Group #28479125 — subgroups

Subgroups — #28479125

Order 15104.

478 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14273637	C₂	1	3	yes	maximal
2	C₅₉⋊#1273	C₂	1	3	yes	maximal
3	C₅₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#14273637	C₄	1	6	yes	—
5	C₂×#14273637	C₄	1	6	yes	—
6	C₂×C₄×C₅₉⋊C₈	C₂²	1	3	yes	—
7	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₅₉	C₂²	1	3	yes	—
9	C₂²×C₅₉⋊C₈	C₂×C₄	1	6	yes	—
10	C₂×C₄×Dic₅₉	C₂×C₄	1	3	yes	—
11	C₂×C₄×Dic₅₉	C₂×C₄	1	3	yes	—
12	#14273637	—	2	12	no	—
13	#14273637	—	2	12	no	—
14	C₄×C₅₉⋊C₈	—	2	3	no	—
15	C₄×C₅₉⋊C₈	—	2	3	no	—
16	C₂²×C₈×C₅₉	C₂×C₄	1	6	yes	—
17	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
18	C₄×C₈×C₅₉	—	2	6	no	—
19	C₂²×C₄×C₅₉	C₂²×C₄	1	3	yes	—
20	C₂²×Dic₅₉	C₄²	1	1	yes	characteristic
21	C₂²×Dic₅₉	C₄²	1	3	yes	—
22	C₂×C₈×C₅₉	—	2	6	no	—
23	C₂×C₈×C₅₉	—	2	6	no	—
24	C₂×C₈×C₅₉	M₁₆	1	12	yes	—
25	C₄²×C₅₉	#41	1	3	yes	—
26	C₄²×C₅₉	#41	1	1	yes	characteristic
27	C₄×Dic₅₉	—	2	6	no	—
28	C₄×Dic₅₉	—	2	6	no	—
29	C₂×C₅₉⋊C₈	—	2	6	no	—
30	C₂×C₅₉⋊C₈	—	2	6	no	—
31	C₂×C₅₉⋊C₈	M₁₆	1	12	yes	—
32	C₂³×C₅₉	C₂×C₄²	1	1	yes	characteristic
33	C₂×C₄×C₅₉	#117	1	3	yes	—
34	C₂×C₄×C₅₉	#117	1	3	yes	—
35	C₂×C₄×C₅₉	C₂×M₁₆	1	6	yes	—
36	C₂×C₄×C₅₉	C₂×M₁₆	1	6	yes	—
37	C₂×Dic₅₉	—	2	3	no	—
38	C₂×Dic₅₉	—	2	3	no	—
39	C₂×Dic₅₉	—	2	6	no	—
40	C₈×C₅₉	—	2	12	no	—
41	C₅₉⋊C₈	—	2	12	no	—
42	#8136	—	59	1	no	maximal, Sylow
43	C₂²×C₅₉	#376	1	1	yes	characteristic
44	C₂²×C₅₉	C₄×M₁₆	1	3	yes	—
45	C₂²×C₅₉	C₄×M₁₆	1	3	yes	—
46	C₄×C₅₉	#432	1	6	yes	—
47	C₄×C₅₉	#432	1	6	yes	—
48	Dic₅₉	—	4	1	no	—
49	Dic₅₉	—	4	3	no	—
50	C₄×#97	—	59	3	no	—
51	#1273	—	59	3	no	—
52	#1273	D₅₉	1	1	yes	characteristic
53	C₂×C₅₉	#1455	1	1	yes	characteristic
54	C₂×C₅₉	#1455	1	3	yes	—
55	C₂×C₅₉	#1745	1	3	yes	—
56	C₂×#97	—	59	6	no	—
57	C₂×#97	—	59	6	no	—
58	C₂×C₄×C₈	—	59	3	no	—
59	C₂×C₄×C₈	C₂×D₅₉	1	3	yes	—
60	C₄³	—	59	1	no	—
61	C₅₉	#8136	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	59	6	no	—
63	C₂²×C₈	C₄×D₅₉	1	6	yes	—
64	C₂×C₄²	—	59	3	no	—
65	C₂×C₄²	—	59	3	no	—
66	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
67	#97	—	118	12	no	—
68	#97	—	118	12	no	—
69	C₄×C₈	—	2	6	no	—
70	C₄×C₈	—	118	3	no	—
71	C₄×C₈	—	118	3	no	—
72	C₂²×C₄	—	59	1	no	—
73	C₂²×C₄	—	59	3	no	—
74	C₂²×C₄	C₂×C₄×D₅₉	1	3	yes	—
75	C₂×C₈	—	2	6	no	—
76	C₂×C₈	—	2	6	no	—
77	C₂×C₈	—	59	12	no	—
78	C₂×C₈	—	118	6	no	—
79	C₂×C₈	—	118	6	no	—
80	C₂×C₈	#11745659	1	12	yes	—
81	C₄²	—	118	6	no	—
82	C₄²	—	118	6	no	—
83	C₄²	#11745687	1	3	yes	—
84	C₄²	#11745689	1	1	yes	characteristic
85	C₂³	C₄²×D₅₉	1	1	yes	characteristic
86	C₂×C₄	—	118	3	no	—
87	C₂×C₄	—	118	3	no	—
88	C₂×C₄	—	118	6	no	—
89	C₂×C₄	#14273683	1	3	yes	—
90	C₂×C₄	#14273685	1	3	yes	—
91	C₂×C₄	M₁₆×D₅₉	1	6	yes	—
92	C₂×C₄	C₂×#11745659	1	6	yes	—
93	C₈	—	2	12	no	—
94	C₈	—	118	12	no	—
95	C₂²	#16837247	1	1	yes	characteristic
96	C₂²	C₄×#11745659	1	3	yes	—
97	C₂²	#16837354	1	3	yes	—
98	C₄	—	236	1	no	—
99	C₄	—	236	3	no	—
100	C₄	#16837456	1	6	yes	—
101	C₄	#16837458	1	6	yes	—
102	C₂	#21422398	1	1	yes	characteristic
103	C₂	#21422400	1	3	yes	—
104	C₂	#21423843	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#14273637

C₂

yes

maximal

C₅₉⋊#1273

C₂

yes

maximal

C₅₉×#1273

C₂

yes

maximal, characteristic

C₂×#14273637

C₄

yes

—

C₂×#14273637

C₄

yes

—

C₂×C₄×C₅₉⋊C₈

C₂²

yes

—

C₄²×Dic₅₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₅₉

C₂²

yes

—

C₂²×C₅₉⋊C₈

C₂×C₄

yes

—

C₂×C₄×Dic₅₉

C₂×C₄

yes

—

C₂×C₄×Dic₅₉

C₂×C₄

yes

—

#14273637

—

#14273637

—

C₄×C₅₉⋊C₈

—

C₄×C₅₉⋊C₈

—

C₂²×C₈×C₅₉

C₂×C₄

yes

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₄×C₈×C₅₉

—

C₂²×C₄×C₅₉

C₂²×C₄

yes

—

C₂²×Dic₅₉

C₄²

yes

characteristic

C₂²×Dic₅₉

C₄²

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

M₁₆

yes

—

C₄²×C₅₉

#41

yes

—

C₄²×C₅₉

#41

yes

characteristic

C₄×Dic₅₉

—

C₄×Dic₅₉

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

M₁₆

yes

—

C₂³×C₅₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₅₉

#117

yes

—

C₂×C₄×C₅₉

#117

yes

—

C₂×C₄×C₅₉

C₂×M₁₆

yes

—

C₂×C₄×C₅₉

C₂×M₁₆

yes

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

—

C₂²×C₅₉

yes

C₂²×C₅₉

C₄×M₁₆

yes

—

C₂²×C₅₉

C₄×M₁₆

yes

—

C₄×C₅₉

#432

yes

—

C₄×C₅₉

#432

yes

—

Dic₅₉

—

Dic₅₉

—

C₄×#97

—

#1273

—

#1273

D₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#1745

yes

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₅₉

yes

—

C₄³

—

C₅₉

#8136

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₄×D₅₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₅₉

yes

characteristic

#97

—

118

—

#97

—

118

—

C₄×C₈

—

C₄×C₈

—

118

—

C₄×C₈

—

118

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₅₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₂×C₈

#11745659

yes

—

C₄²

—

118

—

C₄²

—

118

—

C₄²

#11745687

yes

—

C₄²

#11745689

yes

characteristic

C₂³

C₄²×D₅₉

yes

characteristic

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

—

118

—

C₂×C₄

#14273683

yes

—

C₂×C₄

#14273685

yes

—

C₂×C₄

M₁₆×D₅₉

yes

—

C₂×C₄

C₂×#11745659

yes

—

C₈

—

C₈

—

118

—

C₂²

#16837247

yes

characteristic

C₂²

C₄×#11745659

yes

—

C₂²

#16837354

yes

—

C₄

—

236

—

C₄

—

236

—

100

C₄

#16837456

yes

—

101

C₄

#16837458

yes

—

102

C₂

#21422398

yes

characteristic

103

C₂

#21422400

yes

—

104

C₂

#21423843

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₅₉
commutator, socle, prime radical	C₂³×C₅₉	C₂×C₄²
Fitting	C₅₉×#1273	C₂
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	#1273	D₅₉
hypocenter	C₅₉	#8136
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₅₉

commutator, socle, prime radical

C₂³×C₅₉

C₂×C₄²

Fitting

C₅₉×#1273

C₂

cosocle

C₂×C₄²×C₅₉

C₂³

D₅₉

C₅₉

G ▷ C₂³×C₅₉ ▷ C₅₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
61. C₅₉	#8136	semidirect

H ≅ G/N

type

61. C₅₉

#8136

semidirect

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

subgroup	index
C₄×#14273637	2
C₅₉⋊#1273	2
C₅₉×#1273	2
#8136	59

subgroup

index

C₄×#14273637

C₅₉⋊#1273

C₅₉×#1273

#8136

Subgroups — #28479125

Conjugacy classes of subgroups

Complements

Maximal subgroups