Finite Group Databasebeta

← #28399840

Subgroups — #28399840

Order 14464.

784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813668C211yesmaximal, characteristic, complemented
2C2×#16813648C211yesmaximal, characteristic, complemented
3C22×#14268632C211yesmaximal, characteristic, complemented
4#20298741C214yesmaximal, complemented
5#20298731C214yesmaximal, complemented
6#20298602C211yesmaximal, characteristic, complemented
7#20298592C211yesmaximal, characteristic, complemented
8#20298565C211yesmaximal, characteristic, complemented
9#535×C113C211yesmaximal, characteristic, complemented
10#16813668—24no—
11#16813668—24no—
12C2×#14268648—21no—
13C2×#14268647C2211yescharacteristic
14C2×#14268647C2212yescomplemented
15C22×D452C2211yescharacteristic
16C22×D452C2212yescomplemented
17C2×D4×D113—22no—
18C2×D4×D113—21no—
19#16813648—24no—
20C2×#14268635C2212yescomplemented
21C2×#14268632—24no—
22C2×#14268632C2214yescomplemented
23C2×#14268632C2212yescomplemented
24C2×#14268631C2211yescharacteristic, complemented
25C22×#11744751C2211yescharacteristic, complemented
26#16813545C2212yescomplemented
27#16813542C2212yescomplemented
28#16813542C2214yescomplemented
29C22⋊#11744751C2214yescomplemented
30C2×#41×C113C2211yescharacteristic
31C22×D4×C113C2211yescharacteristic, complemented
32#127×C113—21no—
33#124×C113—21no—
34#121×C113C2214yescomplemented
35#120×C113—22no—
36#117×C113C2211yescharacteristic, complemented
37C23×D113—21no—
38C23×D113—22no—
39#14268648—28no—
40#14268647—22no—
41#14268647—24no—
42#14268647—24no—
43#14268647D414yescomplemented
44C2×Dic226C2311yescharacteristic
45C2×D452—21no—
46C2×D452—22no—
47C2×D452—22no—
48C2×D452—24no—
49C2×D452—24no—
50C2×D452D414yescomplemented
51C2×D452C2312yes—
52C2×D452C2311yescharacteristic
53C2×C22⋊D113—21no—
54C2×C22⋊D113—22no—
55D4×D113—216no—
56D4×D113—28no—
57C2×C4×D113—21no—
58C2×C4×D113—22no—
59#14268635—24no—
60#14268632—28no—
61#14268632—24no—
62#14268631—22no—
63C2×#11744751—22no—
64C2×#11744751C2312yes—
65C2×#11744751C2312yes—
66C24×C113—21no—
67#41×C113—22no—
68#41×C113—22no—
69C2×Q8×C113D411yescharacteristic
70C2×D4×C113—24no—
71C2×D4×C113—22no—
72C2×D4×C113—22no—
73C2×D4×C113—21no—
74C2×D4×C113D412yes—
75C2×D4×C113D411yescharacteristic
76C2×D4×C113C2312yes—
77C22×C4×C113C2312yes—
78C22×C4×C113C2311yescharacteristic
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—21no—
81C22⋊C4×C113—24no—
82C42×C113—21no—
83C23×C113—22no—
84C23×C113—42no—
85C23×C113—82no—
86C23×C113C2×D412yes—
87C23×C113C2×D411yescharacteristic
88C22×D113—21no—
89C22×D113—22no—
90C22×D113—28no—
91C22×D113—24no—
92C22×D113—82no—
93C22×D113—84no—
94Q8×C113—22no—
95D4×C113—24no—
96D4×C113—22no—
97D4×C113—22no—
98D4×C113—22no—
99D4×C113—42no—
100D4×C113—84no—
101C2×C4×C113—22no—
102C2×C4×C113—22no—
103C2×C4×C113—22no—
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2×D412yes—
106C2×C4×C113C2×D412yes—
107C2×C4×C113C2×D411yescharacteristic
108C2×C4×C113C2411yescharacteristic
109C22⋊D113—28no—
110C22⋊D113—24no—
111C2×Dic113—21no—
112D452—28no—
113D452—24no—
114D452—21no—
115D452—22no—
116D452C2×D412yes—
117D452C2×D414yes—
118C4×D113—28no—
119C4×D113—24no—
120Dic226—21no—
121Dic226C2×D412yes—
122#11744751—22no—
123#11744751—22no—
124C22×C113—22no—
125C22×C113—22no—
126C22×C113—24no—
127C22×C113—42no—
128C22×C113—44no—
129C22×C113—84no—
130C22×C113#12012yes—
131C22×C113C22×D411yescharacteristic
132C2×D113—24no—
133C2×D113—22no—
134C2×D113—44no—
135C2×D113—42no—
136C2×D113—84no—
137C2×D113—88no—
138C4×C113—22no—
139C4×C113—42no—
140C4×C113#12012yes—
141C4×C113C22×D411yescharacteristic
142C4×C113C22×D411yescharacteristic
143Dic113—22no—
144C2×C113—22no—
145C2×C113—42no—
146C2×C113—82no—
147C2×C113C2×#12011yescharacteristic
148C2×C113#57612yes—
149D113—44no—
150D113—42no—
151#3008—1131nomaximal, Sylow
152C113#300811yescharacteristic, complemented, Sylow
153C2×H(5,𝔽2)—1131no—
154C2×AGL(1,ℤ/8)—1131no—
155C22×D8—1131no—
156#535D11311yescharacteristic, complemented
157#449—1134no—
158#447—1134no—
159#418—1131no—
160#416—1131no—
161#408—1131no—
162H(5,𝔽2)—2264no—
163H(5,𝔽2)—2264no—
164C2×#41—1131no—
165C2×#41—1132no—
166C2×#41—2261no—
167C2×#41C2×D11311yescharacteristic
168C22×D4—1131no—
169C22×D4—1132no—
170C22×D4—2262no—
171C22×D4—2261no—
172C22×D4C2×D11311yescharacteristic, complemented
173AGL(1,ℤ/8)—2264no—
174C2×SD16—1132no—
175C2×D8—1134no—
176C2×D8—1132no—
177C2×D8—2264no—
178C2×M16—1131no—
179C22×C8—1131no—
180#127—21no—
181#124—21no—
182#121C2×D11314yescomplemented
183#120—22no—
184#117C2×D11311yescharacteristic, complemented
185#103—1132no—
186#102—1132no—
187#102—1134no—
188C22⋊C8—1134no—
189C24—21no—
190C24—2262no—
191C24—2261no—
192#41—22no—
193#41—22no—
194#41—1134no—
195#41—2264no—
196#41—2264no—
197#41—2268no—
198#41—2262no—
199C2×Q8—1131no—
200C2×Q8C22⋊D11311yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—22no—
204C2×D4—21no—
205C2×D4—1134no—
206C2×D4—1132no—
207C2×D4—1131no—
208C2×D4—2264no—
209C2×D4—2264no—
210C2×D4—22616no—
211C2×D4—2268no—
212C2×D4—2262no—
213C2×D4—2261no—
214C2×D4—2262no—
215C2×D4—2262no—
216C2×D4—2261no—
217C2×D4C22⋊D11312yes—
218C2×D4C22⋊D11311yescharacteristic
219C2×D4C22×D11312yes—
220C22×C4—2262no—
221C22×C4—2261no—
222C22×C4C22×D11312yes—
223C22×C4C22×D11311yescharacteristic
224SD16—2264no—
225D8—2268no—
226D8—2264no—
227M16—2262no—
228C2×C8—1132no—
229C2×C8—1132no—
230C2×C8—2262no—
231C4⋊C4C22×D11312yes—
232C22⋊C4—21no—
233C22⋊C4—24no—
234C42—21no—
235C23—22no—
236C23—42no—
237C23—82no—
238C23—9042no—
239C23—9044no—
240C23—2268no—
241C23—2264no—
242C23—2262no—
243C23—2261no—
244C23C2×C22⋊D11312yes—
245C23C2×C22⋊D11311yescharacteristic
246Q8—22no—
247Q8—1132no—
248Q8—2261no—
249D4—24no—
250D4—22no—
251D4—22no—
252D4—22no—
253D4—42no—
254D4—84no—
255D4—1134no—
256D4—1132no—
257D4—2268no—
258D4—2268no—
259D4—2264no—
260D4—2264no—
261D4—2261no—
262D4—2262no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—2268no—
267C2×C4—2261no—
268C2×C4—2264no—
269C2×C4D4×D11312yes—
270C2×C4D4×D11312yes—
271C2×C4C2×C22⋊D11312yes—
272C2×C4C2×C22⋊D11311yescharacteristic
273C2×C4C23×D11311yescharacteristic
274C8—2262no—
275C8—2262no—
276C22—22no—
277C22—22no—
278C22—24no—
279C22—42no—
280C22—44no—
281C22—84no—
282C22—9044no—
283C22—9048no—
284C22—4524no—
285C22—4522no—
286C22—2264no—
287C22—2262no—
288C22#1681359012yes—
289C22C22×C22⋊D11311yescharacteristic
290C4—22no—
291C4—42no—
292C4—2262no—
293C4#1681359012yes—
294C4C2×D4×D11311yescharacteristic
295C4C2×D4×D11311yescharacteristic
296C2—22no—
297C2—42no—
298C2—82no—
299C2—4524no—
300C2—4522no—
301C2C2×#1681359011yescharacteristic
302C2#2029940112yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC22×C113C22×D4
hypercenter#535D113
hypocenterC113#3008
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#16813668C2semidirect
2. C2×#16813648C2semidirect
3. C22×#14268632C2semidirect
4. #20298741C2semidirect
5. #20298731C2semidirect
6. #20298602C2semidirect
7. #20298592C2semidirect
8. #20298565C2semidirect
9. #535×C113C2semidirect
14. C2×#14268647C22semidirect
16. C22×D452C22semidirect
20. C2×#14268635C22semidirect
22. C2×#14268632C22semidirect
23. C2×#14268632C22semidirect
24. C2×#14268631C22semidirect
25. C22×#11744751C22semidirect
26. #16813545C22semidirect
27. #16813542C22semidirect
28. #16813542C22semidirect
29. C22⋊#11744751C22semidirect
31. C22×D4×C113C22semidirect
34. #121×C113C22semidirect
36. #117×C113C22semidirect
43. #14268647D4semidirect
50. C2×D452D4semidirect
152. C113#3008semidirect
156. #535D113semidirect
172. C22×D4C2×D113semidirect
182. #121C2×D113semidirect
184. #117C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136682
C2×#168136482
C22×#142686322
#202987412
#202987312
#202986022
#202985922
#202985652
#535×C1132
#3008113