Subgroups — #23752580

Order 9664.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#18012731	C₂	1	1	yes	maximal, characteristic
2	#18012663	C₂	1	4	yes	maximal
3	#18012650	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₁₅₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₅₁⋊C₈	C₂²	1	2	yes	—
6	C₄⋊Dic₁₅₁	C₂²	1	2	yes	—
7	Dic₁₅₁⋊C₄	—	2	2	no	—
8	C₂×Q₈×C₁₅₁	C₂²	1	2	yes	—
9	C₄⋊C₄×C₁₅₁	—	2	2	no	—
10	C₄²×C₁₅₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₅₁	—	2	2	no	—
12	C₁₅₁⋊C₈	—	2	2	no	—
13	Q₈×C₁₅₁	—	2	4	no	—
14	C₂×C₄×C₁₅₁	—	2	2	no	—
15	C₂×C₄×C₁₅₁	D₄	1	2	yes	—
16	C₂×C₄×C₁₅₁	C₂³	1	1	yes	characteristic
17	C₂²×C₁₅₁	C₂×D₄	1	1	yes	characteristic
18	C₄×C₁₅₁	—	2	2	no	—
19	C₄×C₁₅₁	—	4	2	no	—
20	C₄×C₁₅₁	#41	1	2	yes	—
21	Dic₁₅₁	—	4	2	no	—
22	C₂×C₁₅₁	#124	1	1	yes	characteristic
23	C₂×C₁₅₁	#137	1	2	yes	—
24	C₁₅₁	#491	1	1	yes	characteristic, complemented, Sylow
25	#491	—	151	1	no	maximal, Sylow
26	C₄⋊Q₈	D₁₅₁	1	1	yes	characteristic
27	#125	—	151	1	no	—
28	#103	—	151	4	no	—
29	#97	—	151	1	no	—
30	C₂×Q₈	C₂×D₁₅₁	1	2	yes	—
31	C₂×C₈	—	151	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	302	2	no	—
34	C₄⋊C₄	—	151	2	no	—
35	C₄²	C₂×D₁₅₁	1	1	yes	characteristic
36	Q₈	—	2	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	302	2	no	—
39	C₂×C₄	C₂²⋊D₁₅₁	1	2	yes	—
40	C₂×C₄	C₂²×D₁₅₁	1	1	yes	characteristic
41	C₈	—	302	2	no	—
42	C₂²	C₂×C₂²⋊D₁₅₁	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	604	2	no	—
46	C₄	#14559003	1	2	yes	—
47	C₂	#18012726	1	1	yes	characteristic
48	C₂	#18012770	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₅₁
commutator, cosocle	C₂×C₄×C₁₅₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₅₁
Fitting	C₄⋊Q₈×C₁₅₁	C₂
socle, prime radical	C₂²×C₁₅₁	C₂×D₄
hypercenter	C₄⋊Q₈	D₁₅₁
hypocenter	C₁₅₁	#491
LCS	G ▷ C₂×C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
24. C₁₅₁	#491	semidirect