Subgroups — #21424227

Order 7552.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837268	C₂	1	2	yes	maximal
2	#16837165	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	—
5	C₅₉⋊#95	—	2	4	no	—
6	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₅₉	C₄	1	4	yes	complemented
9	C₂²×C₄×C₅₉	D₄	1	2	yes	—
10	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
11	C₂²×Dic₅₉	—	2	4	no	—
12	C₂×C₈×C₅₉	—	2	4	no	—
13	C₂×C₈×C₅₉	C₂×C₄	1	4	yes	—
14	C₄²×C₅₉	C₂×C₄	1	2	yes	—
15	C₄²×C₅₉	Q₈	1	2	yes	—
16	C₄⋊Dic₅₉	—	2	8	no	—
17	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₅₉	—	2	4	no	—
19	C₂×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
20	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₅₉	#41	1	4	yes	—
23	C₂×Dic₅₉	—	4	4	no	—
24	C₂×Dic₅₉	—	4	8	no	—
25	C₈×C₅₉	—	2	4	no	—
26	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₅₉	#124	1	2	yes	—
28	C₂²×C₅₉	#135	1	4	yes	—
29	C₄×C₅₉	—	2	4	no	—
30	C₄×C₅₉	#117	1	2	yes	—
31	C₄×C₅₉	#125	1	2	yes	—
32	Dic₅₉	—	8	4	no	—
33	#1835	—	59	1	no	maximal, Sylow
34	C₂×C₅₉	#382	1	1	yes	characteristic
35	C₂×C₅₉	#427	1	2	yes	—
36	C₂×C₅₉	#488	1	4	yes	—
37	C₂×C₄×C₈	D₅₉	1	1	yes	characteristic
38	#382	—	59	2	no	—
39	#340	—	59	4	no	—
40	C₅₉	#1835	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	C₂×D₅₉	1	2	yes	—
42	C₂×C₄⋊C₄	—	59	4	no	—
43	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
44	C₄×C₈	Dic₅₉	1	4	yes	complemented
45	#95	—	118	4	no	—
46	C₂²×C₄	—	118	4	no	—
47	C₂²×C₄	D₂₃₆	1	2	yes	—
48	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
49	C₂×C₈	—	2	4	no	—
50	C₂×C₈	C₂×Dic₅₉	1	4	yes	—
51	C₄⋊C₄	—	118	8	no	—
52	C₄²	Dic₁₁₈	1	2	yes	—
53	C₄²	C₂×Dic₅₉	1	2	yes	—
54	C₂³	C₂×D₂₃₆	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	236	4	no	—
57	C₂×C₄	—	236	8	no	—
58	C₂×C₄	C₄⋊Dic₅₉	1	4	yes	—
59	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
60	C₂×C₄	#11745685	1	4	yes	—
61	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
62	C₈	—	2	4	no	—
63	C₂²	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
64	C₂²	#14273715	1	2	yes	—
65	C₂²	#14273749	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	472	4	no	—
68	C₄	#14273686	1	2	yes	—
69	C₄	#14273719	1	2	yes	—
70	C₂	#16837268	1	1	yes	characteristic
71	C₂	#16837440	1	2	yes	—
72	C₂	#16837757	1	4	yes	—

	subgroup	G/H
center	C₂³	C₂×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₂×C₄×C₈×C₅₉	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	C₂×C₄×C₈	D₅₉
hypocenter	C₅₉	#1835
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×C₈×C₅₉	C₄	semidirect
40. C₅₉	#1835	semidirect
44. C₄×C₈	Dic₅₉	semidirect