Finite Group Databasebeta

← #14647149

Subgroups — #14647149

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#380C211yesmaximal, characteristic
2#13068525C211yesmaximal, characteristic
3(C2×D11)⋊#95C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic, complemented
5#13066495C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×(C2×D11)⋊C4—21no—
10C2×C4⋊C4×D11C411yescharacteristic, complemented
11C2×C4⋊C4×D11C411yescharacteristic, complemented
12C2×C22⋊C4×D11—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C11×#380C2211yescharacteristic
15C2×C11×#95C2211yescharacteristic
16#10622825C2211yescharacteristic
17C2×C11⋊#95—21no—
18C2×C11⋊#95C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20C2×(C2×D11)⋊C8—21no—
21C2×(C2×D11)⋊C8—21no—
22#10622600C411yescharacteristic, complemented
23#10622600C411yescharacteristic, complemented
24#10622555—21no—
25#10622280—21no—
26D11×#95—21no—
27C24×D11D411yescharacteristic
28C23×C4×C11—21no—
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—21no—
31C23×Dic11D411yescharacteristic
32C22×C4×D11—21no—
33C22×C4×D11—21no—
34C22×C4×D11—21no—
35C22×C4×D11—21no—
36C22×C4×D11—21no—
37C22×C4×D11—21no—
38C22×C4×D11—42no—
39C22×C4×D11—42no—
40C22×C4×D11C2×C411yescharacteristic
41C22×C4×D11C2×C411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11D411yescharacteristic
44C22×C8×C11—21no—
45C2×C11×C4⋊C4C2×C411yescharacteristic
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C22⋊Dic11—21no—
49C2×(C2×D11)⋊C4—24no—
50C2×(C2×D11)⋊C4—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—42no—
53C2×(C2×D11)⋊C4—42no—
54C2×C4⋊Dic11C2×C411yescharacteristic
55C2×C4⋊Dic11C2×C411yescharacteristic
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C22×C11⋊C8—21no—
59C4⋊C4×D11—42no—
60C4⋊C4×D11—42no—
61C22⋊C4×D11—42no—
62C22⋊C4×D11—42no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×#95—21no—
66C11×#95—21no—
67C11×#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72C11⋊#95—21no—
73C11⋊#95—42no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76(C2×D11)⋊C8—42no—
77(C2×D11)⋊C8—42no—
78#8713—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C23×D11—21no—
81C23×D11—21no—
82C23×D11—21no—
83C23×D11—21no—
84C23×D11—22no—
85C23×D11—22no—
86C23×D11—41no—
87C23×D11—41no—
88C23×D11C22⋊C411yescharacteristic
89C23×D11C22⋊C411yescharacteristic
90C23×D11SD1612yes—
91C23×D11Q1612yes—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11C22⋊C411yescharacteristic
123C22×Dic11C22⋊C411yescharacteristic
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—21no—
129C2×C4×D11—21no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—44no—
145C2×C4×D11—44no—
146C2×C4×D11—44no—
147C2×C4×D11—44no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C8×C11—41no—
151C2×C8×C11—41no—
152C2×C8×C11—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C22⋊C4—41no—
156C11×C22⋊C4—41no—
157C22⋊Dic11—41no—
158C22⋊Dic11—41no—
159(C2×D11)⋊C4—42no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—48no—
162C4⋊Dic11—41no—
163C4⋊Dic11—41no—
164Dic11⋊C4—42no—
165Dic11⋊C4—42no—
166C2×C11⋊C8—41no—
167C2×C11⋊C8—41no—
168C2×C11⋊C8—41no—
169C2×#380—111no—
170#1779—111no—
171C22⋊#95—111no—
172#1294—111no—
173#1294—111no—
174#1294—111no—
175#1294D1111yescharacteristic, complemented
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11C2×C22⋊C411yescharacteristic
181C23×C11#12311yescharacteristic
182C23×C11#12311yescharacteristic
183C23×C11C2×SD1611yescharacteristic
184C23×C11C2×Q1611yescharacteristic
185C23×C11AGL(1,ℤ/8)11yescharacteristic
186C23×C11AGL(1,ℤ/8)11yescharacteristic
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—21no—
190C22×D11—21no—
191C22×D11—21no—
192C22×D11—21no—
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—21no—
196C22×D11—21no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11#9912yes—
214C22×D11#10312yes—
215C22×D11#10312yes—
216C22×D11#10412yes—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—81no—
235C2×C4×C11—81no—
236C2×C4×C11—81no—
237C2×C4×C11—81no—
238C2×C4×C11#11711yescharacteristic
239C2×C4×C11#11711yescharacteristic
240C2×C4×C11#12311yescharacteristic
241C2×C4×C11#12311yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—81no—
259C2×Dic11—81no—
260C2×Dic11—81no—
261C2×Dic11—81no—
262C2×Dic11#9912yes—
263C4×D11—24no—
264C4×D11—24no—
265C4×D11—42no—
266C4×D11—42no—
267C4×D11—42no—
268C4×D11—42no—
269C4×D11—42no—
270C4×D11—42no—
271C4×D11—84no—
272C4×D11—84no—
273C8×C11—81no—
274C11⋊C8—81no—
275C24×C4—111no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—111no—
278C22×C22⋊C4—221no—
279C22×C22⋊C4—221no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8—221no—
282C2×C22⋊C8—221no—
283C2×C22⋊C8C2×D1111yescharacteristic
284#380—111no—
285#380—111no—
286#380—111no—
287#380—221no—
288#380—221no—
289#380C2×D1111yescharacteristic
290C2×#95—111no—
291C2×#95—221no—
292C2×#95—221no—
293C2×#95C2×D1111yescharacteristic
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11#38111yescharacteristic
307C22×C11C2×#9911yescharacteristic
308C22×C11C2×#9911yescharacteristic
309C22×C11C2×#10311yescharacteristic
310C22×C11#41811yescharacteristic
311C22×C11C2×#10411yescharacteristic
312C22×C11#42111yescharacteristic
313C22×C11#48111yescharacteristic
314C22×C11#48111yescharacteristic
315C22×C11#48411yescharacteristic
316C22×C11#48411yescharacteristic
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—22no—
321C2×D11—22no—
322C2×D11—22no—
323C2×D11—22no—
324C2×D11—22no—
325C2×D11—22no—
326C2×D11—44no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C2×D11#32814yes—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—82no—
340C4×C11—81no—
341C4×C11—81no—
342Dic11—22no—
343Dic11—41no—
344Dic11—82no—
345Dic11—81no—
346Dic11—81no—
347C25—111no—
348C23×C4—21no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—221no—
355C23×C4—221no—
356C23×C4—221no—
357C23×C4—221no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4—221no—
361C23×C4—442no—
362C23×C4—442no—
363C23×C4C22×D1111yescharacteristic
364C22×C8—21no—
365C22×C8—221no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—442no—
371C2×C4⋊C4—442no—
372C2×C4⋊C4C4×D1111yescharacteristic
373C2×C4⋊C4C4×D1111yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—442no—
380C2×C22⋊C4—442no—
381C2×C22⋊C4—442no—
382C2×C22⋊C4—442no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8—221no—
386C22⋊C8—221no—
387C22⋊C8—442no—
388C22⋊C8—442no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—221no—
393#95—221no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—442no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11C2×#32811yescharacteristic
403C2×C11#150711yescharacteristic
404C2×C11#151011yescharacteristic
405C2×C11#152011yescharacteristic
406C2×C11#181911yescharacteristic
407C2×C11#182411yescharacteristic
408C2×C11#182611yescharacteristic
409D11—24no—
410D11—42no—
411C24—111no—
412C24—111no—
413C24—112no—
414C24—112no—
415C24—222no—
416C24—222no—
417C24—221no—
418C24—221no—
419C24—221no—
420C24—221no—
421C24—441no—
422C24—441no—
423C24D4×D1111yescharacteristic
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—441no—
456C22×C4—441no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—444no—
460C22×C4—444no—
461C22×C4—444no—
462C22×C4—444no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4—442no—
467C22×C4—442no—
468C22×C4—442no—
469C22×C4—441no—
470C22×C4—441no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4—441no—
476C22×C4C2×C4×D1111yescharacteristic
477C22×C4#433911yescharacteristic
478C22×C4#433911yescharacteristic
479C22×C4D4×D1111yescharacteristic
480C22×C4#434111yescharacteristic
481C22×C4#434311yescharacteristic
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—441no—
486C2×C8—441no—
487C2×C8—441no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—448no—
497C22⋊C4—442no—
498C22⋊C4—442no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C11#871311yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—112no—
507C23—112no—
508C23—112no—
509C23—112no—
510C23—224no—
511C23—224no—
512C23—221no—
513C23—221no—
514C23—221no—
515C23—221no—
516C23—222no—
517C23—222no—
518C23—221no—
519C23—221no—
520C23—221no—
521C23—221no—
522C23—222no—
523C23—222no—
524C23—221no—
525C23—221no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23C22⋊C4×D1111yescharacteristic
537C23#6693611yescharacteristic
538C23#6694711yescharacteristic
539C23#6696411yescharacteristic
540C23SD16×D1111yescharacteristic
541C23#6696711yescharacteristic
542C23Q16×D1111yescharacteristic
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—112no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—884no—
590C2×C4—884no—
591C2×C4—881no—
592C2×C4—881no—
593C2×C4—881no—
594C2×C4—881no—
595C2×C4#6692511yescharacteristic
596C2×C4#6693611yescharacteristic
597C2×C4#6694511yescharacteristic
598C2×C4#6694711yescharacteristic
599C8—81no—
600C8—881no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—114no—
614C22—222no—
615C22—222no—
616C22—222no—
617C22—222no—
618C22—222no—
619C22—222no—
620C22—222no—
621C22—222no—
622C22—222no—
623C22—444no—
624C22—444no—
625C22—444no—
626C22—444no—
627C22—441no—
628C22—441no—
629C22—441no—
630C22—441no—
631C22#1062227711yescharacteristic
632C22D11×#9911yescharacteristic
633C22D11×#9911yescharacteristic
634C22#1062238311yescharacteristic
635C22#1062239011yescharacteristic
636C22D11×#10311yescharacteristic
637C22#1062242211yescharacteristic
638C22D11×#10411yescharacteristic
639C22#1062243411yescharacteristic
640C22#1062247611yescharacteristic
641C22#1062249711yescharacteristic
642C4—21no—
643C4—21no—
644C4—21no—
645C4—21no—
646C4—82no—
647C4—81no—
648C4—81no—
649C4—222no—
650C4—441no—
651C4—882no—
652C4—881no—
653C4—881no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—224no—
659C2—442no—
660C2D11×#32811yescharacteristic
661C2#1306713011yescharacteristic
662C2#1306714311yescharacteristic
663C2#1306718611yescharacteristic
664C2#1306868911yescharacteristic
665C2#1306870511yescharacteristic
666C2#1306871411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#8713
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #13066496C2semidirect
5. #13066495C2semidirect
6. #13066494C2semidirect
7. C11×#1294C2semidirect
10. C2×C4⋊C4×D11C4semidirect
11. C2×C4⋊C4×D11C4semidirect
22. #10622600C4semidirect
23. #10622600C4semidirect
175. #1294D11semidirect
501. C11#8713semidirect

Maximal subgroups

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

subgroupindex
D11×#3802
#130685252
(C2×D11)⋊#952
#130664962
#130664952
#130664942
C11×#12942
#871311