Finite Group Databasebeta

← #28400675

Subgroups — #28400675

Order 14464.

444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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#20299153C211yesmaximal, characteristic, complemented
2C4×D4×D113C211yesmaximal, characteristic
3#20298935C212yesmaximal, complemented
4#20298875C211yesmaximal, characteristic, complemented
5#20298804C211yesmaximal, characteristic, complemented
6#20298803C211yesmaximal, characteristic, complemented
7#20298750C212yesmaximal
8#20298697C212yesmaximal, complemented
9#20298695C212yesmaximal, complemented
10#20298654C211yesmaximal, characteristic, complemented
11#474×C113C211yesmaximal, characteristic, complemented
12C2×D4×D113C2211yescharacteristic
13C22×C4×D113—21no—
14C2×#14268636C2212yes—
15C2×#14268635C2212yes—
16#16813622C2211yescharacteristic, complemented
17#16813613—21no—
18#16813602C2212yes—
19#16813598—21no—
20Q8×Dic113—21no—
21#16813587C2212yescomplemented
22C4×D452C2211yescharacteristic
23D4×Dic113C2211yescharacteristic
24#16813584C2211yescharacteristic
25C4×C22⋊D113—21no—
26#16813582—21no—
27#16813580—21no—
28C4⋊C4×D113C2211yescharacteristic
29C22⋊C4×D113—21no—
30C42×D113C2211yescharacteristic
31#16813555C2212yescomplemented
32C4⋊#11744751C2211yescharacteristic, complemented
33#16813547C2212yescomplemented
34#16813545C2212yescomplemented
35#16813542C2212yes—
36#16813534C2212yes—
37#16813532C2212yescomplemented
38C4⋊Q8×C113C2211yescharacteristic, complemented
39C4×D4×C113C2211yescharacteristic
40#107×C113C2212yescomplemented
41C4⋊C8×C113C2211yescharacteristic, complemented
42#102×C113C2212yes—
43C23×D113—21no—
44C2×Dic226C2312yes—
45C2×D452C2311yescharacteristic
46C2×C22⋊D113—21no—
47D4×D113—22no—
48D4×D113—22no—
49C22×Dic113—21no—
50C2×C4×D113—21no—
51C2×C4×D113—21no—
52C2×C4×D113—21no—
53C2×C4×D113—44no—
54C2×C4×D113D411yescharacteristic
55C2×C4×D113D411yescharacteristic
56C2×C4×D113C2311yescharacteristic
57#14268636—24no—
58#14268635—24no—
59C2×#11744751C2312yes—
60C4⋊Dic113—21no—
61C4⋊Dic113—21no—
62C4⋊Dic113—22no—
63C4⋊Dic113C2311yescharacteristic
64#14268626—21no—
65#14268626—22no—
66C22⋊Dic113—21no—
67#14268624—22no—
68#14268624—21no—
69#14268624—21no—
70C4×Dic113—22no—
71C4×Dic113D411yescharacteristic
72C4×Dic113D411yescharacteristic
73C4×Dic113C2311yescharacteristic
74C2×Q8×C113—21no—
75C2×D4×C113C2311yescharacteristic
76C22×C4×C113—21no—
77C2×C8×C113C2312yes—
78C4⋊C4×C113—21no—
79C4⋊C4×C113C2311yescharacteristic
80C4⋊C4×C113C2312yes—
81C22⋊C4×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113—21no—
84C22×D113—24no—
85C22×D113—21no—
86C22×D113—42no—
87C22×D113—42no—
88C22×D113C2×D411yescharacteristic
89Q8×C113—42no—
90D4×C113—21no—
91D4×C113#4112yes—
92C2×C4×C113—21no—
93C2×C4×C113—22no—
94C2×C4×C113—42no—
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2411yescharacteristic
98C22⋊D113—24no—
99C2×Dic113—22no—
100C2×Dic113—21no—
101C2×Dic113—42no—
102C2×Dic113C2×D411yescharacteristic
103C2×Dic113C2×D411yescharacteristic
104C2×Dic113C2×D411yescharacteristic
105D452—21no—
106D452#4112yes—
107C4×D113—22no—
108C4×D113—22no—
109C4×D113—21no—
110C4×D113—21no—
111C4×D113—42no—
112C4×D113—42no—
113C4×D113—42no—
114Dic226—22no—
115Dic226—22no—
116C8×C113—22no—
117#11744751—22no—
118C22×C113—22no—
119C22×C113—41no—
120C22×C113—41no—
121C22×C113C22×D411yescharacteristic
122C2×D113—21no—
123C2×D113—21no—
124C2×D113—22no—
125C2×D113—48no—
126C2×D113—41no—
127C2×D113—41no—
128C2×D113#13712yes—
129C4×C113—21no—
130C4×C113—41no—
131C4×C113—42no—
132C4×C113AGL(1,ℤ/8)12yes—
133C4×C113C2×#4111yescharacteristic
134C4×C113C2×#4111yescharacteristic
135Dic113—21no—
136Dic113—21no—
137Dic113—21no—
138Dic113—42no—
139Dic113—41no—
140C2×C113—42no—
141C2×C113#52511yescharacteristic
142C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
143C2×C113C2×#13711yescharacteristic
144D113—22no—
145D113—42no—
146#3110—1131nomaximal, Sylow
147C113#311011yescharacteristic, complemented, Sylow
148#533—1131no—
149C2×C4×D4—1131no—
150#484—1132no—
151#474—1131no—
152#474D11311yescharacteristic, complemented
153#461—1131no—
154#461—1131no—
155#450—1132no—
156#440—1132no—
157#440—1132no—
158#432—1131no—
159C22×D4—1131no—
160C23×C4—2261no—
161C2×SD16—1132no—
162C2×SD16—1132no—
163C4⋊Q8—1131no—
164C4⋊Q8C2×D11311yescharacteristic, complemented
165#125—2261no—
166C22⋊Q8—1132no—
167C22⋊Q8—2261no—
168C4×Q8—1132no—
169C4×Q8—2261no—
170C4×D4—1131no—
171C4×D4—1131no—
172C4×D4—1131no—
173C4×D4—2261no—
174C4×D4—2261no—
175C4×D4C2×D11311yescharacteristic
176#117—2261no—
177C2×C4⋊C4—1131no—
178C2×C22⋊C4—2261no—
179C2×C42—1131no—
180#107—1132no—
181#107C2×D11312yescomplemented
182C4⋊C8—1131no—
183C4⋊C8C2×D11311yescharacteristic, complemented
184#103—1132no—
185#103—1132no—
186#102—1132no—
187#102C2×D11312yes—
188C22⋊C8—1132no—
189#97—1132no—
190C24—2261no—
191C2×Q8—21no—
192C2×Q8—1132no—
193C2×D4—1131no—
194C2×D4—2261no—
195C2×D4—2262no—
196C2×D4—2262no—
197C2×D4C22×D11311yescharacteristic
198C22×C4—21no—
199C22×C4—1131no—
200C22×C4—1131no—
201C22×C4—1131no—
202C22×C4—4524no—
203C22×C4—2261no—
204C22×C4—2261no—
205C22×C4—2261no—
206C22×C4—2261no—
207SD16—2264no—
208SD16—2264no—
209C2×C8—1132no—
210C2×C8C22×D11312yes—
211C4⋊C4—21no—
212C4⋊C4—1131no—
213C4⋊C4—2261no—
214C4⋊C4—2262no—
215C4⋊C4—2262no—
216C4⋊C4—2261no—
217C4⋊C4—2261no—
218C4⋊C4C22×D11312yes—
219C4⋊C4C22×D11311yescharacteristic
220C22⋊C4—21no—
221C22⋊C4—2261no—
222C22⋊C4—2262no—
223C22⋊C4—2261no—
224C22⋊C4—2261no—
225C42—1131no—
226C42—1131no—
227C42—1131no—
228C42—2262no—
229C42C22×D11311yescharacteristic
230C23—21no—
231C23—1131no—
232C23—4522no—
233C23—4522no—
234C23—2264no—
235C23—2261no—
236Q8—42no—
237Q8—2262no—
238Q8—2262no—
239D4—21no—
240D4—1132no—
241D4—2264no—
242D4—2261no—
243D4#1426864812yes—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—1131no—
248C2×C4—1131no—
249C2×C4—1131no—
250C2×C4—4522no—
251C2×C4—4522no—
252C2×C4—4522no—
253C2×C4—4522no—
254C2×C4—2262no—
255C2×C4—2262no—
256C2×C4—2261no—
257C2×C4—2262no—
258C2×C4—2261no—
259C2×C4—2261no—
260C2×C4D4×D11311yescharacteristic
261C2×C4D4×D11311yescharacteristic
262C2×C4C23×D11311yescharacteristic
263C8—22no—
264C8—2262no—
265C22—22no—
266C22—41no—
267C22—41no—
268C22—1132no—
269C22—4528no—
270C22—4521no—
271C22—4521no—
272C22—2262no—
273C22—2261no—
274C22—2261no—
275C22C2×D4×D11311yescharacteristic
276C4—21no—
277C4—41no—
278C4—42no—
279C4—4522no—
280C4—4521no—
281C4—2261no—
282C4—2261no—
283C4—2261no—
284C4#1681364612yes—
285C4#41×D11311yescharacteristic
286C4C2×#1426864811yescharacteristic
287C2—42no—
288C2—4522no—
289C2—2262no—
290C2#2029911111yescharacteristic
291C2C2×#1681364611yescharacteristic
292C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#474×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
hypercenter#474D113
hypocenterC113#3110
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #20299153C2semidirect
3. #20298935C2semidirect
4. #20298875C2semidirect
5. #20298804C2semidirect
6. #20298803C2semidirect
8. #20298697C2semidirect
9. #20298695C2semidirect
10. #20298654C2semidirect
11. #474×C113C2semidirect
16. #16813622C22semidirect
21. #16813587C22semidirect
31. #16813555C22semidirect
32. C4⋊#11744751C22semidirect
33. #16813547C22semidirect
34. #16813545C22semidirect
37. #16813532C22semidirect
38. C4⋊Q8×C113C22semidirect
40. #107×C113C22semidirect
41. C4⋊C8×C113C22semidirect
147. C113#3110semidirect
152. #474D113semidirect
164. C4⋊Q8C2×D113semidirect
181. #107C2×D113semidirect
183. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991532
C4×D4×D1132
#202989352
#202988752
#202988042
#202988032
#202987502
#202986972
#202986952
#202986542
#474×C1132
#3110113