Finite Group Databasebeta

← #14721770

Subgroups — #14721770

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082594C211yesmaximal, characteristic
2#13077044C211yesmaximal, characteristic, complemented
3#13067237C212yesmaximal, complemented
4#13067232C211yesmaximal, characteristic, complemented
5#13067224C211yesmaximal, characteristic, complemented
6#13067219C212yesmaximal, complemented
7#13067210C211yesmaximal, characteristic, complemented
8#13067205C211yesmaximal, characteristic, complemented
9#13067202C212yesmaximal, complemented
10C2×#10622103C212yesmaximal, complemented
11C11×#2970C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623355—21no—
14C2×#67001—21no—
15#10623114—21no—
16#10623110C411yescharacteristic
17#10623098C411yescharacteristic
18#10623096C412yes—
19#10623095—22no—
20#10623086C411yescharacteristic
21#10623077—21no—
22#10623074C411yescharacteristic
23#10623072C412yes—
24#10623062—22no—
25#10623060—21no—
26#10623010C2212yes—
27#10623010C2211yescharacteristic
28#10623001C2211yescharacteristic
29C2×#66923C2212yes—
30C11×#446—21no—
31C11×#435—22no—
32C8×D4×C11—21no—
33C11×#432C2212yes—
34C11×#432C2211yescharacteristic
35C4×C11×M16C2211yescharacteristic
36C2×C11×#97C2212yes—
37#10622610—21no—
38#10622610—22no—
39C4×#4318C2212yes—
40C4×#4318C2211yescharacteristic
41C2×#66867C2212yes—
42C2×#66867C2211yescharacteristic
43#10622103C2211yescharacteristic
44#10622103C2212yes—
45#10622103C2212yes—
46#10622103C2212yes—
47#10622103C2212yes—
48#10622103C2211yescharacteristic
49#10622103C2212yes—
50#10622102C2211yescharacteristic
51#10622102C2212yes—
52#10622102C2211yescharacteristic
53C2×C11×#41D411yescharacteristic
54C2×#4341—21no—
55C2×C11×M16—21no—
56C22×C8×C11—22no—
57C4×Q8×C11C2×C411yescharacteristic
58C4×Q8×C11D411yescharacteristic
59C4×D4×C11C2×C412yes—
60C4×D4×C11C2×C411yescharacteristic
61C4×D4×C11D411yescharacteristic
62C4×D4×C11D412yes—
63C11×#117D411yescharacteristic
64C11×#117D412yes—
65C2×C42×C11C2312yes—
66C2×C42×C11C2311yescharacteristic
67#67001—28no—
68#66999—21no—
69#66997—21no—
70#66992—22no—
71#66988—22no—
72D4×Dic11—21no—
73#66983C2×C412yes—
74#66983C2×C411yescharacteristic
75#66982—22no—
76#66982—21no—
77C4×C22⋊D11—21no—
78C4×C22⋊D11—22no—
79#66979C2×C412yes—
80C2×C4⋊Dic11C2×C412yes—
81C2×C4⋊Dic11C2×C412yes—
82#66977—21no—
83#66977—21no—
84#66977C2×C411yescharacteristic
85#66977C2×C412yes—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—22no—
88C2×#4318—22no—
89C2×#4318—21no—
90C22×C11⋊C8—22no—
91C22×C11⋊C8—21no—
92#66951—22no—
93#66950—21no—
94#66949—22no—
95C4⋊C4×D11—21no—
96#66943—21no—
97#66942—22no—
98#66942—22no—
99#66940—21no—
100#66939—22no—
101#66936—22no—
102(C22⋊D11)⋊C4—22no—
103#66932—22no—
104#66931—22no—
105#66930—22no—
106#66929—21no—
107#66929—22no—
108#66928C2311yescharacteristic
109C4×D44C2×C411yescharacteristic
110C4×D44C2×C412yes—
111#66925—22no—
112#66925—21no—
113#66923—22no—
114#66923—22no—
115#66923C2×C412yes—
116#66923C2×C412yes—
117#66923C2311yescharacteristic
118#66923C2312yes—
119#66922C2×C411yescharacteristic
120#66922C2×C411yescharacteristic
121C4×Dic22—21no—
122C4×Dic22—21no—
123C4×Dic22C2×C412yes—
124C4×Dic22C2×C411yescharacteristic
125C11×C4⋊C8—21no—
126C11×C4⋊C8—22no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8—21no—
129C11×#97—22no—
130C11×#97C2311yescharacteristic
131C11×#97C2312yes—
132C11×#97C2311yescharacteristic
133C4×C8×C11—21no—
134#66867—21no—
135#66867—22no—
136#66867C2311yescharacteristic
137#66867C2312yes—
138#66867C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—22no—
141#17653—111nomaximal, Sylow
142C11×#41—24no—
143C2×Q8×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C412yes—
145C2×D4×C11C22⋊C411yescharacteristic
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C2×C22⋊D11—22no—
153C2×C22⋊D11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156#4341—44no—
157C2×D44C22×C411yescharacteristic
158C2×C4×D11—21no—
159C2×C4×D11—22no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C11×M16—42no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—22no—
167C2×C8×C11—44no—
168C11×C4⋊C4C22⋊C411yescharacteristic
169C11×C4⋊C4C22⋊C412yes—
170C11×C4⋊C4C22⋊C412yes—
171C11×C4⋊C4C22⋊C411yescharacteristic
172C11×C22⋊C4C22⋊C412yes—
173C11×C22⋊C4C22⋊C412yes—
174C11×C22⋊C4C22⋊C412yes—
175C42×C11C22×C411yescharacteristic
176C42×C11C22×C412yes—
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D412yes—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D412yes—
181C42×C11C2411yescharacteristic
182C22⋊Dic11—22no—
183C22⋊Dic11—21no—
184C22⋊Dic11—22no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—22no—
194C4⋊Dic11—22no—
195C4⋊Dic11C22×C412yes—
196C4⋊Dic11C22×C411yescharacteristic
197C4⋊Dic11C22×C412yes—
198C4⋊Dic11C22×C411yescharacteristic
199Dic11⋊C4—21no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—21no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—21no—
210Dic11⋊C4—21no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213C4×Dic11—21no—
214#4318—28no—
215#4318—24no—
216C2×C11⋊C8—28no—
217C2×C11⋊C8—24no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221#3515—111no—
222#2970D1111yescharacteristic, complemented
223#2875—111no—
224#1532—112no—
225#1531—111no—
226#1529—111no—
227#1528—112no—
228#1526—111no—
229#1524—111no—
230#1524—112no—
231C2×#330—112no—
232C23×C11C2×C22⋊C411yescharacteristic
233C23×C11C2×C22⋊C412yes—
234C22×D11—21no—
235Q8×C11—22no—
236D4×C11—24no—
237D4×C11#10414yes—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11C2×C22⋊C411yescharacteristic
245C2×C4×C11C2×C22⋊C412yes—
246C2×C4×C11C2×C22⋊C412yes—
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C22⋊D11—44no—
254C22⋊D11—81no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—44no—
261C2×Dic11—82no—
262D44—41no—
263C4×D11—42no—
264C4×D11—82no—
265Dic22—42no—
266Dic22—41no—
267Dic22—81no—
268C8×C11—22no—
269C8×C11—42no—
270C8×C11—41no—
271C11⋊C8—22no—
272C11⋊C8—24no—
273C11⋊C8—22no—
274C2×#131—221no—
275#557—111no—
276#554—111no—
277#554—111no—
278#553—112no—
279#552—112no—
280#552—221no—
281#552—222no—
282#547—111no—
283#547—221no—
284#541—221no—
285#539—222no—
286#533—111no—
287#529—111no—
288#529—112no—
289C2×#125—112no—
290#520—221no—
291C4×#41C2×D1111yescharacteristic
292#446—21no—
293#435—22no—
294C8×D4—21no—
295#432C2×D1112yes—
296#432C2×D1111yescharacteristic
297#405—221no—
298#405—222no—
299C4×M16—112no—
300C4×M16—111no—
301C4×M16C2×D1111yescharacteristic
302C2×#97—112no—
303C2×#97—111no—
304C2×#97C2×D1112yes—
305#330—111no—
306#330—112no—
307#330—112no—
308#330—112no—
309#330—111no—
310#330—112no—
311#330—112no—
312#329—111no—
313#329—112no—
314#329—111no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11C2×#10414yes—
321C22×C11C22×C22⋊C411yescharacteristic
322C2×D11—41no—
323C2×D11—41no—
324C2×D11—41no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—22no—
328C4×C11—21no—
329C4×C11—22no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—22no—
333C4×C11C2×#10412yes—
334Dic11—41no—
335Dic11—42no—
336Dic11—41no—
337Dic11—42no—
338Dic11—41no—
339C2×#41—221no—
340C2×#41D4411yescharacteristic
341#131—228no—
342C2×M16—21no—
343C2×M16—222no—
344C2×M16—221no—
345C22×C8—22no—
346C22×C8—222no—
347C22×C8—221no—
348C4⋊Q8—111no—
349C4⋊Q8—111no—
350C4⋊Q8—221no—
351#126—222no—
352#126—222no—
353#126—221no—
354#126—222no—
355#125—112no—
356#125—112no—
357#125—111no—
358#125—112no—
359#125—222no—
360#125—222no—
361#125—221no—
362#125—222no—
363#125—222no—
364#124—111no—
365#123—222no—
366#123—222no—
367#123—221no—
368#123—222no—
369#123—222no—
370C22⋊Q8—111no—
371C22⋊Q8—112no—
372C22⋊Q8—221no—
373C22⋊Q8—221no—
374C22⋊Q8—221no—
375C22⋊Q8—222no—
376C22⋊Q8—221no—
377C22⋊Q8—222no—
378#121—112no—
379#121—111no—
380#121—222no—
381C4×Q8—112no—
382C4×Q8—111no—
383C4×Q8—221no—
384C4×Q8—221no—
385C4×Q8—221no—
386C4×Q8C4×D1111yescharacteristic
387C4×Q8C22⋊D1111yescharacteristic
388C4×D4—111no—
389C4×D4—112no—
390C4×D4—221no—
391C4×D4—221no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4C4×D1111yescharacteristic
395C4×D4C4×D1112yes—
396C4×D4C22⋊D1111yescharacteristic
397C4×D4C22⋊D1112yes—
398#117—112no—
399#117—222no—
400#117—222no—
401#117—221no—
402#117D4411yescharacteristic
403#117D4412yes—
404C2×C4⋊C4—112no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—222no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C42C22×D1112yes—
410C2×C42C22×D1111yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—22no—
413C22⋊C8—22no—
414C22⋊C8—21no—
415#97—22no—
416#97—111no—
417#97—111no—
418#97—112no—
419#97—222no—
420#97—221no—
421#97C22×D1111yescharacteristic
422#97C22×D1112yes—
423#97C22×D1111yescharacteristic
424C4×C8—21no—
425C4×C8—222no—
426C4×C8—221no—
427C2×C11—24no—
428C2×C11—41no—
429C2×C11#288911yescharacteristic
430C2×C11C22×#10411yescharacteristic
431C2×C11#290111yescharacteristic
432D11—81no—
433#41—24no—
434#41—444no—
435C2×Q8—111no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8(C2×D11)⋊C411yescharacteristic
439C2×D4—111no—
440C2×D4—222no—
441C2×D4—221no—
442C2×D4(C2×D11)⋊C412yes—
443C2×D4(C2×D11)⋊C411yescharacteristic
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—221no—
447C22×C4—222no—
448C22×C4C2×C4×D1112yes—
449C22×C4C2×C4×D1111yescharacteristic
450C22×C4C2×D4412yes—
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454M16—42no—
455M16—228no—
456M16—224no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—22no—
460C2×C8—44no—
461C2×C8—228no—
462C2×C8—224no—
463C2×C8—221no—
464C2×C8—222no—
465C2×C8—221no—
466C4⋊C4—111no—
467C4⋊C4—111no—
468C4⋊C4—112no—
469C4⋊C4—112no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—222no—
473C4⋊C4—221no—
474C4⋊C4—222no—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C4⋊C4—221no—
478C4⋊C4—222no—
479C4⋊C4—221no—
480C4⋊C4—222no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—222no—
484C4⋊C4—221no—
485C4⋊C4—222no—
486C4⋊C4(C2×D11)⋊C411yescharacteristic
487C4⋊C4(C2×D11)⋊C411yescharacteristic
488C4⋊C4(C2×D11)⋊C412yes—
489C4⋊C4(C2×D11)⋊C412yes—
490C22⋊C4—222no—
491C22⋊C4—222no—
492C22⋊C4—221no—
493C22⋊C4—221no—
494C22⋊C4—222no—
495C22⋊C4—222no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4(C2×D11)⋊C412yes—
500C22⋊C4(C2×D11)⋊C412yes—
501C22⋊C4(C2×D11)⋊C412yes—
502C42—222no—
503C42—222no—
504C42—221no—
505C42C2×C4×D1112yes—
506C42C2×C4×D1111yescharacteristic
507C42C2×D4412yes—
508C42C2×D4411yescharacteristic
509C42C2×C22⋊D1111yescharacteristic
510C42C2×C22⋊D1112yes—
511C42C23×D1111yescharacteristic
512C11#1765311yescharacteristic, complemented, Sylow
513C23—221no—
514C23C2×(C2×D11)⋊C411yescharacteristic
515C23C2×(C2×D11)⋊C412yes—
516Q8—22no—
517Q8—441no—
518Q8—442no—
519Q8—881no—
520D4—24no—
521D4—441no—
522D4—444no—
523D4—881no—
524D4#6688914yes—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—221no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—444no—
537C2×C4—442no—
538C2×C4—882no—
539C2×C4—882no—
540C2×C4C2×(C2×D11)⋊C411yescharacteristic
541C2×C4C2×(C2×D11)⋊C412yes—
542C2×C4C2×(C2×D11)⋊C411yescharacteristic
543C2×C4C2×(C2×D11)⋊C412yes—
544C2×C4C2×(C2×D11)⋊C412yes—
545C2×C4C2×(C2×D11)⋊C411yescharacteristic
546C2×C4C22×C4×D1111yescharacteristic
547C2×C4C22×D4411yescharacteristic
548C2×C4C22×C22⋊D1111yescharacteristic
549C8—22no—
550C8—42no—
551C8—41no—
552C8—222no—
553C8—224no—
554C8—222no—
555C22—22no—
556C22—22no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—441no—
561C22—441no—
562C22—441no—
563C22C2×#6688914yes—
564C22C22×(C2×D11)⋊C411yescharacteristic
565C4—21no—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—441no—
574C4—441no—
575C4—442no—
576C4—441no—
577C4—442no—
578C4C2×#6688912yes—
579C2—24no—
580C2—41no—
581C2—881no—
582C2#1307709811yescharacteristic
583C2C22×#6688911yescharacteristic
584C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2970C2
socleC22×C11C22×C22⋊C4
prime radical#13082594C2
cosocleC42×C11C24
hypercenter#2970D11
hypocenterC11#17653
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #13077044C2semidirect
3. #13067237C2semidirect
4. #13067232C2semidirect
5. #13067224C2semidirect
6. #13067219C2semidirect
7. #13067210C2semidirect
8. #13067205C2semidirect
9. #13067202C2semidirect
10. C2×#10622103C2semidirect
11. C11×#2970C2semidirect
222. #2970D11semidirect
512. C11#17653semidirect

Maximal subgroups

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

subgroupindex
#130825942
#130770442
#130672372
#130672322
#130672242
#130672192
#130672102
#130672052
#130672022
C2×#106221032
C11×#29702
#1765311