Finite Group Databasebeta

← #28399815

Subgroups — #28399815

Order 14464.

758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 758 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C22×#14268648C211yesmaximal, characteristic, complemented
2C2×#16813647C211yesmaximal, characteristic, complemented
3#20299105C211yesmaximal, characteristic, complemented
4#20298759C214yesmaximal, complemented
5#20298742C214yesmaximal, complemented
6#20298607C211yesmaximal, characteristic, complemented
7#20298604C211yesmaximal, characteristic, complemented
8#20298561C211yesmaximal, characteristic, complemented
9C2×#137×C113C211yesmaximal, characteristic, complemented
10C2×#14268648—24no—
11C2×#14268648—22no—
12C2×#14268648—24no—
13C2×#14268648C2214yes—
14C22×D452—21no—
15C22×D452C2211yescharacteristic
16C22×C4×D113—21no—
17C22×C4×D113C2211yescharacteristic
18#16813647—24no—
19C2×#14268634C2212yescomplemented
20C2×#14268632C2212yescomplemented
21C2×#14268631C2211yescharacteristic
22#16813603—21no—
23#16813598C2212yescomplemented
24#16813593C2212yescomplemented
25#16813590—21no—
26C4×C22⋊D113—22no—
27#16813581C2211yescharacteristic
28#16813546C2214yescomplemented
29#16813544C2214yescomplemented
30#16813534C2214yescomplemented
31C2×#41×C113C2211yescharacteristic
32C22×Q8×C113C2211yescharacteristic
33#137×C113—24no—
34C2×Q16×C113C2212yescomplemented
35C2×SD16×C113C2212yescomplemented
36C2×M16×C113C2211yescharacteristic
37C23×D113—21no—
38C23×D113D411yescharacteristic
39#14268648—216no—
40#14268648—28no—
41#14268648—28no—
42C2×D452—28no—
43C2×D452—24no—
44C2×D452—21no—
45C2×D452—22no—
46C2×D452D414yescomplemented
47C2×D452C2312yes—
48C2×C22⋊D113—22no—
49C22×Dic113D411yescharacteristic
50C2×C4×D113—28no—
51C2×C4×D113—22no—
52C2×C4×D113—22no—
53C2×C4×D113—24no—
54C2×C4×D113D412yes—
55C2×C4×D113C2312yes—
56#14268634—24no—
57#14268632—24no—
58#14268631—22no—
59C2×#11744751C2312yes—
60C4⋊Dic113C2312yes—
61#14268626—22no—
62C22⋊Dic113—21no—
63C22⋊Dic113—22no—
64#14268624—22no—
65C4×Dic113—21no—
66#41×C113—22no—
67#41×C113—22no—
68C2×Q8×C113—22no—
69C2×Q8×C113—21no—
70C2×Q8×C113D414yescomplemented
71C2×Q8×C113C2311yescharacteristic
72C2×Q8×C113C2312yes—
73C2×D4×C113—21no—
74C2×D4×C113C2311yescharacteristic
75C22×C4×C113—21no—
76C22×C4×C113—21no—
77C22×C4×C113C2311yescharacteristic
78Q16×C113—24no—
79SD16×C113—24no—
80M16×C113—22no—
81C2×C8×C113C2312yes—
82C23×C113—21no—
83C23×C113C2×D411yescharacteristic
84C22×D113—22no—
85C22×D113—24no—
86C22×D113—22no—
87C22×D113—42no—
88C22×D113—44no—
89C22×D113C2×D412yes—
90Q8×C113—24no—
91Q8×C113—22no—
92Q8×C113—21no—
93Q8×C113—21no—
94Q8×C113C2×D414yes—
95D4×C113—21no—
96D4×C113—21no—
97D4×C113—42no—
98C2×C4×C113—24no—
99C2×C4×C113—22no—
100C2×C4×C113—21no—
101C2×C4×C113—42no—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2×D412yes—
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2411yescharacteristic
106C22⋊D113—44no—
107C2×Dic113—22no—
108C2×Dic113—22no—
109C2×Dic113C2×D412yes—
110D452—216no—
111D452—24no—
112D452—22no—
113D452C2×D414yes—
114C4×D113—216no—
115C4×D113—24no—
116C4×D113—22no—
117C4×D113—22no—
118C8×C113—22no—
119#11744751—22no—
120C22×C113—22no—
121C22×C113—41no—
122C22×C113—42no—
123C22×C113#12012yes—
124C22×C113C22×D411yescharacteristic
125C2×D113—22no—
126C2×D113—24no—
127C2×D113—22no—
128C2×D113—22no—
129C2×D113—44no—
130C2×D113—48no—
131C2×D113—44no—
132C4×C113—24no—
133C4×C113—41no—
134C4×C113#12012yes—
135C4×C113C22×D411yescharacteristic
136C4×C113C22×D411yescharacteristic
137Dic113—22no—
138Dic113—42no—
139C2×C113—22no—
140C2×C113—81no—
141C2×C113C2×#12011yescharacteristic
142C2×C113#57512yes—
143D113—42no—
144D113—44no—
145#3005—1131nomaximal, Sylow
146C113#300511yescharacteristic, complemented, Sylow
147C22×#41—1131no—
148C2×#137D11311yescharacteristic, complemented
149C2×AGL(1,ℤ/8)—1131no—
150#525—1131no—
151#452—1134no—
152#449—1134no—
153#419—1131no—
154#418—1131no—
155#407—1131no—
156C2×#41—1134no—
157C2×#41—2262no—
158C2×#41—2264no—
159C2×#41—2264no—
160C2×#41C2×D11311yescharacteristic
161C22×Q8C2×D11311yescharacteristic
162C22×D4—1131no—
163C22×D4—2261no—
164C23×C4—1131no—
165C23×C4—2261no—
166#137—24no—
167AGL(1,ℤ/8)—2264no—
168C2×Q16C2×D11312yescomplemented
169C2×SD16—1132no—
170C2×SD16C2×D11312yescomplemented
171C2×D8—1132no—
172C2×M16—1131no—
173C2×M16C2×D11311yescharacteristic
174#123—2261no—
175C22⋊Q8—1132no—
176#121—1132no—
177#120—2261no—
178C4×D4—2262no—
179#117—1131no—
180#103—1134no—
181#102—1134no—
182C22⋊C8—1134no—
183C24—1131no—
184C24—2261no—
185#41—22no—
186#41—22no—
187#41—2268no—
188#41—22616no—
189#41—2268no—
190C2×Q8—22no—
191C2×Q8—21no—
192C2×Q8C22⋊D11314yescomplemented
193C2×Q8C22×D11311yescharacteristic
194C2×Q8C22×D11312yes—
195C2×D4—21no—
196C2×D4—1134no—
197C2×D4—1132no—
198C2×D4—2264no—
199C2×D4—2268no—
200C2×D4—2262no—
201C2×D4—2261no—
202C2×D4—2262no—
203C2×D4C22×D11311yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—1131no—
207C22×C4—1132no—
208C22×C4—1132no—
209C22×C4—2264no—
210C22×C4—2268no—
211C22×C4—2262no—
212C22×C4—2262no—
213C22×C4C22×D11311yescharacteristic
214Q16—24no—
215SD16—24no—
216SD16—2264no—
217D8—2264no—
218M16—22no—
219M16—2262no—
220C2×C8—1132no—
221C2×C8C22×D11312yes—
222C4⋊C4—1132no—
223C4⋊C4—2262no—
224C22⋊C4—2262no—
225C22⋊C4—2262no—
226C22⋊C4—2261no—
227C42—2261no—
228C23—21no—
229C23—1132no—
230C23—4524no—
231C23—4522no—
232C23—2264no—
233C23—2262no—
234C23—2262no—
235C23D4×D11311yescharacteristic
236Q8—24no—
237Q8—22no—
238Q8—21no—
239Q8—21no—
240Q8C2×C22⋊D11314yes—
241D4—21no—
242D4—21no—
243D4—42no—
244D4—1134no—
245D4—4524no—
246D4—22616no—
247D4—2264no—
248D4—2262no—
249C2×C4—24no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—42no—
253C2×C4—1132no—
254C2×C4—22616no—
255C2×C4—2262no—
256C2×C4—2262no—
257C2×C4—2264no—
258C2×C4—2262no—
259C2×C4—2262no—
260C2×C4D4×D11311yescharacteristic
261C2×C4D4×D11312yes—
262C2×C4C2×C22⋊D11312yes—
263C2×C4C23×D11311yescharacteristic
264C8—22no—
265C8—2262no—
266C22—22no—
267C22—41no—
268C22—42no—
269C22—4528no—
270C22—4524no—
271C22—4524no—
272C22—2264no—
273C22—2262no—
274C22—2262no—
275C22—2262no—
276C22#1681359012yes—
277C22C2×D4×D11311yescharacteristic
278C4—24no—
279C4—41no—
280C4—4522no—
281C4—2262no—
282C4#1681359012yes—
283C4C2×D4×D11311yescharacteristic
284C4C22×C22⋊D11311yescharacteristic
285C2—22no—
286C2—81no—
287C2—4524no—
288C2—4522no—
289C2C2×#1681359011yescharacteristic
290C2#2029939712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#137×C113C2
socleC22×C113C22×D4
hypercenterC2×#137D113
hypocenterC113#3005
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#14268648C2semidirect
2. C2×#16813647C2semidirect
3. #20299105C2semidirect
4. #20298759C2semidirect
5. #20298742C2semidirect
6. #20298607C2semidirect
7. #20298604C2semidirect
8. #20298561C2semidirect
9. C2×#137×C113C2semidirect
19. C2×#14268634C22semidirect
20. C2×#14268632C22semidirect
23. #16813598C22semidirect
24. #16813593C22semidirect
28. #16813546C22semidirect
29. #16813544C22semidirect
30. #16813534C22semidirect
34. C2×Q16×C113C22semidirect
35. C2×SD16×C113C22semidirect
46. C2×D452D4semidirect
70. C2×Q8×C113D4semidirect
146. C113#3005semidirect
148. C2×#137D113semidirect
168. C2×Q16C2×D113semidirect
170. C2×SD16C2×D113semidirect
192. C2×Q8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686482
C2×#168136472
#202991052
#202987592
#202987422
#202986072
#202986042
#202985612
C2×#137×C1132
#3005113