Group #21421968 — subgroups

Subgroups — #21421968

Order 7552.

138 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 57 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	#16837459	C₂	1	1	yes	maximal, characteristic
2	#16837459	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
5	C₄⋊(C₅₉⋊C₈)	C₄	1	2	yes	—
6	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
7	C₂²⋊(C₅₉⋊C₈)	C₄	1	2	yes	—
8	#14273638	—	2	1	no	—
9	#14273638	—	2	1	no	—
10	C₂×M₁₆×C₅₉	—	2	1	no	—
11	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
12	#97×C₅₉	—	2	1	no	—
13	C₄×C₈×C₅₉	C₄	1	2	yes	—
14	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₅₉	Q₈	1	1	yes	characteristic
17	M₁₆×C₅₉	—	2	4	no	—
18	C₂×C₈×C₅₉	—	2	2	no	—
19	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₅₉	D₄	1	1	yes	characteristic
22	C₄²×C₅₉	D₄	1	1	yes	characteristic
23	C₂×C₅₉⋊C₈	—	2	2	no	—
24	C₂×C₅₉⋊C₈	—	2	2	no	—
25	C₂³×C₅₉	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₅₉	—	2	2	no	—
27	C₂×C₄×C₅₉	—	4	1	no	—
28	C₂×C₄×C₅₉	—	4	1	no	—
29	C₂×C₄×C₅₉	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
35	C₈×C₅₉	—	2	4	no	—
36	C₅₉⋊C₈	—	4	2	no	—
37	C₅₉⋊C₈	—	4	2	no	—
38	C₂²×C₅₉	—	2	1	no	—
39	C₂²×C₅₉	—	2	1	no	—
40	C₂²×C₅₉	—	2	1	no	—
41	C₂²×C₅₉	#95	1	1	yes	characteristic
42	C₄×C₅₉	—	2	1	no	—
43	C₄×C₅₉	—	2	1	no	—
44	C₄×C₅₉	—	2	1	no	—
45	C₄×C₅₉	—	2	1	no	—
46	C₄×C₅₉	—	2	1	no	—
47	C₄×C₅₉	#104	1	2	yes	—
48	#1291	—	59	1	no	maximal, Sylow
49	C₂×C₅₉	—	4	1	no	—
50	C₂×C₅₉	#338	1	1	yes	characteristic
51	C₂×C₅₉	#339	1	1	yes	characteristic
52	C₂×C₅₉	#344	1	1	yes	characteristic
53	#432	—	59	1	no	—
54	#432	—	59	1	no	—
55	C₄×M₁₆	D₅₉	1	1	yes	characteristic
56	C₅₉	#1291	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	2	1	no	—
58	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
59	C₄⋊C₈	—	59	2	no	—
60	C₄⋊C₈	—	118	1	no	—
61	C₂²⋊C₈	—	59	2	no	—
62	C₂²⋊C₈	—	118	1	no	—
63	#97	—	2	1	no	—
64	#97	—	118	1	no	—
65	#97	—	118	1	no	—
66	C₄×C₈	Dic₅₉	1	2	yes	—
67	C₂²×C₄	Dic₁₁₈	1	1	yes	characteristic
68	C₂²×C₄	C₄×D₅₉	1	1	yes	characteristic
69	C₂²×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
70	M₁₆	—	2	4	no	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	118	2	no	—
73	C₂×C₈	—	118	2	no	—
74	C₄²	C₄×D₅₉	1	1	yes	characteristic
75	C₄²	D₂₃₆	1	1	yes	characteristic
76	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
77	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
78	C₂³	Dic₅₉⋊C₄	1	1	yes	characteristic
79	C₂×C₄	—	2	2	no	—
80	C₂×C₄	—	4	1	no	—
81	C₂×C₄	—	4	1	no	—
82	C₂×C₄	C₄×Dic₅₉	1	1	yes	characteristic
83	C₂×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
84	C₂×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
85	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
86	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
87	C₂×C₄	C₂²⋊Dic₅₉	1	1	yes	characteristic
88	C₈	—	2	4	no	—
89	C₈	—	236	2	no	—
90	C₈	—	236	2	no	—
91	C₂²	—	2	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	—	2	1	no	—
94	C₂²	C₅₉⋊#95	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	2	1	no	—
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	#14273655	1	2	yes	—
101	C₂	—	4	1	no	—
102	C₂	C₅₉⋊#338	1	1	yes	characteristic
103	C₂	#16837162	1	1	yes	characteristic
104	C₂	#16837173	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837459

C₂

yes

maximal, characteristic

#16837459

C₂

yes

maximal, characteristic

C₄×M₁₆×C₅₉

C₂

yes

maximal, characteristic

C₄⋊(C₅₉⋊C₈)

—

C₄⋊(C₅₉⋊C₈)

C₄

yes

—

C₂²⋊(C₅₉⋊C₈)

—

C₂²⋊(C₅₉⋊C₈)

C₄

yes

—

#14273638

—

#14273638

—

C₂×M₁₆×C₅₉

—

C₂×C₄²×C₅₉

C₂²

yes

characteristic

#97×C₅₉

—

C₄×C₈×C₅₉

C₄

yes

—

C₂²×C₄×C₅₉

C₂×C₄

yes

characteristic

C₂²×C₄×C₅₉

D₄

yes

characteristic

C₂²×C₄×C₅₉

Q₈

yes

characteristic

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₄²×C₅₉

C₂×C₄

yes

characteristic

C₄²×C₅₉

C₂×C₄

yes

characteristic

C₄²×C₅₉

D₄

yes

characteristic

C₄²×C₅₉

D₄

yes

characteristic

C₂×C₅₉⋊C₈

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₄²

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄⋊C₄

yes

characteristic

C₂×C₄×C₅₉

C₄⋊C₄

yes

characteristic

C₈×C₅₉

—

C₅₉⋊C₈

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

#95

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#104

yes

—

#1291

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

—

C₄×M₁₆

D₅₉

yes

characteristic

C₅₉

#1291

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

118

—

C₂²⋊C₈

—

C₂²⋊C₈

—

118

—

#97

—

#97

—

118

—

#97

—

118

—

C₄×C₈

Dic₅₉

yes

—

C₂²×C₄

Dic₁₁₈

yes

characteristic

C₂²×C₄

C₄×D₅₉

yes

characteristic

C₂²×C₄

C₂²⋊D₅₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

—

118

—

C₄²

C₄×D₅₉

yes

characteristic

C₄²

D₂₃₆

yes

characteristic

C₄²

C₂×Dic₅₉

yes

characteristic

C₄²

C₂²⋊D₅₉

yes

characteristic

C₂³

Dic₅₉⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₅₉

yes

characteristic

C₂×C₄

Dic₅₉⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₅₉

yes

characteristic

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₅₉)⋊C₄

yes

characteristic

C₂×C₄

C₂²⋊Dic₅₉

yes

characteristic

C₈

—

C₈

—

236

—

C₈

—

236

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₅₉⋊#95

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

100

C₄

#14273655

yes

—

101

C₂

—

102

C₂

C₅₉⋊#338

yes

characteristic

103

C₂

#16837162

yes

characteristic

104

C₂

#16837173

yes

characteristic

	subgroup	G/H
center	C₂²	C₅₉⋊#95
commutator	C₂×C₄×C₅₉	C₄²
Frattini	C₂×C₄²	C₂×D₅₉
Fitting	C₄×M₁₆×C₅₉	C₂
socle	C₂²×C₅₉	#95
hypercenter	C₄×M₁₆	D₅₉
hypocenter	C₅₉	#1291
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₅₉⋊#95

commutator

C₂×C₄×C₅₉

C₄²

Frattini

C₂×C₄²

C₂×D₅₉

Fitting

C₄×M₁₆×C₅₉

C₂

socle

C₂²×C₅₉

#95

hypercenter

C₄×M₁₆

D₅₉

hypocenter

C₅₉

#1291

LCS

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
56. C₅₉	#1291	semidirect

H ≅ G/N

type

56. C₅₉

#1291

semidirect

Subgroups — #21421968

Conjugacy classes of subgroups

Complements