Group #21425649 — subgroups

Subgroups — #21425649

Order 7552.

210 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 65 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	#16837451	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837428	C₂	1	2	yes	maximal, complemented
3	#16837419	C₂	1	2	yes	maximal
4	#16837159	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#408	C₂	1	1	yes	maximal, characteristic
6	C₂×#11745664	C₂²	1	2	yes	—
7	#14273686	C₂²	1	2	yes	—
8	#14273663	—	2	2	no	—
9	Dic₅₉⋊C₈	—	2	4	no	—
10	#14273654	—	2	4	no	—
11	C₂×#41×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂²⋊C₈×C₅₉	—	2	2	no	—
15	#41×C₅₉	—	2	2	no	—
16	#41×C₅₉	—	2	2	no	—
17	C₂×Q₈×C₅₉	Q₈	1	1	yes	characteristic
18	C₂×D₄×C₅₉	—	2	1	no	—
19	C₂×D₄×C₅₉	Q₈	1	1	yes	characteristic
20	C₂²×C₄×C₅₉	—	2	1	no	—
21	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₅₉	—	2	2	no	—
23	C₂×C₈×C₅₉	—	2	1	no	—
24	C₂×C₈×C₅₉	—	2	2	no	—
25	C₂×C₈×C₅₉	D₄	1	2	yes	—
26	C₂²⋊Dic₅₉	—	2	2	no	—
27	C₄⋊Dic₅₉	—	2	2	no	—
28	C₄×Dic₅₉	D₄	1	4	yes	—
29	#11745664	—	2	2	no	—
30	#11745664	—	2	2	no	—
31	C₂×C₅₉⋊C₈	—	2	2	no	—
32	C₂³×C₅₉	—	2	1	no	—
33	C₂³×C₅₉	#41	1	1	yes	characteristic
34	Q₈×C₅₉	—	2	2	no	—
35	D₄×C₅₉	—	2	2	no	—
36	D₄×C₅₉	—	4	2	no	—
37	C₂×C₄×C₅₉	—	2	1	no	—
38	C₂×C₄×C₅₉	—	4	1	no	—
39	C₂×C₄×C₅₉	—	4	1	no	—
40	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
41	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
43	C₂×C₄×C₅₉	#41	1	2	yes	—
44	C₂×Dic₅₉	—	2	4	no	—
45	C₈×C₅₉	—	2	2	no	—
46	C₈×C₅₉	—	4	1	no	—
47	C₅₉⋊C₈	—	4	2	no	—
48	C₂²×C₅₉	—	4	1	no	—
49	C₂²×C₅₉	—	4	2	no	—
50	C₂²×C₅₉	—	4	1	no	—
51	C₂²×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
52	C₂²×C₅₉	#123	1	2	yes	—
53	C₄×C₅₉	—	4	1	no	—
54	C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
55	C₄×C₅₉	#123	1	1	yes	characteristic
56	C₄×C₅₉	#127	1	1	yes	characteristic
57	Dic₅₉	—	4	4	no	—
58	#2098	—	59	1	no	maximal, Sylow
59	C₂×C₅₉	—	2	2	no	—
60	C₂×C₅₉	—	2	1	no	—
61	C₂×C₅₉	—	8	1	no	—
62	C₂×C₅₉	#399	1	1	yes	characteristic
63	#430	—	59	1	no	—
64	#424	—	59	2	no	—
65	#421	—	59	2	no	—
66	#408	D₅₉	1	1	yes	characteristic
67	H(3,ℤ/4)	—	59	1	no	—
68	C₅₉	#2098	1	1	yes	characteristic, complemented, Sylow
69	C₂×#41	C₂×D₅₉	1	1	yes	characteristic
70	C₂×M₁₆	—	59	2	no	—
71	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
72	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
73	#117	—	59	2	no	—
74	#108	—	118	2	no	—
75	C₄⋊C₈	—	118	4	no	—
76	#104	—	118	4	no	—
77	C₂²⋊C₈	—	2	2	no	—
78	#41	—	2	2	no	—
79	#41	—	2	2	no	—
80	C₂×Q₈	Dic₁₁₈	1	1	yes	characteristic
81	C₂×D₄	—	2	1	no	—
82	C₂×D₄	Dic₁₁₈	1	1	yes	characteristic
83	C₂²×C₄	—	2	1	no	—
84	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	118	2	no	—
87	M₁₆	—	118	2	no	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	118	2	no	—
91	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
92	C₄⋊C₄	—	118	2	no	—
93	C₂²⋊C₄	—	118	2	no	—
94	C₄²	—	59	4	no	—
95	C₂³	—	2	1	no	—
96	C₂³	#11745685	1	1	yes	characteristic
97	Q₈	—	2	2	no	—
98	D₄	—	2	2	no	—
99	D₄	—	4	2	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	4	1	no	—
102	C₂×C₄	—	4	1	no	—
103	C₂×C₄	—	118	4	no	—
104	C₂×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
105	C₂×C₄	D₄×D₅₉	1	2	yes	—
106	C₂×C₄	#11745687	1	2	yes	—
107	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
108	C₈	—	2	2	no	—
109	C₈	—	4	1	no	—
110	C₈	—	236	2	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	4	2	no	—
113	C₂²	—	4	1	no	—
114	C₂²	#14273706	1	1	yes	characteristic
115	C₂²	#14273709	1	2	yes	—
116	C₄	—	4	1	no	—
117	C₄	—	236	4	no	—
118	C₄	#14273704	1	2	yes	—
119	C₄	#14273708	1	1	yes	characteristic
120	C₄	#14273723	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	8	1	no	—
124	C₂	#16837338	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16837451

C₂

yes

maximal, characteristic, complemented

#16837428

C₂

yes

maximal, complemented

#16837419

C₂

yes

maximal

#16837159

C₂

yes

maximal, characteristic, complemented

C₅₉×#408

C₂

yes

maximal, characteristic

C₂×#11745664

C₂²

yes

—

#14273686

C₂²

yes

—

#14273663

—

Dic₅₉⋊C₈

—

#14273654

—

C₂×#41×C₅₉

C₂²

yes

characteristic

C₂×M₁₆×C₅₉

C₂²

yes

characteristic

C₂²×C₈×C₅₉

C₂²

yes

characteristic

C₂²⋊C₈×C₅₉

—

#41×C₅₉

—

#41×C₅₉

—

C₂×Q₈×C₅₉

Q₈

yes

characteristic

C₂×D₄×C₅₉

—

C₂×D₄×C₅₉

Q₈

yes

characteristic

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂³

yes

characteristic

M₁₆×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

D₄

yes

—

C₂²⋊Dic₅₉

—

C₄⋊Dic₅₉

—

C₄×Dic₅₉

D₄

yes

—

#11745664

—

#11745664

—

C₂×C₅₉⋊C₈

—

C₂³×C₅₉

—

C₂³×C₅₉

#41

yes

characteristic

Q₈×C₅₉

—

D₄×C₅₉

—

D₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

C₂×D₄

yes

—

C₂×C₄×C₅₉

C₂×D₄

yes

characteristic

C₂×C₄×C₅₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₅₉

#41

yes

—

C₂×Dic₅₉

—

C₈×C₅₉

—

C₈×C₅₉

—

C₅₉⋊C₈

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

—

C₂²×C₅₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₅₉

#123

yes

—

C₄×C₅₉

—

C₄×C₅₉

C₂²⋊Q₈

yes

—

C₄×C₅₉

yes

C₄×C₅₉

yes

Dic₅₉

—

#2098

—

maximal, Sylow

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

—

C₂×C₅₉

yes

—

—

—

D₅₉

yes

characteristic

H(3,ℤ/4)

—

C₅₉

#2098

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₅₉

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₂×D₅₉

yes

characteristic

C₂²×C₈

C₂×D₅₉

yes

characteristic

#117

—

#108

—

118

—

C₄⋊C₈

—

118

—

#104

—

118

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

Dic₁₁₈

yes

characteristic

C₂×D₄

—

C₂×D₄

Dic₁₁₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₂²×D₅₉

yes

characteristic

M₁₆

—

M₁₆

—

118

—

M₁₆

—

118

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

118

—

C₂×C₈

C₂²⋊D₅₉

yes

—

C₄⋊C₄

—

118

—

C₂²⋊C₄

—

118

—

C₄²

—

C₂³

—

C₂³

#11745685

yes

characteristic

Q₈

—

D₄

—

D₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

118

—

104

C₂×C₄

C₂×Dic₁₁₈

yes

characteristic

105

C₂×C₄

D₄×D₅₉

yes

—

106

C₂×C₄

#11745687

yes

—

107

C₂×C₄

C₂×C₂²⋊D₅₉

yes

characteristic

108

C₈

—

109

C₈

—

110

C₈

—

236

—

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

#14273706

yes

characteristic

115

C₂²

#14273709

yes

—

116

C₄

—

117

C₄

—

236

—

118

C₄

#14273704

yes

—

119

C₄

#14273708

yes

characteristic

120

C₄

#14273723

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

124

C₂

#16837338

yes

characteristic

	subgroup	G/H
center	C₄	#14273723
commutator	C₂²×C₄×C₅₉	C₂³
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#408	C₂
socle	C₂×C₅₉	#399
hypercenter	#408	D₅₉
hypocenter	C₅₉	#2098
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #408

subgroup

G/H

center

C₄

#14273723

commutator

C₂²×C₄×C₅₉

C₂³

Frattini

C₂²×C₄

C₂²×D₅₉

Fitting

C₅₉×#408

C₂

C₂×C₅₉

D₅₉

C₅₉

G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #408

N	H ≅ G/N	type
1. #16837451	C₂	semidirect
2. #16837428	C₂	semidirect
4. #16837159	C₂	semidirect
68. C₅₉	#2098	semidirect

H ≅ G/N

type

1. #16837451

C₂

semidirect

2. #16837428

C₂

semidirect

4. #16837159

C₂

semidirect

68. C₅₉

#2098

semidirect

Subgroups — #21425649

Conjugacy classes of subgroups

Complements