Group #21424260 — subgroups

Subgroups — #21424260

Order 7552.

248 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14273661	C₂	1	2	yes	maximal
2	C₂×#14273659	C₂	1	2	yes	maximal
3	#16837268	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₅₉	C₂²	1	4	yes	—
6	#14273661	—	2	4	no	—
7	#14273659	—	2	4	no	—
8	C₅₉⋊#95	—	2	4	no	—
9	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₅₉	C₄	1	4	yes	complemented
13	C₂²×C₄×C₅₉	D₄	1	2	yes	—
14	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
15	C₂²×Dic₅₉	—	2	4	no	—
16	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₅₉	D₄	1	2	yes	—
19	C₂×C₈×C₅₉	D₄	1	2	yes	—
20	C₂×C₈×C₅₉	Q₈	1	2	yes	—
21	C₂×C₈×C₅₉	Q₈	1	2	yes	—
22	C₄²×C₅₉	C₂×C₄	1	2	yes	—
23	C₄²×C₅₉	Q₈	1	2	yes	—
24	C₄⋊Dic₅₉	—	2	4	no	—
25	C₄⋊Dic₅₉	—	2	4	no	—
26	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₅₉	—	2	4	no	—
28	C₂×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
29	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×Dic₅₉	—	4	4	no	—
36	C₂×Dic₅₉	—	4	8	no	—
37	C₈×C₅₉	C₄⋊C₄	1	4	yes	—
38	C₈×C₅₉	C₄⋊C₄	1	4	yes	—
39	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₅₉	#127	1	1	yes	characteristic
41	C₂²×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
42	C₂²×C₅₉	#135	1	4	yes	—
43	C₄×C₅₉	—	2	4	no	—
44	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
47	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
48	Dic₅₉	—	8	4	no	—
49	#1846	—	59	1	no	maximal, Sylow
50	C₂×C₅₉	#384	1	1	yes	characteristic
51	C₂×C₅₉	#427	1	2	yes	—
52	C₂×C₅₉	#495	1	2	yes	—
53	C₂×C₅₉	#499	1	2	yes	—
54	C₂×#107	—	59	2	no	—
55	C₂×#106	—	59	2	no	—
56	C₂×C₄×C₈	D₅₉	1	1	yes	characteristic
57	#382	—	59	2	no	—
58	C₅₉	#1846	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
60	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
61	C₂×C₄⋊C₄	—	59	4	no	—
62	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
63	#107	—	118	4	no	—
64	#106	—	118	4	no	—
65	C₄×C₈	Dic₅₉	1	4	yes	complemented
66	#95	—	118	4	no	—
67	C₂²×C₄	—	118	4	no	—
68	C₂²×C₄	D₂₃₆	1	2	yes	—
69	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
70	C₂×C₈	Dic₁₁₈	1	2	yes	—
71	C₂×C₈	Dic₁₁₈	1	2	yes	—
72	C₂×C₈	D₂₃₆	1	2	yes	—
73	C₂×C₈	D₂₃₆	1	2	yes	—
74	C₂×C₈	C₂×Dic₅₉	1	2	yes	—
75	C₂×C₈	C₂×Dic₅₉	1	2	yes	—
76	C₄⋊C₄	—	118	4	no	—
77	C₄⋊C₄	—	118	4	no	—
78	C₄²	Dic₁₁₈	1	2	yes	—
79	C₄²	C₂×Dic₅₉	1	2	yes	—
80	C₂³	C₂×D₂₃₆	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	236	4	no	—
83	C₂×C₄	—	236	8	no	—
84	C₂×C₄	C₄⋊Dic₅₉	1	4	yes	—
85	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
86	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
87	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
88	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
89	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
90	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
91	C₈	C₄⋊Dic₅₉	1	4	yes	—
92	C₈	C₄⋊Dic₅₉	1	4	yes	—
93	C₂²	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
94	C₂²	#14273724	1	1	yes	characteristic
95	C₂²	#14273727	1	1	yes	characteristic
96	C₂²	#14273749	1	4	yes	—
97	C₄	—	2	4	no	—
98	C₄	—	472	4	no	—
99	C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
100	C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
101	C₄	#14273727	1	1	yes	characteristic
102	C₄	#14273727	1	1	yes	characteristic
103	C₂	#16837272	1	1	yes	characteristic
104	C₂	#16837440	1	2	yes	—
105	C₂	#16837786	1	2	yes	—
106	C₂	#16837804	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14273661

C₂

yes

maximal

C₂×#14273659

C₂

yes

maximal

#16837268

C₂

yes

maximal

C₂×C₄×C₈×C₅₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₅₉

C₂²

yes

—

#14273661

—

#14273659

—

C₅₉⋊#95

—

C₂²×C₈×C₅₉

C₂²

yes

characteristic

C₂²×C₈×C₅₉

C₂²

yes

characteristic

C₂×C₄²×C₅₉

C₂²

yes

characteristic

C₄×C₈×C₅₉

C₄

yes

complemented

C₂²×C₄×C₅₉

D₄

yes

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

C₂²×Dic₅₉

—

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

C₂×C₄

yes

—

C₂×C₈×C₅₉

D₄

yes

—

C₂×C₈×C₅₉

D₄

yes

—

C₂×C₈×C₅₉

Q₈

yes

—

C₂×C₈×C₅₉

Q₈

yes

—

C₄²×C₅₉

C₂×C₄

yes

—

C₄²×C₅₉

Q₈

yes

—

C₄⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₂³×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₄⋊C₄

yes

—

C₂×C₄×C₅₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×Dic₅₉

—

C₂×Dic₅₉

—

C₈×C₅₉

C₄⋊C₄

yes

—

C₈×C₅₉

C₄⋊C₄

yes

—

C₂²×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₅₉

#127

yes

characteristic

C₂²×C₅₉

C₄⋊Q₈

yes

characteristic

C₂²×C₅₉

#135

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₅₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₅₉

C₄⋊Q₈

yes

characteristic

C₄×C₅₉

C₄⋊Q₈

yes

characteristic

Dic₅₉

—

—

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#495

yes

—

C₂×C₅₉

#499

yes

—

C₂×#107

—

C₂×#106

—

C₂×C₄×C₈

D₅₉

yes

characteristic

#382

—

C₅₉

#1846

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₅₉

yes

characteristic

C₂²×C₈

C₂×D₅₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₅₉

yes

characteristic

#107

—

118

—

#106

—

118

—

C₄×C₈

Dic₅₉

yes

complemented

#95

—

118

—

C₂²×C₄

—

118

—

C₂²×C₄

D₂₃₆

yes

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

C₂×C₈

Dic₁₁₈

yes

—

C₂×C₈

Dic₁₁₈

yes

—

C₂×C₈

D₂₃₆

yes

—

C₂×C₈

D₂₃₆

yes

—

C₂×C₈

C₂×Dic₅₉

yes

—

C₂×C₈

C₂×Dic₅₉

yes

—

C₄⋊C₄

—

118

—

C₄⋊C₄

—

118

—

C₄²

Dic₁₁₈

yes

—

C₄²

C₂×Dic₅₉

yes

—

C₂³

C₂×D₂₃₆

yes

characteristic

C₂×C₄

—

C₂×C₄

—

236

—

C₂×C₄

—

236

—

C₂×C₄

C₄⋊Dic₅₉

yes

—

C₂×C₄

C₂×Dic₁₁₈

yes

characteristic

C₂×C₄

C₂×Dic₁₁₈

yes

characteristic

C₂×C₄

C₂×Dic₁₁₈

yes

characteristic

C₂×C₄

C₂×D₂₃₆

yes

characteristic

C₂×C₄

C₂×D₂₃₆

yes

characteristic

C₂×C₄

C₂²×Dic₅₉

yes

characteristic

C₈

C₄⋊Dic₅₉

yes

—

C₈

C₄⋊Dic₅₉

yes

—

C₂²

C₂×C₄⋊Dic₅₉

yes

C₂²

yes

C₂²

yes

C₂²

yes

—

C₄

—

C₄

—

472

—

C₄

C₂×C₄⋊Dic₅₉

yes

characteristic

100

C₄

C₂×C₄⋊Dic₅₉

yes

characteristic

101

C₄

#14273727

yes

characteristic

102

C₄

#14273727

yes

characteristic

103

C₂

#16837272

yes

characteristic

104

C₂

#16837440

yes

—

105

C₂

#16837786

yes

—

106

C₂

#16837804

yes

—

	subgroup	G/H
center	C₂³	C₂×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₂×C₄×C₈×C₅₉	C₂
socle	C₂³×C₅₉	C₂×D₄
hypercenter	C₂×C₄×C₈	D₅₉
hypocenter	C₅₉	#1846
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₂₃₆

commutator

C₂×C₄×C₅₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₂×C₄×C₈×C₅₉

C₂

socle

C₂³×C₅₉

C₂×D₄

hypercenter

C₂×C₄×C₈

D₅₉

hypocenter

C₅₉

#1846

LCS

G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
12. C₄×C₈×C₅₉	C₄	semidirect
58. C₅₉	#1846	semidirect
65. C₄×C₈	Dic₅₉	semidirect

H ≅ G/N

type

12. C₄×C₈×C₅₉

C₄

semidirect

58. C₅₉

#1846

semidirect

65. C₄×C₈

Dic₅₉

semidirect

Subgroups — #21424260

Conjugacy classes of subgroups

Complements