Finite Group Databasebeta

← #28402804

Subgroups — #28402804

Order 14464.

448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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
1#20299322C211yesmaximal, characteristic, complemented
2#20299233C211yesmaximal, characteristic
3#20298921C212yesmaximal, complemented
4#20298875C211yesmaximal, characteristic, complemented
5#20298843C212yesmaximal, complemented
6#20298795C211yesmaximal, characteristic, complemented
7#20298750C212yesmaximal, complemented
8C4×#14268636C211yesmaximal, characteristic, complemented
9#20298677C211yesmaximal, characteristic, complemented
10#20298601C212yesmaximal, complemented
11#486×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113—21no—
13C2×D4×D113C2212yes—
14C2×#14268636C2211yescharacteristic
15C2×#14268635C2212yescomplemented
16C2×#14268630C2212yescomplemented
17#16813617—22no—
18#16813611—21no—
19#16813602C2212yescomplemented
20#16813593—21no—
21#16813593C2212yes—
22#16813590—22no—
23Q8×Dic113—21no—
24C4×Dic226C2211yescharacteristic, complemented
25C4×D452C2211yescharacteristic
26C4×D452C2211yescharacteristic
27#16813580C2212yescomplemented
28#16813555C2212yescomplemented
29#16813554C2211yescharacteristic, complemented
30C4⋊#11744751C2211yescharacteristic, complemented
31#16813547C2211yescharacteristic, complemented
32#16813544C2211yescharacteristic
33#16813543C2212yescomplemented
34#16813542C2212yes—
35#16813534C2212yescomplemented
36C4⋊Q8×C113C2211yescharacteristic, complemented
37#127×C113C2211yescharacteristic
38#102×C113C2212yescomplemented
39#102×C113C2212yescomplemented
40C4×C8×C113C2211yescharacteristic, complemented
41C23×D113—22no—
42C2×Dic226C2311yescharacteristic
43C2×D452D411yescharacteristic
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—22no—
46C2×C22⋊D113—22no—
47D4×D113—24no—
48D4×D113—42no—
49D4×D113—44no—
50C2×C4×D113—21no—
51C2×C4×D113C2312yes—
52#14268636—22no—
53#14268635—42no—
54#14268630—42no—
55C2×#11744751C2312yes—
56C4⋊Dic113—22no—
57C4⋊Dic113D411yescharacteristic
58C4⋊Dic113C2311yescharacteristic
59C4⋊Dic113C2311yescharacteristic
60#14268626—21no—
61C22⋊Dic113—22no—
62#14268624—22no—
63#14268624—22no—
64#14268624—21no—
65#14268624D412yes—
66C4×Dic113—21no—
67C4×Dic113—22no—
68C2×Q8×C113—21no—
69C2×D4×C113—21no—
70C2×D4×C113—21no—
71C2×D4×C113C2312yes—
72C2×C8×C113C2311yescharacteristic
73C2×C8×C113C2311yescharacteristic
74C4⋊C4×C113—21no—
75C4⋊C4×C113C2312yes—
76C42×C113C2311yescharacteristic
77C23×C113—22no—
78C22×D113—21no—
79C22×D113—44no—
80C22×D113—44no—
81C22×D113—82no—
82C22×D113C2×D412yes—
83Q8×C113—42no—
84D4×C113—22no—
85D4×C113—22no—
86D4×C113—42no—
87D4×C113—81no—
88C2×C4×C113—22no—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2411yescharacteristic
92C22⋊D113—44no—
93C22⋊D113—44no—
94C2×Dic113—21no—
95C2×Dic113—21no—
96C2×Dic113—21no—
97C2×Dic113C2×D412yes—
98D452—22no—
99D452—21no—
100D452#4112yes—
101C4×D113—22no—
102C4×D113—22no—
103C4×D113—42no—
104Dic226—21no—
105Dic226—21no—
106C8×C113—21no—
107C8×C113—21no—
108#11744751—22no—
109C22×C113—42no—
110C22×C113—42no—
111C22×C113—42no—
112C22×C113C22×D411yescharacteristic
113C2×D113—22no—
114C2×D113—22no—
115C2×D113—22no—
116C2×D113—22no—
117C2×D113—41no—
118C2×D113—41no—
119C2×D113—88no—
120C4×C113—21no—
121C4×C113—42no—
122C4×C113AGL(1,ℤ/8)12yes—
123C4×C113C2×#4111yescharacteristic
124C4×C113H(5,𝔽2)11yescharacteristic
125Dic113—22no—
126Dic113—41no—
127Dic113—41no—
128Dic113—41no—
129C2×C113—82no—
130C2×C113#54611yescharacteristic
131C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C113#57711yescharacteristic
133D113—42no—
134D113—42no—
135#3324—1131nomaximal, Sylow
136C113#332411yescharacteristic, complemented, Sylow
137#556—1131no—
138D42—1131no—
139#486D11311yescharacteristic, complemented
140#482—1132no—
141#474—1131no—
142#468—1132no—
143#460—1131no—
144#450—1132no—
145C4×SD16—1131no—
146#436—1131no—
147#418—1132no—
148C22×D4—1132no—
149C22×D4—2261no—
150C2×SD16—1132no—
151C2×SD16—1131no—
152C2×M16—1132no—
153C4⋊Q8C2×D11311yescharacteristic, complemented
154#127C2×D11311yescharacteristic
155#126—2262no—
156#124—2261no—
157C22⋊Q8—1132no—
158#121—1132no—
159#121—2261no—
160#120—2262no—
161C4×Q8—1131no—
162C4×Q8—2261no—
163C4×D4—1131no—
164C4×D4—1131no—
165#117—1132no—
166#107—1132no—
167#106—1131no—
168C4⋊C8—1131no—
169#103—1131no—
170#102—1132no—
171#102—1131no—
172#102—1132no—
173#102C2×D11312yescomplemented
174#102C2×D11312yescomplemented
175C22⋊C8—1132no—
176C4×C8C2×D11311yescharacteristic, complemented
177C24—2262no—
178C2×Q8—21no—
179C2×Q8—1131no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—1131no—
183C2×D4—1131no—
184C2×D4—4524no—
185C2×D4—4522no—
186C2×D4—2262no—
187C2×D4—2264no—
188C2×D4—2262no—
189C2×D4C22×D11312yes—
190C22×C4—1132no—
191C22×C4—2261no—
192SD16—4522no—
193SD16—2262no—
194M16—4522no—
195C2×C8—1132no—
196C2×C8C22×D11311yescharacteristic
197C2×C8C22×D11311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—1131no—
200C4⋊C4—1131no—
201C4⋊C4—1131no—
202C4⋊C4—2262no—
203C4⋊C4—2261no—
204C4⋊C4C22×D11312yes—
205C22⋊C4—1132no—
206C22⋊C4—2262no—
207C22⋊C4—2262no—
208C22⋊C4—2262no—
209C22⋊C4—2261no—
210C42—2262no—
211C42—2261no—
212C42C22×D11311yescharacteristic
213C23—22no—
214C23—1132no—
215C23—9042no—
216C23—4524no—
217C23—4524no—
218C23—2261no—
219Q8—42no—
220Q8—2261no—
221Q8—2261no—
222D4—22no—
223D4—22no—
224D4—42no—
225D4—81no—
226D4—1132no—
227D4—4524no—
228D4—4524no—
229D4—2262no—
230D4—2261no—
231C2×C4—22no—
232C2×C4—1132no—
233C2×C4—4522no—
234C2×C4—2261no—
235C2×C4—2261no—
236C2×C4—2261no—
237C2×C4—2262no—
238C2×C4—2262no—
239C2×C4D4×D11311yescharacteristic
240C2×C4D4×D11311yescharacteristic
241C2×C4C23×D11311yescharacteristic
242C8—21no—
243C8—21no—
244C8—2262no—
245C22—42no—
246C22—42no—
247C22—42no—
248C22—9048no—
249C22—4521no—
250C22—4521no—
251C22—2262no—
252C22—2262no—
253C22—2262no—
254C22—2262no—
255C22C2×D4×D11311yescharacteristic
256C4—21no—
257C4—42no—
258C4—4521no—
259C4—4521no—
260C4—4521no—
261C4—2262no—
262C4#1681364612yes—
263C4#41×D11311yescharacteristic
264C4#1681366811yescharacteristic
265C2—82no—
266C2—4522no—
267C2—4522no—
268C2#2029924111yescharacteristic
269C2C2×#1681364611yescharacteristic
270C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#486×C113C2
socleC22×C113C22×D4
prime radical#20299233C2
hypercenter#486D113
hypocenterC113#3324
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #20299322C2semidirect
3. #20298921C2semidirect
4. #20298875C2semidirect
5. #20298843C2semidirect
6. #20298795C2semidirect
7. #20298750C2semidirect
8. C4×#14268636C2semidirect
9. #20298677C2semidirect
10. #20298601C2semidirect
11. #486×C113C2semidirect
15. C2×#14268635C22semidirect
16. C2×#14268630C22semidirect
19. #16813602C22semidirect
24. C4×Dic226C22semidirect
27. #16813580C22semidirect
28. #16813555C22semidirect
29. #16813554C22semidirect
30. C4⋊#11744751C22semidirect
31. #16813547C22semidirect
33. #16813543C22semidirect
35. #16813534C22semidirect
36. C4⋊Q8×C113C22semidirect
38. #102×C113C22semidirect
39. #102×C113C22semidirect
40. C4×C8×C113C22semidirect
136. C113#3324semidirect
139. #486D113semidirect
153. C4⋊Q8C2×D113semidirect
173. #102C2×D113semidirect
174. #102C2×D113semidirect
176. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993222
#202992332
#202989212
#202988752
#202988432
#202987952
#202987502
C4×#142686362
#202986772
#202986012
#486×C1132
#3324113