Finite Group Databasebeta

← #14762862

Subgroups — #14762862

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic, complemented
4#13069053C212yesmaximal, complemented
5#13069046C212yesmaximal, complemented
6#13068933C211yesmaximal, characteristic, complemented
7#13068931C211yesmaximal, characteristic, complemented
8#13068924C211yesmaximal, characteristic, complemented
9#13068709C212yesmaximal, complemented
10#13068555C212yesmaximal, complemented
11C11×#1872C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C2×C11×C22⋊Q8C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×(C2×D11)⋊C4—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4313C2212yes—
21#10623158—24no—
22#10623158C418yescomplemented
23C2×#66948C2211yescharacteristic
24C2×#66947—21no—
25C2×#66946—21no—
26C2×#66945C2211yescharacteristic
27C2×#66935—21no—
28C2×(C22⋊D11)⋊C4—21no—
29C2×C11×#103C2212yescomplemented
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×#66899C2212yescomplemented
32C2×C11⋊#95—21no—
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×#66885C2212yescomplemented
35C2×(C2×D11)⋊C8C2212yes—
36#10622600—21no—
37#10622600—21no—
38#10622600C2212yes—
39#10622600C2212yes—
40C2×#66873C2212yescomplemented
41#10622339—24no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C23×Dic11—21no—
52C23×Dic11D411yescharacteristic
53C2×#4343—22no—
54C2×#4343—42no—
55C2×#4343—42no—
56C2×#4343C2×C414yescomplemented
57C22×D44—21no—
58C22×D44—21no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—42no—
62C22×C4×D11—42no—
63C22×C4×D11C2×C414yes—
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11D414yes—
67C22×C4×D11C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C22×C8×C11C2312yes—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8C2×C414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—42no—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78#66999—22no—
79#66999C2×C414yescomplemented
80#66983—22no—
81#66983C2×C414yes—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—44no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—42no—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2312yes—
96C2×#4313—24no—
97C2×#4313—42no—
98C2×#4313—42no—
99#66948—22no—
100#66948C2×C414yescomplemented
101#66947—28no—
102#66946—28no—
103#66945—22no—
104#66945C2×C414yescomplemented
105#66935—28no—
106(C22⋊D11)⋊C4—28no—
107C11×#103—42no—
108C11×C22⋊C8—22no—
109#66899—42no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C22⋊(C11⋊C8)—22no—
113#66885—42no—
114(C2×D11)⋊C8—24no—
115#66873—42no—
116#21769—111nomaximal, Sylow
117C24×C11C2×D411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—21no—
121C23×D11—41no—
122C23×D11—41no—
123C23×D11—41no—
124C23×D11—41no—
125C23×D11C22⋊C414yes—
126C23×D11C2×D411yescharacteristic
127C23×D11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11C22×C412yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—41no—
150C22×Dic11—41no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11C22⋊C414yes—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157#4343—48no—
158#4343—48no—
159C2×D44—24no—
160C2×D44—24no—
161C2×D44—21no—
162C2×D44—22no—
163C2×D44—22no—
164C2×D44—42no—
165C2×D44—42no—
166C2×D44—42no—
167C2×D44—42no—
168C2×D44C22×C412yes—
169C2×C4×D11—24no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—41no—
175C2×C4×D11—41no—
176C2×C4×D11—41no—
177C2×C4×D11—41no—
178C2×C4×D11—48no—
179C2×C4×D11—48no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
182C2×C4×D11C22⋊C414yes—
183C2×C4×D11C22⋊C414yes—
184C2×C4×D11C22×C412yes—
185C2×C4×D11C22×C412yes—
186C2×C4×D11C2×D412yes—
187C2×C4×D11C2×D412yes—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—42no—
196C11×C4⋊C4C22×C412yes—
197C11×C22⋊C4—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—44no—
203(C2×D11)⋊C4—44no—
204C4⋊Dic11—21no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11—42no—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—24no—
210C4×Dic11—24no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214#4313—48no—
215C2×#525—111no—
216C2×#407—111no—
217C2×#380—111no—
218#1895—112no—
219#1894—112no—
220#1874—111no—
221#1874—111no—
222#1872—111no—
223#1872D1111yescharacteristic, complemented
224#1825—112no—
225#1788—112no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11C2×C22⋊C412yes—
231C23×C11AGL(1,ℤ/8)12yes—
232C23×C11#13712yes—
233C23×C11C22×D411yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—28no—
247C22×D11—22no—
248C22×D11—44no—
249C22×D11—44no—
250C22×D11—44no—
251C22×D11—44no—
252C22×D11—44no—
253C22×D11—44no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11C2×C22⋊C412yes—
261C22×D11C2×C22⋊C412yes—
262Q8×C11—24no—
263Q8×C11—42no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—84no—
278C2×C4×C11C2×C22⋊C412yes—
279C2×C4×C11C23×C411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11H(5,𝔽2)12yes—
282C2×C4×C11H(5,𝔽2)12yes—
283C22⋊D11—48no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—22no—
289C2×Dic11—44no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—84no—
296C2×Dic11C2×C22⋊C412yes—
297C2×Dic11C2×C22⋊C412yes—
298D44—24no—
299D44—48no—
300D44—48no—
301D44—42no—
302C4×D11—24no—
303C4×D11—24no—
304C4×D11—24no—
305C4×D11—24no—
306C4×D11—44no—
307C4×D11—44no—
308C4×D11—48no—
309C8×C11—42no—
310C11⋊C8—42no—
311C22×#41—111no—
312C24×C4—111no—
313C22×M16—112no—
314#525—118no—
315#525—224no—
316C2×#123—221no—
317C2×C22⋊Q8—111no—
318C2×C22⋊Q8C2×D1111yescharacteristic
319C2×#121—111no—
320C2×#121—111no—
321C2×#120—221no—
322C2×C4×D4—221no—
323C2×C4×D4—221no—
324C2×#117—111no—
325C22×C4⋊C4—111no—
326C22×C4⋊C4C2×D1111yescharacteristic
327C22×C22⋊C4—221no—
328C2×#103—112no—
329C2×#103C2×D1112yescomplemented
330C2×#102—112no—
331C2×#102—112no—
332#407—224no—
333C2×C22⋊C8—111no—
334C2×C22⋊C8—112no—
335C2×C22⋊C8C2×D1111yescharacteristic
336#380—112no—
337#380—112no—
338#380—221no—
339#380—221no—
340C2×#95—221no—
341#340—112no—
342#340—112no—
343#340—112no—
344#340C2×D1112yescomplemented
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11#41714yes—
352C22×C11C22×C22⋊C411yescharacteristic
353C22×C11#53411yescharacteristic
354C22×C11#53411yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C11C2×#13711yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57511yescharacteristic
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—416no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—42no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C4×C11—22no—
382C4×C11—42no—
383C4×C11—42no—
384C4×C11—82no—
385C4×C11#51812yes—
386C4×C11#53412yes—
387Dic11—22no—
388Dic11—22no—
389Dic11—42no—
390Dic11—82no—
391C25—111no—
392C2×#41—114no—
393C2×#41—222no—
394C2×#41—442no—
395C2×#41—442no—
396C22×Q8C22×D1111yescharacteristic
397C22×D4—111no—
398C22×D4—221no—
399C22×D4—221no—
400C22×D4—221no—
401C23×C4—21no—
402C23×C4—111no—
403C23×C4—111no—
404C23×C4—111no—
405C23×C4—114no—
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—114no—
409C23×C4—221no—
410C23×C4—221no—
411C23×C4—442no—
412C23×C4—442no—
413C23×C4C22×D1111yescharacteristic
414C2×M16—224no—
415C2×M16—442no—
416C2×M16—442no—
417C22×C8—112no—
418C22×C8C22×D1112yes—
419#123—228no—
420C22⋊Q8—22no—
421C22⋊Q8—114no—
422C22⋊Q8—222no—
423C22⋊Q8C4×D1114yes—
424#121—114no—
425#121—114no—
426#121—222no—
427#121—222no—
428#120—228no—
429C4×D4—228no—
430C4×D4—228no—
431#117—114no—
432#117—222no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—442no—
441C2×C4⋊C4C22×D1112yes—
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—222no—
450C2×C22⋊C4—444no—
451C2×C42—221no—
452#103—42no—
453#103—442no—
454#102—442no—
455#102—442no—
456C22⋊C8—22no—
457C22⋊C8—224no—
458C22⋊C8—222no—
459#95—222no—
460#95—222no—
461C2×C11—24no—
462C2×C11#230811yescharacteristic
463C2×C11C2×#41711yescharacteristic
464C2×C11#289611yescharacteristic
465C2×C11#319411yescharacteristic
466C2×C11#319411yescharacteristic
467C2×C11#319611yescharacteristic
468C2×C11#319611yescharacteristic
469D11—42no—
470D11—42no—
471D11—82no—
472C24—111no—
473C24—111no—
474C24—114no—
475C24—222no—
476C24—222no—
477C24—221no—
478C24—441no—
479C24—441no—
480C24—441no—
481C24—441no—
482C24D4×D1111yescharacteristic
483#41—448no—
484#41—448no—
485C2×Q8—21no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8C2×C4×D1112yes—
489C2×D4—112no—
490C2×D4—224no—
491C2×D4—224no—
492C2×D4—224no—
493C2×D4—221no—
494C2×D4—222no—
495C2×D4—222no—
496C2×D4—442no—
497C2×D4—442no—
498C2×D4—442no—
499C2×D4—442no—
500C2×D4—442no—
501C2×D4—442no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—114no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—112no—
517C22×C4—114no—
518C22×C4—114no—
519C22×C4—224no—
520C22×C4—222no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—221no—
525C22×C4—222no—
526C22×C4—448no—
527C22×C4—448no—
528C22×C4—441no—
529C22×C4—441no—
530C22×C4—441no—
531C22×C4—441no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4—441no—
535C22×C4—441no—
536C22×C4—442no—
537C22×C4—442no—
538C22×C4—442no—
539C22×C4C2×C4×D1112yes—
540C22×C4D4×D1111yescharacteristic
541C22×C4D4×D1112yes—
542C22×C4C23×D1111yescharacteristic
543M16—448no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—222no—
548C2×C8—222no—
549C2×C8—222no—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—42no—
555C4⋊C4—112no—
556C4⋊C4—224no—
557C4⋊C4—221no—
558C4⋊C4—222no—
559C4⋊C4—222no—
560C4⋊C4—442no—
561C4⋊C4C2×C4×D1112yes—
562C22⋊C4—24no—
563C22⋊C4—224no—
564C22⋊C4—224no—
565C22⋊C4—224no—
566C22⋊C4—224no—
567C22⋊C4—444no—
568C22⋊C4—444no—
569C42—224no—
570C11#2176911yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—112no—
576C23—112no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23—221no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—228no—
588C23—221no—
589C23—221no—
590C23—222no—
591C23—444no—
592C23—444no—
593C23—444no—
594C23—444no—
595C23—444no—
596C23—444no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23—441no—
602C23—441no—
603C23C22⋊C4×D1112yes—
604C23#6696712yes—
605C23#6697112yes—
606C23C2×D4×D1111yescharacteristic
607Q8—24no—
608Q8—42no—
609D4—224no—
610D4—448no—
611D4—448no—
612D4—448no—
613D4—442no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—84no—
628C2×C4—112no—
629C2×C4—112no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—224no—
635C2×C4—224no—
636C2×C4—224no—
637C2×C4—224no—
638C2×C4—222no—
639C2×C4—444no—
640C2×C4—444no—
641C2×C4—448no—
642C2×C4—444no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—884no—
649C2×C4C22⋊C4×D1112yes—
650C2×C4C22×C4×D1111yescharacteristic
651C2×C4C2×D4×D1111yescharacteristic
652C2×C4#6703712yes—
653C2×C4#6704212yes—
654C8—42no—
655C8—442no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—222no—
663C22—222no—
664C22—222no—
665C22—222no—
666C22—222no—
667C22—222no—
668C22—4416no—
669C22—441no—
670C22—441no—
671C22—441no—
672C22—441no—
673C22—441no—
674C22—441no—
675C22—441no—
676C22—441no—
677C22—442no—
678C22—442no—
679C22—442no—
680C22—881no—
681C22—881no—
682C22—881no—
683C22—881no—
684C22#1062241614yes—
685C22C2×C22⋊C4×D1111yescharacteristic
686C22#1062312011yescharacteristic
687C22#1062318411yescharacteristic
688C22C2×#6696711yescharacteristic
689C22C2×#6697111yescharacteristic
690C22#1062330411yescharacteristic
691C22#1062330811yescharacteristic
692C4—22no—
693C4—42no—
694C4—42no—
695C4—82no—
696C4—222no—
697C4—222no—
698C4—442no—
699C4—882no—
700C4#1062307612yes—
701C4#1062313612yes—
702C2—24no—
703C2—442no—
704C2—442no—
705C2—882no—
706C2#1307119011yescharacteristic
707C2C2×#1062241611yescharacteristic
708C2#1307713211yescharacteristic
709C2#1307943311yescharacteristic
710C2#1307943511yescharacteristic
711C2#1307944911yescharacteristic
712C2#1307945111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC2×#10623158C2
cosocleC22×C4×C11C24
hypercenter#1872D11
hypocenterC11#21769
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#10622339C2semidirect
3. C2×#10622600C2semidirect
4. #13069053C2semidirect
5. #13069046C2semidirect
6. #13068933C2semidirect
7. #13068931C2semidirect
8. #13068924C2semidirect
9. #13068709C2semidirect
10. #13068555C2semidirect
11. C11×#1872C2semidirect
22. #10623158C4semidirect
29. C2×C11×#103C22semidirect
31. C2×#66899C22semidirect
34. C2×#66885C22semidirect
40. C2×#66873C22semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
56. C2×#4343C2×C4semidirect
79. #66999C2×C4semidirect
100. #66948C2×C4semidirect
104. #66945C2×C4semidirect
223. #1872D11semidirect
329. C2×#103C2×D11semidirect
344. #340C2×D11semidirect
570. C11#21769semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106223392
C2×#106226002
#130690532
#130690462
#130689332
#130689312
#130689242
#130687092
#130685552
C11×#18722
#2176911