Finite Group Databasebeta

← #14782484

Subgroups — #14782484

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622494C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic
3C2×#10622415C211yesmaximal, characteristic
4C2×#10622415C211yesmaximal, characteristic
5#13071097C211yesmaximal, characteristic
6D11×#391C211yesmaximal, characteristic
7#13070008C211yesmaximal, characteristic, complemented
8#13070007C211yesmaximal, characteristic, complemented
9#13070006C211yesmaximal, characteristic, complemented
10#13069998C211yesmaximal, characteristic, complemented
11#13069997C211yesmaximal, characteristic, complemented
12#13069996C211yesmaximal, characteristic, complemented
13#13069995C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic
15C11×#2068C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#389C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622602—21no—
38#10622598C2211yescharacteristic
39C4⋊C4×Dic11—21no—
40#10622587C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622494—24no—
50#10622450—24no—
51#10622415—24no—
52#10622415—24no—
53#10622281—21no—
54D11×#95—21no—
55D11×#95—21no—
56#10622262—21no—
57#10622259—21no—
58#10622259—21no—
59C11×#340C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C2×Q8×D11—22no—
65C2×Q8×D11—22no—
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11—22no—
69C2×Q8×D11Q814yes—
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11D411yescharacteristic
73C22×C4×D11D411yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×Dic22—21no—
76C22×Dic22C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C2×#4313—22no—
101C2×#4313—22no—
102C2×#4313—22no—
103C2×#4313—22no—
104C2×#4313—22no—
105C2×#4313D414yes—
106#66945—22no—
107#66945—22no—
108#66945—22no—
109#66945D414yes—
110C4⋊C4×D11—22no—
111C4⋊C4×D11—22no—
112C42×D11—22no—
113C42×D11—22no—
114C11×#107—22no—
115C11×C4⋊C8—22no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121#66899—22no—
122#66899—22no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132#66881—22no—
133#66880—22no—
134#66880—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137#66874—22no—
138#66874—22no—
139#66872—22no—
140#66871—22no—
141C4⋊(C11⋊C8)—22no—
142#23619—111nomaximal, Sylow
143C23×D11C2×D411yescharacteristic
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×Q812yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164Q8×D11—28no—
165Q8×D11—28no—
166Q8×D11—44no—
167Q8×D11—44no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—24no—
172C2×C4×D11—22no—
173C2×C4×D11—41no—
174C2×C4×D11—41no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×C4×D11—42no—
180C2×C4×D11C2×D412yes—
181C2×C4×D11C2×D412yes—
182C2×C4×D11C2×Q812yes—
183C2×C4×D11#4112yes—
184C2×C4×D11#4112yes—
185C2×C4×D11#4112yes—
186C2×Dic22—24no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—42no—
193C2×Dic22—42no—
194C2×Dic22C2×Q812yes—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11C2×D412yes—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—42no—
207C11×C4⋊C4C2×D412yes—
208C42×C11—21no—
209C42×C11—21no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—42no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—42no—
218C4⋊Dic11C2×D412yes—
219Dic11⋊C4—42no—
220Dic11⋊C4—42no—
221Dic11⋊C4—42no—
222C4×Dic11—22no—
223C4×Dic11—22no—
224C4×Dic11—24no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—42no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8C2×D412yes—
234#4313—28no—
235#4313—44no—
236C2×#428—111no—
237C2×#423—111no—
238C2×#419—111no—
239C2×#419—111no—
240#2296—111no—
241C2×#391—111no—
242#2068—111no—
243#2068—111no—
244#2068—111no—
245#2068D1111yescharacteristic, complemented
246#2066—111no—
247#2066—111no—
248#2066—111no—
249#2066—111no—
250#1736—111no—
251C23×C11C22×D411yescharacteristic
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11#12112yes—
257C22×D11#12112yes—
258C22×D11C22⋊Q812yes—
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—41no—
262Q8×C11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11#13712yes—
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×Q811yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11#12112yes—
305C2×Dic11#12112yes—
306C2×Dic11C22⋊Q812yes—
307C2×Dic11#13712yes—
308C4×D11—44no—
309C4×D11—44no—
310C4×D11—48no—
311C4×D11—84no—
312C4×D11#12114yes—
313C4×D11C22⋊Q814yes—
314C4×D11C22⋊Q814yes—
315C4×D11#12614yes—
316Dic22—22no—
317Dic22—22no—
318Dic22—41no—
319Dic22—41no—
320Dic22—48no—
321C8×C11—22no—
322C8×C11—41no—
323C11⋊C8—22no—
324C11⋊C8—41no—
325C23×Q8—111no—
326C22×M16—111no—
327C22×M16—111no—
328C2×#117—111no—
329C2×#117—111no—
330C22×C4⋊C4—111no—
331C22×C42—111no—
332#428—224no—
333C2×#107—111no—
334C2×#107C2×D1111yescharacteristic
335C2×#106—111no—
336C2×#106—111no—
337#423—224no—
338C2×C4⋊C8—111no—
339C2×C4⋊C8—111no—
340C2×C4⋊C8—111no—
341C2×C4⋊C8C2×D1111yescharacteristic
342#419—224no—
343#419—224no—
344C2×#103—111no—
345C2×#103—111no—
346C2×#103—111no—
347C2×#103—111no—
348C2×#103—111no—
349C2×#103—111no—
350C2×#103C2×D1111yescharacteristic
351C2×#103C2×D1111yescharacteristic
352#391—111no—
353#391—111no—
354#391—111no—
355#391—221no—
356#391—221no—
357#391C2×D1111yescharacteristic
358#389—111no—
359#389—111no—
360#389—111no—
361#389C2×D1111yescharacteristic
362#385—221no—
363#385—221no—
364C4×C4⋊C4—221no—
365C4×C4⋊C4—221no—
366C2×#95—221no—
367C2×#95—221no—
368#340—111no—
369#340—111no—
370#340—111no—
371#340C2×D1111yescharacteristic
372C22×C11C2×#12111yescharacteristic
373C22×C11C2×#12111yescharacteristic
374C22×C11C2×C22⋊Q811yescharacteristic
375C22×C11C2×#13711yescharacteristic
376C22×C11C2×#13711yescharacteristic
377C22×C11#57511yescharacteristic
378C22×C11#57511yescharacteristic
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—22no—
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—22no—
385C2×D11#39614yes—
386C4×C11—22no—
387C4×C11—42no—
388C4×C11—42no—
389C4×C11—41no—
390C4×C11—81no—
391C4×C11—81no—
392C4×C11C2×#12111yescharacteristic
393C4×C11C2×C22⋊Q811yescharacteristic
394C4×C11C2×C22⋊Q811yescharacteristic
395C4×C11C2×#12611yescharacteristic
396Dic11—22no—
397Dic11—42no—
398Dic11—42no—
399Dic11—41no—
400Dic11—81no—
401Dic11—81no—
402Dic11#39614yes—
403C22×Q8—114no—
404C22×Q8—111no—
405C22×Q8—221no—
406C22×Q8—222no—
407C22×Q8—222no—
408C22×Q8—222no—
409C22×Q8—222no—
410C22×Q8—222no—
411C22×Q8C22×D1111yescharacteristic
412C23×C4—111no—
413C23×C4—111no—
414C23×C4—111no—
415C23×C4—221no—
416C23×C4—221no—
417C2×M16—114no—
418C2×M16—222no—
419C2×M16—222no—
420C2×M16—222no—
421C2×M16—222no—
422C2×M16—222no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8C22×D1111yescharacteristic
426C22×C8C22×D1111yescharacteristic
427#117—114no—
428#117—222no—
429#117—222no—
430#117—222no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—222no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—222no—
450C2×C42—222no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42C22×D1111yescharacteristic
454#107—22no—
455#107—222no—
456#106—222no—
457#106—222no—
458C4⋊C8—22no—
459C4⋊C8—222no—
460C4⋊C8—222no—
461C4⋊C8—222no—
462#103—22no—
463#103—22no—
464#103—222no—
465#103—222no—
466#103—222no—
467#103—222no—
468#103—222no—
469#103—222no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95—221no—
478#95—221no—
479#95—221no—
480#95—221no—
481#95—221no—
482C2×C11C2×#39611yescharacteristic
483C2×C11#303911yescharacteristic
484C2×C11#304011yescharacteristic
485C2×C11#305611yescharacteristic
486C2×C11#305611yescharacteristic
487C2×C11#307811yescharacteristic
488C2×C11#307811yescharacteristic
489D11—24no—
490C24—111no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—112no—
497C2×Q8—224no—
498C2×Q8—228no—
499C2×Q8—228no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8—221no—
503C2×Q8—221no—
504C2×Q8—221no—
505C2×Q8—442no—
506C2×Q8—442no—
507C2×Q8—444no—
508C2×Q8—444no—
509C2×Q8Q8×D1112yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—111no—
515C22×C4—112no—
516C22×C4—112no—
517C22×C4—112no—
518C22×C4—112no—
519C22×C4—112no—
520C22×C4—112no—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—224no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—222no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—441no—
533C22×C4—441no—
534C22×C4—442no—
535C22×C4—442no—
536C22×C4—442no—
537C22×C4—442no—
538C22×C4—442no—
539C22×C4D4×D1111yescharacteristic
540C22×C4D4×D1111yescharacteristic
541C22×C4C23×D1111yescharacteristic
542M16—228no—
543M16—444no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—112no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8D4×D1112yes—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—42no—
562C4⋊C4—112no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4—221no—
568C4⋊C4—442no—
569C4⋊C4—442no—
570C4⋊C4—442no—
571C4⋊C4—442no—
572C4⋊C4D4×D1112yes—
573C22⋊C4—224no—
574C22⋊C4—442no—
575C42—21no—
576C42—21no—
577C42—222no—
578C42—222no—
579C42—224no—
580C42—221no—
581C42—221no—
582C42—442no—
583C11#2361911yescharacteristic, complemented, Sylow
584C23—112no—
585C23—112no—
586C23—112no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23C2×D4×D1111yescharacteristic
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—222no—
597Q8—222no—
598Q8—448no—
599Q8—441no—
600Q8—441no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—112no—
619C2×C4—112no—
620C2×C4—112no—
621C2×C4—114no—
622C2×C4—114no—
623C2×C4—114no—
624C2×C4—114no—
625C2×C4—112no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—444no—
634C2×C4—444no—
635C2×C4—448no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—884no—
647C2×C4#6697112yes—
648C2×C4C2×D4×D1111yescharacteristic
649C2×C4C2×D4×D1111yescharacteristic
650C2×C4C2×Q8×D1111yescharacteristic
651C2×C4#41×D1111yescharacteristic
652C2×C4#41×D1111yescharacteristic
653C2×C4#41×D1111yescharacteristic
654C8—22no—
655C8—41no—
656C8—222no—
657C8—441no—
658C22—114no—
659C22—222no—
660C22—222no—
661C22—222no—
662C22—222no—
663C22—222no—
664C22—222no—
665C22D11×#12111yescharacteristic
666C22D11×#12111yescharacteristic
667C22D11×C22⋊Q811yescharacteristic
668C22C2×#6697111yescharacteristic
669C22#1062329911yescharacteristic
670C22#1062330411yescharacteristic
671C22D11×#13711yescharacteristic
672C4—22no—
673C4—42no—
674C4—42no—
675C4—41no—
676C4—81no—
677C4—81no—
678C4—114no—
679C4—222no—
680C4—442no—
681C4—442no—
682C4—441no—
683C4—881no—
684C4—881no—
685C4D11×#12111yescharacteristic
686C4D11×C22⋊Q811yescharacteristic
687C4D11×C22⋊Q811yescharacteristic
688C4D11×#12611yescharacteristic
689C2—224no—
690C2D11×#39611yescharacteristic
691C2#1307810011yescharacteristic
692C2#1307810511yescharacteristic
693C2#1307824111yescharacteristic
694C2#1307824311yescharacteristic
695C2#1307841911yescharacteristic
696C2#1307842211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2068C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2068D11
hypocenterC11#23619
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2068

Complements

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

NH ≅ G/Ntype
7. #13070008C2semidirect
8. #13070007C2semidirect
9. #13070006C2semidirect
10. #13069998C2semidirect
11. #13069997C2semidirect
12. #13069996C2semidirect
13. #13069995C2semidirect
15. C11×#2068C2semidirect
245. #2068D11semidirect
583. C11#23619semidirect

Maximal subgroups

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

subgroupindex
C2×#106224942
C2×#106224502
C2×#106224152
#130710972
D11×#3912
#130700082
#130700072
#130700062
#130699982
#130699972
#130699962
#130699952
#130683342
C11×#20682
#2361911