Finite Group Databasebeta

← #14647159

Subgroups — #14647159

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070998C211yesmaximal, 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×#66945C411yescharacteristic, complemented
11C2×#66945C411yescharacteristic, complemented
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622825C2211yescharacteristic
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19C2×(C2×D11)⋊C8—21no—
20C2×(C2×D11)⋊C8—21no—
21#10622600C411yescharacteristic, complemented
22#10622600C411yescharacteristic, complemented
23#10622568—21no—
24C22⋊C4×Dic11—21no—
25#10622279—21no—
26#10622277—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—42no—
37C22×C4×D11—42no—
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2×C411yescharacteristic
40C22×C4×D11D411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C8×C11—21no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C4⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C22⋊Dic11—21no—
47C2×(C2×D11)⋊C4—24no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
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×C4×Dic11—21no—
57C2×C4×Dic11—21no—
58C22×C11⋊C8—21no—
59#66945—42no—
60#66945—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—42no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74(C2×D11)⋊C8—42no—
75(C2×D11)⋊C8—42no—
76#8715—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C23×D11—21no—
79C23×D11—21no—
80C23×D11—22no—
81C23×D11—22no—
82C23×D11—21no—
83C23×D11—21no—
84C23×D11—21no—
85C23×D11—21no—
86C23×D11—41no—
87C23×D11—41no—
88C23×D11C22⋊C411yescharacteristic
89C23×D11C22⋊C411yescharacteristic
90C22×C4×C11—22no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
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×C11C22×C411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11C22⋊C411yescharacteristic
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—21no—
127C2×C4×D11—21no—
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—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—44no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11—44no—
142C2×C8×C11—41no—
143C2×C8×C11—41no—
144C2×C8×C11—41no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151(C2×D11)⋊C4—42no—
152(C2×D11)⋊C4—42no—
153(C2×D11)⋊C4—48no—
154(C2×D11)⋊C4—42no—
155(C2×D11)⋊C4—42no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158C4×Dic11—42no—
159C4×Dic11—42no—
160C2×C11⋊C8—41no—
161C2×C11⋊C8—41no—
162C2×C11⋊C8—41no—
163#2280—111no—
164#1779—111no—
165C22⋊#95—111no—
166#1294—111no—
167#1294—111no—
168#1294—111no—
169#1294D1111yescharacteristic, complemented
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11C2×C22⋊C411yescharacteristic
175C23×C11#12311yescharacteristic
176C23×C11#12311yescharacteristic
177C23×C11#13511yescharacteristic
178C23×C11#13511yescharacteristic
179C23×C11AGL(1,ℤ/8)11yescharacteristic
180C23×C11#13711yescharacteristic
181C22×D11—24no—
182C22×D11—24no—
183C22×D11—21no—
184C22×D11—21no—
185C22×D11—21no—
186C22×D11—21no—
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—42no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11#9912yes—
210C22×D11#10412yes—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—81no—
229C2×C4×C11—81no—
230C2×C4×C11—81no—
231C2×C4×C11—81no—
232C2×C4×C11#11711yescharacteristic
233C2×C4×C11#11711yescharacteristic
234C2×C4×C11#12311yescharacteristic
235C2×C4×C11#12311yescharacteristic
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—81no—
253C2×Dic11—81no—
254C2×Dic11—81no—
255C2×Dic11—81no—
256C2×Dic11#9912yes—
257C4×D11—24no—
258C4×D11—24no—
259C4×D11—42no—
260C4×D11—42no—
261C4×D11—42no—
262C4×D11—42no—
263C4×D11—42no—
264C4×D11—42no—
265C8×C11—81no—
266C11⋊C8—81no—
267C24×C4—111no—
268C2×#117—111no—
269C2×#117—111no—
270C22×C22⋊C4—221no—
271C2×C22⋊C8—111no—
272C2×C22⋊C8—221no—
273C2×C22⋊C8—221no—
274C2×C22⋊C8C2×D1111yescharacteristic
275#381—221no—
276#380—111no—
277#380—111no—
278#380—111no—
279#380C2×D1111yescharacteristic
280#379—221no—
281C4×C22⋊C4—221no—
282C4×C22⋊C4—221no—
283C2×#95—111no—
284C2×#95—221no—
285C2×#95C2×D1111yescharacteristic
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11#38111yescharacteristic
299C22×C11C2×#9911yescharacteristic
300C22×C11C2×#9911yescharacteristic
301C22×C11#41611yescharacteristic
302C22×C11#41711yescharacteristic
303C22×C11C2×#10411yescharacteristic
304C22×C11#42111yescharacteristic
305C22×C11#48211yescharacteristic
306C22×C11#48211yescharacteristic
307C22×C11#48511yescharacteristic
308C22×C11#48511yescharacteristic
309C2×D11—22no—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—22no—
313C2×D11—22no—
314C2×D11—22no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—41no—
320C2×D11—41no—
321C2×D11—41no—
322C2×D11—41no—
323C2×D11—41no—
324C2×D11—41no—
325C2×D11—41no—
326C2×D11—41no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—82no—
332C4×C11—81no—
333C4×C11—81no—
334Dic11—22no—
335Dic11—41no—
336Dic11—82no—
337Dic11—81no—
338Dic11—81no—
339C25—111no—
340C23×C4—21no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—221no—
347C23×C4—221no—
348C23×C4—221no—
349C23×C4—221no—
350C23×C4—221no—
351C23×C4—442no—
352C23×C4—442no—
353C23×C4C22×D1111yescharacteristic
354C22×C8—21no—
355C22×C8—221no—
356#117—442no—
357#117—442no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4C4×D1111yescharacteristic
361C2×C4⋊C4C4×D1111yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—442no—
370C2×C22⋊C4—442no—
371C2×C42—221no—
372C2×C42—221no—
373C22⋊C8—21no—
374C22⋊C8—21no—
375C22⋊C8—221no—
376C22⋊C8—221no—
377C22⋊C8—442no—
378C22⋊C8—442no—
379#95—21no—
380#95—21no—
381#95—21no—
382#95—221no—
383#95—221no—
384#95—221no—
385#95—221no—
386#95—221no—
387#95—442no—
388C2×C11—21no—
389C2×C11—21no—
390C2×C11—21no—
391C2×C11—21no—
392C2×C11#150111yescharacteristic
393C2×C11#150411yescharacteristic
394C2×C11#151311yescharacteristic
395C2×C11#151611yescharacteristic
396C2×C11#181911yescharacteristic
397C2×C11#182511yescharacteristic
398C2×C11#182611yescharacteristic
399D11—42no—
400D11—42no—
401C24—111no—
402C24—111no—
403C24—222no—
404C24—222no—
405C24—221no—
406C24—221no—
407C24—221no—
408C24—221no—
409C24—221no—
410C24—221no—
411C24—441no—
412C24—441no—
413C24D4×D1111yescharacteristic
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—222no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—441no—
449C22×C4—444no—
450C22×C4—444no—
451C22×C4—444no—
452C22×C4—444no—
453C22×C4—441no—
454C22×C4—441no—
455C22×C4—441no—
456C22×C4—441no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4C2×C4×D1111yescharacteristic
461C22×C4#433911yescharacteristic
462C22×C4#433911yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4#434111yescharacteristic
465C22×C4#434311yescharacteristic
466C2×C8—41no—
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—441no—
470C2×C8—441no—
471C2×C8—441no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—441no—
475C4⋊C4—441no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C22⋊C4—448no—
481C22⋊C4—442no—
482C22⋊C4—442no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C42—442no—
486C42—442no—
487C11#871511yescharacteristic, complemented, Sylow
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—112no—
493C23—112no—
494C23—224no—
495C23—224no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23—221no—
507C23—221no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—441no—
519C23—441no—
520C23—441no—
521C23—441no—
522C23C22⋊C4×D1111yescharacteristic
523C23#6693611yescharacteristic
524C23#6694711yescharacteristic
525C23#6696411yescharacteristic
526C23#6696811yescharacteristic
527C23#6696911yescharacteristic
528C23#6697211yescharacteristic
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—112no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—881no—
576C2×C4—881no—
577C2×C4—881no—
578C2×C4—881no—
579C2×C4#6692511yescharacteristic
580C2×C4#6693611yescharacteristic
581C2×C4#6694511yescharacteristic
582C2×C4#6694711yescharacteristic
583C8—81no—
584C8—881no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—222no—
598C22—222no—
599C22—222no—
600C22—222no—
601C22—222no—
602C22—222no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22—444no—
607C22—441no—
608C22—441no—
609C22—441no—
610C22—441no—
611C22—441no—
612C22—441no—
613C22—441no—
614C22—441no—
615C22#1062227711yescharacteristic
616C22D11×#9911yescharacteristic
617C22D11×#9911yescharacteristic
618C22#1062238411yescharacteristic
619C22#1062239211yescharacteristic
620C22#1062241711yescharacteristic
621C22#1062242711yescharacteristic
622C22D11×#10411yescharacteristic
623C22#1062243411yescharacteristic
624C22#1062248011yescharacteristic
625C22#1062249811yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—82no—
631C4—81no—
632C4—81no—
633C4—222no—
634C4—441no—
635C4—882no—
636C4—881no—
637C4—881no—
638C2—21no—
639C2—21no—
640C2—21no—
641C2—21no—
642C2—442no—
643C2—442no—
644C2#1306710611yescharacteristic
645C2#1306711711yescharacteristic
646C2#1306715611yescharacteristic
647C2#1306717111yescharacteristic
648C2#1306868911yescharacteristic
649C2#1306871011yescharacteristic
650C2#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#8715
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×#66945C4semidirect
11. C2×#66945C4semidirect
21. #10622600C4semidirect
22. #10622600C4semidirect
169. #1294D11semidirect
487. C11#8715semidirect

Maximal subgroups

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

subgroupindex
#130709982
#130685252
(C2×D11)⋊#952
#130664962
#130664952
#130664942
C11×#12942
#871511