Finite Group Databasebeta

← #28402189

Subgroups — #28402189

Order 14464.

556 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 125 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×#16813649C212yesmaximal, complemented
2#20299270C211yesmaximal, characteristic, complemented
3#20299233C211yesmaximal, characteristic, complemented
4#20298974C211yesmaximal, characteristic, complemented
5#20298850C212yesmaximal, complemented
6#20298794C211yesmaximal, characteristic, complemented
7#20298742C212yesmaximal, complemented
8#20298733C212yesmaximal, complemented
9C4×#14268634C211yesmaximal, characteristic, complemented
10#20298675C211yesmaximal, characteristic, complemented
11#460×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2212yescomplemented
13C2×D4×D113—21no—
14C2×D4×D113C2212yes—
15#16813649—28no—
16C2×#14268634C2211yescharacteristic
17C2×D904C2212yes—
18C2×#14268632C2212yescomplemented
19C2×#14268632C2212yescomplemented
20C2×#14268630C2212yescomplemented
21#16813619—21no—
22#16813619C2211yescharacteristic, complemented
23#16813597—22no—
24#16813597C2212yescomplemented
25#16813593—21no—
26#16813593C2212yes—
27#16813590—22no—
28C4×D452—21no—
29C4×D452C2211yescharacteristic
30C4×D452C2211yescharacteristic
31#16813553C2211yescharacteristic, complemented
32#16813546C2211yescharacteristic, complemented
33#16813544C2212yescomplemented
34#16813542C2211yescharacteristic
35#16813534C2212yescomplemented
36C4×#11744751C2211yescharacteristic, complemented
37C2×SD16×C113C2212yescomplemented
38#127×C113C2211yescharacteristic
39C4×Q8×C113C2211yescharacteristic, complemented
40C4⋊C8×C113C2211yescharacteristic, complemented
41#102×C113C2212yescomplemented
42C23×D113—22no—
43#14268648—24no—
44#14268648—42no—
45C2×D452—22no—
46C2×D452—21no—
47C2×D452—22no—
48C2×D452—21no—
49C2×D452D411yescharacteristic
50C2×D452C2312yes—
51C2×D452C2311yescharacteristic
52C2×C22⋊D113—22no—
53C2×C22⋊D113—22no—
54D4×D113—24no—
55D4×D113—42no—
56D4×D113—44no—
57C2×C4×D113—21no—
58C2×C4×D113—22no—
59C2×C4×D113C2312yes—
60#14268634D414yescomplemented
61D904—24no—
62#14268632—24no—
63#14268632—42no—
64#14268630—24no—
65C2×#11744751C2311yescharacteristic
66C2×#11744751C2311yescharacteristic
67C4⋊Dic113D411yescharacteristic
68C4⋊Dic113C2311yescharacteristic
69C22⋊Dic113—22no—
70#14268624—21no—
71#14268624—22no—
72#14268624D412yes—
73C2×Q8×C113C2311yescharacteristic
74C2×D4×C113—21no—
75C2×D4×C113—21no—
76C2×D4×C113C2312yes—
77SD16×C113—24no—
78C2×C8×C113C2312yes—
79C4⋊C4×C113—21no—
80C4⋊C4×C113C2311yescharacteristic
81C42×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113—22no—
84C22×D113—21no—
85C22×D113—22no—
86C22×D113—44no—
87C22×D113—44no—
88C22×D113—82no—
89C22×D113C2×D412yes—
90Q8×C113—21no—
91Q8×C113C2×D412yescomplemented
92D4×C113—22no—
93D4×C113—22no—
94D4×C113—42no—
95D4×C113—81no—
96C2×C4×C113—21no—
97C2×C4×C113—21no—
98C2×C4×C113C2×D411yescharacteristic
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2411yescharacteristic
101C22⋊D113—44no—
102C22⋊D113—44no—
103C2×Dic113—21no—
104C2×Dic113C2×D412yes—
105D452—22no—
106D452—22no—
107D452—21no—
108D452—22no—
109D452—44no—
110D452—42no—
111D452—81no—
112D452—82no—
113D452C2×D412yes—
114C4×D113—22no—
115C4×D113—22no—
116C4×D113—44no—
117C4×D113—42no—
118C8×C113—22no—
119#11744751—21no—
120#11744751C2×D412yescomplemented
121C22×C113—42no—
122C22×C113—42no—
123C22×C113—42no—
124C22×C113C22×D411yescharacteristic
125C2×D113—22no—
126C2×D113—22no—
127C2×D113—22no—
128C2×D113—22no—
129C2×D113—41no—
130C2×D113—41no—
131C2×D113—42no—
132C2×D113—42no—
133C2×D113—42no—
134C2×D113—88no—
135C4×C113—22no—
136C4×C113—21no—
137C4×C113—41no—
138C4×C113AGL(1,ℤ/8)12yescomplemented
139C4×C113C22×D411yescharacteristic
140C4×C113H(5,𝔽2)11yescharacteristic
141Dic113—22no—
142Dic113—41no—
143C2×C113—82no—
144C2×C113D4211yescharacteristic
145C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C113#57611yescharacteristic
147D113—42no—
148D113—42no—
149D113—82no—
150#3274—1131nomaximal, Sylow
151C113#327411yescharacteristic, complemented, Sylow
152C2×AGL(1,ℤ/8)—1132no—
153#550—1131no—
154D42—1131no—
155#493—1131no—
156#469—1132no—
157#460D11311yescharacteristic, complemented
158#459—1131no—
159#449—1132no—
160#447—1132no—
161C4×SD16—1131no—
162#436—1131no—
163C2×#41—1132no—
164C22×D4—1132no—
165C22×D4—2261no—
166AGL(1,ℤ/8)—2268no—
167C2×SD16—1131no—
168C2×SD16C2×D11312yescomplemented
169C2×D8—1132no—
170C2×D8—1132no—
171C2×D8—1132no—
172C2×M16—1132no—
173#127—1131no—
174#127—2261no—
175#127C2×D11311yescharacteristic
176#121—1132no—
177#121—1132no—
178#121—2262no—
179#121—2261no—
180#120—2262no—
181C4×Q8C2×D11311yescharacteristic, complemented
182C4×D4—1131no—
183C4×D4—1131no—
184C4×D4—2261no—
185#106—1131no—
186C4⋊C8C2×D11311yescharacteristic, complemented
187#103—1131no—
188#102—1132no—
189#102—1131no—
190#102C2×D11312yescomplemented
191C22⋊C8—1132no—
192C4×C8—1131no—
193C24—2262no—
194#41—4522no—
195#41—2264no—
196C2×Q8C22×D11311yescharacteristic
197C2×D4—21no—
198C2×D4—21no—
199C2×D4—1131no—
200C2×D4—1131no—
201C2×D4—1132no—
202C2×D4—4524no—
203C2×D4—4522no—
204C2×D4—2262no—
205C2×D4—2262no—
206C2×D4—2262no—
207C2×D4—2264no—
208C2×D4—2262no—
209C2×D4—2261no—
210C2×D4—2261no—
211C2×D4C22×D11312yes—
212C22×C4—1132no—
213C22×C4—2262no—
214C22×C4—2261no—
215SD16—24no—
216SD16—1134no—
217D8—4522no—
218D8—2264no—
219D8—2264no—
220M16—2264no—
221C2×C8—1131no—
222C2×C8—1131no—
223C2×C8C22×D11312yes—
224C4⋊C4—21no—
225C4⋊C4—1131no—
226C4⋊C4—1131no—
227C4⋊C4C22×D11311yescharacteristic
228C22⋊C4—1132no—
229C22⋊C4—2262no—
230C22⋊C4—2262no—
231C22⋊C4—2261no—
232C42—21no—
233C42C22×D11311yescharacteristic
234C23—22no—
235C23—1132no—
236C23—9042no—
237C23—4524no—
238C23—4524no—
239C23—2262no—
240C23—2261no—
241Q8—21no—
242Q8D4×D11312yescomplemented
243D4—22no—
244D4—22no—
245D4—42no—
246D4—81no—
247D4—1132no—
248D4—9041no—
249D4—9042no—
250D4—4524no—
251D4—4524no—
252D4—4524no—
253D4—4522no—
254D4—2262no—
255D4—2262no—
256D4—2262no—
257D4—2261no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—1132no—
261C2×C4—4524no—
262C2×C4—4522no—
263C2×C4—2261no—
264C2×C4—2262no—
265C2×C4—2262no—
266C2×C4D4×D11311yescharacteristic
267C2×C4D4×D11311yescharacteristic
268C2×C4C23×D11311yescharacteristic
269C8—22no—
270C8—1132no—
271C8—2261no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—9048no—
276C22—4522no—
277C22—4522no—
278C22—4522no—
279C22—4521no—
280C22—4521no—
281C22—2262no—
282C22—2262no—
283C22—2262no—
284C22—2262no—
285C22C2×D4×D11311yescharacteristic
286C4—21no—
287C4—22no—
288C4—41no—
289C4—4521no—
290C4—2262no—
291C4#1681364912yescomplemented
292C4C2×D4×D11311yescharacteristic
293C4#1681366811yescharacteristic
294C2—82no—
295C2—9042no—
296C2—4522no—
297C2—4522no—
298C2#2029923211yescharacteristic
299C2C2×#1681364911yescharacteristic
300C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
hypercenter#460D113
hypocenterC113#3274
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. #20299270C2semidirect
3. #20299233C2semidirect
4. #20298974C2semidirect
5. #20298850C2semidirect
6. #20298794C2semidirect
7. #20298742C2semidirect
8. #20298733C2semidirect
9. C4×#14268634C2semidirect
10. #20298675C2semidirect
11. #460×C113C2semidirect
12. C2×#14268648C22semidirect
18. C2×#14268632C22semidirect
19. C2×#14268632C22semidirect
20. C2×#14268630C22semidirect
22. #16813619C22semidirect
24. #16813597C22semidirect
31. #16813553C22semidirect
32. #16813546C22semidirect
33. #16813544C22semidirect
35. #16813534C22semidirect
36. C4×#11744751C22semidirect
37. C2×SD16×C113C22semidirect
39. C4×Q8×C113C22semidirect
40. C4⋊C8×C113C22semidirect
41. #102×C113C22semidirect
60. #14268634D4semidirect
91. Q8×C113C2×D4semidirect
120. #11744751C2×D4semidirect
138. C4×C113AGL(1,ℤ/8)semidirect
151. C113#3274semidirect
157. #460D113semidirect
168. C2×SD16C2×D113semidirect
181. C4×Q8C2×D113semidirect
186. C4⋊C8C2×D113semidirect
190. #102C2×D113semidirect
242. Q8D4×D113semidirect
291. C4#16813649semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
#202992702
#202992332
#202989742
#202988502
#202987942
#202987422
#202987332
C4×#142686342
#202986752
#460×C1132
#3274113