Subgroups — #21422089

Order 7552.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837660	C₂	1	1	yes	maximal, characteristic
2	#16837184	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#338	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₃₆	C₄	1	1	yes	characteristic
5	#14273706	—	2	1	no	—
6	#14273667	—	2	1	no	—
7	#14273659	C₄	1	1	yes	characteristic
8	#14273652	—	2	1	no	—
9	C₂×M₁₆×C₅₉	—	2	1	no	—
10	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
12	C₂×Dic₁₁₈	—	2	1	no	—
13	M₁₆×C₅₉	—	4	1	no	—
14	M₁₆×C₅₉	—	4	1	no	—
15	M₁₆×C₅₉	—	4	1	no	—
16	C₂×C₈×C₅₉	—	2	2	no	—
17	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
19	C₂²⋊Dic₅₉	—	4	1	no	—
20	C₄⋊Dic₅₉	—	2	1	no	—
21	Dic₅₉⋊C₄	—	4	1	no	—
22	Dic₂₃₆	—	4	1	no	—
23	C₅₉⋊C₁₆	—	4	1	no	—
24	C₂³×C₅₉	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₅₉	—	2	1	no	—
26	C₂×C₄×C₅₉	—	2	1	no	—
27	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
29	C₂×Dic₅₉	—	4	1	no	—
30	C₂×Dic₅₉	—	4	1	no	—
31	Dic₁₁₈	—	4	1	no	—
32	Dic₁₁₈	—	4	1	no	—
33	C₈×C₅₉	—	2	1	no	—
34	C₈×C₅₉	—	2	1	no	—
35	C₈×C₅₉	—	4	2	no	—
36	C₂²×C₅₉	—	2	1	no	—
37	C₂²×C₅₉	—	4	1	no	—
38	C₂²×C₅₉	#102	1	1	yes	characteristic
39	C₄×C₅₉	—	2	1	no	—
40	C₄×C₅₉	#99	1	1	yes	characteristic
41	C₄×C₅₉	#104	1	1	yes	characteristic
42	Dic₅₉	—	8	1	no	—
43	Dic₅₉	—	8	1	no	—
44	#1342	—	59	1	no	maximal, Sylow
45	C₂×C₅₉	—	2	1	no	—
46	C₂×C₅₉	—	4	1	no	—
47	C₂×C₅₉	#327	1	1	yes	characteristic
48	#470	—	59	1	no	—
49	#349	—	59	1	no	—
50	#338	D₅₉	1	1	yes	characteristic
51	C₅₉	#1342	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	—	59	1	no	—
53	C₂×M₁₆	—	2	1	no	—
54	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
55	C₂²⋊Q₈	—	118	1	no	—
56	M₃₂	—	118	1	no	—
57	#106	—	59	1	no	—
58	#103	—	118	1	no	—
59	C₂×Q₈	—	118	1	no	—
60	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
61	Q₁₆	—	236	1	no	—
62	M₁₆	—	4	1	no	—
63	M₁₆	—	4	1	no	—
64	M₁₆	—	4	1	no	—
65	C₂×C₈	—	2	2	no	—
66	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
67	C₂×C₈	D₂₃₆	1	1	yes	characteristic
68	C₄⋊C₄	—	118	1	no	—
69	C₄⋊C₄	—	236	1	no	—
70	C₂²⋊C₄	—	236	1	no	—
71	C₁₆	—	236	1	no	—
72	C₂³	#11745671	1	1	yes	characteristic
73	Q₈	—	236	1	no	—
74	Q₈	—	236	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	236	1	no	—
78	C₂×C₄	—	236	1	no	—
79	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
80	C₂×C₄	#11745669	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	2	1	no	—
83	C₈	—	4	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#14273647	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	472	1	no	—
89	C₄	—	472	1	no	—
90	C₄	#14273641	1	1	yes	characteristic
91	C₄	#14273655	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#16837135	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837135
commutator	C₂×C₈×C₅₉	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₅₉
Fitting	C₅₉×#338	C₂
socle	C₂×C₅₉	#327
hypercenter	#338	D₅₉
hypocenter	C₅₉	#1342
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #338

Complements

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

N	H ≅ G/N	type
51. C₅₉	#1342	semidirect