Finite Group Databasebeta

← #28399945

Subgroups — #28399945

Order 14464.

736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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#20299434C211yesmaximal, characteristic, complemented
2C2×#16813648C212yesmaximal, complemented
3#20298770C214yesmaximal, complemented
4#20298765C214yesmaximal, complemented
5#20298616C212yesmaximal, complemented
6#20298582C211yesmaximal, characteristic, complemented
7#535×C113C211yesmaximal, characteristic, complemented
8#16813670C2212yescomplemented
9#16813669—22no—
10#16813668—22no—
11#16813667—22no—
12#16813667C2212yescomplemented
13C2×#14268647—22no—
14C2×#14268647C2212yes—
15#41×D113—24no—
16#16813648—24no—
17#16813648C2218yescomplemented
18C2×#14268635—22no—
19C2×#14268632—22no—
20C2×#14268631C2212yescomplemented
21#16813550C2218yescomplemented
22#16813541C2212yescomplemented
23#16813539C2212yescomplemented
24C2×#41×C113C2211yescharacteristic
25C22×D4×C113C2211yescharacteristic, complemented
26#127×C113C2212yescomplemented
27#124×C113C2212yescomplemented
28#121×C113—22no—
29#120×C113—22no—
30#117×C113C2211yescharacteristic, complemented
31#14268648—24no—
32#14268647—24no—
33#14268647—24no—
34#14268647—22no—
35#14268647—24no—
36#14268647—22no—
37#14268647D414yescomplemented
38#14268647C2314yes—
39#14268646—28no—
40#14268646—24no—
41C2×Dic226—22no—
42C2×Dic226D412yescomplemented
43Q8×D113—24no—
44C2×D452—22no—
45C2×D452D412yescomplemented
46C2×C22⋊D113—24no—
47C2×C22⋊D113—22no—
48D4×D113—28no—
49D4×D113—24no—
50C2×C4×D113—24no—
51C2×C4×D113—22no—
52#14268635—28no—
53#14268632—28no—
54#14268631—22no—
55#14268631C2314yes—
56C2×#11744751—22no—
57C24×C113—21no—
58#41×C113—22no—
59#41×C113—22no—
60C2×Q8×C113C2311yescharacteristic
61C2×D4×C113—24no—
62C2×D4×C113—22no—
63C2×D4×C113—22no—
64C2×D4×C113—21no—
65C2×D4×C113D412yes—
66C2×D4×C113C2312yes—
67C2×D4×C113C2311yescharacteristic
68C22×C4×C113D412yes—
69C22×C4×C113C2311yescharacteristic
70C4⋊C4×C113—21no—
71C22⋊C4×C113—21no—
72C22⋊C4×C113—24no—
73C42×C113C2312yes—
74C23×C113—22no—
75C23×C113—42no—
76C23×C113—82no—
77C23×C113C2×D412yes—
78C23×C113C2×D411yescharacteristic
79C22×D113—24no—
80C22×D113—22no—
81Q8×C113—22no—
82D4×C113—24no—
83D4×C113—22no—
84D4×C113—24no—
85D4×C113—41no—
86D4×C113—41no—
87D4×C113—84no—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—22no—
91C2×C4×C113C2×D412yes—
92C2×C4×C113C2×D412yes—
93C2×C4×C113C2×D412yes—
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—28no—
97C22⋊D113—24no—
98C22⋊D113—24no—
99C2×Dic113—24no—
100C2×Dic113—22no—
101D452—24no—
102D452—22no—
103D452C2×D414yes—
104C4×D113—28no—
105C4×D113—24no—
106C4×D113—24no—
107Dic226—24no—
108Dic226—22no—
109Dic226C2×D414yes—
110#11744751—24no—
111C22×C113—22no—
112C22×C113—41no—
113C22×C113—42no—
114C22×C113—44no—
115C22×C113—42no—
116C22×C113—84no—
117C22×C113#12012yes—
118C22×C113C22×D411yescharacteristic
119C2×D113—24no—
120C2×D113—82no—
121C2×D113—84no—
122C4×C113—22no—
123C4×C113—42no—
124C4×C113#12011yescharacteristic
125C4×C113#12011yescharacteristic
126C4×C113C22×D412yes—
127Dic113—24no—
128C2×C113—21no—
129C2×C113—22no—
130C2×C113—42no—
131C2×C113—82no—
132C2×C113C2×#12011yescharacteristic
133D113—44no—
134#3021—1131nomaximal, Sylow
135C113#302111yescharacteristic, complemented, Sylow
136#585—1131no—
137C2×AGL(1,ℤ/8)—1132no—
138#535D11311yescharacteristic, complemented
139#454—1134no—
140#453—1134no—
141#421—1132no—
142#413—1131no—
1432−1+4—1132no—
1442−1+4—2262no—
145H(5,𝔽2)—1132no—
146H(5,𝔽2)—2262no—
147H(5,𝔽2)—2262no—
148C2×#41—1132no—
149C2×#41—2264no—
150C2×#41—2262no—
151C2×#41C2×D11311yescharacteristic
152C22×D4C2×D11311yescharacteristic, complemented
153AGL(1,ℤ/8)—1138no—
154AGL(1,ℤ/8)—2264no—
155C2×SD16—2262no—
156C2×D8—2262no—
157C2×M16—1132no—
158#127C2×D11312yescomplemented
159#124C2×D11312yescomplemented
160#121—22no—
161#120—22no—
162#117C2×D11311yescharacteristic, complemented
163#104—1138no—
164#101—1132no—
165#100—1132no—
166C24—21no—
167#41—22no—
168#41—22no—
169#41—1134no—
170#41—1134no—
171#41—2264no—
172#41—2264no—
173#41—2264no—
174#41—2268no—
175#41—2264no—
176#41—2262no—
177#41—2262no—
178#41—2264no—
179C2×Q8—1132no—
180C2×Q8—2262no—
181C2×Q8—2264no—
182C2×Q8C22×D11311yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—21no—
187C2×D4—1132no—
188C2×D4—2262no—
189C2×D4—2264no—
190C2×D4—2268no—
191C2×D4—2262no—
192C2×D4—2264no—
193C2×D4C22⋊D11312yes—
194C2×D4C22×D11312yes—
195C2×D4C22×D11311yescharacteristic
196C22×C4—2264no—
197C22×C4—2262no—
198C22×C4C22⋊D11312yes—
199C22×C4C22×D11311yescharacteristic
200SD16—2268no—
201D8—2268no—
202M16—1134no—
203M16—2262no—
204C2×C8—2262no—
205C4⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—24no—
208C42C22×D11312yes—
209C23—22no—
210C23—42no—
211C23—82no—
212C23—2264no—
213C23—2262no—
214C23C2×C22⋊D11312yes—
215C23C2×C22⋊D11311yescharacteristic
216Q8—22no—
217Q8—1134no—
218Q8—2264no—
219Q8—2262no—
220D4—24no—
221D4—22no—
222D4—24no—
223D4—41no—
224D4—41no—
225D4—84no—
226D4—1134no—
227D4—2264no—
228D4—2268no—
229D4—2264no—
230D4—2264no—
231D4—2262no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—2268no—
236C2×C4—2264no—
237C2×C4—2262no—
238C2×C4—2264no—
239C2×C4—2264no—
240C2×C4D4×D11312yes—
241C2×C4D4×D11312yes—
242C2×C4C2×C22⋊D11312yes—
243C2×C4C2×C22⋊D11311yescharacteristic
244C2×C4C23×D11311yescharacteristic
245C8—2264no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—44no—
250C22—42no—
251C22—84no—
252C22—9042no—
253C22—9044no—
254C22—2264no—
255C22#1681359012yes—
256C22C22×C22⋊D11311yescharacteristic
257C4—22no—
258C4—42no—
259C4—2264no—
260C4#1681359011yescharacteristic
261C4#1681359011yescharacteristic
262C4C2×D4×D11312yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—4524no—
268C2C2×#1681359011yescharacteristic
subgroupG/H
centerC2C2×#16813590
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC2×C113C2×#120
hypercenter#535D113
hypocenterC113#3021
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #20299434C2semidirect
2. C2×#16813648C2semidirect
3. #20298770C2semidirect
4. #20298765C2semidirect
5. #20298616C2semidirect
6. #20298582C2semidirect
7. #535×C113C2semidirect
8. #16813670C22semidirect
12. #16813667C22semidirect
17. #16813648C22semidirect
20. C2×#14268631C22semidirect
21. #16813550C22semidirect
22. #16813541C22semidirect
23. #16813539C22semidirect
25. C22×D4×C113C22semidirect
26. #127×C113C22semidirect
27. #124×C113C22semidirect
30. #117×C113C22semidirect
37. #14268647D4semidirect
42. C2×Dic226D4semidirect
45. C2×D452D4semidirect
135. C113#3021semidirect
138. #535D113semidirect
152. C22×D4C2×D113semidirect
158. #127C2×D113semidirect
159. #124C2×D113semidirect
162. #117C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994342
C2×#168136482
#202987702
#202987652
#202986162
#202985822
#535×C1132
#3021113