Finite Group Databasebeta

← #14727886

Subgroups — #14727886

Order 2816.

1402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1402 conjugacy classes of subgroups — too many to draw. Only its 183 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
1#13079422C212yesmaximal, complemented
2#13073774C211yesmaximal, characteristic, complemented
3#13067602C214yesmaximal, complemented
4#13067568C214yesmaximal, complemented
5#13067132C212yesmaximal, complemented
6#13066943C211yesmaximal, characteristic, complemented
7C2×C11×#534C211yesmaximal, characteristic
8C23×D4×C11—21no—
9C11×#534—24no—
10C11×#534—22no—
11C11×#534C2214yes—
12C2×C11×#123—22no—
13C2×C11×#121—21no—
14C2×C11×#121C2212yes—
15C2×C11×#120—22no—
16C22×C11×C22⋊C4C2211yescharacteristic
17C2×#66977C2211yescharacteristic, complemented
18#10622860—21no—
19#10622831—22no—
20#10622824—21no—
21C4×C22⋊Dic11C2211yescharacteristic, complemented
22#10622820C2212yescomplemented
23#10622655—24no—
24#10622653C2214yescomplemented
25#10622646C2214yescomplemented
26#10622583—22no—
27#10622566C2212yescomplemented
28#10622560C2212yescomplemented
29#10622558—22no—
30#10622175C2218yescomplemented
31#10622163C2214yescomplemented
32C25×C11—21no—
33C25×C11D411yescharacteristic
34C22×D4×C11—22no—
35C22×D4×C11—24no—
36C22×D4×C11—22no—
37C22×D4×C11—24no—
38C22×D4×C11—21no—
39C22×D4×C11—48no—
40C22×D4×C11D412yes—
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×Dic22C2311yescharacteristic, complemented
45C11×#123—28no—
46C11×#123—28no—
47C11×#121—24no—
48C11×#121—24no—
49C11×#121—22no—
50C11×#121—22no—
51C11×#121D414yes—
52C11×#121C2314yes—
53C11×#120—28no—
54C11×#120—28no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4D412yes—
62C2×C11×C22⋊C4C2312yes—
63C2×C22⋊Dic11—21no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—22no—
67C2×#4324—24no—
68C2×C4⋊Dic11C2311yescharacteristic, complemented
69#66977—22no—
70#66977—22no—
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11—21no—
73C2×#4318—22no—
74#66896—24no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95C2312yescomplemented
78C22⋊(C11⋊C8)—22no—
79C22⋊(C11⋊C8)C2314yescomplemented
80#66874—24no—
81#66871—24no—
82#18317—111nomaximal, Sylow
83C24×C11—21no—
84C24×C11—21no—
85C24×C11—24no—
86C24×C11—24no—
87C24×C11—22no—
88C24×C11—44no—
89C24×C11—42no—
90C24×C11—81no—
91C24×C11—82no—
92C24×C11—82no—
93C24×C11C2×D411yescharacteristic
94C24×C11C2×D412yes—
95C2×D4×C11—28no—
96C2×D4×C11—24no—
97C2×D4×C11—24no—
98C2×D4×C11—24no—
99C2×D4×C11—22no—
100C2×D4×C11—48no—
101C2×D4×C11—416no—
102C2×D4×C11—48no—
103C2×D4×C11—48no—
104C2×D4×C11—48no—
105C2×D4×C11—82no—
106C2×D4×C11—82no—
107C2×D4×C11C2×D414yes—
108C22×C4×C11—24no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—44no—
113C22×C4×C11—42no—
114C22×C4×C11—81no—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—21no—
123C2×Dic22—22no—
124C2×Dic22—81no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4C2×D414yes—
128C11×C22⋊C4—28no—
129C11×C22⋊C4—24no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—24no—
133C22⋊Dic11—42no—
134C22⋊Dic11—41no—
135C22⋊Dic11—41no—
136C22⋊Dic11—44no—
137C22⋊Dic11—82no—
138#4324—84no—
139C4⋊Dic11—22no—
140Dic11⋊C4—42no—
141C4×Dic11—81no—
142#4318—82no—
143C2×C11⋊C8—24no—
144C2×#534D1111yescharacteristic
145#3193—112no—
146#2561—111no—
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—24no—
158C23×C11—41no—
159C23×C11—42no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—44no—
163C23×C11—48no—
164C23×C11—44no—
165C23×C11—42no—
166C23×C11—44no—
167C23×C11—81no—
168C23×C11—81no—
169C23×C11—88no—
170C23×C11—84no—
171C23×C11—84no—
172C23×C11—816no—
173C23×C11#12011yescharacteristic
174C23×C11#12011yescharacteristic
175C23×C11AGL(1,ℤ/8)14yes—
176C23×C11C22×D411yescharacteristic
177D4×C11—44no—
178D4×C11—416no—
179D4×C11—48no—
180D4×C11—48no—
181D4×C11—82no—
182D4×C11—84no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—44no—
190C2×C4×C11—48no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—81no—
194C2×C4×C11#12012yes—
195C2×C4×C11C22×D412yes—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203Dic22—44no—
204C11⋊C8—44no—
205C23×D4—21no—
206#534—24no—
207#534—22no—
208#534C2×D1114yes—
209C2×#123—22no—
210C2×C22⋊Q8—111no—
211C2×#121—21no—
212C2×#121C2×D1112yes—
213C2×#120—22no—
214C22×C22⋊C4C2×D1111yescharacteristic
215#484—222no—
216#480—114no—
217#468—224no—
218#450—222no—
219#448—114no—
220#407—112no—
221#397—112no—
222#393—112no—
223#388—222no—
224#381—221no—
225#379—221no—
226C4×C22⋊C4—111no—
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—44no—
243C22×C11—44no—
244C22×C11—44no—
245C22×C11—82no—
246C22×C11—88no—
247C22×C11—84no—
248C22×C11—816no—
249C22×C11#45512yes—
250C22×C11C2×#12011yescharacteristic
251C22×C11C2×AGL(1,ℤ/8)12yes—
252C4×C11—22no—
253C4×C11—22no—
254C4×C11—44no—
255C4×C11—42no—
256Dic11—82no—
257Dic11—81no—
258Dic11—81no—
259C25—21no—
260C25C22⋊D1111yescharacteristic
261C22×Q8—111no—
262C22×D4—22no—
263C22×D4—24no—
264C22×D4—22no—
265C22×D4—24no—
266C22×D4—21no—
267C22×D4—48no—
268C22×D4C22⋊D1112yes—
269C23×C4—21no—
270C23×C4C22⋊D1111yescharacteristic
271C23×C4C22×D1111yescharacteristic
272C2×SD16—224no—
273C2×M16—222no—
274#123—28no—
275#123—28no—
276C22⋊Q8—222no—
277C22⋊Q8—222no—
278#121—24no—
279#121—24no—
280#121—22no—
281#121—22no—
282#121C22⋊D1114yes—
283#121C22×D1114yes—
284#120—28no—
285#120—28no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4C22⋊D1112yes—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—221no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4C22⋊D1112yes—
299C2×C22⋊C4C22×D1112yes—
300C2×C42—221no—
301#107—224no—
302#103—224no—
303#102—224no—
304C22⋊C8—114no—
305C22⋊C8—222no—
306#95—112no—
307#95—222no—
308#95—222no—
309C2×C11—22no—
310C2×C11—22no—
311C2×C11—41no—
312C2×C11—44no—
313C2×C11—84no—
314C2×C11#300311yescharacteristic
315C2×C11C2×#45511yescharacteristic
316C2×C11#302611yescharacteristic
317C24—21no—
318C24—24no—
319C24—21no—
320C24—24no—
321C24—22no—
322C24—44no—
323C24—42no—
324C24—81no—
325C24—82no—
326C24—82no—
327C24C2×C22⋊D1111yescharacteristic
328C24C2×C22⋊D1112yes—
329C2×Q8—222no—
330C2×Q8—881no—
331C2×D4—28no—
332C2×D4—24no—
333C2×D4—24no—
334C2×D4—24no—
335C2×D4—22no—
336C2×D4—48no—
337C2×D4—416no—
338C2×D4—48no—
339C2×D4—48no—
340C2×D4—48no—
341C2×D4—82no—
342C2×D4—82no—
343C2×D4C2×C22⋊D1114yes—
344C22×C4—24no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—44no—
349C22×C4—42no—
350C22×C4—81no—
351C22×C4—222no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4C2×C22⋊D1112yes—
355C22×C4C2×C22⋊D1111yescharacteristic
356C22×C4C2×C22⋊D1112yes—
357C22×C4C2×C22⋊D1112yes—
358C22×C4C23×D1111yescharacteristic
359SD16—884no—
360M16—882no—
361C2×C8—224no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—222no—
365C4⋊C4—442no—
366C4⋊C4C2×C22⋊D1114yes—
367C22⋊C4—28no—
368C22⋊C4—24no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—442no—
373C22⋊C4—444no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—882no—
377C42—881no—
378C11#1831711yescharacteristic, complemented, Sylow
379C23—24no—
380C23—24no—
381C23—22no—
382C23—22no—
383C23—22no—
384C23—22no—
385C23—24no—
386C23—41no—
387C23—42no—
388C23—42no—
389C23—42no—
390C23—44no—
391C23—48no—
392C23—44no—
393C23—42no—
394C23—44no—
395C23—81no—
396C23—81no—
397C23—88no—
398C23—84no—
399C23—84no—
400C23—816no—
401C23#6698514yes—
402C23#6700611yescharacteristic
403C23#6700611yescharacteristic
404C23C22×C22⋊D1111yescharacteristic
405Q8—444no—
406D4—44no—
407D4—416no—
408D4—48no—
409D4—48no—
410D4—82no—
411D4—84no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—44no—
419C2×C4—48no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—81no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4#6700612yes—
431C2×C4C22×C22⋊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—44no—
447C22—44no—
448C22—44no—
449C22—82no—
450C22—88no—
451C22—84no—
452C22—816no—
453C22#1062285512yes—
454C22C2×#6698512yes—
455C22C2×#6700611yescharacteristic
456C4—22no—
457C4—22no—
458C4—44no—
459C4—42no—
460C4—882no—
461C4—881no—
462C4—881no—
463C2—22no—
464C2—22no—
465C2—41no—
466C2—44no—
467C2—84no—
468C2#1307784311yescharacteristic
469C2C2×#1062285511yescharacteristic
470C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#534C2
socleC22×C11C2×#120
hypercenterC2×#534D11
hypocenterC11#18317
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. #13079422C2semidirect
2. #13073774C2semidirect
3. #13067602C2semidirect
4. #13067568C2semidirect
5. #13067132C2semidirect
6. #13066943C2semidirect
17. C2×#66977C22semidirect
21. C4×C22⋊Dic11C22semidirect
22. #10622820C22semidirect
24. #10622653C22semidirect
25. #10622646C22semidirect
27. #10622566C22semidirect
28. #10622560C22semidirect
30. #10622175C22semidirect
31. #10622163C22semidirect
44. C22×Dic22C23semidirect
68. C2×C4⋊Dic11C23semidirect
77. C11⋊#95C23semidirect
79. C22⋊(C11⋊C8)C23semidirect
378. C11#18317semidirect

Maximal subgroups

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

subgroupindex
#130794222
#130737742
#130676022
#130675682
#130671322
#130669432
C2×C11×#5342
#1831711