Finite Group Databasebeta

← #28405979

Subgroups — #28405979

Order 14464.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299570C211yesmaximal, characteristic, complemented
2#20299541C211yesmaximal, characteristic, complemented
3#20299449C214yesmaximal, complemented
4C2×#16813593C211yesmaximal, characteristic
5C2×#14268656—21no—
6C2×C22⋊#90673—21no—
7#16813679—21no—
8#16813679C2212yescomplemented
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4C2212yescomplemented
11C22×C22⋊D113—21no—
12C22×C4×D113C2211yescharacteristic
13#16813593—21no—
14#16813593—21no—
15#16813593C412yescomplemented
16#16813593C2212yes—
17C2×C4⋊Dic113C411yescharacteristic, complemented
18C2×C22⋊Dic113—21no—
19C22×D4×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21#14268656—42no—
22C2×#11744753—22no—
23C22⋊#90673—42no—
24C23×D113D411yescharacteristic
25C2×C22⋊D113—22no—
26C2×C22⋊D113—22no—
27C2×C22⋊D113—44no—
28C22×Dic113—21no—
29C22×Dic113D411yescharacteristic
30C2×C4×D113—42no—
31C2×C4×D113C2×C411yescharacteristic
32C2×C4×D113D411yescharacteristic
33C2×C4×D113D411yescharacteristic
34C2×C4×D113C2311yescharacteristic
35C4⋊Dic113—21no—
36C4⋊Dic113C2×C412yes—
37C22⋊Dic113—22no—
38C22⋊Dic113—22no—
39C24×C113—21no—
40C2×D4×C113—21no—
41C2×D4×C113—42no—
42C2×D4×C113C2×C412yes—
43C22×C4×C113C2×C411yescharacteristic
44C23×C113—22no—
45C23×C113—42no—
46C23×C113—42no—
47C23×C113—42no—
48C23×C113C22⋊C411yescharacteristic
49C22×D113—22no—
50C22×D113—22no—
51C22×D113—41no—
52C22×D113C22⋊C411yescharacteristic
53C22×D113C2×D411yescharacteristic
54C2×#90673—42no—
55C2×#90673—42no—
56C2×#90673—42no—
57D4×C113—42no—
58D4×C113—42no—
59C2×C4×C113—22no—
60C2×C4×C113C22⋊C411yescharacteristic
61C2×C4×C113C22×C411yescharacteristic
62C22⋊D113—44no—
63C22⋊D113—44no—
64C2×Dic113—22no—
65C2×Dic113—22no—
66C2×Dic113—42no—
67C2×Dic113C22⋊C411yescharacteristic
68C2×Dic113C2×D411yescharacteristic
69C4×D113—41no—
70C4×D113—41no—
71C4×D113—41no—
72C4×D113—41no—
73#11744753—42no—
74C22×C113—21no—
75C22×C113—21no—
76C22×C113—42no—
77C22×C113—42no—
78C22×C113—42no—
79C22×C113—84no—
80C22×C113#9912yes—
81C22×C113C2×C22⋊C411yescharacteristic
82C2×D113—21no—
83C2×D113—21no—
84C2×D113—21no—
85C2×D113—21no—
86C2×D113—21no—
87C2×D113—44no—
88C2×D113AGL(1,ℤ/8)12yes—
89#90673—82no—
90C4×C113—21no—
91C4×C113—21no—
92Dic113—21no—
93Dic113—21no—
94Dic113—42no—
95C2×C113—22no—
96C2×C113—82no—
97C2×C113C2×#9911yescharacteristic
98C2×C113#41811yescharacteristic
99C2×C113#42111yescharacteristic
100D113—22no—
101D113—41no—
102#1510—1131nomaximal, Sylow
103C113#151011yescharacteristic, complemented, Sylow
104C2×#121—1131no—
105#407—1131no—
106#381—1131no—
107#327—1134no—
108C22×D4—2261no—
109C22×D4#9067311yescharacteristic, complemented
110C23×C4—1131no—
111C2×M16—2261no—
112#121—1132no—
113#121—1132no—
114#121—2261no—
115#121—2261no—
116C2×C4⋊C4—1131no—
117C2×C22⋊C4—2261no—
118C2×C22⋊C4—2261no—
119C22⋊C8—1132no—
120C22⋊C8—2261no—
121#95—1132no—
122#95—2261no—
123C24—21no—
124C24—1131no—
125C2×D4—21no—
126C2×D4—42no—
127C2×D4—4524no—
128C2×D4—2262no—
129C2×D4—2262no—
130C2×D4C2×#9067312yes—
131C22×C4—1131no—
132C22×C4—1131no—
133C22×C4—1131no—
134C22×C4—1131no—
135C22×C4—1131no—
136C22×C4—4522no—
137C22×C4—2262no—
138C22×C4—2261no—
139C22×C4C2×#9067311yescharacteristic
140M16—4522no—
141C2×C8—2262no—
142C4⋊C4—1132no—
143C4⋊C4—2261no—
144C22⋊C4—4522no—
145C22⋊C4—2262no—
146C22⋊C4—2262no—
147C23—22no—
148C23—42no—
149C23—42no—
150C23—42no—
151C23—1131no—
152C23—1131no—
153C23—4521no—
154C23—2262no—
155C23—2262no—
156C23C22⋊#9067311yescharacteristic
157D4—42no—
158D4—42no—
159D4—4524no—
160D4—4524no—
161C2×C4—22no—
162C2×C4—1131no—
163C2×C4—1131no—
164C2×C4—4521no—
165C2×C4—4521no—
166C2×C4—4521no—
167C2×C4—4521no—
168C2×C4—4522no—
169C2×C4—4522no—
170C2×C4—4522no—
171C2×C4—4522no—
172C2×C4—2262no—
173C2×C4—2262no—
174C2×C4C22⋊#9067311yescharacteristic
175C2×C4C22×#9067311yescharacteristic
176C8—4522no—
177C22—21no—
178C22—21no—
179C22—42no—
180C22—42no—
181C22—42no—
182C22—84no—
183C22—1132no—
184C22—4524no—
185C22—2261no—
186C22—2261no—
187C22—2261no—
188C22—2261no—
189C22—2261no—
190C22#1681368012yes—
191C22C2×C22⋊#9067311yescharacteristic
192C4—21no—
193C4—21no—
194C4—9042no—
195C4—4522no—
196C4—2261no—
197C4—2261no—
198C2—22no—
199C2—82no—
200C2—4521no—
201C2—2262no—
202C2C2×#1681368011yescharacteristic
203C2#2029959011yescharacteristic
204C2#2029959611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22×D4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC2×#16813593C2
cosocleC2×C4×D113C23
hypercenterC22×D4#90673
hypocenterC113#1510
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20299570C2semidirect
2. #20299541C2semidirect
3. #20299449C2semidirect
8. #16813679C22semidirect
10. (C2×#90673)⋊C4C22semidirect
15. #16813593C4semidirect
17. C2×C4⋊Dic113C4semidirect
19. C22×D4×C113C4semidirect
103. C113#1510semidirect
109. C22×D4#90673semidirect

Maximal subgroups

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

subgroupindex
#202995702
#202995412
#202994492
C2×#168135932
#1510113