Finite Group Databasebeta

← #14739005

Subgroups — #14739005

Order 2816.

728 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078076C211yesmaximal, characteristic
2C2×#10622696C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic, complemented
4#13068050C214yesmaximal, complemented
5#13068002C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067265C211yesmaximal, characteristic, complemented
9C11×#3226C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67002—21no—
13C22×#4325—21no—
14C2×C4×D44C2211yescharacteristic
15C11×#500C2212yescomplemented
16C11×#486C2212yescomplemented
17C11×#480—22no—
18C11×#474—22no—
19C11×#431C2211yescharacteristic
20#10622845—21no—
21C2×#66899—21no—
22#10622696—22no—
23#10622696C2214yes—
24#10622696C2212yes—
25#10622685C2212yes—
26#10622670—22no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622447—22no—
31D11×C22⋊C8—22no—
32C8×D44C2214yes—
33#10622185C2212yescomplemented
34#10622185C2214yescomplemented
35#10622182C2212yescomplemented
36#10622096C2214yescomplemented
37C2×C11×#41—21no—
38C22×Q8×C11—21no—
39C22×D44D411yescharacteristic
40C22×C4×D11—21no—
41C11×C4⋊Q8—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8C2311yescharacteristic
45C11×C4⋊Q8C2312yes—
46C11×#127C2311yescharacteristic
47C11×#124—21no—
48C11×#121—21no—
49C11×#121—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C42×C11C2311yescharacteristic
55#67002—44no—
56C2×#4325—24no—
57C2×#4325—22no—
58C2×#4325—44no—
59C2×#4323—22no—
60C2×(C2×D11)⋊C4—21no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×#4318—21no—
63C22×C11⋊C8—21no—
64C2×C8×D11—24no—
65C4×D44—21no—
66C4×D44—21no—
67C4×D44D412yes—
68C4×D44C2312yes—
69C11×#107—24no—
70C11×C4⋊C8D412yes—
71C11×#102—24no—
72C11×C22⋊C8D412yes—
73C4×C8×C11C2312yes—
74#66899—24no—
75#66899—22no—
76#66896—22no—
77C22⋊(C11⋊C8)—21no—
78(C2×D11)⋊C8—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84C4×C11⋊C8—21no—
85#19392—111nomaximal, Sylow
86C23×D11—21no—
87C11×#41—42no—
88C11×#41—42no—
89C2×Q8×C11—21no—
90C2×Q8×C11—22no—
91C2×Q8×C11—41no—
92C2×Q8×C11—42no—
93C2×Q8×C11—42no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×Dic11—21no—
104C2×D44—21no—
105C2×D44—22no—
106C2×D44D814yes—
107C2×D44C2×D412yes—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—82no—
111C2×C8×C11C2×D414yes—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—41no—
117C11×C4⋊C4—41no—
118C11×C22⋊C4—41no—
119C11×C22⋊C4—41no—
120C42×C11C2×D411yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11#4111yescharacteristic
123C42×C11C2411yescharacteristic
124#4325—48no—
125#4325—44no—
126#4323—44no—
127(C2×D11)⋊C4—22no—
128(C2×D11)⋊C4—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11C2×D412yes—
131#4318—42no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—42no—
136C8×D11—84no—
137#3226D1111yescharacteristic, complemented
138#3036—111no—
139C2×#461—111no—
140#2972—111no—
141#1681—114no—
142#1673—114no—
143#1571—111no—
144#1546—111no—
145#1540—111no—
146C23×C11—41no—
147C23×C11#12111yescharacteristic
148C22×D11—22no—
149C22×D11—24no—
150C22×D11—81no—
151C22×D11—81no—
152Q8×C11—42no—
153Q8×C11—41no—
154Q8×C11—42no—
155Q8×C11—41no—
156Q8×C11—82no—
157D4×C11—41no—
158D4×C11—41no—
159D4×C11—42no—
160D4×C11—81no—
161D4×C11—82no—
162C2×C4×C11—22no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—42no—
166C2×C4×C11—82no—
167C2×C4×C11—82no—
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11C2×D812yes—
172C2×C4×C11#13512yes—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×Dic11—22no—
177C2×Dic11—81no—
178D44—22no—
179D44—24no—
180D44C2×D814yes—
181C4×D11—44no—
182C4×D11—82no—
183C8×C11—24no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C2×AGL(1,ℤ/8)—221no—
188C22×SD16—221no—
189#532C2×D1111yescharacteristic
190C2×C4⋊Q8C2×D1111yescharacteristic
191C2×C4×D4—111no—
192#500C2×D1112yescomplemented
193#486C2×D1112yescomplemented
194#480—22no—
195#474—22no—
196#463—222no—
197#461—112no—
198#461—114no—
199#461—222no—
200#459—112no—
201C8×D4—114no—
202C8×D4—222no—
203#431—111no—
204#431C2×D1111yescharacteristic
205#423—111no—
206C2×C4⋊C8—111no—
207#417—221no—
208C2×#103—221no—
209C2×C22⋊C8—222no—
210#335—114no—
211#332—112no—
212#332—114no—
213#331—112no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11#46612yes—
220C22×C11C2×#12111yescharacteristic
221C2×D11—24no—
222C2×D11—42no—
223C2×D11—42no—
224C2×D11—84no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—81no—
229C4×C11—82no—
230C4×C11#46612yes—
231C4×C11C22×D811yescharacteristic
232C4×C11C2×#13511yescharacteristic
233C4×C11#57712yes—
234Dic11—42no—
235C2×#41—21no—
236C22×Q8—21no—
237C22×D4—111no—
238C23×C4—221no—
239AGL(1,ℤ/8)—444no—
240C2×SD16—224no—
241C2×SD16—222no—
242C2×SD16—444no—
243C2×D8—222no—
244C2×M16—221no—
245C22×C8—221no—
246C22×C8—224no—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C22×D1112yes—
251C4⋊Q8C22×D1111yescharacteristic
252#127C22×D1111yescharacteristic
253#124—21no—
254#121—21no—
255#121—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—112no—
259C4×D4—112no—
260C4×D4—221no—
261C4×D4—221no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—111no—
265C2×C22⋊C4—221no—
266C2×C42C22×D1111yescharacteristic
267#107—24no—
268C4⋊C8—112no—
269C4⋊C8—112no—
270C4⋊C8—112no—
271C4⋊C8—221no—
272C4⋊C8—221no—
273C4⋊C8C22⋊D1112yes—
274#103—224no—
275#103—222no—
276#102—24no—
277#102—222no—
278C22⋊C8—221no—
279C22⋊C8—224no—
280C22⋊C8C22⋊D1112yes—
281C4×C8—221no—
282C4×C8C22×D1112yes—
283C2×C11—22no—
284C2×C11—161no—
285C2×C11#304211yescharacteristic
286C2×C11C2×#46611yescharacteristic
287C2×C11#306911yescharacteristic
288D11—44no—
289C24—221no—
290#41—42no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—42no—
296C2×Q8—42no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—41no—
301C2×D4—114no—
302C2×D4—112no—
303C2×D4—222no—
304C2×D4—221no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—221no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—882no—
311C22×C4D4×D1111yescharacteristic
312C22×C4#434111yescharacteristic
313C22×C4C2×C22⋊D1111yescharacteristic
314SD16—448no—
315SD16—444no—
316D8—444no—
317M16—442no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8—442no—
322C2×C8—884no—
323C2×C8C2×C22⋊D1114yes—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—112no—
331C4⋊C4—221no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—222no—
335C22⋊C4—222no—
336C42D4×D1111yescharacteristic
337C42#434111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C42C23×D1111yescharacteristic
340C11#1939211yescharacteristic, complemented, Sylow
341C23—41no—
342C23—222no—
343C23—224no—
344C23—881no—
345C23—881no—
346C23#6699111yescharacteristic
347Q8—42no—
348Q8—41no—
349Q8—42no—
350Q8—41no—
351Q8—82no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—81no—
356D4—82no—
357D4—114no—
358D4—224no—
359D4—222no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—222no—
367C2×C4—444no—
368C2×C4—882no—
369C2×C4—881no—
370C2×C4D8×D1112yes—
371C2×C4#6696512yes—
372C2×C4#6699111yescharacteristic
373C2×C4#6699111yescharacteristic
374C2×C4#6699111yescharacteristic
375C2×C4C2×D4×D1111yescharacteristic
376C2×C4C2×#434111yescharacteristic
377C2×C4C22×C22⋊D1111yescharacteristic
378C8—24no—
379C8—442no—
380C8—442no—
381C8—442no—
382C22—21no—
383C22—21no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22—224no—
388C22—442no—
389C22—442no—
390C22—884no—
391C22#1062277012yes—
392C22C2×#6699111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—81no—
397C4—82no—
398C4—442no—
399C4#1062277012yes—
400C4C2×D8×D1111yescharacteristic
401C4C2×#6696511yescharacteristic
402C4#1062336812yes—
403C2—22no—
404C2—161no—
405C2—444no—
406C2#1307812411yescharacteristic
407C2C2×#1062277011yescharacteristic
408C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3226C2
socleC22×C11C2×#121
prime radical#13078076C2
hypercenter#3226D11
hypocenterC11#19392
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. C2×#10622696C2semidirect
3. #13077639C2semidirect
4. #13068050C2semidirect
5. #13068002C2semidirect
6. #13067391C2semidirect
7. #13067288C2semidirect
8. #13067265C2semidirect
9. C11×#3226C2semidirect
15. C11×#500C22semidirect
16. C11×#486C22semidirect
33. #10622185C22semidirect
34. #10622185C22semidirect
35. #10622182C22semidirect
36. #10622096C22semidirect
137. #3226D11semidirect
192. #500C2×D11semidirect
193. #486C2×D11semidirect
340. C11#19392semidirect

Maximal subgroups

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

subgroupindex
#130780762
C2×#106226962
#130776392
#130680502
#130680022
#130673912
#130672882
#130672652
C11×#32262
#1939211