Subgroups — #16837657

Order 3776.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11745659	C₂	1	1	yes	maximal, characteristic
2	#14273703	C₂	1	2	yes	maximal
3	#14273659	C₂	1	1	yes	maximal, characteristic, complemented
4	#14273651	C₂	1	2	yes	maximal, complemented
5	C₂×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₅₉	C₂²	1	2	yes	—
7	C₂×C₄×D₅₉	C₂²	1	1	yes	characteristic
8	Q₁₆×C₅₉	—	2	2	no	—
9	C₂×C₈×C₅₉	C₂²	1	1	yes	characteristic
10	(C₂×D₅₉)⋊C₄	—	2	2	no	—
11	C₄⋊Dic₅₉	C₂²	1	2	yes	—
12	Dic₅₉⋊C₄	—	2	2	no	—
13	C₂×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
14	#11745659	—	2	2	no	—
15	C₂²×D₅₉	D₄	1	1	yes	characteristic
16	Q₈×C₅₉	—	2	2	no	—
17	Q₈×C₅₉	—	2	2	no	—
18	C₂×C₄×C₅₉	—	2	2	no	—
19	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
20	C₂×Dic₅₉	—	2	2	no	—
21	C₂×Dic₅₉	D₄	1	1	yes	characteristic
22	C₄×D₅₉	—	2	1	no	—
23	C₄×D₅₉	—	2	1	no	—
24	C₈×C₅₉	D₄	1	2	yes	—
25	C₅₉⋊C₈	—	2	1	no	—
26	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
27	C₂×D₅₉	—	2	1	no	—
28	C₂×D₅₉	—	2	2	no	—
29	C₄×C₅₉	—	4	2	no	—
30	C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₅₉	#41	1	1	yes	characteristic
32	Dic₅₉	—	2	1	no	—
33	Dic₅₉	—	4	2	no	—
34	C₂×C₅₉	#121	1	1	yes	characteristic
35	C₂×C₅₉	#137	1	2	yes	—
36	D₅₉	—	4	1	no	—
37	#470	—	59	1	no	maximal, Sylow
38	C₅₉	#470	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₁₆	D₅₉	1	1	yes	characteristic, complemented
40	C₂×M₁₆	—	59	1	no	—
41	C₂²⋊Q₈	—	59	2	no	—
42	#106	—	59	1	no	—
43	#103	—	59	2	no	—
44	C₂×Q₈	C₂×D₅₉	1	2	yes	—
45	C₂²×C₄	—	59	1	no	—
46	Q₁₆	—	2	2	no	—
47	M₁₆	—	118	2	no	—
48	C₂×C₈	—	59	1	no	—
49	C₂×C₈	C₂×D₅₉	1	1	yes	characteristic
50	C₄⋊C₄	—	59	2	no	—
51	C₄⋊C₄	—	118	2	no	—
52	C₂²⋊C₄	—	118	2	no	—
53	C₂³	—	59	1	no	—
54	Q₈	—	2	2	no	—
55	Q₈	—	2	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	59	1	no	—
58	C₂×C₄	—	118	1	no	—
59	C₂×C₄	—	118	1	no	—
60	C₂×C₄	—	118	2	no	—
61	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
62	C₈	—	118	1	no	—
63	C₈	C₂²⋊D₅₉	1	2	yes	—
64	C₂²	—	118	1	no	—
65	C₂²	—	118	2	no	—
66	C₂²	D₄×D₅₉	1	1	yes	characteristic
67	C₄	—	4	2	no	—
68	C₄	—	118	1	no	—
69	C₄	—	236	2	no	—
70	C₄	#11745687	1	1	yes	characteristic
71	C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
72	C₂	—	236	1	no	—
73	C₂	#14273698	1	1	yes	characteristic
74	C₂	#14273759	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₅₉
commutator, cosocle	C₂×C₄×C₅₉	C₂³
Frattini	C₂×C₄	C₂²×D₅₉
Fitting	C₂×Q₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₄
prime radical	C₂²×D₅₉	D₄
hypercenter	C₂×Q₁₆	D₅₉
hypocenter	C₅₉	#470
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #14273659	C₂	semidirect
4. #14273651	C₂	semidirect
5. C₂×Q₁₆×C₅₉	C₂	semidirect
38. C₅₉	#470	semidirect
39. C₂×Q₁₆	D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11745659	2
#14273703	2
#14273659	2
#14273651	2
C₂×Q₁₆×C₅₉	2
#470	59