Finite Group Databasebeta

← #14659206

Subgroups — #14659206

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66954C211yesmaximal, characteristic
2C2×#10622745C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4C2×#10622197C211yesmaximal, characteristic, complemented
5C2×#10622171C211yesmaximal, characteristic, complemented
6#13068312C211yesmaximal, characteristic, complemented
7C11×#1729C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C2×#66954—22no—
16C2×#66954—22no—
17C2×#66954—22no—
18C2×#66954—22no—
19C2×#66954—22no—
20C2×#66954—22no—
21C22×#4313C412yescomplemented
22C22×C8×D11C412yescomplemented
23C2×#66888C412yescomplemented
24#10622745—22no—
25#10622745—22no—
26C2×#66887C412yescomplemented
27#10622619—22no—
28#10622619—22no—
29C2×#66870C414yes—
30C11×#336—22no—
31#10622197—22no—
32#10622188—22no—
33#10622171—22no—
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11C2×C412yes—
36C2×#4339—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339D412yes—
45C2×#4339D412yes—
46C2×#4339D412yes—
47C2×#4339Q812yes—
48C22×D44C2×C411yescharacteristic
49C22×C4×D11C2×C412yes—
50C22×Dic22C2×C411yescharacteristic
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16C2×C412yes—
57C22×C8×C11—21no—
58C22×C8×C11—21no—
59C22×C8×C11—21no—
60C22×C8×C11—21no—
61C22×C8×C11—21no—
62C22×C8×C11C2×C411yescharacteristic
63C22×C8×C11C2×C411yescharacteristic
64C22×C8×C11D412yes—
65C22×C8×C11D412yes—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C22⋊C4C2×C412yes—
72C2×C42×C11—21no—
73C2×C22⋊Dic11C2×C412yes—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979—21no—
78C2×C4⋊Dic11—21no—
79C2×C4×Dic11—21no—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—21no—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318C2×C412yes—
90C2×#4318D412yes—
91C2×#4318D412yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8C2×C412yes—
94#66954—28no—
95#66954—28no—
96#66954—28no—
97#66954—28no—
98C2×#4313—24no—
99C2×#4313—24no—
100C2×#4313—24no—
101C2×C8×D11—24no—
102C2×C8×D11—24no—
103C2×C8×D11—24no—
104#66888—24no—
105#66887—24no—
106#66870—28no—
107#10764—111nomaximal, Sylow
108C24×C11C22×C411yescharacteristic
109C23×D11C4212yes—
110C22×C4×C11—22no—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×Q811yescharacteristic
121C22×C4×C11#4111yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×C22⋊D11—22no—
126C2×C22⋊D11—22no—
127C2×C22⋊D11—22no—
128C2×C22⋊D11—22no—
129C2×C22⋊D11C22⋊C414yes—
130C2×C22⋊D11C4⋊C414yes—
131C22×Dic11—22no—
132C22×Dic11C4212yes—
133#4339—22no—
134#4339—22no—
135#4339—22no—
136#4339—22no—
137#4339—22no—
138#4339—22no—
139#4339—22no—
140#4339—22no—
141#4339—22no—
142#4339—22no—
143#4339—22no—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—22no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44C22⋊C412yes—
154C2×D44C4⋊C412yes—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11C22⋊C414yes—
160C2×C4×D11C4⋊C414yes—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22C22⋊C412yes—
166C2×Dic22C4⋊C412yes—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—41no—
170C11×M16—41no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C2×C8×C11C22⋊C412yes—
183C2×C8×C11C22⋊C412yes—
184C11×C4⋊C4—41no—
185C11×C4⋊C4—41no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C42×C11—41no—
189C42×C11—41no—
190C22⋊Dic11—22no—
191C22⋊Dic11—22no—
192C4⋊Dic11—41no—
193C4⋊Dic11—41no—
194C4×Dic11—41no—
195C4×Dic11—41no—
196#4318—22no—
197#4318—22no—
198#4318—22no—
199#4318—22no—
200#4318—22no—
201#4318—22no—
202#4318—41no—
203#4318—41no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—41no—
208C2×C11⋊C8—41no—
209C2×C11⋊C8C22⋊C414yes—
210#4313—216no—
211C8×D11—216no—
212C22×#131—111no—
213C2×#413—111no—
214C2×#410—111no—
215C2×#344—111no—
216C2×#344—111no—
217#1729—111no—
218#1729D1111yescharacteristic, complemented
219C23×C11—42no—
220C23×C11C2×C4211yescharacteristic
221C23×C11C2×C22⋊C411yescharacteristic
222C23×C11C2×C4⋊C411yescharacteristic
223C23×C11C4×D411yescharacteristic
224C23×C11C4×D411yescharacteristic
225C23×C11C4×D411yescharacteristic
226C23×C11C4×D411yescharacteristic
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—44no—
230C22×D11#9514yes—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11C2×C22⋊C411yescharacteristic
234C2×C4×C11C2×C22⋊C411yescharacteristic
235C2×C4×C11C2×C22⋊C411yescharacteristic
236C2×C4×C11C2×C22⋊C411yescharacteristic
237C2×C4×C11C2×C4⋊C411yescharacteristic
238C2×C4×C11C2×C4⋊C411yescharacteristic
239C2×C4×C11#11711yescharacteristic
240C2×C4×C11#11711yescharacteristic
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11C22⋊Q811yescharacteristic
254C2×C4×C11C22⋊Q811yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11#12311yescharacteristic
258C2×C4×C11#12311yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C22⋊D11—24no—
262C22⋊D11—24no—
263C22⋊D11—24no—
264C22⋊D11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—44no—
268C2×Dic11—42no—
269C2×Dic11#9514yes—
270D44—22no—
271D44—22no—
272D44—22no—
273D44—22no—
274C4×D11—24no—
275C4×D11—24no—
276C4×D11—24no—
277C4×D11—24no—
278Dic22—22no—
279Dic22—22no—
280Dic22—22no—
281Dic22—22no—
282C8×C11—22no—
283C8×C11—22no—
284C8×C11—42no—
285C11⋊C8—24no—
286C11⋊C8—42no—
287C22×#41—111no—
288C2×#131—222no—
289C2×#131—222no—
290C2×#131—222no—
291C2×#131—222no—
292C2×#131—222no—
293C2×#131—222no—
294C22×M16—111no—
295C22×M16—112no—
296C22×M16—111no—
297C22×M16C2×D1111yescharacteristic
298C23×C8—112no—
299C23×C8C2×D1111yescharacteristic
300C2×#117—111no—
301C2×#117C2×D1111yescharacteristic
302#413—222no—
303#413—222no—
304C2×#101—112no—
305C2×#100—112no—
306#410—222no—
307#410—222no—
308C2×#99—114no—
309#344—222no—
310#344—222no—
311#336—22no—
312#336—222no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—41no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11C2×#9511yescharacteristic
321C22×C11C4×C22⋊C411yescharacteristic
322C22×C11C4×C22⋊C411yescharacteristic
323C22×C11#38511yescharacteristic
324C22×C11#38511yescharacteristic
325C22×C11#38611yescharacteristic
326C22×C11#38611yescharacteristic
327C2×D11—24no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C4×C11—82no—
332C4×C11#37911yescharacteristic
333C4×C11#38011yescharacteristic
334C4×C11#38011yescharacteristic
335C4×C11#38111yescharacteristic
336C4×C11#38511yescharacteristic
337C4×C11#38511yescharacteristic
338C4×C11#38611yescharacteristic
339C4×C11#38611yescharacteristic
340Dic11—24no—
341Dic11—82no—
342C2×#41—112no—
343C2×#41—112no—
344C2×#41—112no—
345C2×#41—112no—
346C2×#41—221no—
347C2×#41—221no—
348C2×#41—221no—
349C2×#41—221no—
350C2×#41—221no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—221no—
354C22×Q8—111no—
355C22×D4—112no—
356C22×D4—111no—
357C23×C4—112no—
358C23×C4C22×D1111yescharacteristic
359#131—228no—
360#131—228no—
361#131—228no—
362#131—228no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—112no—
369C2×M16—112no—
370C2×M16—112no—
371C2×M16—224no—
372C2×M16—224no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C2×M16—221no—
378C2×M16—224no—
379C2×M16—221no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16C4×D1112yes—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—112no—
390C22×C8—224no—
391C22×C8—224no—
392C22×C8—224no—
393C22×C8—221no—
394C22×C8C4×D1111yescharacteristic
395C22×C8C4×D1111yescharacteristic
396C22×C8D4412yes—
397C22×C8C22⋊D1112yes—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—221no—
403#117—221no—
404#117—221no—
405#117—221no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—221no—
408C2×C22⋊C4—112no—
409C2×C22⋊C4C4×D1112yes—
410C2×C42—21no—
411C2×C42—221no—
412#101—224no—
413#100—224no—
414#99—228no—
415C2×C11—21no—
416C2×C11—21no—
417C2×C11—21no—
418C2×C11—21no—
419C2×C11—21no—
420C2×C11—21no—
421C2×C11C22⋊#9511yescharacteristic
422C2×C11#175712yes—
423D11—44no—
424C24—112no—
425C24C2×C4×D1111yescharacteristic
426#41—222no—
427#41—222no—
428#41—222no—
429#41—222no—
430#41—222no—
431#41—222no—
432#41—222no—
433#41—222no—
434#41—222no—
435#41—222no—
436#41—222no—
437#41—222no—
438#41—222no—
439#41—222no—
440#41—222no—
441#41—222no—
442C2×Q8—112no—
443C2×Q8—112no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×D4—114no—
449C2×D4—114no—
450C2×D4—112no—
451C2×D4—112no—
452C2×D4—222no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C22×C4—22no—
461C22×C4—112no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4C2×C4×D1111yescharacteristic
470C22×C4C2×C4×D1111yescharacteristic
471C22×C4C2×D4411yescharacteristic
472C22×C4#433911yescharacteristic
473C22×C4#433911yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C22×C4#434111yescharacteristic
480C22×C4Q8×D1111yescharacteristic
481C22×C4#434311yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483M16—22no—
484M16—22no—
485M16—41no—
486M16—41no—
487M16—2216no—
488M16—222no—
489M16—222no—
490M16—222no—
491M16—222no—
492M16—222no—
493M16—222no—
494M16—441no—
495M16—441no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—114no—
508C2×C8—2216no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—222no—
512C2×C8—441no—
513C2×C8—441no—
514C2×C8(C2×D11)⋊C412yes—
515C2×C8(C2×D11)⋊C412yes—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—441no—
519C4⋊C4—441no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C42—41no—
525C42—41no—
526C42—441no—
527C42—441no—
528C11#1076411yescharacteristic, complemented, Sylow
529C23—42no—
530C23—114no—
531C23—222no—
532C23—222no—
533C23—444no—
534C23C42×D1111yescharacteristic
535C23C4×D4411yescharacteristic
536C23C22⋊C4×D1111yescharacteristic
537C23(C22⋊D11)⋊C411yescharacteristic
538C23C4⋊C4×D1111yescharacteristic
539C23#6694611yescharacteristic
540C23C4×C22⋊D1111yescharacteristic
541Q8—222no—
542Q8—222no—
543Q8—222no—
544Q8—222no—
545D4—224no—
546D4—224no—
547D4—224no—
548D4—224no—
549D4—222no—
550D4—222no—
551D4—222no—
552D4—222no—
553C2×C4—44no—
554C2×C4—42no—
555C2×C4—114no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—444no—
563C2×C4—442no—
564C2×C4#6692511yescharacteristic
565C2×C4C4×D4411yescharacteristic
566C2×C4C22⋊C4×D1111yescharacteristic
567C2×C4C22⋊C4×D1111yescharacteristic
568C2×C4C22⋊C4×D1111yescharacteristic
569C2×C4(C22⋊D11)⋊C411yescharacteristic
570C2×C4#6693511yescharacteristic
571C2×C4#6693511yescharacteristic
572C2×C4#6693611yescharacteristic
573C2×C4#6693611yescharacteristic
574C2×C4#6693711yescharacteristic
575C2×C4#6693711yescharacteristic
576C2×C4C4⋊C4×D1111yescharacteristic
577C2×C4C4⋊C4×D1111yescharacteristic
578C2×C4#6694511yescharacteristic
579C2×C4#6694611yescharacteristic
580C2×C4#6694711yescharacteristic
581C2×C4#6694711yescharacteristic
582C2×C4#6694811yescharacteristic
583C2×C4#6694911yescharacteristic
584C2×C4#6694911yescharacteristic
585C2×C4#6695011yescharacteristic
586C2×C4C2×(C2×D11)⋊C411yescharacteristic
587C2×C4C4×C22⋊D1111yescharacteristic
588C2×C4#6699011yescharacteristic
589C2×C4#6699011yescharacteristic
590C2×C4#6699111yescharacteristic
591C2×C4#6699911yescharacteristic
592C8—22no—
593C8—22no—
594C8—42no—
595C8—224no—
596C8—442no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—224no—
605C22—444no—
606C22—444no—
607C22—444no—
608C22D11×#9511yescharacteristic
609C22#1062227811yescharacteristic
610C22#1062227911yescharacteristic
611C22#1062228111yescharacteristic
612C22C4×(C2×D11)⋊C411yescharacteristic
613C22#1062256911yescharacteristic
614C22#1062260211yescharacteristic
615C4—82no—
616C4—224no—
617C4—882no—
618C4#1062227711yescharacteristic
619C4#1062227811yescharacteristic
620C4#1062228011yescharacteristic
621C4#1062228111yescharacteristic
622C4#1062256811yescharacteristic
623C4#1062256911yescharacteristic
624C4#1062260011yescharacteristic
625C4#1062260211yescharacteristic
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—444no—
633C2(C2×D11)⋊#9511yescharacteristic
634C2#1306841712yes—
subgroupG/H
centerC2×C4C2×(C2×D11)⋊C4
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1729C2
socleC22×C11C4×C22⋊C4
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#1729D11
hypocenterC11#10764
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #1729

Complements

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

NH ≅ G/Ntype
4. C2×#10622197C2semidirect
5. C2×#10622171C2semidirect
6. #13068312C2semidirect
7. C11×#1729C2semidirect
21. C22×#4313C4semidirect
22. C22×C8×D11C4semidirect
23. C2×#66888C4semidirect
26. C2×#66887C4semidirect
218. #1729D11semidirect
528. C11#10764semidirect

Maximal subgroups

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

subgroupindex
C22×#669542
C2×#106227452
C2×#106226192
C2×#106221972
C2×#106221712
#130683122
C11×#17292
#1076411