Finite Group Databasebeta

← #28400152

Subgroups — #28400152

Order 14464.

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

normal subgroups only

This group has 520 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
1C2×#16813642C211yesmaximal, characteristic, complemented
2C23×#11744751C211yesmaximal, characteristic, complemented
3#20299109C211yesmaximal, characteristic, complemented
4#20298837C212yesmaximal, complemented
5#20298832C212yesmaximal, complemented
6#20298829C212yesmaximal, complemented
7#20298825C212yesmaximal, complemented
8#20298634C211yesmaximal, characteristic, complemented
9#20298594C211yesmaximal, characteristic, complemented
10#20298592C211yesmaximal, characteristic, complemented
11#525×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13#16813642—24no—
14C2×#14268637C2211yescharacteristic, complemented
15C2×#14268635C2211yescharacteristic, complemented
16C2×#14268634C2211yescharacteristic, complemented
17C2×#14268632C2211yescharacteristic, complemented
18C22×#11744751—24no—
19C22×#11744751C2212yes—
20C22×#11744751C2212yes—
21C22×#11744751C2211yescharacteristic
22C22×#11744751C2211yescharacteristic
23#16813605—21no—
24#16813601C2212yes—
25#16813596C2212yes—
26#16813591—21no—
27C4×C22⋊D113—22no—
28#16813581C2211yescharacteristic
29#16813555C2212yescomplemented
30#16813553C2212yescomplemented
31#16813546C2212yescomplemented
32#16813545C2212yescomplemented
33#16813543C2212yescomplemented
34#16813542C2212yescomplemented
35C2×#41×C113C2211yescharacteristic
36C23×C4×C113C2211yescharacteristic
37#123×C113—21no—
38C22⋊Q8×C113C2212yes—
39#121×C113C2212yes—
40#120×C113—21no—
41C4×D4×C113—22no—
42#117×C113C2211yescharacteristic
43#14268647—22no—
44#14268647—22no—
45C2×Dic226C2311yescharacteristic
46C2×D452C2311yescharacteristic
47C2×C22⋊D113—22no—
48C2×C22⋊D113—21no—
49C2×C4×D113—21no—
50#14268637—22no—
51#14268635—22no—
52#14268634—22no—
53#14268632—22no—
54C2×#11744751—22no—
55C2×#11744751—24no—
56C2×#11744751—24no—
57C2×#11744751D414yescomplemented
58C2×#11744751C2312yes—
59C2×#11744751C2311yescharacteristic
60C2×#11744751C2311yescharacteristic
61C4⋊Dic113C2312yes—
62#14268626—22no—
63C22⋊Dic113—21no—
64C22⋊Dic113—22no—
65#14268624—22no—
66C4×Dic113—21no—
67C24×C113D411yescharacteristic
68#41×C113—22no—
69#41×C113—22no—
70C2×Q8×C113C2311yescharacteristic
71C2×D4×C113—22no—
72C2×D4×C113—21no—
73C2×D4×C113C2311yescharacteristic
74C22×C4×C113—22no—
75C22×C4×C113—22no—
76C22×C4×C113—21no—
77C22×C4×C113D412yes—
78C22×C4×C113D411yescharacteristic
79C22×C4×C113C2312yes—
80C22×C4×C113C2311yescharacteristic
81C4⋊C4×C113—22no—
82C4⋊C4×C113C2312yes—
83C22⋊C4×C113—21no—
84C22⋊C4×C113—22no—
85C22⋊C4×C113—22no—
86C42×C113—21no—
87C23×C113—22no—
88C23×C113—24no—
89C23×C113—21no—
90C23×C113C2×D411yescharacteristic
91C23×C113C2×D412yes—
92C22×D113—21no—
93Q8×C113—21no—
94Q8×C113—21no—
95D4×C113—21no—
96D4×C113—21no—
97D4×C113—42no—
98D4×C113—44no—
99C2×C4×C113—22no—
100C2×C4×C113—24no—
101C2×C4×C113—22no—
102C2×C4×C113—22no—
103C2×C4×C113—22no—
104C2×C4×C113—21no—
105C2×C4×C113—42no—
106C2×C4×C113C2×D412yes—
107C2×C4×C113C2×D412yes—
108C2×C4×C113C2×D411yescharacteristic
109C2×C4×C113#4112yes—
110C2×C4×C113C2411yescharacteristic
111C22⋊D113—42no—
112C22⋊D113—44no—
113C2×Dic113—22no—
114C2×Dic113—21no—
115D452—21no—
116D452—21no—
117C4×D113—42no—
118Dic226—21no—
119Dic226—21no—
120#11744751—22no—
121#11744751C2×D412yes—
122#11744751C2×D412yes—
123C22×C113—28no—
124C22×C113—22no—
125C22×C113—22no—
126C22×C113—22no—
127C22×C113—41no—
128C22×C113—42no—
129C22×C113#12112yes—
130C22×C113#13514yescomplemented
131C22×C113C22×D411yescharacteristic
132C2×D113—41no—
133C2×D113—42no—
134C4×C113—22no—
135C4×C113—41no—
136C4×C113—42no—
137C4×C113#12112yes—
138C4×C113C22×D411yescharacteristic
139C4×C113C2×#4111yescharacteristic
140Dic113—41no—
141Dic113—42no—
142C2×C113—22no—
143C2×C113—24no—
144C2×C113—81no—
145C2×C113C2×#12111yescharacteristic
146C2×C113C2×#13512yes—
147D113—81no—
148#3050—1131nomaximal, Sylow
149C113#305011yescharacteristic, complemented, Sylow
150C2×#135—1131no—
151C23×C8—1131no—
152#525—1131no—
153#525D11311yescharacteristic, complemented
154#467—1132no—
155#466—1132no—
156#465—1132no—
157#465—1132no—
158#427—1131no—
159#416—1131no—
160#416—1131no—
161C2×#41—1131no—
162C2×#41C2×D11311yescharacteristic
163C23×C4C2×D11311yescharacteristic
164#135—2264no—
165C2×Q16—1131no—
166C2×SD16—1131no—
167C2×SD16—1131no—
168C2×D8—1131no—
169C22×C8—1131no—
170C22×C8—1131no—
171C22×C8—1132no—
172C22×C8—1132no—
173C22×C8—2264no—
174#123—21no—
175#123—2261no—
176C22⋊Q8—1132no—
177C22⋊Q8C2×D11312yes—
178#121—1132no—
179#121C2×D11312yes—
180#120—21no—
181#120—2261no—
182C4×D4—22no—
183C4×D4—2262no—
184#117—1131no—
185#117C2×D11311yescharacteristic
186#107—1132no—
187#106—1132no—
188#103—1132no—
189#103—1132no—
190#102—1132no—
191#102—1132no—
192C24C22⋊D11311yescharacteristic
193#41—22no—
194#41—22no—
195#41—2262no—
196#41—2262no—
197C2×Q8—1131no—
198C2×Q8C22×D11311yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—1131no—
202C2×D4—2262no—
203C2×D4—2261no—
204C2×D4C22×D11311yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—2261no—
209C22×C4C22⋊D11311yescharacteristic
210C22×C4C22⋊D11312yes—
211C22×C4C22×D11312yes—
212C22×C4C22×D11311yescharacteristic
213Q16—2262no—
214SD16—2262no—
215SD16—2262no—
216D8—2262no—
217C2×C8—1134no—
218C2×C8—1131no—
219C2×C8—1131no—
220C2×C8—1132no—
221C2×C8—2264no—
222C2×C8—2264no—
223C2×C8—2262no—
224C4⋊C4—22no—
225C4⋊C4—1132no—
226C4⋊C4—2262no—
227C4⋊C4C22×D11312yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—2261no—
232C22⋊C4—2262no—
233C22⋊C4—2262no—
234C42—21no—
235C42—2261no—
236C23—22no—
237C23—24no—
238C23—21no—
239C23—2261no—
240C23C2×C22⋊D11311yescharacteristic
241C23C2×C22⋊D11312yes—
242Q8—21no—
243Q8—21no—
244Q8—2261no—
245Q8—2261no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—44no—
250D4—4522no—
251D4—4524no—
252D4—2261no—
253D4—2261no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—4522no—
262C2×C4—2262no—
263C2×C4—2261no—
264C2×C4D4×D11312yes—
265C2×C4C2×C22⋊D11312yes—
266C2×C4C2×C22⋊D11311yescharacteristic
267C2×C4#1426864612yes—
268C2×C4C23×D11311yescharacteristic
269C8—1132no—
270C8—1132no—
271C8—2262no—
272C22—28no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—42no—
278C22—4521no—
279C22—4522no—
280C22#1681359412yes—
281C22#1681364214yescomplemented
282C22C22×C22⋊D11311yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—4521no—
287C4—4522no—
288C4#1681359412yes—
289C4C2×D4×D11311yescharacteristic
290C4C2×#1426864611yescharacteristic
291C2—22no—
292C2—24no—
293C2—81no—
294C2—9041no—
295C2C2×#1681359411yescharacteristic
296C2C2×#1681364212yes—
subgroupG/H
centerC2×C4C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#525×C113C2
socleC22×C113C22×D4
hypercenter#525D113
hypocenterC113#3050
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#16813642C2semidirect
2. C23×#11744751C2semidirect
3. #20299109C2semidirect
4. #20298837C2semidirect
5. #20298832C2semidirect
6. #20298829C2semidirect
7. #20298825C2semidirect
8. #20298634C2semidirect
9. #20298594C2semidirect
10. #20298592C2semidirect
11. #525×C113C2semidirect
14. C2×#14268637C22semidirect
15. C2×#14268635C22semidirect
16. C2×#14268634C22semidirect
17. C2×#14268632C22semidirect
29. #16813555C22semidirect
30. #16813553C22semidirect
31. #16813546C22semidirect
32. #16813545C22semidirect
33. #16813543C22semidirect
34. #16813542C22semidirect
57. C2×#11744751D4semidirect
130. C22×C113#135semidirect
149. C113#3050semidirect
153. #525D113semidirect
281. C22#16813642semidirect

Maximal subgroups

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

subgroupindex
C2×#168136422
C23×#117447512
#202991092
#202988372
#202988322
#202988292
#202988252
#202986342
#202985942
#202985922
#525×C1132
#3050113