Finite Group Databasebeta

← #14675736

Subgroups — #14675736

Order 2816.

2222 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
1C22×#66945C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic
3C2×#10622600C212yesmaximal
4C2×D11×#95C211yesmaximal, characteristic
5#13066881C211yesmaximal, characteristic, complemented
6#13066875C211yesmaximal, characteristic, complemented
7#13066872C211yesmaximal, characteristic, complemented
8#13066850C212yesmaximal, complemented
9#13066848C212yesmaximal, complemented
10(C2×D11)⋊#95C212yesmaximal
11C11×#1444C211yesmaximal, characteristic, complemented
12C23×C4×D11C2212yes—
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2212yes—
21C22×C4×Dic11C2212yes—
22C2×#66945—24no—
23C2×#66945—28no—
24C2×C11×#95C2212yes—
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622600—28no—
38#10622277—24no—
39D11×#95C418yescomplemented
40C24×D11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—24no—
54C22×C4×D11—24no—
55C22×C4×D11—24no—
56C22×C4×D11—24no—
57C22×C4×D11—42no—
58C22×C4×D11—42no—
59C22×C4×D11C2×C418yes—
60C22×C4×D11C2×C414yes—
61C22×C4×D11D414yes—
62C22×C4×D11Q814yes—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—24no—
67C2×C11×C4⋊C4—42no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4D418yes—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—24no—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—42no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—24no—
83#66945—232no—
84C11×#95—22no—
85C11×#95—24no—
86C11×#95C2×C414yes—
87C11⋊#95—22no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—24no—
93C11⋊#95—42no—
94C11⋊#95—42no—
95C11⋊#95C2×C414yes—
96C11⋊#95C2×C418yes—
97#13878—111nomaximal, Sylow
98C24×C11C2411yescharacteristic
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—21no—
102C23×D11—21no—
103C23×D11—21no—
104C23×D11—21no—
105C23×D11C22×C412yes—
106C23×D11C2×D412yes—
107C23×D11C2×D414yes—
108C23×D11C2×Q812yes—
109C23×D11#4114yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×Q812yes—
137C22×C4×C11#4114yes—
138C22×C4×C11#4114yes—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11C22×C414yes—
164C22×Dic11C22×C412yes—
165C22×Dic11C2×D414yes—
166C22×Dic11C2×D412yes—
167C22×Dic11C2×Q812yes—
168C2×C4×D11—216no—
169C2×C4×D11—216no—
170C2×C4×D11—28no—
171C2×C4×D11—216no—
172C2×C4×D11—28no—
173C2×C4×D11—216no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C2×C4×D11—48no—
177C2×C4×D11—48no—
178C2×C4×D11—48no—
179C2×C4×D11C4⋊C4116yescomplemented
180C11×C4⋊C4—28no—
181C11×C4⋊C4—48no—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—44no—
184(C2×D11)⋊C4—44no—
185C4⋊Dic11—28no—
186C4⋊Dic11—48no—
187C4×Dic11—216no—
188C22×#117—111no—
189C2×#381—111no—
190C2×#380—112no—
191C22×#95—111no—
192#1444—111no—
193#1444D1111yescharacteristic, complemented
194#1442—111no—
195#1442—111no—
196#1436—112no—
197#1436—112no—
198C22⋊#95—112no—
199C23×C11C23×C411yescharacteristic
200C23×C11C22×D411yescharacteristic
201C23×C11C22×D412yes—
202C23×C11C22×Q811yescharacteristic
203C23×C11C2×#4112yes—
204C23×C11C2×#4112yes—
205C23×C11C2×#4112yes—
206C23×C11H(5,𝔽2)11yescharacteristic
207C23×C11H(5,𝔽2)11yescharacteristic
208C23×C112−1+411yescharacteristic
209C23×C112−1+411yescharacteristic
210C22×D11—24no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—24no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11C2×C4⋊C414yes—
229C22×D11C4×D418yes—
230C22×D11#12014yes—
231C22×D11C22⋊Q818yes—
232C22×D11#12314yes—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11C2×C4⋊C414yes—
261C2×C4×C11#11718yescomplemented
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11C2×C4⋊C414yes—
291C4×D11—232no—
292C4×D11—432no—
293C24×C4—111no—
294C24×C4—112no—
295C2×#117—228no—
296C2×#117—224no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—112no—
299C22×C4⋊C4C2×D1111yescharacteristic
300C22×C4⋊C4C2×D1112yes—
301C22×C22⋊C4—112no—
302C22×C22⋊C4—111no—
303C22×C22⋊C4—111no—
304C22×C42—112no—
305#381—224no—
306#380—228no—
307C2×#95—112no—
308C2×#95—111no—
309C2×#95—118no—
310C2×#95—112no—
311C2×#95—111no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—111no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95C2×D1112yes—
319C2×#95C2×D1111yescharacteristic
320C2×#95C2×D1111yescharacteristic
321C22×C11C22×C4⋊C411yescharacteristic
322C22×C11C2×#11712yes—
323C22×C11C2×C4×D412yes—
324C22×C11#51811yescharacteristic
325C22×C11#51911yescharacteristic
326C22×C11C2×#12011yescharacteristic
327C22×C11C2×C22⋊Q812yes—
328C22×C11C2×#12311yescharacteristic
329C22×C11#53211yescharacteristic
330C22×C11#53211yescharacteristic
331C22×C11#53312yes—
332C22×C11#53711yescharacteristic
333C22×C11#53711yescharacteristic
334C22×C11#54411yescharacteristic
335C22×C11#54411yescharacteristic
336C22×C11#54612yes—
337C22×C11#54612yes—
338C22×C11#54712yes—
339C22×C11#54712yes—
340C22×C11#55112yes—
341C22×C11#55112yes—
342C22×C11#55212yes—
343C22×C11#55212yes—
344C2×D11—24no—
345C2×D11—28no—
346C2×D11—28no—
347C2×D11—24no—
348C2×D11—24no—
349C2×D11—28no—
350C2×D11—28no—
351C2×D11—24no—
352C2×D11—24no—
353C2×D11—24no—
354C2×D11#38518yes—
355C4×C11—28no—
356C4×C11—24no—
357C4×C11—44no—
358C4×C11—81no—
359C4×C11—81no—
360Dic11—24no—
361Dic11—44no—
362Dic11—44no—
363Dic11—81no—
364Dic11—81no—
365C25—111no—
366C23×C4—111no—
367C23×C4—114no—
368C23×C4—114no—
369C23×C4—114no—
370C23×C4—112no—
371C23×C4—112no—
372C23×C4—118no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—224no—
376C23×C4—224no—
377C23×C4—224no—
378C23×C4—224no—
379C23×C4—224no—
380C23×C4—224no—
381C23×C4—442no—
382C23×C4—442no—
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1112yes—
388#117—2232no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—224no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—224no—
397C2×C4⋊C4—224no—
398C2×C4⋊C4—442no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—224no—
406C2×C42—224no—
407C2×C42—224no—
408C2×C42—224no—
409#95—22no—
410#95—24no—
411#95—118no—
412#95—114no—
413#95—224no—
414#95—222no—
415#95—222no—
416#95—224no—
417#95—222no—
418#95—224no—
419#95—442no—
420#95—442no—
421#95C4×D1114yes—
422C2×C11#228511yescharacteristic
423C2×C11C2×#38511yescharacteristic
424C2×C11#231611yescharacteristic
425C2×C11#234212yes—
426C2×C11#234412yes—
427C2×C11#243011yescharacteristic
428C2×C11#243011yescharacteristic
429C2×C11#243812yes—
430C2×C11#243812yes—
431C2×C11#249811yescharacteristic
432C2×C11#249811yescharacteristic
433D11—28no—
434C24—112no—
435C24—114no—
436C24—112no—
437C24—112no—
438C24—114no—
439C24—222no—
440C24—221no—
441C24—222no—
442C24—221no—
443C24—221no—
444C24—221no—
445C24C23×D1111yescharacteristic
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—112no—
471C22×C4—1116no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—228no—
475C22×C4—2216no—
476C22×C4—2216no—
477C22×C4—228no—
478C22×C4—2216no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—2216no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—221no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—448no—
505C22×C4—448no—
506C22×C4—448no—
507C22×C4—448no—
508C22×C4—448no—
509C22×C4C2×C4×D1112yes—
510C22×C4C2×C4×D1114yes—
511C22×C4D4×D1114yes—
512C22×C4D4×D1112yes—
513C22×C4#434114yes—
514C22×C4Q8×D1112yes—
515C22×C4#434314yes—
516C4⋊C4—28no—
517C4⋊C4—48no—
518C4⋊C4—228no—
519C4⋊C4—448no—
520C22⋊C4—2216no—
521C22⋊C4—444no—
522C22⋊C4—444no—
523C42—2216no—
524C11#1387811yescharacteristic, complemented, Sylow
525C23—114no—
526C23—118no—
527C23—114no—
528C23—118no—
529C23—114no—
530C23—222no—
531C23—222no—
532C23—224no—
533C23—224no—
534C23—222no—
535C23—224no—
536C23—222no—
537C23—222no—
538C23—224no—
539C23—222no—
540C23—224no—
541C23—222no—
542C23—224no—
543C23—224no—
544C23—224no—
545C23—224no—
546C23—222no—
547C23—224no—
548C23C22×C4×D1111yescharacteristic
549C23C2×D4×D1111yescharacteristic
550C23C2×D4×D1112yes—
551C23C2×#434112yes—
552C23#6703711yescharacteristic
553C23C2×Q8×D1111yescharacteristic
554C23C2×#434312yes—
555C23#6704011yescharacteristic
556C23#41×D1112yes—
557C23#6704211yescharacteristic
558C23#6704311yescharacteristic
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—114no—
587C2×C4—2232no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—4432no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—442no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—441no—
616C2×C4—442no—
617C2×C4C4⋊C4×D1114yes—
618C2×C4#6694518yescomplemented
619C22—118no—
620C22—224no—
621C22—224no—
622C22—228no—
623C22—228no—
624C22—224no—
625C22—228no—
626C22—224no—
627C22—228no—
628C22—224no—
629C22—224no—
630C22C2×C4⋊C4×D1111yescharacteristic
631C22C2×#6694512yes—
632C22C4×D4×D1112yes—
633C22#1062307611yescharacteristic
634C22#1062310311yescharacteristic
635C22D11×#12011yescharacteristic
636C22#1062312212yes—
637C22#1062313911yescharacteristic
638C22#1062314212yes—
639C22D11×C22⋊Q812yes—
640C22#1062316011yescharacteristic
641C22#1062316112yes—
642C22#1062316812yes—
643C22#1062317012yes—
644C22D11×#12311yescharacteristic
645C22#1062318912yes—
646C22#1062322011yescharacteristic
647C22#1062322512yes—
648C22#1062324711yescharacteristic
649C22#1062325611yescharacteristic
650C22#1062325712yes—
651C22#1062325912yes—
652C22#1062326011yescharacteristic
653C4—28no—
654C4—24no—
655C4—44no—
656C4—81no—
657C4—81no—
658C4—224no—
659C4—444no—
660C4—444no—
661C4—881no—
662C4—881no—
663C2—228no—
664C2#1307102111yescharacteristic
665C2D11×#38511yescharacteristic
666C2#1307123111yescharacteristic
667C2#1307146312yes—
668C2#1307148412yes—
669C2#1307221911yescharacteristic
670C2#1307222711yescharacteristic
671C2#1307228512yes—
672C2#1307229312yes—
673C2#1307305311yescharacteristic
674C2#1307306111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1444D11
hypocenterC11#13878
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
5. #13066881C2semidirect
6. #13066875C2semidirect
7. #13066872C2semidirect
8. #13066850C2semidirect
9. #13066848C2semidirect
11. C11×#1444C2semidirect
39. D11×#95C4semidirect
179. C2×C4×D11C4⋊C4semidirect
193. #1444D11semidirect
261. C2×C4×C11#117semidirect
524. C11#13878semidirect
618. C2×C4#66945semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106222772
C2×#106226002
C2×D11×#952
#130668812
#130668752
#130668722
#130668502
#130668482
(C2×D11)⋊#952
C11×#14442
#1387811