Subgroups — #21423848

Order 7552.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273638	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#16837157	C₂	1	4	yes	maximal
4	C₅₉×#376	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
6	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
7	#14273638	C₄	1	4	yes	complemented
8	C₄×C₅₉⋊C₈	C₄	1	4	yes	complemented
9	C₂×C₄²×C₅₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
11	#95×C₅₉	C₄	1	4	yes	—
12	C₂²×C₄×C₅₉	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
15	C₄²×C₅₉	—	2	4	no	—
16	C₄²×C₅₉	C₂×C₄	1	2	yes	—
17	C₄²×C₅₉	C₂×C₄	1	2	yes	—
18	C₂×C₅₉⋊C₈	—	2	4	no	—
19	C₂×C₅₉⋊C₈	—	2	4	no	—
20	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
21	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
22	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₅₉	—	2	4	no	—
24	C₂×C₄×C₅₉	—	2	4	no	—
25	C₂×C₄×C₅₉	—	2	8	no	—
26	C₂×C₄×C₅₉	C₄²	1	4	yes	—
27	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₅₉	#41	1	4	yes	—
30	C₅₉⋊C₈	—	2	4	no	—
31	C₅₉⋊C₈	—	2	4	no	—
32	C₂²×C₅₉	C₂×C₄²	1	1	yes	characteristic
33	C₂²×C₅₉	#117	1	2	yes	—
34	C₂²×C₅₉	#131	1	4	yes	—
35	C₄×C₅₉	—	2	4	no	—
36	C₄×C₅₉	—	4	4	no	—
37	C₄×C₅₉	#117	1	2	yes	—
38	C₄×C₅₉	#117	1	2	yes	—
39	#1746	—	59	1	no	maximal, Sylow
40	C₂×C₅₉	#376	1	1	yes	characteristic
41	C₂×C₅₉	#405	1	2	yes	—
42	C₂×C₅₉	#433	1	4	yes	—
43	C₂×#97	—	59	1	no	—
44	C₂×C₄×C₈	—	59	1	no	—
45	#376	D₅₉	1	1	yes	characteristic
46	#336	—	59	4	no	—
47	C₅₉	#1746	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₈	—	59	2	no	—
49	C₂²×C₈	—	59	2	no	—
50	C₂×C₄²	C₂×D₅₉	1	2	yes	—
51	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
52	#97	—	59	4	no	—
53	C₄×C₈	—	59	4	no	—
54	#95	Dic₅₉	1	4	yes	—
55	C₂²×C₄	C₂×Dic₅₉	1	4	yes	—
56	C₂²×C₄	C₂×Dic₅₉	1	2	yes	—
57	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
58	C₂×C₈	—	59	4	no	—
59	C₂×C₈	—	59	4	no	—
60	C₂×C₈	—	118	4	no	—
61	C₂×C₈	—	118	4	no	—
62	C₄²	—	2	4	no	—
63	C₄²	C₄×D₅₉	1	2	yes	—
64	C₄²	C₄×D₅₉	1	2	yes	—
65	C₂³	C₂²×Dic₅₉	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	4	no	—
68	C₂×C₄	—	2	8	no	—
69	C₂×C₄	C₄×Dic₅₉	1	4	yes	—
70	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
71	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
72	C₂×C₄	#11745685	1	4	yes	—
73	C₈	—	118	4	no	—
74	C₈	—	118	4	no	—
75	C₂²	C₂×C₄×Dic₅₉	1	1	yes	characteristic
76	C₂²	#14273686	1	2	yes	—
77	C₂²	#14273734	1	4	yes	—
78	C₄	—	2	4	no	—
79	C₄	—	4	4	no	—
80	C₄	#14273684	1	2	yes	—
81	C₄	#14273684	1	2	yes	—
82	C₂	#16837248	1	1	yes	characteristic
83	C₂	#16837358	1	2	yes	—
84	C₂	#16837463	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₉
commutator	C₂²×C₅₉	C₂×C₄²
Fitting	C₅₉×#376	C₂
socle	C₂³×C₅₉	C₂²×C₄
hypercenter	#376	D₅₉
hypocenter	C₅₉	#1746
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
7. #14273638	C₄	semidirect
8. C₄×C₅₉⋊C₈	C₄	semidirect
47. C₅₉	#1746	semidirect