Finite Group Databasebeta

← #28401624

Subgroups — #28401624

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#20298988C211yesmaximal, characteristic, complemented
3#20298974C211yesmaximal, characteristic, complemented
4#20298962C211yesmaximal, characteristic, complemented
5#20298952C211yesmaximal, characteristic, complemented
6#20298810C212yesmaximal, complemented
7#20298790C212yesmaximal, complemented
8#20298743C212yesmaximal, complemented
9#20298732C212yesmaximal, complemented
10#20298659C211yesmaximal, characteristic, complemented
11#535×C113C211yesmaximal, characteristic, complemented
12C2×#14268634C2212yescomplemented
13C2×#14268632C2212yes—
14C2×#14268632C2212yes—
15C2×#14268632C2212yescomplemented
16#16813619C2211yescharacteristic, complemented
17#16813614C2211yescharacteristic, complemented
18#16813607—22no—
19#16813596C2212yes—
20#16813595—22no—
21C4×D452C2212yescomplemented
22C4⋊#11744751C2212yescomplemented
23#16813546C2212yescomplemented
24#16813543C2212yes—
25#16813543C2212yes—
26#16813543C2212yescomplemented
27C22⋊#11744751C2212yes—
28#16813533C2211yescharacteristic, complemented
29C4×#11744751C2211yescharacteristic, complemented
30C2×#41×C113C2211yescharacteristic
31C22×D4×C113C2211yescharacteristic
32#127×C113C2211yescharacteristic
33#127×C113C2211yescharacteristic
34#124×C113C2211yescharacteristic
35#124×C113C2211yescharacteristic
36#121×C113—22no—
37#120×C113—22no—
38#117×C113C2211yescharacteristic
39C2×D452—22no—
40C2×D452C2312yes—
41C2×C22⋊D113—22no—
42C2×C4×D113—22no—
43#14268634—42no—
44#14268632—42no—
45#14268632—42no—
46#14268632—42no—
47C2×#11744751C2312yes—
48C2×#11744751C2312yes—
49C4⋊Dic113C2312yes—
50#14268626—22no—
51#14268624—22no—
52#14268624—22no—
53C24×C113—21no—
54#41×C113—42no—
55C2×Q8×C113C2311yescharacteristic
56C2×D4×C113—21no—
57C2×D4×C113—21no—
58C2×D4×C113—22no—
59C2×D4×C113—22no—
60C2×D4×C113—42no—
61C2×D4×C113C2311yescharacteristic
62C2×D4×C113C2311yescharacteristic
63C2×D4×C113C2311yescharacteristic
64C22×C4×C113—21no—
65C22×C4×C113C2311yescharacteristic
66C4⋊C4×C113D412yes—
67C22⋊C4×C113—22no—
68C22⋊C4×C113—22no—
69C22⋊C4×C113D412yes—
70C42×C113C2311yescharacteristic
71C42×C113C2311yescharacteristic
72C23×C113—21no—
73C23×C113—21no—
74C23×C113—21no—
75C23×C113—42no—
76C23×C113—82no—
77C23×C113C2×D411yescharacteristic
78C22×D113—22no—
79Q8×C113—22no—
80D4×C113—22no—
81D4×C113—22no—
82D4×C113—22no—
83D4×C113—42no—
84D4×C113—42no—
85D4×C113—82no—
86D4×C113—82no—
87C2×C4×C113—22no—
88C2×C4×C113—21no—
89C2×C4×C113—42no—
90C2×C4×C113C2×D412yes—
91C2×C4×C113C2×D412yes—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2411yescharacteristic
94C22⋊D113—82no—
95C2×Dic113—22no—
96D452—22no—
97D452—22no—
98D452—82no—
99C4×D113—82no—
100#11744751—22no—
101#11744751—22no—
102C22×C113—21no—
103C22×C113—22no—
104C22×C113—41no—
105C22×C113—41no—
106C22×C113—41no—
107C22×C113—42no—
108C22×C113—42no—
109C22×C113—42no—
110C22×C113—84no—
111C22×C113C22×D411yescharacteristic
112C2×D113—42no—
113C2×D113—42no—
114C2×D113—42no—
115C4×C113—21no—
116C4×C113—22no—
117C4×C113—22no—
118C4×C113—41no—
119C4×C113H(5,𝔽2)12yes—
120Dic113—42no—
121C2×C113—41no—
122C2×C113—81no—
123C2×C113—81no—
124C2×C113—81no—
125C2×C113#53511yescharacteristic
126C2×C113#57612yes—
127D113—82no—
128#3220—1131nomaximal, Sylow
129C113#322011yescharacteristic, complemented, Sylow
130#540—1131no—
131#535D11311yescharacteristic, complemented
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×#41C2×D11311yescharacteristic
142C22×D4C2×D11311yescharacteristic
143C2×SD16—1132no—
144C2×D8—1132no—
145C2×D8—1132no—
146C2×D8—1132no—
147#127—1131no—
148#127C2×D11311yescharacteristic
149#127C2×D11311yescharacteristic
150#125—1131no—
151#124C2×D11311yescharacteristic
152#124C2×D11311yescharacteristic
153#123—2262no—
154#121—22no—
155#121—1132no—
156#121—2262no—
157#120—22no—
158C4×D4—1132no—
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—21no—
169#41—42no—
170C2×Q8C22×D11311yescharacteristic
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—22no—
174C2×D4—22no—
175C2×D4—42no—
176C2×D4—1132no—
177C2×D4—2262no—
178C2×D4—2262no—
179C2×D4C22×D11311yescharacteristic
180C2×D4C22×D11311yescharacteristic
181C2×D4C22×D11311yescharacteristic
182C22×C4—21no—
183C22×C4—2262no—
184C22×C4C22×D11311yescharacteristic
185SD16—4522no—
186D8—4522no—
187D8—4522no—
188D8—4522no—
189C2×C8—1132no—
190C2×C8—1132no—
191C4⋊C4—1132no—
192C4⋊C4—2262no—
193C4⋊C4C22⋊D11312yes—
194C22⋊C4—22no—
195C22⋊C4—22no—
196C22⋊C4—2262no—
197C22⋊C4—2262no—
198C22⋊C4C22⋊D11312yes—
199C42C22×D11311yescharacteristic
200C42C22×D11311yescharacteristic
201C23—21no—
202C23—21no—
203C23—21no—
204C23—42no—
205C23—82no—
206C23—2262no—
207C23C2×C22⋊D11311yescharacteristic
208Q8—22no—
209D4—22no—
210D4—22no—
211D4—22no—
212D4—42no—
213D4—42no—
214D4—82no—
215D4—82no—
216D4—9042no—
217D4—9042no—
218D4—2262no—
219D4—2262no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—9042no—
224C2×C4—2262no—
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—41no—
237C22—41no—
238C22—41no—
239C22—84no—
240C22—4522no—
241C22—4522no—
242C22—4522no—
243C22C22×C22⋊D11311yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—4522no—
249C4#1681366712yes—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—81no—
254C2—9042no—
255C2#2029916511yescharacteristic
256C2#2029940112yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC22×C113C22×D4
hypercenter#535D113
hypocenterC113#3220
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20299203C2semidirect
2. #20298988C2semidirect
3. #20298974C2semidirect
4. #20298962C2semidirect
5. #20298952C2semidirect
6. #20298810C2semidirect
7. #20298790C2semidirect
8. #20298743C2semidirect
9. #20298732C2semidirect
10. #20298659C2semidirect
11. #535×C113C2semidirect
12. C2×#14268634C22semidirect
15. C2×#14268632C22semidirect
16. #16813619C22semidirect
17. #16813614C22semidirect
21. C4×D452C22semidirect
22. C4⋊#11744751C22semidirect
23. #16813546C22semidirect
26. #16813543C22semidirect
28. #16813533C22semidirect
29. C4×#11744751C22semidirect
129. C113#3220semidirect
131. #535D113semidirect

Maximal subgroups

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

subgroupindex
#202992032
#202989882
#202989742
#202989622
#202989522
#202988102
#202987902
#202987432
#202987322
#202986592
#535×C1132
#3220113