Finite Group Databasebeta

← #14755012

Subgroups — #14755012

Order 2816.

1934 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C211yesmaximal, characteristic
2C2×D11×#117C211yesmaximal, characteristic
3C2×#10622415C212yesmaximal, complemented
4C2×#10622339C211yesmaximal, characteristic
5#13068929C211yesmaximal, characteristic, complemented
6#13068928C211yesmaximal, characteristic, complemented
7#13068926C211yesmaximal, characteristic, complemented
8#13068922C212yesmaximal, complemented
9#13068920C212yesmaximal, complemented
10#13068334C212yesmaximal, complemented
11C11×#1873C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C2×#66999C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C22×#4313C2212yes—
20D11×C22⋊Q8—24no—
21D11×C22⋊Q8C418yescomplemented
22D11×#117—28no—
23C2×#66950C2211yescharacteristic
24C2×#66949—21no—
25C2×#66945C2212yes—
26C2×C4⋊C4×D11—21no—
27C2×C4⋊C4×D11C2212yes—
28C2×C4⋊C4×D11C2211yescharacteristic
29C2×C22⋊C4×D11—21no—
30C2×C22⋊C4×D11—21no—
31C2×#66931—21no—
32C2×#66930—21no—
33C2×#66925—21no—
34C2×C42×D11—21no—
35C2×C11×#103C2212yescomplemented
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×#66899C2212yescomplemented
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×(C2×D11)⋊C8C2212yes—
40C2×#66880C2212yescomplemented
41C2×#66874C2212yescomplemented
42#10622415—28no—
43#10622339—24no—
44C11×#340C2212yescomplemented
45#10622189C2212yescomplemented
46#10622167C2212yescomplemented
47#10622167C2212yescomplemented
48C24×D11D411yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11D411yescharacteristic
52C2×Q8×D11—22no—
53C2×Q8×D11—24no—
54C2×Q8×D11—24no—
55C2×Q8×D11C2×C414yescomplemented
56C22×C4×D11—24no—
57C22×C4×D11—24no—
58C22×C4×D11—22no—
59C22×C4×D11—21no—
60C22×C4×D11—21no—
61C22×C4×D11C2×C414yes—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D414yes—
65C22×C4×D11C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×Dic22—21no—
68C22×Dic22C2311yescharacteristic
69C22×C8×C11C2312yes—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8C2×C414yescomplemented
72C11×#117—24no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81#66999—22no—
82#66999C2×C414yes—
83C2×(C2×D11)⋊C4—22no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86#66979—24no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90#66977—22no—
91#66977C2×C414yescomplemented
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—22no—
98C22×C11⋊C8C2312yes—
99C2×#4313—24no—
100C2×#4313—24no—
101C2×#4313—24no—
102#66950—22no—
103#66950C2×C414yes—
104#66949—28no—
105#66945—24no—
106#66945D418yes—
107C4⋊C4×D11—28no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—24no—
110C4⋊C4×D11—24no—
111C4⋊C4×D11C2×C414yescomplemented
112C22⋊C4×D11—28no—
113C22⋊C4×D11—28no—
114#66931—28no—
115#66930—28no—
116#66925—28no—
117C42×D11—28no—
118C11×#103—24no—
119C11×C22⋊C8—22no—
120#66899—24no—
121C22⋊(C11⋊C8)—22no—
122(C2×D11)⋊C8—24no—
123#66880—24no—
124#66874—24no—
125#20911—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—24no—
130C23×D11—42no—
131C23×D11C22⋊C414yes—
132C23×D11C2×D411yescharacteristic
133C23×D11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11C22×C412yes—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C22⋊C414yes—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155Q8×D11—216no—
156Q8×D11—48no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—216no—
160C2×C4×D11—216no—
161C2×C4×D11—28no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—44no—
169C2×C4×D11—44no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—44no—
173C2×C4×D11C22⋊C414yes—
174C2×C4×D11C22⋊C414yes—
175C2×C4×D11C22×C412yes—
176C2×C4×D11C22×C412yes—
177C2×C4×D11C2×D412yes—
178C2×C4×D11C2×D412yes—
179C2×C4×D11C2×D414yes—
180C2×C4×D11#4114yes—
181C2×Dic22—24no—
182C2×Dic22—22no—
183C2×Dic22—21no—
184C2×Dic22—22no—
185C2×Dic22—42no—
186C2×Dic22—42no—
187C2×Dic22C22×C412yes—
188C2×C8×C11—22no—
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4C22×C412yes—
195C11×C4⋊C4C2×D414yes—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C42×C11—24no—
199C22⋊Dic11—24no—
200C22⋊Dic11—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—28no—
204C4⋊Dic11—24no—
205C4⋊Dic11—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22×C412yes—
208C4⋊Dic11C2×D414yes—
209Dic11⋊C4—28no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—24no—
213C4×Dic11—24no—
214C4×Dic11—28no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218#4313—48no—
219C22×C22⋊Q8—111no—
220C22×#117—111no—
221C2×#419—112no—
222C2×#407—111no—
223#1873—111no—
224#1873—111no—
225#1873—111no—
226#1873D1111yescharacteristic, complemented
227#1872—112no—
228#1872—112no—
229#1736—112no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11C2×C22⋊C412yes—
235C23×C11C22×D411yescharacteristic
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—28no—
242C22×D11—28no—
243C22×D11—44no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11C2×C22⋊C412yes—
247C22×D11C2×C22⋊C412yes—
248C22×D11#12012yes—
249C22×D11#12312yes—
250C22×D11#13714yes—
251Q8×C11—24no—
252Q8×C11—42no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—24no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D412yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4112yes—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—28no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11C2×C22⋊C412yes—
282C2×Dic11C2×C22⋊C412yes—
283C2×Dic11#12012yes—
284C2×Dic11#12312yes—
285C4×D11—28no—
286C4×D11—24no—
287C4×D11—24no—
288C4×D11—28no—
289C4×D11—48no—
290C4×D11—416no—
291C4×D11—48no—
292C4×D11C4×D418yes—
293C4×D11#12118yes—
294Dic22—24no—
295Dic22—42no—
296Dic22—48no—
297C8×C11—42no—
298C11⋊C8—42no—
299C23×Q8—111no—
300C24×C4—111no—
301C22×M16—112no—
302C2×C22⋊Q8—111no—
303C2×C22⋊Q8—111no—
304C2×C22⋊Q8—118no—
305C2×C22⋊Q8—111no—
306C2×C22⋊Q8—221no—
307C2×C22⋊Q8—221no—
308C2×C22⋊Q8—224no—
309C2×C22⋊Q8C2×D1111yescharacteristic
310C2×#117—111no—
311C2×#117—112no—
312C2×#117—221no—
313C2×#117—221no—
314C2×#117—228no—
315C2×#117C2×D1111yescharacteristic
316C22×C4⋊C4—111no—
317C22×C4⋊C4—112no—
318C22×C4⋊C4—221no—
319C22×C22⋊C4—221no—
320C22×C22⋊C4—221no—
321C22×C42—221no—
322#419—228no—
323C2×#103—112no—
324C2×#103—112no—
325C2×#103—112no—
326C2×#103C2×D1112yescomplemented
327#407—224no—
328C2×C22⋊C8—111no—
329C2×C22⋊C8—112no—
330C2×C22⋊C8C2×D1111yescharacteristic
331#340—112no—
332#340—112no—
333#340—112no—
334#340C2×D1112yescomplemented
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11C22×C22⋊C411yescharacteristic
341C22×C11C2×#12011yescharacteristic
342C22×C11C2×#12311yescharacteristic
343C22×C11C2×#13712yes—
344C22×C11#57512yes—
345C2×D11—24no—
346C2×D11—24no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—24no—
351C2×D11—24no—
352C2×D11—22no—
353C2×D11—416no—
354C2×D11#38614yes—
355C2×D11#41914yescomplemented
356C4×C11—22no—
357C4×C11—42no—
358C4×C11—44no—
359C4×C11—42no—
360C4×C11C2×C4×D412yes—
361C4×C11C2×#12112yes—
362Dic11—22no—
363Dic11—42no—
364Dic11—44no—
365Dic11—42no—
366Dic11#38614yes—
367C25—111no—
368C22×Q8—114no—
369C22×Q8—111no—
370C22×Q8—221no—
371C22×Q8—222no—
372C22×Q8—224no—
373C22×Q8—224no—
374C22×Q8C22×D1111yescharacteristic
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—114no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—224no—
383C23×C4—224no—
384C23×C4—221no—
385C23×C4—222no—
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C2×M16—224no—
389C2×M16—224no—
390C2×M16—224no—
391C22×C8—112no—
392C22×C8C22×D1112yes—
393C22⋊Q8—22no—
394C22⋊Q8—114no—
395C22⋊Q8—114no—
396C22⋊Q8—114no—
397C22⋊Q8—228no—
398C22⋊Q8—228no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401C22⋊Q8—222no—
402C22⋊Q8C4×D1114yescomplemented
403#117—24no—
404#117—118no—
405#117—228no—
406#117—228no—
407#117—224no—
408#117—224no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—114no—
413C2×C4⋊C4—224no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—228no—
416C2×C4⋊C4—222no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—224no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1112yes—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—228no—
427C2×C22⋊C4—228no—
428C2×C22⋊C4—222no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—21no—
434C2×C42—228no—
435C2×C42—222no—
436C2×C42—221no—
437#103—24no—
438#103—224no—
439#103—224no—
440#103—224no—
441C22⋊C8—22no—
442C22⋊C8—224no—
443C22⋊C8—222no—
444C2×C11—42no—
445C2×C11C2×#38611yescharacteristic
446C2×C11C2×#41911yescharacteristic
447C2×C11#289611yescharacteristic
448C2×C11#300712yes—
449C2×C11#309512yes—
450D11—24no—
451D11—24no—
452C24—111no—
453C24—111no—
454C24—114no—
455C24—222no—
456C24—222no—
457C24—224no—
458C24—442no—
459C24D4×D1111yescharacteristic
460C2×Q8—21no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—112no—
464C2×Q8—224no—
465C2×Q8—2216no—
466C2×Q8—221no—
467C2×Q8—222no—
468C2×Q8—222no—
469C2×Q8—442no—
470C2×Q8—442no—
471C2×Q8—448no—
472C2×Q8C2×C4×D1112yes—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—111no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—111no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—2216no—
492C22×C4—2216no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—228no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—444no—
508C22×C4—444no—
509C22×C4—444no—
510C22×C4C2×C4×D1112yes—
511C22×C4D4×D1111yescharacteristic
512C22×C4D4×D1112yes—
513C22×C4C23×D1111yescharacteristic
514M16—448no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—222no—
519C2×C8—222no—
520C2×C8—222no—
521C4⋊C4—24no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—112no—
525C4⋊C4—114no—
526C4⋊C4—224no—
527C4⋊C4—224no—
528C4⋊C4—224no—
529C4⋊C4—228no—
530C4⋊C4—224no—
531C4⋊C4—222no—
532C4⋊C4—221no—
533C4⋊C4C2×C4×D1112yes—
534C4⋊C4D4×D1114yes—
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—228no—
538C22⋊C4—224no—
539C22⋊C4—224no—
540C22⋊C4—224no—
541C22⋊C4—224no—
542C42—24no—
543C42—228no—
544C42—224no—
545C11#2091111yescharacteristic, complemented, Sylow
546C23—22no—
547C23—22no—
548C23—21no—
549C23—21no—
550C23—112no—
551C23—112no—
552C23—114no—
553C23—112no—
554C23—112no—
555C23—228no—
556C23—228no—
557C23—222no—
558C23—222no—
559C23—222no—
560C23—221no—
561C23—221no—
562C23—444no—
563C23—448no—
564C23—448no—
565C23C22⋊C4×D1112yes—
566C23C2×D4×D1111yescharacteristic
567Q8—24no—
568Q8—42no—
569Q8—224no—
570Q8—448no—
571Q8—442no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—118no—
588C2×C4—118no—
589C2×C4—112no—
590C2×C4—228no—
591C2×C4—228no—
592C2×C4—228no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—448no—
601C2×C4—4416no—
602C2×C4—448no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4C22⋊C4×D1112yes—
609C2×C4C22×C4×D1111yescharacteristic
610C2×C4C2×D4×D1112yes—
611C2×C4C2×D4×D1111yescharacteristic
612C2×C4#41×D1112yes—
613C8—42no—
614C8—442no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—42no—
619C22—42no—
620C22—114no—
621C22—114no—
622C22—224no—
623C22—224no—
624C22—224no—
625C22—224no—
626C22—222no—
627C22—222no—
628C22—222no—
629C22—222no—
630C22—4416no—
631C22C2×C22⋊C4×D1111yescharacteristic
632C22D11×#12011yescharacteristic
633C22D11×#12311yescharacteristic
634C22#1062329912yes—
635C22D11×#13712yes—
636C4—22no—
637C4—44no—
638C4—42no—
639C4—42no—
640C4—114no—
641C4—222no—
642C4—444no—
643C4—442no—
644C4—442no—
645C4C4×D4×D1112yes—
646C4D11×#12112yes—
647C2—42no—
648C2—224no—
649C2—224no—
650C2D11×#38611yescharacteristic
651C2D11×#41911yescharacteristic
652C2#1307713111yescharacteristic
653C2#1307787312yes—
654C2#1307856312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1873D11
hypocenterC11#20911
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
3. C2×#10622415C2semidirect
5. #13068929C2semidirect
6. #13068928C2semidirect
7. #13068926C2semidirect
8. #13068922C2semidirect
9. #13068920C2semidirect
10. #13068334C2semidirect
11. C11×#1873C2semidirect
21. D11×C22⋊Q8C4semidirect
35. C2×C11×#103C22semidirect
37. C2×#66899C22semidirect
40. C2×#66880C22semidirect
41. C2×#66874C22semidirect
44. C11×#340C22semidirect
45. #10622189C22semidirect
46. #10622167C22semidirect
47. #10622167C22semidirect
55. C2×Q8×D11C2×C4semidirect
71. C11×C22⋊Q8C2×C4semidirect
91. #66977C2×C4semidirect
111. C4⋊C4×D11C2×C4semidirect
226. #1873D11semidirect
326. C2×#103C2×D11semidirect
334. #340C2×D11semidirect
355. C2×D11#419semidirect
402. C22⋊Q8C4×D11semidirect
545. C11#20911semidirect

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×D11×#1172
C2×#106224152
C2×#106223392
#130689292
#130689282
#130689262
#130689222
#130689202
#130683342
C11×#18732
#2091111