Finite Group Databasebeta

← #14786422

Subgroups — #14786422

Order 2816.

1520 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×#10622584C211yesmaximal, characteristic, complemented
3C2×#10622580C211yesmaximal, characteristic, complemented
4#13069819C212yesmaximal, complemented
5#13069805C212yesmaximal, complemented
6#13068933C211yesmaximal, characteristic, complemented
7#13068923C211yesmaximal, characteristic, complemented
8#13068813C212yesmaximal, complemented
9#13068554C212yesmaximal, complemented
10#13068526C211yesmaximal, characteristic, complemented
11C2×C11×#380C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4—21no—
17C2×#67006—21no—
18#10623322—24no—
19#10623322—24no—
20C2×#66983C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66982—21no—
23C2×C4×C22⋊D11—21no—
24C2×C4×C22⋊D11—21no—
25C2×#66979C2211yescharacteristic
26C2×#66977C2211yescharacteristic
27C2×#66977C2211yescharacteristic
28C11×#380—21no—
29C11×#380—21no—
30C11×#380C2212yes—
31C11×#380C2212yes—
32C2×C11×#95—21no—
33C2×C22⋊(C11⋊C8)C2212yes—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622584—24no—
38C2×#66874C2212yescomplemented
39C2×#66874C2212yescomplemented
40#10622580—24no—
41C2×#66873C2212yescomplemented
42C2×#66873C2212yescomplemented
43C2×#66872C2212yescomplemented
44C2×#66871C2212yescomplemented
45#10622167C2212yescomplemented
46#10622167C2212yescomplemented
47C25×C11D411yescharacteristic
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—24no—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C23×C4×C11—42no—
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C2×#4339—22no—
64C2×#4339—24no—
65C2×#4339—22no—
66C2×#4339—42no—
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×Dic22C2311yescharacteristic
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—42no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—44no—
80#67006—28no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#66983—22no—
85#66983—22no—
86#66983—22no—
87#66983D414yes—
88#66982—28no—
89C4×C22⋊D11—28no—
90C4×C22⋊D11—28no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93#66979—22no—
94#66979—22no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97#66977—22no—
98#66977—22no—
99#66977—22no—
100#66977D414yes—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C22×C11⋊C8C2312yes—
105C22×C11⋊C8C2312yes—
106C11×#95—22no—
107C11×#95—22no—
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—22no—
110C22⋊(C11⋊C8)—24no—
111C22⋊(C11⋊C8)—42no—
112#66874—24no—
113#66874—42no—
114#66873—24no—
115#66873—42no—
116#66872—24no—
117#66871—24no—
118#24004—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—41no—
125C24×C11—41no—
126C24×C11C2×D411yescharacteristic
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—48no—
151C22×C4×C11—48no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D412yes—
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4114yes—
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—24no—
166C2×C22⋊D11—24no—
167C2×C22⋊D11—24no—
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C2×C22⋊D11—42no—
172C2×C22⋊D11—42no—
173C2×C22⋊D11—42no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177#4339—48no—
178#4339—48no—
179C2×D44—21no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44C2×D412yes—
183C2×C4×D11—24no—
184C2×C4×D11—42no—
185C2×C4×D11—42no—
186C2×Dic22—21no—
187C2×Dic22—22no—
188C2×Dic22—22no—
189C2×Dic22C2×D412yes—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4—42no—
196C11×C22⋊C4—44no—
197C11×C22⋊C4—44no—
198C22⋊Dic11—24no—
199C22⋊Dic11—24no—
200C22⋊Dic11—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2×D412yes—
206C4⋊Dic11C2×D412yes—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209C4×Dic11—24no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×#525—111no—
217C2×#483—111no—
218C2×#480—111no—
219C2×#380D1111yescharacteristic, complemented
220#2036—112no—
221#2034—112no—
222#1874—111no—
223#1872—111no—
224#1854—112no—
225#1788—112no—
226#1779—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—28no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—44no—
245C23×C11—44no—
246C23×C11—44no—
247C23×C11—44no—
248C23×C11—44no—
249C23×C11—44no—
250C23×C11#12012yes—
251C23×C11#12312yes—
252C23×C11#13512yes—
253C23×C11AGL(1,ℤ/8)12yes—
254C23×C11#13712yes—
255C23×C11C22×D411yescharacteristic
256C22×D11—22no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—44no—
275C2×C4×C11—44no—
276C2×C4×C11—44no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—42no—
285C2×C4×C11—84no—
286C2×C4×C11—84no—
287C2×C4×C11#12012yes—
288C2×C4×C11#12312yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C2×#4112yes—
292C2×C4×C11H(5,𝔽2)12yes—
293C22⋊D11—48no—
294C22⋊D11—48no—
295C22⋊D11—48no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305D44—24no—
306D44—42no—
307C4×D11—48no—
308Dic22—24no—
309Dic22—42no—
310C11⋊C8—42no—
311C11⋊C8—42no—
312C22×#41—111no—
313C24×C4C2×D1111yescharacteristic
314#525—224no—
315#525—224no—
316C2×#123—221no—
317C2×C22⋊Q8—111no—
318C2×C22⋊Q8—111no—
319C2×#121—111no—
320C2×#121—111no—
321C2×#120—221no—
322C2×C4×D4—221no—
323C2×C4×D4—221no—
324C2×#117—111no—
325C22×C4⋊C4C2×D1111yescharacteristic
326C22×C4⋊C4C2×D1111yescharacteristic
327C22×C22⋊C4—21no—
328#483—224no—
329#480—224no—
330C2×#107—112no—
331C2×#106—112no—
332C2×#103—112no—
333C2×#103—112no—
334C2×#102—112no—
335C2×#102—112no—
336C2×C22⋊C8—111no—
337C2×C22⋊C8—111no—
338C2×C22⋊C8—112no—
339C2×C22⋊C8—112no—
340#380—21no—
341#380—21no—
342#380C2×D1112yes—
343#380C2×D1112yes—
344C2×#95—21no—
345#340—112no—
346#340—112no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—416no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11#44914yes—
369C22×C11C2×#12011yescharacteristic
370C22×C11C2×#12311yescharacteristic
371C22×C11#53411yescharacteristic
372C22×C11C2×#13511yescharacteristic
373C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C11C2×#13711yescharacteristic
375C22×C11#57511yescharacteristic
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C4×C11—22no—
384C4×C11—22no—
385C4×C11—41no—
386C4×C11—82no—
387C4×C11—82no—
388C4×C11#54612yes—
389C4×C11#54612yes—
390Dic11—42no—
391Dic11—42no—
392Dic11—42no—
393C25C22⋊D1111yescharacteristic
394C2×#41—222no—
395C2×#41—222no—
396C2×#41—224no—
397C2×#41—442no—
398C22×Q8—111no—
399C22×D4—111no—
400C22×D4—221no—
401C22×D4—221no—
402C22×D4—221no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—42no—
409C23×C4—221no—
410C23×C4C22⋊D1111yescharacteristic
411C23×C4C22⋊D1111yescharacteristic
412C23×C4C22⋊D1111yescharacteristic
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1111yescharacteristic
415C23×C4C22×D1111yescharacteristic
416C22×C8—112no—
417C22×C8—112no—
418#123—228no—
419C22⋊Q8—114no—
420C22⋊Q8—222no—
421C22⋊Q8—222no—
422C22⋊Q8—222no—
423#121—114no—
424#121—222no—
425#121—222no—
426#121—222no—
427#120—228no—
428C4×D4—228no—
429C4×D4—228no—
430#117—222no—
431#117—222no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4C22×D1112yes—
442C2×C4⋊C4C22×D1112yes—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C42—221no—
452#107—224no—
453#106—224no—
454#103—224no—
455#103—442no—
456#102—224no—
457#102—442no—
458C22⋊C8—224no—
459C22⋊C8—222no—
460C22⋊C8—222no—
461C22⋊C8—442no—
462#95—22no—
463#95—22no—
464C2×C11—24no—
465C2×C11—42no—
466C2×C11—42no—
467C2×C11#240511yescharacteristic
468C2×C11C2×#44911yescharacteristic
469C2×C11#300711yescharacteristic
470C2×C11#309111yescharacteristic
471C2×C11#309211yescharacteristic
472C2×C11#319011yescharacteristic
473C2×C11#319411yescharacteristic
474D11—82no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—41no—
481C24—41no—
482C24—221no—
483C24C2×C22⋊D1111yescharacteristic
484C24C2×C22⋊D1111yescharacteristic
485C24C2×C22⋊D1111yescharacteristic
486#41—448no—
487#41—448no—
488C2×Q8—112no—
489C2×Q8—221no—
490C2×Q8—222no—
491C2×Q8—222no—
492C2×D4—112no—
493C2×D4—224no—
494C2×D4—224no—
495C2×D4—224no—
496C2×D4—222no—
497C2×D4—221no—
498C2×D4—222no—
499C2×D4—442no—
500C2×D4—442no—
501C2×D4—442no—
502C2×D4—442no—
503C2×D4—442no—
504C2×D4—442no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—224no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4—221no—
537C22×C4—442no—
538C22×C4—442no—
539C22×C4#433914yes—
540C22×C4D4×D1112yes—
541C22×C4D4×D1112yes—
542C22×C4C2×C22⋊D1111yescharacteristic
543C22×C4C2×C22⋊D1111yescharacteristic
544C22×C4C2×C22⋊D1111yescharacteristic
545C22×C4C23×D1111yescharacteristic
546C2×C8—222no—
547C2×C8—222no—
548C2×C8—222no—
549C2×C8—222no—
550C2×C8—222no—
551C2×C8—222no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—112no—
559C4⋊C4—112no—
560C4⋊C4—224no—
561C4⋊C4—224no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C22⋊C4—44no—
565C22⋊C4—44no—
566C22⋊C4—224no—
567C22⋊C4—224no—
568C22⋊C4—224no—
569C22⋊C4—224no—
570C22⋊C4—224no—
571C42—224no—
572C11#2400411yescharacteristic, complemented, Sylow
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—28no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—44no—
591C23—44no—
592C23—44no—
593C23—44no—
594C23—44no—
595C23—44no—
596C23—222no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23—441no—
602C23—441no—
603C23#6698212yes—
604C23#6698512yes—
605C23#6699012yes—
606C23#6699512yes—
607C23#6700312yes—
608C23C22×C22⋊D1111yescharacteristic
609Q8—224no—
610Q8—442no—
611D4—224no—
612D4—448no—
613D4—448no—
614D4—448no—
615D4—442no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—44no—
628C2×C4—44no—
629C2×C4—44no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—84no—
639C2×C4—84no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—222no—
643C2×C4—448no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4#6698212yes—
651C2×C4#6699012yes—
652C2×C4C2×#433912yes—
653C2×C4C2×D4×D1111yescharacteristic
654C2×C4C2×D4×D1111yescharacteristic
655C2×C4#6703712yes—
656C8—442no—
657C8—442no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—416no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—442no—
680C22—442no—
681C22—442no—
682C22—881no—
683C22—881no—
684C22—881no—
685C22—881no—
686C22#1062265014yes—
687C22C2×#6698211yescharacteristic
688C22C2×#6698511yescharacteristic
689C22C2×#6699011yescharacteristic
690C22#1062333511yescharacteristic
691C22C2×#6699511yescharacteristic
692C22C2×#6700311yescharacteristic
693C22#1062335311yescharacteristic
694C4—22no—
695C4—22no—
696C4—41no—
697C4—82no—
698C4—82no—
699C4—442no—
700C4—442no—
701C4—442no—
702C4#1062302112yes—
703C4#1062302112yes—
704C2—24no—
705C2—42no—
706C2—42no—
707C2—882no—
708C2#1307194311yescharacteristic
709C2C2×#1062265011yescharacteristic
710C2#1307787411yescharacteristic
711C2#1307852911yescharacteristic
712C2#1307853911yescharacteristic
713C2#1307939711yescharacteristic
714C2#1307943011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#380C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
hypercenterC2×#380D11
hypocenterC11#24004
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#10622584C2semidirect
3. C2×#10622580C2semidirect
4. #13069819C2semidirect
5. #13069805C2semidirect
6. #13068933C2semidirect
7. #13068923C2semidirect
8. #13068813C2semidirect
9. #13068554C2semidirect
10. #13068526C2semidirect
11. C2×C11×#380C2semidirect
38. C2×#66874C22semidirect
39. C2×#66874C22semidirect
41. C2×#66873C22semidirect
42. C2×#66873C22semidirect
43. C2×#66872C22semidirect
44. C2×#66871C22semidirect
45. #10622167C22semidirect
46. #10622167C22semidirect
219. C2×#380D11semidirect
572. C11#24004semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×#106225842
C2×#106225802
#130698192
#130698052
#130689332
#130689232
#130688132
#130685542
#130685262
C2×C11×#3802
#2400411