42	D₄	—	167	8	no	—
43	C₂×C₄	D₆₆₈	1	3	yes	—
44	C₂×C₄	C₂²×D₁₆₇	1	3	yes	—
45	C₈	C₂²×D₁₆₇	1	4	yes	complemented
46	C₂²	—	334	8	no	—
47	C₂²	—	668	24	no	—
48	C₂²	D₁₃₃₆	1	4	yes	direct product factor
49	C₂²	C₂×D₆₆₈	1	3	yes	—
50	C₄	C₂×D₆₆₈	1	3	yes	—
51	C₄	C₂³×D₁₆₇	1	1	yes	characteristic
52	C₂	—	668	8	no	—
53	C₂	C₂×D₁₃₃₆	1	6	yes	direct product factor
54	C₂	C₂²×D₆₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₆₆₈
commutator, cosocle	C₄×C₁₆₇	C₂⁴
Frattini	C₄	C₂³×D₁₆₇
Fitting	C₂²×C₈×C₁₆₇	C₂
socle	C₂³×C₁₆₇	D₄
hypercenter	C₂²×C₈	D₁₆₇
hypocenter	C₁₆₇	C₂²×D₈
LCS	G ▷ C₄×C₁₆₇ ▷ C₂×C₁₆₇ ▷ C₁₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×D₆₆₈	C₂	semidirect
2. C₂×D₁₃₃₆	C₂	direct (N × H)
3. C₂²×C₈×C₁₆₇	C₂	semidirect
6. C₂×D₆₆₈	C₂²	semidirect
7. D₁₃₃₆	C₂²	direct (N × H)
9. C₂×C₈×C₁₆₇	C₂²	semidirect
13. D₆₆₈	C₂³	semidirect
17. C₈×C₁₆₇	C₂³	semidirect
18. C₂²×C₁₆₇	D₈	semidirect
24. C₂×C₁₆₇	C₂×D₈	semidirect
27. C₁₆₇	C₂²×D₈	semidirect
31. C₂²×C₈	D₁₆₇	semidirect
37. C₂×C₈	C₂×D₁₆₇	semidirect
45. C₈	C₂²×D₁₆₇	semidirect
48. C₂²	D₁₃₃₆	direct (N × H)
53. C₂	C₂×D₁₃₃₆	direct (N × H)

Subgroups — C22×D1336 #24924039

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×D₁₃₃₆ #24924039