Finite Group Databasebeta

← #14727885

Subgroups — #14727885

Order 2816.

1402 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 1402 conjugacy classes of subgroups — too many to draw. Only its 167 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×#10623024C211yesmaximal, characteristic
2#13079418C212yesmaximal, complemented
3#13067601C214yesmaximal, complemented
4#13067567C214yesmaximal, complemented
5#13067131C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic, complemented
7C11×#2561C211yesmaximal, characteristic, complemented
8C23×C22⋊D11—21no—
9C2×C11×C22⋊Q8C2211yescharacteristic, complemented
10C22×C11×C22⋊C4C2211yescharacteristic
11C2×#66983—21no—
12C2×#66983C2212yes—
13#10623024—22no—
14#10623024—24no—
15#10623024C2214yes—
16C2×#66939—22no—
17C2×#66935—22no—
18C11×#397C2212yescomplemented
19C11×#393C2212yescomplemented
20C11×#388—22no—
21C11×#381—21no—
22C11×#379—21no—
23C4×C11×C22⋊C4C2211yescharacteristic, complemented
24#10622840C2214yescomplemented
25#10622820C2212yescomplemented
26#10622662—24no—
27#10622659—22no—
28#10622657—22no—
29#10622580C2214yescomplemented
30#10622163C2214yescomplemented
31#10622089C2218yescomplemented
32C25×C11D411yescharacteristic
33C24×D11—21no—
34C22×Q8×C11C2311yescharacteristic, complemented
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—22no—
38C22×C22⋊D11—24no—
39C22×C22⋊D11—24no—
40C22×C22⋊D11—22no—
41C22×C22⋊D11—48no—
42C23×Dic11—21no—
43C22×D44—21no—
44C22×D44D412yes—
45C11×C22⋊Q8—22no—
46C11×C22⋊Q8—22no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4C2311yescharacteristic, complemented
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4—22no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4D412yes—
56C2×C11×C22⋊C4C2312yes—
57C2×C42×C11—21no—
58C2×#4325—24no—
59#66983—24no—
60#66983—22no—
61#66983—22no—
62#66983—24no—
63#66983D414yes—
64#66983C2314yes—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11D412yes—
69C2×#4318—22no—
70#66939—28no—
71#66939—28no—
72#66935—28no—
73#66935—28no—
74C11×#95—22no—
75C11×#95—22no—
76C11×#95C2312yescomplemented
77#66899—24no—
78C22⋊(C11⋊C8)—22no—
79C22⋊(C11⋊C8)C2314yescomplemented
80#66873—24no—
81#66871—24no—
82#18317—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—24no—
86C24×C11—42no—
87C24×C11—81no—
88C24×C11C2×D411yescharacteristic
89C24×C11C2×D412yes—
90C23×D11—22no—
91C23×D11—24no—
92C23×D11—44no—
93C23×D11—82no—
94C23×D11—82no—
95C2×Q8×C11—22no—
96C2×Q8×C11—81no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—42no—
103C22×C4×C11—81no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C2×C22⋊D11—28no—
110C2×C22⋊D11—24no—
111C2×C22⋊D11—24no—
112C2×C22⋊D11—48no—
113C2×C22⋊D11—416no—
114C2×C22⋊D11—48no—
115C2×C22⋊D11—48no—
116C2×C22⋊D11—48no—
117C22×Dic11—24no—
118C22×Dic11—22no—
119C22×Dic11—44no—
120C2×D44—24no—
121C2×D44—22no—
122C2×D44—82no—
123C2×D44—82no—
124C2×D44C2×D414yes—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—42no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—24no—
129C11×C22⋊C4—42no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—44no—
133C11×C22⋊C4—82no—
134C42×C11—81no—
135#4325—84no—
136(C2×D11)⋊C4—28no—
137(C2×D11)⋊C4—24no—
138(C2×D11)⋊C4—24no—
139C4⋊Dic11—24no—
140C4⋊Dic11—22no—
141C4⋊Dic11C2×D414yes—
142#4318—82no—
143C2×C11⋊C8—24no—
144C2×#534—111no—
145#3193—112no—
146#2561D1111yescharacteristic, complemented
147#1607—114no—
148#1601—114no—
149#1507—112no—
150#1462—111no—
151C23×C11—24no—
152C23×C11—24no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—41no—
158C23×C11—42no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—81no—
163C23×C11—81no—
164C23×C11—88no—
165C23×C11#12011yescharacteristic
166C23×C11#12011yescharacteristic
167C23×C11AGL(1,ℤ/8)14yes—
168C23×C11C22×D411yescharacteristic
169C22×D11—24no—
170C22×D11—44no—
171C22×D11—44no—
172C22×D11—48no—
173C22×D11—44no—
174C22×D11—84no—
175C22×D11—84no—
176C22×D11—816no—
177Q8×C11—44no—
178C2×C4×C11—22no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—81no—
193C2×C4×C11#12012yes—
194C2×C4×C11C22×D412yes—
195C22⋊D11—416no—
196C22⋊D11—48no—
197C22⋊D11—48no—
198C2×Dic11—24no—
199C2×Dic11—44no—
200C2×Dic11—48no—
201D44—44no—
202D44—82no—
203D44—84no—
204C11⋊C8—44no—
205C23×D4—221no—
206#534—114no—
207#534—224no—
208#534—222no—
209C2×#123—222no—
210C2×C22⋊Q8C2×D1111yescharacteristic, complemented
211C2×#121—112no—
212C2×#121—221no—
213C2×#120—222no—
214C22×C22⋊C4C2×D1111yescharacteristic
215#484—222no—
216#480—114no—
217#468—224no—
218#450—222no—
219#448—114no—
220#407—112no—
221#397C2×D1112yescomplemented
222#393C2×D1112yescomplemented
223#388—22no—
224#381—21no—
225#379—21no—
226C4×C22⋊C4C2×D1111yescharacteristic, complemented
227#327—118no—
228#323—114no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—24no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—44no—
238C22×C11—44no—
239C22×C11—48no—
240C22×C11—42no—
241C22×C11—42no—
242C22×C11—82no—
243C22×C11—84no—
244C22×C11#45512yes—
245C22×C11C2×#12011yescharacteristic
246C22×C11C2×AGL(1,ℤ/8)12yes—
247C2×D11—44no—
248C2×D11—44no—
249C2×D11—44no—
250C2×D11—88no—
251C2×D11—816no—
252C4×C11—22no—
253C4×C11—22no—
254C4×C11—42no—
255C4×C11—82no—
256C4×C11—81no—
257C4×C11—81no—
258Dic11—44no—
259C25—221no—
260C25C22⋊D1111yescharacteristic
261C22×Q8C22×D1111yescharacteristic, complemented
262C22×D4—112no—
263C22×D4—221no—
264C22×D4—222no—
265C22×D4—224no—
266C22×D4—222no—
267C22×D4—224no—
268C22×D4—448no—
269C23×C4—221no—
270C23×C4C22⋊D1111yescharacteristic
271C23×C4C22×D1111yescharacteristic
272C2×SD16—224no—
273C2×M16—222no—
274#123—228no—
275#123—228no—
276C22⋊Q8—22no—
277C22⋊Q8—22no—
278#121—114no—
279#121—114no—
280#121—224no—
281#121—222no—
282#121—222no—
283#121—224no—
284#120—228no—
285#120—228no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4C22×D1111yescharacteristic, complemented
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4C22⋊D1112yes—
299C2×C22⋊C4C22×D1112yes—
300C2×C42—21no—
301#107—224no—
302#103—224no—
303#102—224no—
304C22⋊C8—114no—
305C22⋊C8—222no—
306#95—22no—
307#95—22no—
308#95C22×D1112yescomplemented
309C2×C11—22no—
310C2×C11—22no—
311C2×C11—44no—
312C2×C11—41no—
313C2×C11#300311yescharacteristic
314C2×C11C2×#45511yescharacteristic
315C2×C11#302611yescharacteristic
316D11—84no—
317C24—21no—
318C24—21no—
319C24—24no—
320C24—42no—
321C24—81no—
322C24—224no—
323C24—222no—
324C24—444no—
325C24—882no—
326C24—882no—
327C24C2×C22⋊D1111yescharacteristic
328C24C2×C22⋊D1112yes—
329C2×Q8—22no—
330C2×Q8—81no—
331C2×D4—114no—
332C2×D4—224no—
333C2×D4—228no—
334C2×D4—224no—
335C2×D4—224no—
336C2×D4—222no—
337C2×D4—448no—
338C2×D4—4416no—
339C2×D4—448no—
340C2×D4—448no—
341C2×D4—448no—
342C2×D4—882no—
343C2×D4—882no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—81no—
351C22×C4—224no—
352C22×C4—222no—
353C22×C4—444no—
354C22×C4D4×D1112yes—
355C22×C4D4×D1112yes—
356C22×C4C2×C22⋊D1112yes—
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C23×D1111yescharacteristic
359SD16—884no—
360M16—882no—
361C2×C8—224no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4—114no—
365C4⋊C4—224no—
366C4⋊C4—222no—
367C22⋊C4—24no—
368C22⋊C4—24no—
369C22⋊C4—42no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—44no—
373C22⋊C4—82no—
374C22⋊C4—228no—
375C22⋊C4—224no—
376C22⋊C4—224no—
377C42—81no—
378C11#1831711yescharacteristic, complemented, Sylow
379C23—24no—
380C23—24no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—22no—
385C23—41no—
386C23—42no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—81no—
391C23—81no—
392C23—88no—
393C23—224no—
394C23—444no—
395C23—448no—
396C23—444no—
397C23—444no—
398C23—884no—
399C23—884no—
400C23—8816no—
401C23#6699011yescharacteristic
402C23#6699011yescharacteristic
403C23#6700214yes—
404C23C22×C22⋊D1111yescharacteristic
405Q8—44no—
406D4—444no—
407D4—4416no—
408D4—448no—
409D4—448no—
410D4—882no—
411D4—884no—
412C2×C4—22no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—81no—
427C2×C4—224no—
428C2×C4—444no—
429C2×C4—448no—
430C2×C4#6699012yes—
431C2×C4C2×D4×D1112yes—
432C8—444no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—24no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—44no—
442C22—44no—
443C22—48no—
444C22—42no—
445C22—42no—
446C22—82no—
447C22—84no—
448C22—444no—
449C22—444no—
450C22—444no—
451C22—888no—
452C22—8816no—
453C22#1062267412yes—
454C22C2×#6699011yescharacteristic
455C22C2×#6700212yes—
456C4—22no—
457C4—22no—
458C4—42no—
459C4—82no—
460C4—81no—
461C4—81no—
462C4—444no—
463C2—22no—
464C2—22no—
465C2—41no—
466C2—44no—
467C2—884no—
468C2#1307784211yescharacteristic
469C2C2×#1062267411yescharacteristic
470C2#1307801211yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2561C2
socleC22×C11C2×#120
prime radicalC2×#10623024C2
hypercenter#2561D11
hypocenterC11#18317
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2561

Complements

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

NH ≅ G/Ntype
2. #13079418C2semidirect
3. #13067601C2semidirect
4. #13067567C2semidirect
5. #13067131C2semidirect
6. #13066943C2semidirect
7. C11×#2561C2semidirect
9. C2×C11×C22⋊Q8C22semidirect
18. C11×#397C22semidirect
19. C11×#393C22semidirect
23. C4×C11×C22⋊C4C22semidirect
24. #10622840C22semidirect
25. #10622820C22semidirect
29. #10622580C22semidirect
30. #10622163C22semidirect
31. #10622089C22semidirect
34. C22×Q8×C11C23semidirect
48. C2×C11×C4⋊C4C23semidirect
76. C11×#95C23semidirect
79. C22⋊(C11⋊C8)C23semidirect
146. #2561D11semidirect
210. C2×C22⋊Q8C2×D11semidirect
221. #397C2×D11semidirect
222. #393C2×D11semidirect
226. C4×C22⋊C4C2×D11semidirect
261. C22×Q8C22×D11semidirect
289. C2×C4⋊C4C22×D11semidirect
308. #95C22×D11semidirect
378. C11#18317semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
#130794182
#130676012
#130675672
#130671312
#130669432
C11×#25612
#1831711