Subgroups — #21422130

Order 7552.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837771	C₂	1	1	yes	maximal, characteristic
2	#16837180	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#347	C₂	1	1	yes	maximal, characteristic
4	#14273727	C₄	1	1	yes	characteristic
5	#14273719	C₄	1	1	yes	characteristic
6	#14273667	—	2	1	no	—
7	#14273652	—	2	1	no	—
8	#14273652	—	2	1	no	—
9	M₃₂×C₅₉	—	2	1	no	—
10	#97×C₅₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₁₈	—	2	1	no	—
12	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
14	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₅₉	—	2	1	no	—
16	C₄⋊Dic₅₉	—	4	1	no	—
17	Dic₅₉⋊C₄	—	4	1	no	—
18	C₁₆×C₅₉	—	2	2	no	—
19	C₅₉⋊C₁₆	—	2	2	no	—
20	C₂×C₄×C₅₉	—	2	1	no	—
21	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₅₉	—	4	1	no	—
23	C₂×Dic₅₉	—	4	1	no	—
24	Dic₁₁₈	—	4	1	no	—
25	Dic₁₁₈	—	4	1	no	—
26	C₈×C₅₉	—	2	1	no	—
27	C₈×C₅₉	—	2	1	no	—
28	C₂²×C₅₉	#100	1	1	yes	characteristic
29	C₄×C₅₉	—	4	1	no	—
30	C₄×C₅₉	#104	1	1	yes	characteristic
31	C₄×C₅₉	#104	1	1	yes	characteristic
32	Dic₅₉	—	8	1	no	—
33	Dic₅₉	—	8	1	no	—
34	#1356	—	59	1	no	maximal, Sylow
35	C₂×C₅₉	—	2	1	no	—
36	C₂×C₅₉	#329	1	1	yes	characteristic
37	#491	—	59	1	no	—
38	#347	—	59	1	no	—
39	#347	D₅₉	1	1	yes	characteristic
40	C₅₉	#1356	1	1	yes	characteristic, complemented, Sylow
41	C₄⋊Q₈	—	59	1	no	—
42	#125	—	59	1	no	—
43	M₃₂	—	2	1	no	—
44	M₃₂	—	118	1	no	—
45	#103	—	118	1	no	—
46	#103	—	118	1	no	—
47	#97	C₂×D₅₉	1	1	yes	characteristic
48	C₂×Q₈	—	118	1	no	—
49	C₂×C₈	D₂₃₆	1	1	yes	characteristic
50	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
51	C₄⋊C₄	—	118	1	no	—
52	C₄⋊C₄	—	236	1	no	—
53	C₄⋊C₄	—	236	1	no	—
54	C₄²	C₄×D₅₉	1	1	yes	characteristic
55	C₁₆	—	2	2	no	—
56	C₁₆	—	118	2	no	—
57	Q₈	—	236	1	no	—
58	Q₈	—	236	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	236	1	no	—
61	C₂×C₄	—	236	1	no	—
62	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	2	1	no	—
65	C₂²	#14273643	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	—	472	1	no	—
68	C₄	—	472	1	no	—
69	C₄	#14273653	1	1	yes	characteristic
70	C₄	#14273655	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#16837141	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837141
commutator	C₄²×C₅₉	C₂×C₄
Frattini	#97	C₂×D₅₉
Fitting	C₅₉×#347	C₂
socle	C₂×C₅₉	#329
hypercenter	#347	D₅₉
hypocenter	C₅₉	#1356
LCS	G ▷ C₄²×C₅₉ ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

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

N	H ≅ G/N	type
40. C₅₉	#1356	semidirect