Finite Group Databasebeta

← #28402170

Subgroups — #28402170

Order 14464.

546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#16813648C212yesmaximal, complemented
2#20299253C211yesmaximal, characteristic, complemented
3#20298970C211yesmaximal, characteristic, complemented
4#20298842C212yesmaximal, complemented
5#20298803C211yesmaximal, characteristic, complemented
6#20298790C211yesmaximal, characteristic, complemented
7#20298749C212yesmaximal, complemented
8#20298741C212yesmaximal, complemented
9C4×#14268632C211yesmaximal, characteristic, complemented
10#20298676C211yesmaximal, characteristic, complemented
11D42×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2212yescomplemented
13#16813648—28no—
14C2×#14268635C2212yes—
15C2×#14268635C2212yescomplemented
16C2×#14268635C2212yescomplemented
17C2×#14268632C2211yescharacteristic
18C2×#14268632C2212yescomplemented
19C2×#14268631C2212yescomplemented
20#16813622C2211yescharacteristic, complemented
21#16813604—22no—
22#16813601C2212yescomplemented
23#16813593—21no—
24C4×D452C2211yescharacteristic, complemented
25C4⋊C4×D113—21no—
26#16813555C2211yescharacteristic, complemented
27C4⋊#11744751C2211yescharacteristic, complemented
28#16813545C2212yescomplemented
29#16813543C2211yescharacteristic
30#16813543C2212yescomplemented
31#16813542C2211yescharacteristic, complemented
32C22⋊#11744751C2212yescomplemented
33C4×#11744751C2211yescharacteristic, complemented
34C22×D4×C113—21no—
35C22×D4×C113C2212yes—
36#127×C113C2211yescharacteristic
37#121×C113—21no—
38#121×C113C2212yes—
39#120×C113—22no—
40C4×D4×C113C2211yescharacteristic
41C4×D4×C113C2211yescharacteristic
42#14268647—24no—
43#14268647—42no—
44C2×Dic226C2312yes—
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—22no—
47C2×C4×D113—21no—
48C2×C4×D113—22no—
49#14268635—24no—
50#14268635—24no—
51#14268635—42no—
52#14268632—24no—
53#14268632D414yescomplemented
54#14268631—24no—
55C2×#11744751C2312yes—
56C2×#11744751C2311yescharacteristic
57C2×#11744751C2311yescharacteristic
58C4⋊Dic113—21no—
59C4⋊Dic113—21no—
60C4⋊Dic113C2311yescharacteristic
61#14268626—22no—
62C22⋊Dic113—22no—
63#14268624—21no—
64C24×C113—22no—
65C2×D4×C113—24no—
66C2×D4×C113—22no—
67C2×D4×C113—22no—
68C2×D4×C113—21no—
69C2×D4×C113—21no—
70C2×D4×C113—42no—
71C2×D4×C113—44no—
72C2×D4×C113D411yescharacteristic
73C2×D4×C113C2312yes—
74C2×D4×C113C2311yescharacteristic
75C22×C4×C113—21no—
76C22×C4×C113C2312yes—
77C4⋊C4×C113D411yescharacteristic
78C4⋊C4×C113C2311yescharacteristic
79C22⋊C4×C113—21no—
80C22⋊C4×C113—22no—
81C22⋊C4×C113D412yes—
82C42×C113C2311yescharacteristic
83C23×C113—21no—
84C23×C113—22no—
85C23×C113—44no—
86C23×C113—44no—
87C23×C113—82no—
88C23×C113C2×D412yes—
89C22×D113—21no—
90D4×C113—22no—
91D4×C113—22no—
92D4×C113—21no—
93D4×C113—22no—
94D4×C113—44no—
95D4×C113—44no—
96D4×C113—42no—
97D4×C113—81no—
98D4×C113C2×D412yes—
99C2×C4×C113—22no—
100C2×C4×C113—22no—
101C2×C4×C113—21no—
102C2×C4×C113—42no—
103C2×C4×C113C2×D411yescharacteristic
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2×D411yescharacteristic
106C2×C4×C113C2411yescharacteristic
107C22⋊D113—44no—
108C2×Dic113—21no—
109C2×Dic113—22no—
110D452—21no—
111D452C2×D412yescomplemented
112C4×D113—44no—
113C4×D113—42no—
114Dic226—22no—
115Dic226—22no—
116#11744751—22no—
117#11744751—21no—
118#11744751C2×D412yescomplemented
119C22×C113—22no—
120C22×C113—22no—
121C22×C113—22no—
122C22×C113—22no—
123C22×C113—41no—
124C22×C113—41no—
125C22×C113—42no—
126C22×C113—42no—
127C22×C113—42no—
128C22×C113—88no—
129C22×C113C22×D411yescharacteristic
130C2×D113—22no—
131C2×D113—41no—
132C2×D113—41no—
133C4×C113—22no—
134C4×C113—21no—
135C4×C113—41no—
136C4×C113AGL(1,ℤ/8)12yescomplemented
137C4×C113C22×D411yescharacteristic
138C4×C113H(5,𝔽2)11yescharacteristic
139Dic113—42no—
140Dic113—41no—
141C2×C113—42no—
142C2×C113—42no—
143C2×C113—82no—
144C2×C113D4211yescharacteristic
145C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C113#57711yescharacteristic
147D113—42no—
148#3272—1131nomaximal, Sylow
149C113#327211yescharacteristic, complemented, Sylow
150C2×AGL(1,ℤ/8)—1132no—
151#547—1131no—
152D42D11311yescharacteristic, complemented
153#492—1131no—
154#468—1132no—
155#461—1131no—
156#459—1131no—
157#450—1132no—
158#449—1132no—
159C4×D8—1131no—
160#436—1131no—
161C2×#41—1132no—
162C22×D4—21no—
163C22×D4C2×D11312yes—
164AGL(1,ℤ/8)—2268no—
165C2×SD16—1132no—
166C2×SD16—1132no—
167C2×SD16—1132no—
168C2×D8—1131no—
169C2×D8—1132no—
170C2×M16—1132no—
171C4⋊Q8—1131no—
172#127C2×D11311yescharacteristic
173#123—2262no—
174C22⋊Q8—1132no—
175#121—21no—
176#121—2261no—
177#121C2×D11312yes—
178#120—22no—
179C4×D4—1131no—
180C4×D4C2×D11311yescharacteristic
181C4×D4C2×D11311yescharacteristic
182C2×C4⋊C4—2261no—
183#107—1131no—
184C4⋊C8—1131no—
185#103—1132no—
186#102—1131no—
187#102—1132no—
188#102—1131no—
189C22⋊C8—1132no—
190C4×C8—1131no—
191C24—22no—
192#41—4522no—
193#41—2264no—
194C2×Q8—1132no—
195C2×D4—24no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—21no—
199C2×D4—21no—
200C2×D4—42no—
201C2×D4—44no—
202C2×D4—1131no—
203C2×D4—2262no—
204C2×D4C22⋊D11311yescharacteristic
205C2×D4C22×D11312yes—
206C2×D4C22×D11311yescharacteristic
207C22×C4—21no—
208C22×C4—2261no—
209C22×C4—2262no—
210C22×C4C22×D11312yes—
211SD16—4522no—
212SD16—2264no—
213SD16—2264no—
214D8—1134no—
215D8—2264no—
216M16—2264no—
217C2×C8—1131no—
218C2×C8—1131no—
219C2×C8—1132no—
220C4⋊C4—1131no—
221C4⋊C4—2261no—
222C4⋊C4—2262no—
223C4⋊C4—2261no—
224C4⋊C4C22⋊D11311yescharacteristic
225C4⋊C4C22×D11311yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—22no—
228C22⋊C4—2262no—
229C22⋊C4—2261no—
230C22⋊C4C22⋊D11312yes—
231C42C22×D11311yescharacteristic
232C23—21no—
233C23—22no—
234C23—44no—
235C23—44no—
236C23—82no—
237C23—2261no—
238C23C2×C22⋊D11312yes—
239Q8—2262no—
240Q8—2262no—
241D4—22no—
242D4—22no—
243D4—21no—
244D4—22no—
245D4—44no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—1132no—
250D4—4524no—
251D4—2261no—
252D4D4×D11312yes—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—4524no—
258C2×C4—4522no—
259C2×C4—2261no—
260C2×C4—2262no—
261C2×C4C2×C22⋊D11311yescharacteristic
262C2×C4C2×C22⋊D11312yes—
263C2×C4C2×C22⋊D11311yescharacteristic
264C2×C4C23×D11311yescharacteristic
265C8—1132no—
266C8—2262no—
267C8—2261no—
268C22—22no—
269C22—22no—
270C22—22no—
271C22—22no—
272C22—41no—
273C22—41no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—88no—
278C22—4521no—
279C22—4521no—
280C22—2262no—
281C22C22×C22⋊D11311yescharacteristic
282C4—21no—
283C4—22no—
284C4—41no—
285C4—4521no—
286C4—4522no—
287C4#1681364812yescomplemented
288C4C2×D4×D11311yescharacteristic
289C4#1681366711yescharacteristic
290C2—42no—
291C2—42no—
292C2—82no—
293C2—4522no—
294C2D4×C22⋊D11311yescharacteristic
295C2C2×#1681364811yescharacteristic
296C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingD42×C113C2
socleC22×C113C22×D4
hypercenterD42D113
hypocenterC113#3272
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. #20299253C2semidirect
3. #20298970C2semidirect
4. #20298842C2semidirect
5. #20298803C2semidirect
6. #20298790C2semidirect
7. #20298749C2semidirect
8. #20298741C2semidirect
9. C4×#14268632C2semidirect
10. #20298676C2semidirect
11. D42×C113C2semidirect
12. C2×#14268647C22semidirect
15. C2×#14268635C22semidirect
16. C2×#14268635C22semidirect
18. C2×#14268632C22semidirect
19. C2×#14268631C22semidirect
20. #16813622C22semidirect
22. #16813601C22semidirect
24. C4×D452C22semidirect
26. #16813555C22semidirect
27. C4⋊#11744751C22semidirect
28. #16813545C22semidirect
30. #16813543C22semidirect
31. #16813542C22semidirect
32. C22⋊#11744751C22semidirect
33. C4×#11744751C22semidirect
53. #14268632D4semidirect
111. D452C2×D4semidirect
118. #11744751C2×D4semidirect
136. C4×C113AGL(1,ℤ/8)semidirect
149. C113#3272semidirect
152. D42D113semidirect
287. C4#16813648semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202992532
#202989702
#202988422
#202988032
#202987902
#202987492
#202987412
C4×#142686322
#202986762
D42×C1132
#3272113