Finite Group Databasebeta

← #28406010

Subgroups — #28406010

Order 14464.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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#20299566C211yesmaximal, characteristic, complemented
2#20299540C211yesmaximal, characteristic, complemented
3#20299449C214yesmaximal, complemented
4C2×#16813593C211yesmaximal, characteristic
5C2×#14268655—21no—
6C2×C4⋊#90673—21no—
7C2×C22⋊#90673—21no—
8#16813679C2212yescomplemented
9C22⋊#11744753—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#14268655—42no—
22C2×#11744753—22no—
23C4⋊#90673—42no—
24C22⋊#90673—42no—
25C23×D113D411yescharacteristic
26C2×C22⋊D113—22no—
27C2×C22⋊D113—22no—
28C2×C22⋊D113—42no—
29C2×C22⋊D113—42no—
30C22×Dic113—21no—
31C22×Dic113D411yescharacteristic
32C2×C4×D113—42no—
33C2×C4×D113C2×C411yescharacteristic
34C2×C4×D113D411yescharacteristic
35C2×C4×D113D411yescharacteristic
36C2×C4×D113C2311yescharacteristic
37C4⋊Dic113—21no—
38C4⋊Dic113C2×C412yes—
39C22⋊Dic113—22no—
40C22⋊Dic113—22no—
41C24×C113—21no—
42C2×D4×C113—21no—
43C2×D4×C113—42no—
44C2×D4×C113C2×C412yes—
45C22×C4×C113C2×C411yescharacteristic
46C23×C113—22no—
47C23×C113—42no—
48C23×C113—42no—
49C23×C113—42no—
50C23×C113C22⋊C411yescharacteristic
51C22×D113—41no—
52C22×D113—41no—
53C22×D113C22⋊C411yescharacteristic
54C22×D113D812yes—
55C22×D113SD1612yes—
56C22×D113C2×D411yescharacteristic
57C2×#90673—42no—
58C2×#90673—42no—
59C2×#90673—42no—
60D4×C113—42no—
61D4×C113—42no—
62C2×C4×C113—22no—
63C2×C4×C113C22⋊C411yescharacteristic
64C2×C4×C113C22×C411yescharacteristic
65C22⋊D113—44no—
66C22⋊D113—42no—
67C22⋊D113—42no—
68C2×Dic113—22no—
69C2×Dic113—41no—
70C2×Dic113—42no—
71C2×Dic113C22⋊C411yescharacteristic
72C2×Dic113C2×D411yescharacteristic
73C4×D113—22no—
74C4×D113—22no—
75C4×D113—41no—
76C4×D113—41no—
77#11744753—42no—
78C22×C113—21no—
79C22×C113—21no—
80C22×C113—42no—
81C22×C113—42no—
82C22×C113—42no—
83C22×C113—84no—
84C22×C113#10212yes—
85C22×C113C2×C22⋊C411yescharacteristic
86C2×D113—21no—
87C2×D113—21no—
88C2×D113—21no—
89C2×D113—21no—
90C2×D113—42no—
91C2×D113—42no—
92C2×D113#10212yes—
93C2×D113C2×D811yescharacteristic
94C2×D113C2×SD1611yescharacteristic
95#90673—82no—
96C4×C113—21no—
97C4×C113#9912yes—
98Dic113—21no—
99Dic113—21no—
100Dic113—42no—
101C2×C113—22no—
102C2×C113—82no—
103C2×C113C2×#9911yescharacteristic
104C2×C113C2×#10211yescharacteristic
105C2×C113#42111yescharacteristic
106D113—21no—
107D113—22no—
108D113—21no—
109#1519—1131nomaximal, Sylow
110C113#151911yescharacteristic, complemented, Sylow
111C2×#121—1131no—
112C2×C22⋊C8—1131no—
113#380—1131no—
114#327—1134no—
115C22×D4—2261no—
116C22×D4#9067311yescharacteristic, complemented
117C23×C4—1131no—
118C22×C8—2261no—
119#121—1132no—
120#121—1132no—
121#121—2261no—
122#121—2261no—
123C2×C4⋊C4—1131no—
124C2×C4⋊C4—2261no—
125C2×C22⋊C4—2261no—
126C2×C22⋊C4—2261no—
127C22⋊C8—1132no—
128C22⋊C8—2261no—
129#95—1132no—
130C24—21no—
131C24—1131no—
132C2×D4—21no—
133C2×D4—42no—
134C2×D4—4522no—
135C2×D4—4522no—
136C2×D4—2262no—
137C2×D4—2262no—
138C2×D4C2×#9067312yes—
139C22×C4—1131no—
140C22×C4—1131no—
141C22×C4—1131no—
142C22×C4—1131no—
143C22×C4—1131no—
144C22×C4—4522no—
145C22×C4—2262no—
146C22×C4—2261no—
147C22×C4C2×#9067311yescharacteristic
148C2×C8—4522no—
149C2×C8—2262no—
150C4⋊C4—1132no—
151C4⋊C4—4522no—
152C4⋊C4—2261no—
153C22⋊C4—4522no—
154C22⋊C4—2262no—
155C22⋊C4—2262no—
156C23—22no—
157C23—42no—
158C23—42no—
159C23—42no—
160C23—1132no—
161C23—1132no—
162C23—1131no—
163C23—1131no—
164C23—4521no—
165C23—4521no—
166C23C22⋊#9067311yescharacteristic
167D4—42no—
168D4—42no—
169D4—4522no—
170D4—4524no—
171D4—4522no—
172C2×C4—22no—
173C2×C4—1131no—
174C2×C4—1131no—
175C2×C4—4521no—
176C2×C4—4521no—
177C2×C4—4522no—
178C2×C4—4522no—
179C2×C4—4522no—
180C2×C4—4522no—
181C2×C4—4521no—
182C2×C4—2262no—
183C2×C4—2262no—
184C2×C4—2262no—
185C2×C4C22⋊#9067311yescharacteristic
186C2×C4C22×#9067311yescharacteristic
187C8—4522no—
188C22—21no—
189C22—21no—
190C22—42no—
191C22—42no—
192C22—42no—
193C22—84no—
194C22—1131no—
195C22—1132no—
196C22—1131no—
197C22—4522no—
198C22—4522no—
199C22—2261no—
200C22—2261no—
201C22—2261no—
202C22—2261no—
203C22#1681368412yes—
204C22C2×C22⋊#9067311yescharacteristic
205C4—21no—
206C4—9042no—
207C4—4522no—
208C4—2261no—
209C4—2261no—
210C4#1681368012yes—
211C2—22no—
212C2—82no—
213C2—2261no—
214C2—2262no—
215C2—2261no—
216C2C2×#1681368011yescharacteristic
217C2C2×#1681368411yescharacteristic
218C2#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#1519
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. #20299566C2semidirect
2. #20299540C2semidirect
3. #20299449C2semidirect
8. #16813679C22semidirect
10. (C2×#90673)⋊C4C22semidirect
15. #16813593C4semidirect
17. C2×C4⋊Dic113C4semidirect
19. C22×D4×C113C4semidirect
110. C113#1519semidirect
116. C22×D4#90673semidirect

Maximal subgroups

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

subgroupindex
#202995662
#202995402
#202994492
C2×#168135932
#1519113