Finite Group Databasebeta

← #14780640

Subgroups — #14780640

Order 2816.

2014 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2C2×#10623364C211yesmaximal, characteristic
3C2×#10622615C211yesmaximal, characteristic, complemented
4C22×#66899C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic, complemented
6#13069624C214yesmaximal, complemented
7#13069617C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C2×C11×#536C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C22×#4339C2211yescharacteristic
13C11×#536—24no—
14C11×#536—24no—
15C2×C11×C4⋊Q8—21no—
16C2×C11×#124—21no—
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8C2214yes—
19C2×C11×#117C2211yescharacteristic
20#10623364—24no—
21#10623364—24no—
22C2×#66999—21no—
23C22×#4326C2212yes—
24C2×#66995—24no—
25C2×#66995—24no—
26C2×#66995—24no—
27C22×#4325C2212yes—
28C2×#66992—22no—
29C2×#66991—21no—
30C2×#66983C2212yes—
31C22×C4⋊Dic11C2211yescharacteristic
32C2×#66977C2212yes—
33C22×#4318C2211yescharacteristic
34C23×C11⋊C8C2211yescharacteristic
35#10622847—24no—
36C2×#66899—24no—
37C2×#66899C2214yes—
38C2×C22⋊(C11⋊C8)C2214yes—
39#10622615—24no—
40C2×#66874C2212yes—
41C2×#66873C2212yes—
42#10622167C2214yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C22×Q8×C11—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—22no—
54C22×Q8×C11—22no—
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11D414yescomplemented
57C22×Q8×C11C2312yes—
58C22×D4×C11D411yescharacteristic
59C22×D4×C11D412yes—
60C23×C4×C11—21no—
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×C22⋊D11—22no—
65C23×Dic11—21no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339D414yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×Dic22C2311yescharacteristic
75C11×C4⋊Q8—28no—
76C11×#124—28no—
77C11×#123—216no—
78C11×C22⋊Q8—28no—
79C11×C22⋊Q8—28no—
80C11×#117—22no—
81C11×#117D414yescomplemented
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—24no—
86C2×C42×C11—21no—
87C2×C22⋊Dic11—22no—
88#66999—28no—
89C2×#4326—24no—
90C2×#4326—24no—
91C2×#4326—24no—
92#66995—232no—
93C2×#4325—24no—
94C2×#4325—24no—
95C2×#4325—24no—
96#66992—216no—
97#66991—28no—
98#66983—24no—
99#66983—24no—
100C2×(C2×D11)⋊C4—22no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11D414yes—
104C2×C4⋊Dic11C2312yes—
105#66977—24no—
106#66977—24no—
107C2×Dic11⋊C4—22no—
108C2×#4318—22no—
109C2×#4318—22no—
110C2×#4318D414yescomplemented
111C22×C11⋊C8—22no—
112C22×C11⋊C8—22no—
113C22×C11⋊C8—22no—
114C22×C11⋊C8C2312yes—
115C22×C11⋊C8C2312yes—
116#66899—28no—
117C22⋊(C11⋊C8)—28no—
118#66874—24no—
119#66873—24no—
120#23394—111nomaximal, Sylow
121C24×C11C2×D412yes—
122C24×C11C2×D411yescharacteristic
123C23×D11—21no—
124C11×#41—44no—
125C11×#41—44no—
126C11×#41—44no—
127C11×#41—44no—
128C2×Q8×C11—22no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—28no—
134C2×Q8×C11—28no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11—22no—
139C2×Q8×C11—42no—
140C2×Q8×C11—42no—
141C2×Q8×C11—44no—
142C2×Q8×C11—44no—
143C2×Q8×C11C2×D414yes—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—28no—
171C2×C22⋊D11—24no—
172C2×C22⋊D11—42no—
173C2×C22⋊D11—42no—
174C2×C22⋊D11—84no—
175C22×Dic11—24no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—82no—
179#4339—28no—
180#4339—28no—
181#4339—44no—
182#4339—44no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44C2×D412yes—
189C2×C4×D11—24no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×Dic22—21no—
193C2×Dic22—21no—
194C2×Dic22—21no—
195C2×Dic22—21no—
196C2×Dic22—21no—
197C2×Dic22C2×D412yes—
198C11×C4⋊C4—216no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4C2×D414yes—
201C11×C22⋊C4—216no—
202C11×C22⋊C4—24no—
203C42×C11—24no—
204C22⋊Dic11—28no—
205#4326—216no—
206#4325—216no—
207(C2×D11)⋊C4—28no—
208C4⋊Dic11—24no—
209C4⋊Dic11—22no—
210C4⋊Dic11C2×D414yes—
211Dic11⋊C4—28no—
212#4318—28no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—44no—
219C2×C11⋊C8C2×D414yes—
220C22×#137—111no—
221C2×#537—111no—
222C2×#536D1111yescharacteristic, complemented
223C2×#416—111no—
224C22×#103—111no—
225C2×#408—111no—
226#2001—114no—
227#2000—114no—
228#1736—111no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11#12012yes—
237C23×C11#12012yes—
238C23×C11#12112yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—42no—
244C22×D11—42no—
245Q8×C11—24no—
246Q8×C11—24no—
247Q8×C11—42no—
248Q8×C11—42no—
249Q8×C11—48no—
250Q8×C11—44no—
251D4×C11—48no—
252D4×C11—44no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—48no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11#12014yes—
268C2×C4×C11#12012yes—
269C2×C4×C11#12012yes—
270C2×C4×C11#12114yes—
271C2×C4×C11#12114yes—
272C2×C4×C11#12112yes—
273C2×C4×C11#12714yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C22⋊D11—48no—
281C22⋊D11—88no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—44no—
287C2×Dic11—84no—
288D44—22no—
289D44—22no—
290D44—41no—
291D44—41no—
292C4×D11—48no—
293Dic22—22no—
294Dic22—22no—
295Dic22—41no—
296Dic22—41no—
297C11⋊C8—24no—
298C11⋊C8—42no—
299C22×#41—111no—
300C22×#41C2×D1111yescharacteristic
301C23×Q8C2×D1111yescharacteristic
302C2×#137—224no—
303C2×#137—224no—
304C2×#137—224no—
305C22×Q16—112no—
306C22×SD16—112no—
307C22×M16—111no—
308C23×C8—111no—
309#537—224no—
310#537—224no—
311#536—24no—
312#536—24no—
313C2×C4⋊Q8—21no—
314C2×#124—21no—
315C2×#123—22no—
316C2×C22⋊Q8—112no—
317C2×C22⋊Q8—221no—
318C2×C22⋊Q8C2×D1114yes—
319C2×#121—112no—
320C2×#121—221no—
321C2×#121—222no—
322C2×#117C2×D1111yescharacteristic
323C22×C4⋊C4—111no—
324#416—224no—
325C2×#103—114no—
326C2×#103—112no—
327C2×#103—224no—
328C2×#102—112no—
329#408—224no—
330C2×C22⋊C8—114no—
331#340—114no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11—24no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—42no—
339C22×C11—44no—
340C22×C11—44no—
341C22×C11#39214yes—
342C22×C11C2×#12011yescharacteristic
343C22×C11C2×#12011yescharacteristic
344C22×C11C2×#12111yescharacteristic
345C22×C11#57712yes—
346C22×C11#57812yes—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—82no—
351C2×D11—82no—
352C4×C11—42no—
353C4×C11—44no—
354C4×C11—44no—
355C4×C11#39214yes—
356C4×C11C2×#12011yescharacteristic
357C4×C11C2×#12111yescharacteristic
358C4×C11C2×#12111yescharacteristic
359C4×C11C2×#12711yescharacteristic
360Dic11—42no—
361Dic11—44no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—114no—
369C2×#41—222no—
370C2×#41—222no—
371C2×#41—222no—
372C2×#41—222no—
373C2×#41—222no—
374C22×Q8—21no—
375C22×Q8—22no—
376C22×Q8—22no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—111no—
381C22×Q8C22⋊D1111yescharacteristic
382C22×Q8C22⋊D1114yescomplemented
383C22×Q8C22×D1112yes—
384C22×D4—111no—
385C22×D4—221no—
386C22×D4—222no—
387C22×D4C22⋊D1112yes—
388C22×D4C22⋊D1111yescharacteristic
389C23×C4—21no—
390C23×C4—221no—
391C23×C4—221no—
392C23×C4C22×D1112yes—
393C23×C4C22×D1111yescharacteristic
394#137—2232no—
395C2×Q16—224no—
396C2×Q16—224no—
397C2×Q16—224no—
398C2×SD16—224no—
399C2×SD16—224no—
400C2×SD16—224no—
401C2×M16—114no—
402C2×M16—222no—
403C2×M16—222no—
404C22×C8—112no—
405C22×C8—112no—
406C22×C8—222no—
407C22×C8—222no—
408C22×C8—222no—
409C4⋊Q8—28no—
410#124—28no—
411#123—216no—
412C22⋊Q8—28no—
413C22⋊Q8—28no—
414C22⋊Q8—224no—
415C22⋊Q8—224no—
416C22⋊Q8—228no—
417#121—224no—
418#121—224no—
419#121—228no—
420#121—2216no—
421#117—22no—
422#117C22⋊D1114yescomplemented
423C2×C4⋊C4—24no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4C22×D1112yes—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—222no—
434C2×C42—21no—
435#103—228no—
436#103—224no—
437#102—224no—
438C22⋊C8—228no—
439C2×C11—24no—
440C2×C11—82no—
441C2×C11C2×#39211yescharacteristic
442C2×C11#300911yescharacteristic
443C2×C11#301111yescharacteristic
444C2×C11#301312yes—
445C2×C11#306312yes—
446D11—82no—
447C24—221no—
448C24C2×C22⋊D1112yes—
449C24C2×C22⋊D1111yescharacteristic
450#41—44no—
451#41—44no—
452#41—44no—
453#41—44no—
454#41—228no—
455#41—228no—
456#41—444no—
457#41—444no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—24no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—42no—
470C2×Q8—44no—
471C2×Q8—42no—
472C2×Q8—44no—
473C2×Q8—112no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8C2×C22⋊D1114yes—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—112no—
487C2×D4—224no—
488C2×D4—228no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—442no—
495C2×D4—442no—
496C2×D4—884no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—222no—
509C22×C4—221no—
510C22×C4—224no—
511C22×C4—224no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—882no—
515C22×C4D4×D1112yes—
516C22×C4D4×D1112yes—
517C22×C4D4×D1112yes—
518C22×C4#434112yes—
519C22×C4C2×C22⋊D1112yes—
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1112yes—
522C22×C4C2×C22⋊D1112yes—
523C22×C4C23×D1111yescharacteristic
524Q16—2216no—
525SD16—2216no—
526M16—228no—
527C2×C8—114no—
528C2×C8—222no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8—222no—
532C2×C8—222no—
533C2×C8—444no—
534C4⋊C4—216no—
535C4⋊C4—22no—
536C4⋊C4—114no—
537C4⋊C4—228no—
538C4⋊C4—224no—
539C4⋊C4—222no—
540C4⋊C4C2×C22⋊D1114yes—
541C22⋊C4—216no—
542C22⋊C4—24no—
543C22⋊C4—228no—
544C22⋊C4—228no—
545C42—24no—
546C11#2339411yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—24no—
552C23—24no—
553C23—22no—
554C23—222no—
555C23—441no—
556C23—442no—
557C23—442no—
558C23—441no—
559C23#6699012yes—
560C23#6699212yes—
561C23#6700612yes—
562C23C22×C22⋊D1111yescharacteristic
563Q8—24no—
564Q8—24no—
565Q8—42no—
566Q8—42no—
567Q8—48no—
568Q8—44no—
569Q8—222no—
570Q8—222no—
571Q8—441no—
572Q8—441no—
573D4—48no—
574D4—44no—
575D4—222no—
576D4—222no—
577D4—448no—
578D4—441no—
579D4—441no—
580D4—888no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—22no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—48no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—441no—
598C2×C4—444no—
599C2×C4—441no—
600C2×C4—448no—
601C2×C4—884no—
602C2×C4#6699014yes—
603C2×C4#6699012yes—
604C2×C4#6699114yes—
605C2×C4#6699214yes—
606C2×C4#6699212yes—
607C2×C4#6699314yes—
608C2×C4#6700612yes—
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4C2×#434111yescharacteristic
613C2×C4C22×C22⋊D1111yescharacteristic
614C2×C4C22×C22⋊D1111yescharacteristic
615C8—224no—
616C8—442no—
617C22—24no—
618C22—22no—
619C22—22no—
620C22—24no—
621C22—44no—
622C22—42no—
623C22—42no—
624C22—44no—
625C22—42no—
626C22—442no—
627C22—442no—
628C22—442no—
629C22—882no—
630C22—882no—
631C22#1062283614yes—
632C22C2×#6699011yescharacteristic
633C22C2×#6699211yescharacteristic
634C22#1062336812yes—
635C22#1062336912yes—
636C22C2×#6700611yescharacteristic
637C4—44no—
638C4—42no—
639C4—44no—
640C4—444no—
641C4—442no—
642C4#1062283614yes—
643C4C2×#6699011yescharacteristic
644C4C2×#6699111yescharacteristic
645C4C2×#6699211yescharacteristic
646C4C2×#6699311yescharacteristic
647C2—24no—
648C2—82no—
649C2—882no—
650C2C2×#1062283611yescharacteristic
651C2#1307789111yescharacteristic
652C2#1307790911yescharacteristic
653C2#1307793112yes—
654C2#1307830312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC2×#536D11
hypocenterC11#23394
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
3. C2×#10622615C2semidirect
4. C22×#66899C2semidirect
5. C2×#10622847C2semidirect
6. #13069624C2semidirect
7. #13069617C2semidirect
8. #13068337C2semidirect
9. C2×C11×#536C2semidirect
56. C22×Q8×C11D4semidirect
81. C11×#117D4semidirect
110. C2×#4318D4semidirect
222. C2×#536D11semidirect
382. C22×Q8C22⋊D11semidirect
422. #117C22⋊D11semidirect
546. C11#23394semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106233642
C2×#106226152
C22×#668992
C2×#106228472
#130696242
#130696172
#130683372
C2×C11×#5362
#2339411