Subgroups — #21422253

Order 7552.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837199	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837197	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#496	C₂	1	1	yes	maximal, characteristic
4	#14273646	—	2	1	no	—
5	#14273642	—	2	1	no	—
6	C₂×SD₁₆×C₅₉	—	2	1	no	—
7	C₂×D₈×C₅₉	—	2	1	no	—
8	#127×C₅₉	C₄	1	1	yes	characteristic, complemented
9	#124×C₅₉	C₂²	1	1	yes	characteristic
10	#97×C₅₉	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
12	C₂×D₄×C₅₉	—	2	1	no	—
13	C₂×D₄×C₅₉	—	4	1	no	—
14	C₂×D₄×C₅₉	D₄	1	1	yes	characteristic
15	SD₁₆×C₅₉	—	4	2	no	—
16	D₈×C₅₉	—	4	2	no	—
17	C₂×C₈×C₅₉	—	2	1	no	—
18	C₂²⋊C₄×C₅₉	—	4	1	no	—
19	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
20	C₂²⋊Dic₅₉	—	4	1	no	—
21	#11745664	—	4	1	no	—
22	C₂³×C₅₉	—	2	1	no	—
23	C₂³×C₅₉	—	4	1	no	—
24	Q₈×C₅₉	—	4	1	no	—
25	D₄×C₅₉	—	4	1	no	—
26	D₄×C₅₉	—	4	1	no	—
27	D₄×C₅₉	—	4	1	no	—
28	D₄×C₅₉	—	8	2	no	—
29	C₂×C₄×C₅₉	—	2	1	no	—
30	C₂×C₄×C₅₉	—	2	1	no	—
31	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×Dic₅₉	—	8	1	no	—
33	C₈×C₅₉	—	2	2	no	—
34	C₅₉⋊C₈	—	8	1	no	—
35	C₂²×C₅₉	—	4	1	no	—
36	C₂²×C₅₉	—	8	1	no	—
37	C₂²×C₅₉	—	8	2	no	—
38	C₂²×C₅₉	—	8	1	no	—
39	C₂²×C₅₉	#99	1	1	yes	characteristic
40	C₄×C₅₉	—	2	1	no	—
41	C₄×C₅₉	—	4	1	no	—
42	C₄×C₅₉	—	4	1	no	—
43	Dic₅₉	—	16	1	no	—
44	#1406	—	59	1	no	maximal, Sylow
45	C₂×C₅₉	—	2	1	no	—
46	C₂×C₅₉	—	8	1	no	—
47	C₂×C₅₉	—	16	1	no	—
48	C₂×C₅₉	#353	1	1	yes	characteristic
49	#496	D₅₉	1	1	yes	characteristic
50	#355	—	59	1	no	—
51	#354	—	59	1	no	—
52	C₅₉	#1406	1	1	yes	characteristic, complemented, Sylow
53	C₂×SD₁₆	—	2	1	no	—
54	C₂×D₈	—	2	1	no	—
55	#127	Dic₅₉	1	1	yes	characteristic, complemented
56	#124	C₂×D₅₉	1	1	yes	characteristic
57	#101	—	118	1	no	—
58	#99	—	118	1	no	—
59	#97	Dic₅₉	1	1	yes	characteristic, complemented
60	C₂×Q₈	C₂²⋊D₅₉	1	1	yes	characteristic
61	C₂×D₄	—	2	1	no	—
62	C₂×D₄	—	4	1	no	—
63	C₂×D₄	C₂²⋊D₅₉	1	1	yes	characteristic
64	SD₁₆	—	4	2	no	—
65	D₈	—	4	2	no	—
66	M₁₆	—	236	1	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	236	1	no	—
70	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	4	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	4	1	no	—
76	D₄	—	4	1	no	—
77	D₄	—	8	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	472	1	no	—
81	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	472	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	8	2	no	—
87	C₂²	—	8	1	no	—
88	C₂²	#14273642	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	944	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	16	1	no	—
96	C₂	#16837195	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837195
commutator	C₄²×C₅₉	C₂×C₄
Frattini	#124	C₂×D₅₉
Fitting	C₅₉×#496	C₂
socle	C₂×C₅₉	#353
hypercenter	#496	D₅₉
hypocenter	C₅₉	#1406
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #496

Complements

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

N	H ≅ G/N	type
1. #16837199	C₂	semidirect
2. #16837197	C₂	semidirect
8. #127×C₅₉	C₄	semidirect
10. #97×C₅₉	C₄	semidirect
52. C₅₉	#1406	semidirect
55. #127	Dic₅₉	semidirect
59. #97	Dic₅₉	semidirect