Subgroups — #21422255

Order 7552.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837797	C₂	1	1	yes	maximal, characteristic
2	#16837199	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#354	C₂	1	1	yes	maximal, characteristic
4	C₂×#11745672	—	2	1	no	—
5	C₂×#11745670	—	2	1	no	—
6	#14273727	C₄	1	1	yes	characteristic, complemented
7	#14273646	—	2	1	no	—
8	#14273638	C₄	1	1	yes	characteristic, complemented
9	#124×C₅₉	C₂²	1	1	yes	characteristic
10	#99×C₅₉	—	2	1	no	—
11	C₂×Q₈×C₅₉	D₄	1	1	yes	characteristic
12	C₂×D₄×C₅₉	D₄	1	1	yes	characteristic
13	C₂×Dic₁₁₈	—	2	1	no	—
14	C₂²⋊C₄×C₅₉	—	4	1	no	—
15	C₂²⋊C₄×C₅₉	—	4	1	no	—
16	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
17	#11745672	—	4	2	no	—
18	#11745670	—	4	2	no	—
19	C₄⋊Dic₅₉	—	4	1	no	—
20	#11745664	—	4	1	no	—
21	C₂×C₅₉⋊C₈	—	2	1	no	—
22	C₂³×C₅₉	—	2	1	no	—
23	Q₈×C₅₉	—	4	1	no	—
24	D₄×C₅₉	—	4	1	no	—
25	C₂×C₄×C₅₉	—	2	1	no	—
26	C₂×C₄×C₅₉	—	2	1	no	—
27	C₂×C₄×C₅₉	—	8	1	no	—
28	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₅₉	—	4	1	no	—
30	Dic₁₁₈	—	4	1	no	—
31	Dic₁₁₈	—	4	1	no	—
32	C₅₉⋊C₈	—	2	2	no	—
33	C₅₉⋊C₈	—	8	1	no	—
34	C₂²×C₅₉	—	4	1	no	—
35	C₂²×C₅₉	—	8	1	no	—
36	C₂²×C₅₉	#99	1	1	yes	characteristic
37	C₄×C₅₉	—	2	1	no	—
38	C₄×C₅₉	—	4	1	no	—
39	C₄×C₅₉	—	4	1	no	—
40	C₄×C₅₉	—	16	1	no	—
41	Dic₅₉	—	8	1	no	—
42	#1407	—	59	1	no	maximal, Sylow
43	C₂×C₅₉	—	2	1	no	—
44	C₂×C₅₉	—	8	1	no	—
45	C₂×C₅₉	#353	1	1	yes	characteristic
46	#497	—	59	1	no	—
47	#355	—	59	1	no	—
48	#354	D₅₉	1	1	yes	characteristic
49	C₅₉	#1407	1	1	yes	characteristic, complemented, Sylow
50	C₂×Q₁₆	—	118	1	no	—
51	C₂×SD₁₆	—	118	1	no	—
52	C₄⋊Q₈	—	59	1	no	—
53	#124	C₂×D₅₉	1	1	yes	characteristic
54	#101	—	118	1	no	—
55	#99	—	2	1	no	—
56	#97	—	59	1	no	—
57	C₂×Q₈	—	118	1	no	—
58	C₂×Q₈	D₂₃₆	1	1	yes	characteristic
59	C₂×D₄	C₂²⋊D₅₉	1	1	yes	characteristic
60	Q₁₆	—	236	2	no	—
61	SD₁₆	—	236	2	no	—
62	M₁₆	—	236	1	no	—
63	C₂×C₈	—	118	1	no	—
64	C₄⋊C₄	—	236	1	no	—
65	C₂²⋊C₄	—	4	1	no	—
66	C₂²⋊C₄	—	4	1	no	—
67	C₄²	C₄×D₅₉	1	1	yes	characteristic
68	C₂³	—	2	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	236	1	no	—
71	Q₈	—	236	1	no	—
72	D₄	—	4	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	236	1	no	—
77	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
78	C₈	—	118	2	no	—
79	C₈	—	472	1	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	8	1	no	—
82	C₂²	#14273641	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	16	1	no	—
87	C₄	—	472	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	8	1	no	—
90	C₂	#16837194	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837194
commutator	C₄²×C₅₉	C₂×C₄
Frattini	#124	C₂×D₅₉
Fitting	C₅₉×#354	C₂
socle	C₂×C₅₉	#353
hypercenter	#354	D₅₉
hypocenter	C₅₉	#1407
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂²×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
6. #14273727	C₄	semidirect
8. #14273638	C₄	semidirect
49. C₅₉	#1407	semidirect