Finite Group Databasebeta

← #14780637

Subgroups — #14780637

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
1C2×#10623364C211yesmaximal, characteristic
2C2×#10623347C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C22×#66899C211yesmaximal, characteristic, complemented
5C2×#10622742C211yesmaximal, characteristic, complemented
6#13069623C214yesmaximal, complemented
7#13069616C214yesmaximal, complemented
8#13068336C211yesmaximal, characteristic, complemented
9C22×C11×#137C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C22×#4339C2211yescharacteristic
13C2×C11×#137—24no—
14C2×C11×#137—24no—
15C2×C11×#137—24no—
16C22×C11×Q16C2212yes—
17C22×C11×SD16C2212yes—
18C22×C11×M16C2211yescharacteristic
19#10623364—24no—
20#10623364—24no—
21#10623347—24no—
22#10623347—24no—
23C2×#67000—21no—
24C2×#66999C2214yes—
25C2×#66999C2212yes—
26C2×#66997—21no—
27C2×#66992—22no—
28C2×#66991C2212yes—
29C2×#66983—21no—
30C2×#66982—22no—
31C2×#66979C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C2×#66977—21no—
34C23×C11⋊C8C2211yescharacteristic
35#10622846—24no—
36C2×#66899—24no—
37C2×#66899C2214yes—
38C2×#66899C2212yes—
39C2×#66896C2212yes—
40#10622742—24no—
41C2×(C2×D11)⋊C8C2214yes—
42#10622189C2214yes—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41D414yes—
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×C11D414yescomplemented
56C22×Q8×C11C2312yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—22no—
64C22×C22⋊D11D412yes—
65C23×Dic11—21no—
66C2×#4339—22no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339—22no—
72C22×D44D411yescharacteristic
73C22×C4×D11C2312yes—
74C22×Dic22D411yescharacteristic
75C11×#137—232no—
76C2×C11×Q16—24no—
77C2×C11×Q16—24no—
78C2×C11×Q16—24no—
79C2×C11×SD16—24no—
80C2×C11×SD16—24no—
81C2×C11×SD16—24no—
82C2×C11×M16—22no—
83C2×C11×M16—22no—
84C2×C11×M16D414yescomplemented
85C22×C8×C11C2312yes—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—22no—
88#67000—28no—
89#66999—28no—
90#66999—24no—
91#66999—28no—
92#66999—24no—
93#66997—28no—
94#66992—216no—
95#66991—24no—
96#66991—24no—
97#66983—28no—
98#66982—216no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—22no—
101#66979—22no—
102#66979D414yescomplemented
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11D414yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2312yes—
108#66977—28no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—24no—
111C2×C4×Dic11—21no—
112C22×C11⋊C8—22no—
113C22×C11⋊C8—22no—
114C22×C11⋊C8—22no—
115C22×C11⋊C8C2312yes—
116#66899—28no—
117#66899—24no—
118#66896—24no—
119(C2×D11)⋊C8—28no—
120#23394—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D411yescharacteristic
123C23×D11C2×D412yes—
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—44no—
127C11×#41—44no—
128C2×Q8×C11—24no—
129C2×Q8×C11—22no—
130C2×Q8×C11—21no—
131C2×Q8×C11—28no—
132C2×Q8×C11—28no—
133C2×Q8×C11—22no—
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—22no—
140C2×Q8×C11—21no—
141C2×Q8×C11—42no—
142C2×Q8×C11—42no—
143C2×Q8×C11—44no—
144C2×Q8×C11—44no—
145C2×Q8×C11C2×D414yes—
146C2×Q8×C11C2×D412yes—
147C2×D4×C11—24no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—42no—
154C2×D4×C11—42no—
155C2×D4×C11C2×D412yes—
156C22×C4×C11—24no—
157C22×C4×C11—21no—
158C22×C4×C11—22no—
159C22×C4×C11—24no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—28no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11—24no—
175C2×C22⋊D11—24no—
176C2×C22⋊D11—84no—
177C22×Dic11—24no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—82no—
181C22×Dic11C2×D412yes—
182#4339—44no—
183#4339—44no—
184#4339—44no—
185#4339—44no—
186C2×D44—22no—
187C2×D44—22no—
188C2×D44—22no—
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×C4×D11—22no—
192C2×C4×D11—22no—
193C2×C4×D11—22no—
194C2×C4×D11—22no—
195C2×Dic22—22no—
196C2×Dic22—22no—
197C2×Dic22—22no—
198C11×Q16—216no—
199C11×SD16—216no—
200C11×M16—28no—
201C2×C8×C11—22no—
202C2×C8×C11—22no—
203C2×C8×C11C2×D414yes—
204C22⋊Dic11—28no—
205C22⋊Dic11—24no—
206(C2×D11)⋊C4—216no—
207(C2×D11)⋊C4—28no—
208C4⋊Dic11—24no—
209C4⋊Dic11—22no—
210C4⋊Dic11—22no—
211C4⋊Dic11C2×D414yes—
212C4⋊Dic11C2×D414yes—
213Dic11⋊C4—28no—
214Dic11⋊C4—216no—
215C4×Dic11—24no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—44no—
220C22×#137D1111yescharacteristic, complemented
221C2×#537—111no—
222C2×#536—111no—
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—41no—
233C23×C11—41no—
234C23×C11—42no—
235C23×C11—42no—
236C23×C11#12012yes—
237C23×C11#12012yes—
238C23×C11#12112yes—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—24no—
245Q8×C11—24no—
246Q8×C11—22no—
247Q8×C11—24no—
248Q8×C11—22no—
249Q8×C11—42no—
250Q8×C11—41no—
251Q8×C11—42no—
252Q8×C11—41no—
253Q8×C11—48no—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11—48no—
257D4×C11—41no—
258D4×C11—41no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—48no—
266C2×C4×C11—48no—
267C2×C4×C11#12012yes—
268C2×C4×C11#12012yes—
269C2×C4×C11#12014yes—
270C2×C4×C11#12112yes—
271C2×C4×C11#12114yes—
272C2×C4×C11#12114yes—
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—24no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—22no—
287C2×Dic11—42no—
288C2×Dic11—44no—
289C2×Dic11—42no—
290C2×Dic11—84no—
291D44—44no—
292C4×D11—42no—
293C4×D11—42no—
294C4×D11—42no—
295C4×D11—42no—
296Dic22—44no—
297C8×C11—24no—
298C11⋊C8—42no—
299C22×#41—111no—
300C22×#41C2×D1111yescharacteristic
301C23×Q8C2×D1111yescharacteristic
302C2×#137—24no—
303C2×#137—24no—
304C2×#137—24no—
305C22×Q16C2×D1112yes—
306C22×SD16C2×D1112yes—
307C22×M16C2×D1111yescharacteristic
308C23×C8—111no—
309#537—224no—
310#537—224no—
311#536—224no—
312#536—224no—
313C2×C4⋊Q8—221no—
314C2×#124—221no—
315C2×#123—222no—
316C2×C22⋊Q8—114no—
317C2×C22⋊Q8—112no—
318C2×C22⋊Q8—221no—
319C2×#121—112no—
320C2×#121—221no—
321C2×#121—222no—
322C2×#117—111no—
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—82no—
340C22×C11—82no—
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—44no—
351C2×D11—44no—
352C4×C11—42no—
353C4×C11—44no—
354C4×C11#39214yes—
355C4×C11C2×#12011yescharacteristic
356C4×C11C2×#12111yescharacteristic
357C4×C11C2×#12111yescharacteristic
358C4×C11C2×#12711yescharacteristic
359Dic11—42no—
360Dic11—44no—
361Dic11—44no—
362C2×#41—22no—
363C2×#41—22no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—222no—
368C2×#41—222no—
369C2×#41—222no—
370C2×#41—222no—
371C2×#41—222no—
372C2×#41—222no—
373C2×#41C22⋊D1114yes—
374C22×Q8—21no—
375C22×Q8—22no—
376C22×Q8—22no—
377C22×Q8—22no—
378C22×Q8—22no—
379C22×Q8—22no—
380C22×Q8—111no—
381C22×Q8C22⋊D1114yescomplemented
382C22×Q8C22×D1112yes—
383C22×Q8C22×D1111yescharacteristic
384C22×D4—21no—
385C22×D4—112no—
386C22×D4—111no—
387C22×D4—222no—
388C22×D4C22×D1111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—112no—
392C23×C4—221no—
393C23×C4C22×D1111yescharacteristic
394#137—232no—
395C2×Q16—24no—
396C2×Q16—24no—
397C2×Q16—24no—
398C2×SD16—24no—
399C2×SD16—24no—
400C2×SD16—24no—
401C2×M16—22no—
402C2×M16—22no—
403C2×M16C22⋊D1114yescomplemented
404C22×C8—112no—
405C22×C8—222no—
406C22×C8—222no—
407C22×C8—222no—
408C22×C8C22×D1112yes—
409C4⋊Q8—228no—
410#124—228no—
411#123—2216no—
412C22⋊Q8—228no—
413C22⋊Q8—224no—
414C22⋊Q8—228no—
415C22⋊Q8—228no—
416C22⋊Q8—224no—
417#121—224no—
418#121—228no—
419#121—2216no—
420#121—224no—
421#117—114no—
422#117—222no—
423C2×C4⋊C4—114no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—224no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—222no—
430C2×C22⋊C4—222no—
431C2×C22⋊C4—224no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—221no—
434C2×C42—221no—
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—21no—
448C24—112no—
449C24D4×D1111yescharacteristic
450#41—28no—
451#41—28no—
452#41—44no—
453#41—44no—
454#41—444no—
455#41—444no—
456#41—444no—
457#41—444no—
458C2×Q8—24no—
459C2×Q8—22no—
460C2×Q8—21no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—22no—
464C2×Q8—21no—
465C2×Q8—22no—
466C2×Q8—21no—
467C2×Q8—22no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—222no—
476C2×Q8—222no—
477C2×Q8—222no—
478C2×Q8C2×C22⋊D1114yes—
479C2×Q8C2×C22⋊D1112yes—
480C2×D4—24no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—224no—
489C2×D4—224no—
490C2×D4—224no—
491C2×D4—228no—
492C2×D4—222no—
493C2×D4—222no—
494C2×D4—222no—
495C2×D4—884no—
496C2×D4C2×C22⋊D1112yes—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—112no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—224no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—882no—
516C22×C4D4×D1111yescharacteristic
517C22×C4D4×D1112yes—
518C22×C4D4×D1112yes—
519C22×C4#434112yes—
520C22×C4C2×C22⋊D1112yes—
521C22×C4C2×C22⋊D1112yes—
522C22×C4C2×C22⋊D1112yes—
523C22×C4C23×D1111yescharacteristic
524Q16—216no—
525SD16—216no—
526M16—28no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8—222no—
532C2×C8—444no—
533C2×C8C2×C22⋊D1114yes—
534C4⋊C4—114no—
535C4⋊C4—114no—
536C4⋊C4—228no—
537C4⋊C4—2216no—
538C4⋊C4—224no—
539C4⋊C4—222no—
540C4⋊C4—222no—
541C22⋊C4—228no—
542C22⋊C4—2216no—
543C22⋊C4—228no—
544C22⋊C4—224no—
545C42—224no—
546C11#2339411yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23—41no—
553C23—41no—
554C23—224no—
555C23—224no—
556C23—222no—
557C23—222no—
558C23—222no—
559C23#6699012yes—
560C23#6699012yes—
561C23#6699112yes—
562C23C2×D4×D1111yescharacteristic
563Q8—24no—
564Q8—22no—
565Q8—24no—
566Q8—22no—
567Q8—42no—
568Q8—41no—
569Q8—42no—
570Q8—41no—
571Q8—48no—
572Q8—444no—
573D4—22no—
574D4—22no—
575D4—48no—
576D4—41no—
577D4—41no—
578D4—448no—
579D4—444no—
580D4—888no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—42no—
587C2×C4—48no—
588C2×C4—48no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—444no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—884no—
602C2×C4#6699012yes—
603C2×C4#6699012yes—
604C2×C4#6699112yes—
605C2×C4#6699214yes—
606C2×C4#6699214yes—
607C2×C4#6699314yes—
608C2×C4#6700614yes—
609C2×C4C2×D4×D1111yescharacteristic
610C2×C4C2×D4×D1111yescharacteristic
611C2×C4C2×#434111yescharacteristic
612C2×C4C22×C22⋊D1111yescharacteristic
613C2×C4C22×C22⋊D1111yescharacteristic
614C2×C4C22×C22⋊D1111yescharacteristic
615C8—24no—
616C8—442no—
617C22—24no—
618C22—22no—
619C22—22no—
620C22—24no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—82no—
625C22—82no—
626C22—444no—
627C22—442no—
628C22—442no—
629C22—444no—
630C22—442no—
631C22#1062283614yes—
632C22#1062330912yes—
633C22#1062331012yes—
634C22C2×#6699011yescharacteristic
635C22C2×#6699011yescharacteristic
636C22C2×#6699111yescharacteristic
637C4—42no—
638C4—44no—
639C4—444no—
640C4—444no—
641C4—442no—
642C4#1062283614yes—
643C4C2×#6699211yescharacteristic
644C4C2×#6699211yescharacteristic
645C4C2×#6699311yescharacteristic
646C4C2×#6700611yescharacteristic
647C2—24no—
648C2—82no—
649C2—882no—
650C2C2×#1062283611yescharacteristic
651C2#1307789211yescharacteristic
652C2#1307791011yescharacteristic
653C2#1307793012yes—
654C2#1307830112yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC2×#10623364C2
hypercenterC22×#137D11
hypocenterC11#23394
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C2×#10623347C2semidirect
3. C2×#10622846C2semidirect
4. C22×#66899C2semidirect
5. C2×#10622742C2semidirect
6. #13069623C2semidirect
7. #13069616C2semidirect
8. #13068336C2semidirect
9. C22×C11×#137C2semidirect
55. C22×Q8×C11D4semidirect
84. C2×C11×M16D4semidirect
102. #66979D4semidirect
220. C22×#137D11semidirect
381. C22×Q8C22⋊D11semidirect
403. C2×M16C22⋊D11semidirect
546. C11#23394semidirect

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106233472
C2×#106228462
C22×#668992
C2×#106227422
#130696232
#130696162
#130683362
C22×C11×#1372
#2339411