Finite Group Databasebeta

← #28401626

Subgroups — #28401626

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#20299203C211yesmaximal, characteristic, complemented
2#20299167C211yesmaximal, characteristic, complemented
3#20298987C211yesmaximal, characteristic, complemented
4#20298975C211yesmaximal, characteristic, complemented
5#20298963C211yesmaximal, characteristic, complemented
6#20298953C211yesmaximal, characteristic, complemented
7#20298814C212yesmaximal, complemented
8#20298794C212yesmaximal, complemented
9#20298745C212yesmaximal, complemented
10#20298734C212yesmaximal, complemented
11#433×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×D452C2211yescharacteristic
14C2×#14268636C2212yescomplemented
15C2×D904C2212yes—
16C2×D904C2212yes—
17C2×D904C2212yescomplemented
18#16813619C2211yescharacteristic
19#16813619C2211yescharacteristic
20#16813619C2211yescharacteristic, complemented
21#16813614C2211yescharacteristic, complemented
22#16813610C2211yescharacteristic
23#16813610C2211yescharacteristic
24#16813607—22no—
25#16813597—22no—
26#16813596C2212yes—
27#16813595—22no—
28#16813592—22no—
29C4×D452C2212yescomplemented
30#16813547C2212yescomplemented
31#16813544C2212yes—
32#16813544C2212yes—
33#16813544C2212yescomplemented
34#117×C113C2211yescharacteristic
35C4⋊C8×C113C2212yescomplemented
36C22⋊C8×C113C2212yes—
37#97×C113C2211yescharacteristic, complemented
38C4×C8×C113C2211yescharacteristic, complemented
39C23×D113—21no—
40#14268647—42no—
41C2×Dic226C2311yescharacteristic
42C2×D452—21no—
43C2×D452—22no—
44C2×D452—22no—
45C2×D452—22no—
46C2×D452—42no—
47C2×D452C2312yes—
48C2×D452C2311yescharacteristic
49C2×D452C2311yescharacteristic
50C2×D452C2311yescharacteristic
51C2×C22⋊D113—21no—
52C2×C22⋊D113—22no—
53C2×C4×D113—21no—
54C2×C4×D113—22no—
55#14268636—42no—
56D904—42no—
57D904—42no—
58D904—42no—
59C4⋊Dic113C2312yes—
60#14268626—22no—
61#14268624—22no—
62#14268624—22no—
63#14268624—22no—
64#14268624—22no—
65C22×C4×C113C2311yescharacteristic
66C2×C8×C113C2312yes—
67C2×C8×C113C2312yes—
68C4⋊C4×C113D412yes—
69C22⋊C4×C113D412yes—
70C42×C113C2311yescharacteristic
71C42×C113C2311yescharacteristic
72C23×C113C2×D411yescharacteristic
73C22×D113—22no—
74C22×D113—21no—
75C22×D113—21no—
76C22×D113—21no—
77C22×D113—42no—
78C22×D113—82no—
79C2×C4×C113—22no—
80C2×C4×C113C2×D412yes—
81C2×C4×C113C2×D412yes—
82C2×C4×C113C2×D411yescharacteristic
83C2×C4×C113C2411yescharacteristic
84C22⋊D113—42no—
85C22⋊D113—82no—
86C2×Dic113—21no—
87C2×Dic113—22no—
88D452—22no—
89D452—22no—
90D452—22no—
91D452—22no—
92D452—22no—
93D452—42no—
94D452—82no—
95D452—82no—
96D452—82no—
97C4×D113—42no—
98C4×D113—82no—
99Dic226—22no—
100C8×C113—22no—
101C8×C113—22no—
102C22×C113—21no—
103C22×C113—22no—
104C22×C113C22×D411yescharacteristic
105C2×D113—41no—
106C2×D113—41no—
107C2×D113—41no—
108C2×D113—42no—
109C2×D113—42no—
110C2×D113—42no—
111C2×D113—42no—
112C2×D113—42no—
113C2×D113—42no—
114C2×D113—84no—
115C4×C113—21no—
116C4×C113—22no—
117C4×C113—22no—
118C4×C113H(5,𝔽2)12yes—
119Dic113—41no—
120Dic113—42no—
121C2×C113—41no—
122C2×C113#53511yescharacteristic
123C2×C113#57612yes—
124D113—81no—
125D113—82no—
126D113—81no—
127D113—81no—
128#3220—1131nomaximal, Sylow
129C113#322011yescharacteristic, complemented, Sylow
130#540—1131no—
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#433D11311yescharacteristic, complemented
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#127—1131no—
150#125—1131no—
151#124—1131no—
152#124—1131no—
153#123—2262no—
154#121—1132no—
155#121—2262no—
156#121—2262no—
157#120—2262no—
158C4×D4—1132no—
159#117C2×D11311yescharacteristic
160C4⋊C8C2×D11312yescomplemented
161#103—1132no—
162#102—1132no—
163#102—1132no—
164#102—1132no—
165C22⋊C8C2×D11312yes—
166#97C2×D11311yescharacteristic, complemented
167C4×C8C2×D11311yescharacteristic, complemented
168C24—2261no—
169#41—4522no—
170C2×Q8—1131no—
171C2×D4—1131no—
172C2×D4—1131no—
173C2×D4—1131no—
174C2×D4—1132no—
175C2×D4—4522no—
176C2×D4—2262no—
177C2×D4—2261no—
178C2×D4—2262no—
179C2×D4—2262no—
180C2×D4—2262no—
181C2×D4—2261no—
182C22×C4—2262no—
183C22×C4—2261no—
184C22×C4C22×D11311yescharacteristic
185SD16—4522no—
186D8—4522no—
187D8—4522no—
188D8—4522no—
189C2×C8C22×D11312yes—
190C2×C8C22×D11312yes—
191C4⋊C4—1132no—
192C4⋊C4—2262no—
193C4⋊C4D45212yes—
194C22⋊C4—2262no—
195C22⋊C4—2262no—
196C22⋊C4—2262no—
197C22⋊C4—2262no—
198C22⋊C4D45212yes—
199C42C22×D11311yescharacteristic
200C42C22×D11311yescharacteristic
201C23—9042no—
202C23—4522no—
203C23—2262no—
204C23—2261no—
205C23—2261no—
206C23—2261no—
207C23C2×D45211yescharacteristic
208Q8—2262no—
209D4—9042no—
210D4—9042no—
211D4—9042no—
212D4—9042no—
213D4—4522no—
214D4—4522no—
215D4—2262no—
216D4—2262no—
217D4—2262no—
218D4—2262no—
219D4—2262no—
220C2×C4—22no—
221C2×C4—9042no—
222C2×C4—4522no—
223C2×C4—2261no—
224C2×C4—2262no—
225C2×C4C2×D45212yes—
226C2×C4C2×D45212yes—
227C2×C4C2×D45211yescharacteristic
228C2×C4C23×D11311yescharacteristic
229C8—22no—
230C8—22no—
231C22—22no—
232C22—21no—
233C22—9044no—
234C22—4522no—
235C22—4522no—
236C22—4522no—
237C22—4522no—
238C22—4522no—
239C22—4521no—
240C22—4521no—
241C22—4521no—
242C22—4522no—
243C22C22×D45211yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—4522no—
248C4—4521no—
249C4#1681366812yes—
250C2—41no—
251C2—9041no—
252C2—9041no—
253C2—9042no—
254C2—9041no—
255C2#2029916711yescharacteristic
256C2#2029940312yes—
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#433×C113C2
socleC22×C113C22×D4
hypercenter#433D113
hypocenterC113#3220
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20299203C2semidirect
2. #20299167C2semidirect
3. #20298987C2semidirect
4. #20298975C2semidirect
5. #20298963C2semidirect
6. #20298953C2semidirect
7. #20298814C2semidirect
8. #20298794C2semidirect
9. #20298745C2semidirect
10. #20298734C2semidirect
11. #433×C113C2semidirect
14. C2×#14268636C22semidirect
17. C2×D904C22semidirect
20. #16813619C22semidirect
21. #16813614C22semidirect
29. C4×D452C22semidirect
30. #16813547C22semidirect
33. #16813544C22semidirect
35. C4⋊C8×C113C22semidirect
37. #97×C113C22semidirect
38. C4×C8×C113C22semidirect
129. C113#3220semidirect
140. #433D113semidirect
160. C4⋊C8C2×D113semidirect
166. #97C2×D113semidirect
167. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202991672
#202989872
#202989752
#202989632
#202989532
#202988142
#202987942
#202987452
#202987342
#433×C1132
#3220113