Finite Group Databasebeta

← #14659122

Subgroups — #14659122

Order 2816.

1246 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623276C211yesmaximal, characteristic
2C2×#10622745C211yesmaximal, characteristic
3#13071106C211yesmaximal, characteristic
4C2×#10622197C211yesmaximal, characteristic, complemented
5C2×#10622194C211yesmaximal, characteristic, complemented
6#13068310C211yesmaximal, characteristic, complemented
7C11×#1728C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×#4318C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15#10623276—22no—
16#10623276—22no—
17#10623276—22no—
18#10623276C414yescomplemented
19C2×#66960—22no—
20C2×M16×D11—22no—
21C2×#66954—22no—
22#10622826C414yes—
23C2×#66888—21no—
24#10622745—22no—
25#10622745C414yescomplemented
26C2×#66887—21no—
27#10622552—21no—
28C4×(C2×D11)⋊C4—22no—
29#10622542—21no—
30C11×#336—22no—
31#10622197—22no—
32#10622194—22no—
33#10622162—22no—
34C23×C4×C11C2×C412yes—
35C23×C4×C11C2311yescharacteristic
36C22×C22⋊D11C2×C412yes—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339C2×C412yes—
46C2×#4339C2×C412yes—
47C2×#4339D412yes—
48C2×#4339Q812yes—
49C22×D44D411yescharacteristic
50C22×C4×D11D412yes—
51C22×Dic22D411yescharacteristic
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16—21no—
61C2×C11×M16C2×C412yes—
62C2×C11×M16C2×C412yes—
63C2×C11×M16D412yes—
64C22×C8×C11—21no—
65C22×C8×C11D412yes—
66C2×C42×C11—21no—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C22⋊Dic11C2×C412yes—
73C2×(C2×D11)⋊C4—24no—
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×#4318C2×C412yes—
91C2×#4318D412yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8D412yes—
94#66960—28no—
95#66960—28no—
96M16×D11—28no—
97M16×D11—28no—
98#66954—28no—
99#66954—28no—
100C2×#4313—24no—
101C2×C8×D11—24no—
102C11⋊#95—24no—
103#66888—24no—
104#66887—24no—
105#10746—111nomaximal, Sylow
106C24×C11C22×C411yescharacteristic
107C23×D11C22⋊C412yes—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—44no—
112C22×C4×C11C22×C411yescharacteristic
113C22×C4×C11C22×C411yescharacteristic
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×D411yescharacteristic
121C22×C4×C11C2×Q811yescharacteristic
122C22×C4×C11#4111yescharacteristic
123C22×C4×C11#4111yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—22no—
127C2×C22⋊D11—22no—
128C2×C22⋊D11—22no—
129C2×C22⋊D11—22no—
130C2×C22⋊D11C4214yes—
131C2×C22⋊D11C4⋊C414yes—
132C22×Dic11—22no—
133C22×Dic11C22⋊C412yes—
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—
149#4339—22no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44C22⋊C412yes—
155C2×D44C4⋊C412yes—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11C22⋊C414yes—
161C2×C4×D11C4⋊C414yes—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22C22⋊C412yes—
167C2×Dic22C4⋊C412yes—
168C11×M16—22no—
169C11×M16—22no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—22no—
173C11×M16—22no—
174C11×M16—41no—
175C11×M16—41no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—41no—
180C2×C8×C11—41no—
181C2×C8×C11C22⋊C414yescomplemented
182C42×C11—41no—
183C42×C11—41no—
184C42×C11—41no—
185C42×C11—41no—
186C22⋊Dic11—22no—
187C22⋊Dic11—22no—
188(C2×D11)⋊C4—48no—
189C4⋊Dic11—41no—
190C4⋊Dic11—41no—
191C4×Dic11—41no—
192C4×Dic11—41no—
193#4318—22no—
194#4318—22no—
195#4318—22no—
196#4318—22no—
197#4318—22no—
198#4318—22no—
199#4318—41no—
200#4318—41no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—41no—
205C2×C11⋊C8—41no—
206C2×C11⋊C8C22⋊C414yescomplemented
207#4313—216no—
208C8×D11—216no—
209C2×#568—111no—
210C2×#413—111no—
211#2297—111no—
212C2×#344—111no—
213C2×#344—111no—
214#1728—111no—
215#1728D1111yescharacteristic, complemented
216C23×C11—42no—
217C23×C11C2×C4211yescharacteristic
218C23×C11C2×C22⋊C411yescharacteristic
219C23×C11C2×C4⋊C411yescharacteristic
220C23×C11C4×D411yescharacteristic
221C23×C11C4×D411yescharacteristic
222C23×C11C4×D411yescharacteristic
223C23×C11C4×D411yescharacteristic
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—44no—
227C22×D11#9514yes—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11C2×C22⋊C411yescharacteristic
236C2×C4×C11C2×C22⋊C411yescharacteristic
237C2×C4×C11C2×C22⋊C411yescharacteristic
238C2×C4×C11C2×C22⋊C411yescharacteristic
239C2×C4×C11C2×C4⋊C411yescharacteristic
240C2×C4×C11C2×C4⋊C411yescharacteristic
241C2×C4×C11#11711yescharacteristic
242C2×C4×C11#11711yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C4×D411yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22⋊Q811yescharacteristic
256C2×C4×C11C22⋊Q811yescharacteristic
257C2×C4×C11C22⋊Q811yescharacteristic
258C2×C4×C11C22⋊Q811yescharacteristic
259C2×C4×C11#12311yescharacteristic
260C2×C4×C11#12311yescharacteristic
261C2×C4×C11#12311yescharacteristic
262C2×C4×C11#12311yescharacteristic
263C22⋊D11—24no—
264C22⋊D11—24no—
265C22⋊D11—24no—
266C22⋊D11—24no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—44no—
270C2×Dic11—42no—
271C2×Dic11#9514yes—
272D44—22no—
273D44—22no—
274D44—22no—
275D44—22no—
276C4×D11—24no—
277C4×D11—24no—
278C4×D11—24no—
279C4×D11—24no—
280Dic22—22no—
281Dic22—22no—
282Dic22—22no—
283Dic22—22no—
284C8×C11—24no—
285C8×C11—42no—
286C11⋊C8—24no—
287C11⋊C8—42no—
288C22×#41—111no—
289#568—114no—
290#568—222no—
291#568—222no—
292#568—222no—
293C2×#131—222no—
294C2×#131—222no—
295C22×M16—111no—
296C22×M16—111no—
297C22×M16—222no—
298C22×M16C2×D1111yescharacteristic
299C22×M16C2×D1111yescharacteristic
300C2×#117—111no—
301C22×C42C2×D1111yescharacteristic
302#413—114no—
303#413—222no—
304C2×#101—221no—
305C2×#100—221no—
306#391—221no—
307#390—221no—
308#386—114no—
309C4×C22⋊C4—222no—
310#344—222no—
311#344—222no—
312#336—22no—
313#336—222no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11C2×#9511yescharacteristic
322C22×C11C4×C22⋊C411yescharacteristic
323C22×C11C4×C22⋊C411yescharacteristic
324C22×C11#38511yescharacteristic
325C22×C11#38511yescharacteristic
326C22×C11#38611yescharacteristic
327C22×C11#38611yescharacteristic
328C2×D11—24no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—82no—
332C4×C11—44no—
333C4×C11#37911yescharacteristic
334C4×C11#38011yescharacteristic
335C4×C11#38011yescharacteristic
336C4×C11#38111yescharacteristic
337C4×C11#38511yescharacteristic
338C4×C11#38511yescharacteristic
339C4×C11#38611yescharacteristic
340C4×C11#38611yescharacteristic
341Dic11—24no—
342Dic11—82no—
343C2×#41—112no—
344C2×#41—112no—
345C2×#41—112no—
346C2×#41—112no—
347C2×#41—221no—
348C2×#41—221no—
349C2×#41—221no—
350C2×#41—221no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—221no—
354C2×#41—221no—
355C22×Q8—111no—
356C22×D4—112no—
357C22×D4—111no—
358C23×C4—112no—
359C23×C4C4×D1112yes—
360C23×C4C22×D1111yescharacteristic
361#131—228no—
362#131—228no—
363#131—228no—
364#131—228no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—112no—
375C2×M16—112no—
376C2×M16—112no—
377C2×M16—224no—
378C2×M16—228no—
379C2×M16—228no—
380C2×M16—221no—
381C2×M16—221no—
382C2×M16—221no—
383C2×M16—221no—
384C2×M16—221no—
385C2×M16—221no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16C4×D1112yes—
390C2×M16C4×D1112yes—
391C2×M16D4412yes—
392C22×C8—21no—
393C22×C8—112no—
394C22×C8—224no—
395C22×C8—221no—
396C22×C8C22⋊D1112yes—
397#117—221no—
398#117—221no—
399#117—221no—
400#117—221no—
401C2×C4⋊C4—221no—
402C2×C22⋊C4—112no—
403C2×C22⋊C4—224no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—221no—
411#101—224no—
412#100—224no—
413#95—224no—
414C2×C11—21no—
415C2×C11—21no—
416C2×C11—21no—
417C2×C11—21no—
418C2×C11—21no—
419C2×C11—21no—
420C2×C11C22⋊#9511yescharacteristic
421C2×C11#189112yes—
422D11—44no—
423C24—112no—
424C24C2×C4×D1111yescharacteristic
425#41—222no—
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—
441C2×Q8—112no—
442C2×Q8—112no—
443C2×Q8—221no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×D4—114no—
448C2×D4—114no—
449C2×D4—112no—
450C2×D4—112no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—112no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4C2×C4×D1111yescharacteristic
472C22×C4C2×C4×D1111yescharacteristic
473C22×C4C2×D4411yescharacteristic
474C22×C4#433911yescharacteristic
475C22×C4#433911yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4D4×D1111yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4#434111yescharacteristic
482C22×C4Q8×D1111yescharacteristic
483C22×C4#434311yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485M16—22no—
486M16—22no—
487M16—22no—
488M16—22no—
489M16—22no—
490M16—22no—
491M16—41no—
492M16—41no—
493M16—2216no—
494M16—222no—
495M16—222no—
496M16—222no—
497M16—222no—
498M16—222no—
499M16—222no—
500M16—441no—
501M16—441no—
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)⋊C414yescomplemented
515C4⋊C4—441no—
516C4⋊C4—441no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—448no—
520C42—41no—
521C42—41no—
522C42—41no—
523C42—41no—
524C42—441no—
525C42—441no—
526C11#1074611yescharacteristic, complemented, Sylow
527C23—42no—
528C23—114no—
529C23—222no—
530C23—222no—
531C23—444no—
532C23C42×D1111yescharacteristic
533C23C4×D4411yescharacteristic
534C23C22⋊C4×D1111yescharacteristic
535C23(C22⋊D11)⋊C411yescharacteristic
536C23C4⋊C4×D1111yescharacteristic
537C23#6694611yescharacteristic
538C23C4×C22⋊D1111yescharacteristic
539Q8—222no—
540Q8—222no—
541Q8—222no—
542Q8—222no—
543D4—224no—
544D4—224no—
545D4—224no—
546D4—224no—
547D4—222no—
548D4—222no—
549D4—222no—
550D4—222no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—114no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—444no—
566C2×C4—442no—
567C2×C4#6692511yescharacteristic
568C2×C4C4×D4411yescharacteristic
569C2×C4C22⋊C4×D1111yescharacteristic
570C2×C4C22⋊C4×D1111yescharacteristic
571C2×C4C22⋊C4×D1111yescharacteristic
572C2×C4(C22⋊D11)⋊C411yescharacteristic
573C2×C4#6693511yescharacteristic
574C2×C4#6693511yescharacteristic
575C2×C4#6693611yescharacteristic
576C2×C4#6693611yescharacteristic
577C2×C4#6693711yescharacteristic
578C2×C4#6693711yescharacteristic
579C2×C4C4⋊C4×D1111yescharacteristic
580C2×C4C4⋊C4×D1111yescharacteristic
581C2×C4#6694511yescharacteristic
582C2×C4#6694611yescharacteristic
583C2×C4#6694711yescharacteristic
584C2×C4#6694711yescharacteristic
585C2×C4#6694811yescharacteristic
586C2×C4#6694911yescharacteristic
587C2×C4#6694911yescharacteristic
588C2×C4#6695011yescharacteristic
589C2×C4C2×(C2×D11)⋊C411yescharacteristic
590C2×C4C4×C22⋊D1111yescharacteristic
591C2×C4#6699011yescharacteristic
592C2×C4#6699011yescharacteristic
593C2×C4#6699111yescharacteristic
594C2×C4#6699911yescharacteristic
595C8—24no—
596C8—42no—
597C8—224no—
598C8—442no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—224no—
607C22—444no—
608C22—444no—
609C22—882no—
610C22D11×#9511yescharacteristic
611C22#1062227811yescharacteristic
612C22#1062227911yescharacteristic
613C22#1062228111yescharacteristic
614C22C4×(C2×D11)⋊C411yescharacteristic
615C22#1062256911yescharacteristic
616C22#1062260211yescharacteristic
617C4—44no—
618C4—224no—
619C4—882no—
620C4#1062227711yescharacteristic
621C4#1062227811yescharacteristic
622C4#1062228011yescharacteristic
623C4#1062228111yescharacteristic
624C4#1062256811yescharacteristic
625C4#1062256911yescharacteristic
626C4#1062260011yescharacteristic
627C4#1062260211yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—444no—
635C2(C2×D11)⋊#9511yescharacteristic
636C2#1306903112yes—
subgroupG/H
centerC2×C4#66990
commutatorC23×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1728C2
socleC22×C11#386
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#1728D11
hypocenterC11#10746
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1728

Complements

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

NH ≅ G/Ntype
4. C2×#10622197C2semidirect
5. C2×#10622194C2semidirect
6. #13068310C2semidirect
7. C11×#1728C2semidirect
18. #10623276C4semidirect
25. #10622745C4semidirect
181. C2×C8×C11C22⋊C4semidirect
206. C2×C11⋊C8C22⋊C4semidirect
215. #1728D11semidirect
514. C2×C8(C2×D11)⋊C4semidirect
526. C11#10746semidirect

Maximal subgroups

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

subgroupindex
C2×#106232762
C2×#106227452
#130711062
C2×#106221972
C2×#106221942
#130683102
C11×#17282
#1074611