Finite Group Databasebeta

← #14721571

Subgroups — #14721571

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082481C211yesmaximal, characteristic
2#13077701C211yesmaximal, characteristic, complemented
3#13067191C212yesmaximal, complemented
4#13067166C211yesmaximal, characteristic, complemented
5#13067162C211yesmaximal, characteristic
6#13067152C212yesmaximal, complemented
7#13067139C212yesmaximal, complemented
8#13067127C211yesmaximal, characteristic, complemented
9#13067123C211yesmaximal, characteristic
10#13067100C212yesmaximal, complemented
11C11×#2356C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13#10623347—21no—
14#10623116C412yescomplemented
15#10623115C412yescomplemented
16#10623112—22no—
17#10623110C412yescomplemented
18#10623099—22no—
19#10623098C412yescomplemented
20#10623046—21no—
21#10623046—21no—
22#10623035—21no—
23#10623010C2212yes—
24#10623010C2212yes—
25#10623008C2211yescharacteristic
26#10623001C2211yescharacteristic
27C11×#391—21no—
28C11×#387—21no—
29C11×#387—21no—
30C11×#383C2211yescharacteristic
31C11×#383C2211yescharacteristic
32C11×#382C2211yescharacteristic
33C4×C11×C4⋊C4—21no—
34C4×C11×C4⋊C4C2211yescharacteristic
35C11×#376C2211yescharacteristic
36C11×#376C2211yescharacteristic
37#10622637—22no—
38#10622637—22no—
39#10622539C2211yescharacteristic
40#10622539C2211yescharacteristic
41#10622539C2212yes—
42#10622538C2212yes—
43#10622090C2212yes—
44#10622090C2212yes—
45#10622090C2212yes—
46#10622090C2212yes—
47#10622089C2212yes—
48#10622089C2212yes—
49#10622089C2212yes—
50#10622089C2212yes—
51C22×Q8×C11D411yescharacteristic
52C2×#4339—21no—
53C4×Q8×C11C2×C412yes—
54C4×Q8×C11C2×C412yes—
55C4×Q8×C11D412yes—
56C4×Q8×C11D412yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11—21no—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68#67000—22no—
69#66999—22no—
70#66999—22no—
71#66997—22no—
72#66983—21no—
73#66983C2312yes—
74#66982—22no—
75#66982—22no—
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78#66979—21no—
79#66977—21no—
80#66977C2312yes—
81#66951—22no—
82#66951—22no—
83#66949—22no—
84#66949—22no—
85#66947—22no—
86#66947—22no—
87#66946—22no—
88#66945—22no—
89C4⋊C4×D11—22no—
90#66942—22no—
91#66942—22no—
92#66940—22no—
93#66929—22no—
94#66929—22no—
95#66928—21no—
96#66928C2×C412yes—
97#66928C2×C412yes—
98#66927C2×C411yescharacteristic
99C4×D44—21no—
100C4×D44C2×C412yes—
101C4×D44C2×C412yes—
102C4×D44C2×C412yes—
103#66925—22no—
104#66925—22no—
105#66923—21no—
106#66923C2×C412yes—
107#66923C2×C412yes—
108#66922C2×C411yescharacteristic
109#66922C2×C411yescharacteristic
110#66922C2×C411yescharacteristic
111C4×Dic22—21no—
112C4×Dic22C2×C412yes—
113C4×Dic22C2×C412yes—
114C4×Dic22C2×C412yes—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122C11×#95C2311yescharacteristic
123C11×#95C2311yescharacteristic
124C11×#95C2311yescharacteristic
125C11×#95C2311yescharacteristic
126C22⋊(C11⋊C8)C2312yes—
127C22⋊(C11⋊C8)C2312yes—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—22no—
132#66867—21no—
133#66867—21no—
134#66867—22no—
135C4×C11⋊C8—22no—
136#17624—111nomaximal, Sylow
137C2×Q8×C11—41no—
138C2×Q8×C11—41no—
139C2×Q8×C11C22⋊C412yes—
140C2×Q8×C11C22⋊C412yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—22no—
153#4339—42no—
154#4339—42no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44C22×C412yes—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22C22×C412yes—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4C22⋊C412yes—
167C11×C4⋊C4C22⋊C412yes—
168C11×C4⋊C4C22⋊C412yes—
169C11×C4⋊C4C22⋊C412yes—
170C11×C4⋊C4C22⋊C412yes—
171C11×C4⋊C4C22⋊C412yes—
172C42×C11—42no—
173C42×C11—42no—
174C42×C11—42no—
175C42×C11C22×C411yescharacteristic
176C42×C11C22×C412yes—
177C42×C11C22×C412yes—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D412yes—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D412yes—
183C22⋊Dic11—22no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—22no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—22no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C22×C412yes—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211#3507—111no—
212#2983—111no—
213#2356D1111yescharacteristic, complemented
214#1521—112no—
215#1515—111no—
216#1514—111no—
217#1512—112no—
218#1509—112no—
219#1506—111no—
220#1505—111no—
221#1500—112no—
222C23×C11C22×D411yescharacteristic
223C22×D11—22no—
224Q8×C11—42no—
225Q8×C11—42no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C2×C22⋊C412yes—
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C22⋊D11—42no—
259C22⋊D11—42no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263D44—42no—
264D44—42no—
265D44—81no—
266C4×D11—44no—
267C4×D11—82no—
268C4×D11—82no—
269Dic22—42no—
270Dic22—42no—
271Dic22—81no—
272C11⋊C8—42no—
273C11⋊C8—42no—
274#559—112no—
275#557—112no—
276#556—112no—
277#556—222no—
278#554—112no—
279#552—222no—
280#539—221no—
281#539—221no—
282#536—221no—
283#533—111no—
284#532—111no—
285#529—112no—
286#529—112no—
287#520—221no—
288C2×C4×Q8C2×D1111yescharacteristic
289#446—222no—
290#446—222no—
291#432—111no—
292#432—111no—
293#432—112no—
294#431—112no—
295#391—21no—
296#387—21no—
297#387—21no—
298#383C2×D1111yescharacteristic
299#383C2×D1111yescharacteristic
300#382C2×D1111yescharacteristic
301C4×C4⋊C4—21no—
302C4×C4⋊C4C2×D1111yescharacteristic
303#376C2×D1111yescharacteristic
304#376C2×D1111yescharacteristic
305#328—112no—
306#328—112no—
307#328—112no—
308#328—112no—
309#327—112no—
310#327—112no—
311#327—112no—
312#327—112no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11C22×C22⋊C411yescharacteristic
316C22×C11#57511yescharacteristic
317C22×C11#57511yescharacteristic
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—42no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—21no—
331C4×C11—42no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11—81no—
335Dic11—42no—
336Dic11—42no—
337Dic11—42no—
338C2×#41—221no—
339C22×Q8C22⋊D1111yescharacteristic
340C4⋊Q8—111no—
341C4⋊Q8—111no—
342C4⋊Q8—111no—
343C4⋊Q8—222no—
344#127—111no—
345#126—222no—
346#126—222no—
347#126—222no—
348#126—222no—
349#125—112no—
350#125—112no—
351#125—222no—
352#125—222no—
353#125—221no—
354#124—112no—
355#124—112no—
356#124—222no—
357#124—221no—
358#123—222no—
359#123—222no—
360#123—222no—
361#123—222no—
362C22⋊Q8—112no—
363C22⋊Q8—222no—
364C22⋊Q8—222no—
365C22⋊Q8—221no—
366C22⋊Q8—222no—
367C22⋊Q8—222no—
368#121—112no—
369#121—221no—
370C4×Q8—112no—
371C4×Q8—112no—
372C4×Q8—112no—
373C4×Q8—222no—
374C4×Q8—221no—
375C4×Q8C4×D1112yes—
376C4×Q8C4×D1112yes—
377C4×Q8D4412yes—
378C4×Q8D4412yes—
379C4×D4—112no—
380C4×D4—112no—
381C4×D4—112no—
382C4×D4—222no—
383C4×D4—222no—
384C4×D4—222no—
385C4×D4—221no—
386#117—221no—
387#117—222no—
388#117—222no—
389#117—222no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4C22⋊D1111yescharacteristic
394C2×C4⋊C4C22⋊D1111yescharacteristic
395C2×C4⋊C4C22⋊D1111yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402C4⋊C8—222no—
403C4⋊C8—222no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C22⋊C8—112no—
407C22⋊C8—112no—
408#97—222no—
409#97—221no—
410#97—221no—
411C4×C8—222no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95C22×D1111yescharacteristic
420#95C22×D1111yescharacteristic
421#95C22×D1111yescharacteristic
422#95C22×D1111yescharacteristic
423C2×C11—21no—
424C2×C11—21no—
425C2×C11#288411yescharacteristic
426C2×C11#289611yescharacteristic
427C2×C11#290111yescharacteristic
428D11—82no—
429#41—442no—
430#41—442no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—112no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8(C2×D11)⋊C412yes—
437C2×Q8(C2×D11)⋊C412yes—
438C2×D4—112no—
439C2×D4—222no—
440C2×D4—221no—
441C2×D4—221no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456C2×C8—222no—
457C2×C8—222no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—112no—
461C4⋊C4—112no—
462C4⋊C4—221no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C4⋊C4—221no—
466C4⋊C4—222no—
467C4⋊C4—222no—
468C4⋊C4—221no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—221no—
473C4⋊C4—222no—
474C4⋊C4(C2×D11)⋊C412yes—
475C4⋊C4(C2×D11)⋊C412yes—
476C4⋊C4(C2×D11)⋊C412yes—
477C4⋊C4(C2×D11)⋊C412yes—
478C4⋊C4(C2×D11)⋊C412yes—
479C4⋊C4(C2×D11)⋊C412yes—
480C22⋊C4—222no—
481C22⋊C4—222no—
482C22⋊C4—222no—
483C22⋊C4—222no—
484C22⋊C4—222no—
485C22⋊C4—222no—
486C22⋊C4—222no—
487C22⋊C4—222no—
488C22⋊C4—222no—
489C42—42no—
490C42—42no—
491C42—42no—
492C42—222no—
493C42—222no—
494C42—222no—
495C42C2×C4×D1111yescharacteristic
496C42C2×C4×D1112yes—
497C42C2×C4×D1112yes—
498C42C2×C4×D1111yescharacteristic
499C42C2×D4412yes—
500C42C2×D4412yes—
501C42C2×D4411yescharacteristic
502C42C2×D4411yescharacteristic
503C11#1762411yescharacteristic, complemented, Sylow
504C23—222no—
505C23C22×C22⋊D1111yescharacteristic
506Q8—42no—
507Q8—42no—
508Q8—442no—
509Q8—442no—
510Q8—881no—
511D4—442no—
512D4—442no—
513D4—442no—
514D4—442no—
515D4—881no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—444no—
542C2×C4—882no—
543C2×C4—882no—
544C2×C4C2×(C2×D11)⋊C411yescharacteristic
545C2×C4C2×(C2×D11)⋊C412yes—
546C2×C4C2×(C2×D11)⋊C412yes—
547C2×C4C2×(C2×D11)⋊C412yes—
548C2×C4C2×(C2×D11)⋊C412yes—
549C2×C4C2×(C2×D11)⋊C411yescharacteristic
550C2×C4C2×(C2×D11)⋊C411yescharacteristic
551C2×C4C2×(C2×D11)⋊C411yescharacteristic
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4C22×D4411yescharacteristic
554C8—442no—
555C8—442no—
556C22—21no—
557C22—21no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22C22×(C2×D11)⋊C411yescharacteristic
562C22#1062335311yescharacteristic
563C22#1062335311yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—21no—
573C4—21no—
574C4—42no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—442no—
579C4—442no—
580C4—442no—
581C2—21no—
582C2—21no—
583C2—882no—
584C2#1307707911yescharacteristic
585C2#1307713311yescharacteristic
586C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2356C2
socleC22×C11C22×C22⋊C4
prime radical#10623008C22
cosocleC22×C4×C11C24
hypercenter#2356D11
hypocenterC11#17624
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #2356

Complements

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

NH ≅ G/Ntype
2. #13077701C2semidirect
3. #13067191C2semidirect
4. #13067166C2semidirect
6. #13067152C2semidirect
7. #13067139C2semidirect
8. #13067127C2semidirect
10. #13067100C2semidirect
11. C11×#2356C2semidirect
14. #10623116C4semidirect
15. #10623115C4semidirect
17. #10623110C4semidirect
19. #10623098C4semidirect
213. #2356D11semidirect
503. C11#17624semidirect

Maximal subgroups

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

subgroupindex
#130824812
#130777012
#130671912
#130671662
#130671622
#130671522
#130671392
#130671272
#130671232
#130671002
C11×#23562
#1762411