Finite Group Databasebeta

← #14727743

Subgroups — #14727743

Order 2816.

1312 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081949C211yesmaximal, characteristic, complemented
2#13079534C212yesmaximal, complemented
3#13067550C214yesmaximal, complemented
4#13067533C214yesmaximal, complemented
5#13067175C212yesmaximal, complemented
6#13066930C211yesmaximal, characteristic, complemented
7C11×#2619C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C2×C11×#127C2211yescharacteristic, complemented
10C2×C11×#121—21no—
11C2×C11×#117C2211yescharacteristic
12#10623057—22no—
13#10623056—22no—
14#10623055—24no—
15#10623041—21no—
16#10623041C2212yes—
17#10623024—21no—
18#10623024C2212yes—
19#10623008—21no—
20#10623008C2212yes—
21C11×#394—21no—
22C11×#394C2212yescomplemented
23C11×#392—21no—
24C11×#392C2212yes—
25C11×#390—21no—
26C11×#382C2211yescharacteristic, complemented
27#10622830C2218yescomplemented
28#10622686—22no—
29#10622685—24no—
30#10622683—22no—
31#10622538C2212yescomplemented
32#10622166C2212yescomplemented
33#10622163C2212yes—
34#10622089C2218yescomplemented
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11—21no—
38C22×D4×C11C2312yes—
39C23×C4×C11D411yescharacteristic
40C22×C22⋊D11—22no—
41C2×#4339—22no—
42C2×#4339—22no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—44no—
46C2×#4339—44no—
47C22×D44—21no—
48C22×C4×D11—22no—
49C22×Dic22—21no—
50C11×#127—22no—
51C11×#127—22no—
52C11×#121—44no—
53C11×#117—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4D411yescharacteristic
62C2×C11×C22⋊C4C2311yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×#4323—28no—
66#66983—22no—
67#66983—22no—
68#66983—22no—
69#66983C2314yes—
70#66950—24no—
71#66950—24no—
72#66948—24no—
73#66948—24no—
74#66939—24no—
75#66939—24no—
76#66935—24no—
77#66935—24no—
78#66928—22no—
79#66928—22no—
80#66927—21no—
81#66927D412yescomplemented
82C4×D44—22no—
83C4×D44—22no—
84C4×D44—22no—
85C4×D44D414yescomplemented
86#66922—21no—
87#66922D412yescomplemented
88C11×#95—21no—
89C11×#95C2312yes—
90#66896—28no—
91C22⋊(C11⋊C8)C2314yes—
92C4⋊(C11⋊C8)—22no—
93C4×C11⋊C8—22no—
94#18300—111nomaximal, Sylow
95C24×C11—22no—
96C24×C11C2×D411yescharacteristic
97C23×D11—22no—
98C2×D4×C11—24no—
99C2×D4×C11—44no—
100C2×D4×C11—42no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—82no—
106C2×D4×C11—82no—
107C2×D4×C11—82no—
108C2×D4×C11—82no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11D814yescomplemented
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2411yescharacteristic
120C2×C22⋊D11—24no—
121C2×C22⋊D11—24no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—44no—
124C22×Dic11—22no—
125#4339—44no—
126#4339—48no—
127#4339—48no—
128#4339—44no—
129#4339—44no—
130#4339—44no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—44no—
137C2×D44C2×D414yes—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—48no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—44no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—42no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—44no—
150C11×C22⋊C4—82no—
151C11×C22⋊C4—82no—
152C42×C11—21no—
153C42×C11—21no—
154C42×C11C2×D412yes—
155C42×C11C2×D412yes—
156#4323—88no—
157(C2×D11)⋊C4—24no—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11C2×D414yes—
165C2×C11⋊C8—24no—
166#3449—111no—
167#3205—112no—
168#2619D1111yescharacteristic, complemented
169#1598—114no—
170#1595—114no—
171#1517—112no—
172#1458—111no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11C2×D812yes—
185C23×C11C22×D411yescharacteristic
186C22×D11—24no—
187C22×D11—44no—
188C22×D11—82no—
189C22×D11—82no—
190D4×C11—48no—
191D4×C11—84no—
192D4×C11—88no—
193D4×C11—82no—
194D4×C11—82no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11#12012yes—
209C2×C4×C11#12011yescharacteristic
210C2×C4×C11#12011yescharacteristic
211C2×C4×C11C2×D812yes—
212C2×C4×C11C2×D812yes—
213C2×C4×C11AGL(1,ℤ/8)12yes—
214C2×C4×C11C22×D412yes—
215C22⋊D11—48no—
216C22⋊D11—44no—
217C22⋊D11—44no—
218C2×Dic11—24no—
219C2×Dic11—44no—
220D44—44no—
221D44—44no—
222D44—44no—
223D44—82no—
224D44—82no—
225D44—82no—
226C4×D11—48no—
227C4×D11—48no—
228Dic22—44no—
229Dic22—44no—
230C11⋊C8—44no—
231C22×#41—221no—
232#537—112no—
233#537—221no—
234#536—222no—
235#535—222no—
236#534—112no—
237#534—221no—
238#532—112no—
239#532—221no—
240C2×#127C2×D1111yescharacteristic, complemented
241#525—224no—
242C2×#121—21no—
243C2×#117C2×D1111yescharacteristic
244#493—222no—
245#486—222no—
246#459—224no—
247#447—118no—
248#431—112no—
249#394—21no—
250#394C2×D1112yescomplemented
251#392—21no—
252#392C2×D1112yes—
253#390—21no—
254#382C2×D1111yescharacteristic, complemented
255#327—118no—
256#324—112no—
257#323—112no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—22no—
261C22×C11—42no—
262C22×C11—41no—
263C22×C11—41no—
264C22×C11—81no—
265C22×C11—82no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11—82no—
269C22×C11—82no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11C2×#12011yescharacteristic
273C22×C11C22×D811yescharacteristic
274C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C2×D11—44no—
276C2×D11—44no—
277C2×D11—44no—
278C2×D11—88no—
279C4×C11—22no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—41no—
283C4×C11—41no—
284C4×C11—82no—
285C4×C11#44712yes—
286C4×C11#44712yes—
287Dic11—44no—
288C2×#41—222no—
289C2×#41—222no—
290C2×#41—222no—
291C2×#41—222no—
292C2×#41—444no—
293C2×#41—444no—
294C22×Q8—221no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—221no—
299C22×D4—222no—
300C22×D4C22×D1112yes—
301C23×C4—222no—
302C23×C4C22⋊D1111yescharacteristic
303C2×D8—228no—
304C4⋊Q8—112no—
305C4⋊Q8—221no—
306#127—22no—
307#127—22no—
308#127—112no—
309#127—221no—
310#124—222no—
311#124—222no—
312#123—224no—
313#123—224no—
314C22⋊Q8—224no—
315C22⋊Q8—224no—
316#121—44no—
317#121—114no—
318#121—224no—
319#121—224no—
320#121—222no—
321#121—222no—
322#121—222no—
323#120—224no—
324#120—224no—
325C4×D4—114no—
326C4×D4—222no—
327C4×D4—222no—
328C4×D4—222no—
329#117—22no—
330#117—22no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4C22⋊D1111yescharacteristic
333C2×C4⋊C4C22×D1111yescharacteristic
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4C22⋊D1111yescharacteristic
338C2×C22⋊C4C22×D1111yescharacteristic
339C2×C42C22⋊D1111yescharacteristic
340C2×C42C22×D1111yescharacteristic
341C4⋊C8—222no—
342#102—228no—
343C22⋊C8—114no—
344C4×C8—222no—
345#95—21no—
346#95C22×D1112yes—
347C2×C11—21no—
348C2×C11—21no—
349C2×C11—42no—
350C2×C11—162no—
351C2×C11C2×#44711yescharacteristic
352C2×C11#302111yescharacteristic
353C2×C11#302711yescharacteristic
354D11—84no—
355C24—22no—
356C24—222no—
357C24C2×C22⋊D1111yescharacteristic
358#41—444no—
359#41—448no—
360#41—448no—
361#41—444no—
362#41—444no—
363#41—444no—
364C2×Q8—222no—
365C2×Q8—222no—
366C2×Q8—444no—
367C2×D4—24no—
368C2×D4—44no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—42no—
374C2×D4—82no—
375C2×D4—82no—
376C2×D4—82no—
377C2×D4—82no—
378C2×D4—114no—
379C2×D4—222no—
380C2×D4—222no—
381C2×D4—222no—
382C2×D4—224no—
383C2×D4—224no—
384C2×D4—222no—
385C2×D4—222no—
386C2×D4—444no—
387C2×D4—444no—
388C2×D4—444no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—224no—
394C22×C4—222no—
395C22×C4—224no—
396C22×C4—448no—
397C22×C4#432314yescomplemented
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C23×D1111yescharacteristic
404D8—888no—
405C2×C8—224no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—42no—
409C4⋊C4—114no—
410C4⋊C4—222no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—44no—
416C22⋊C4—82no—
417C22⋊C4—82no—
418C22⋊C4—224no—
419C22⋊C4—224no—
420C22⋊C4—224no—
421C22⋊C4—224no—
422C42—21no—
423C42—21no—
424C42D4×D1112yes—
425C42D4×D1112yes—
426C11#1830011yescharacteristic, complemented, Sylow
427C23—21no—
428C23—21no—
429C23—41no—
430C23—41no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—224no—
439C23—444no—
440C23—882no—
441C23—882no—
442C23C2×#432312yes—
443C23C22×C22⋊D1111yescharacteristic
444Q8—444no—
445Q8—444no—
446D4—48no—
447D4—84no—
448D4—88no—
449D4—82no—
450D4—82no—
451D4—444no—
452D4—444no—
453D4—448no—
454D4—444no—
455D4—444no—
456D4—444no—
457D4—882no—
458D4—882no—
459D4—882no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—224no—
474C2×C4—448no—
475C2×C4—444no—
476C2×C4—448no—
477C2×C4C2×#432312yes—
478C2×C4C2×#432312yes—
479C2×C4#6699012yes—
480C2×C4#6699011yescharacteristic
481C2×C4#6699011yescharacteristic
482C2×C4#6700212yes—
483C2×C4C2×D4×D1112yes—
484C8—444no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—42no—
489C22—41no—
490C22—41no—
491C22—81no—
492C22—82no—
493C22—82no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—82no—
499C22—444no—
500C22—444no—
501C22—444no—
502C22—888no—
503C22C22×#432311yescharacteristic
504C22C2×#6699011yescharacteristic
505C22C2×#6700211yescharacteristic
506C4—22no—
507C4—22no—
508C4—22no—
509C4—41no—
510C4—41no—
511C4—82no—
512C4—444no—
513C4#1062264912yes—
514C4#1062264912yes—
515C2—21no—
516C2—21no—
517C2—42no—
518C2—162no—
519C2—884no—
520C2C2×#1062264911yescharacteristic
521C2#1307798711yescharacteristic
522C2#1307801711yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2619C2
socleC22×C11C2×#120
hypercenter#2619D11
hypocenterC11#18300
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. #13081949C2semidirect
2. #13079534C2semidirect
3. #13067550C2semidirect
4. #13067533C2semidirect
5. #13067175C2semidirect
6. #13066930C2semidirect
7. C11×#2619C2semidirect
9. C2×C11×#127C22semidirect
22. C11×#394C22semidirect
26. C11×#382C22semidirect
27. #10622830C22semidirect
31. #10622538C22semidirect
32. #10622166C22semidirect
34. #10622089C22semidirect
81. #66927D4semidirect
85. C4×D44D4semidirect
87. #66922D4semidirect
113. C22×C4×C11D8semidirect
168. #2619D11semidirect
240. C2×#127C2×D11semidirect
250. #394C2×D11semidirect
254. #382C2×D11semidirect
397. C22×C4#4323semidirect
426. C11#18300semidirect

Maximal subgroups

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

subgroupindex
#130819492
#130795342
#130675502
#130675332
#130671752
#130669302
C11×#26192
#1830011