Subgroups — #16837709

Order 3776.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14273719	C₂	1	1	yes	maximal, characteristic
2	#14273660	C₂	1	1	yes	maximal, characteristic
3	#14273658	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₅₉⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	#14273651	C₂	1	1	yes	maximal, characteristic
6	#14273651	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₅₉	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₅₉	—	2	1	no	—
10	C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
11	C₄²×C₅₉	—	2	1	no	—
12	C₄²×C₅₉	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
15	Dic₅₉⋊C₄	—	2	1	no	—
16	Dic₅₉⋊C₄	—	2	1	no	—
17	C₂×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈×C₅₉	—	2	1	no	—
20	Q₈×C₅₉	Q₈	1	2	yes	—
21	C₂×C₄×C₅₉	—	2	1	no	—
22	C₂×C₄×C₅₉	—	2	1	no	—
23	C₂×C₄×C₅₉	D₄	1	1	yes	characteristic
24	C₂×C₄×C₅₉	D₄	1	1	yes	characteristic
25	C₂×C₄×C₅₉	C₂³	1	1	yes	characteristic
26	C₂×Dic₅₉	—	2	1	no	—
27	C₂×Dic₅₉	—	2	1	no	—
28	C₅₉⋊C₈	—	2	1	no	—
29	C₅₉⋊C₈	—	2	1	no	—
30	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₄×C₅₉	—	2	2	no	—
32	C₄×C₅₉	—	2	1	no	—
33	C₄×C₅₉	—	2	1	no	—
34	C₄×C₅₉	—	4	1	no	—
35	C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
36	C₄×C₅₉	#41	1	1	yes	characteristic
37	Dic₅₉	—	4	1	no	—
38	Dic₅₉	—	4	1	no	—
39	C₂×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₅₉	#135	1	1	yes	characteristic
41	C₂×C₅₉	#137	1	1	yes	characteristic
42	#479	—	59	1	no	maximal, Sylow
43	C₅₉	#479	1	1	yes	characteristic, complemented, Sylow
44	#125	—	59	1	no	—
45	C₄×Q₈	D₅₉	1	1	yes	characteristic
46	#107	—	59	1	no	—
47	#106	—	59	1	no	—
48	C₄⋊C₈	—	59	1	no	—
49	#103	—	59	1	no	—
50	#103	—	59	1	no	—
51	C₂×Q₈	C₂×D₅₉	1	1	yes	characteristic
52	C₂×C₈	—	59	1	no	—
53	C₂×C₈	—	59	1	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	59	1	no	—
56	C₄⋊C₄	—	59	1	no	—
57	C₄⋊C₄	—	118	1	no	—
58	C₄⋊C₄	—	118	1	no	—
59	C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
60	C₄²	—	2	1	no	—
61	C₄²	C₂×D₅₉	1	1	yes	characteristic
62	Q₈	—	2	1	no	—
63	Q₈	Dic₁₁₈	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	118	1	no	—
67	C₂×C₄	—	118	1	no	—
68	C₂×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
69	C₂×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₅₉	1	1	yes	characteristic
71	C₈	—	118	1	no	—
72	C₈	—	118	1	no	—
73	C₂²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	1	no	—
76	C₄	—	2	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	236	1	no	—
79	C₄	—	236	1	no	—
80	C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
81	C₄	#11745685	1	1	yes	characteristic
82	C₂	#14273706	1	1	yes	characteristic
83	C₂	#14273747	1	1	yes	characteristic
84	C₂	#14273758	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₅₉
commutator, cosocle	C₂×C₄×C₅₉	C₂³
Frattini	C₂×C₄	C₂²×D₅₉
Fitting	C₄×Q₈×C₅₉	C₂
socle, prime radical	C₂²×C₅₉	C₂×D₄
hypercenter	C₄×Q₈	D₅₉
hypocenter	C₅₉	#479
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
43. C₅₉	#479	semidirect

Maximal subgroups

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

subgroup	index
#14273719	2
#14273660	2
#14273658	2
C₄⋊(C₅₉⋊C₈)	2
#14273651	2
C₄×Q₈×C₅₉	2
#479	59