Subgroups — C₄×#14523496 #22553262

Order 8384.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14523496	C₂	1	2	yes	maximal
2	C₄²×D₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#16862156	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₃₁	C₄	1	2	yes	—
7	C₂×C₄×D₁₃₁	C₂²	1	1	yes	characteristic
8	#14523496	C₄	1	8	yes	direct product factor
9	C₂×C₁₃₁⋊C₈	C₂²	1	2	yes	—
10	C₄×Dic₁₃₁	C₄	1	2	yes	—
11	C₄×Dic₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₃₁	C₂²	1	2	yes	—
13	C₄²×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂²×D₁₃₁	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₃₁	C₂×C₄	1	2	yes	—
16	C₂×Dic₁₃₁	C₂×C₄	1	1	yes	characteristic
17	C₄×D₁₃₁	—	2	4	no	—
18	C₄×D₁₃₁	C₂×C₄	1	4	yes	—
19	C₁₃₁⋊C₈	C₂×C₄	1	4	yes	complemented
20	C₂×C₄×C₁₃₁	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
22	C₈×C₁₃₁	C₂×C₄	1	4	yes	complemented
23	C₂²×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₁₃₁	—	2	2	no	—
25	C₂×D₁₃₁	C₄²	1	2	yes	—
26	C₄×C₁₃₁	M₁₆	1	4	yes	complemented
27	C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
28	Dic₁₃₁	—	2	2	no	—
29	Dic₁₃₁	C₄²	1	2	yes	—
30	C₂×C₁₃₁	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₁₃₁	C₂×M₁₆	1	2	yes	—
32	D₁₃₁	—	2	2	no	—
33	C₁₃₁	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×M₁₆	—	131	1	no	maximal, Sylow
35	C₂×M₁₆	—	131	2	no	—
36	C₂×C₄²	—	131	1	no	—
37	#97	—	131	2	no	—
38	C₄×C₈	—	131	1	no	—
39	C₄×C₈	D₁₃₁	1	1	yes	characteristic, complemented
40	C₂²×C₄	—	131	2	no	—
41	C₂²×C₄	—	131	1	no	—
42	M₁₆	—	131	8	no	—
43	C₂×C₈	—	131	2	no	—
44	C₂×C₈	C₂×D₁₃₁	1	2	yes	—
45	C₄²	—	131	2	no	—
46	C₄²	—	131	1	no	—
47	C₄²	C₂×D₁₃₁	1	1	yes	characteristic
48	C₂³	—	131	1	no	—
49	C₂×C₄	—	262	4	no	—
50	C₂×C₄	—	131	2	no	—
51	C₂×C₄	—	131	1	no	—
52	C₂×C₄	—	131	4	no	—
53	C₂×C₄	C₄×D₁₃₁	1	2	yes	—
54	C₂×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
55	C₈	—	131	4	no	—
56	C₈	C₄×D₁₃₁	1	4	yes	complemented
57	C₂²	—	262	2	no	—
58	C₂²	—	131	2	no	—
59	C₂²	C₂×C₄×D₁₃₁	1	1	yes	characteristic
60	C₄	—	262	2	no	—
61	C₄	—	131	2	no	—
62	C₄	#14523496	1	4	yes	direct product factor
63	C₄	C₂×C₄×D₁₃₁	1	2	yes	—
64	C₂	—	262	2	no	—
65	C₂	C₄²×D₁₃₁	1	1	yes	characteristic
66	C₂	C₂×#14523496	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×D₁₃₁
commutator	C₂×C₁₃₁	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₁₃₁
Fitting	C₄×C₈×C₁₃₁	C₂
socle	C₂²×C₁₃₁	C₂²×C₄
hypercenter	C₄×C₈	D₁₃₁
hypocenter	C₁₃₁	C₄×M₁₆
LCS	G ▷ C₂×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #16862156	C₂	semidirect
4. C₄×C₁₃₁⋊C₈	C₂	semidirect
5. C₄×C₈×C₁₃₁	C₂	semidirect
8. #14523496	C₄	direct (N × H)
19. C₁₃₁⋊C₈	C₂×C₄	semidirect
22. C₈×C₁₃₁	C₂×C₄	semidirect
26. C₄×C₁₃₁	M₁₆	semidirect
33. C₁₃₁	C₄×M₁₆	semidirect
39. C₄×C₈	D₁₃₁	semidirect
56. C₈	C₄×D₁₃₁	semidirect
62. C₄	#14523496	direct (N × H)

Subgroups — C4×#14523496 #22553262

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14523496 #22553262