Subgroups — #21422267

Order 7552.

94 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×#490	C₂	1	1	yes	maximal, characteristic
3	#14273642	—	2	2	no	—
4	#127×C₅₉	C₂²	1	1	yes	characteristic
5	#125×C₅₉	C₄	1	1	yes	characteristic, complemented
6	#102×C₅₉	—	2	2	no	—
7	#97×C₅₉	C₄	1	1	yes	characteristic, complemented
8	C₂×D₄×C₅₉	—	4	1	no	—
9	C₂×D₄×C₅₉	D₄	1	2	yes	—
10	C₂×C₈×C₅₉	—	2	1	no	—
11	C₄⋊C₄×C₅₉	—	2	1	no	—
12	C₄⋊C₄×C₅₉	—	4	1	no	—
13	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
14	C₂²⋊Dic₅₉	—	4	2	no	—
15	C₂³×C₅₉	—	2	2	no	—
16	D₄×C₅₉	—	4	2	no	—
17	D₄×C₅₉	—	8	2	no	—
18	C₂×C₄×C₅₉	—	2	1	no	—
19	C₂×C₄×C₅₉	—	4	1	no	—
20	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×Dic₅₉	—	8	2	no	—
22	C₈×C₅₉	—	4	1	no	—
23	C₂²×C₅₉	—	4	2	no	—
24	C₂²×C₅₉	—	8	2	no	—
25	C₂²×C₅₉	#99	1	1	yes	characteristic
26	C₄×C₅₉	—	2	1	no	—
27	C₄×C₅₉	—	4	1	no	—
28	C₄×C₅₉	—	8	1	no	—
29	Dic₅₉	—	16	2	no	—
30	#1412	—	59	1	no	maximal, Sylow
31	C₂×C₅₉	—	2	1	no	—
32	C₂×C₅₉	—	8	2	no	—
33	C₂×C₅₉	#354	1	1	yes	characteristic
34	#490	D₅₉	1	1	yes	characteristic
35	#353	—	59	2	no	—
36	C₅₉	#1412	1	1	yes	characteristic, complemented, Sylow
37	#127	C₂×D₅₉	1	1	yes	characteristic
38	#125	Dic₅₉	1	1	yes	characteristic, complemented
39	#102	—	2	2	no	—
40	#99	—	118	2	no	—
41	#97	Dic₅₉	1	1	yes	characteristic, complemented
42	C₂×D₄	—	4	1	no	—
43	C₂×D₄	C₂²⋊D₅₉	1	2	yes	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₂²⋊C₄	—	236	2	no	—
48	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
49	C₂³	—	2	2	no	—
50	D₄	—	4	2	no	—
51	D₄	—	8	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	472	2	no	—
55	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
56	C₈	—	4	1	no	—
57	C₂²	—	4	2	no	—
58	C₂²	—	8	2	no	—
59	C₂²	#14273642	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₄	—	944	2	no	—
64	C₂	—	2	1	no	—
65	C₂	—	8	2	no	—
66	C₂	#16837197	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837197
commutator	C₄²×C₅₉	C₂×C₄
Frattini	#127	C₂×D₅₉
Fitting	C₅₉×#490	C₂
socle	C₂×C₅₉	#354
hypercenter	#490	D₅₉
hypocenter	C₅₉	#1412
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #490

Complements

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

N	H ≅ G/N	type
5. #125×C₅₉	C₄	semidirect
7. #97×C₅₉	C₄	semidirect
36. C₅₉	#1412	semidirect
38. #125	Dic₅₉	semidirect
41. #97	Dic₅₉	semidirect