Finite Group Databasebeta

← #14659017

Subgroups — #14659017

Order 2816.

1414 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622739C211yesmaximal, characteristic
3#13070995C211yesmaximal, characteristic
4C2×#10622193C211yesmaximal, characteristic, complemented
5C2×#10622161C211yesmaximal, characteristic, complemented
6C2×#10622170C211yesmaximal, characteristic, complemented
7C2×C11×#339C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C22×C11×M16C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C42×C11C2211yescharacteristic
12C22×(C2×D11)⋊C4—21no—
13C2×#66979C2211yescharacteristic
14C22×Dic11⋊C4—21no—
15C22×C4×Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×#66925—22no—
18C2×#66925—22no—
19C2×#66925—22no—
20C2×#66925—22no—
21C2×#66925—22no—
22C2×#66925C414yescomplemented
23#10622739—22no—
24#10622739C414yescomplemented
25C2×(C2×D11)⋊C8—22no—
26#10622600C414yescomplemented
27#10622568—21no—
28#10622556—21no—
29C4×(C2×D11)⋊C4—22no—
30C11×#339—22no—
31#10622193—22no—
32#10622170—22no—
33#10622161—22no—
34C24×D11D411yescharacteristic
35C23×C4×C11—21no—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11—21no—
38C23×Dic11D411yescharacteristic
39C22×C4×D11—21no—
40C22×C4×D11—21no—
41C22×C4×D11—21no—
42C22×C4×D11—21no—
43C22×C4×D11—21no—
44C22×C4×D11—21no—
45C22×C4×D11—21no—
46C22×C4×D11—21no—
47C22×C4×D11C2×C412yes—
48C22×C4×D11C2×C412yes—
49C22×C4×D11C2×C412yes—
50C22×C4×D11D412yes—
51C22×C4×D11D412yes—
52C22×C4×D11Q812yes—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16C2×C412yes—
59C22×C8×C11—21no—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
64C2×C11×C4⋊C4C2×C412yes—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11—21no—
70C2×C42×C11C2×C412yes—
71C2×C42×C11D412yes—
72C2×C42×C11D412yes—
73C2×C22⋊Dic11—21no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78#66979—21no—
79#66979—21no—
80#66979—21no—
81#66979—21no—
82C2×C4⋊Dic11C2×C412yes—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—24no—
85C2×Dic11⋊C4—24no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2×C412yes—
91C2×C4×Dic11D412yes—
92C2×C4×Dic11D412yes—
93C2×#4318—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318—21no—
97C2×#4318—21no—
98C2×#4318C2×C412yes—
99C22×C11⋊C8—21no—
100#66925—28no—
101#66925—28no—
102#66925—28no—
103#66925—28no—
104C11⋊#95—24no—
105(C2×D11)⋊C8—28no—
106#10720—111nomaximal, Sylow
107C24×C11C2×D411yescharacteristic
108C23×D11—21no—
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—44no—
113C23×D11C22⋊C412yes—
114C23×D11C22⋊C412yes—
115C23×D11C4⋊C412yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—44no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×Q811yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C22×C4×C11#4111yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—44no—
144C22×Dic11C22⋊C412yes—
145C22×Dic11C22⋊C412yes—
146C22×Dic11C4⋊C412yes—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11C4214yes—
172C2×C4×D11C22⋊C414yes—
173C2×C4×D11C4⋊C414yes—
174C2×C4×D11C4⋊C414yes—
175C11×M16—22no—
176C11×M16—22no—
177C11×M16—41no—
178C11×M16—41no—
179C2×C8×C11—22no—
180C2×C8×C11—41no—
181C2×C8×C11—41no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—22no—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—41no—
190C42×C11—41no—
191C42×C11C22⋊C414yescomplemented
192C22⋊Dic11—41no—
193C22⋊Dic11—41no—
194(C2×D11)⋊C4—216no—
195(C2×D11)⋊C4—48no—
196C4⋊Dic11—22no—
197C4⋊Dic11—22no—
198Dic11⋊C4—216no—
199C4×Dic11—22no—
200C4×Dic11—22no—
201C4×Dic11—22no—
202C4×Dic11—41no—
203C4×Dic11—41no—
204C4×Dic11C22⋊C414yescomplemented
205#4318—22no—
206#4318—22no—
207#4318—41no—
208#4318—41no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—41no—
211C2×C11⋊C8—41no—
212C22×#117—111no—
213C2×#407—111no—
214#2280—111no—
215C2×#339—111no—
216C2×#339—111no—
217C2×#339—111no—
218C2×#339D1111yescharacteristic, complemented
219C23×C11—24no—
220C23×C11C2×C22⋊C411yescharacteristic
221C23×C11C2×C22⋊C411yescharacteristic
222C23×C11C2×C4⋊C411yescharacteristic
223C23×C11#12011yescharacteristic
224C23×C11#12011yescharacteristic
225C23×C11#12311yescharacteristic
226C23×C11#12311yescharacteristic
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—44no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11#9514yes—
242C2×C4×C11—24no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11—44no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11C2×C4211yescharacteristic
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11C2×C22⋊C411yescharacteristic
252C2×C4×C11C2×C4⋊C411yescharacteristic
253C2×C4×C11C2×C4⋊C411yescharacteristic
254C2×C4×C11#11711yescharacteristic
255C2×C4×C11#11711yescharacteristic
256C2×C4×C11C4×D411yescharacteristic
257C2×C4×C11C4×D411yescharacteristic
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11#12011yescharacteristic
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12111yescharacteristic
267C2×C4×C11#12111yescharacteristic
268C2×C4×C11#12111yescharacteristic
269C2×C4×C11#12111yescharacteristic
270C2×C4×C11C22⋊Q811yescharacteristic
271C2×C4×C11C22⋊Q811yescharacteristic
272C2×C4×C11C22⋊Q811yescharacteristic
273C2×C4×C11C22⋊Q811yescharacteristic
274C2×C4×C11#12311yescharacteristic
275C2×C4×C11#12311yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—44no—
284C2×Dic11—44no—
285C2×Dic11—44no—
286C2×Dic11—42no—
287C2×Dic11—44no—
288C2×Dic11#9514yes—
289C4×D11—24no—
290C4×D11—24no—
291C4×D11—24no—
292C4×D11—24no—
293C4×D11—24no—
294C4×D11—24no—
295C4×D11—24no—
296C4×D11—24no—
297C8×C11—42no—
298C11⋊C8—42no—
299C24×C4—111no—
300C22×M16—111no—
301C22×M16C2×D1111yescharacteristic
302C2×#117—114no—
303C2×#117—111no—
304C2×#117—222no—
305C2×#117—222no—
306C2×#117—222no—
307C2×#117—222no—
308C2×#117—222no—
309C2×#117C2×D1111yescharacteristic
310C22×C4⋊C4—221no—
311C22×C22⋊C4—221no—
312C22×C42—111no—
313C22×C42C2×D1111yescharacteristic
314#407—114no—
315#407—222no—
316C2×C22⋊C8—222no—
317#381—221no—
318#380—114no—
319#379—221no—
320C4×C22⋊C4—222no—
321#339—22no—
322#339—222no—
323#339—222no—
324#339—222no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11C2×#9511yescharacteristic
332C22×C11#37911yescharacteristic
333C22×C11#38111yescharacteristic
334C22×C11#38511yescharacteristic
335C22×C11#38511yescharacteristic
336C22×C11#38611yescharacteristic
337C22×C11#38611yescharacteristic
338C22×C11#42114yes—
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C2×D11—44no—
348C4×C11—44no—
349C4×C11—82no—
350C4×C11C4×C22⋊C411yescharacteristic
351C4×C11C4×C22⋊C411yescharacteristic
352C4×C11#38011yescharacteristic
353C4×C11#38011yescharacteristic
354C4×C11#38511yescharacteristic
355C4×C11#38511yescharacteristic
356C4×C11#38611yescharacteristic
357C4×C11#38611yescharacteristic
358Dic11—24no—
359Dic11—44no—
360Dic11—82no—
361C25—111no—
362C23×C4—21no—
363C23×C4—111no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—112no—
367C23×C4—112no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—221no—
371C23×C4—221no—
372C23×C4—221no—
373C23×C4—221no—
374C23×C4—221no—
375C23×C4—221no—
376C23×C4—221no—
377C23×C4—221no—
378C23×C4—221no—
379C23×C4C22×D1111yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—112no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—221no—
390C2×M16—221no—
391C2×M16C4×D1112yes—
392C22×C8—21no—
393C22×C8—221no—
394#117—21no—
395#117—21no—
396#117—21no—
397#117—21no—
398#117—228no—
399#117—228no—
400#117—228no—
401#117—228no—
402#117—221no—
403#117—221no—
404#117—221no—
405#117—221no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4—224no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4C4×D1112yes—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—224no—
413C2×C22⋊C4—224no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—224no—
416C2×C22⋊C4—221no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—112no—
422C2×C42—112no—
423C2×C42—112no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42C4×D1112yes—
429C2×C42D4412yes—
430C2×C42C22⋊D1112yes—
431C22⋊C8—228no—
432#95—224no—
433C2×C11—21no—
434C2×C11—21no—
435C2×C11—21no—
436C2×C11—21no—
437C2×C11C22⋊#9511yescharacteristic
438C2×C11#173312yes—
439C2×C11#189712yes—
440C2×C11#189712yes—
441D11—44no—
442C24—112no—
443C24—112no—
444C24—112no—
445C24—221no—
446C24—221no—
447C24—221no—
448C24—221no—
449C24—444no—
450C24D4×D1111yescharacteristic
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—44no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—114no—
461C22×C4—114no—
462C22×C4—114no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
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—222no—
494C22×C4—222no—
495C22×C4—444no—
496C22×C4C2×C4×D1111yescharacteristic
497C22×C4C2×C4×D1111yescharacteristic
498C22×C4C2×C4×D1111yescharacteristic
499C22×C4C2×D4411yescharacteristic
500C22×C4#433911yescharacteristic
501C22×C4#433911yescharacteristic
502C22×C4D4×D1111yescharacteristic
503C22×C4D4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4D4×D1111yescharacteristic
506C22×C4#434111yescharacteristic
507C22×C4Q8×D1111yescharacteristic
508C22×C4#434311yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510M16—22no—
511M16—22no—
512M16—41no—
513M16—41no—
514M16—222no—
515M16—222no—
516M16—441no—
517M16—441no—
518C2×C8—22no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—222no—
522C2×C8—441no—
523C2×C8—441no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—2216no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—2216no—
532C22⋊C4—448no—
533C22⋊C4—441no—
534C22⋊C4—441no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—41no—
539C42—41no—
540C42—114no—
541C42—222no—
542C42—222no—
543C42—222no—
544C42—441no—
545C42—441no—
546C42(C2×D11)⋊C414yescomplemented
547C11#1072011yescharacteristic, complemented, Sylow
548C23—24no—
549C23—114no—
550C23—222no—
551C23—222no—
552C23—222no—
553C23—222no—
554C23—222no—
555C23—222no—
556C23—224no—
557C23—224no—
558C23—444no—
559C23—444no—
560C23—444no—
561C23—444no—
562C23—444no—
563C23—444no—
564C23C22⋊C4×D1111yescharacteristic
565C23C22⋊C4×D1111yescharacteristic
566C23#6693511yescharacteristic
567C23#6693611yescharacteristic
568C23C4⋊C4×D1111yescharacteristic
569C23#6694711yescharacteristic
570C23#6699011yescharacteristic
571C2×C4—24no—
572C2×C4—44no—
573C2×C4—44no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—44no—
577C2×C4—114no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—444no—
594C2×C4—444no—
595C2×C4—444no—
596C2×C4—442no—
597C2×C4—444no—
598C2×C4C42×D1111yescharacteristic
599C2×C4#6692511yescharacteristic
600C2×C4C4×D4411yescharacteristic
601C2×C4C4×D4411yescharacteristic
602C2×C4C22⋊C4×D1111yescharacteristic
603C2×C4C22⋊C4×D1111yescharacteristic
604C2×C4(C22⋊D11)⋊C411yescharacteristic
605C2×C4(C22⋊D11)⋊C411yescharacteristic
606C2×C4#6693511yescharacteristic
607C2×C4#6693611yescharacteristic
608C2×C4#6693711yescharacteristic
609C2×C4#6693711yescharacteristic
610C2×C4C4⋊C4×D1111yescharacteristic
611C2×C4C4⋊C4×D1111yescharacteristic
612C2×C4#6694511yescharacteristic
613C2×C4#6694611yescharacteristic
614C2×C4#6694611yescharacteristic
615C2×C4#6694711yescharacteristic
616C2×C4#6694811yescharacteristic
617C2×C4#6694911yescharacteristic
618C2×C4#6694911yescharacteristic
619C2×C4#6695011yescharacteristic
620C2×C4C2×(C2×D11)⋊C411yescharacteristic
621C2×C4C4×C22⋊D1111yescharacteristic
622C2×C4C4×C22⋊D1111yescharacteristic
623C2×C4#6699011yescharacteristic
624C2×C4#6699111yescharacteristic
625C2×C4#6699911yescharacteristic
626C8—42no—
627C8—442no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—224no—
635C22—224no—
636C22—224no—
637C22—444no—
638C22—444no—
639C22—444no—
640C22—444no—
641C22—444no—
642C22—444no—
643C22D11×#9511yescharacteristic
644C22#1062227711yescharacteristic
645C22#1062227811yescharacteristic
646C22#1062228111yescharacteristic
647C22#1062243414yes—
648C22#1062256811yescharacteristic
649C22#1062256911yescharacteristic
650C22#1062260211yescharacteristic
651C4—44no—
652C4—82no—
653C4—224no—
654C4—444no—
655C4—882no—
656C4#1062227811yescharacteristic
657C4#1062227911yescharacteristic
658C4#1062228011yescharacteristic
659C4#1062228111yescharacteristic
660C4C4×(C2×D11)⋊C411yescharacteristic
661C4#1062256911yescharacteristic
662C4#1062260011yescharacteristic
663C4#1062260211yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—444no—
669C2(C2×D11)⋊#9511yescharacteristic
670C2#1306832412yes—
671C2#1306906112yes—
672C2#1306906312yes—
subgroupG/H
centerC22×C4D4×D11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC2×C11×#339C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenterC2×#339D11
hypocenterC11#10720
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#10622193C2semidirect
5. C2×#10622161C2semidirect
6. C2×#10622170C2semidirect
7. C2×C11×#339C2semidirect
22. C2×#66925C4semidirect
24. #10622739C4semidirect
26. #10622600C4semidirect
191. C42×C11C22⋊C4semidirect
204. C4×Dic11C22⋊C4semidirect
218. C2×#339D11semidirect
546. C42(C2×D11)⋊C4semidirect
547. C11#10720semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106227392
#130709952
C2×#106221932
C2×#106221612
C2×#106221702
C2×C11×#3392
#1072011