Subgroups — #22553600

Order 8384.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16862245	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×Dic₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#16862178	C₂	1	1	yes	maximal, characteristic, complemented
4	#16862177	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#16862167	C₂	1	1	yes	maximal, characteristic
7	#102×C₁₃₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₆₂	—	2	1	no	—
9	C₂²×Dic₁₃₁	—	2	1	no	—
10	C₂×C₁₃₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₃₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₃₁	C₂²	1	1	yes	characteristic
13	Dic₁₃₁⋊C₄	—	2	1	no	—
14	C₂²⋊Dic₁₃₁	—	2	1	no	—
15	C₄×Dic₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₃₁	C₂²	1	1	yes	characteristic
19	Dic₂₆₂	—	4	2	no	—
20	C₂×Dic₁₃₁	—	2	1	no	—
21	C₂×Dic₁₃₁	—	2	1	no	—
22	C₂×Dic₁₃₁	—	4	2	no	—
23	C₂×Dic₁₃₁	D₄	1	1	yes	characteristic
24	C₂×Dic₁₃₁	D₄	1	1	yes	characteristic
25	C₁₃₁⋊C₈	—	2	1	no	—
26	C₂³×C₁₃₁	—	2	1	no	—
27	D₄×C₁₃₁	—	2	1	no	—
28	D₄×C₁₃₁	Q₈	1	2	yes	complemented
29	C₂×C₄×C₁₃₁	—	2	1	no	—
30	C₂×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
31	C₈×C₁₃₁	—	2	1	no	—
32	C₂²×C₁₃₁	—	2	2	no	—
33	C₂²×C₁₃₁	—	4	1	no	—
34	C₂²×C₁₃₁	—	4	1	no	—
35	C₂²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
36	C₄×C₁₃₁	—	4	1	no	—
37	C₄×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₁₃₁	#41	1	1	yes	characteristic
39	Dic₁₃₁	—	2	1	no	—
40	Dic₁₃₁	—	4	1	no	—
41	Dic₁₃₁	—	4	1	no	—
42	Dic₁₃₁	SD₁₆	1	2	yes	—
43	C₂×C₁₃₁	—	4	2	no	—
44	C₂×C₁₃₁	C₂²⋊Q₈	1	1	yes	characteristic
45	C₂×C₁₃₁	C₂×SD₁₆	1	1	yes	characteristic
46	C₂×C₁₃₁	AGL(1,ℤ/8)	1	1	yes	characteristic
47	C₁₃₁	#476	1	1	yes	characteristic, complemented, Sylow
48	#476	—	131	1	no	maximal, Sylow
49	C₄⋊Q₈	—	131	1	no	—
50	C₄×D₄	—	131	1	no	—
51	#106	—	131	1	no	—
52	#106	—	131	1	no	—
53	C₄⋊C₈	—	131	1	no	—
54	#102	—	131	1	no	—
55	#102	D₁₃₁	1	1	yes	characteristic
56	C₂×Q₈	—	262	1	no	—
57	C₂×D₄	C₂×D₁₃₁	1	1	yes	characteristic
58	C₂²×C₄	—	262	1	no	—
59	C₂×C₈	—	131	1	no	—
60	C₂×C₈	C₂×D₁₃₁	1	1	yes	characteristic
61	C₄⋊C₄	—	262	1	no	—
62	C₄⋊C₄	—	131	1	no	—
63	C₄⋊C₄	—	131	1	no	—
64	C₄⋊C₄	C₂×D₁₃₁	1	1	yes	characteristic
65	C₂²⋊C₄	—	262	1	no	—
66	C₄²	—	131	1	no	—
67	C₂³	—	2	1	no	—
68	Q₈	—	524	2	no	—
69	D₄	—	2	1	no	—
70	D₄	Dic₂₆₂	1	2	yes	complemented
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	262	1	no	—
73	C₂×C₄	—	262	1	no	—
74	C₂×C₄	—	524	2	no	—
75	C₂×C₄	—	131	1	no	—
76	C₂×C₄	—	131	1	no	—
77	C₂×C₄	C₂²×D₁₃₁	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	262	1	no	—
80	C₂²	—	2	2	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	D₄×D₁₃₁	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	262	1	no	—
86	C₄	—	524	1	no	—
87	C₄	—	524	1	no	—
88	C₄	—	131	2	no	—
89	C₄	C₂×Dic₂₆₂	1	1	yes	characteristic
90	C₄	#14523512	1	1	yes	characteristic
91	C₂	—	4	2	no	—
92	C₂	#16862223	1	1	yes	characteristic
93	C₂	SD₁₆×D₁₃₁	1	1	yes	characteristic
94	C₂	#16862270	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃₁
commutator	C₂×C₄×C₁₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₃₁
Fitting	#102×C₁₃₁	C₂
socle	C₂²×C₁₃₁	C₂×D₄
hypercenter	#102	D₁₃₁
hypocenter	C₁₃₁	#476
LCS	G ▷ C₂×C₄×C₁₃₁ ▷ C₂×C₁₃₁ ▷ C₁₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
1. #16862245	C₂	semidirect
3. #16862178	C₂	semidirect
4. #16862177	C₂	semidirect
5. Dic₁₃₁⋊C₈	C₂	semidirect
28. D₄×C₁₃₁	Q₈	semidirect
47. C₁₃₁	#476	semidirect
70. D₄	Dic₂₆₂	semidirect