Finite Group Databasebeta

← #14727452

Subgroups — #14727452

Order 2816.

984 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078536C211yesmaximal, characteristic, complemented
2C2×#10622647C211yesmaximal, characteristic, complemented
3#13073102C211yesmaximal, characteristic, complemented
4#13067653C214yesmaximal, complemented
5#13067647C214yesmaximal, complemented
6#13067132C211yesmaximal, characteristic, complemented
7#13067107C211yesmaximal, characteristic, complemented
8#13066980C211yesmaximal, characteristic, complemented
9C11×#3536C211yesmaximal, characteristic
10C11×#562—22no—
11C11×#554—21no—
12C11×#548—21no—
13C11×#547—21no—
14C11×#546—21no—
15C11×#546—22no—
16C11×#543—21no—
17C11×#542—21no—
18C11×#539C2212yes—
19C11×#538—21no—
20C11×#537—21no—
21C11×#537C2212yes—
22C11×#525C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26#10622845—21no—
27#10622843—21no—
28C2×#66896—21no—
29C4×C22⋊Dic11C2211yescharacteristic
30#10622820C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622657C2212yescomplemented
33#10622656—21no—
34#10622647—22no—
35#10622647C2214yes—
36#10622647C2212yescomplemented
37#10622646—21no—
38#10622608—21no—
39#10622599C2214yescomplemented
40#10622590—21no—
41C2×#66872—21no—
42#10622556—22no—
43#10622176C2212yescomplemented
44#10622175C2214yes—
45#10622175C2212yescomplemented
46#10622166C2214yescomplemented
47C2×C11×#41—21no—
48C2×C11×#41—22no—
49C2×C11×#41D411yescharacteristic
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—21no—
55C11×C4⋊Q8—21no—
56C11×#126—22no—
57C11×#125—22no—
58C11×#124—22no—
59C11×#124—21no—
60C11×#124—22no—
61C11×#123—22no—
62C11×#123—22no—
63C11×#123—22no—
64C11×#123—21no—
65C11×#123—22no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8D411yescharacteristic
78C11×C22⋊Q8C2311yescharacteristic
79C11×#121—21no—
80C11×#121—22no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—21no—
85C11×#121—21no—
86C11×#121—22no—
87C11×#121D412yes—
88C11×#121D411yescharacteristic
89C11×#121C2312yes—
90C11×#121C2311yescharacteristic
91C11×#120—22no—
92C11×#120—21no—
93C4×Q8×C11—21no—
94C4×D4×C11—22no—
95C4×D4×C11—21no—
96C4×D4×C11—21no—
97C4×D4×C11—21no—
98C4×D4×C11—22no—
99C11×#117D411yescharacteristic
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C4⋊C4D411yescharacteristic
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4D412yes—
107C2×C22⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11C2312yes—
114C2×C4×Dic11—21no—
115C2×#4318—21no—
116C22×C11⋊C8—21no—
117#66899—22no—
118#66896—24no—
119#66896—22no—
120C11⋊#95—24no—
121C11⋊#95—24no—
122C11⋊#95C2312yes—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)C2312yes—
126C22⋊(C11⋊C8)C2312yes—
127#66872—24no—
128#66872—22no—
129#66871—22no—
130#18271—111nomaximal, Sylow
131C24×C11—21no—
132C24×C11C2×D411yescharacteristic
133C11×#41—42no—
134C11×#41—84no—
135C11×#41—82no—
136C2×Q8×C11—22no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—42no—
140C2×Q8×C11C2×D411yescharacteristic
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11—82no—
151C2×D4×C11C2×D411yescharacteristic
152C2×D4×C11C2×D412yes—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—42no—
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—44no—
170C22×Dic11—41no—
171C22×Dic11—41no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D411yescharacteristic
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—21no—
200C42×C11—22no—
201C42×C11—21no—
202C22⋊Dic11—42no—
203C4⋊Dic11—22no—
204C4⋊Dic11—22no—
205C4⋊Dic11—41no—
206C4⋊Dic11—41no—
207C4×Dic11—42no—
208#4318—42no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—42no—
212#3536D1111yescharacteristic
213#3092—111no—
214C2×#481—111no—
215#2503—111no—
216#1616—114no—
217#1615—114no—
218#1507—111no—
219#1501—111no—
220#1472—111no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—21no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—81no—
228C23×C11—81no—
229C23×C11#12011yescharacteristic
230C23×C11#12011yescharacteristic
231C23×C11C22×D411yescharacteristic
232Q8×C11—41no—
233Q8×C11—42no—
234Q8×C11—81no—
235Q8×C11—82no—
236D4×C11—42no—
237D4×C11—41no—
238D4×C11—44no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11—42no—
242D4×C11—82no—
243D4×C11—81no—
244D4×C11—82no—
245D4×C11—82no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—81no—
262C2×C4×C11—82no—
263C2×C4×C11—82no—
264C2×C4×C11—82no—
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—44no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—82no—
275C2×Dic11—82no—
276C11⋊C8—42no—
277C11⋊C8—42no—
278#562—22no—
279#554—21no—
280#548—21no—
281#547—21no—
282#546—21no—
283#546—22no—
284#543—21no—
285#542—21no—
286#539C2×D1112yes—
287#538—21no—
288#537—21no—
289#537C2×D1112yes—
290#525C2×D1111yescharacteristic
291C2×C22⋊Q8C2×D1111yescharacteristic
292C2×#121C2×D1111yescharacteristic
293C22×C4⋊C4—111no—
294#484—112no—
295#483—221no—
296#481—114no—
297#481—112no—
298#481—222no—
299#480—221no—
300#428—221no—
301C2×#106—221no—
302#417—221no—
303C2×#102—221no—
304#407—111no—
305C2×C22⋊C8—111no—
306#400—114no—
307#391—221no—
308#382—221no—
309#381—222no—
310C4×C22⋊C4—111no—
311#328—112no—
312#327—114no—
313#327—112no—
314#324—114no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—44no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—41no—
326C22×C11—42no—
327C22×C11—41no—
328C22×C11—42no—
329C22×C11—162no—
330C22×C11#45412yes—
331C22×C11C2×#12011yescharacteristic
332C22×C11#57712yes—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—42no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11#45812yes—
343Dic11—82no—
344Dic11—82no—
345C2×#41—21no—
346C2×#41—22no—
347C2×#41C22⋊D1111yescharacteristic
348C22×Q8C22⋊D1111yescharacteristic
349C22×D4—21no—
350C22×D4C22⋊D1111yescharacteristic
351C23×C4—221no—
352C23×C4C22×D1111yescharacteristic
353C2×M16—221no—
354C22×C8—221no—
355C4⋊Q8—21no—
356#126—22no—
357#125—22no—
358#124—22no—
359#124—21no—
360#124—22no—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—21no—
365#123—22no—
366C22⋊Q8—21no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8C22⋊D1111yescharacteristic
378C22⋊Q8C22×D1111yescharacteristic
379#121—21no—
380#121—22no—
381#121—22no—
382#121—22no—
383#121—22no—
384#121—21no—
385#121—21no—
386#121—22no—
387#121C22⋊D1112yes—
388#121C22⋊D1111yescharacteristic
389#121C22×D1112yes—
390#121C22×D1111yescharacteristic
391#120—22no—
392#120—21no—
393C4×Q8—21no—
394C4×D4—22no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—22no—
399#117C22⋊D1111yescharacteristic
400C2×C4⋊C4—21no—
401C2×C4⋊C4—112no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4C22⋊D1111yescharacteristic
408C2×C4⋊C4C22⋊D1111yescharacteristic
409C2×C4⋊C4C22×D1112yes—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4C22⋊D1112yes—
414C2×C42—221no—
415#107—222no—
416#106—224no—
417#106—222no—
418#103—222no—
419#102—224no—
420#102—222no—
421C22⋊C8—112no—
422C22⋊C8—112no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425#95—112no—
426#95—224no—
427#95—224no—
428C2×C11—22no—
429C2×C11—22no—
430C2×C11—41no—
431C2×C11—81no—
432C2×C11—82no—
433C2×C11#300911yescharacteristic
434C2×C11C2×#45411yescharacteristic
435C2×C11C2×#45811yescharacteristic
436C24—21no—
437C24C2×C22⋊D1111yescharacteristic
438#41—42no—
439#41—84no—
440#41—82no—
441C2×Q8—22no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8C2×C22⋊D1111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—42no—
455C2×D4—82no—
456C2×D4C2×C22⋊D1111yescharacteristic
457C2×D4C2×C22⋊D1112yes—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—444no—
467C22×C4—441no—
468C22×C4—441no—
469C22×C4C2×C22⋊D1112yes—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477M16—442no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—442no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—441no—
495C4⋊C4—441no—
496C4⋊C4C2×C22⋊D1112yes—
497C4⋊C4C2×C22⋊D1111yescharacteristic
498C4⋊C4C2×C22⋊D1111yescharacteristic
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—442no—
514C42—22no—
515C42—21no—
516C42—442no—
517C11#1827111yescharacteristic, complemented, Sylow
518C23—22no—
519C23—22no—
520C23—22no—
521C23—21no—
522C23—41no—
523C23—42no—
524C23—81no—
525C23—81no—
526C23#6700611yescharacteristic
527C23#6700611yescharacteristic
528C23C22×C22⋊D1111yescharacteristic
529Q8—41no—
530Q8—42no—
531Q8—81no—
532Q8—82no—
533D4—42no—
534D4—41no—
535D4—44no—
536D4—42no—
537D4—42no—
538D4—42no—
539D4—82no—
540D4—81no—
541D4—82no—
542D4—82no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—81no—
559C2×C4—82no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—444no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—882no—
568C2×C4—882no—
569C2×C4#6700611yescharacteristic
570C2×C4#6700611yescharacteristic
571C2×C4C22×C22⋊D1111yescharacteristic
572C2×C4C22×C22⋊D1111yescharacteristic
573C8—442no—
574C8—442no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—44no—
583C22—41no—
584C22—42no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—162no—
590C22#1062285812yes—
591C22#1062336712yes—
592C22C2×#6700611yescharacteristic
593C4—21no—
594C4—21no—
595C4—21no—
596C4—42no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—42no—
602C4—882no—
603C4—882no—
604C4#1062285612yes—
605C2—22no—
606C2—22no—
607C2—41no—
608C2—82no—
609C2—81no—
610C2#1307789311yescharacteristic
611C2C2×#1062285811yescharacteristic
612C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3536C2
socleC22×C11C2×#120
hypercenter#3536D11
hypocenterC11#18271
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3536

Complements

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

NH ≅ G/Ntype
1. #13078536C2semidirect
2. C2×#10622647C2semidirect
3. #13073102C2semidirect
4. #13067653C2semidirect
5. #13067647C2semidirect
6. #13067132C2semidirect
7. #13067107C2semidirect
8. #13066980C2semidirect
32. #10622657C22semidirect
36. #10622647C22semidirect
39. #10622599C22semidirect
43. #10622176C22semidirect
45. #10622175C22semidirect
46. #10622166C22semidirect
517. C11#18271semidirect

Maximal subgroups

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

subgroupindex
#130785362
C2×#106226472
#130731022
#130676532
#130676472
#130671322
#130671072
#130669802
C11×#35362
#1827111