Finite Group Databasebeta

← #28400051

Subgroups — #28400051

Order 14464.

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

normal subgroups only

This group has 584 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×#16813649C212yesmaximal, complemented
2#127×D113C211yesmaximal, characteristic, complemented
3C4×#14268648C211yesmaximal, characteristic, complemented
4#20298798C211yesmaximal, characteristic, complemented
5#20298796C212yesmaximal, complemented
6#20298794C211yesmaximal, characteristic, complemented
7#20298792C212yesmaximal, complemented
8#20298790C211yesmaximal, characteristic, complemented
9#20298620C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11#460×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×D4×D113—21no—
14C2×D4×D113—21no—
15C2×D4×D113C2212yes—
16#16813649—28no—
17C2×#14268634C2212yescomplemented
18C2×D904C2212yescomplemented
19C2×#14268632C2212yescomplemented
20C2×#14268630C2212yes—
21#16813619C2211yescharacteristic
22#16813618—21no—
23#16813618—21no—
24#16813618C2212yes—
25Q8×Dic113C2211yescharacteristic, complemented
26C4×D452—21no—
27C4×D452C2211yescharacteristic, complemented
28#16813584—21no—
29#16813584C2211yescharacteristic, complemented
30#16813580—21no—
31#16813580C2211yescharacteristic
32C42×D113—21no—
33C42×D113C2211yescharacteristic
34C4⋊#11744751C2211yescharacteristic, complemented
35#16813551C2212yescomplemented
36#16813544C2212yescomplemented
37#16813543C2212yescomplemented
38#16813542C2212yescomplemented
39C2×SD16×C113C2212yescomplemented
40#127×C113C2211yescharacteristic
41C4×Q8×C113C2211yescharacteristic, complemented
42C4⋊C8×C113C2211yescharacteristic, complemented
43#102×C113C2212yescomplemented
44C23×D113—22no—
45#14268648—22no—
46#14268648D414yescomplemented
47C2×D452—21no—
48C2×D452—21no—
49C2×D452—21no—
50C2×D452C2312yes—
51C2×D452C2311yescharacteristic
52C2×C22⋊D113—22no—
53C2×C22⋊D113—22no—
54C2×C22⋊D113—22no—
55D4×D113—24no—
56D4×D113—24no—
57D4×D113—44no—
58D4×D113—44no—
59C2×C4×D113—21no—
60C2×C4×D113—21no—
61C2×C4×D113—21no—
62C2×C4×D113D411yescharacteristic
63C2×C4×D113D411yescharacteristic
64C2×C4×D113C2311yescharacteristic
65#14268634—24no—
66D904—24no—
67#14268632—24no—
68#14268630—24no—
69C2×#11744751C2312yes—
70C4⋊Dic113—21no—
71C4⋊Dic113C2311yescharacteristic
72#14268624—21no—
73#14268624—21no—
74#14268624—21no—
75C4×Dic113—21no—
76C4×Dic113—21no—
77C4×Dic113D411yescharacteristic
78C4×Dic113D411yescharacteristic
79C4×Dic113C2311yescharacteristic
80C2×Q8×C113C2311yescharacteristic
81C2×D4×C113—21no—
82C2×D4×C113—21no—
83C2×D4×C113C2312yes—
84SD16×C113—24no—
85C2×C8×C113C2312yes—
86C4⋊C4×C113—21no—
87C4⋊C4×C113C2311yescharacteristic
88C42×C113—21no—
89C42×C113C2311yescharacteristic
90C23×C113—22no—
91C22×D113—21no—
92C22×D113—22no—
93C22×D113—44no—
94C22×D113—44no—
95C22×D113—44no—
96C22×D113C2×D411yescharacteristic
97Q8×C113—21no—
98Q8×C113C2×D412yescomplemented
99D4×C113—22no—
100D4×C113—22no—
101D4×C113—42no—
102D4×C113—42no—
103C2×C4×C113—21no—
104C2×C4×C113—21no—
105C2×C4×C113C2×D411yescharacteristic
106C2×C4×C113C2×D411yescharacteristic
107C2×C4×C113C2411yescharacteristic
108C22⋊D113—44no—
109C22⋊D113—44no—
110C22⋊D113—44no—
111C2×Dic113—21no—
112C2×Dic113C2×D411yescharacteristic
113C2×Dic113C2×D411yescharacteristic
114C2×Dic113C2×D411yescharacteristic
115D452—24no—
116D452—22no—
117D452—21no—
118D452—22no—
119D452—42no—
120D452—42no—
121D452C2×D412yescomplemented
122C4×D113—22no—
123C4×D113—24no—
124C4×D113—22no—
125C4×D113—42no—
126C4×D113—42no—
127C4×D113C2×D412yes—
128C4×D113#4112yes—
129C8×C113—22no—
130#11744751—22no—
131C22×C113—42no—
132C22×C113—42no—
133C22×C113—42no—
134C22×C113C22×D411yescharacteristic
135C2×D113—21no—
136C2×D113—21no—
137C2×D113—22no—
138C2×D113—41no—
139C2×D113—41no—
140C2×D113—42no—
141C2×D113—42no—
142C2×D113—42no—
143C2×D113—88no—
144C2×D113#12112yes—
145C4×C113—22no—
146C4×C113—21no—
147C4×C113—41no—
148C4×C113AGL(1,ℤ/8)12yescomplemented
149C4×C113C22×D411yescharacteristic
150C4×C113C2×#4111yescharacteristic
151Dic113—21no—
152Dic113—41no—
153Dic113#12112yes—
154Dic113AGL(1,ℤ/8)12yescomplemented
155C2×C113—82no—
156C2×C113C2×#12111yescharacteristic
157C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
158C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
159D113—22no—
160D113—42no—
161D113—82no—
162#3038—1131nomaximal, Sylow
163C113#303811yescharacteristic, complemented, Sylow
164C2×AGL(1,ℤ/8)—1132no—
165C2×#127—1131no—
166C4×#41—1131no—
167#460—1132no—
168#460—1131no—
169#460D11311yescharacteristic, complemented
170#459—1131no—
171#459—1131no—
172#459—1132no—
173#423—1131no—
174#418—1132no—
175C2×#41—1131no—
176C22×D4—1132no—
177C22×D4—2261no—
178C22×D4—2261no—
179AGL(1,ℤ/8)—2268no—
180C2×SD16—1132no—
181C2×SD16C2×D11312yescomplemented
182C2×D8—1132no—
183C2×D8—1132no—
184C2×M16—1132no—
185#127—1132no—
186#127—1131no—
187#127—2261no—
188#127—2261no—
189#127C2×D11311yescharacteristic
190C4×Q8—1131no—
191C4×Q8C2×D11311yescharacteristic, complemented
192C4×D4—1131no—
193C4×D4—1131no—
194C4×D4—2261no—
195C4×D4—2261no—
196#117—1131no—
197#117—2261no—
198C2×C42—1131no—
199C2×C42—2261no—
200C4⋊C8—1132no—
201C4⋊C8—1131no—
202C4⋊C8C2×D11311yescharacteristic, complemented
203#102—1132no—
204#102—1132no—
205#102—1132no—
206#102C2×D11312yescomplemented
207C24—2262no—
208#41—1134no—
209#41—2262no—
210C2×Q8C22×D11311yescharacteristic
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—1131no—
214C2×D4—1132no—
215C2×D4—4524no—
216C2×D4—4524no—
217C2×D4—2261no—
218C2×D4—2264no—
219C2×D4—2264no—
220C2×D4—2262no—
221C2×D4—2262no—
222C2×D4—2262no—
223C2×D4—2261no—
224C2×D4—2261no—
225C2×D4C22×D11312yes—
226C22×C4—1131no—
227C22×C4—1131no—
228C22×C4—1131no—
229C22×C4—2261no—
230C22×C4—2261no—
231C22×C4—2261no—
232SD16—24no—
233SD16—2264no—
234D8—2264no—
235D8—2264no—
236M16—2264no—
237C2×C8—1132no—
238C2×C8C22×D11312yes—
239C4⋊C4—21no—
240C4⋊C4—1131no—
241C4⋊C4—2261no—
242C4⋊C4C22×D11311yescharacteristic
243C22⋊C4—2261no—
244C22⋊C4—2261no—
245C22⋊C4—2261no—
246C42—21no—
247C42—1131no—
248C42—1131no—
249C42—1131no—
250C42—2261no—
251C42—2261no—
252C42C22×D11311yescharacteristic
253C23—22no—
254C23—1131no—
255C23—4524no—
256C23—4524no—
257C23—4524no—
258C23—2262no—
259C23—2261no—
260Q8—21no—
261Q8D4×D11312yescomplemented
262D4—22no—
263D4—22no—
264D4—42no—
265D4—42no—
266D4—1132no—
267D4—4522no—
268D4—4524no—
269D4—4524no—
270D4—4524no—
271D4—4522no—
272D4—2264no—
273D4—2262no—
274D4—2262no—
275D4—2261no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—1131no—
279C2×C4—1131no—
280C2×C4—1132no—
281C2×C4—1132no—
282C2×C4—1131no—
283C2×C4—4522no—
284C2×C4—4522no—
285C2×C4—2262no—
286C2×C4—2264no—
287C2×C4—2261no—
288C2×C4—2262no—
289C2×C4D4×D11311yescharacteristic
290C2×C4D4×D11311yescharacteristic
291C2×C4C23×D11311yescharacteristic
292C8—22no—
293C8—2262no—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—1132no—
298C22—9048no—
299C22—4522no—
300C22—4522no—
301C22—4522no—
302C22—4521no—
303C22—4521no—
304C22—2262no—
305C22—2261no—
306C22—2261no—
307C22C2×D4×D11311yescharacteristic
308C4—22no—
309C4—21no—
310C4—41no—
311C4—1132no—
312C4—1132no—
313C4—4521no—
314C4—2261no—
315C4#1681364912yescomplemented
316C4C2×D4×D11311yescharacteristic
317C4#41×D11311yescharacteristic
318C2—82no—
319C2—9042no—
320C2—4522no—
321C2—2262no—
322C2#121×D11311yescharacteristic
323C2AGL(1,ℤ/8)×D11311yescharacteristic
324C2C2×#1681364911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#460×C113C2
socleC22×C113C22×D4
hypercenter#460D113
hypocenterC113#3038
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. #127×D113C2semidirect
3. C4×#14268648C2semidirect
4. #20298798C2semidirect
5. #20298796C2semidirect
6. #20298794C2semidirect
7. #20298792C2semidirect
8. #20298790C2semidirect
9. #20298620C2semidirect
10. #20298601C2semidirect
11. #460×C113C2semidirect
17. C2×#14268634C22semidirect
18. C2×D904C22semidirect
19. C2×#14268632C22semidirect
25. Q8×Dic113C22semidirect
27. C4×D452C22semidirect
29. #16813584C22semidirect
34. C4⋊#11744751C22semidirect
35. #16813551C22semidirect
36. #16813544C22semidirect
37. #16813543C22semidirect
38. #16813542C22semidirect
39. C2×SD16×C113C22semidirect
41. C4×Q8×C113C22semidirect
42. C4⋊C8×C113C22semidirect
43. #102×C113C22semidirect
46. #14268648D4semidirect
98. Q8×C113C2×D4semidirect
121. D452C2×D4semidirect
148. C4×C113AGL(1,ℤ/8)semidirect
154. Dic113AGL(1,ℤ/8)semidirect
163. C113#3038semidirect
169. #460D113semidirect
181. C2×SD16C2×D113semidirect
191. C4×Q8C2×D113semidirect
202. C4⋊C8C2×D113semidirect
206. #102C2×D113semidirect
261. Q8D4×D113semidirect
315. C4#16813649semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
#127×D1132
C4×#142686482
#202987982
#202987962
#202987942
#202987922
#202987902
#202986202
#202986012
#460×C1132
#3038113