Subgroups — #21423698

Order 7552.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837775	C₂	1	1	yes	maximal, characteristic
2	#16837752	C₂	1	2	yes	maximal, complemented
3	#16837750	C₂	1	2	yes	maximal
4	C₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11745660	—	2	2	no	—
7	#14273727	C₂²	1	1	yes	characteristic
8	#14273724	C₂²	1	1	yes	characteristic
9	#14273651	—	2	4	no	—
10	#14273647	—	2	4	no	—
11	C₄×C₅₉⋊C₈	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
13	#106×C₅₉	—	2	2	no	—
14	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₅₉	—	2	2	no	—
16	C₂×D₂₃₆	—	2	2	no	—
17	C₂×D₂₃₆	—	2	1	no	—
18	C₂×Dic₁₁₈	—	2	1	no	—
19	C₂×C₈×C₅₉	D₄	1	2	yes	—
20	C₄⋊C₄×C₅₉	—	2	2	no	—
21	C₄⋊C₄×C₅₉	—	2	2	no	—
22	C₄²×C₅₉	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₅₉	—	2	2	no	—
24	C₂×C₅₉⋊C₈	D₄	1	4	yes	—
25	#11745660	—	4	4	no	—
26	C₂²×D₅₉	—	4	1	no	—
27	Q₈×C₅₉	—	4	4	no	—
28	C₂×C₄×C₅₉	—	4	2	no	—
29	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
30	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₅₉	—	4	1	no	—
32	D₂₃₆	—	4	2	no	—
33	D₂₃₆	—	4	4	no	—
34	Dic₁₁₈	—	4	2	no	—
35	C₈×C₅₉	SD₁₆	1	4	yes	—
36	C₅₉⋊C₈	—	2	4	no	—
37	C₂²×C₅₉	#127	1	1	yes	characteristic
38	C₂×D₅₉	—	8	1	no	—
39	C₂×D₅₉	—	8	2	no	—
40	C₄×C₅₉	—	8	2	no	—
41	C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
42	C₄×C₅₉	#135	1	4	yes	—
43	Dic₅₉	—	8	1	no	—
44	#1708	—	59	1	no	maximal, Sylow
45	C₂×C₅₉	#492	1	1	yes	characteristic
46	C₂×C₅₉	#495	1	2	yes	—
47	D₅₉	—	16	1	no	—
48	#498	D₅₉	1	1	yes	characteristic, complemented
49	#492	—	59	1	no	—
50	#487	—	59	2	no	—
51	#486	—	59	2	no	—
52	C₈²	—	59	1	no	—
53	C₅₉	#1708	1	1	yes	characteristic, complemented, Sylow
54	C₂×SD₁₆	—	118	2	no	—
55	C₄⋊Q₈	—	59	1	no	—
56	C₄⋊Q₈	C₂×D₅₉	1	2	yes	—
57	#127	—	59	1	no	—
58	#106	—	2	2	no	—
59	#103	—	118	4	no	—
60	#102	—	118	4	no	—
61	C₄×C₈	—	59	2	no	—
62	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
63	C₂×Q₈	—	2	2	no	—
64	C₂×Q₈	—	118	1	no	—
65	C₂×D₄	—	118	2	no	—
66	C₂×D₄	—	118	1	no	—
67	SD₁₆	—	236	4	no	—
68	C₂×C₈	—	59	4	no	—
69	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
70	C₄⋊C₄	—	2	2	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	118	2	no	—
73	C₄²	C₂²×D₅₉	1	1	yes	characteristic
74	C₂³	—	236	1	no	—
75	Q₈	—	4	4	no	—
76	Q₈	—	236	2	no	—
77	D₄	—	236	2	no	—
78	D₄	—	236	4	no	—
79	C₂×C₄	—	4	2	no	—
80	C₂×C₄	—	236	1	no	—
81	C₂×C₄	D₄×D₅₉	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
83	C₈	—	118	4	no	—
84	C₈	#11745671	1	4	yes	—
85	C₂²	—	472	1	no	—
86	C₂²	—	472	2	no	—
87	C₂²	#14273723	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	—	472	1	no	—
90	C₄	C₂×#11745671	1	2	yes	—
91	C₄	#14273748	1	4	yes	—
92	C₂	—	944	1	no	—
93	C₂	#16837776	1	1	yes	characteristic
94	C₂	#16837783	1	2	yes	—

	subgroup	G/H
center	C₂²	#14273723
commutator	C₄²×C₅₉	C₂³
Frattini	C₄²	C₂²×D₅₉
Fitting	C₅₉×#498	C₂
socle	C₂²×C₅₉	#127
hypercenter	#498	D₅₉
hypocenter	C₅₉	#1708
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
2. #16837752	C₂	semidirect
4. C₈×C₅₉⋊C₈	C₂	semidirect
5. C₅₉×#498	C₂	semidirect
48. #498	D₅₉	semidirect
53. C₅₉	#1708	semidirect