Finite Group Databasebeta

← #14753604

Subgroups — #14753604

Order 2816.

1470 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#117C211yesmaximal, characteristic
2C2×#10622739C211yesmaximal, characteristic
3#13070995C211yesmaximal, characteristic
4#13068714C218yesmaximal, complemented
5#13068327C211yesmaximal, characteristic, complemented
6#13068326C211yesmaximal, characteristic, complemented
7#13068325C211yesmaximal, characteristic, complemented
8C11×#1733C211yesmaximal, characteristic, complemented
9C23×C4×D11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16D11×#117—22no—
17D11×#117—22no—
18D11×#117C414yescomplemented
19D11×#117C2214yes—
20C2×#66945C412yescomplemented
21C2×C4⋊C4×D11C412yescomplemented
22C2×C22⋊C4×D11—21no—
23C2×#66930—21no—
24C2×#66925—21no—
25C2×C42×D11—21no—
26#10622739—21no—
27#10622739—21no—
28#10622739C2214yes—
29C2×(C2×D11)⋊C8—22no—
30#10622600—22no—
31#10622568—21no—
32#10622556—21no—
33C4×(C2×D11)⋊C4C2214yes—
34C11×#339C2214yescomplemented
35#10622193C2214yescomplemented
36#10622170C2214yescomplemented
37#10622161C2214yescomplemented
38C24×D11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11D411yescharacteristic
41C22×C4×D11—22no—
42C22×C4×D11—22no—
43C22×C4×D11—22no—
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11C2×C411yescharacteristic
47C22×C4×D11C2×C411yescharacteristic
48C22×C4×D11C2×C412yes—
49C22×C4×D11D412yes—
50C22×C4×D11D412yes—
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11C2312yes—
54C2×C11×M16—21no—
55C2×C11×M16—22no—
56C2×C11×M16—22no—
57C2×C11×M16C2312yes—
58C22×C8×C11—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117—22no—
62C11×#117—22no—
63C11×#117C2×C412yes—
64C11×#117C2312yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—21no—
70C2×C42×C11C2312yes—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—24no—
75#66979—21no—
76#66979—21no—
77#66979—22no—
78#66979—22no—
79#66979C2×C412yes—
80#66979C2312yes—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2×C412yes—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11C2312yes—
87C2×#4318—21no—
88C2×#4318—22no—
89C2×#4318—22no—
90C2×#4318C2312yes—
91C22×C11⋊C8—21no—
92#66945—24no—
93#66945C2×C418yes—
94C4⋊C4×D11—22no—
95C4⋊C4×D11—22no—
96C4⋊C4×D11C2×C414yes—
97C4⋊C4×D11C2×C414yes—
98C22⋊C4×D11—24no—
99C22⋊C4×D11—24no—
100#66930—24no—
101#66930—24no—
102#66925—24no—
103#66925—24no—
104C42×D11—24no—
105C42×D11—24no—
106C11⋊#95—24no—
107(C2×D11)⋊C8—24no—
108(C2×D11)⋊C8—24no—
109#20705—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—44no—
114C23×D11C22⋊C411yescharacteristic
115C23×D11C22⋊C412yes—
116C23×D11C22⋊C411yescharacteristic
117C23×D11C2×D412yes—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11C22⋊C412yes—
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137C22×Dic11C2×D412yes—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—24no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—24no—
146C2×C4×D11—24no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—24no—
150C2×C4×D11—24no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—24no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—48no—
159C2×C4×D11C22⋊C412yes—
160C2×C4×D11C22⋊C412yes—
161C2×C4×D11C22⋊C412yes—
162C2×C4×D11C22⋊C412yes—
163C2×C4×D11C22×C412yes—
164C2×C4×D11C22×C412yes—
165C2×C4×D11C2×D412yes—
166C2×C4×D11C2×D412yes—
167C11×M16—22no—
168C11×M16—22no—
169C11×M16—42no—
170C2×C8×C11—22no—
171C2×C8×C11—42no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C22×C414yes—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—42no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—22no—
182C22⋊Dic11—22no—
183C22⋊Dic11—22no—
184C22⋊Dic11—42no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—48no—
187C4⋊Dic11—22no—
188C4⋊Dic11—42no—
189C4⋊Dic11C22×C414yes—
190Dic11⋊C4—24no—
191Dic11⋊C4—24no—
192C4×Dic11—28no—
193C4×Dic11—22no—
194C4×Dic11—22no—
195C4×Dic11—22no—
196C4×Dic11—22no—
197#4318—22no—
198#4318—22no—
199#4318—42no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—42no—
202C22×#117—111no—
203C2×#407—111no—
204#2280—111no—
205#1826—118no—
206#1733—111no—
207#1733—111no—
208#1733—111no—
209#1733D1111yescharacteristic, complemented
210C23×C11—42no—
211C23×C11C2×C22⋊C411yescharacteristic
212C23×C11C2×C22⋊C411yescharacteristic
213C23×C11#12312yes—
214C23×C11#12312yes—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—24no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—48no—
228C22×D11—48no—
229C22×D11C2×C22⋊C412yes—
230C22×D11C2×C22⋊C412yes—
231C2×C4×C11—24no—
232C2×C4×C11—44no—
233C2×C4×C11—44no—
234C2×C4×C11—42no—
235C2×C4×C11C2×C22⋊C411yescharacteristic
236C2×C4×C11C2×C22⋊C411yescharacteristic
237C2×C4×C11#11712yes—
238C2×C4×C11#11712yes—
239C2×C4×C11#11712yes—
240C2×C4×C11#11712yes—
241C2×C4×C11#12312yes—
242C2×C4×C11#12312yes—
243C2×C4×C11#12312yes—
244C2×C4×C11#12312yes—
245C2×C4×C11#12312yes—
246C2×C4×C11#12312yes—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11—42no—
262C2×Dic11C2×C22⋊C412yes—
263C2×Dic11C2×C22⋊C412yes—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—24no—
273C4×D11—24no—
274C4×D11—24no—
275C4×D11—24no—
276C4×D11—48no—
277C4×D11—48no—
278C8×C11—42no—
279C11⋊C8—42no—
280C24×C4—111no—
281C22×M16—111no—
282C22×M16C2×D1111yescharacteristic
283C2×#117—111no—
284C2×#117—111no—
285C2×#117—114no—
286C2×#117—114no—
287C2×#117—112no—
288C2×#117—221no—
289C2×#117—221no—
290C2×#117—222no—
291C2×#117—222no—
292C2×#117C2×D1111yescharacteristic
293C2×#117C2×D1111yescharacteristic
294C22×C4⋊C4—112no—
295C22×C22⋊C4—221no—
296C22×C42—221no—
297#407—114no—
298#407—221no—
299#407—221no—
300C2×C22⋊C8—222no—
301#381—221no—
302#380—222no—
303#379—221no—
304C4×C22⋊C4—114no—
305#339—114no—
306#339—114no—
307#339—114no—
308#339C2×D1114yescomplemented
309C22×C11—22no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11#38112yes—
315C22×C11#38112yes—
316C22×C11C22×C22⋊C411yescharacteristic
317C22×C11C2×#12311yescharacteristic
318C22×C11C2×#12311yescharacteristic
319C2×D11—28no—
320C2×D11—22no—
321C2×D11—22no—
322C2×D11—22no—
323C2×D11—22no—
324C2×D11—22no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—48no—
328C2×D11—44no—
329C2×D11#42114yes—
330C4×C11—44no—
331C4×C11—82no—
332C4×C11#38112yes—
333C4×C11#38112yes—
334C4×C11C2×#11711yescharacteristic
335C4×C11C2×#11711yescharacteristic
336C4×C11C2×#12311yescharacteristic
337C4×C11C2×#12311yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—44no—
341Dic11—82no—
342C25—111no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4—112no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—112no—
352C23×C4—222no—
353C23×C4—222no—
354C23×C4—222no—
355C23×C4—222no—
356C23×C4—222no—
357C23×C4C22×D1111yescharacteristic
358C2×M16—21no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16—112no—
362C2×M16—221no—
363C2×M16—222no—
364C2×M16—222no—
365C2×M16C22×D1112yes—
366C22×C8—21no—
367C22×C8—221no—
368#117—21no—
369#117—21no—
370#117—22no—
371#117—22no—
372#117—112no—
373#117—112no—
374#117—118no—
375#117—224no—
376#117—224no—
377#117—224no—
378#117—224no—
379#117—224no—
380#117—221no—
381#117—221no—
382#117—222no—
383#117—222no—
384#117C4×D1112yes—
385#117C22×D1112yes—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4C4×D1112yes—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—221no—
403C2×C42—21no—
404C2×C42—112no—
405C2×C42—224no—
406C2×C42—224no—
407C2×C42—222no—
408C2×C42—221no—
409C2×C42C22×D1112yes—
410C22⋊C8—224no—
411C22⋊C8—224no—
412#95—224no—
413C2×C11—21no—
414C2×C11—21no—
415C2×C11—22no—
416C2×C11—22no—
417C2×C11C2×#38111yescharacteristic
418C2×C11C2×#42112yes—
419D11—24no—
420D11—42no—
421C24—111no—
422C24—112no—
423C24—112no—
424C24—111no—
425C24—222no—
426C24—222no—
427C24—444no—
428C24D4×D1111yescharacteristic
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—224no—
444C22×C4—224no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—448no—
468C22×C4C2×C4×D1111yescharacteristic
469C22×C4C2×C4×D1111yescharacteristic
470C22×C4#433912yes—
471C22×C4#433912yes—
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475C22×C4#434112yes—
476C22×C4#434312yes—
477C22×C4C23×D1111yescharacteristic
478M16—22no—
479M16—22no—
480M16—42no—
481M16—222no—
482M16—222no—
483M16—442no—
484C2×C8—22no—
485C2×C8—42no—
486C2×C8—222no—
487C2×C8—442no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—114no—
491C4⋊C4—224no—
492C4⋊C4—224no—
493C4⋊C4—222no—
494C4⋊C4—442no—
495C4⋊C4C2×C4×D1114yes—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—42no—
499C22⋊C4—228no—
500C22⋊C4—222no—
501C22⋊C4—222no—
502C22⋊C4—448no—
503C22⋊C4—442no—
504C42—22no—
505C42—22no—
506C42—22no—
507C42—22no—
508C42—228no—
509C42—222no—
510C42—222no—
511C42—222no—
512C42—222no—
513C11#2070511yescharacteristic, complemented, Sylow
514C23—42no—
515C23—112no—
516C23—112no—
517C23—224no—
518C23—224no—
519C23—224no—
520C23—222no—
521C23—222no—
522C23—222no—
523C23—224no—
524C23—222no—
525C23—442no—
526C23—442no—
527C23—442no—
528C23—448no—
529C23—448no—
530C23C22⋊C4×D1111yescharacteristic
531C23C22⋊C4×D1111yescharacteristic
532C23#6693612yes—
533C23#6694712yes—
534C23C2×D4×D1111yescharacteristic
535C2×C4—24no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—448no—
560C2×C4—448no—
561C2×C4—444no—
562C2×C4—444no—
563C2×C4—442no—
564C2×C4#6692512yes—
565C2×C4#6692512yes—
566C2×C4C22⋊C4×D1111yescharacteristic
567C2×C4C22⋊C4×D1111yescharacteristic
568C2×C4#6693612yes—
569C2×C4#6693612yes—
570C2×C4#6693612yes—
571C2×C4#6694512yes—
572C2×C4#6694512yes—
573C2×C4#6694712yes—
574C2×C4#6694712yes—
575C2×C4#6694712yes—
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C2×#433911yescharacteristic
578C2×C4C2×#433911yescharacteristic
579C2×C4C2×D4×D1111yescharacteristic
580C2×C4C2×#434111yescharacteristic
581C2×C4C2×#434311yescharacteristic
582C8—42no—
583C8—442no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—42no—
588C22—42no—
589C22—114no—
590C22—228no—
591C22—222no—
592C22—222no—
593C22—222no—
594C22—222no—
595C22—222no—
596C22—444no—
597C22—444no—
598C22—448no—
599C22—444no—
600C22#1062227712yes—
601C22#1062227712yes—
602C22C2×C22⋊C4×D1111yescharacteristic
603C22C2×#6693611yescharacteristic
604C22C2×#6694711yescharacteristic
605C4—44no—
606C4—82no—
607C4—222no—
608C4—222no—
609C4—444no—
610C4—882no—
611C4#1062227712yes—
612C4#1062227712yes—
613C4C2×#6692511yescharacteristic
614C4C2×#6693611yescharacteristic
615C4C2×#6694511yescharacteristic
616C4C2×#6694711yescharacteristic
617C2—21no—
618C2—21no—
619C2—22no—
620C2—22no—
621C2—224no—
622C2—442no—
623C2C2×#1062227711yescharacteristic
624C2D11×#42112yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1733C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1733D11
hypocenterC11#20705
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #13068714C2semidirect
5. #13068327C2semidirect
6. #13068326C2semidirect
7. #13068325C2semidirect
8. C11×#1733C2semidirect
18. D11×#117C4semidirect
20. C2×#66945C4semidirect
21. C2×C4⋊C4×D11C4semidirect
34. C11×#339C22semidirect
35. #10622193C22semidirect
36. #10622170C22semidirect
37. #10622161C22semidirect
209. #1733D11semidirect
308. #339C2×D11semidirect
513. C11#20705semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1172
C2×#106227392
#130709952
#130687142
#130683272
#130683262
#130683252
C11×#17332
#2070511