Group #21425928 — subgroups

Subgroups — #21425928

Order 7552.

162 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 87 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	C₂×#14273667	C₂	1	2	yes	maximal, complemented
2	C₄⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₅₉⋊C₁₆)	C₂	1	2	yes	maximal, complemented
4	C₄×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×D₄×C₅₉	C₂	1	1	yes	maximal, characteristic
6	#14273667	—	2	4	no	—
7	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₅₉⋊C₁₆	C₂²	1	2	yes	—
9	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
11	C₄×D₄×C₅₉	C₄	1	1	yes	characteristic
12	C₄⋊C₈×C₅₉	C₄	1	1	yes	characteristic
13	C₂²⋊C₈×C₅₉	C₄	1	2	yes	—
14	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×D₄×C₅₉	C₈	1	1	yes	characteristic
16	C₂²×C₄×C₅₉	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₅₉	—	2	2	no	—
18	C₂×C₈×C₅₉	—	2	2	no	—
19	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
21	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₅₉	C₈	1	1	yes	characteristic
23	C₂²⋊C₄×C₅₉	C₈	1	2	yes	—
24	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
25	C₅₉⋊C₁₆	—	2	2	no	—
26	C₅₉⋊C₁₆	—	2	1	no	—
27	C₅₉⋊C₁₆	D₄	1	2	yes	complemented
28	C₂³×C₅₉	C₂×C₈	1	2	yes	—
29	D₄×C₅₉	—	2	2	no	—
30	C₂×C₄×C₅₉	—	2	2	no	—
31	C₂×C₄×C₅₉	—	2	2	no	—
32	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₅₉	C₂×C₈	1	2	yes	—
34	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₅₉	—	2	2	no	—
37	C₈×C₅₉	—	2	1	no	—
38	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
39	C₈×C₅₉	#41	1	1	yes	characteristic
40	C₂²×C₅₉	—	2	2	no	—
41	C₂²×C₅₉	—	2	2	no	—
42	C₂²×C₅₉	—	2	2	no	—
43	C₂²×C₅₉	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₅₉	—	2	2	no	—
45	C₄×C₅₉	—	2	1	no	—
46	C₄×C₅₉	M₃₂	1	2	yes	complemented
47	C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
48	C₄×C₅₉	#131	1	1	yes	characteristic
49	#2169	—	59	1	no	maximal, Sylow
50	C₂×C₅₉	—	4	2	no	—
51	C₂×C₅₉	C₈×D₄	1	1	yes	characteristic
52	C₂×C₅₉	C₂×M₃₂	1	1	yes	characteristic
53	C₂×C₅₉	#504	1	1	yes	characteristic
54	C₂×M₃₂	—	59	2	no	—
55	C₈×D₄	D₅₉	1	1	yes	characteristic
56	C₄⋊C₁₆	—	59	1	no	—
57	C₂²⋊C₁₆	—	59	2	no	—
58	C₄×C₁₆	—	59	1	no	—
59	C₅₉	#2169	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	C₂×D₅₉	1	2	yes	—
61	C₄×D₄	Dic₅₉	1	1	yes	characteristic
62	M₃₂	—	118	4	no	—
63	C₂×C₁₆	—	59	1	no	—
64	C₂×C₁₆	—	59	1	no	—
65	C₂×C₁₆	—	59	2	no	—
66	C₄⋊C₈	Dic₅₉	1	1	yes	characteristic
67	C₂²⋊C₈	Dic₅₉	1	2	yes	—
68	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
69	C₂×D₄	C₅₉⋊C₈	1	1	yes	characteristic
70	C₂²×C₄	C₂×Dic₅₉	1	2	yes	—
71	C₂×C₈	—	2	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
74	C₂×C₈	C₂×Dic₅₉	1	2	yes	—
75	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
76	C₄⋊C₄	C₅₉⋊C₈	1	1	yes	characteristic
77	C₂²⋊C₄	C₅₉⋊C₈	1	2	yes	—
78	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
79	C₁₆	—	59	2	no	—
80	C₁₆	—	118	2	no	—
81	C₁₆	—	118	1	no	—
82	C₂³	C₂×C₅₉⋊C₈	1	2	yes	—
83	D₄	—	2	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
87	C₂×C₄	C₂×C₅₉⋊C₈	1	2	yes	—
88	C₂×C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
89	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
90	C₈	—	2	2	no	—
91	C₈	—	2	1	no	—
92	C₈	D₄×D₅₉	1	1	yes	characteristic
93	C₈	#11745687	1	1	yes	characteristic
94	C₂²	—	2	2	no	—
95	C₂²	—	2	2	no	—
96	C₂²	—	2	2	no	—
97	C₂²	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	2	1	no	—
100	C₄	#14273667	1	2	yes	complemented
101	C₄	D₄×Dic₅₉	1	1	yes	characteristic
102	C₄	#14273734	1	1	yes	characteristic
103	C₂	—	4	2	no	—
104	C₂	D₄×C₅₉⋊C₈	1	1	yes	characteristic
105	C₂	C₂×#14273667	1	1	yes	characteristic
106	C₂	#16837819	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273667

C₂

yes

maximal, complemented

C₄⋊(C₅₉⋊C₁₆)

C₂

yes

maximal, characteristic, complemented

C₂²⋊(C₅₉⋊C₁₆)

C₂

yes

maximal, complemented

C₄×C₅₉⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₈×D₄×C₅₉

C₂

yes

maximal, characteristic

#14273667

—

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₅₉⋊C₁₆

C₂²

yes

—

C₂×C₅₉⋊C₁₆

C₂²

yes

characteristic

C₂²×C₈×C₅₉

C₂²

yes

—

C₄×D₄×C₅₉

C₄

yes

characteristic

C₄⋊C₈×C₅₉

C₄

yes

characteristic

C₂²⋊C₈×C₅₉

C₄

yes

—

C₄×C₈×C₅₉

C₂²

yes

characteristic

C₂×D₄×C₅₉

C₈

yes

characteristic

C₂²×C₄×C₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

characteristic

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

C₂³

yes

characteristic

C₄⋊C₄×C₅₉

C₈

yes

characteristic

C₂²⋊C₄×C₅₉

C₈

yes

—

C₄²×C₅₉

C₂×C₄

yes

characteristic

C₅₉⋊C₁₆

—

C₅₉⋊C₁₆

—

C₅₉⋊C₁₆

D₄

yes

complemented

C₂³×C₅₉

C₂×C₈

yes

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

C₂×C₈

yes

—

C₂×C₄×C₅₉

C₂×C₈

yes

characteristic

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₈×C₅₉

—

C₈×C₅₉

—

C₈×C₅₉

C₂×D₄

yes

characteristic

C₈×C₅₉

#41

yes

characteristic

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂²×C₈

yes

characteristic

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

M₃₂

yes

complemented

C₄×C₅₉

C₄×D₄

yes

C₄×C₅₉

yes

—

C₂×C₅₉

—

C₂×C₅₉

C₈×D₄

yes

characteristic

C₂×C₅₉

C₂×M₃₂

yes

characteristic

C₂×C₅₉

#504

yes

characteristic

C₂×M₃₂

—

C₈×D₄

D₅₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₅₉

#2169

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₅₉

yes

—

C₄×D₄

Dic₅₉

yes

characteristic

M₃₂

—

118

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

Dic₅₉

yes

characteristic

C₂²⋊C₈

Dic₅₉

yes

—

C₄×C₈

C₂×D₅₉

yes

characteristic

C₂×D₄

C₅₉⋊C₈

yes

characteristic

C₂²×C₄

C₂×Dic₅₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×Dic₅₉

yes

characteristic

C₂×C₈

C₂×Dic₅₉

yes

—

C₂×C₈

C₂²×D₅₉

yes

characteristic

C₄⋊C₄

C₅₉⋊C₈

yes

characteristic

C₂²⋊C₄

C₅₉⋊C₈

yes

—

C₄²

C₂×Dic₅₉

yes

characteristic

C₁₆

—

C₁₆

—

118

—

C₁₆

—

118

—

C₂³

C₂×C₅₉⋊C₈

yes

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₅₉⋊C₈

yes

characteristic

C₂×C₄

C₂×C₅₉⋊C₈

yes

—

C₂×C₄

C₂×C₅₉⋊C₈

yes

characteristic

C₂×C₄

C₂²×Dic₅₉

yes

characteristic

C₈

—

C₈

—

C₈

D₄×D₅₉

yes

characteristic

C₈

#11745687

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂²×C₅₉⋊C₈

yes

characteristic

C₄

—

C₄

—

100

C₄

#14273667

yes

complemented

101

C₄

D₄×Dic₅₉

yes

characteristic

102

C₄

#14273734

yes

characteristic

103

C₂

—

104

C₂

D₄×C₅₉⋊C₈

yes

characteristic

105

C₂

C₂×#14273667

yes

characteristic

106

C₂

#16837819

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₅₉
commutator, socle	C₂²×C₅₉	C₂²×C₈
Fitting	C₈×D₄×C₅₉	C₂
hypercenter	C₈×D₄	D₅₉
hypocenter	C₅₉	#2169
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₅₉

commutator, socle

C₂²×C₅₉

C₂²×C₈

Fitting

C₈×D₄×C₅₉

C₂

hypercenter

C₈×D₄

D₅₉

C₅₉

G ▷ C₂²×C₅₉ ▷ C₅₉

C₁ ◁ C₂×C₈ ◁ C₈×D₄

N	H ≅ G/N	type
1. C₂×#14273667	C₂	semidirect
2. C₄⋊(C₅₉⋊C₁₆)	C₂	semidirect
3. C₂²⋊(C₅₉⋊C₁₆)	C₂	semidirect
4. C₄×C₅₉⋊C₁₆	C₂	semidirect
27. C₅₉⋊C₁₆	D₄	semidirect
46. C₄×C₅₉	M₃₂	semidirect
59. C₅₉	#2169	semidirect
100. C₄	#14273667	semidirect

H ≅ G/N

type

1. C₂×#14273667

C₂

semidirect

2. C₄⋊(C₅₉⋊C₁₆)

C₂

semidirect

3. C₂²⋊(C₅₉⋊C₁₆)

C₂

semidirect

4. C₄×C₅₉⋊C₁₆

C₂

semidirect

27. C₅₉⋊C₁₆

D₄

semidirect

46. C₄×C₅₉

M₃₂

semidirect

59. C₅₉

#2169

semidirect

100. C₄

#14273667

semidirect

Subgroups — #21425928

Conjugacy classes of subgroups

Complements