Finite Group Databasebeta

← #14721954

Subgroups — #14721954

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082594C211yesmaximal, characteristic
2#13077636C211yesmaximal, characteristic, complemented
3#13067248C212yesmaximal, complemented
4#13067242C212yesmaximal, complemented
5#13067230C211yesmaximal, characteristic, complemented
6#13067224C212yesmaximal, complemented
7#13067221C211yesmaximal, characteristic, complemented
8#13067219C212yesmaximal, complemented
9#13067210C211yesmaximal, characteristic, complemented
10#13067202C211yesmaximal, characteristic, complemented
11C11×#2923C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623355—21no—
14#10623114—21no—
15#10623110C411yescharacteristic
16#10623098C411yescharacteristic
17#10623096C412yes—
18#10623095—22no—
19#10623086C411yescharacteristic
20#10623077—21no—
21#10623074C411yescharacteristic
22#10623072C412yes—
23#10623062—22no—
24#10623060—21no—
25#10623010C2211yescharacteristic
26#10623010C2212yes—
27#10623001C2211yescharacteristic
28C2×#66923C2212yes—
29C11×#433—22no—
30C11×#432C2212yes—
31C11×#432C2212yes—
32C11×#424—21no—
33C11×#408—21no—
34C4×C11×M16C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic
36Q8×C11⋊C8—21no—
37#10622625—21no—
38#10622625—22no—
39#10622539C2211yescharacteristic
40#10622539C2212yes—
41C4×#4318C2211yescharacteristic
42C4×#4318C2212yes—
43#10622103C2211yescharacteristic
44#10622103C2211yescharacteristic
45#10622103C2212yes—
46#10622103C2212yes—
47#10622103C2212yes—
48#10622103C2212yes—
49#10622103C2212yes—
50#10622102C2211yescharacteristic
51#10622102C2211yescharacteristic
52#10622102C2212yes—
53C2×C11×#41D411yescharacteristic
54C2×#4341—21no—
55C2×C11×M16—21no—
56C22×C8×C11—21no—
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#66999—21no—
68#66997—21no—
69#66992—22no—
70#66988—22no—
71D4×Dic11—21no—
72#66983C2×C412yes—
73#66983C2×C411yescharacteristic
74#66982—22no—
75#66982—21no—
76C4×C22⋊D11—21no—
77C4×C22⋊D11—22no—
78#66979C2×C412yes—
79C2×C4⋊Dic11C2×C412yes—
80C2×C4⋊Dic11C2×C412yes—
81#66977—21no—
82#66977—21no—
83#66977C2×C411yescharacteristic
84#66977C2×C412yes—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×#4318—22no—
88C2×#4318—21no—
89#66951—22no—
90#66950—21no—
91#66949—22no—
92C4⋊C4×D11—21no—
93#66943—21no—
94#66942—22no—
95#66942—22no—
96#66940—21no—
97#66939—22no—
98#66936—22no—
99(C22⋊D11)⋊C4—22no—
100#66932—22no—
101#66931—22no—
102#66930—22no—
103#66929—21no—
104#66929—22no—
105#66928C2311yescharacteristic
106C4×D44C2×C411yescharacteristic
107C4×D44C2×C412yes—
108#66925—22no—
109#66925—21no—
110#66923—22no—
111#66923—22no—
112#66923C2×C412yes—
113#66923C2×C412yes—
114#66923C2311yescharacteristic
115#66923C2312yes—
116#66922C2×C411yescharacteristic
117#66922C2×C411yescharacteristic
118C4×Dic22—21no—
119C4×Dic22—21no—
120C4×Dic22C2×C412yes—
121C4×Dic22C2×C411yescharacteristic
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×#97—21no—
127C11×#97C2311yescharacteristic
128C11×#97C2311yescharacteristic
129C11×#97C2312yes—
130C4×C8×C11—21no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)—22no—
135#66867C2311yescharacteristic
136#66867C2311yescharacteristic
137#66867C2312yes—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—22no—
140#17682—111nomaximal, Sylow
141C11×#41—42no—
142C2×Q8×C11C22⋊C411yescharacteristic
143C2×D4×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C412yes—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C2×C22⋊D11—22no—
152C2×C22⋊D11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155#4341—44no—
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—22no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22×C411yescharacteristic
162C11×M16—42no—
163C2×C8×C11—22no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—42no—
167C11×C4⋊C4C22⋊C411yescharacteristic
168C11×C4⋊C4C22⋊C412yes—
169C11×C4⋊C4C22⋊C412yes—
170C11×C4⋊C4C22⋊C411yescharacteristic
171C11×C22⋊C4C22⋊C412yes—
172C11×C22⋊C4C22⋊C412yes—
173C11×C22⋊C4C22⋊C412yes—
174C42×C11C22×C411yescharacteristic
175C42×C11C22×C412yes—
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D412yes—
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D412yes—
180C42×C11C2411yescharacteristic
181C22⋊Dic11—22no—
182C22⋊Dic11—21no—
183C22⋊Dic11—22no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—22no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—22no—
193C4⋊Dic11—22no—
194C4⋊Dic11C22×C412yes—
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C412yes—
197C4⋊Dic11C22×C411yescharacteristic
198Dic11⋊C4—21no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—21no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—21no—
209Dic11⋊C4—21no—
210C4×Dic11—22no—
211C4×Dic11—22no—
212C4×Dic11—21no—
213#4318—42no—
214#4318—44no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—22no—
218#3515—111no—
219#2971—111no—
220#2923D1111yescharacteristic, complemented
221#1535—112no—
222#1534—112no—
223#1531—111no—
224#1529—112no—
225#1529—111no—
226#1528—112no—
227#1526—111no—
228#1524—111no—
229C23×C11C2×C22⋊C411yescharacteristic
230C23×C11C2×C22⋊C412yes—
231C22×D11—21no—
232Q8×C11—22no—
233D4×C11—22no—
234D4×C11—42no—
235C2×C4×C11—22no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11C2×C22⋊C411yescharacteristic
242C2×C4×C11C2×C22⋊C412yes—
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11C2×C22⋊C412yes—
245C2×C4×C11C2×C22⋊C411yescharacteristic
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C22⋊D11—44no—
251C22⋊D11—81no—
252C2×Dic11—21no—
253C2×Dic11—22no—
254C2×Dic11—21no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—44no—
258C2×Dic11—82no—
259D44—41no—
260C4×D11—42no—
261C4×D11—82no—
262Dic22—42no—
263Dic22—41no—
264Dic22—81no—
265C8×C11—41no—
266C8×C11—41no—
267C8×C11—42no—
268C11⋊C8—22no—
269C11⋊C8—41no—
270C11⋊C8—42no—
271#557—111no—
272#554—111no—
273#554—111no—
274#553—112no—
275#552—112no—
276#552—221no—
277#552—222no—
278#547—111no—
279#547—221no—
280#541—221no—
281#539—222no—
282#533—111no—
283#529—111no—
284#529—112no—
285C2×#125—112no—
286#520—221no—
287C4×#41C2×D1111yescharacteristic
288C8×Q8—221no—
289#436—221no—
290#436—222no—
291#433—22no—
292#432—111no—
293#432—112no—
294#432C2×D1112yes—
295#432C2×D1112yes—
296#424—21no—
297#408—21no—
298C4×M16—111no—
299C4×M16—112no—
300C4×M16C2×D1111yescharacteristic
301C2×#97C2×D1111yescharacteristic
302#330—111no—
303#330—111no—
304#330—112no—
305#330—112no—
306#330—112no—
307#330—112no—
308#330—112no—
309#329—111no—
310#329—111no—
311#329—112no—
312C22×C11—21no—
313C22×C11—22no—
314C22×C11—21no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—21no—
318C22×C11C22×C22⋊C411yescharacteristic
319C2×D11—41no—
320C2×D11—41no—
321C2×D11—41no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—22no—
325C4×C11—21no—
326C4×C11—22no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—22no—
330C4×C11#42112yes—
331Dic11—41no—
332Dic11—42no—
333Dic11—41no—
334Dic11—42no—
335Dic11—41no—
336C2×#41—221no—
337C2×#41C22⋊D1111yescharacteristic
338C2×M16—21no—
339C2×M16—222no—
340C2×M16—221no—
341C22×C8—21no—
342C4⋊Q8—111no—
343C4⋊Q8—111no—
344C4⋊Q8—221no—
345#126—222no—
346#126—222no—
347#126—222no—
348#126—221no—
349#125—112no—
350#125—112no—
351#125—111no—
352#125—112no—
353#125—222no—
354#125—222no—
355#125—221no—
356#125—222no—
357#125—222no—
358#124—111no—
359#123—222no—
360#123—221no—
361#123—222no—
362#123—222no—
363#123—222no—
364C22⋊Q8—111no—
365C22⋊Q8—112no—
366C22⋊Q8—221no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369C22⋊Q8—222no—
370C22⋊Q8—221no—
371C22⋊Q8—222no—
372#121—112no—
373#121—111no—
374#121—222no—
375C4×Q8—112no—
376C4×Q8—111no—
377C4×Q8—221no—
378C4×Q8—221no—
379C4×Q8—221no—
380C4×Q8C4×D1111yescharacteristic
381C4×Q8D4411yescharacteristic
382C4×D4—111no—
383C4×D4—112no—
384C4×D4—221no—
385C4×D4—222no—
386C4×D4—221no—
387C4×D4—222no—
388C4×D4C4×D1111yescharacteristic
389C4×D4C4×D1112yes—
390C4×D4D4411yescharacteristic
391C4×D4D4412yes—
392#117—112no—
393#117—222no—
394#117—221no—
395#117—222no—
396#117C22⋊D1111yescharacteristic
397#117C22⋊D1112yes—
398C2×C4⋊C4—112no—
399C2×C4⋊C4—112no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—221no—
403C2×C42C22×D1112yes—
404C2×C42C22×D1111yescharacteristic
405C4⋊C8—22no—
406C4⋊C8—22no—
407C4⋊C8—221no—
408C4⋊C8—222no—
409C22⋊C8—22no—
410C22⋊C8—22no—
411C22⋊C8—222no—
412C22⋊C8—221no—
413#97—21no—
414#97—111no—
415#97—111no—
416#97—112no—
417#97C22×D1111yescharacteristic
418#97C22×D1111yescharacteristic
419#97C22×D1112yes—
420C4×C8—21no—
421C4×C8—221no—
422C4×C8—222no—
423C2×C11—41no—
424C2×C11—42no—
425C2×C11#288911yescharacteristic
426C2×C11C2×#42111yescharacteristic
427C2×C11#290111yescharacteristic
428D11—81no—
429#41—42no—
430#41—444no—
431C2×Q8—111no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8(C2×D11)⋊C411yescharacteristic
435C2×D4—111no—
436C2×D4—222no—
437C2×D4—221no—
438C2×D4(C2×D11)⋊C411yescharacteristic
439C2×D4(C2×D11)⋊C412yes—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—221no—
443C22×C4—222no—
444C22×C4C2×C4×D1112yes—
445C22×C4C2×C4×D1111yescharacteristic
446C22×C4C2×D4412yes—
447C22×C4C2×D4411yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1112yes—
450M16—42no—
451M16—444no—
452M16—442no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—42no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—222no—
460C4⋊C4—111no—
461C4⋊C4—111no—
462C4⋊C4—112no—
463C4⋊C4—112no—
464C4⋊C4—222no—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C4⋊C4—221no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—221no—
472C4⋊C4—222no—
473C4⋊C4—221no—
474C4⋊C4—222no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—222no—
478C4⋊C4—221no—
479C4⋊C4—222no—
480C4⋊C4(C2×D11)⋊C411yescharacteristic
481C4⋊C4(C2×D11)⋊C411yescharacteristic
482C4⋊C4(C2×D11)⋊C412yes—
483C4⋊C4(C2×D11)⋊C412yes—
484C22⋊C4—222no—
485C22⋊C4—222no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—222no—
489C22⋊C4—222no—
490C22⋊C4—221no—
491C22⋊C4—221no—
492C22⋊C4—221no—
493C22⋊C4(C2×D11)⋊C412yes—
494C22⋊C4(C2×D11)⋊C412yes—
495C22⋊C4(C2×D11)⋊C412yes—
496C42—222no—
497C42—222no—
498C42—221no—
499C42C2×C4×D1112yes—
500C42C2×C4×D1111yescharacteristic
501C42C2×D4411yescharacteristic
502C42C2×D4412yes—
503C42C2×C22⋊D1111yescharacteristic
504C42C2×C22⋊D1112yes—
505C42C23×D1111yescharacteristic
506C11#1768211yescharacteristic, complemented, Sylow
507C23—221no—
508C23C2×(C2×D11)⋊C411yescharacteristic
509C23C2×(C2×D11)⋊C412yes—
510Q8—22no—
511Q8—441no—
512Q8—442no—
513Q8—881no—
514D4—22no—
515D4—42no—
516D4—441no—
517D4—444no—
518D4—881no—
519C2×C4—22no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—221no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—444no—
531C2×C4—442no—
532C2×C4—882no—
533C2×C4—882no—
534C2×C4C2×(C2×D11)⋊C411yescharacteristic
535C2×C4C2×(C2×D11)⋊C412yes—
536C2×C4C2×(C2×D11)⋊C412yes—
537C2×C4C2×(C2×D11)⋊C411yescharacteristic
538C2×C4C2×(C2×D11)⋊C412yes—
539C2×C4C2×(C2×D11)⋊C411yescharacteristic
540C2×C4C22×C4×D1111yescharacteristic
541C2×C4C22×D4411yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—41no—
544C8—41no—
545C8—42no—
546C8—222no—
547C8—441no—
548C8—442no—
549C22—21no—
550C22—22no—
551C22—21no—
552C22—22no—
553C22—22no—
554C22—21no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22C22×(C2×D11)⋊C411yescharacteristic
559C4—21no—
560C4—21no—
561C4—22no—
562C4—21no—
563C4—22no—
564C4—21no—
565C4—22no—
566C4—21no—
567C4—441no—
568C4—441no—
569C4—442no—
570C4—441no—
571C4—442no—
572C4#1062261812yes—
573C2—41no—
574C2—42no—
575C2—881no—
576C2#1307709811yescharacteristic
577C2C2×#1062261811yescharacteristic
578C2#1307716111yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2923C2
socleC22×C11C22×C22⋊C4
prime radical#13082594C2
cosocleC42×C11C24
hypercenter#2923D11
hypocenterC11#17682
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #13077636C2semidirect
3. #13067248C2semidirect
4. #13067242C2semidirect
5. #13067230C2semidirect
6. #13067224C2semidirect
7. #13067221C2semidirect
8. #13067219C2semidirect
9. #13067210C2semidirect
10. #13067202C2semidirect
11. C11×#2923C2semidirect
220. #2923D11semidirect
506. C11#17682semidirect

Maximal subgroups

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

subgroupindex
#130825942
#130776362
#130672482
#130672422
#130672302
#130672242
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C11×#29232
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