Subgroups — #16837334

Order 3776.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₅₉	C₂	1	2	yes	maximal
3	C₂×Dic₅₉⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅₉⋊#95	C₂	1	2	yes	maximal
5	#95×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₅₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₅₉	C₂²	1	2	yes	—
8	C₂²×Dic₅₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₅₉	C₂²	1	2	yes	—
10	C₂²×Dic₅₉	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₅₉	—	2	2	no	—
12	C₄⋊Dic₅₉	—	2	4	no	—
13	Dic₅₉⋊C₄	—	2	2	no	—
14	C₂³×C₅₉	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₅₉	—	2	2	no	—
16	C₂×C₄×C₅₉	—	2	2	no	—
17	C₂×C₄×C₅₉	—	2	2	no	—
18	C₂×C₄×C₅₉	D₄	1	2	yes	—
19	C₂×C₄×C₅₉	Q₈	1	4	yes	—
20	C₂×Dic₅₉	—	2	1	no	—
21	C₂×Dic₅₉	—	2	1	no	—
22	C₂×Dic₅₉	—	2	1	no	—
23	C₂×Dic₅₉	—	2	2	no	—
24	C₂×Dic₅₉	—	2	2	no	—
25	C₂×Dic₅₉	—	2	2	no	—
26	C₂×Dic₅₉	—	2	2	no	—
27	C₂×Dic₅₉	D₄	1	2	yes	—
28	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
29	C₂²×C₅₉	C₂×D₄	1	1	yes	characteristic
30	C₂²×C₅₉	C₂×Q₈	1	2	yes	—
31	C₂²×C₅₉	#41	1	2	yes	—
32	C₂²×C₅₉	#41	1	1	yes	characteristic
33	C₄×C₅₉	—	2	4	no	—
34	C₄×C₅₉	—	2	2	no	—
35	Dic₅₉	—	2	2	no	—
36	Dic₅₉	—	4	2	no	—
37	Dic₅₉	—	4	1	no	—
38	C₂×C₅₉	#121	1	1	yes	characteristic
39	C₂×C₅₉	C₂²⋊Q₈	1	2	yes	—
40	C₂×C₅₉	#123	1	1	yes	characteristic
41	C₂×C₅₉	#125	1	2	yes	—
42	C₂×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
43	#398	—	59	1	no	maximal, Sylow
44	C₅₉	#398	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₄⋊C₄	—	59	1	no	—
46	C₂×C₄⋊C₄	—	59	2	no	—
47	C₂×C₄⋊C₄	—	59	1	no	—
48	#95	—	59	2	no	—
49	#95	D₅₉	1	1	yes	characteristic
50	C₂²×C₄	—	59	1	no	—
51	C₂²×C₄	—	59	1	no	—
52	C₂²×C₄	—	59	2	no	—
53	C₂²×C₄	C₂×D₅₉	1	2	yes	—
54	C₂²×C₄	C₂×D₅₉	1	1	yes	characteristic
55	C₄⋊C₄	—	118	4	no	—
56	C₄⋊C₄	—	118	2	no	—
57	C₄⋊C₄	—	118	2	no	—
58	C₂³	C₂²×D₅₉	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	59	2	no	—
63	C₂×C₄	—	118	1	no	—
64	C₂×C₄	—	118	1	no	—
65	C₂×C₄	—	118	2	no	—
66	C₂×C₄	—	118	1	no	—
67	C₂×C₄	—	118	2	no	—
68	C₂×C₄	—	118	2	no	—
69	C₂×C₄	—	118	2	no	—
70	C₂×C₄	Dic₁₁₈	1	4	yes	—
71	C₂×C₄	D₂₃₆	1	2	yes	—
72	C₂²	C₂×Dic₁₁₈	1	2	yes	—
73	C₂²	C₂×D₂₃₆	1	1	yes	characteristic
74	C₂²	D₄×D₅₉	1	1	yes	characteristic
75	C₂²	#11745687	1	2	yes	—
76	C₂²	#11745689	1	1	yes	characteristic
77	C₄	—	2	4	no	—
78	C₄	—	2	2	no	—
79	C₄	—	118	2	no	—
80	C₄	—	236	2	no	—
81	C₄	—	236	1	no	—
82	C₂	#14273702	1	1	yes	characteristic
83	C₂	#14273704	1	2	yes	—
84	C₂	#14273711	1	1	yes	characteristic
85	C₂	#14273718	1	2	yes	—
86	C₂	#14273727	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₅₉
commutator, socle, prime radical, cosocle	C₂³×C₅₉	C₂³
Fitting	#95×C₅₉	C₂
hypercenter	#95	D₅₉
hypocenter	C₅₉	#398
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
44. C₅₉	#398	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊Dic₅₉	2
C₂×Dic₅₉⋊C₄	2
C₅₉⋊#95	2
#95×C₅₉	2
#398	59