Finite Group Databasebeta

← #14765655

Subgroups — #14765655

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078525C211yesmaximal, characteristic
2#13077320C211yesmaximal, characteristic
3#13077179C211yesmaximal, characteristic, complemented
4#13069368C211yesmaximal, characteristic, complemented
5#13069363C211yesmaximal, characteristic, complemented
6#13069324C211yesmaximal, characteristic, complemented
7#13069317C211yesmaximal, characteristic, complemented
8#13069213C211yesmaximal, characteristic, complemented
9#13069213C211yesmaximal, characteristic, complemented
10#13068889C211yesmaximal, characteristic, complemented
11#13068889C211yesmaximal, characteristic, complemented
12#13068821C211yesmaximal, characteristic, complemented
13#13068716C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#1871C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C11×#525C2211yescharacteristic
18C2×#67001C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×C11×#104C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23C4×C11×C22⋊C4C2211yescharacteristic
24#10622847C2211yescharacteristic
25#10622846C2211yescharacteristic
26#10622846C2211yescharacteristic
27#10622820C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66886C2211yescharacteristic
30C2×#66886C2211yescharacteristic
31#10622732C2211yescharacteristic
32#10622732C2211yescharacteristic
33#10622732C2211yescharacteristic
34#10622732C2211yescharacteristic
35#10622731—21no—
36#10622731—21no—
37#10622715—21no—
38#10622715—21no—
39#10622658C411yescharacteristic, complemented
40#10622658C411yescharacteristic, complemented
41#10622657C411yescharacteristic, complemented
42#10622656C411yescharacteristic, complemented
43#10622648C411yescharacteristic, complemented
44#10622648C411yescharacteristic, complemented
45#10622647C411yescharacteristic, complemented
46#10622646C411yescharacteristic, complemented
47#10622625—21no—
48#10622625—21no—
49#10622624—21no—
50#10622624—21no—
51#10622612C2211yescharacteristic
52#10622611C2211yescharacteristic
53#10622611C2211yescharacteristic
54#10622610C2211yescharacteristic
55C2×#66867C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57C11×#339C2211yescharacteristic
58C11×#339C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63#10622161C2211yescharacteristic
64#10622161C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—41no—
71C2×C11×M16—41no—
72C2×C11×M16C2311yescharacteristic
73C2×C11×M16C2311yescharacteristic
74C22×C8×C11—21no—
75C11×#123—21no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×C22⋊Q8C2×C411yescharacteristic
78C11×#121C2×C411yescharacteristic
79C11×#121C2×C411yescharacteristic
80C11×#120—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C11×#117C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88#67001—41no—
89#67001—41no—
90#66979—21no—
91#66979—21no—
92#66979C2×C411yescharacteristic
93#66979C2×C411yescharacteristic
94#66979C2311yescharacteristic
95#66979C2311yescharacteristic
96C2×C4⋊Dic11C2×C411yescharacteristic
97C2×C4⋊Dic11C2×C411yescharacteristic
98C2×C4×Dic11—21no—
99C2×#4318—21no—
100C2×#4318—41no—
101C2×#4318—41no—
102C2×#4318D411yescharacteristic
103C2×#4318D411yescharacteristic
104C2×#4318D411yescharacteristic
105C2×#4318D411yescharacteristic
106C2×#4318C2311yescharacteristic
107C2×#4318C2311yescharacteristic
108C22×C11⋊C8—21no—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C11×#104—41no—
114C11×#104—41no—
115C11×#95—21no—
116#66899C2×C411yescharacteristic
117#66899C2×C411yescharacteristic
118#66899C2×C411yescharacteristic
119#66899C2×C411yescharacteristic
120#66896C2×C411yescharacteristic
121#66896C2×C411yescharacteristic
122#66896C2×C411yescharacteristic
123#66896C2×C411yescharacteristic
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127C22⋊(C11⋊C8)—21no—
128C22⋊(C11⋊C8)C2×C411yescharacteristic
129C22⋊(C11⋊C8)C2×C411yescharacteristic
130C22⋊(C11⋊C8)C2×C411yescharacteristic
131C22⋊(C11⋊C8)C2×C411yescharacteristic
132#66886—41no—
133#66886—41no—
134Dic11⋊C8—21no—
135Dic11⋊C8—21no—
136Dic11⋊C8—21no—
137Dic11⋊C8—21no—
138Dic11⋊C8—21no—
139Dic11⋊C8—21no—
140Dic11⋊C8—21no—
141Dic11⋊C8—21no—
142#66872C2×C411yescharacteristic
143#66872C2×C411yescharacteristic
144#66872C2×C411yescharacteristic
145#66872C2×C411yescharacteristic
146#66871C2×C411yescharacteristic
147#66871C2×C411yescharacteristic
148#66871C2×C411yescharacteristic
149#66871C2×C411yescharacteristic
150C4⋊(C11⋊C8)—21no—
151C4⋊(C11⋊C8)—21no—
152#66867—21no—
153#66867—41no—
154C4×C11⋊C8—21no—
155C4×C11⋊C8—41no—
156#22097—111nomaximal, Sylow
157C24×C11#4111yescharacteristic
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C2×Q8×C11C22×C411yescharacteristic
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11C22×C411yescharacteristic
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C22×C411yescharacteristic
175C22×C4×C11C22×C411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11#4111yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×Dic11—21no—
181C22×Dic11—21no—
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C11×M16—42no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—42no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C4⋊C4C22×C411yescharacteristic
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C11×C22⋊C4—42no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—21no—
207C22⋊Dic11—21no—
208C22⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11C22×C411yescharacteristic
212C4⋊Dic11C22×C411yescharacteristic
213C4⋊Dic11C22×C411yescharacteristic
214C4⋊Dic11C22×C411yescharacteristic
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219#4318—21no—
220#4318—21no—
221#4318—21no—
222#4318—21no—
223#4318—41no—
224#4318—41no—
225#4318—41no—
226#4318—41no—
227#4318—42no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—42no—
239C2×C11⋊C8C22×C411yescharacteristic
240C2×C11⋊C8C22×C411yescharacteristic
241C2×C11⋊C8C22×C411yescharacteristic
242C2×C11⋊C8C22×C411yescharacteristic
243C2×C11⋊C8C2×D411yescharacteristic
244C2×C11⋊C8C2×D411yescharacteristic
245C2×C11⋊C8C2×D411yescharacteristic
246C2×C11⋊C8C2×D411yescharacteristic
247#3091—111no—
248#2930—111no—
249#2905—111no—
250#1946—111no—
251#1945—111no—
252#1938—111no—
253#1937—111no—
254#1922—111no—
255#1922—111no—
256#1871D1111yescharacteristic
257#1866—111no—
258#1866—111no—
259#1855—111no—
260#1826—111no—
261#1753—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11C4×D411yescharacteristic
268C23×C11C4×D411yescharacteristic
269C23×C11C2×#4111yescharacteristic
270Q8×C11—21no—
271Q8×C11—21no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—41no—
275D4×C11—41no—
276D4×C11—81no—
277D4×C11—81no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11C4×D411yescharacteristic
300C2×C4×C11C4×D411yescharacteristic
301C2×C4×C11C23×C411yescharacteristic
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11H(5,𝔽2)11yescharacteristic
304C2×C4×C11H(5,𝔽2)11yescharacteristic
305C2×C4×C112−1+411yescharacteristic
306C2×C4×C112−1+411yescharacteristic
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—81no—
312C2×Dic11—81no—
313C8×C11—41no—
314C8×C11—41no—
315C11⋊C8—21no—
316C11⋊C8—21no—
317C11⋊C8—21no—
318C11⋊C8—21no—
319C11⋊C8—21no—
320C11⋊C8—21no—
321C11⋊C8—21no—
322C11⋊C8—21no—
323C11⋊C8—41no—
324C11⋊C8—41no—
325C2×#131—111no—
326C22×M16—111no—
327C22×M16C2×D1111yescharacteristic
328#525C2×D1111yescharacteristic
329C2×#117—111no—
330#485—111no—
331#485—111no—
332#484—111no—
333#483—111no—
334#482—111no—
335#482—111no—
336#481—111no—
337#480—111no—
338#436—221no—
339#436—221no—
340#435—221no—
341#435—221no—
342C2×#108—111no—
343C2×#108—111no—
344#427—111no—
345#427—111no—
346#424—111no—
347#424—111no—
348#424—111no—
349#424—111no—
350#424—111no—
351#424—221no—
352#424—221no—
353#423—221no—
354#423—221no—
355C2×#104C2×D1111yescharacteristic
356C2×#104C2×D1111yescharacteristic
357#416—111no—
358#416—111no—
359#408—111no—
360#407—111no—
361C2×C22⋊C8—111no—
362#405—111no—
363C2×#97—111no—
364C2×C4×C8—111no—
365C4×C22⋊C4C2×D1111yescharacteristic
366#341—111no—
367#341—111no—
368#339—111no—
369#339—111no—
370#339—111no—
371#339—111no—
372#339C2×D1111yescharacteristic
373#339C2×D1111yescharacteristic
374#336—111no—
375#336—111no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—81no—
388C22×C11—81no—
389C22×C11C2×C4×D411yescharacteristic
390C22×C11#53911yescharacteristic
391C22×C11#53911yescharacteristic
392C4×C11—21no—
393C4×C11—21no—
394C4×C11—42no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—81no—
399C4×C11#52011yescharacteristic
400C4×C11#52011yescharacteristic
401C4×C11#53411yescharacteristic
402C4×C11#53611yescharacteristic
403Dic11—41no—
404Dic11—41no—
405Dic11—41no—
406Dic11—41no—
407C2×#41C22×D1111yescharacteristic
408C23×C4C22×D1111yescharacteristic
409#131—441no—
410#131—441no—
411C2×M16—21no—
412C2×M16—41no—
413C2×M16—41no—
414C2×M16—111no—
415C2×M16—111no—
416C2×M16—111no—
417C2×M16—111no—
418C2×M16—111no—
419C2×M16—111no—
420C2×M16—221no—
421C2×M16—441no—
422C2×M16—441no—
423C2×M16C22×D1111yescharacteristic
424C2×M16C22×D1111yescharacteristic
425C22×C8—21no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8—111no—
429C22×C8—111no—
430C22×C8—221no—
431#123—21no—
432C22⋊Q8C4×D1111yescharacteristic
433C22⋊Q8C4×D1111yescharacteristic
434#121C4×D1111yescharacteristic
435#121C4×D1111yescharacteristic
436#120—21no—
437C4×D4—21no—
438C4×D4—21no—
439#117—111no—
440#117—111no—
441#117—111no—
442#117—111no—
443#117—221no—
444#117—221no—
445#117C22×D1111yescharacteristic
446C2×C4⋊C4—111no—
447C2×C4⋊C4—111no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—221no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452C2×C42C22×D1111yescharacteristic
453#108—441no—
454#108—441no—
455#107—111no—
456#107—111no—
457#107—111no—
458#107—111no—
459#106—111no—
460#106—111no—
461#106—111no—
462#106—111no—
463C4⋊C8—221no—
464C4⋊C8—221no—
465C4⋊C8—221no—
466C4⋊C8—221no—
467C4⋊C8—221no—
468C4⋊C8—221no—
469C4⋊C8—221no—
470C4⋊C8—221no—
471C4⋊C8—221no—
472C4⋊C8—221no—
473#104—41no—
474#104—41no—
475#103—111no—
476#103—111no—
477#103—111no—
478#103—111no—
479#102—111no—
480#102—111no—
481#102—111no—
482#102—111no—
483C22⋊C8—111no—
484C22⋊C8—111no—
485C22⋊C8—111no—
486C22⋊C8—111no—
487C22⋊C8—221no—
488C22⋊C8—221no—
489C22⋊C8—221no—
490C22⋊C8—221no—
491#97—221no—
492#97—441no—
493C4×C8—221no—
494C4×C8—441no—
495#95—21no—
496C2×C11—21no—
497C2×C11—21no—
498C2×C11—41no—
499C2×C11—41no—
500C2×C11—81no—
501C2×C11#232211yescharacteristic
502C2×C11#295611yescharacteristic
503C2×C11#295711yescharacteristic
504C24#434111yescharacteristic
505#41—21no—
506#41—21no—
507#41—21no—
508#41—21no—
509C2×Q8C2×C4×D1111yescharacteristic
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4C2×C4×D1111yescharacteristic
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4C2×C4×D1111yescharacteristic
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4D4×D1111yescharacteristic
527C22×C4#434111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—42no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—221no—
538M16—441no—
539M16—441no—
540M16—441no—
541M16—441no—
542M16—442no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—42no—
546C2×C8—111no—
547C2×C8—111no—
548C2×C8—111no—
549C2×C8—111no—
550C2×C8—111no—
551C2×C8—111no—
552C2×C8—111no—
553C2×C8—111no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—442no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—111no—
568C4⋊C4—111no—
569C4⋊C4—111no—
570C4⋊C4—111no—
571C4⋊C4—221no—
572C4⋊C4—221no—
573C4⋊C4C2×C4×D1111yescharacteristic
574C4⋊C4C2×C4×D1111yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—21no—
580C22⋊C4—42no—
581C22⋊C4—221no—
582C22⋊C4—221no—
583C22⋊C4—221no—
584C22⋊C4—221no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—221no—
591C42—221no—
592C42—221no—
593C42—221no—
594C11#2209711yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23(C22⋊D11)⋊C411yescharacteristic
601C23(C22⋊D11)⋊C411yescharacteristic
602C23C2×#434111yescharacteristic
603Q8—21no—
604Q8—21no—
605D4—21no—
606D4—21no—
607D4—41no—
608D4—41no—
609D4—81no—
610D4—81no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—881no—
637C2×C4—881no—
638C2×C4(C22⋊D11)⋊C411yescharacteristic
639C2×C4(C22⋊D11)⋊C411yescharacteristic
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4#6704311yescharacteristic
645C2×C4#6704311yescharacteristic
646C8—41no—
647C8—41no—
648C8—221no—
649C8—221no—
650C8—221no—
651C8—221no—
652C8—221no—
653C8—221no—
654C8—221no—
655C8—221no—
656C8—441no—
657C8—441no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—81no—
670C22—81no—
671C22C2×(C22⋊D11)⋊C411yescharacteristic
672C22#1062313311yescharacteristic
673C22#1062313311yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—81no—
681C4—441no—
682C4—441no—
683C4—441no—
684C4—441no—
685C4#1062307711yescharacteristic
686C4#1062307711yescharacteristic
687C4#1062312011yescharacteristic
688C4#1062317911yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—81no—
694C2#1307129011yescharacteristic
695C2#1307752211yescharacteristic
696C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1871C2
socleC22×C11C2×C4×D4
prime radicalC11×#525C22
cosocleC22×C4×C11C24
hypercenter#1871D11
hypocenterC11#22097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
3. #13077179C2semidirect
4. #13069368C2semidirect
5. #13069363C2semidirect
6. #13069324C2semidirect
7. #13069317C2semidirect
8. #13069213C2semidirect
9. #13069213C2semidirect
10. #13068889C2semidirect
11. #13068889C2semidirect
12. #13068821C2semidirect
13. #13068716C2semidirect
14. #13068400C2semidirect
39. #10622658C4semidirect
40. #10622658C4semidirect
41. #10622657C4semidirect
42. #10622656C4semidirect
43. #10622648C4semidirect
44. #10622648C4semidirect
45. #10622647C4semidirect
46. #10622646C4semidirect
594. C11#22097semidirect

Maximal subgroups

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

subgroupindex
#130785252
#130773202
#130771792
#130693682
#130693632
#130693242
#130693172
#130692132
#130688892
#130688212
#130687162
#130684002
C11×#18712
#2209711