Finite Group Databasebeta

← #14727850

Subgroups — #14727850

Order 2816.

910 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#13079764C211yesmaximal, characteristic, complemented
2#13079741C211yesmaximal, characteristic, complemented
3#13074437C211yesmaximal, characteristic, complemented
4#13067664C214yesmaximal, complemented
5#13067647C214yesmaximal, complemented
6#13067180C211yesmaximal, characteristic, complemented
7#13067176C211yesmaximal, characteristic, complemented
8#13066930C211yesmaximal, characteristic, complemented
9C11×#3455C211yesmaximal, characteristic
10C11×#542—21no—
11C11×#542—21no—
12C11×#541—21no—
13C11×#540—21no—
14C11×#539—21no—
15C11×#539C2212yes—
16C11×#538—21no—
17C11×#538C2212yes—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#529—22no—
21C11×#529—22no—
22C11×#525—21no—
23C4×C11×#41—21no—
24C2×C11×#117C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26#10622825—21no—
27#10622694—21no—
28#10622692—21no—
29#10622691—21no—
30#10622683—21no—
31#10622657C2214yes—
32#10622647C2214yes—
33#10622634—22no—
34#10622621—22no—
35#10622599C2212yes—
36#10622592—21no—
37#10622562C2212yes—
38#10622560—21no—
39#10622549C2211yescharacteristic
40#10622541—21no—
41#10622538C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622176C2214yes—
44#10622175C2214yes—
45#10622166C2212yes—
46#10622163C2212yes—
47C2×C11×#41—21no—
48C23×C4×C11D411yescharacteristic
49C22×Dic22—21no—
50C11×C4⋊Q8D411yescharacteristic
51C11×C4⋊Q8D411yescharacteristic
52C11×C4⋊Q8D411yescharacteristic
53C11×#127D411yescharacteristic
54C11×#126—22no—
55C11×#126—22no—
56C11×#126—22no—
57C11×#126—22no—
58C11×#125—22no—
59C11×#125—22no—
60C11×#125—21no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#124—21no—
64C11×#123—22no—
65C11×#123—22no—
66C11×#123—22no—
67C11×#123—22no—
68C11×#123—22no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8—21no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8C2312yes—
75C11×#121—21no—
76C11×#121—21no—
77C11×#121—22no—
78C11×#121—22no—
79C11×#121—21no—
80C11×#121C2312yes—
81C11×#120—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11D412yes—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—22no—
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—22no—
92C4×D4×C11—21no—
93C4×D4×C11D412yes—
94C11×#117—22no—
95C11×#117—21no—
96C11×#117—21no—
97C11×#117—21no—
98C11×#117—21no—
99C11×#117—21no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4C2311yescharacteristic
104C2×C42×C11—22no—
105C2×C42×C11D411yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—22no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2312yes—
111C2×Dic11⋊C4—22no—
112#66922—21no—
113#66922—21no—
114#66922—21no—
115#66922—21no—
116#66899—24no—
117#66896—24no—
118C11⋊#95—22no—
119C11⋊#95—21no—
120C11⋊#95—22no—
121C11⋊#95C2312yes—
122C22⋊(C11⋊C8)C2312yes—
123C22⋊(C11⋊C8)C2312yes—
124#66872—24no—
125#66871—24no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4×C11⋊C8—21no—
129C4×C11⋊C8—21no—
130#18313—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C11×#41—42no—
133C11×#41—42no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11C2×D412yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—22no—
157C22×Dic11—22no—
158C2×Dic22—41no—
159C2×Dic22—41no—
160C2×Dic22—82no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—22no—
190C42×C11—22no—
191C42×C11—22no—
192C42×C11—21no—
193C42×C11—22no—
194C42×C11—21no—
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C22⋊Dic11—82no—
200C4⋊Dic11—22no—
201C4⋊Dic11—22no—
202C4⋊Dic11—41no—
203C4⋊Dic11—41no—
204C4⋊Dic11—42no—
205Dic11⋊C4—82no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208#3455D1111yescharacteristic
209#3230—111no—
210#3227—111no—
211#2628—111no—
212#1618—114no—
213#1615—114no—
214#1518—111no—
215#1517—111no—
216#1458—111no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11C22×D411yescharacteristic
224Q8×C11—42no—
225Q8×C11—42no—
226Q8×C11—81no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—81no—
232D4×C11—82no—
233D4×C11—82no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—44no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—82no—
250C2×C4×C11—82no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11#12011yescharacteristic
255C2×C4×C11#13512yes—
256C2×C4×C11#13712yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265Dic22—82no—
266Dic22—82no—
267C11⋊C8—42no—
268C11⋊C8—42no—
269#542—21no—
270#542—21no—
271#541—21no—
272#540—21no—
273#539—21no—
274#539C2×D1112yes—
275#538—21no—
276#538C2×D1112yes—
277#533C2×D1111yescharacteristic
278#532C2×D1111yescharacteristic
279C2×C4⋊Q8—111no—
280#529—22no—
281#529—22no—
282#525—21no—
283C4×#41—21no—
284C2×#117C2×D1111yescharacteristic
285#500—221no—
286#498—221no—
287#487—221no—
288#486—221no—
289#484—114no—
290#481—114no—
291#477—222no—
292#476—222no—
293#431—111no—
294#431—111no—
295#400—112no—
296#399—112no—
297#395—221no—
298#393—221no—
299#389—221no—
300#382—111no—
301#380—221no—
302#328—114no—
303#327—114no—
304#324—112no—
305#323—112no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—42no—
309C22×C11—41no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—41no—
313C22×C11—42no—
314C22×C11—41no—
315C22×C11—81no—
316C22×C11C2×#12011yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11C2×#13711yescharacteristic
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—41no—
324C4×C11—42no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—42no—
329C4×C11#45212yes—
330C4×C11#45212yes—
331Dic11—82no—
332Dic11—82no—
333C2×#41—21no—
334C22×Q8—221no—
335C23×C4C22⋊D1111yescharacteristic
336C4⋊Q8—221no—
337C4⋊Q8—221no—
338C4⋊Q8—221no—
339C4⋊Q8—221no—
340C4⋊Q8C22⋊D1111yescharacteristic
341C4⋊Q8C22⋊D1111yescharacteristic
342C4⋊Q8C22⋊D1111yescharacteristic
343#127C22⋊D1111yescharacteristic
344#126—22no—
345#126—22no—
346#126—22no—
347#126—22no—
348#125—22no—
349#125—22no—
350#125—21no—
351#124—22no—
352#124—22no—
353#124—21no—
354#123—22no—
355#123—22no—
356#123—22no—
357#123—22no—
358#123—22no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8C22×D1112yes—
365#121—21no—
366#121—21no—
367#121—22no—
368#121—22no—
369#121—21no—
370#121C22×D1112yes—
371#120—22no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C22⋊D1112yes—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—21no—
383C4×D4C22⋊D1112yes—
384#117—22no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390C2×C4⋊C4—112no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4C22⋊D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C22⋊C4—222no—
397C2×C22⋊C4C22⋊D1111yescharacteristic
398C2×C22⋊C4C22×D1111yescharacteristic
399C2×C42—22no—
400C2×C42C22⋊D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402#107—224no—
403#106—224no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406#103—224no—
407#102—224no—
408C22⋊C8—112no—
409C22⋊C8—112no—
410C4×C8—221no—
411C4×C8—221no—
412#95—112no—
413#95—222no—
414#95—221no—
415#95—222no—
416C2×C11—21no—
417C2×C11—21no—
418C2×C11—82no—
419C2×C11—81no—
420C2×C11C2×#45211yescharacteristic
421C2×C11#302111yescharacteristic
422C2×C11#302811yescharacteristic
423C24C2×C22⋊D1111yescharacteristic
424#41—42no—
425#41—42no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—441no—
429C2×Q8—441no—
430C2×Q8—882no—
431C2×Q8C2×C22⋊D1112yes—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—22no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4C2×C22⋊D1112yes—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C23×D1111yescharacteristic
453C2×C8—222no—
454C2×C8—222no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—22no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—442no—
472C4⋊C4—441no—
473C4⋊C4—441no—
474C4⋊C4—882no—
475C4⋊C4C2×C22⋊D1112yes—
476C4⋊C4C2×C22⋊D1112yes—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—22no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—882no—
491C42—22no—
492C42—22no—
493C42—21no—
494C42—22no—
495C42—21no—
496C42C2×C22⋊D1111yescharacteristic
497C42C2×C22⋊D1111yescharacteristic
498C42C2×C22⋊D1111yescharacteristic
499C42C2×C22⋊D1111yescharacteristic
500C11#1831311yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23—22no—
504C23—21no—
505C23—41no—
506C23—41no—
507C23C22×C22⋊D1111yescharacteristic
508Q8—42no—
509Q8—42no—
510Q8—81no—
511Q8—882no—
512Q8—882no—
513D4—42no—
514D4—42no—
515D4—42no—
516D4—42no—
517D4—81no—
518D4—82no—
519D4—82no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4#6700312yes—
544C2×C4#6700412yes—
545C2×C4#6700611yescharacteristic
546C2×C4#6700611yescharacteristic
547C2×C4#6700611yescharacteristic
548C2×C4#6700611yescharacteristic
549C2×C4C22×C22⋊D1111yescharacteristic
550C2×C4C22×C22⋊D1111yescharacteristic
551C8—442no—
552C8—442no—
553C22—21no—
554C22—21no—
555C22—42no—
556C22—42no—
557C22—41no—
558C22—41no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—81no—
563C22C2×#6700311yescharacteristic
564C22C2×#6700411yescharacteristic
565C22C2×#6700611yescharacteristic
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—41no—
571C4—42no—
572C4—41no—
573C4—42no—
574C4—41no—
575C4—42no—
576C4—882no—
577C4—882no—
578C4#1062285212yes—
579C4#1062285212yes—
580C2—21no—
581C2—21no—
582C2—81no—
583C2—82no—
584C2C2×#1062285211yescharacteristic
585C2#1307798811yescharacteristic
586C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3455C2
socleC22×C11C2×#120
hypercenter#3455D11
hypocenterC11#18313
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. #13079764C2semidirect
2. #13079741C2semidirect
3. #13074437C2semidirect
4. #13067664C2semidirect
5. #13067647C2semidirect
6. #13067180C2semidirect
7. #13067176C2semidirect
8. #13066930C2semidirect
500. C11#18313semidirect

Maximal subgroups

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

subgroupindex
#130797642
#130797412
#130744372
#130676642
#130676472
#130671802
#130671762
#130669302
C11×#34552
#1831311