Finite Group Databasebeta

← #14675781

Subgroups — #14675781

Order 2816.

1862 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×Dic11C211yesmaximal, characteristic
2C22×C11⋊#95C211yesmaximal, characteristic
3#13066876C212yesmaximal, complemented
4#13066875C212yesmaximal, complemented
5#13066848C212yesmaximal, complemented
6#13066840C212yesmaximal, complemented
7#13066839C211yesmaximal, characteristic
8#13066838C211yesmaximal, characteristic
9#13066838C211yesmaximal, characteristic
10#13066838C211yesmaximal, characteristic
11C2×C11×#380C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C24×Dic11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C11×#380—24no—
22C2×C11×#95C2212yes—
23C2×C11⋊#95C418yescomplemented
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C22⋊C4×Dic11—24no—
38C25×C11C2311yescharacteristic
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—24no—
42C23×C4×C11—42no—
43C23×C4×C11C2×C414yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—22no—
49C23×Dic11—22no—
50C23×Dic11—22no—
51C23×Dic11—22no—
52C23×Dic11—24no—
53C23×Dic11—42no—
54C23×Dic11—42no—
55C23×Dic11—42no—
56C23×Dic11C2×C414yes—
57C23×Dic11C2×C414yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2311yescharacteristic
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—42no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4—22no—
72C2×C11×C22⋊C4D414yes—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11Q814yes—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—42no—
82C11×#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89C11⋊#95—42no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95C2×C414yes—
93C11⋊#95C2×C414yes—
94C11⋊#95C2×C414yes—
95C11⋊#95C2×C414yes—
96#13883—111nomaximal, Sylow
97C24×C11—22no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11C22×C412yes—
102C24×C11C2×D412yes—
103C24×C11C2×Q812yes—
104C24×C11#4112yes—
105C24×C11#4112yes—
106C24×C11#4112yes—
107C24×C11#4112yes—
108C24×C11C2411yescharacteristic
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—28no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—28no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—44no—
132C22×C4×C11—48no—
133C22×C4×C11—48no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D414yes—
137C22×C4×C11#4114yes—
138C22×Dic11—28no—
139C22×Dic11—28no—
140C22×Dic11—28no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—44no—
170C22×Dic11—44no—
171C22×Dic11—44no—
172C22×Dic11—48no—
173C22×Dic11—48no—
174C22×Dic11—48no—
175C22×Dic11—48no—
176C22×Dic11C22×C412yes—
177C22×Dic11C22×C412yes—
178C22×Dic11C22×C412yes—
179C22×Dic11C22×C412yes—
180C22×Dic11C2×Q814yes—
181C22×Dic11#4114yes—
182C11×C4⋊C4—48no—
183C11×C22⋊C4—28no—
184C11×C22⋊C4—44no—
185C22⋊Dic11—28no—
186C22⋊Dic11—44no—
187C4×Dic11—48no—
188C2×#380D1111yescharacteristic
189C2×C4×C22⋊C4—111no—
190C22×#95—111no—
191#1443—112no—
192#1442—112no—
193#1436—112no—
194#1434—112no—
195C22⋊#95—111no—
196C22⋊#95—111no—
197C22⋊#95—111no—
198C22⋊#95—111no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11#11714yes—
216C23×C11C4×D414yes—
217C23×C11C4×Q814yes—
218C23×C11C22⋊Q814yes—
219C23×C11#12314yes—
220C23×C11#12514yes—
221C23×C11#12614yes—
222C23×C11C23×C411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C22×Q811yescharacteristic
225C23×C11C2×#4111yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4112yes—
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4112yes—
231C23×C11H(5,𝔽2)12yes—
232C23×C11H(5,𝔽2)12yes—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—416no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11#11714yes—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—416no—
275C2×Dic11—416no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11#11714yes—
294C24×C4—111no—
295C24×C4—111no—
296C24×C4C2×D1111yescharacteristic
297C22×C4⋊C4C2×D1112yes—
298C22×C22⋊C4—111no—
299C22×C22⋊C4—111no—
300C22×C22⋊C4C2×D1111yescharacteristic
301C22×C22⋊C4C2×D1111yescharacteristic
302C22×C42—112no—
303#380—24no—
304C4×C22⋊C4—224no—
305C2×#95—111no—
306C2×#95—111no—
307C2×#95—111no—
308C2×#95—111no—
309C2×#95—118no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95C2×D1112yes—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—24no—
324C22×C11—24no—
325C22×C11—28no—
326C22×C11—28no—
327C22×C11—28no—
328C22×C11—28no—
329C22×C11—24no—
330C22×C11#38718yes—
331C22×C11C2×#11711yescharacteristic
332C22×C11C2×#11711yescharacteristic
333C22×C11C2×#11711yescharacteristic
334C22×C11C2×C4×D411yescharacteristic
335C22×C11C2×C4×Q811yescharacteristic
336C22×C11#51811yescharacteristic
337C22×C11#51811yescharacteristic
338C22×C11C2×C22⋊Q811yescharacteristic
339C22×C11C2×#12311yescharacteristic
340C22×C11C2×#12511yescharacteristic
341C22×C11C2×#12611yescharacteristic
342C22×C11#52912yes—
343C22×C11#52912yes—
344C22×C11#53812yes—
345C22×C11#53812yes—
346C22×C11#54612yes—
347C22×C11#54612yes—
348C22×C11#55112yes—
349C22×C11#55112yes—
350C22×C11#55312yes—
351C22×C11#55312yes—
352C22×C11#55412yes—
353C22×C11#55412yes—
354C4×C11—24no—
355C4×C11—42no—
356C4×C11—44no—
357C4×C11—82no—
358Dic11—24no—
359Dic11—42no—
360Dic11—42no—
361Dic11—42no—
362Dic11—44no—
363Dic11—82no—
364C25C22×D1111yescharacteristic
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—42no—
369C23×C4—111no—
370C23×C4—112no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—114no—
375C23×C4—114no—
376C23×C4—112no—
377C23×C4—224no—
378C23×C4—222no—
379C23×C4—222no—
380C23×C4—222no—
381C23×C4—222no—
382C23×C4—442no—
383C23×C4—442no—
384C23×C4—442no—
385C23×C4C4×D1114yes—
386C23×C4C22×D1112yes—
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1112yes—
389C23×C4C22×D1111yescharacteristic
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4C22⋊D1114yes—
405C2×C42—224no—
406C2×C42—224no—
407C2×C42—442no—
408#95—24no—
409#95—114no—
410#95—114no—
411#95—114no—
412#95—114no—
413#95—224no—
414#95—224no—
415#95—224no—
416#95—442no—
417#95—442no—
418#95—442no—
419#95—442no—
420#95—442no—
421#95—442no—
422C2×C11—28no—
423C2×C11#228311yescharacteristic
424C2×C11C2×#38711yescharacteristic
425C2×C11#231211yescharacteristic
426C2×C11#234211yescharacteristic
427C2×C11#234211yescharacteristic
428C2×C11#234511yescharacteristic
429C2×C11#234511yescharacteristic
430C2×C11#244412yes—
431C2×C11#245012yes—
432C2×C11#250512yes—
433C2×C11#251012yes—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24C2×C4×D1112yes—
439C24#433912yes—
440C24#434112yes—
441C24#434112yes—
442C24Q8×D1112yes—
443C24#434312yes—
444C24C2×C22⋊D1112yes—
445C24C23×D1111yescharacteristic
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—28no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—28no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—44no—
469C22×C4—48no—
470C22×C4—48no—
471C22×C4—112no—
472C22×C4—114no—
473C22×C4—112no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—228no—
478C22×C4—221no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—228no—
482C22×C4—228no—
483C22×C4—221no—
484C22×C4—222no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—444no—
509C22×C4—444no—
510C22×C4—444no—
511C22×C4—448no—
512C22×C4—448no—
513C22×C4—448no—
514C22×C4—448no—
515C22×C4C2×C4×D1112yes—
516C22×C4C2×C4×D1112yes—
517C22×C4#434114yes—
518C22×C4C2×C22⋊D1114yes—
519C4⋊C4—48no—
520C22⋊C4—28no—
521C22⋊C4—44no—
522C22⋊C4—228no—
523C22⋊C4—444no—
524C42—448no—
525C11#1388311yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—24no—
529C23—22no—
530C23—22no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23#6694014yes—
543C23#6694214yes—
544C23#6694514yes—
545C23#6695114yes—
546C23C4×C22⋊D1114yes—
547C23#6698814yes—
548C23#6699914yes—
549C23C22×C4×D1111yescharacteristic
550C23C2×#433911yescharacteristic
551C23C2×#434112yes—
552C23C2×#434111yescharacteristic
553C23C2×#434111yescharacteristic
554C23#6703712yes—
555C23C2×Q8×D1111yescharacteristic
556C23C2×#434311yescharacteristic
557C23#41×D1112yes—
558C23#6704212yes—
559C23C22×C22⋊D1111yescharacteristic
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—416no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—114no—
585C2×C4—222no—
586C2×C4—224no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—4416no—
602C2×C4—4416no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4#6693014yes—
621C22—28no—
622C22—28no—
623C22—24no—
624C22—24no—
625C22—24no—
626C22—24no—
627C22—24no—
628C22—24no—
629C22—28no—
630C22—28no—
631C22#1062259118yes—
632C22C2×#6693011yescharacteristic
633C22#1062301711yescharacteristic
634C22#1062302612yes—
635C22C2×#6694011yescharacteristic
636C22C2×#6694211yescharacteristic
637C22C2×#6694511yescharacteristic
638C22C2×#6695111yescharacteristic
639C22D11×#11711yescharacteristic
640C22#1062305211yescharacteristic
641C22#1062305812yes—
642C22#1062313112yes—
643C22#1062313212yes—
644C22#1062314812yes—
645C22#1062314912yes—
646C22#1062315512yes—
647C22#1062316612yes—
648C22#1062316712yes—
649C22#1062317512yes—
650C22C2×C4×C22⋊D1111yescharacteristic
651C22C2×#6698811yescharacteristic
652C22#1062333712yes—
653C22C2×#6699911yescharacteristic
654C22#1062336012yes—
655C4—24no—
656C4—42no—
657C4—44no—
658C4—82no—
659C4—224no—
660C4—444no—
661C4—442no—
662C4—442no—
663C4—442no—
664C4—882no—
665C2—28no—
666C2#1307101111yescharacteristic
667C2C2×#1062259111yescharacteristic
668C2#1307121311yescharacteristic
669C2#1307146111yescharacteristic
670C2#1307146611yescharacteristic
671C2#1307148811yescharacteristic
672C2#1307149511yescharacteristic
673C2#1307236212yes—
674C2#1307243612yes—
675C2#1307311312yes—
676C2#1307317212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11#13883
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. #13066876C2semidirect
4. #13066875C2semidirect
5. #13066848C2semidirect
6. #13066840C2semidirect
23. C2×C11⋊#95C4semidirect
525. C11#13883semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×Dic112
C22×C11⋊#952
#130668762
#130668752
#130668482
#130668402
#130668392
#130668382
C2×C11×#3802
#1388311