Finite Group Databasebeta

← #14721982

Subgroups — #14721982

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082622C211yesmaximal, characteristic
2#13077267C211yesmaximal, characteristic, complemented
3#13067250C212yesmaximal, complemented
4#13067248C212yesmaximal, complemented
5#13067234C212yesmaximal, complemented
6#13067228C211yesmaximal, characteristic, complemented
7#13067226C212yesmaximal, complemented
8#13067224C211yesmaximal, characteristic, complemented
9#13067207C211yesmaximal, characteristic, complemented
10#13067205C211yesmaximal, characteristic, complemented
11C11×#2970C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623365—21no—
14#10623108C411yescharacteristic
15#10623105—21no—
16#10623101C411yescharacteristic
17#10623093—21no—
18#10623093—22no—
19#10623084C411yescharacteristic
20#10623084C412yes—
21#10623082C411yescharacteristic
22#10623082C412yes—
23#10623061—21no—
24#10623061—22no—
25#10623010C2211yescharacteristic
26#10623010C2212yes—
27#10623008C2211yescharacteristic
28#10623008C2212yes—
29C11×#446—21no—
30C11×#435—22no—
31C8×D4×C11—21no—
32C11×#432C2211yescharacteristic
33C11×#432C2212yes—
34C4×C11×M16C2211yescharacteristic
35C2×C11×#97C2212yes—
36#10622847—21no—
37#10622613—22no—
38#10622612—21no—
39#10622539C2212yes—
40#10622539C2212yes—
41C4×#4318C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43#10622103C2211yescharacteristic
44#10622103C2211yescharacteristic
45#10622103C2212yes—
46#10622102C2211yescharacteristic
47#10622102C2211yescharacteristic
48#10622102C2212yes—
49#10622102C2212yes—
50#10622102C2212yes—
51#10622102C2212yes—
52#10622102C2212yes—
53C2×C11×#41D411yescharacteristic
54C2×#4343—21no—
55C2×#4339C2×C412yes—
56C2×#4339C2×C412yes—
57C2×#4339C2×C412yes—
58C2×C11×M16—21no—
59C22×C8×C11—22no—
60C4×Q8×C11C2×C411yescharacteristic
61C4×Q8×C11D411yescharacteristic
62C4×D4×C11C2×C411yescharacteristic
63C4×D4×C11C2×C412yes—
64C4×D4×C11D411yescharacteristic
65C4×D4×C11D412yes—
66C11×#117D411yescharacteristic
67C11×#117D412yes—
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2312yes—
70Q8×Dic11—21no—
71#66993—21no—
72#66993—22no—
73#66991—21no—
74#66991—22no—
75#66983—21no—
76#66983—22no—
77#66983—22no—
78#66983—21no—
79#66983C2×C411yescharacteristic
80#66983C2×C412yes—
81#66982—22no—
82#66982—21no—
83C4×C22⋊D11—21no—
84C4×C22⋊D11—22no—
85#66977C2×C411yescharacteristic
86#66977C2×C412yes—
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89#66948—22no—
90#66948—21no—
91#66946—22no—
92#66946—21no—
93C4⋊C4×D11—22no—
94C4⋊C4×D11—21no—
95#66943—22no—
96#66943—21no—
97#66937—22no—
98#66937—22no—
99#66937—22no—
100#66936—22no—
101#66936—22no—
102#66936—22no—
103#66929—21no—
104#66929—22no—
105#66928C2312yes—
106#66928C2311yescharacteristic
107#66927C2×C411yescharacteristic
108#66927C2×C412yes—
109C4×D44—21no—
110C4×D44—22no—
111C4×D44—21no—
112C4×D44—22no—
113C4×D44C2×C411yescharacteristic
114C4×D44C2×C412yes—
115#66925—21no—
116#66925—22no—
117#66923C2311yescharacteristic
118#66922C2×C411yescharacteristic
119#66922C2×C412yes—
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22C2×C412yes—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—21no—
126C11×#97—22no—
127C11×#97C2311yescharacteristic
128C11×#97C2312yes—
129C11×#97C2311yescharacteristic
130C4×C8×C11—21no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133C4⋊(C11⋊C8)—22no—
134C4⋊(C11⋊C8)—22no—
135#66867—21no—
136#66867C2311yescharacteristic
137#66867C2311yescharacteristic
138#66867C2312yes—
139C4×C11⋊C8—21no—
140#17684—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×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C2×C22⋊D11—22no—
152C2×C22⋊D11—22no—
153C2×C22⋊D11—22no—
154C2×C22⋊D11—21no—
155C2×C22⋊D11—22no—
156#4343—44no—
157#4339—82no—
158#4339—82no—
159#4339—82no—
160C2×D44—22no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—22no—
164C2×D44C22×C411yescharacteristic
165C2×D44C22×C412yes—
166C2×C4×D11—22no—
167C2×C4×D11—21no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×Dic22C22×C411yescharacteristic
172C2×Dic22C22×C412yes—
173C11×M16—42no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—22no—
177C2×C8×C11—44no—
178C11×C4⋊C4C22⋊C412yes—
179C11×C4⋊C4C22⋊C411yescharacteristic
180C11×C4⋊C4C22⋊C412yes—
181C11×C4⋊C4C22⋊C411yescharacteristic
182C11×C22⋊C4C22⋊C412yes—
183C11×C22⋊C4C22⋊C412yes—
184C11×C22⋊C4C22⋊C412yes—
185C42×C11C22×C412yes—
186C42×C11C22×C411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D412yes—
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D412yes—
191C42×C11C2411yescharacteristic
192C22⋊Dic11—21no—
193C22⋊Dic11—22no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—21no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—21no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—21no—
206C4⋊Dic11C22×C411yescharacteristic
207C4⋊Dic11C22×C411yescharacteristic
208Dic11⋊C4—21no—
209Dic11⋊C4—22no—
210Dic11⋊C4—21no—
211Dic11⋊C4—22no—
212Dic11⋊C4—21no—
213Dic11⋊C4—21no—
214C4×Dic11—22no—
215C4×Dic11—21no—
216#4318—42no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—42no—
221#3517—111no—
222#2970D1111yescharacteristic, complemented
223#2923—111no—
224#1536—112no—
225#1535—112no—
226#1532—112no—
227#1530—111no—
228#1530—112no—
229#1529—111no—
230#1525—111no—
231#1524—111no—
232C23×C11C2×C22⋊C411yescharacteristic
233C23×C11C2×C22⋊C412yes—
234C22×D11—22no—
235C22×D11—21no—
236Q8×C11—22no—
237D4×C11—22no—
238D4×C11—42no—
239C2×C4×C11—22no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11C2×C22⋊C412yes—
246C2×C4×C11C2×C22⋊C411yescharacteristic
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C22⋊D11—82no—
255C22⋊D11—82no—
256C22⋊D11—82no—
257C22⋊D11—82no—
258C22⋊D11—81no—
259C2×Dic11—21no—
260C2×Dic11—22no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263D44—41no—
264D44—42no—
265D44—44no—
266D44—42no—
267D44—82no—
268D44—81no—
269C4×D11—44no—
270C4×D11—42no—
271C4×D11—82no—
272C4×D11—82no—
273C4×D11—82no—
274Dic22—41no—
275Dic22—42no—
276C8×C11—22no—
277C8×C11—42no—
278C8×C11—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—42no—
282#557—111no—
283#553—221no—
284#553—222no—
285#550—111no—
286#550—111no—
287#550—112no—
288#550—221no—
289#547—111no—
290#547—112no—
291#540—221no—
292#540—222no—
293#532—112no—
294#532—111no—
295#529—111no—
296#529—112no—
297#520—221no—
298C4×#41C2×D1111yescharacteristic
299#446—21no—
300#435—22no—
301C8×D4—21no—
302#433—222no—
303#432—112no—
304#432—112no—
305#432C2×D1112yes—
306#432C2×D1111yescharacteristic
307#424—221no—
308#408—221no—
309C4×M16—111no—
310C4×M16C2×D1111yescharacteristic
311C2×#97—111no—
312C2×#97C2×D1112yes—
313#330—111no—
314#330—111no—
315#330—112no—
316#329—111no—
317#329—112no—
318#329—112no—
319#329—112no—
320#329—111no—
321#329—112no—
322#329—112no—
323C22×C11—21no—
324C22×C11—22no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—21no—
329C22×C11C22×C22⋊C411yescharacteristic
330C2×D11—42no—
331C2×D11—41no—
332C2×D11—42no—
333C2×D11—41no—
334C2×D11—42no—
335C2×D11—41no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—22no—
341C4×C11—21no—
342C4×C11—22no—
343C4×C11—21no—
344C4×C11#42112yes—
345Dic11—42no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349C2×#41—112no—
350C2×#41—112no—
351C2×#41—112no—
352C2×#41—221no—
353C2×#41D4411yescharacteristic
354C2×M16—21no—
355C2×M16—221no—
356C22×C8—22no—
357C22×C8—221no—
358C4⋊Q8—112no—
359C4⋊Q8—111no—
360#127—112no—
361#127—111no—
362#127—221no—
363#127—222no—
364#126—221no—
365#126—222no—
366#125—111no—
367#125—222no—
368#125—221no—
369#124—111no—
370#124—112no—
371#123—222no—
372#123—221no—
373#123—222no—
374#123—222no—
375#123—222no—
376C22⋊Q8—111no—
377C22⋊Q8—112no—
378#121—111no—
379#121—112no—
380#121—221no—
381#121—222no—
382#121—221no—
383#121—222no—
384#121—222no—
385#121—221no—
386#121—222no—
387#121—221no—
388#121—222no—
389#121—222no—
390#121—222no—
391C4×Q8—111no—
392C4×Q8—112no—
393C4×Q8—221no—
394C4×Q8C4×D1111yescharacteristic
395C4×Q8C22⋊D1111yescharacteristic
396C4×D4—111no—
397C4×D4—112no—
398C4×D4—221no—
399C4×D4—222no—
400C4×D4—222no—
401C4×D4—221no—
402C4×D4—221no—
403C4×D4—222no—
404C4×D4—221no—
405C4×D4—222no—
406C4×D4C4×D1111yescharacteristic
407C4×D4C4×D1112yes—
408C4×D4C22⋊D1111yescharacteristic
409C4×D4C22⋊D1112yes—
410#117—221no—
411#117—222no—
412#117D4411yescharacteristic
413#117D4412yes—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—221no—
416C2×C42C22×D1111yescharacteristic
417C2×C42C22×D1112yes—
418C4⋊C8—21no—
419C4⋊C8—22no—
420C4⋊C8—222no—
421C4⋊C8—222no—
422C22⋊C8—22no—
423C22⋊C8—21no—
424C22⋊C8—222no—
425C22⋊C8—222no—
426#97—22no—
427#97—111no—
428#97—111no—
429#97—112no—
430#97—221no—
431#97C22×D1111yescharacteristic
432#97C22×D1112yes—
433#97C22×D1111yescharacteristic
434C4×C8—21no—
435C4×C8—221no—
436C2×C11—41no—
437C2×C11—42no—
438C2×C11#288811yescharacteristic
439C2×C11C2×#42111yescharacteristic
440C2×C11#290111yescharacteristic
441D11—82no—
442D11—81no—
443#41—42no—
444#41—444no—
445#41—882no—
446#41—882no—
447#41—882no—
448C2×Q8—111no—
449C2×Q8—112no—
450C2×Q8(C2×D11)⋊C411yescharacteristic
451C2×D4—111no—
452C2×D4—112no—
453C2×D4—221no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—222no—
462C2×D4(C2×D11)⋊C411yescharacteristic
463C2×D4(C2×D11)⋊C412yes—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4C2×C4×D1111yescharacteristic
470C22×C4C2×C4×D1112yes—
471C22×C4C2×D4411yescharacteristic
472C22×C4C2×D4412yes—
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1111yescharacteristic
475M16—42no—
476M16—442no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—22no—
480C2×C8—44no—
481C2×C8—222no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—442no—
485C4⋊C4—111no—
486C4⋊C4—111no—
487C4⋊C4—221no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—222no—
493C4⋊C4—221no—
494C4⋊C4—222no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4(C2×D11)⋊C412yes—
498C4⋊C4(C2×D11)⋊C411yescharacteristic
499C4⋊C4(C2×D11)⋊C412yes—
500C4⋊C4(C2×D11)⋊C411yescharacteristic
501C22⋊C4—221no—
502C22⋊C4—222no—
503C22⋊C4—221no—
504C22⋊C4—222no—
505C22⋊C4—221no—
506C22⋊C4—222no—
507C22⋊C4—221no—
508C22⋊C4—222no—
509C22⋊C4—221no—
510C22⋊C4—222no—
511C22⋊C4(C2×D11)⋊C412yes—
512C22⋊C4(C2×D11)⋊C412yes—
513C22⋊C4(C2×D11)⋊C412yes—
514C42—222no—
515C42—221no—
516C42C2×C4×D1112yes—
517C42C2×C4×D1111yescharacteristic
518C42C2×D4411yescharacteristic
519C42C2×D4412yes—
520C42C2×C22⋊D1111yescharacteristic
521C42C2×C22⋊D1112yes—
522C42C23×D1111yescharacteristic
523C11#1768411yescharacteristic, complemented, Sylow
524C23—222no—
525C23—221no—
526C23C2×(C2×D11)⋊C411yescharacteristic
527C23C2×(C2×D11)⋊C412yes—
528Q8—22no—
529Q8—441no—
530Q8—442no—
531D4—22no—
532D4—42no—
533D4—441no—
534D4—442no—
535D4—444no—
536D4—442no—
537D4—882no—
538D4—881no—
539D4—882no—
540D4—882no—
541D4—882no—
542D4—882no—
543D4—881no—
544C2×C4—22no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—221no—
551C2×C4—222no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—444no—
555C2×C4—442no—
556C2×C4—882no—
557C2×C4—882no—
558C2×C4—882no—
559C2×C4C2×(C2×D11)⋊C412yes—
560C2×C4C2×(C2×D11)⋊C411yescharacteristic
561C2×C4C2×(C2×D11)⋊C412yes—
562C2×C4C2×(C2×D11)⋊C411yescharacteristic
563C2×C4C2×(C2×D11)⋊C412yes—
564C2×C4C2×(C2×D11)⋊C411yescharacteristic
565C2×C4C22×C4×D1111yescharacteristic
566C2×C4C22×D4411yescharacteristic
567C2×C4C22×C22⋊D1111yescharacteristic
568C8—22no—
569C8—42no—
570C8—41no—
571C8—441no—
572C8—441no—
573C8—442no—
574C22—21no—
575C22—22no—
576C22—21no—
577C22—22no—
578C22—22no—
579C22—21no—
580C22—442no—
581C22—441no—
582C22—442no—
583C22—441no—
584C22—442no—
585C22—441no—
586C22C22×(C2×D11)⋊C411yescharacteristic
587C4—21no—
588C4—21no—
589C4—22no—
590C4—21no—
591C4—22no—
592C4—21no—
593C4—22no—
594C4—21no—
595C4—442no—
596C4—441no—
597C4—441no—
598C4—441no—
599C4#1062275212yes—
600C2—41no—
601C2—42no—
602C2—882no—
603C2—881no—
604C2#1307709411yescharacteristic
605C2C2×#1062275211yescharacteristic
606C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2970C2
socleC22×C11C22×C22⋊C4
prime radical#13082622C2
cosocleC42×C11C24
hypercenter#2970D11
hypocenterC11#17684
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. #13077267C2semidirect
3. #13067250C2semidirect
4. #13067248C2semidirect
5. #13067234C2semidirect
6. #13067228C2semidirect
7. #13067226C2semidirect
8. #13067224C2semidirect
9. #13067207C2semidirect
10. #13067205C2semidirect
11. C11×#2970C2semidirect
222. #2970D11semidirect
523. C11#17684semidirect

Maximal subgroups

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

subgroupindex
#130826222
#130772672
#130672502
#130672482
#130672342
#130672282
#130672262
#130672242
#130672072
#130672052
C11×#29702
#1768411