Finite Group Databasebeta

← #28402248

Subgroups — #28402248

Order 14464.

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

normal subgroups only

This group has 620 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
1C22×D904C211yesmaximal, characteristic, complemented
2C2×D8×D113C211yesmaximal, characteristic, complemented
3#20299232C212yesmaximal, complemented
4#20298973C211yesmaximal, characteristic, complemented
5#20298835C211yesmaximal, characteristic, complemented
6#20298792C212yesmaximal, complemented
7#20298733C212yesmaximal, complemented
8#20298731C212yesmaximal, complemented
9#20298680C211yesmaximal, characteristic, complemented
10C8×C22⋊D113C211yesmaximal, characteristic, complemented
11#466×C113C211yesmaximal, characteristic, complemented
12C22×D452C2212yescomplemented
13C2×D4×D113—22no—
14C2×D4×D113C2212yescomplemented
15C2×D904—24no—
16C2×D904C2211yescharacteristic
17C2×D904C2212yescomplemented
18C2×D904C2211yescharacteristic, complemented
19C2×#14268632C2212yescomplemented
20C2×#14268632C2212yescomplemented
21D8×D113—24no—
22C2×C8×D113C2211yescharacteristic, complemented
23#16813618C2212yescomplemented
24#16813597C2212yescomplemented
25#16813595—22no—
26#16813592—22no—
27#16813590—22no—
28#16813584C2212yescomplemented
29C4×C22⋊D113C2211yescharacteristic
30#16813551C2211yescharacteristic, complemented
31#16813542C2212yescomplemented
32#16813542C2212yescomplemented
33C22⋊#11744751C2211yescharacteristic, complemented
34#16813534C2211yescharacteristic, complemented
35C8×Dic113C2211yescharacteristic, complemented
36C2×D8×C113C2211yescharacteristic, complemented
37C22×C8×C113C2211yescharacteristic, complemented
38#121×C113C2212yescomplemented
39#107×C113C2211yescharacteristic, complemented
40#102×C113C2212yescomplemented
41C23×D113—22no—
42C23×D113—22no—
43C2×D452—24no—
44C2×D452—22no—
45C2×D452—22no—
46C2×D452—42no—
47C2×D452C2312yes—
48C2×D452C2312yes—
49C2×C22⋊D113—22no—
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52C2×C22⋊D113D411yescharacteristic
53D4×D113—24no—
54D4×D113—42no—
55D4×D113—48no—
56C2×C4×D113—22no—
57C2×C4×D113C2311yescharacteristic
58D904—24no—
59D904—22no—
60D904D414yescomplemented
61#14268632—24no—
62#14268632—42no—
63C2×#11744751C2311yescharacteristic
64C2×#11744751C2311yescharacteristic
65C8×D113—22no—
66#14268626D411yescharacteristic
67C22⋊Dic113D411yescharacteristic
68#14268624—22no—
69#14268624—22no—
70#14268624D411yescharacteristic
71C4×Dic113C2311yescharacteristic
72C2×D4×C113—22no—
73C2×D4×C113C2312yes—
74C22×C4×C113C2311yescharacteristic
75D8×C113—22no—
76C2×C8×C113—22no—
77C2×C8×C113C2311yescharacteristic
78C2×C8×C113C2311yescharacteristic
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—22no—
81C23×C113—22no—
82C23×C113C2×D411yescharacteristic
83C22×D113—22no—
84C22×D113—22no—
85C22×D113—44no—
86C22×D113—44no—
87C22×D113—44no—
88C22×D113—44no—
89C22×D113—82no—
90C22×D113—82no—
91C22×D113C2×D411yescharacteristic
92D4×C113—22no—
93D4×C113—22no—
94D4×C113—44no—
95C2×C4×C113—21no—
96C2×C4×C113—21no—
97C2×C4×C113—22no—
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—44no—
101C22⋊D113—44no—
102C22⋊D113—82no—
103C22⋊D113D814yescomplemented
104C2×Dic113C2×D411yescharacteristic
105C2×Dic113C2×D411yescharacteristic
106C2×Dic113C2×D411yescharacteristic
107D452—22no—
108D452—22no—
109D452—22no—
110D452—44no—
111D452—44no—
112D452C2×D414yescomplemented
113C4×D113—21no—
114C4×D113—21no—
115C4×D113—44no—
116C8×C113—21no—
117C8×C113C2×D412yescomplemented
118#11744751—21no—
119#11744751—21no—
120C22×C113—21no—
121C22×C113—21no—
122C22×C113—42no—
123C22×C113—42no—
124C22×C113—42no—
125C22×C113C2×D812yescomplemented
126C22×C113C22×D411yescharacteristic
127C2×D113—21no—
128C2×D113—21no—
129C2×D113—24no—
130C2×D113—42no—
131C2×D113—42no—
132C2×D113—42no—
133C2×D113—42no—
134C2×D113—42no—
135C2×D113—88no—
136C2×D113—88no—
137C2×D113C2×D812yescomplemented
138C4×C113—21no—
139C4×C113—42no—
140C4×C113C22×D411yescharacteristic
141C4×C113H(5,𝔽2)11yescharacteristic
142Dic113—21no—
143Dic113—21no—
144Dic113C2×D812yescomplemented
145C2×C113—22no—
146C2×C113—82no—
147C2×C113D4211yescharacteristic
148C2×C113C22×D811yescharacteristic
149C2×C113#57611yescharacteristic
150D113—22no—
151D113—44no—
152D113—82no—
153D4×D8—1131nomaximal, Sylow
154C113D4×D811yescharacteristic, complemented, Sylow
155C22×D8—1131no—
156C22×D8—1131no—
157D42—1132no—
158#493—1131no—
159#466—1131no—
160#466D11311yescharacteristic, complemented
161#459—1132no—
162#447—1132no—
163#447—1132no—
164C4×D8—1131no—
165C8×D4—1131no—
166C22×D4—1132no—
167C22×D4—1132no—
168C22×D4—2262no—
169C2×D8—1132no—
170C2×D8—1132no—
171C2×D8—1131no—
172C2×D8—1132no—
173C2×D8—1131no—
174C2×D8—2264no—
175C2×D8—2264no—
176C2×D8C2×D11311yescharacteristic, complemented
177C22×C8—1131no—
178C22×C8C2×D11311yescharacteristic, complemented
179#127—1132no—
180#121—1132no—
181#121—2262no—
182#121C2×D11312yescomplemented
183#120—2262no—
184#120—2262no—
185C4×D4—1131no—
186C4×D4—1132no—
187#107C2×D11311yescharacteristic, complemented
188C4⋊C8—1131no—
189#102—1132no—
190#102—1132no—
191#102C2×D11312yescomplemented
192C22⋊C8—1131no—
193C22⋊C8—1131no—
194C4×C8—1131no—
195C24—2262no—
196C24—2262no—
197C2×D4—22no—
198C2×D4—1131no—
199C2×D4—1132no—
200C2×D4—1132no—
201C2×D4—4522no—
202C2×D4—4528no—
203C2×D4—4522no—
204C2×D4—2264no—
205C2×D4—2262no—
206C2×D4—2262no—
207C2×D4—2262no—
208C2×D4—2262no—
209C2×D4—2264no—
210C2×D4—2262no—
211C2×D4C22×D11312yes—
212C22×C4—1131no—
213C22×C4—2262no—
214C22×C4C22×D11311yescharacteristic
215D8—22no—
216D8—1134no—
217D8—4522no—
218D8—2264no—
219D8—2264no—
220D8—2262no—
221C2×C8—22no—
222C2×C8—1131no—
223C2×C8—1131no—
224C2×C8—2262no—
225C2×C8C22×D11311yescharacteristic
226C2×C8C22×D11311yescharacteristic
227C4⋊C4—1131no—
228C4⋊C4C22×D11312yes—
229C22⋊C4—22no—
230C22⋊C4—1131no—
231C22⋊C4—1131no—
232C22⋊C4—2262no—
233C22⋊C4—2262no—
234C42—1131no—
235C23—22no—
236C23—1131no—
237C23—9042no—
238C23—9042no—
239C23—4524no—
240C23—4524no—
241C23—4524no—
242C23—4524no—
243C23—2262no—
244C23—2262no—
245C23D4×D11311yescharacteristic
246D4—22no—
247D4—22no—
248D4—44no—
249D4—1134no—
250D4—1134no—
251D4—9042no—
252D4—4524no—
253D4—4524no—
254D4—4524no—
255D4—4524no—
256D4—2262no—
257D4—2262no—
258D4—2262no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—1131no—
263C2×C4—1131no—
264C2×C4—1131no—
265C2×C4—4524no—
266C2×C4—2261no—
267C2×C4—2261no—
268C2×C4D4×D11311yescharacteristic
269C2×C4C23×D11311yescharacteristic
270C8—21no—
271C8—2261no—
272C8—2261no—
273C8D4×D11312yescomplemented
274C22—21no—
275C22—21no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—1132no—
280C22—9048no—
281C22—9048no—
282C22—4522no—
283C22—4522no—
284C22—4522no—
285C22—4522no—
286C22—4522no—
287C22—2264no—
288C22—2261no—
289C22—2261no—
290C22D8×D11312yescomplemented
291C22C2×D4×D11311yescharacteristic
292C4—21no—
293C4—42no—
294C4—1132no—
295C4—2261no—
296C4—2261no—
297C4C2×D4×D11311yescharacteristic
298C4#1681366811yescharacteristic
299C2—22no—
300C2—82no—
301C2—9042no—
302C2—4524no—
303C2—2262no—
304C2#2029923211yescharacteristic
305C2C2×D8×D11311yescharacteristic
306C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#466×C113C2
socleC22×C113C22×D4
hypercenter#466D113
hypocenterC113D4×D8
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C22×D904C2semidirect
2. C2×D8×D113C2semidirect
3. #20299232C2semidirect
4. #20298973C2semidirect
5. #20298835C2semidirect
6. #20298792C2semidirect
7. #20298733C2semidirect
8. #20298731C2semidirect
9. #20298680C2semidirect
10. C8×C22⋊D113C2semidirect
11. #466×C113C2semidirect
12. C22×D452C22semidirect
14. C2×D4×D113C22semidirect
17. C2×D904C22semidirect
18. C2×D904C22semidirect
19. C2×#14268632C22semidirect
20. C2×#14268632C22semidirect
22. C2×C8×D113C22semidirect
23. #16813618C22semidirect
24. #16813597C22semidirect
28. #16813584C22semidirect
30. #16813551C22semidirect
31. #16813542C22semidirect
32. #16813542C22semidirect
33. C22⋊#11744751C22semidirect
34. #16813534C22semidirect
35. C8×Dic113C22semidirect
36. C2×D8×C113C22semidirect
37. C22×C8×C113C22semidirect
38. #121×C113C22semidirect
39. #107×C113C22semidirect
40. #102×C113C22semidirect
60. D904D4semidirect
103. C22⋊D113D8semidirect
112. D452C2×D4semidirect
117. C8×C113C2×D4semidirect
125. C22×C113C2×D8semidirect
137. C2×D113C2×D8semidirect
144. Dic113C2×D8semidirect
154. C113D4×D8semidirect
160. #466D113semidirect
176. C2×D8C2×D113semidirect
178. C22×C8C2×D113semidirect
182. #121C2×D113semidirect
187. #107C2×D113semidirect
191. #102C2×D113semidirect
273. C8D4×D113semidirect
290. C22D8×D113semidirect

Maximal subgroups

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

subgroupindex
C22×D9042
C2×D8×D1132
#202992322
#202989732
#202988352
#202987922
#202987332
#202987312
#202986802
C8×C22⋊D1132
#466×C1132
D4×D8113