Subgroups — #21422261

Order 7552.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837195	C₂	1	2	yes	maximal
2	C₅₉×#492	C₂	1	1	yes	maximal, characteristic
3	#14273642	—	2	2	no	—
4	C₂×SD₁₆×C₅₉	—	2	2	no	—
5	C₄⋊Q₈×C₅₉	C₄	1	1	yes	characteristic, complemented
6	#127×C₅₉	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₅₉	C₄	1	1	yes	characteristic, complemented
8	C₂×Q₈×C₅₉	—	2	1	no	—
9	C₂×D₄×C₅₉	—	4	1	no	—
10	C₂×D₄×C₅₉	D₄	1	2	yes	—
11	SD₁₆×C₅₉	—	4	4	no	—
12	C₂×C₈×C₅₉	—	2	1	no	—
13	C₄⋊C₄×C₅₉	—	4	1	no	—
14	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊Dic₅₉	—	4	2	no	—
16	C₂³×C₅₉	—	2	2	no	—
17	Q₈×C₅₉	—	4	2	no	—
18	D₄×C₅₉	—	4	2	no	—
19	D₄×C₅₉	—	8	2	no	—
20	C₂×C₄×C₅₉	—	2	1	no	—
21	C₂×C₄×C₅₉	—	4	1	no	—
22	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₅₉	—	8	2	no	—
24	C₈×C₅₉	—	2	2	no	—
25	C₂²×C₅₉	—	4	2	no	—
26	C₂²×C₅₉	—	8	2	no	—
27	C₂²×C₅₉	#99	1	1	yes	characteristic
28	C₄×C₅₉	—	2	2	no	—
29	C₄×C₅₉	—	2	1	no	—
30	C₄×C₅₉	—	8	1	no	—
31	Dic₅₉	—	16	2	no	—
32	#1409	—	59	1	no	maximal, Sylow
33	C₂×C₅₉	—	2	1	no	—
34	C₂×C₅₉	—	8	2	no	—
35	C₂×C₅₉	#353	1	1	yes	characteristic
36	#492	D₅₉	1	1	yes	characteristic
37	#353	—	59	2	no	—
38	C₅₉	#1409	1	1	yes	characteristic, complemented, Sylow
39	C₂×SD₁₆	—	2	2	no	—
40	C₄⋊Q₈	Dic₅₉	1	1	yes	characteristic, complemented
41	#127	C₂×D₅₉	1	1	yes	characteristic
42	#99	—	118	2	no	—
43	C₄×C₈	Dic₅₉	1	1	yes	characteristic, complemented
44	C₂×Q₈	—	2	1	no	—
45	C₂×D₄	—	4	1	no	—
46	C₂×D₄	C₂²⋊D₅₉	1	2	yes	—
47	SD₁₆	—	4	4	no	—
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	—	4	1	no	—
50	C₂²⋊C₄	—	236	2	no	—
51	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
52	C₂³	—	2	2	no	—
53	Q₈	—	4	2	no	—
54	D₄	—	4	2	no	—
55	D₄	—	8	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	4	1	no	—
58	C₂×C₄	—	472	2	no	—
59	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₂²	—	4	2	no	—
62	C₂²	—	8	2	no	—
63	C₂²	#14273642	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	2	1	no	—
66	C₄	—	8	1	no	—
67	C₄	—	944	2	no	—
68	C₂	—	2	1	no	—
69	C₂	—	8	2	no	—
70	C₂	#16837195	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837195
commutator	C₄²×C₅₉	C₂×C₄
Frattini	#127	C₂×D₅₉
Fitting	C₅₉×#492	C₂
socle	C₂×C₅₉	#353
hypercenter	#492	D₅₉
hypocenter	C₅₉	#1409
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #492

Complements

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

N	H ≅ G/N	type
5. C₄⋊Q₈×C₅₉	C₄	semidirect
7. C₄×C₈×C₅₉	C₄	semidirect
38. C₅₉	#1409	semidirect
40. C₄⋊Q₈	Dic₅₉	semidirect
43. C₄×C₈	Dic₅₉	semidirect