Subgroups — #23752570

Order 9664.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18012738	C₂	1	1	yes	maximal, characteristic, complemented
2	#18012726	C₂	1	1	yes	maximal, characteristic
3	#18012664	C₂	1	1	yes	maximal, characteristic, complemented
4	#18012662	C₂	1	1	yes	maximal, characteristic, complemented
5	#18012660	C₂	1	1	yes	maximal, characteristic
6	#18012649	C₂	1	1	yes	maximal, characteristic, complemented
7	#102×C₁₅₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₀₂	—	2	1	no	—
9	C₂×Dic₃₀₂	C₂²	1	1	yes	characteristic
10	C₂×C₁₅₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₅₁	C₂²	1	1	yes	characteristic
12	Dic₁₅₁⋊C₄	—	2	1	no	—
13	C₂²⋊Dic₁₅₁	—	2	1	no	—
14	C₂²⋊Dic₁₅₁	—	2	1	no	—
15	C₄×Dic₁₅₁	C₂²	1	1	yes	characteristic
16	C₂×D₄×C₁₅₁	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₅₁	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₅₁	C₂²	1	1	yes	characteristic
19	Dic₃₀₂	—	2	1	no	—
20	Dic₃₀₂	—	2	1	no	—
21	Dic₃₀₂	—	4	2	no	—
22	C₂×Dic₁₅₁	—	2	1	no	—
23	C₂×Dic₁₅₁	—	2	1	no	—
24	C₂×Dic₁₅₁	D₄	1	1	yes	characteristic
25	C₂×Dic₁₅₁	D₄	1	1	yes	characteristic
26	C₁₅₁⋊C₈	—	2	1	no	—
27	C₂³×C₁₅₁	—	2	1	no	—
28	D₄×C₁₅₁	—	2	1	no	—
29	D₄×C₁₅₁	—	2	1	no	—
30	C₂×C₄×C₁₅₁	—	2	1	no	—
31	C₂×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
32	C₈×C₁₅₁	—	2	1	no	—
33	C₂²×C₁₅₁	—	4	1	no	—
34	C₂²×C₁₅₁	—	4	1	no	—
35	C₂²×C₁₅₁	—	4	1	no	—
36	C₂²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
37	C₄×C₁₅₁	—	4	1	no	—
38	C₄×C₁₅₁	#41	1	1	yes	characteristic
39	C₄×C₁₅₁	#41	1	1	yes	characteristic
40	Dic₁₅₁	—	2	1	no	—
41	Dic₁₅₁	—	2	1	no	—
42	Dic₁₅₁	—	4	1	no	—
43	Dic₁₅₁	—	4	1	no	—
44	C₂×C₁₅₁	—	8	1	no	—
45	C₂×C₁₅₁	#124	1	1	yes	characteristic
46	C₂×C₁₅₁	AGL(1,ℤ/8)	1	1	yes	characteristic
47	C₂×C₁₅₁	#137	1	1	yes	characteristic
48	C₁₅₁	#489	1	1	yes	characteristic, complemented, Sylow
49	#489	—	151	1	no	maximal, Sylow
50	C₄⋊Q₈	—	151	1	no	—
51	#124	—	151	1	no	—
52	#103	—	151	1	no	—
53	#103	—	151	1	no	—
54	#102	—	151	1	no	—
55	#102	D₁₅₁	1	1	yes	characteristic
56	#97	—	151	1	no	—
57	C₂×Q₈	—	302	1	no	—
58	C₂×Q₈	—	151	1	no	—
59	C₂×D₄	C₂×D₁₅₁	1	1	yes	characteristic
60	C₂×C₈	—	151	1	no	—
61	C₂×C₈	C₂×D₁₅₁	1	1	yes	characteristic
62	C₄⋊C₄	—	302	1	no	—
63	C₄⋊C₄	—	151	1	no	—
64	C₄⋊C₄	C₂×D₁₅₁	1	1	yes	characteristic
65	C₂²⋊C₄	—	302	1	no	—
66	C₂²⋊C₄	—	302	1	no	—
67	C₄²	—	151	1	no	—
68	C₂³	—	2	1	no	—
69	Q₈	—	302	1	no	—
70	Q₈	—	302	1	no	—
71	Q₈	—	604	2	no	—
72	D₄	—	2	1	no	—
73	D₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	302	1	no	—
76	C₂×C₄	—	302	1	no	—
77	C₂×C₄	—	151	1	no	—
78	C₂×C₄	—	151	1	no	—
79	C₂×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	302	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	D₄×D₁₅₁	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	302	1	no	—
88	C₄	—	302	1	no	—
89	C₄	—	604	1	no	—
90	C₄	—	604	1	no	—
91	C₄	#14559003	1	1	yes	characteristic
92	C₄	#14559004	1	1	yes	characteristic
93	C₂	—	8	1	no	—
94	C₂	#18012725	1	1	yes	characteristic
95	C₂	#18012763	1	1	yes	characteristic
96	C₂	#18012768	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₅₁
commutator, cosocle	C₂×C₄×C₁₅₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₁
Fitting	#102×C₁₅₁	C₂
socle	C₂²×C₁₅₁	C₂×D₄
prime radical	C₂×D₄×C₁₅₁	C₂²
hypercenter	#102	D₁₅₁
hypocenter	C₁₅₁	#489
LCS	G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
1. #18012738	C₂	semidirect
3. #18012664	C₂	semidirect
4. #18012662	C₂	semidirect
6. #18012649	C₂	semidirect
48. C₁₅₁	#489	semidirect