Finite Group Databasebeta

← #14722010

Subgroups — #14722010

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082538C211yesmaximal, characteristic
2#13077630C211yesmaximal, characteristic, complemented
3#13067250C211yesmaximal, characteristic, complemented
4#13067248C212yesmaximal, complemented
5#13067237C212yesmaximal, complemented
6#13067221C212yesmaximal, complemented
7#13067219C211yesmaximal, characteristic, complemented
8#13067217C211yesmaximal, characteristic, complemented
9#13067207C211yesmaximal, characteristic, complemented
10#13067205C212yesmaximal, complemented
11C11×#2971C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623364C411yescharacteristic
14#10623364C411yescharacteristic
15#10623112—21no—
16#10623112—21no—
17#10623089—21no—
18#10623089—21no—
19#10623071—22no—
20#10623071—22no—
21#10623066C412yes—
22#10623054C411yescharacteristic
23#10623054C411yescharacteristic
24#10623049C412yes—
25#10623010C2212yes—
26#10623010C2212yes—
27#10623008C2211yescharacteristic
28C2×#66923C2211yescharacteristic
29C8×Q8×C11—21no—
30C11×#436—22no—
31C11×#436—21no—
32C11×#432C2211yescharacteristic
33C11×#432C2212yes—
34C4×C11×M16C2212yes—
35C4×C11×M16C2211yescharacteristic
36#10622637—21no—
37#10622624—22no—
38D4×C11⋊C8—21no—
39#10622539C2211yescharacteristic
40#10622539C2212yes—
41C4×#4318C2211yescharacteristic
42C2×#66867C2212yes—
43#10622103C2212yes—
44#10622103C2212yes—
45#10622103C2212yes—
46#10622103C2212yes—
47#10622102C2211yescharacteristic
48#10622102C2212yes—
49#10622102C2211yescharacteristic
50#10622102C2211yescharacteristic
51#10622102C2211yescharacteristic
52#10622102C2212yes—
53C2×C11×#41C2×C411yescharacteristic
54C2×#4339C2×C411yescharacteristic
55C2×#4339C2×C411yescharacteristic
56C2×C11×M16—21no—
57C2×C11×M16—22no—
58C4×Q8×C11D411yescharacteristic
59C4×Q8×C11D411yescharacteristic
60C4×D4×C11D412yes—
61C4×D4×C11D411yescharacteristic
62C4×D4×C11D412yes—
63C4×D4×C11D411yescharacteristic
64C11×#117C2×C412yes—
65C11×#117C2×C411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2312yes—
68#66999—21no—
69#66999—21no—
70#66992—22no—
71#66992—22no—
72#66991—21no—
73#66991—21no—
74#66983—21no—
75#66983—21no—
76#66983C2×C412yes—
77#66983C2×C412yes—
78#66982—22no—
79#66982—22no—
80C4×C22⋊D11—22no—
81C4×C22⋊D11—22no—
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84#66977C2×C412yes—
85#66977C2×C412yes—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×#4318—21no—
89C22×C11⋊C8—22no—
90#66947—22no—
91#66947—22no—
92#66945—21no—
93#66945—21no—
94C4⋊C4×D11—21no—
95C4⋊C4×D11—21no—
96#66942—22no—
97#66942—22no—
98#66937—22no—
99#66937—22no—
100(C22⋊D11)⋊C4—22no—
101(C22⋊D11)⋊C4—22no—
102#66932—22no—
103#66932—22no—
104#66929—22no—
105#66929—22no—
106#66928C2311yescharacteristic
107#66928C2311yescharacteristic
108#66927C2×C411yescharacteristic
109C4×D44—21no—
110C4×D44—21no—
111C4×D44C2×C412yes—
112C4×D44C2×C412yes—
113#66925—22no—
114#66925—22no—
115#66923—21no—
116#66923—21no—
117#66923C2×C412yes—
118#66923C2312yes—
119#66922C2×C411yescharacteristic
120C4×Dic22C2×C412yes—
121C4×Dic22C2×C412yes—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—22no—
126C11×#97C2311yescharacteristic
127C11×#97C2312yes—
128C11×#97C2311yescharacteristic
129C4×C8×C11—21no—
130C4×C8×C11—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—22no—
135#66867—22no—
136#66867C2311yescharacteristic
137#66867C2312yes—
138#66867C2311yescharacteristic
139C4×C11⋊C8—21no—
140#17687—111nomaximal, Sylow
141C11×#41—42no—
142C2×Q8×C11C22⋊C411yescharacteristic
143C2×D4×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C412yes—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157#4339—42no—
158#4339—42no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44C22×C411yescharacteristic
162C2×D44C22×C411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×Dic22C22×C411yescharacteristic
168C2×Dic22C22×C411yescharacteristic
169C11×M16—44no—
170C11×M16—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—22no—
174C11×C4⋊C4C22⋊C412yes—
175C11×C4⋊C4C22⋊C412yes—
176C11×C4⋊C4C22⋊C411yescharacteristic
177C11×C4⋊C4C22⋊C411yescharacteristic
178C11×C22⋊C4C22⋊C412yes—
179C11×C22⋊C4C22⋊C412yes—
180C11×C22⋊C4C22⋊C412yes—
181C42×C11C22×C412yes—
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D412yes—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D412yes—
187C42×C11C2411yescharacteristic
188C22⋊Dic11—22no—
189C22⋊Dic11—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C22×C412yes—
203C4⋊Dic11C22×C412yes—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212C4×Dic11—22no—
213C4×Dic11—22no—
214#4318—42no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—44no—
219#3512—111no—
220#2971D1111yescharacteristic, complemented
221#2970—111no—
222#1536—111no—
223#1535—112no—
224#1532—112no—
225#1529—112no—
226#1528—111no—
227#1528—111no—
228#1525—111no—
229#1524—112no—
230C23×C11C2×C22⋊C412yes—
231C23×C11C2×C22⋊C411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234Q8×C11—22no—
235D4×C11—22no—
236D4×C11—42no—
237C2×C4×C11—22no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11C2×C22⋊C412yes—
245C2×C4×C11C2×C22⋊C411yescharacteristic
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C22⋊D11—42no—
253C22⋊D11—42no—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—81no—
261C2×Dic11—81no—
262D44—41no—
263D44—41no—
264D44—81no—
265D44—81no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—82no—
269C4×D11—82no—
270Dic22—41no—
271Dic22—41no—
272C8×C11—22no—
273C8×C11—41no—
274C8×C11—42no—
275C11⋊C8—22no—
276C11⋊C8—42no—
277C11⋊C8—41no—
278#553—222no—
279#553—221no—
280#553—222no—
281#553—221no—
282#552—221no—
283#552—221no—
284#541—112no—
285#540—112no—
286#537—111no—
287#537—111no—
288#532—111no—
289#529—112no—
290#529—112no—
291C2×#125—111no—
292#520—111no—
293#520—111no—
294C4×#41C2×D1111yescharacteristic
295#446—221no—
296C8×Q8—21no—
297#436—22no—
298#436—21no—
299#435—222no—
300C8×D4—221no—
301#432—111no—
302#432—112no—
303#432C2×D1111yescharacteristic
304#432C2×D1112yes—
305C4×M16—111no—
306C4×M16C2×D1112yes—
307C4×M16C2×D1111yescharacteristic
308C2×#97—112no—
309#330—112no—
310#330—112no—
311#330—112no—
312#330—112no—
313#329—112no—
314#329—112no—
315#329—111no—
316#329—111no—
317#329—111no—
318#329—111no—
319C22×C11—21no—
320C22×C11—22no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11C22×C22⋊C411yescharacteristic
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C4×C11—21no—
333C4×C11—22no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11#41312yes—
341Dic11—41no—
342Dic11—41no—
343Dic11—42no—
344Dic11—42no—
345C2×#41—111no—
346C2×#41—111no—
347C2×#41C4×D1111yescharacteristic
348C2×M16—21no—
349C2×M16—22no—
350C2×M16—221no—
351C22×C8—222no—
352C4⋊Q8—111no—
353#127—111no—
354#126—222no—
355#126—222no—
356#126—222no—
357#126—222no—
358#125—112no—
359#125—112no—
360#125—222no—
361#125—222no—
362#125—221no—
363#125—221no—
364#124—111no—
365#124—111no—
366#123—222no—
367#123—222no—
368#123—222no—
369#123—222no—
370C22⋊Q8—112no—
371C22⋊Q8—112no—
372C22⋊Q8—221no—
373C22⋊Q8—221no—
374#121—112no—
375#121—112no—
376#121—221no—
377#121—221no—
378#121—222no—
379#121—222no—
380#121—221no—
381#121—221no—
382#121—222no—
383#121—222no—
384C4×Q8—112no—
385C4×Q8—112no—
386C4×Q8D4411yescharacteristic
387C4×Q8C22⋊D1111yescharacteristic
388C4×D4—112no—
389C4×D4—112no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—221no—
395C4×D4—221no—
396C4×D4D4411yescharacteristic
397C4×D4D4412yes—
398C4×D4C22⋊D1112yes—
399C4×D4C22⋊D1111yescharacteristic
400#117—221no—
401#117—221no—
402#117—222no—
403#117—222no—
404#117C4×D1111yescharacteristic
405#117C4×D1112yes—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1112yes—
414C4⋊C8—22no—
415C4⋊C8—21no—
416C4⋊C8—221no—
417C4⋊C8—222no—
418C22⋊C8—21no—
419C22⋊C8—22no—
420C22⋊C8—222no—
421C22⋊C8—221no—
422#97—111no—
423#97—112no—
424#97—111no—
425#97—222no—
426#97C22×D1111yescharacteristic
427#97C22×D1112yes—
428#97C22×D1111yescharacteristic
429C4×C8—22no—
430C4×C8—21no—
431C4×C8—221no—
432C2×C11—41no—
433C2×C11—42no—
434C2×C11C2×#41311yescharacteristic
435C2×C11#290111yescharacteristic
436C2×C11#290111yescharacteristic
437D11—81no—
438D11—81no—
439#41—42no—
440#41—442no—
441#41—442no—
442C2×Q8—111no—
443C2×Q8—111no—
444C2×Q8(C2×D11)⋊C411yescharacteristic
445C2×D4—111no—
446C2×D4—111no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—222no—
450C2×D4—222no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4(C2×D11)⋊C411yescharacteristic
454C2×D4(C2×D11)⋊C412yes—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4C2×C4×D1111yescharacteristic
462C22×C4C2×C4×D1112yes—
463C22×C4C2×D4411yescharacteristic
464C22×C4C2×D4412yes—
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1112yes—
467M16—44no—
468M16—42no—
469M16—442no—
470C2×C8—21no—
471C2×C8—22no—
472C2×C8—21no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—222no—
476C2×C8—444no—
477C4⋊C4—112no—
478C4⋊C4—112no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4(C2×D11)⋊C411yescharacteristic
492C4⋊C4(C2×D11)⋊C411yescharacteristic
493C4⋊C4(C2×D11)⋊C412yes—
494C4⋊C4(C2×D11)⋊C412yes—
495C22⋊C4—222no—
496C22⋊C4—222no—
497C22⋊C4—222no—
498C22⋊C4—222no—
499C22⋊C4—222no—
500C22⋊C4—222no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4(C2×D11)⋊C412yes—
506C22⋊C4(C2×D11)⋊C412yes—
507C22⋊C4(C2×D11)⋊C412yes—
508C42—222no—
509C42—222no—
510C42C2×C4×D1112yes—
511C42C2×C4×D1111yescharacteristic
512C42C2×D4411yescharacteristic
513C42C2×D4412yes—
514C42C2×C22⋊D1112yes—
515C42C2×C22⋊D1111yescharacteristic
516C42C23×D1111yescharacteristic
517C11#1768711yescharacteristic, complemented, Sylow
518C23—221no—
519C23—221no—
520C23C2×(C2×D11)⋊C412yes—
521C23C2×(C2×D11)⋊C411yescharacteristic
522Q8—22no—
523Q8—441no—
524Q8—441no—
525D4—22no—
526D4—42no—
527D4—441no—
528D4—441no—
529D4—442no—
530D4—442no—
531D4—881no—
532D4—881no—
533D4—882no—
534D4—882no—
535C2×C4—22no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—882no—
548C2×C4—882no—
549C2×C4—881no—
550C2×C4—881no—
551C2×C4C2×(C2×D11)⋊C412yes—
552C2×C4C2×(C2×D11)⋊C412yes—
553C2×C4C2×(C2×D11)⋊C411yescharacteristic
554C2×C4C2×(C2×D11)⋊C411yescharacteristic
555C2×C4C2×(C2×D11)⋊C412yes—
556C2×C4C2×(C2×D11)⋊C411yescharacteristic
557C2×C4C22×C4×D1111yescharacteristic
558C2×C4C22×D4411yescharacteristic
559C2×C4C22×C22⋊D1111yescharacteristic
560C8—22no—
561C8—42no—
562C8—41no—
563C8—222no—
564C8—442no—
565C8—441no—
566C22—21no—
567C22—22no—
568C22—21no—
569C22—22no—
570C22—21no—
571C22—22no—
572C22—441no—
573C22—441no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22C22×(C2×D11)⋊C411yescharacteristic
579C4—21no—
580C4—22no—
581C4—21no—
582C4—22no—
583C4—21no—
584C4—21no—
585C4—22no—
586C4—21no—
587C4—441no—
588C4—441no—
589C4—442no—
590C4—442no—
591C4#1062274512yes—
592C2—41no—
593C2—42no—
594C2—881no—
595C2—881no—
596C2C2×#1062274511yescharacteristic
597C2#1307716111yescharacteristic
598C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C22×C22⋊C4
prime radical#13082538C2
cosocleC42×C11C24
hypercenter#2971D11
hypocenterC11#17687
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #13077630C2semidirect
3. #13067250C2semidirect
4. #13067248C2semidirect
5. #13067237C2semidirect
6. #13067221C2semidirect
7. #13067219C2semidirect
8. #13067217C2semidirect
9. #13067207C2semidirect
10. #13067205C2semidirect
11. C11×#2971C2semidirect
220. #2971D11semidirect
517. C11#17687semidirect

Maximal subgroups

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

subgroupindex
#130825382
#130776302
#130672502
#130672482
#130672372
#130672212
#130672192
#130672172
#130672072
#130672052
C11×#29712
#1768711