Finite Group Databasebeta

← #28401618

Subgroups — #28401618

Order 14464.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299167C211yesmaximal, characteristic, complemented
2#20298985C211yesmaximal, characteristic, complemented
3#20298974C211yesmaximal, characteristic, complemented
4#20298964C211yesmaximal, characteristic, complemented
5#20298955C211yesmaximal, characteristic, complemented
6#20298813C212yesmaximal, complemented
7#20298793C212yesmaximal, complemented
8#20298741C212yesmaximal, complemented
9#20298731C212yesmaximal, complemented
10#20298659C211yesmaximal, characteristic, complemented
11#540×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×D452C2211yescharacteristic
14C2×#14268635C2212yescomplemented
15C2×#14268632C2212yes—
16C2×#14268632C2212yes—
17C2×#14268632C2212yescomplemented
18#16813619C2211yescharacteristic
19#16813619C2211yescharacteristic
20#16813610C2211yescharacteristic
21#16813610C2211yescharacteristic
22#16813597—22no—
23#16813592—22no—
24C4⋊#11744751C2212yescomplemented
25#16813545C2212yescomplemented
26#16813542C2212yes—
27#16813542C2212yes—
28#16813542C2212yescomplemented
29C22⋊#11744751C2212yes—
30#16813533C2211yescharacteristic, complemented
31C4×#11744751C2211yescharacteristic, complemented
32#127×C113C2211yescharacteristic, complemented
33#125×C113C2211yescharacteristic, complemented
34#123×C113—22no—
35#121×C113—22no—
36#121×C113C2212yes—
37C4×D4×C113C2212yescomplemented
38#117×C113C2211yescharacteristic
39C23×D113—21no—
40#14268647—42no—
41C2×Dic226C2311yescharacteristic
42C2×D452—21no—
43C2×D452—22no—
44C2×D452—22no—
45C2×D452—42no—
46C2×D452C2311yescharacteristic
47C2×D452C2311yescharacteristic
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—21no—
50C2×C4×D113—21no—
51#14268635—42no—
52#14268632—42no—
53#14268632—42no—
54#14268632—42no—
55C2×#11744751C2312yes—
56C2×#11744751C2312yes—
57#14268624—22no—
58#14268624—22no—
59C2×D4×C113—22no—
60C2×D4×C113—22no—
61C2×D4×C113C2312yes—
62C22×C4×C113—22no—
63C22×C4×C113C2311yescharacteristic
64C4⋊C4×C113—22no—
65C4⋊C4×C113D412yes—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C22⋊C4×C113—22no—
69C22⋊C4×C113D412yes—
70C42×C113C2311yescharacteristic
71C42×C113C2311yescharacteristic
72C23×C113—22no—
73C23×C113C2×D411yescharacteristic
74C22×D113—21no—
75C22×D113—21no—
76C22×D113—21no—
77C22×D113—42no—
78C22×D113—82no—
79D4×C113—22no—
80D4×C113—22no—
81D4×C113—82no—
82D4×C113—82no—
83C2×C4×C113—22no—
84C2×C4×C113—22no—
85C2×C4×C113—82no—
86C2×C4×C113C2×D412yes—
87C2×C4×C113C2×D412yes—
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2411yescharacteristic
90C22⋊D113—42no—
91C2×Dic113—21no—
92D452—22no—
93D452—22no—
94D452—22no—
95D452—42no—
96D452—82no—
97D452—82no—
98C4×D113—42no—
99Dic226—22no—
100#11744751—22no—
101#11744751—22no—
102C22×C113—21no—
103C22×C113—22no—
104C22×C113—42no—
105C22×C113—42no—
106C22×C113—42no—
107C22×C113C22×D411yescharacteristic
108C2×D113—41no—
109C2×D113—41no—
110C2×D113—41no—
111C2×D113—42no—
112C2×D113—42no—
113C2×D113—42no—
114C2×D113—84no—
115C4×C113—21no—
116C4×C113—22no—
117C4×C113—22no—
118C4×C113—42no—
119C4×C113H(5,𝔽2)12yes—
120Dic113—41no—
121C2×C113—41no—
122C2×C113—82no—
123C2×C113#53511yescharacteristic
124C2×C113#57612yes—
125D113—81no—
126D113—81no—
127D113—81no—
128#3220—1131nomaximal, Sylow
129C113#322011yescharacteristic, complemented, Sylow
130#540D11311yescharacteristic, complemented
131#535—1131no—
132#496—1131no—
133#493—1131no—
134#490—1131no—
135#488—1131no—
136#463—1132no—
137#459—1132no—
138#449—1132no—
139#447—1132no—
140#433—1131no—
141C2×#41—1131no—
142C22×D4—1131no—
143C2×SD16—1132no—
144C2×D8—1132no—
145C2×D8—1132no—
146C2×D8—1132no—
147#127—1131no—
148#127—1131no—
149#127C2×D11311yescharacteristic, complemented
150#125C2×D11311yescharacteristic, complemented
151#124—1131no—
152#124—1131no—
153#123—22no—
154#121—22no—
155#121—2262no—
156#121C2×D11312yes—
157#120—2262no—
158C4×D4C2×D11312yescomplemented
159#117C2×D11311yescharacteristic
160C4⋊C8—1132no—
161#103—1132no—
162#102—1132no—
163#102—1132no—
164#102—1132no—
165C22⋊C8—1132no—
166#97—1131no—
167C4×C8—1131no—
168C24—2261no—
169#41—4522no—
170C2×Q8—1131no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—1131no—
174C2×D4—1131no—
175C2×D4—1131no—
176C2×D4—4522no—
177C2×D4—2261no—
178C2×D4—2262no—
179C2×D4—2262no—
180C2×D4—2261no—
181C2×D4C22×D11312yes—
182C22×C4—22no—
183C22×C4—2261no—
184C22×C4C22×D11311yescharacteristic
185SD16—4522no—
186D8—4522no—
187D8—4522no—
188D8—4522no—
189C2×C8—1132no—
190C2×C8—1132no—
191C4⋊C4—22no—
192C4⋊C4C22⋊D11312yes—
193C4⋊C4C22×D11312yes—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—2262no—
197C22⋊C4—2262no—
198C22⋊C4C22⋊D11312yes—
199C42C22×D11311yescharacteristic
200C42C22×D11311yescharacteristic
201C23—22no—
202C23—9042no—
203C23—4522no—
204C23—2261no—
205C23—2261no—
206C23—2261no—
207C23C2×C22⋊D11311yescharacteristic
208Q8—2262no—
209D4—22no—
210D4—22no—
211D4—82no—
212D4—82no—
213D4—9042no—
214D4—9042no—
215D4—4522no—
216D4—4522no—
217D4—2262no—
218D4—2262no—
219D4—2262no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—82no—
223C2×C4—4522no—
224C2×C4—2261no—
225C2×C4C2×C22⋊D11312yes—
226C2×C4C2×C22⋊D11312yes—
227C2×C4C2×C22⋊D11311yescharacteristic
228C2×C4C23×D11311yescharacteristic
229C8—2262no—
230C8—2262no—
231C22—22no—
232C22—21no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—9044no—
237C22—4522no—
238C22—4522no—
239C22—4522no—
240C22—4521no—
241C22—4521no—
242C22—4521no—
243C22C22×C22⋊D11311yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—42no—
248C4—4521no—
249C4#1681366812yes—
250C2—41no—
251C2—82no—
252C2—9041no—
253C2—9041no—
254C2—9041no—
255C2#2029916211yescharacteristic
256C2#2029940112yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#540×C113C2
socleC22×C113C22×D4
hypercenter#540D113
hypocenterC113#3220
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #20299167C2semidirect
2. #20298985C2semidirect
3. #20298974C2semidirect
4. #20298964C2semidirect
5. #20298955C2semidirect
6. #20298813C2semidirect
7. #20298793C2semidirect
8. #20298741C2semidirect
9. #20298731C2semidirect
10. #20298659C2semidirect
11. #540×C113C2semidirect
14. C2×#14268635C22semidirect
17. C2×#14268632C22semidirect
24. C4⋊#11744751C22semidirect
25. #16813545C22semidirect
28. #16813542C22semidirect
30. #16813533C22semidirect
31. C4×#11744751C22semidirect
32. #127×C113C22semidirect
33. #125×C113C22semidirect
37. C4×D4×C113C22semidirect
129. C113#3220semidirect
130. #540D113semidirect
149. #127C2×D113semidirect
150. #125C2×D113semidirect
158. C4×D4C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991672
#202989852
#202989742
#202989642
#202989552
#202988132
#202987932
#202987412
#202987312
#202986592
#540×C1132
#3220113