Finite Group Databasebeta

← #28400182

Subgroups — #28400182

Order 14464.

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

normal subgroups only

This group has 500 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×#16813642C211yesmaximal, characteristic, complemented
2C22×#14268630C211yesmaximal, characteristic, complemented
3#20299110C211yesmaximal, characteristic, complemented
4#20299105C211yesmaximal, characteristic, complemented
5#20298855C212yesmaximal, complemented
6#20298850C212yesmaximal, complemented
7#20298847C212yesmaximal, complemented
8#20298843C212yesmaximal, complemented
9#20298634C211yesmaximal, characteristic, complemented
10#20298595C211yesmaximal, characteristic, complemented
11#416×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C22×C4×D113C2211yescharacteristic
14#16813642—24no—
15C2×#14268637C2211yescharacteristic, complemented
16C2×#14268635C2211yescharacteristic, complemented
17C2×#14268634C2211yescharacteristic, complemented
18C2×#14268632C2211yescharacteristic, complemented
19C2×#14268630—24no—
20C2×#14268630C2212yes—
21C2×#14268630C2212yes—
22C22×#11744751C2211yescharacteristic
23#16813606—21no—
24#16813603—21no—
25#16813602C2212yes—
26#16813598C2212yes—
27#16813597C2212yes—
28#16813593C2212yes—
29#16813592—21no—
30#16813590—21no—
31C4×D452—22no—
32C4×C22⋊D113—22no—
33#16813581C2211yescharacteristic
34#16813555C2212yescomplemented
35#16813553C2212yescomplemented
36#16813547C2212yescomplemented
37#16813544C2212yescomplemented
38C2×#41×C113C2211yescharacteristic
39C22×C8×C113C2211yescharacteristic
40#117×C113C2211yescharacteristic
41#103×C113C2212yescomplemented
42#102×C113C2212yescomplemented
43C23×D113D411yescharacteristic
44#14268647—22no—
45#14268647—22no—
46C2×Dic226C2311yescharacteristic
47C2×D452—22no—
48C2×D452C2311yescharacteristic
49C2×C22⋊D113—21no—
50C2×C22⋊D113—22no—
51C22×Dic113D411yescharacteristic
52C2×C4×D113—22no—
53C2×C4×D113—22no—
54C2×C4×D113—21no—
55C2×C4×D113D412yes—
56C2×C4×D113C2312yes—
57#14268637—22no—
58#14268635—22no—
59#14268634—22no—
60#14268632—22no—
61#14268630—24no—
62#14268630—24no—
63C2×#11744751D414yescomplemented
64C2×#11744751C2311yescharacteristic
65C2×#11744751C2311yescharacteristic
66C4⋊Dic113—22no—
67C4⋊Dic113C2312yes—
68#14268626—22no—
69C22⋊Dic113—21no—
70C22⋊Dic113—22no—
71#14268624—22no—
72#14268624—22no—
73#14268624—22no—
74C4×Dic113—21no—
75#41×C113—22no—
76#41×C113—22no—
77C2×Q8×C113C2311yescharacteristic
78C2×D4×C113—21no—
79C2×D4×C113C2311yescharacteristic
80C22×C4×C113—21no—
81C22×C4×C113C2311yescharacteristic
82C2×C8×C113—22no—
83C2×C8×C113C2312yes—
84C4⋊C4×C113C2312yes—
85C22⋊C4×C113—21no—
86C42×C113—21no—
87C23×C113—21no—
88C23×C113C2×D411yescharacteristic
89C22×D113—22no—
90C22×D113—21no—
91C22×D113—42no—
92C22×D113C2×D412yes—
93Q8×C113—21no—
94Q8×C113—21no—
95D4×C113—21no—
96D4×C113—21no—
97D4×C113—42no—
98C2×C4×C113—22no—
99C2×C4×C113—21no—
100C2×C4×C113—42no—
101C2×C4×C113C2×D412yes—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113#4112yes—
104C2×C4×C113C2411yescharacteristic
105C22⋊D113—44no—
106C22⋊D113—42no—
107C2×Dic113—22no—
108C2×Dic113—22no—
109C2×Dic113—21no—
110C2×Dic113C2×D412yes—
111D452—21no—
112D452—21no—
113D452—44no—
114C4×D113—24no—
115C4×D113—22no—
116C4×D113—22no—
117C4×D113—42no—
118Dic226—21no—
119Dic226—21no—
120C8×C113—22no—
121#11744751C2×D412yes—
122#11744751C2×D412yes—
123C22×C113—22no—
124C22×C113—41no—
125C22×C113—42no—
126C22×C113#12112yes—
127C22×C113C22×D411yescharacteristic
128C2×D113—22no—
129C2×D113—22no—
130C2×D113—22no—
131C2×D113—44no—
132C2×D113—41no—
133C2×D113—42no—
134C4×C113—41no—
135C4×C113—42no—
136C4×C113#12112yes—
137C4×C113C22×D411yescharacteristic
138C4×C113C2×#4111yescharacteristic
139Dic113—22no—
140Dic113—41no—
141Dic113—42no—
142C2×C113—22no—
143C2×C113—81no—
144C2×C113C2×#12111yescharacteristic
145C2×C113#57512yes—
146D113—42no—
147D113—81no—
148#3054—1131nomaximal, Sylow
149C113#305411yescharacteristic, complemented, Sylow
150C2×#135—1131no—
151C22×M16—1131no—
152#525—1131no—
153#525—1131no—
154#470—1132no—
155#469—1132no—
156#468—1132no—
157#468—1132no—
158#427—1131no—
159#416—1131no—
160#416D11311yescharacteristic, complemented
161C2×#41—1131no—
162C2×#41C2×D11311yescharacteristic
163C23×C4—1131no—
164#135—2264no—
165C2×Q16—1131no—
166C2×SD16—1131no—
167C2×SD16—1131no—
168C2×D8—1131no—
169C2×M16—1132no—
170C2×M16—1132no—
171C2×M16—2264no—
172C22×C8—1131no—
173C22×C8C2×D11311yescharacteristic
174#123—2261no—
175#123—2261no—
176C22⋊Q8—1132no—
177C22⋊Q8—1132no—
178#121—1132no—
179#121—1132no—
180#120—2261no—
181#120—2261no—
182C4×D4—2262no—
183C4×D4—2262no—
184#117—1131no—
185#117C2×D11311yescharacteristic
186#107—1132no—
187#106—1132no—
188#103—1132no—
189#103C2×D11312yescomplemented
190#102—1132no—
191#102C2×D11312yescomplemented
192C24—1131no—
193#41—22no—
194#41—22no—
195#41—2262no—
196#41—2262no—
197C2×Q8—1131no—
198C2×Q8C22×D11311yescharacteristic
199C2×D4—21no—
200C2×D4—1131no—
201C2×D4—2262no—
202C2×D4—2262no—
203C2×D4—2261no—
204C2×D4C22×D11311yescharacteristic
205C22×C4—21no—
206C22×C4—1131no—
207C22×C4—1132no—
208C22×C4—1132no—
209C22×C4—2261no—
210C22×C4—2262no—
211C22×C4—2262no—
212C22×C4C22×D11311yescharacteristic
213Q16—2262no—
214SD16—2262no—
215SD16—2262no—
216D8—2262no—
217M16—2264no—
218M16—2264no—
219C2×C8—22no—
220C2×C8—1134no—
221C2×C8—1131no—
222C2×C8—1131no—
223C2×C8C22×D11312yes—
224C4⋊C4—1132no—
225C4⋊C4—2262no—
226C4⋊C4—2262no—
227C4⋊C4C22×D11312yes—
228C22⋊C4—21no—
229C22⋊C4—2262no—
230C22⋊C4—2262no—
231C22⋊C4—2262no—
232C22⋊C4—2262no—
233C22⋊C4—2261no—
234C42—21no—
235C42—2261no—
236C23—21no—
237C23—1132no—
238C23—4522no—
239C23—2261no—
240C23—2262no—
241C23D4×D11311yescharacteristic
242Q8—21no—
243Q8—21no—
244Q8—2261no—
245Q8—2261no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—4524no—
250D4—4524no—
251D4—4522no—
252D4—2261no—
253D4—2261no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—42no—
257C2×C4—1132no—
258C2×C4—4522no—
259C2×C4—2262no—
260C2×C4—2261no—
261C2×C4—2262no—
262C2×C4—2264no—
263C2×C4—2262no—
264C2×C4—2262no—
265C2×C4D4×D11312yes—
266C2×C4D4×D11311yescharacteristic
267C2×C4#1426864712yes—
268C2×C4C23×D11311yescharacteristic
269C8—22no—
270C8—1132no—
271C8—1132no—
272C22—22no—
273C22—41no—
274C22—42no—
275C22—4524no—
276C22—4521no—
277C22—4522no—
278C22—2262no—
279C22—2262no—
280C22—2262no—
281C22#1681359512yes—
282C22C2×D4×D11311yescharacteristic
283C4—41no—
284C4—42no—
285C4—4521no—
286C4—4522no—
287C4—2262no—
288C4#1681359512yes—
289C4C2×D4×D11311yescharacteristic
290C4C2×#1426864711yescharacteristic
291C2—22no—
292C2—81no—
293C2—9041no—
294C2—4522no—
295C2C2×#1681359511yescharacteristic
296C2#2029939512yes—
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
hypercenter#416D113
hypocenterC113#3054
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C2×#16813642C2semidirect
2. C22×#14268630C2semidirect
3. #20299110C2semidirect
4. #20299105C2semidirect
5. #20298855C2semidirect
6. #20298850C2semidirect
7. #20298847C2semidirect
8. #20298843C2semidirect
9. #20298634C2semidirect
10. #20298595C2semidirect
11. #416×C113C2semidirect
15. C2×#14268637C22semidirect
16. C2×#14268635C22semidirect
17. C2×#14268634C22semidirect
18. C2×#14268632C22semidirect
34. #16813555C22semidirect
35. #16813553C22semidirect
36. #16813547C22semidirect
37. #16813544C22semidirect
41. #103×C113C22semidirect
42. #102×C113C22semidirect
63. C2×#11744751D4semidirect
149. C113#3054semidirect
160. #416D113semidirect
189. #103C2×D113semidirect
191. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136422
C22×#142686302
#202991102
#202991052
#202988552
#202988502
#202988472
#202988432
#202986342
#202985952
#416×C1132
#3054113