Finite Group Databasebeta

← #28402260

Subgroups — #28402260

Order 14464.

526 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16813641C211yesmaximal, characteristic, complemented
2C2×D8×D113C211yesmaximal, characteristic, complemented
3#20299243C212yesmaximal, complemented
4#20298982C211yesmaximal, characteristic, complemented
5#20298840C211yesmaximal, characteristic, complemented
6#20298835C211yesmaximal, characteristic, complemented
7#20298813C212yesmaximal, complemented
8#20298750C212yesmaximal, complemented
9#20298744C212yesmaximal, complemented
10C8×D452C211yesmaximal, characteristic, complemented
11C4×D8×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2212yescomplemented
13C2×D4×D113C2212yes—
14#16813641—24no—
15C2×Dic452C2211yescharacteristic, complemented
16C2×#14268636C2212yescomplemented
17C2×#14268635C2212yescomplemented
18C2×D904C2211yescharacteristic
19C2×#14268632C2212yes—
20D8×D113—24no—
21C2×C8×D113C2211yescharacteristic
22C2×C8×D113C2211yescharacteristic, complemented
23#16813610C2212yescomplemented
24#16813606—22no—
25#16813602C2212yes—
26#16813597C2212yescomplemented
27#16813596—22no—
28#16813592—22no—
29C4×D452C2211yescharacteristic
30C2×#14268624—22no—
31C4⋊#11744751C2211yescharacteristic, complemented
32#16813545C2212yescomplemented
33#16813542C2212yescomplemented
34#16813534C2211yescharacteristic
35#16813534C2211yescharacteristic, complemented
36C2×D8×C113C2211yescharacteristic
37C4×D4×C113C2212yescomplemented
38#107×C113C2211yescharacteristic, complemented
39#102×C113C2212yescomplemented
40C4×C8×C113C2211yescharacteristic, complemented
41C23×D113—22no—
42#14268646—24no—
43#14268646—42no—
44C2×Dic226C2312yes—
45C2×D452—22no—
46C2×D452D411yescharacteristic
47C2×D452C2312yes—
48C2×C22⋊D113—22no—
49C2×C22⋊D113—22no—
50D4×D113—24no—
51D4×D113—42no—
52C22×Dic113—22no—
53C2×C4×D113C2311yescharacteristic
54C2×C4×D113C2311yescharacteristic
55Dic452—22no—
56#14268636—42no—
57#14268635—24no—
58D904—22no—
59#14268632—24no—
60C2×#11744751C2311yescharacteristic
61C2×#11744751C2311yescharacteristic
62C8×D113—22no—
63C8×D113—22no—
64C4⋊Dic113—22no—
65C4⋊Dic113D411yescharacteristic
66#14268624—22no—
67#14268624—22no—
68#14268624—22no—
69#14268624—22no—
70#14268624D411yescharacteristic
71#14268624D411yescharacteristic
72C2×D4×C113C2312yes—
73C22×C4×C113—22no—
74D8×C113D414yescomplemented
75C2×C8×C113C2311yescharacteristic
76C2×C8×C113C2311yescharacteristic
77C4⋊C4×C113C2312yes—
78C22⋊C4×C113—22no—
79C42×C113C2311yescharacteristic
80C23×C113—22no—
81C22×D113—22no—
82C22×D113—44no—
83C22×D113—44no—
84C22×D113—82no—
85C22×D113C2×D411yescharacteristic
86C22×D113C2×D411yescharacteristic
87D4×C113—22no—
88D4×C113C2×D414yes—
89C2×C4×C113—22no—
90C2×C4×C113—82no—
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2411yescharacteristic
94C22⋊D113—44no—
95C22⋊D113—44no—
96C2×Dic113—22no—
97C2×Dic113—44no—
98C2×Dic113C2×D411yescharacteristic
99C2×Dic113C2×D411yescharacteristic
100D452—22no—
101D452—22no—
102D452—22no—
103D452—82no—
104C4×D113—21no—
105C4×D113—21no—
106C4×D113—21no—
107C4×D113—21no—
108Dic226—22no—
109Dic226—22no—
110C8×C113—21no—
111C8×C113C2×D412yes—
112#11744751—21no—
113#11744751—21no—
114C22×C113—24no—
115C22×C113—42no—
116C22×C113—42no—
117C22×C113C22×D411yescharacteristic
118C2×D113—21no—
119C2×D113—21no—
120C2×D113—21no—
121C2×D113—21no—
122C2×D113—21no—
123C2×D113—42no—
124C2×D113—42no—
125C2×D113—42no—
126C2×D113—88no—
127C2×D113#13512yescomplemented
128C4×C113—21no—
129C4×C113—21no—
130C4×C113—42no—
131C4×C113C22×D411yescharacteristic
132C4×C113H(5,𝔽2)11yescharacteristic
133Dic113—21no—
134Dic113—21no—
135Dic113—42no—
136C2×C113—44no—
137C2×C113D4211yescharacteristic
138C2×C113C2×#13511yescharacteristic
139C2×C113#57611yescharacteristic
140D113—22no—
141D113—41no—
142D113—82no—
143#3280—1131nomaximal, Sylow
144C113#328011yescharacteristic, complemented, Sylow
145C2×#135—1131no—
146C22×D8—1131no—
147#546—1132no—
148#495—1131no—
149#467—1131no—
150#466—1131no—
151#463—1132no—
152#450—1132no—
153#449—1132no—
154C4×D8D11311yescharacteristic, complemented
155C8×D4—1131no—
156C2×#41—1132no—
157C22×D4—1132no—
158#135—2264no—
159C2×Q16—1131no—
160C2×SD16—1132no—
161C2×SD16—1132no—
162C2×D8—1132no—
163C2×D8—1131no—
164C2×D8—2264no—
165C2×D8C2×D11311yescharacteristic
166C22×C8—1131no—
167C22×C8—1131no—
168#124—1132no—
169#123—2262no—
170C22⋊Q8—1132no—
171#121—1132no—
172#121—2262no—
173#120—2262no—
174C4×D4—1131no—
175C4×D4C2×D11312yescomplemented
176C2×C22⋊C4—2262no—
177#107C2×D11311yescharacteristic, complemented
178C4⋊C8—1131no—
179#103—1132no—
180#102—1132no—
181#102C2×D11312yescomplemented
182C22⋊C8—1131no—
183C22⋊C8—1131no—
184C4×C8C2×D11311yescharacteristic, complemented
185C24—2262no—
186#41—4522no—
187#41—2264no—
188C2×Q8—1132no—
189C2×D4—1131no—
190C2×D4—1132no—
191C2×D4—4522no—
192C2×D4—2262no—
193C2×D4—2262no—
194C2×D4—2262no—
195C2×D4—2264no—
196C2×D4C22×D11312yes—
197C22×C4—22no—
198C22×C4—1131no—
199C22×C4—1131no—
200C22×C4—2262no—
201Q16—2262no—
202SD16—4522no—
203SD16—2264no—
204D8—2264no—
205D8—2262no—
206D8D45214yescomplemented
207C2×C8—1131no—
208C2×C8—1131no—
209C2×C8—2262no—
210C2×C8—2262no—
211C2×C8C22×D11311yescharacteristic
212C2×C8C22×D11311yescharacteristic
213C4⋊C4—1131no—
214C4⋊C4—2262no—
215C4⋊C4C22×D11312yes—
216C22⋊C4—22no—
217C22⋊C4—1131no—
218C22⋊C4—1131no—
219C22⋊C4—2262no—
220C22⋊C4—2262no—
221C22⋊C4—2262no—
222C22⋊C4—2262no—
223C42C22×D11311yescharacteristic
224C23—22no—
225C23—1131no—
226C23—1131no—
227C23—9042no—
228C23—4524no—
229C23—4524no—
230C23—2262no—
231Q8—2262no—
232Q8—2262no—
233D4—22no—
234D4—9042no—
235D4—4524no—
236D4—4524no—
237D4—2262no—
238D4—2262no—
239D4—2262no—
240D4C2×D45214yes—
241C2×C4—22no—
242C2×C4—82no—
243C2×C4—1131no—
244C2×C4—1131no—
245C2×C4—4524no—
246C2×C4—2262no—
247C2×C4—2261no—
248C2×C4—2261no—
249C2×C4—2261no—
250C2×C4—2261no—
251C2×C4D4×D11311yescharacteristic
252C2×C4D4×D11311yescharacteristic
253C2×C4C23×D11311yescharacteristic
254C8—21no—
255C8—2261no—
256C8—2261no—
257C8C2×D45212yes—
258C22—24no—
259C22—42no—
260C22—42no—
261C22—1132no—
262C22—9048no—
263C22—4522no—
264C22—4522no—
265C22—4522no—
266C22—2261no—
267C22—2261no—
268C22—2261no—
269C22—2261no—
270C22—2261no—
271C22C2×D4×D11311yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—4522no—
276C4—2261no—
277C4—2261no—
278C4C22×D45211yescharacteristic
279C4#1681366811yescharacteristic
280C2—44no—
281C2—9042no—
282C2—4521no—
283C2—2262no—
284C2D4×D45211yescharacteristic
285C2#135×D11311yescharacteristic
286C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC4×D8×C113C2
socleC22×C113C22×D4
hypercenterC4×D8D113
hypocenterC113#3280
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16813641C2semidirect
2. C2×D8×D113C2semidirect
3. #20299243C2semidirect
4. #20298982C2semidirect
5. #20298840C2semidirect
6. #20298835C2semidirect
7. #20298813C2semidirect
8. #20298750C2semidirect
9. #20298744C2semidirect
10. C8×D452C2semidirect
11. C4×D8×C113C2semidirect
12. C2×#14268646C22semidirect
15. C2×Dic452C22semidirect
16. C2×#14268636C22semidirect
17. C2×#14268635C22semidirect
22. C2×C8×D113C22semidirect
23. #16813610C22semidirect
26. #16813597C22semidirect
31. C4⋊#11744751C22semidirect
32. #16813545C22semidirect
33. #16813542C22semidirect
35. #16813534C22semidirect
37. C4×D4×C113C22semidirect
38. #107×C113C22semidirect
39. #102×C113C22semidirect
40. C4×C8×C113C22semidirect
74. D8×C113D4semidirect
127. C2×D113#135semidirect
144. C113#3280semidirect
154. C4×D8D113semidirect
175. C4×D4C2×D113semidirect
177. #107C2×D113semidirect
181. #102C2×D113semidirect
184. C4×C8C2×D113semidirect
206. D8D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136412
C2×D8×D1132
#202992432
#202989822
#202988402
#202988352
#202988132
#202987502
#202987442
C8×D4522
C4×D8×C1132
#3280113