Finite Group Databasebeta

← #14660201

Subgroups — #14660201

Order 2816.

966 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×#10622752C211yesmaximal, characteristic
2C2×#10622746C211yesmaximal, characteristic
3C2×#10622619C211yesmaximal, characteristic
4#13070972C211yesmaximal, characteristic, complemented
5#13068336C211yesmaximal, characteristic, complemented
6C2×#10622195C211yesmaximal, characteristic, complemented
7C2×C11×#344C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15#10622752—22no—
16#10622752C414yescomplemented
17C2×#66889—22no—
18#10622746—22no—
19#10622746—22no—
20C2×#66885C412yescomplemented
21C2×#66880C412yescomplemented
22#10622619—22no—
23#10622619C414yescomplemented
24C4⋊C4×Dic11—22no—
25C2×#66870—22no—
26C22⋊C4×Dic11—22no—
27C4×C4⋊Dic11—22no—
28C11×#344—22no—
29#10622195—22no—
30#10622189—22no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—21no—
33C23×Dic11—21no—
34C2×#4339—21no—
35C2×#4339—21no—
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×#4339C2×C412yes—
45C2×#4339C2×C412yes—
46C22×D44C2×C411yescharacteristic
47C22×C4×D11—21no—
48C22×Dic22C2×C411yescharacteristic
49C2×C11×M16—21no—
50C2×C11×M16—21no—
51C2×C11×M16—21no—
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×M16C2×C412yes—
61C22×C8×C11—21no—
62C22×C8×C11C2×C412yes—
63C11×#117—21no—
64C11×#117—21no—
65C11×#117C2×C412yes—
66C11×#117D412yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11—21no—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72#66979—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979C2×C412yes—
78#66979C2×C412yes—
79#66979D412yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2×C412yes—
86C2×C4⋊Dic11D412yes—
87C2×C4⋊Dic11D412yes—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—24no—
90C2×C4×Dic11D412yes—
91C11⋊#95—24no—
92#66889—28no—
93#66885—24no—
94#66880—24no—
95#66870—28no—
96#10954—111nomaximal, Sylow
97C24×C11C2×D411yescharacteristic
98C23×D11—21no—
99C22×C4×C11—22no—
100C22×C4×C11C22×C411yescharacteristic
101C22×C4×C11C22×C411yescharacteristic
102C22×C4×C11C22×C411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C22⋊D11—22no—
115C2×C22⋊D11—22no—
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C22×Dic11—21no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—41no—
126C22×Dic11—82no—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—22no—
133#4339—22no—
134#4339—22no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140#4339—41no—
141#4339—41no—
142#4339—41no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44C4212yescomplemented
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—41no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C4212yescomplemented
161C11×M16—22no—
162C11×M16—22no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—41no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4C22⋊C414yes—
179C42×C11—22no—
180C42×C11—22no—
181C22⋊Dic11—22no—
182C22⋊Dic11—22no—
183C22⋊Dic11—22no—
184C22⋊Dic11—41no—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11—22no—
188C4⋊Dic11—22no—
189C4⋊Dic11—22no—
190C4⋊Dic11—22no—
191C4⋊Dic11—41no—
192C4⋊Dic11C22⋊C414yes—
193C4×Dic11—22no—
194C4×Dic11—22no—
195C4×Dic11—41no—
196C4×Dic11—84no—
197C4×Dic11C22⋊C414yes—
198C2×#421—111no—
199C2×#417—111no—
200C2×#410—111no—
201#2274—111no—
202C2×#344D1111yescharacteristic, complemented
203#1736—111no—
204C2×H(3,ℤ/4)—111no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11C2×C22⋊C411yescharacteristic
208C23×C11C4×D411yescharacteristic
209C23×C11C4×D411yescharacteristic
210C23×C11#12011yescharacteristic
211C23×C11#12111yescharacteristic
212C23×C11#12111yescharacteristic
213C23×C11#12311yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—81no—
218C22×D11—81no—
219C2×C4×C11—24no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11C2×C4211yescharacteristic
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11#11711yescharacteristic
226C2×C4×C11#11711yescharacteristic
227C2×C4×C11#11711yescharacteristic
228C2×C4×C11C4×D411yescharacteristic
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11C4×D411yescharacteristic
235C2×C4×C11C4×D411yescharacteristic
236C2×C4×C11C4×D411yescharacteristic
237C2×C4×C11C4×D411yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11#12111yescharacteristic
242C2×C4×C11#12311yescharacteristic
243C2×C4×C11#12311yescharacteristic
244C2×C4×C11#12411yescharacteristic
245C2×C4×C11#12411yescharacteristic
246C2×C4×C11#12411yescharacteristic
247C2×C4×C11#12611yescharacteristic
248C2×C4×C11#12611yescharacteristic
249C2×C4×C11#12711yescharacteristic
250C22⋊D11—42no—
251C22⋊D11—42no—
252C22⋊D11—42no—
253C22⋊D11—42no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—42no—
258C2×Dic11—44no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—42no—
263C2×Dic11—82no—
264C2×Dic11—82no—
265C2×Dic11—81no—
266C2×Dic11—81no—
267D44—22no—
268D44—22no—
269D44—41no—
270D44—41no—
271C4×D11—42no—
272C4×D11—42no—
273C4×D11—42no—
274C4×D11—42no—
275Dic22—22no—
276Dic22—22no—
277Dic22—41no—
278Dic22—41no—
279C8×C11—42no—
280C8×C11—42no—
281C22×#41—111no—
282C22×M16C2×D1111yescharacteristic
283C22×M16C2×D1111yescharacteristic
284C2×#117—111no—
285C2×#117—111no—
286C2×#117C2×D1111yescharacteristic
287C22×C4⋊C4—111no—
288#421—114no—
289#421—222no—
290C2×#104—222no—
291#417—222no—
292#417—222no—
293C2×#103—112no—
294C2×#102—112no—
295#410—114no—
296#410—222no—
297C2×#99—222no—
298C4×C4⋊C4—222no—
299C4×C4⋊C4—222no—
300C4×C22⋊C4—222no—
301#344—22no—
302#340—222no—
303H(3,ℤ/4)—222no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—41no—
311C22×C11—41no—
312C22×C11—41no—
313C22×C11—41no—
314C22×C11C4×C22⋊C411yescharacteristic
315C22×C11#38611yescharacteristic
316C22×C11#38611yescharacteristic
317C22×C11#38611yescharacteristic
318C22×C11#38811yescharacteristic
319C22×C11#38811yescharacteristic
320C22×C11#39011yescharacteristic
321C2×D11—42no—
322C2×D11—82no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—82no—
326C4×C11—44no—
327C4×C11C4×C22⋊C411yescharacteristic
328C4×C11C4×C22⋊C411yescharacteristic
329C4×C11#38811yescharacteristic
330C4×C11#38811yescharacteristic
331C4×C11#38811yescharacteristic
332C4×C11#38811yescharacteristic
333C4×C11#39011yescharacteristic
334C4×C11#39011yescharacteristic
335Dic11—44no—
336Dic11—44no—
337Dic11—42no—
338Dic11—82no—
339C2×#41—112no—
340C2×#41—112no—
341C2×#41—221no—
342C2×#41—221no—
343C2×#41—221no—
344C2×#41—221no—
345C2×#41—221no—
346C2×#41—221no—
347C2×#41—221no—
348C2×#41—221no—
349C2×#41—221no—
350C2×#41—221no—
351C22×Q8—111no—
352C22×D4—111no—
353C22×D4—221no—
354C23×C4—221no—
355C23×C4—221no—
356C23×C4C22×D1111yescharacteristic
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16C4×D1112yes—
369C22×C8—21no—
370C22×C8C4×D1112yes—
371#117—21no—
372#117—21no—
373#117—112no—
374#117—112no—
375#117—112no—
376#117—221no—
377#117—221no—
378#117—221no—
379#117—221no—
380#117—221no—
381#117C4×D1112yes—
382#117C22⋊D1112yes—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—112no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4D4412yes—
395C2×C42—21no—
396C2×C42—112no—
397C2×C42—221no—
398C2×C42—224no—
399#104—228no—
400#103—224no—
401#102—224no—
402#99—228no—
403#95—224no—
404C2×C11—21no—
405C2×C11—21no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—21no—
409C2×C11—21no—
410C2×C11#143711yescharacteristic
411C2×C11#190411yescharacteristic
412C2×C11#190511yescharacteristic
413D11—82no—
414C24—221no—
415C24C2×D4411yescharacteristic
416#41—222no—
417#41—222no—
418#41—222no—
419#41—222no—
420#41—222no—
421#41—222no—
422#41—222no—
423#41—222no—
424#41—441no—
425#41—441no—
426#41—441no—
427#41—441no—
428#41—441no—
429#41—441no—
430#41—441no—
431#41—441no—
432C2×Q8—112no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×D4—112no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—441no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4—441no—
450C22×C4—22no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4—441no—
462C22×C4—441no—
463C22×C4—882no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4C2×C4×D1111yescharacteristic
467C22×C4#433911yescharacteristic
468C22×C4#433911yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4D4×D1111yescharacteristic
471C22×C4D4×D1111yescharacteristic
472C22×C4D4×D1111yescharacteristic
473C22×C4#434111yescharacteristic
474C22×C4#434111yescharacteristic
475C22×C4#434311yescharacteristic
476C22×C4#434311yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—41no—
491C2×C8—41no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—114no—
495C4⋊C4—222no—
496C4⋊C4—222no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—441no—
502C22⋊C4—22no—
503C22⋊C4—222no—
504C22⋊C4—222no—
505C22⋊C4—222no—
506C22⋊C4—441no—
507C22⋊C4(C2×D11)⋊C414yes—
508C42—22no—
509C42—22no—
510C42—114no—
511C42—222no—
512C42—222no—
513C42—441no—
514C42—884no—
515C11#1095411yescharacteristic, complemented, Sylow
516C23—41no—
517C23—41no—
518C23—222no—
519C23—441no—
520C23—441no—
521C23—881no—
522C23—881no—
523C23C4×D4411yescharacteristic
524C23C4×D4411yescharacteristic
525C23#6693511yescharacteristic
526C23#6693911yescharacteristic
527C23#6694811yescharacteristic
528C23#6694811yescharacteristic
529C23C2×(C2×D11)⋊C411yescharacteristic
530Q8—222no—
531Q8—222no—
532Q8—441no—
533Q8—441no—
534D4—222no—
535D4—222no—
536D4—442no—
537D4—442no—
538D4—442no—
539D4—442no—
540D4—441no—
541D4—441no—
542C2×C4—24no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—222no—
548C2×C4—442no—
549C2×C4—444no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—882no—
559C2×C4—882no—
560C2×C4—881no—
561C2×C4—881no—
562C2×C4C42×D1111yescharacteristic
563C2×C4#6692511yescharacteristic
564C2×C4C22⋊C4×D1111yescharacteristic
565C2×C4C22⋊C4×D1111yescharacteristic
566C2×C4(C22⋊D11)⋊C411yescharacteristic
567C2×C4(C22⋊D11)⋊C411yescharacteristic
568C2×C4(C22⋊D11)⋊C411yescharacteristic
569C2×C4(C22⋊D11)⋊C411yescharacteristic
570C2×C4#6693711yescharacteristic
571C2×C4#6693711yescharacteristic
572C2×C4#6693811yescharacteristic
573C2×C4#6693811yescharacteristic
574C2×C4#6694511yescharacteristic
575C2×C4#6694511yescharacteristic
576C2×C4#6694611yescharacteristic
577C2×C4#6694611yescharacteristic
578C2×C4#6694611yescharacteristic
579C2×C4#6694611yescharacteristic
580C2×C4#6694711yescharacteristic
581C2×C4#6694711yescharacteristic
582C2×C4#6695111yescharacteristic
583C2×C4#6695111yescharacteristic
584C2×C4C4×C22⋊D1111yescharacteristic
585C2×C4C4×C22⋊D1111yescharacteristic
586C2×C4#6699211yescharacteristic
587C2×C4#6699211yescharacteristic
588C2×C4#6699311yescharacteristic
589C2×C4#6700011yescharacteristic
590C8—42no—
591C8—42no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—442no—
603C22—882no—
604C22—882no—
605C22—881no—
606C22—881no—
607C22#1062227811yescharacteristic
608C22#1062227811yescharacteristic
609C22#1062228311yescharacteristic
610C22#1062228311yescharacteristic
611C22C4×(C2×D11)⋊C411yescharacteristic
612C22#1062257111yescharacteristic
613C22#1062260111yescharacteristic
614C4—44no—
615C4—444no—
616C4—444no—
617C4—442no—
618C4—882no—
619C4#1062227911yescharacteristic
620C4#1062227911yescharacteristic
621C4#1062228211yescharacteristic
622C4#1062228211yescharacteristic
623C4#1062257011yescharacteristic
624C4#1062257011yescharacteristic
625C4#1062260311yescharacteristic
626C4#1062260311yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—882no—
634C2#1306685211yescharacteristic
635C2#1306910211yescharacteristic
636C2#1306910911yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#344C2
socleC22×C11#386
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenterC2×#344D11
hypocenterC11#10954
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. #13070972C2semidirect
5. #13068336C2semidirect
6. C2×#10622195C2semidirect
7. C2×C11×#344C2semidirect
16. #10622752C4semidirect
20. C2×#66885C4semidirect
21. C2×#66880C4semidirect
23. #10622619C4semidirect
148. C2×D44C42semidirect
160. C2×Dic22C42semidirect
202. C2×#344D11semidirect
515. C11#10954semidirect

Maximal subgroups

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

subgroupindex
C2×#106227522
C2×#106227462
C2×#106226192
#130709722
#130683362
C2×#106221952
C2×C11×#3442
#1095411