Finite Group Databasebeta

← #28402259

Subgroups — #28402259

Order 14464.

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

normal subgroups only

This group has 526 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×#16813641C211yesmaximal, characteristic, complemented
2#20299242C212yesmaximal, complemented
3#20298981C211yesmaximal, characteristic, complemented
4#20298839C211yesmaximal, characteristic, complemented
5#20298831C211yesmaximal, characteristic, complemented
6#20298811C212yesmaximal, complemented
7#20298749C212yesmaximal, complemented
8#20298740C212yesmaximal, complemented
9D8×Dic113C211yesmaximal, characteristic, complemented
10C8×C22⋊D113C211yesmaximal, characteristic, complemented
11C22×D8×C113C211yesmaximal, characteristic, complemented
12C2×#14268646C2212yescomplemented
13#16813641—24no—
14C2×Dic452C2211yescharacteristic, complemented
15C2×#14268635C2212yescomplemented
16C2×#14268635C2212yescomplemented
17C2×C8×D113C2211yescharacteristic, complemented
18#16813609C2212yescomplemented
19#16813603—22no—
20#16813601C2212yes—
21#16813594—22no—
22#16813593C2212yescomplemented
23#16813591—22no—
24D4×Dic113C2212yescomplemented
25C4×C22⋊D113C2211yescharacteristic
26C2×C22⋊Dic113—22no—
27#16813556C2211yescharacteristic, complemented
28#16813551C2211yescharacteristic, complemented
29#16813547C2212yescomplemented
30#16813543C2212yescomplemented
31#16813543C2212yescomplemented
32C22⋊#11744751C2211yescharacteristic
33#16813534C2211yescharacteristic, complemented
34C8×Dic113C2211yescharacteristic, complemented
35C22×D4×C113C2212yes—
36C2×D8×C113—24no—
37C2×D8×C113C2212yes—
38C2×D8×C113C2211yescharacteristic
39C2×D8×C113C2211yescharacteristic
40C22×C8×C113C2211yescharacteristic
41#14268646—24no—
42#14268646—42no—
43C2×Dic226C2312yes—
44C2×C22⋊D113—22no—
45C2×C22⋊D113—22no—
46C2×C22⋊D113D411yescharacteristic
47C22×Dic113—22no—
48C22×Dic113—22no—
49C2×C4×D113C2311yescharacteristic
50Dic452—22no—
51#14268635—24no—
52#14268635—42no—
53C2×#11744751C2311yescharacteristic
54C2×#11744751C2311yescharacteristic
55C8×D113—22no—
56C4⋊Dic113C2312yes—
57#14268626—22no—
58#14268626D411yescharacteristic
59C22⋊Dic113—22no—
60C22⋊Dic113—22no—
61C22⋊Dic113—22no—
62C22⋊Dic113—22no—
63C22⋊Dic113—22no—
64C22⋊Dic113D411yescharacteristic
65#14268624D411yescharacteristic
66C4×Dic113C2311yescharacteristic
67C24×C113—22no—
68C2×D4×C113—24no—
69C2×D4×C113—22no—
70C2×D4×C113—42no—
71C2×D4×C113C2312yes—
72C2×D4×C113C2312yes—
73C22×C4×C113C2311yescharacteristic
74D8×C113—24no—
75D8×C113—22no—
76D8×C113D414yescomplemented
77C2×C8×C113—22no—
78C2×C8×C113C2311yescharacteristic
79C2×C8×C113C2311yescharacteristic
80C23×C113—22no—
81C23×C113—22no—
82C23×C113—44no—
83C23×C113—44no—
84C23×C113—82no—
85C23×C113C2×D411yescharacteristic
86C22×D113C2×D411yescharacteristic
87D4×C113—22no—
88D4×C113—22no—
89D4×C113—22no—
90D4×C113—44no—
91D4×C113C2×D414yes—
92C2×C4×C113—21no—
93C2×C4×C113—21no—
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2411yescharacteristic
96C22⋊D113—22no—
97C22⋊D113—44no—
98C22⋊D113—82no—
99C2×Dic113—22no—
100C2×Dic113—22no—
101C2×Dic113—44no—
102C2×Dic113—82no—
103C2×Dic113C2×D411yescharacteristic
104C2×Dic113C2×D411yescharacteristic
105C2×Dic113C2×D411yescharacteristic
106C4×D113—21no—
107C4×D113—21no—
108Dic226—22no—
109Dic226—22no—
110C8×C113—21no—
111C8×C113C2×D412yes—
112#11744751—21no—
113#11744751—21no—
114C22×C113—21no—
115C22×C113—21no—
116C22×C113—24no—
117C22×C113—42no—
118C22×C113—42no—
119C22×C113—42no—
120C22×C113—42no—
121C22×C113—42no—
122C22×C113—88no—
123C22×C113#13512yescomplemented
124C22×C113C22×D411yescharacteristic
125C2×D113—21no—
126C2×D113—21no—
127C2×D113—21no—
128C4×C113—21no—
129C4×C113C22×D411yescharacteristic
130C4×C113H(5,𝔽2)11yescharacteristic
131Dic113—21no—
132Dic113—21no—
133Dic113—21no—
134Dic113—42no—
135Dic113—42no—
136C2×C113—22no—
137C2×C113—44no—
138C2×C113—82no—
139C2×C113D4211yescharacteristic
140C2×C113C2×#13511yescharacteristic
141C2×C113#57611yescharacteristic
142D113—41no—
143#3280—1131nomaximal, Sylow
144C113#328011yescharacteristic, complemented, Sylow
145C2×#135—1131no—
146C22×D8D11311yescharacteristic, complemented
147#546—1132no—
148#495—1131no—
149#467—1131no—
150#466—1131no—
151#463—1132no—
152#450—1132no—
153#449—1132no—
154C4×D8—1131no—
155C8×D4—1131no—
156C2×#41—1132no—
157C22×D4C2×D11312yes—
158#135—2264no—
159C2×Q16—1131no—
160C2×SD16—1132no—
161C2×SD16—1132no—
162C2×D8—24no—
163C2×D8C2×D11312yes—
164C2×D8C2×D11311yescharacteristic
165C2×D8C2×D11311yescharacteristic
166C22×C8—1131no—
167C22×C8C2×D11311yescharacteristic
168#124—1132no—
169#123—2262no—
170C22⋊Q8—1132no—
171#121—1132no—
172#121—2262no—
173#120—2262no—
174C4×D4—1131no—
175C4×D4—1132no—
176C2×C22⋊C4—2262no—
177#107—1131no—
178C4⋊C8—1131no—
179#103—1132no—
180#102—1132no—
181#102—1132no—
182C22⋊C8—1131no—
183C22⋊C8—1131no—
184C4×C8—1131no—
185C24—22no—
186#41—4522no—
187#41—2264no—
188C2×Q8—1132no—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—42no—
192C2×D4—1131no—
193C2×D4—2262no—
194C2×D4—2262no—
195C2×D4C22×D11312yes—
196C2×D4C22×D11312yes—
197C22×C4—1131no—
198C22×C4—2262no—
199C22×C4—2262no—
200C22×C4C22×D11311yescharacteristic
201Q16—2262no—
202SD16—4522no—
203SD16—2264no—
204D8—24no—
205D8—22no—
206D8C22⋊D11314yescomplemented
207C2×C8—22no—
208C2×C8—1131no—
209C2×C8—1131no—
210C2×C8—2262no—
211C2×C8C22×D11311yescharacteristic
212C2×C8C22×D11311yescharacteristic
213C4⋊C4—1131no—
214C4⋊C4—1132no—
215C4⋊C4—2262no—
216C22⋊C4—1131no—
217C22⋊C4—1131no—
218C22⋊C4—2262no—
219C22⋊C4—2262no—
220C22⋊C4—2262no—
221C22⋊C4—2262no—
222C22⋊C4—2262no—
223C42—1131no—
224C23—22no—
225C23—22no—
226C23—44no—
227C23—44no—
228C23—82no—
229C23—1131no—
230C23D4×D11311yescharacteristic
231Q8—2262no—
232Q8—2262no—
233D4—22no—
234D4—22no—
235D4—22no—
236D4—44no—
237D4—9042no—
238D4—4524no—
239D4—2262no—
240D4C2×C22⋊D11314yes—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—1131no—
244C2×C4—1131no—
245C2×C4—1131no—
246C2×C4—9042no—
247C2×C4—4524no—
248C2×C4—2262no—
249C2×C4—2262no—
250C2×C4—2261no—
251C2×C4—2261no—
252C2×C4D4×D11311yescharacteristic
253C2×C4C23×D11311yescharacteristic
254C8—21no—
255C8—2261no—
256C8—2261no—
257C8C2×C22⋊D11312yes—
258C22—21no—
259C22—21no—
260C22—24no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—88no—
267C22—2261no—
268C22—2261no—
269C22—2261no—
270C22#1681364112yescomplemented
271C22C2×D4×D11311yescharacteristic
272C4—21no—
273C4—4522no—
274C4—4522no—
275C4—2261no—
276C4—2261no—
277C4—2261no—
278C4C22×C22⋊D11311yescharacteristic
279C4#1681366711yescharacteristic
280C2—22no—
281C2—44no—
282C2—82no—
283C2—4521no—
284C2D4×C22⋊D11311yescharacteristic
285C2C2×#1681364111yescharacteristic
286C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×D8×C113C2
socleC22×C113C22×D4
hypercenterC22×D8D113
hypocenterC113#3280
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16813641C2semidirect
2. #20299242C2semidirect
3. #20298981C2semidirect
4. #20298839C2semidirect
5. #20298831C2semidirect
6. #20298811C2semidirect
7. #20298749C2semidirect
8. #20298740C2semidirect
9. D8×Dic113C2semidirect
10. C8×C22⋊D113C2semidirect
11. C22×D8×C113C2semidirect
12. C2×#14268646C22semidirect
14. C2×Dic452C22semidirect
15. C2×#14268635C22semidirect
16. C2×#14268635C22semidirect
17. C2×C8×D113C22semidirect
18. #16813609C22semidirect
22. #16813593C22semidirect
24. D4×Dic113C22semidirect
27. #16813556C22semidirect
28. #16813551C22semidirect
29. #16813547C22semidirect
30. #16813543C22semidirect
31. #16813543C22semidirect
33. #16813534C22semidirect
34. C8×Dic113C22semidirect
76. D8×C113D4semidirect
123. C22×C113#135semidirect
144. C113#3280semidirect
146. C22×D8D113semidirect
206. D8C22⋊D113semidirect
270. C22#16813641semidirect

Maximal subgroups

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

subgroupindex
C2×#168136412
#202992422
#202989812
#202988392
#202988312
#202988112
#202987492
#202987402
D8×Dic1132
C8×C22⋊D1132
C22×D8×C1132
#3280113