Finite Group Databasebeta

← #14786411

Subgroups — #14786411

Order 2816.

1500 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2C2×#10622584C211yesmaximal, characteristic, complemented
3C2×#10622600C211yesmaximal, characteristic
4#13069814C212yesmaximal, complemented
5#13069810C212yesmaximal, complemented
6#13068924C211yesmaximal, characteristic, complemented
7#13068921C211yesmaximal, characteristic, complemented
8#13068807C212yesmaximal, complemented
9#13068549C212yesmaximal, complemented
10#13068525C211yesmaximal, characteristic
11C2×C11×#483C211yesmaximal, 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
20D11×C22⋊Q8—24no—
21D11×C22⋊Q8—24no—
22C2×#66950C2211yescharacteristic
23C2×#66949—21no—
24C2×C4⋊C4×D11—21no—
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×C22⋊C4×D11—21no—
27C2×#66931—21no—
28C11×#483—24no—
29C2×C11×#106C2212yescomplemented
30C2×C11×#103C2212yescomplemented
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×#66899C2212yescomplemented
33C2×C11⋊#95—21no—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×(C2×D11)⋊C8C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37C2×#66880C2212yescomplemented
38#10622600—21no—
39#10622600—21no—
40#10622600C2212yes—
41#10622600C2212yes—
42#10622584—24no—
43C2×#66874C2212yescomplemented
44C2×#66872C2212yescomplemented
45#10622189C2212yescomplemented
46#10622167C2212yescomplemented
47C24×D11D411yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C23×Dic11D411yescharacteristic
53C2×Q8×D11—22no—
54C2×Q8×D11—22no—
55C2×Q8×D11—24no—
56C2×Q8×D11—42no—
57C22×C4×D11—21no—
58C22×C4×D11—21no—
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—24no—
62C22×C4×D11—42no—
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×Dic22—21no—
68C22×Dic22C2311yescharacteristic
69C22×C8×C11C2312yes—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8D414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80#66999—22no—
81#66999—22no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—44no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—42no—
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2311yescharacteristic
92#66977—22no—
93#66977D414yes—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C22×C11⋊C8C2312yes—
98#66950—22no—
99#66950—22no—
100#66949—28no—
101C4⋊C4×D11—28no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—22no—
104C22⋊C4×D11—28no—
105#66931—28no—
106C11×#106—24no—
107C11×#103—24no—
108C11×C22⋊C8—22no—
109#66899—42no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C22⋊(C11⋊C8)—22no—
113(C2×D11)⋊C8—24no—
114(C2×D11)⋊C8—42no—
115#66880—42no—
116#66874—24no—
117#66872—24no—
118#24003—111nomaximal, Sylow
119C24×C11C2×D411yescharacteristic
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—41no—
125C23×D11—41no—
126C23×D11SD1614yes—
127C23×D11C2×D411yescharacteristic
128C23×D11C2×D411yescharacteristic
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11C2×D412yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—22no—
150C22×Dic11—41no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156Q8×D11—48no—
157Q8×D11—48no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—41no—
172C2×C4×D11—41no—
173C2×C4×D11—48no—
174C2×C4×D11—48no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×C4×D11#4114yes—
180C2×Dic22—24no—
181C2×Dic22—21no—
182C2×Dic22—22no—
183C2×Dic22—22no—
184C2×Dic22—42no—
185C2×Dic22—42no—
186C2×Dic22C2×D412yes—
187C2×C8×C11—22no—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C11×C4⋊C4—24no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—24no—
197C22⋊Dic11—24no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—44no—
201(C2×D11)⋊C4—44no—
202C4⋊Dic11—24no—
203C4⋊Dic11—21no—
204C4⋊Dic11—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—42no—
207C4⋊Dic11C2×D412yes—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C22×C22⋊Q8—111no—
215C2×#483—111no—
216C2×#483D1111yescharacteristic, complemented
217C2×#380—111no—
218#2035—112no—
219#2035—112no—
220#1872—111no—
221#1872—111no—
222#1853—112no—
223#1787—112no—
224#1779—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11#12012yes—
230C23×C11C2×SD1612yes—
231C23×C11#13712yes—
232C23×C11C22×D411yescharacteristic
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—21no—
243C22×D11—28no—
244C22×D11—28no—
245C22×D11—44no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11—44no—
250C22×D11#12312yes—
251C22×D11C2×SD1612yes—
252C22×D11C2×SD1612yes—
253C22×D11#13712yes—
254Q8×C11—24no—
255Q8×C11—42no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—42no—
269C2×C4×C11—84no—
270C2×C4×C11#12012yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4112yes—
274C2×C4×C11H(5,𝔽2)12yes—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—44no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—84no—
291C2×Dic11#12312yes—
292C4×D11—24no—
293C4×D11—24no—
294C4×D11—44no—
295C4×D11—44no—
296C4×D11—48no—
297C4×D11—48no—
298C4×D11—42no—
299C4×D11—42no—
300Dic22—24no—
301Dic22—48no—
302Dic22—42no—
303C8×C11—42no—
304C11⋊C8—42no—
305C23×Q8—111no—
306C24×C4—111no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8—111no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—221no—
311C2×C22⋊Q8—221no—
312C2×C22⋊Q8—224no—
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—
321#483—24no—
322#483—224no—
323C2×#106—112no—
324C2×#106C2×D1112yescomplemented
325C2×#103—112no—
326C2×#103—112no—
327C2×#103—112no—
328C2×#103C2×D1112yescomplemented
329C2×C22⋊C8—111no—
330C2×C22⋊C8—112no—
331C2×C22⋊C8—112no—
332C2×C22⋊C8C2×D1111yescharacteristic
333#380—112no—
334#380—112no—
335#380—221no—
336#380—221no—
337C2×#95—221no—
338#340—112no—
339#340—112no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11#44814yes—
347C22×C11C2×#12011yescharacteristic
348C22×C11C2×#12311yescharacteristic
349C22×C11#53411yescharacteristic
350C22×C11C22×SD1611yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11C2×#13711yescharacteristic
353C22×C11#57511yescharacteristic
354C2×D11—22no—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—416no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11#48314yescomplemented
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11—82no—
373C4×C11#54612yes—
374C4×C11#54612yes—
375Dic11—22no—
376Dic11—42no—
377Dic11—41no—
378Dic11—42no—
379Dic11—82no—
380C25—111no—
381C22×Q8—111no—
382C22×Q8—221no—
383C22×Q8—224no—
384C22×Q8—222no—
385C22×Q8—222no—
386C22×Q8—442no—
387C22×Q8C22×D1111yescharacteristic
388C23×C4—21no—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—224no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—222no—
398C23×C4—222no—
399C23×C4—221no—
400C23×C4—442no—
401C23×C4C22×D1111yescharacteristic
402C22×C8—112no—
403C22×C8C22×D1112yes—
404C22⋊Q8—22no—
405C22⋊Q8—114no—
406C22⋊Q8—228no—
407C22⋊Q8—222no—
408C22⋊Q8—228no—
409C22⋊Q8—222no—
410C22⋊Q8—222no—
411C22⋊Q8—222no—
412C22⋊Q8—222no—
413C22⋊Q8C22⋊D1114yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—222no—
421C2×C4⋊C4—228no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—222no—
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#106—24no—
440#106—224no—
441#103—24no—
442#103—224no—
443#103—442no—
444#103—442no—
445C22⋊C8—22no—
446C22⋊C8—224no—
447C22⋊C8—222no—
448C22⋊C8—442no—
449#95—222no—
450#95—222no—
451C2×C11—24no—
452C2×C11#240511yescharacteristic
453C2×C11C2×#44811yescharacteristic
454C2×C11#300711yescharacteristic
455C2×C11C2×#48311yescharacteristic
456C2×C11#309511yescharacteristic
457C2×C11#318711yescharacteristic
458C2×C11#319511yescharacteristic
459D11—24no—
460D11—42no—
461C24—111no—
462C24—111no—
463C24—114no—
464C24—222no—
465C24—222no—
466C24—222no—
467C24—222no—
468C24—441no—
469C24—441no—
470C24D4×D1111yescharacteristic
471C2×Q8—21no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—112no—
475C2×Q8—224no—
476C2×Q8—221no—
477C2×Q8—222no—
478C2×Q8—222no—
479C2×Q8—442no—
480C2×Q8—442no—
481C2×Q8—448no—
482C2×Q8—448no—
483C2×Q8C2×C22⋊D1112yes—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—111no—
493C22×C4—114no—
494C22×C4—111no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—224no—
498C22×C4—224no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4—222no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—221no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—221no—
512C22×C4—222no—
513C22×C4—441no—
514C22×C4—441no—
515C22×C4—448no—
516C22×C4—448no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—441no—
522C22×C4—442no—
523C22×C4—442no—
524C22×C4—442no—
525C22×C4D4×D1111yescharacteristic
526C22×C4D4×D1112yes—
527C22×C4C2×C22⋊D1112yes—
528C22×C4C23×D1111yescharacteristic
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—222no—
533C2×C8—222no—
534C2×C8—222no—
535C4⋊C4—24no—
536C4⋊C4—21no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—42no—
540C4⋊C4—112no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4—221no—
546C4⋊C4—222no—
547C4⋊C4—222no—
548C4⋊C4—442no—
549C4⋊C4C2×C22⋊D1112yes—
550C22⋊C4—24no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—224no—
554C22⋊C4—444no—
555C22⋊C4—444no—
556C11#2400311yescharacteristic, complemented, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—112no—
562C23—112no—
563C23—112no—
564C23—112no—
565C23—228no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—228no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—444no—
578C23—444no—
579C23—444no—
580C23—444no—
581C23—444no—
582C23SD16×D1112yes—
583C23#6696812yes—
584C23#6699012yes—
585C23C2×D4×D1111yescharacteristic
586Q8—24no—
587Q8—42no—
588Q8—224no—
589Q8—448no—
590Q8—442no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—84no—
605C2×C4—112no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
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—442no—
628C2×C4—442no—
629C2×C4—884no—
630C2×C4#6699012yes—
631C2×C4C2×D4×D1111yescharacteristic
632C2×C4#41×D1112yes—
633C2×C4#6704212yes—
634C2×C4C22×C22⋊D1111yescharacteristic
635C8—42no—
636C8—442no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—114no—
644C22—222no—
645C22—222no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—222no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—4416no—
654C22—441no—
655C22—441no—
656C22—441no—
657C22—441no—
658C22#1062278314yes—
659C22D11×#12311yescharacteristic
660C22#1062318411yescharacteristic
661C22C2×SD16×D1111yescharacteristic
662C22C2×#6696811yescharacteristic
663C22D11×#13711yescharacteristic
664C22#1062330811yescharacteristic
665C22C2×#6699011yescharacteristic
666C4—22no—
667C4—42no—
668C4—42no—
669C4—82no—
670C4—222no—
671C4—441no—
672C4—442no—
673C4—442no—
674C4—882no—
675C4#1062318512yes—
676C4#1062336012yes—
677C2—24no—
678C2—224no—
679C2—442no—
680C2#1307194011yescharacteristic
681C2C2×#1062278311yescharacteristic
682C2#1307787211yescharacteristic
683C2D11×#48311yescharacteristic
684C2#1307855911yescharacteristic
685C2#1307937211yescharacteristic
686C2#1307943911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#483C2
socleC23×C11C22×D4
prime radicalC24×D11D4
hypercenterC2×#483D11
hypocenterC11#24003
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
2. C2×#10622584C2semidirect
4. #13069814C2semidirect
5. #13069810C2semidirect
6. #13068924C2semidirect
7. #13068921C2semidirect
8. #13068807C2semidirect
9. #13068549C2semidirect
11. C2×C11×#483C2semidirect
29. C2×C11×#106C22semidirect
30. C2×C11×#103C22semidirect
32. C2×#66899C22semidirect
37. C2×#66880C22semidirect
43. C2×#66874C22semidirect
44. C2×#66872C22semidirect
45. #10622189C22semidirect
46. #10622167C22semidirect
216. C2×#483D11semidirect
324. C2×#106C2×D11semidirect
328. C2×#103C2×D11semidirect
368. C2×D11#483semidirect
556. C11#24003semidirect

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×#106225842
C2×#106226002
#130698142
#130698102
#130689242
#130689212
#130688072
#130685492
#130685252
C2×C11×#4832
#2400311