Subgroups — #21424241

Order 7552.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837157	C₂	1	6	yes	maximal
2	C₅₉×#376	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅₉⋊C₈	C₂²	1	4	yes	—
4	C₂×C₄²×C₅₉	C₂²	1	3	yes	—
5	#95×C₅₉	C₄	1	4	yes	—
6	C₂²×C₄×C₅₉	C₂×C₄	1	6	yes	—
7	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
8	C₄²×C₅₉	—	2	6	no	—
9	C₂×C₅₉⋊C₈	—	2	12	no	—
10	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
11	C₂×C₄×C₅₉	—	2	6	no	—
12	C₂×C₄×C₅₉	—	2	12	no	—
13	C₂×C₄×C₅₉	#41	1	6	yes	—
14	C₅₉⋊C₈	—	4	4	no	—
15	C₂²×C₅₉	#117	1	3	yes	—
16	C₂²×C₅₉	#131	1	4	yes	—
17	C₄×C₅₉	—	4	6	no	—
18	C₄×C₅₉	#126	1	4	yes	—
19	#1840	—	59	1	no	maximal, Sylow
20	C₂×C₅₉	#383	1	1	yes	characteristic
21	C₂×C₅₉	#433	1	6	yes	—
22	#376	D₅₉	1	1	yes	characteristic
23	#336	—	59	6	no	—
24	C₅₉	#1840	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₈	—	59	4	no	—
26	C₂×C₄²	C₂×D₅₉	1	3	yes	—
27	#95	Dic₅₉	1	4	yes	—
28	C₂²×C₄	C₂×Dic₅₉	1	6	yes	—
29	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
30	C₂×C₈	—	118	12	no	—
31	C₄²	—	2	6	no	—
32	C₂³	C₂²×Dic₅₉	1	1	yes	characteristic
33	C₂×C₄	—	2	6	no	—
34	C₂×C₄	—	2	12	no	—
35	C₂×C₄	#11745685	1	6	yes	—
36	C₈	—	236	4	no	—
37	C₂²	#14273686	1	3	yes	—
38	C₂²	#14273734	1	4	yes	—
39	C₄	—	4	6	no	—
40	C₄	#14273721	1	4	yes	—
41	C₂	#16837270	1	1	yes	characteristic
42	C₂	#16837463	1	6	yes	—

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

N	H ≅ G/N	type
24. C₅₉	#1840	semidirect