Finite Group Databasebeta

← #14756223

Subgroups — #14756223

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622474C211yesmaximal, characteristic
2C2×#10622415C211yesmaximal, characteristic
3C2×D11×#103C211yesmaximal, characteristic
4#13071199C211yesmaximal, characteristic
5#13070970C211yesmaximal, characteristic
6#13069260C211yesmaximal, characteristic, complemented
7#13069259C211yesmaximal, characteristic, complemented
8#13069258C211yesmaximal, characteristic, complemented
9#13069257C211yesmaximal, characteristic, complemented
10#13069249C211yesmaximal, characteristic, complemented
11#13069248C211yesmaximal, characteristic, complemented
12#13069247C211yesmaximal, characteristic, complemented
13#13068331C211yesmaximal, characteristic
14#13068311C211yesmaximal, characteristic
15C11×#1927C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622587C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C4×(C2×D11)⋊C4—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×Dic11⋊C4—21no—
44#10622542C2211yescharacteristic
45#10622474—24no—
46#10622415C418yescomplemented
47D11×#103—24no—
48#10622279—21no—
49#10622277—21no—
50#10622277—21no—
51#10622262—21no—
52#10622259—21no—
53#10622259—21no—
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C2×Q8×D11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—22no—
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11C2×C414yes—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11C2311yescharacteristic
72C22×Dic22—21no—
73C22×Dic22C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4D411yescharacteristic
90C2×Dic11⋊C4D411yescharacteristic
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×#4313—22no—
100C2×#4313—22no—
101C2×#4313C2×C414yes—
102C2×C8×D11—22no—
103C2×C8×D11—22no—
104C2×C8×D11—22no—
105#66945—22no—
106#66945—22no—
107#66945—22no—
108#66945C2×C414yes—
109C4⋊C4×D11—22no—
110C4⋊C4×D11D414yes—
111#66925—22no—
112#66925—22no—
113C11×#106—22no—
114C11×#103—22no—
115C11×#103C2×C414yescomplemented
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119#66899—22no—
120#66899C2×C414yescomplemented
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130#66882—22no—
131#66880—22no—
132#66880C2×C414yescomplemented
133#66874—22no—
134#66874C2×C414yescomplemented
135#66872—22no—
136#66871—22no—
137#21064—111nomaximal, Sylow
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159Q8×D11—28no—
160Q8×D11—28no—
161Q8×D11—44no—
162Q8×D11—44no—
163C2×C4×D11—24no—
164C2×C4×D11—24no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—81no—
168C2×C4×D11—81no—
169C2×C4×D11C22×C412yes—
170C2×C4×D11C2×D412yes—
171C2×C4×D11#4112yes—
172C2×C4×D11#4112yes—
173C2×C4×D11#4112yes—
174C2×C4×D11#4112yes—
175C2×Dic22—24no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—42no—
182C2×Dic22—42no—
183C2×Dic22C22×C412yes—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11C22×C412yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4C22×C412yes—
195C11×C4⋊C4C2×D412yes—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—81no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—42no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22×C412yes—
208C4⋊Dic11C2×D412yes—
209Dic11⋊C4—24no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212C4×Dic11—24no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
216C4×Dic11—81no—
217C4×Dic11—81no—
218C4×Dic11—81no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8C22×C412yes—
225#4313—28no—
226C8×D11—44no—
227C2×#428—111no—
228C2×#419—111no—
229C22×#103—111no—
230#2310—111no—
231#2274—111no—
232#1928—111no—
233#1928—111no—
234#1928—111no—
235#1928—111no—
236#1927—111no—
237#1927—111no—
238#1927—111no—
239#1927D1111yescharacteristic, complemented
240#1735—111no—
241#1729—111no—
242C23×C11C22×D411yescharacteristic
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11C4×D412yes—
248C22×D11#12112yes—
249C22×D11#12312yes—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—41no—
253Q8×C11—41no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11C4×D412yes—
297C2×Dic11#12112yes—
298C2×Dic11#12312yes—
299C4×D11—48no—
300C4×D11—84no—
301C4×D11#11714yes—
302C4×D11C4×D414yes—
303C4×D11#12414yes—
304C4×D11#12614yes—
305Dic22—22no—
306Dic22—22no—
307Dic22—41no—
308Dic22—41no—
309Dic22—48no—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—22no—
313C11⋊C8—41no—
314C23×Q8—111no—
315C22×M16—111no—
316C23×C8—111no—
317C2×#117—111no—
318C2×#117—111no—
319C2×#117—111no—
320C22×C4⋊C4—111no—
321#428—224no—
322C2×#107—111no—
323C2×#107—111no—
324C2×#106—111no—
325C2×#106C2×D1111yescharacteristic
326#419—118no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—224no—
334C2×#103C2×D1111yescharacteristic
335C2×#103C2×D1111yescharacteristic
336#391—111no—
337#391—111no—
338#391—111no—
339#391—221no—
340#391—221no—
341#391C2×D1111yescharacteristic
342#381—221no—
343#381—221no—
344C4×C4⋊C4—111no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—111no—
347C4×C4⋊C4—221no—
348C4×C4⋊C4—221no—
349C4×C4⋊C4C2×D1111yescharacteristic
350C4×C22⋊C4—221no—
351C4×C22⋊C4—221no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340C2×D1111yescharacteristic
356#336—111no—
357#336—111no—
358#336—111no—
359#336C2×D1111yescharacteristic
360C22×C11C2×C4×D411yescharacteristic
361C22×C11C2×#12111yescharacteristic
362C22×C11C2×#12311yescharacteristic
363C22×C11#57711yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57811yescharacteristic
366C22×C11#57811yescharacteristic
367C2×D11—22no—
368C2×D11—22no—
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11#38814yes—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11C2×#11711yescharacteristic
381C4×C11C2×C4×D411yescharacteristic
382C4×C11C2×#12411yescharacteristic
383C4×C11C2×#12611yescharacteristic
384Dic11—41no—
385Dic11—41no—
386Dic11—42no—
387Dic11—42no—
388Dic11—42no—
389Dic11—81no—
390Dic11#38814yes—
391C22×Q8—114no—
392C22×Q8—111no—
393C22×Q8—221no—
394C22×Q8—222no—
395C22×Q8—222no—
396C22×Q8—222no—
397C22×Q8—222no—
398C22×Q8—222no—
399C22×Q8C22×D1111yescharacteristic
400C23×C4—111no—
401C23×C4—221no—
402C23×C4—221no—
403C2×M16—114no—
404C2×M16—222no—
405C2×M16—222no—
406C22×C8—111no—
407C22×C8—111no—
408C22×C8—222no—
409C22×C8—222no—
410C22×C8—222no—
411C22×C8C22×D1111yescharacteristic
412C22×C8C22×D1111yescharacteristic
413#117—114no—
414#117—222no—
415#117—222no—
416#117—222no—
417#117—222no—
418#117—222no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—114no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—111no—
431C2×C22⋊C4—111no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C42—21no—
435C2×C42—111no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42C22×D1111yescharacteristic
442#107—222no—
443#107—222no—
444#106—22no—
445#106—222no—
446#103—22no—
447#103—114no—
448#103—114no—
449#103—114no—
450#103—222no—
451#103—222no—
452#103—222no—
453#103C4×D1114yescomplemented
454#95—21no—
455#95—21no—
456#95—21no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11C2×#38811yescharacteristic
467C2×C11#294711yescharacteristic
468C2×C11#294711yescharacteristic
469C2×C11#304211yescharacteristic
470C2×C11#304411yescharacteristic
471C2×C11#309711yescharacteristic
472C2×C11#309711yescharacteristic
473D11—24no—
474C24—111no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—112no—
481C2×Q8—224no—
482C2×Q8—228no—
483C2×Q8—228no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—442no—
490C2×Q8—442no—
491C2×Q8—444no—
492C2×Q8—444no—
493C2×Q8C2×C4×D1112yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—111no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—112no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—224no—
508C22×C4—224no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—881no—
516C22×C4—881no—
517C22×C4D4×D1111yescharacteristic
518C22×C4D4×D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520M16—228no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—112no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—444no—
533C2×C8C2×C4×D1112yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—112no—
539C4⋊C4—112no—
540C4⋊C4—224no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4C2×C4×D1112yes—
548C4⋊C4D4×D1112yes—
549C22⋊C4—222no—
550C22⋊C4—222no—
551C22⋊C4—224no—
552C22⋊C4—442no—
553C42—21no—
554C42—21no—
555C42—81no—
556C42—224no—
557C42—221no—
558C42—221no—
559C42—442no—
560C42—881no—
561C42—881no—
562C42—881no—
563C11#2106411yescharacteristic, complemented, Sylow
564C23—112no—
565C23—112no—
566C23—112no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23C2×D4×D1111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—222no—
577Q8—222no—
578Q8—448no—
579Q8—441no—
580Q8—441no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—112no—
602C2×C4—114no—
603C2×C4—114no—
604C2×C4—114no—
605C2×C4—114no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—448no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—884no—
626C2×C4C22×C4×D1111yescharacteristic
627C2×C4C2×D4×D1111yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C8—22no—
633C8—41no—
634C8—222no—
635C8—441no—
636C22—114no—
637C22—222no—
638C22—222no—
639C22—222no—
640C22—222no—
641C22—222no—
642C22—222no—
643C22C4×D4×D1111yescharacteristic
644C22D11×#12111yescharacteristic
645C22D11×#12311yescharacteristic
646C22#1062329311yescharacteristic
647C22#1062330211yescharacteristic
648C22#1062330911yescharacteristic
649C22#1062331011yescharacteristic
650C4—41no—
651C4—41no—
652C4—42no—
653C4—42no—
654C4—42no—
655C4—81no—
656C4—114no—
657C4—441no—
658C4—441no—
659C4—442no—
660C4—442no—
661C4—442no—
662C4—881no—
663C4D11×#11711yescharacteristic
664C4C4×D4×D1111yescharacteristic
665C4D11×#12411yescharacteristic
666C4D11×#12611yescharacteristic
667C2—224no—
668C2D11×#38811yescharacteristic
669C2#1307745211yescharacteristic
670C2#1307745811yescharacteristic
671C2#1307812311yescharacteristic
672C2#1307814411yescharacteristic
673C2#1307857811yescharacteristic
674C2#1307858011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1927C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1927D11
hypocenterC11#21064
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
6. #13069260C2semidirect
7. #13069259C2semidirect
8. #13069258C2semidirect
9. #13069257C2semidirect
10. #13069249C2semidirect
11. #13069248C2semidirect
12. #13069247C2semidirect
15. C11×#1927C2semidirect
46. #10622415C4semidirect
115. C11×#103C2×C4semidirect
120. #66899C2×C4semidirect
132. #66880C2×C4semidirect
134. #66874C2×C4semidirect
239. #1927D11semidirect
453. #103C4×D11semidirect
563. C11#21064semidirect

Maximal subgroups

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

subgroupindex
C2×#106224742
C2×#106224152
C2×D11×#1032
#130711992
#130709702
#130692602
#130692592
#130692582
#130692572
#130692492
#130692482
#130692472
#130683312
#130683112
C11×#19272
#2106411