Finite Group Databasebeta

← #14765647

Subgroups — #14765647

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#13078531C211yesmaximal, characteristic
2#13077315C211yesmaximal, characteristic
3#13077179C211yesmaximal, characteristic, complemented
4#13069367C211yesmaximal, characteristic, complemented
5#13069362C211yesmaximal, characteristic, complemented
6#13069325C211yesmaximal, characteristic, complemented
7#13069318C211yesmaximal, characteristic, complemented
8#13069214C211yesmaximal, characteristic, complemented
9#13069214C211yesmaximal, characteristic, complemented
10#13068918C211yesmaximal, characteristic
11#13068888C211yesmaximal, characteristic, complemented
12#13068888C211yesmaximal, characteristic, complemented
13#13068713C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1855C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17#10623322C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66960C2211yescharacteristic
21C2×C11×#108C2211yescharacteristic
22C2×C11×#108C2211yescharacteristic
23C11×#407C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C22⋊Dic11C2211yescharacteristic
26C2×#66889C2211yescharacteristic
27C2×#66889C2211yescharacteristic
28#10622742C2211yescharacteristic
29#10622735C2211yescharacteristic
30#10622732C2211yescharacteristic
31#10622732C2211yescharacteristic
32#10622732C2211yescharacteristic
33#10622732C2211yescharacteristic
34#10622732C2211yescharacteristic
35#10622731—21no—
36#10622731—21no—
37#10622726C2211yescharacteristic
38#10622726C2211yescharacteristic
39#10622719C2211yescharacteristic
40#10622719C2211yescharacteristic
41#10622715—21no—
42#10622715—21no—
43C2×#66879C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45#10622350C411yescharacteristic, complemented
46#10622350C411yescharacteristic, complemented
47#10622349C411yescharacteristic, complemented
48#10622348C411yescharacteristic, complemented
49#10622342—21no—
50#10622342—21no—
51#10622341—21no—
52#10622341—21no—
53#10622336C411yescharacteristic, complemented
54#10622336C411yescharacteristic, complemented
55#10622335C411yescharacteristic, complemented
56#10622334C411yescharacteristic, complemented
57C11×#341C2211yescharacteristic
58C11×#341C2211yescharacteristic
59#10622193C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622193C2211yescharacteristic
63#10622193C2211yescharacteristic
64#10622193C2211yescharacteristic
65#10622188C2211yescharacteristic
66#10622188C2211yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C2×C11×M16—21no—
70C2×C11×M16—41no—
71C2×C11×M16—41no—
72C2×C11×M16C2311yescharacteristic
73C2×C11×M16C2311yescharacteristic
74C2×C11×M16C2311yescharacteristic
75C2×C11×M16C2311yescharacteristic
76C22×C8×C11—21no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79#67006—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#66983C2×C411yescharacteristic
83#66983C2×C411yescharacteristic
84#66982—21no—
85C4×C22⋊D11—21no—
86C4×C22⋊D11—21no—
87#66979—21no—
88#66979—21no—
89#66979C2×C411yescharacteristic
90#66979C2×C411yescharacteristic
91#66979C2311yescharacteristic
92#66979C2311yescharacteristic
93#66979C2311yescharacteristic
94C2×C4⋊Dic11C2×C411yescharacteristic
95C2×C4⋊Dic11C2×C411yescharacteristic
96#66977C2×C411yescharacteristic
97#66977C2×C411yescharacteristic
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×#4318—41no—
102C2×#4318—41no—
103C2×#4318D411yescharacteristic
104C2×#4318D411yescharacteristic
105C2×#4318D411yescharacteristic
106C2×#4318D411yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66960—41no—
110#66960—41no—
111C2×#4313—21no—
112C2×C8×D11—21no—
113C11×#108—41no—
114C11×#108—41no—
115C11×C22⋊C8—21no—
116C11×C22⋊C8—21no—
117C11×C22⋊C8C2×C411yescharacteristic
118C11×C22⋊C8C2×C411yescharacteristic
119C11×C22⋊C8C2×C411yescharacteristic
120C11×C22⋊C8C2×C411yescharacteristic
121C11⋊#95—21no—
122#66889—41no—
123#66889—41no—
124#66885C2×C411yescharacteristic
125#66885C2×C411yescharacteristic
126#66885C2×C411yescharacteristic
127#66885C2×C411yescharacteristic
128(C2×D11)⋊C8—21no—
129(C2×D11)⋊C8—21no—
130#66882C2×C411yescharacteristic
131#66882C2×C411yescharacteristic
132#66882C2×C411yescharacteristic
133#66882C2×C411yescharacteristic
134#66881C2×C411yescharacteristic
135#66881C2×C411yescharacteristic
136#66881C2×C411yescharacteristic
137#66881C2×C411yescharacteristic
138#66880C2×C411yescharacteristic
139#66880C2×C411yescharacteristic
140#66880C2×C411yescharacteristic
141#66880C2×C411yescharacteristic
142#66879—21no—
143#66879—41no—
144Dic11⋊C8—21no—
145Dic11⋊C8—21no—
146Dic11⋊C8—21no—
147Dic11⋊C8—21no—
148Dic11⋊C8—21no—
149Dic11⋊C8—21no—
150Dic11⋊C8—21no—
151Dic11⋊C8—21no—
152Dic11⋊C8—21no—
153Dic11⋊C8—21no—
154C8×Dic11—21no—
155C8×Dic11—41no—
156#22097—111nomaximal, Sylow
157C24×C11#4111yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11C22×C411yescharacteristic
163C22×C4×C11C22×C411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—21no—
169C2×C22⋊D11—21no—
170C2×C22⋊D11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175#4339—21no—
176#4339—21no—
177#4339—21no—
178#4339—21no—
179C2×D44C22×C411yescharacteristic
180C2×C4×D11—21no—
181C2×Dic22C22×C411yescharacteristic
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C11×M16—21no—
187C11×M16—21no—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16—42no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—42no—
200C2×C8×C11C22×C411yescharacteristic
201C2×C8×C11C22×C411yescharacteristic
202C2×C8×C11C22×C411yescharacteristic
203C2×C8×C11C22×C411yescharacteristic
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—21no—
207C22⋊Dic11—21no—
208C22⋊Dic11—21no—
209C22⋊Dic11—21no—
210C22⋊Dic11—21no—
211C22⋊Dic11—42no—
212(C2×D11)⋊C4—21no—
213(C2×D11)⋊C4—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11C22×C411yescharacteristic
217C4⋊Dic11C22×C411yescharacteristic
218C4⋊Dic11C22×C411yescharacteristic
219C4⋊Dic11C22×C411yescharacteristic
220C4⋊Dic11C22×C411yescharacteristic
221C4⋊Dic11C22×C411yescharacteristic
222Dic11⋊C4—21no—
223Dic11⋊C4—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233#4318—41no—
234#4318—41no—
235#4318—41no—
236#4318—41no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8C2×D411yescharacteristic
242C2×C11⋊C8C2×D411yescharacteristic
243C2×C11⋊C8C2×D411yescharacteristic
244C2×C11⋊C8C2×D411yescharacteristic
245#4313—42no—
246C8×D11—42no—
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#1871—111no—
257#1866—111no—
258#1866—111no—
259#1855D1111yescharacteristic, complemented
260#1826—111no—
261#1753—111no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11C4×D411yescharacteristic
267C23×C11C4×D411yescharacteristic
268C23×C11C2×#4111yescharacteristic
269C22×D11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11C4×D411yescharacteristic
281C2×C4×C11C4×D411yescharacteristic
282C2×C4×C11C23×C411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C112−1+411yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C22⋊D11—41no—
289C22⋊D11—41no—
290C22⋊D11—81no—
291C22⋊D11—81no—
292C2×Dic11—22no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—81no—
306C2×Dic11—81no—
307D44—21no—
308D44—21no—
309C4×D11—41no—
310C4×D11—41no—
311Dic22—21no—
312Dic22—21no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—21no—
316C8×C11—21no—
317C8×C11—41no—
318C8×C11—41no—
319C8×C11—41no—
320C8×C11—41no—
321C11⋊C8—21no—
322C11⋊C8—21no—
323C11⋊C8—21no—
324C11⋊C8—21no—
325C2×#131—111no—
326C22×M16—111no—
327C22×M16C2×D1111yescharacteristic
328#525—111no—
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×#108C2×D1111yescharacteristic
343C2×#108C2×D1111yescharacteristic
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×#104—111no—
356C2×#104—111no—
357#416—111no—
358#416—111no—
359#408—111no—
360#407C2×D1111yescharacteristic
361C2×C22⋊C8C2×D1111yescharacteristic
362#405—111no—
363C2×#97—111no—
364C2×C4×C8—111no—
365C4×C22⋊C4—111no—
366#341C2×D1111yescharacteristic
367#341C2×D1111yescharacteristic
368#339—111no—
369#339—111no—
370#339—111no—
371#339—111no—
372#339—111no—
373#339—111no—
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—81no—
385C22×C11—81no—
386C22×C11C2×C4×D411yescharacteristic
387C22×C11#53911yescharacteristic
388C22×C11#53911yescharacteristic
389C2×D11—41no—
390C2×D11—41no—
391C2×D11—41no—
392C4×C11—21no—
393C4×C11—21no—
394C4×C11#52011yescharacteristic
395C4×C11#52011yescharacteristic
396C4×C11#53411yescharacteristic
397C4×C11#53611yescharacteristic
398Dic11—42no—
399Dic11—41no—
400Dic11—41no—
401Dic11—41no—
402Dic11—41no—
403Dic11—41no—
404Dic11—41no—
405Dic11—41no—
406Dic11—81no—
407C2×#41—111no—
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—221no—
419C2×M16—441no—
420C2×M16—441no—
421C2×M16C22×D1111yescharacteristic
422C2×M16C22×D1111yescharacteristic
423C2×M16C22×D1111yescharacteristic
424C2×M16C22×D1111yescharacteristic
425C22×C8—21no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8—221no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431#123—221no—
432C22⋊Q8—111no—
433C22⋊Q8—111no—
434#121—111no—
435#121—111no—
436#120—221no—
437C4×D4—221no—
438C4×D4—221no—
439#117—111no—
440#117—111no—
441#117—111no—
442#117—111no—
443#117—111no—
444#117—221no—
445#117—221no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4—111no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—221no—
453#108—41no—
454#108—41no—
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—441no—
474#104—441no—
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—21no—
484C22⋊C8—21no—
485C22⋊C8—221no—
486C22⋊C8—221no—
487C22⋊C8C4×D1111yescharacteristic
488C22⋊C8C4×D1111yescharacteristic
489C22⋊C8C4×D1111yescharacteristic
490C22⋊C8C4×D1111yescharacteristic
491#97—221no—
492#97—441no—
493C4×C8—221no—
494C4×C8—441no—
495#95—221no—
496C2×C11—21no—
497C2×C11—21no—
498C2×C11—41no—
499C2×C11—41no—
500C2×C11#232211yescharacteristic
501C2×C11#295611yescharacteristic
502C2×C11#295711yescharacteristic
503D11—81no—
504C24#434311yescharacteristic
505#41—221no—
506#41—221no—
507#41—221no—
508#41—221no—
509C2×Q8—111no—
510C2×D4—111no—
511C2×D4—221no—
512C2×D4—221no—
513C2×D4—221no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4C2×C4×D1111yescharacteristic
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4D4×D1111yescharacteristic
527C22×C4#434311yescharacteristic
528C22×C4C23×D1111yescharacteristic
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16—42no—
538M16—442no—
539M16—441no—
540M16—441no—
541M16—441no—
542M16—441no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—42no—
552C2×C8—111no—
553C2×C8—111no—
554C2×C8—111no—
555C2×C8—111no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—442no—
561C2×C8C2×C4×D1111yescharacteristic
562C2×C8C2×C4×D1111yescharacteristic
563C2×C8C2×C4×D1111yescharacteristic
564C2×C8C2×C4×D1111yescharacteristic
565C4⋊C4—111no—
566C4⋊C4—111no—
567C4⋊C4—111no—
568C4⋊C4—111no—
569C4⋊C4—111no—
570C4⋊C4—111no—
571C4⋊C4—221no—
572C4⋊C4—221no—
573C4⋊C4—221no—
574C4⋊C4—221no—
575C22⋊C4—221no—
576C22⋊C4—221no—
577C22⋊C4—221no—
578C22⋊C4—221no—
579C22⋊C4—221no—
580C22⋊C4—221no—
581C22⋊C4—221no—
582C22⋊C4—221no—
583C22⋊C4—221no—
584C22⋊C4—442no—
585C42—221no—
586C42—221no—
587C42—221no—
588C42—221no—
589C42—221no—
590C42—221no—
591C42—221no—
592C42—221no—
593C42—221no—
594C11#2209711yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—221no—
600C23#6694611yescharacteristic
601C23#6694611yescharacteristic
602C23C2×#434311yescharacteristic
603Q8—221no—
604Q8—221no—
605D4—221no—
606D4—221no—
607D4—441no—
608D4—441no—
609D4—881no—
610D4—881no—
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—222no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—881no—
637C2×C4—881no—
638C2×C4#6694611yescharacteristic
639C2×C4#6694611yescharacteristic
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4#6704311yescharacteristic
645C2×C4#6704311yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—41no—
651C8—41no—
652C8—41no—
653C8—41no—
654C8—221no—
655C8—221no—
656C8—221no—
657C8—221no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—81no—
667C22—81no—
668C22—441no—
669C22—441no—
670C22—441no—
671C22C2×#6694611yescharacteristic
672C22#1062317611yescharacteristic
673C22#1062317611yescharacteristic
674C4—21no—
675C4—21no—
676C4—442no—
677C4—441no—
678C4—441no—
679C4—441no—
680C4—441no—
681C4—441no—
682C4—441no—
683C4—441no—
684C4—881no—
685C4#1062307711yescharacteristic
686C4#1062307711yescharacteristic
687C4#1062312011yescharacteristic
688C4#1062317911yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—881no—
694C2#1307128411yescharacteristic
695C2#1307752511yescharacteristic
696C2#1307753211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1855C2
socleC22×C11C2×C4×D4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenter#1855D11
hypocenterC11#22097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
3. #13077179C2semidirect
4. #13069367C2semidirect
5. #13069362C2semidirect
6. #13069325C2semidirect
7. #13069318C2semidirect
8. #13069214C2semidirect
9. #13069214C2semidirect
11. #13068888C2semidirect
12. #13068888C2semidirect
13. #13068713C2semidirect
14. #13068402C2semidirect
15. C11×#1855C2semidirect
45. #10622350C4semidirect
46. #10622350C4semidirect
47. #10622349C4semidirect
48. #10622348C4semidirect
53. #10622336C4semidirect
54. #10622336C4semidirect
55. #10622335C4semidirect
56. #10622334C4semidirect
259. #1855D11semidirect
594. C11#22097semidirect

Maximal subgroups

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

subgroupindex
#130785312
#130773152
#130771792
#130693672
#130693622
#130693252
#130693182
#130692142
#130689182
#130688882
#130687132
#130684022
C11×#18552
#2209711