Subgroups — #21422134

Order 7552.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837782	C₂	1	1	yes	maximal, characteristic
2	#16837223	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#364	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₃₆	—	2	1	no	—
5	C₂×Dic₂₃₆	—	2	1	no	—
6	#14273727	C₄	1	2	yes	—
7	#14273667	—	2	1	no	—
8	M₃₂×C₅₉	—	2	1	no	—
9	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₁₈	—	2	2	no	—
11	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
12	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
13	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
14	C₄⋊Dic₅₉	—	4	2	no	—
15	Dic₂₃₆	—	4	1	no	—
16	Dic₂₃₆	—	4	1	no	—
17	Dic₂₃₆	—	4	1	no	—
18	Dic₂₃₆	—	4	1	no	—
19	C₁₆×C₅₉	—	4	1	no	—
20	C₅₉⋊C₁₆	—	4	1	no	—
21	C₂×C₄×C₅₉	—	2	1	no	—
22	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×Dic₅₉	—	4	2	no	—
24	Dic₁₁₈	—	4	2	no	—
25	Dic₁₁₈	—	4	2	no	—
26	C₈×C₅₉	D₈	1	1	yes	characteristic
27	C₈×C₅₉	D₈	1	1	yes	characteristic
28	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
29	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
30	C₂²×C₅₉	#100	1	1	yes	characteristic
31	C₄×C₅₉	—	2	2	no	—
32	C₄×C₅₉	#102	1	1	yes	characteristic
33	C₄×C₅₉	#102	1	1	yes	characteristic
34	Dic₅₉	—	8	2	no	—
35	#1358	—	59	1	no	maximal, Sylow
36	C₂×C₅₉	—	2	1	no	—
37	C₂×C₅₉	#331	1	1	yes	characteristic
38	#494	—	59	1	no	—
39	#364	—	59	1	no	—
40	#364	D₅₉	1	1	yes	characteristic
41	C₅₉	#1358	1	1	yes	characteristic, complemented, Sylow
42	C₂×Q₁₆	—	118	1	no	—
43	C₂×Q₁₆	—	118	1	no	—
44	C₄⋊Q₈	—	59	2	no	—
45	M₃₂	—	2	1	no	—
46	M₃₂	—	118	1	no	—
47	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
48	C₂×Q₈	—	118	2	no	—
49	Q₁₆	—	236	1	no	—
50	Q₁₆	—	236	1	no	—
51	Q₁₆	—	236	1	no	—
52	Q₁₆	—	236	1	no	—
53	C₂×C₈	D₂₃₆	1	1	yes	characteristic
54	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
55	C₄⋊C₄	—	236	2	no	—
56	C₄²	C₄×D₅₉	1	1	yes	characteristic
57	C₁₆	—	4	1	no	—
58	C₁₆	—	236	1	no	—
59	Q₈	—	236	2	no	—
60	Q₈	—	236	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	236	2	no	—
63	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
64	C₈	#11745660	1	1	yes	characteristic
65	C₈	D₄₇₂	1	1	yes	characteristic
66	C₈	#11745669	1	1	yes	characteristic
67	C₈	#11745671	1	1	yes	characteristic
68	C₂²	#14273643	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	472	2	no	—
71	C₄	#14273647	1	1	yes	characteristic
72	C₄	#14273649	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#16837145	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837145
commutator	C₄²×C₅₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₅₉×#364	C₂
socle	C₂×C₅₉	#331
hypercenter	#364	D₅₉
hypocenter	C₅₉	#1358
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
41. C₅₉	#1358	semidirect