Subgroups — #21432485

Order 7552.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837293	C₂	1	7	yes	maximal
2	#16837286	C₂	1	7	yes	maximal, complemented
3	C₄³×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₅₉⋊C₄	C₂²	1	7	yes	—
5	C₂×(C₂×D₅₉)⋊C₄	C₂²	1	7	yes	—
6	C₅₉⋊#95	C₂²	1	14	yes	—
7	C₂×C₄²×C₅₉	C₂²	1	7	yes	—
8	C₂³×D₅₉	C₂³	1	1	yes	characteristic
9	C₂²×C₄×C₅₉	C₂³	1	7	yes	—
10	C₂²×Dic₅₉	C₂³	1	7	yes	—
11	C₄²×C₅₉	—	2	14	no	—
12	(C₂×D₅₉)⋊C₄	—	2	14	no	—
13	Dic₅₉⋊C₄	—	2	14	no	—
14	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
15	C₂²×D₅₉	—	2	7	no	—
16	C₂×C₄×C₅₉	—	2	14	no	—
17	C₂×C₄×C₅₉	#41	1	14	yes	—
18	C₂×Dic₅₉	—	2	14	no	—
19	C₂×Dic₅₉	—	2	7	no	—
20	C₂²×C₅₉	C₂×#41	1	7	yes	—
21	C₂×D₅₉	—	4	7	no	—
22	C₄×C₅₉	—	2	14	no	—
23	Dic₅₉	—	4	7	no	—
24	#2865	—	59	1	no	maximal, Sylow
25	C₂×C₅₉	#529	1	7	yes	—
26	D₅₉	—	8	1	no	—
27	#388	—	59	7	no	—
28	#387	—	59	7	no	—
29	C₄³	D₅₉	1	1	yes	characteristic, complemented
30	C₅₉	#2865	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄⋊C₄	—	59	7	no	—
32	C₂×C₂²⋊C₄	—	59	7	no	—
33	C₂×C₄²	C₂×D₅₉	1	7	yes	—
34	#95	—	59	14	no	—
35	C₂⁴	—	59	1	no	—
36	C₂²×C₄	—	59	7	no	—
37	C₂²×C₄	C₂²×D₅₉	1	7	yes	—
38	C₄⋊C₄	—	118	14	no	—
39	C₂²⋊C₄	—	118	14	no	—
40	C₄²	—	2	14	no	—
41	C₂³	—	118	7	no	—
42	C₂³	C₂³×D₅₉	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	118	7	no	—
45	C₂×C₄	—	118	14	no	—
46	C₂×C₄	#11745685	1	14	yes	—
47	C₂²	—	236	7	no	—
48	C₂²	C₂×#11745685	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	236	7	no	—
51	C₂	—	472	1	no	—
52	C₂	#16837936	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₅₉
commutator, socle	C₂³×C₅₉	C₂⁴
Fitting	C₄³×C₅₉	C₂
hypercenter	C₄³	D₅₉
hypocenter	C₅₉	#2865
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. #16837286	C₂	semidirect
3. C₄³×C₅₉	C₂	semidirect
29. C₄³	D₅₉	semidirect
30. C₅₉	#2865	semidirect