Finite Group Databasebeta

← #14762829

Subgroups — #14762829

Order 2816.

1538 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2C2×#10622339C211yesmaximal, characteristic
3C2×#10622600C211yesmaximal, characteristic
4#13069048C212yesmaximal, complemented
5#13069046C212yesmaximal, complemented
6#13068924C211yesmaximal, characteristic, complemented
7#13068923C211yesmaximal, characteristic, complemented
8#13068921C211yesmaximal, characteristic, complemented
9#13068701C212yesmaximal, complemented
10#13068549C212yesmaximal, complemented
11C11×#1872C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C2×C11×C22⋊Q8C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C22×(C2×D11)⋊C4—21no—
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×#4313C2212yes—
21D11×C22⋊Q8—24no—
22D11×C22⋊Q8C418yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949—21no—
25C2×C4⋊C4×D11—21no—
26C2×C4⋊C4×D11C2211yescharacteristic
27C2×C22⋊C4×D11—21no—
28C2×#66931—21no—
29C2×C11×#103C2212yescomplemented
30C2×C11×C22⋊C8C2211yescharacteristic
31C2×#66899C2212yescomplemented
32C2×C11⋊#95—21no—
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×(C2×D11)⋊C8C2212yes—
35C2×#66880C2212yescomplemented
36#10622600—21no—
37#10622600—21no—
38#10622600C2212yes—
39#10622600C2212yes—
40C2×#66874C2212yescomplemented
41#10622339—24no—
42C11×#340C2212yescomplemented
43#10622189C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11D411yescharacteristic
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C23×Dic11D411yescharacteristic
52C2×Q8×D11—22no—
53C2×Q8×D11—42no—
54C2×Q8×D11—42no—
55C2×Q8×D11C2×C414yescomplemented
56C22×C4×D11—21no—
57C22×C4×D11—21no—
58C22×C4×D11—42no—
59C22×C4×D11—42no—
60C22×C4×D11C2×C414yes—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D414yes—
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×Dic22—21no—
67C22×Dic22C2311yescharacteristic
68C22×C8×C11C2312yes—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8C2×C414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—42no—
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C22⋊Dic11—21no—
78#66999—22no—
79#66999C2×C414yescomplemented
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—44no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—42no—
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2311yescharacteristic
90#66977—22no—
91#66977C2×C414yes—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C22×C11⋊C8C2312yes—
96C2×#4313—24no—
97C2×#4313—42no—
98C2×#4313—42no—
99#66950—22no—
100#66950C2×C414yescomplemented
101#66949—28no—
102C4⋊C4×D11—28no—
103C4⋊C4×D11—22no—
104C4⋊C4×D11C2×C414yescomplemented
105C22⋊C4×D11—28no—
106#66931—28no—
107C11×#103—42no—
108C11×C22⋊C8—22no—
109#66899—42no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C22⋊(C11⋊C8)—22no—
113(C2×D11)⋊C8—24no—
114#66880—42no—
115#66874—42no—
116#21765—111nomaximal, Sylow
117C24×C11C2×D411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—41no—
123C23×D11—41no—
124C23×D11C22⋊C414yes—
125C23×D11C2×D411yescharacteristic
126C23×D11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11C22×C412yes—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—41no—
147C22×Dic11—41no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11C22⋊C414yes—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154Q8×D11—48no—
155Q8×D11—48no—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—41no—
163C2×C4×D11—41no—
164C2×C4×D11—41no—
165C2×C4×D11—41no—
166C2×C4×D11—48no—
167C2×C4×D11—48no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11C22⋊C414yes—
173C2×C4×D11C22⋊C414yes—
174C2×C4×D11C22×C412yes—
175C2×C4×D11C22×C412yes—
176C2×C4×D11C2×D412yes—
177C2×C4×D11C2×D412yes—
178C2×Dic22—24no—
179C2×Dic22—21no—
180C2×Dic22—22no—
181C2×Dic22—22no—
182C2×Dic22—42no—
183C2×Dic22—42no—
184C2×Dic22C22×C412yes—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—22no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4C22×C412yes—
194C11×C22⋊C4—24no—
195C22⋊Dic11—24no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—24no—
198(C2×D11)⋊C4—44no—
199(C2×D11)⋊C4—44no—
200C4⋊Dic11—24no—
201C4⋊Dic11—21no—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11—42no—
205C4⋊Dic11C22×C412yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—22no—
212#4313—48no—
213C22×C22⋊Q8—111no—
214C2×#407—111no—
215C2×#380—111no—
216#1894—112no—
217#1894—112no—
218#1872—111no—
219#1872—111no—
220#1872—111no—
221#1872D1111yescharacteristic, complemented
222#1823—112no—
223#1787—112no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11C2×C22⋊C412yes—
229C23×C11#13712yes—
230C23×C11#13712yes—
231C23×C11C22×D411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
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—28no—
243C22×D11—28no—
244C22×D11—44no—
245C22×D11—44no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11C2×C22⋊C412yes—
250C22×D11C2×C22⋊C412yes—
251C22×D11AGL(1,ℤ/8)12yes—
252C22×D11#13712yes—
253Q8×C11—24no—
254Q8×C11—42no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—84no—
269C2×C4×C11C2×C22⋊C412yes—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11H(5,𝔽2)12yes—
273C2×C4×C11H(5,𝔽2)12yes—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—44no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—84no—
289C2×Dic11C2×C22⋊C412yes—
290C2×Dic11C2×C22⋊C412yes—
291C4×D11—24no—
292C4×D11—24no—
293C4×D11—24no—
294C4×D11—24no—
295C4×D11—44no—
296C4×D11—44no—
297C4×D11—48no—
298C4×D11—48no—
299Dic22—24no—
300Dic22—48no—
301Dic22—42no—
302C8×C11—42no—
303C11⋊C8—42no—
304C23×Q8—111no—
305C24×C4—111no—
306C22×M16—112no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8—111no—
309C2×C22⋊Q8—118no—
310C2×C22⋊Q8—111no—
311C2×C22⋊Q8—221no—
312C2×C22⋊Q8—221no—
313C2×C22⋊Q8—224no—
314C2×C22⋊Q8C2×D1111yescharacteristic
315C22×C4⋊C4—111no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—221no—
318C22×C4⋊C4C2×D1111yescharacteristic
319C22×C22⋊C4—221no—
320C22×C22⋊C4—221no—
321C2×#103—112no—
322C2×#103—112no—
323C2×#103—112no—
324C2×#103C2×D1112yescomplemented
325#407—224no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8—112no—
328C2×C22⋊C8C2×D1111yescharacteristic
329#380—112no—
330#380—112no—
331#380—221no—
332#380—221no—
333C2×#95—221no—
334#340—112no—
335#340—112no—
336#340—112no—
337#340C2×D1112yescomplemented
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11#41914yes—
345C22×C11C22×C22⋊C411yescharacteristic
346C22×C11#53411yescharacteristic
347C22×C11#53411yescharacteristic
348C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C11C2×#13711yescharacteristic
350C22×C11C2×#13711yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—416no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11#41714yes—
367C4×C11—22no—
368C4×C11—42no—
369C4×C11—42no—
370C4×C11—82no—
371C4×C11#51812yes—
372C4×C11#53412yes—
373Dic11—22no—
374Dic11—22no—
375Dic11—42no—
376Dic11—42no—
377Dic11—82no—
378C25—111no—
379C22×Q8—114no—
380C22×Q8—111no—
381C22×Q8—221no—
382C22×Q8—222no—
383C22×Q8—442no—
384C22×Q8—442no—
385C22×Q8C22×D1111yescharacteristic
386C23×C4—21no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—114no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—114no—
394C23×C4—221no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—442no—
398C23×C4—442no—
399C23×C4C22×D1111yescharacteristic
400C2×M16—224no—
401C2×M16—442no—
402C2×M16—442no—
403C22×C8—112no—
404C22×C8C22×D1112yes—
405C22⋊Q8—22no—
406C22⋊Q8—114no—
407C22⋊Q8—114no—
408C22⋊Q8—114no—
409C22⋊Q8—228no—
410C22⋊Q8—228no—
411C22⋊Q8—222no—
412C22⋊Q8—222no—
413C22⋊Q8—222no—
414C22⋊Q8C4×D1114yes—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—228no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—442no—
429C2×C4⋊C4C22×D1112yes—
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—228no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—222no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—444no—
439#103—42no—
440#103—442no—
441#103—442no—
442#103—442no—
443C22⋊C8—22no—
444C22⋊C8—224no—
445C22⋊C8—222no—
446#95—222no—
447#95—222no—
448C2×C11—24no—
449C2×C11#230811yescharacteristic
450C2×C11C2×#41911yescharacteristic
451C2×C11C2×#41711yescharacteristic
452C2×C11#319311yescharacteristic
453C2×C11#319311yescharacteristic
454C2×C11#319511yescharacteristic
455C2×C11#319511yescharacteristic
456D11—24no—
457D11—42no—
458C24—111no—
459C24—111no—
460C24—114no—
461C24—222no—
462C24—222no—
463C24—222no—
464C24—222no—
465C24—441no—
466C24—441no—
467C24D4×D1111yescharacteristic
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—112no—
472C2×Q8—224no—
473C2×Q8—221no—
474C2×Q8—222no—
475C2×Q8—222no—
476C2×Q8—442no—
477C2×Q8—442no—
478C2×Q8—448no—
479C2×Q8—448no—
480C2×Q8C2×C4×D1112yes—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—114no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—112no—
496C22×C4—114no—
497C22×C4—114no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—222no—
507C22×C4—448no—
508C22×C4—448no—
509C22×C4—441no—
510C22×C4—441no—
511C22×C4—441no—
512C22×C4—441no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—441no—
518C22×C4—441no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4C2×C4×D1112yes—
523C22×C4D4×D1111yescharacteristic
524C22×C4D4×D1112yes—
525C22×C4C23×D1111yescharacteristic
526M16—448no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—222no—
531C2×C8—222no—
532C2×C8—222no—
533C4⋊C4—24no—
534C4⋊C4—21no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—42no—
538C4⋊C4—112no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—221no—
544C4⋊C4—222no—
545C4⋊C4—222no—
546C4⋊C4—442no—
547C4⋊C4C2×C4×D1112yes—
548C22⋊C4—24no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C22⋊C4—224no—
552C22⋊C4—444no—
553C22⋊C4—444no—
554C11#2176511yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—112no—
560C23—112no—
561C23—112no—
562C23—112no—
563C23—228no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—228no—
574C23—221no—
575C23—444no—
576C23—444no—
577C23—444no—
578C23—444no—
579C23—444no—
580C23C22⋊C4×D1112yes—
581C23#6696812yes—
582C23#6697112yes—
583C23C2×D4×D1111yescharacteristic
584Q8—24no—
585Q8—42no—
586Q8—224no—
587Q8—448no—
588Q8—442no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—84no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—444no—
616C2×C4—444no—
617C2×C4—448no—
618C2×C4—448no—
619C2×C4—444no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—884no—
628C2×C4C22⋊C4×D1112yes—
629C2×C4C22×C4×D1111yescharacteristic
630C2×C4C2×D4×D1111yescharacteristic
631C2×C4#6703712yes—
632C2×C4#6704212yes—
633C8—42no—
634C8—442no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—114no—
642C22—222no—
643C22—222no—
644C22—222no—
645C22—222no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—222no—
650C22—222no—
651C22—4416no—
652C22—441no—
653C22—441no—
654C22—441no—
655C22—441no—
656C22#1062241514yes—
657C22C2×C22⋊C4×D1111yescharacteristic
658C22#1062312011yescharacteristic
659C22#1062318411yescharacteristic
660C22C2×#6696811yescharacteristic
661C22C2×#6697111yescharacteristic
662C22D11×AGL(1,ℤ/8)11yescharacteristic
663C22D11×#13711yescharacteristic
664C4—22no—
665C4—42no—
666C4—42no—
667C4—82no—
668C4—222no—
669C4—222no—
670C4—442no—
671C4—442no—
672C4—882no—
673C4#1062307612yes—
674C4#1062313612yes—
675C2—24no—
676C2—224no—
677C2—442no—
678C2#1307119011yescharacteristic
679C2C2×#1062241511yescharacteristic
680C2D11×#41711yescharacteristic
681C2#1307941911yescharacteristic
682C2#1307942111yescharacteristic
683C2#1307943811yescharacteristic
684C2#1307943911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1872D11
hypocenterC11#21765
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
4. #13069048C2semidirect
5. #13069046C2semidirect
6. #13068924C2semidirect
7. #13068923C2semidirect
8. #13068921C2semidirect
9. #13068701C2semidirect
10. #13068549C2semidirect
11. C11×#1872C2semidirect
22. D11×C22⋊Q8C4semidirect
29. C2×C11×#103C22semidirect
31. C2×#66899C22semidirect
35. C2×#66880C22semidirect
40. C2×#66874C22semidirect
42. C11×#340C22semidirect
43. #10622189C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
55. C2×Q8×D11C2×C4semidirect
79. #66999C2×C4semidirect
100. #66950C2×C4semidirect
104. C4⋊C4×D11C2×C4semidirect
221. #1872D11semidirect
324. C2×#103C2×D11semidirect
337. #340C2×D11semidirect
554. C11#21765semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
C2×#106223392
C2×#106226002
#130690482
#130690462
#130689242
#130689232
#130689212
#130687012
#130685492
C11×#18722
#2176511