Subgroups — #16837513

Order 3776.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₇₂	C₂	1	1	yes	maximal, characteristic
2	#14273689	C₂	1	2	yes	maximal, complemented
3	#14273647	C₂	1	2	yes	maximal, complemented
4	#14273637	C₂	1	1	yes	maximal, characteristic, complemented
5	#106×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₂₃₆	C₂²	1	2	yes	—
7	C₂×C₄×D₅₉	—	2	2	no	—
8	C₂×C₈×C₅₉	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
10	(C₂×D₅₉)⋊C₄	—	2	2	no	—
11	C₄×Dic₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
13	D₄₇₂	C₄	1	4	yes	complemented
14	C₂²×D₅₉	—	2	2	no	—
15	C₂×C₄×C₅₉	—	2	2	no	—
16	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
17	C₂×Dic₅₉	D₄	1	2	yes	—
18	D₂₃₆	—	2	2	no	—
19	D₂₃₆	C₂×C₄	1	4	yes	complemented
20	C₄×D₅₉	—	4	4	no	—
21	C₈×C₅₉	C₂×C₄	1	2	yes	complemented
22	C₅₉⋊C₈	—	2	1	no	—
23	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
24	C₂×D₅₉	—	2	4	no	—
25	C₂×D₅₉	—	4	2	no	—
26	C₂×D₅₉	—	4	2	no	—
27	C₄×C₅₉	—	4	2	no	—
28	C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₅₉	#41	1	1	yes	characteristic
30	Dic₅₉	—	2	2	no	—
31	C₂×C₅₉	C₄×D₄	1	1	yes	characteristic
32	C₂×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
33	D₅₉	—	4	4	no	—
34	#442	—	59	1	no	maximal, Sylow
35	C₅₉	#442	1	1	yes	characteristic, complemented, Sylow
36	C₂×D₈	—	59	1	no	—
37	C₄×D₄	—	59	2	no	—
38	#106	D₅₉	1	1	yes	characteristic, complemented
39	#102	—	59	2	no	—
40	#97	—	59	1	no	—
41	C₂×D₄	—	59	2	no	—
42	C₂²×C₄	—	118	2	no	—
43	D₈	—	59	4	no	—
44	C₂×C₈	—	59	1	no	—
45	C₂×C₈	C₂×D₅₉	1	1	yes	characteristic
46	C₄⋊C₄	C₂×D₅₉	1	2	yes	—
47	C₂²⋊C₄	—	118	2	no	—
48	C₄²	—	59	1	no	—
49	C₂³	—	118	2	no	—
50	D₄	—	59	4	no	—
51	D₄	—	118	2	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	59	2	no	—
54	C₂×C₄	—	236	4	no	—
55	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
56	C₈	—	118	1	no	—
57	C₈	C₄×D₅₉	1	2	yes	complemented
58	C₂²	—	118	4	no	—
59	C₂²	—	236	2	no	—
60	C₂²	—	236	2	no	—
61	C₂²	D₄×D₅₉	1	1	yes	characteristic
62	C₄	—	4	2	no	—
63	C₄	—	118	2	no	—
64	C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
65	C₄	#11745689	1	1	yes	characteristic
66	C₂	—	236	4	no	—
67	C₂	#14273689	1	1	yes	characteristic
68	C₂	#14273754	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₅₉
commutator	C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅₉
Fitting	#106×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₄
prime radical	C₂×D₄₇₂	C₂
cosocle	C₂×C₄×C₅₉	C₂³
hypercenter	#106	D₅₉
hypocenter	C₅₉	#442
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
2. #14273689	C₂	semidirect
3. #14273647	C₂	semidirect
4. #14273637	C₂	semidirect
5. #106×C₅₉	C₂	semidirect
13. D₄₇₂	C₄	semidirect
19. D₂₃₆	C₂×C₄	semidirect
21. C₈×C₅₉	C₂×C₄	semidirect
35. C₅₉	#442	semidirect
38. #106	D₅₉	semidirect
57. C₈	C₄×D₅₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄₇₂	2
#14273689	2
#14273647	2
#14273637	2
#106×C₅₉	2
#442	59