Subgroups — #21422131

Order 7552.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837180	C₂	1	2	yes	maximal
2	C₅₉×#491	C₂	1	1	yes	maximal, characteristic
3	#14273667	—	2	2	no	—
4	C₄⋊Q₈×C₅₉	C₄	1	1	yes	characteristic
5	#125×C₅₉	C₄	1	1	yes	characteristic
6	#103×C₅₉	—	2	2	no	—
7	#97×C₅₉	C₂²	1	1	yes	characteristic
8	C₂×Q₈×C₅₉	—	2	1	no	—
9	C₂×C₈×C₅₉	D₄	1	2	yes	—
10	C₄⋊C₄×C₅₉	—	2	1	no	—
11	C₄⋊C₄×C₅₉	—	4	1	no	—
12	C₄⋊C₄×C₅₉	—	4	1	no	—
13	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
14	C₅₉⋊C₁₆	—	2	4	no	—
15	Q₈×C₅₉	—	4	2	no	—
16	C₂×C₄×C₅₉	—	2	1	no	—
17	C₂×C₄×C₅₉	—	4	1	no	—
18	C₂×C₄×C₅₉	—	4	1	no	—
19	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₅₉	—	2	2	no	—
21	C₂²×C₅₉	#100	1	1	yes	characteristic
22	C₄×C₅₉	—	4	1	no	—
23	C₄×C₅₉	—	8	1	no	—
24	C₄×C₅₉	—	8	1	no	—
25	C₄×C₅₉	#104	1	2	yes	—
26	#1356	—	59	1	no	maximal, Sylow
27	C₂×C₅₉	—	2	1	no	—
28	C₂×C₅₉	#329	1	1	yes	characteristic
29	#491	D₅₉	1	1	yes	characteristic
30	#347	—	59	2	no	—
31	C₅₉	#1356	1	1	yes	characteristic, complemented, Sylow
32	C₄⋊Q₈	Dic₅₉	1	1	yes	characteristic
33	#125	Dic₅₉	1	1	yes	characteristic
34	M₃₂	—	118	2	no	—
35	#103	—	2	2	no	—
36	#97	C₂×D₅₉	1	1	yes	characteristic
37	C₂×Q₈	—	2	1	no	—
38	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	4	1	no	—
41	C₄⋊C₄	—	4	1	no	—
42	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
43	C₁₆	—	118	4	no	—
44	Q₈	—	4	2	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
49	C₈	—	2	2	no	—
50	C₂²	#14273644	1	1	yes	characteristic
51	C₄	—	4	1	no	—
52	C₄	—	8	1	no	—
53	C₄	—	8	1	no	—
54	C₄	#14273654	1	2	yes	—
55	C₂	—	2	1	no	—
56	C₂	#16837142	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837142
commutator	C₄²×C₅₉	C₂×C₄
Frattini	#97	C₂×D₅₉
Fitting	C₅₉×#491	C₂
socle	C₂×C₅₉	#329
hypercenter	#491	D₅₉
hypocenter	C₅₉	#1356
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #491

Complements

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

N	H ≅ G/N	type
31. C₅₉	#1356	semidirect