Subgroups — #21426342

Order 7552.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837804	C₂	1	1	yes	maximal, characteristic
2	#16837782	C₂	1	1	yes	maximal, characteristic
3	#16837207	C₂	1	4	yes	maximal
4	C₅₉×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₃₆	—	2	1	no	—
6	C₂×Dic₂₃₆	C₂²	1	2	yes	—
7	#14273727	—	2	1	no	—
8	#14273719	—	2	1	no	—
9	#14273661	C₂²	1	2	yes	—
10	#14273659	—	2	1	no	—
11	C₂×C₁₆×C₅₉	C₂²	1	2	yes	—
12	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₁₈	—	2	2	no	—
14	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
15	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
16	C₄²×C₅₉	D₄	1	1	yes	characteristic
17	C₄⋊Dic₅₉	—	2	2	no	—
18	C₄⋊Dic₅₉	—	4	2	no	—
19	Dic₅₉⋊C₄	—	4	2	no	—
20	Dic₂₃₆	—	2	4	no	—
21	Dic₂₃₆	—	4	2	no	—
22	C₁₆×C₅₉	—	2	2	no	—
23	C₂×C₄×C₅₉	D₈	1	2	yes	—
24	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
25	C₂×Dic₅₉	—	4	2	no	—
26	C₂×Dic₅₉	—	4	2	no	—
27	Dic₁₁₈	—	4	2	no	—
28	Dic₁₁₈	—	4	2	no	—
29	C₈×C₅₉	SD₁₆	1	2	yes	—
30	C₈×C₅₉	#41	1	2	yes	—
31	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
32	C₄×C₅₉	—	2	2	no	—
33	C₄×C₅₉	#124	1	1	yes	characteristic
34	C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
35	Dic₅₉	—	8	2	no	—
36	Dic₅₉	—	8	2	no	—
37	#2245	—	59	1	no	maximal, Sylow
38	C₂×C₅₉	#486	1	1	yes	characteristic
39	C₂×C₅₉	#510	1	2	yes	—
40	#499	—	59	1	no	—
41	#494	—	59	1	no	—
42	#358	—	59	4	no	—
43	#346	D₅₉	1	1	yes	characteristic
44	C₅₉	#2245	1	1	yes	characteristic, complemented, Sylow
45	C₂×Q₁₆	—	59	2	no	—
46	C₂×Q₁₆	—	118	1	no	—
47	C₄⋊Q₈	—	118	1	no	—
48	#125	—	118	1	no	—
49	C₂×C₁₆	C₂×D₅₉	1	2	yes	—
50	#107	—	59	2	no	—
51	#106	—	118	1	no	—
52	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
53	C₂×Q₈	—	118	2	no	—
54	Q₁₆	—	118	4	no	—
55	Q₁₆	—	236	2	no	—
56	C₂×C₈	D₂₃₆	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
58	C₄⋊C₄	—	118	2	no	—
59	C₄⋊C₄	—	236	2	no	—
60	C₄⋊C₄	—	236	2	no	—
61	C₄²	D₂₃₆	1	1	yes	characteristic
62	C₁₆	—	2	2	no	—
63	Q₈	—	236	2	no	—
64	Q₈	—	236	2	no	—
65	C₂×C₄	—	236	2	no	—
66	C₂×C₄	—	236	2	no	—
67	C₂×C₄	D₄₇₂	1	2	yes	—
68	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
69	C₈	#11745660	1	2	yes	—
70	C₈	#11745685	1	2	yes	—
71	C₂²	C₂×D₄₇₂	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	472	2	no	—
74	C₄	—	472	2	no	—
75	C₄	#14273715	1	1	yes	characteristic
76	C₄	C₂×#11745660	1	1	yes	characteristic
77	C₂	#16837749	1	1	yes	characteristic
78	C₂	#16837845	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₇₂
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#346	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#346	D₅₉
hypocenter	C₅₉	#2245
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
44. C₅₉	#2245	semidirect