Finite Group Databasebeta

← #14765651

Subgroups — #14765651

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#13077319C211yesmaximal, characteristic
3#13077179C211yesmaximal, characteristic, complemented
4#13069369C211yesmaximal, characteristic, complemented
5#13069364C211yesmaximal, characteristic, complemented
6#13069327C211yesmaximal, characteristic, complemented
7#13069320C211yesmaximal, characteristic, complemented
8#13069216C211yesmaximal, characteristic, complemented
9#13069216C211yesmaximal, characteristic, complemented
10#13068916C211yesmaximal, characteristic
11#13068894C211yesmaximal, characteristic, complemented
12#13068894C211yesmaximal, characteristic, complemented
13#13068823C211yesmaximal, characteristic, complemented
14#13068716C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17#10623322C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66954C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C22⋊C4C2211yescharacteristic
25#10622820C2211yescharacteristic
26#10622741—21no—
27#10622741—21no—
28#10622740—21no—
29#10622740—21no—
30#10622732—21no—
31#10622732—21no—
32#10622731—21no—
33#10622731—21no—
34#10622726C2211yescharacteristic
35#10622726C2211yescharacteristic
36#10622723C2211yescharacteristic
37C2×#66883C2211yescharacteristic
38C2×#66883C2211yescharacteristic
39#10622719C2211yescharacteristic
40#10622719C2211yescharacteristic
41#10622715C2211yescharacteristic
42#10622715C2211yescharacteristic
43#10622715C2211yescharacteristic
44#10622715C2211yescharacteristic
45#10622715C2211yescharacteristic
46#10622714C2211yescharacteristic
47C2×#66869C2211yescharacteristic
48C2×#66869C2211yescharacteristic
49#10622350C411yescharacteristic, complemented
50#10622350C411yescharacteristic, complemented
51#10622349C411yescharacteristic, complemented
52#10622348C411yescharacteristic, complemented
53#10622336C411yescharacteristic, complemented
54#10622336C411yescharacteristic, complemented
55#10622335C411yescharacteristic, complemented
56#10622334C411yescharacteristic, complemented
57C11×#336C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622190C2211yescharacteristic
60#10622190C2211yescharacteristic
61#10622161C2211yescharacteristic
62#10622161C2211yescharacteristic
63#10622161C2211yescharacteristic
64#10622161C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C2×C11×M16—41no—
70C2×C11×M16—41no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C2×C11×M16D411yescharacteristic
74C2×C11×M16D411yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82#67006—21no—
83C2×C22⋊Dic11—21no—
84#66983C2×C411yescharacteristic
85#66983C2×C411yescharacteristic
86#66982—21no—
87C4×C22⋊D11—21no—
88C4×C22⋊D11—21no—
89#66979—21no—
90#66979—21no—
91#66979C2×C411yescharacteristic
92#66979C2×C411yescharacteristic
93#66979C2311yescharacteristic
94#66979C2311yescharacteristic
95#66979C2311yescharacteristic
96C2×C4⋊Dic11C2×C411yescharacteristic
97C2×C4⋊Dic11C2×C411yescharacteristic
98#66977C2×C411yescharacteristic
99#66977C2×C411yescharacteristic
100C2×C4×Dic11—21no—
101C2×#4318—21no—
102C2×#4318—41no—
103C2×#4318—41no—
104C2×#4318C2311yescharacteristic
105C2×#4318C2311yescharacteristic
106C2×#4318C2311yescharacteristic
107C2×#4318C2311yescharacteristic
108C22×C11⋊C8—21no—
109#66954—41no—
110#66954—41no—
111C2×#4313—21no—
112C2×C8×D11—21no—
113C11×C22⋊C8C2×C411yescharacteristic
114C11×C22⋊C8C2×C411yescharacteristic
115C11×C22⋊C8C2×C411yescharacteristic
116C11×C22⋊C8C2×C411yescharacteristic
117C11×#97—41no—
118C4×C8×C11—41no—
119C11×#95—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66885C2×C411yescharacteristic
123#66885C2×C411yescharacteristic
124#66885C2×C411yescharacteristic
125#66885C2×C411yescharacteristic
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128#66883—41no—
129#66883—41no—
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—
143Dic11⋊C8—21no—
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—
153C8×Dic11—21no—
154#66869—41no—
155#66869—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×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C22×C411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—21no—
171C2×C22⋊D11—21no—
172C2×C22⋊D11—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—41no—
183C11×M16—41no—
184C11×M16—41no—
185C11×M16—41no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11C22×C411yescharacteristic
195C2×C8×C11C22×C411yescharacteristic
196C2×C8×C11C22×C411yescharacteristic
197C2×C8×C11C22×C411yescharacteristic
198C2×C8×C11C2×D411yescharacteristic
199C2×C8×C11C2×D411yescharacteristic
200C2×C8×C11C2×D411yescharacteristic
201C2×C8×C11C2×D411yescharacteristic
202C11×C22⋊C4—42no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C22⋊Dic11—21no—
208C22⋊Dic11—21no—
209C22⋊Dic11—21no—
210C22⋊Dic11—21no—
211C22⋊Dic11—21no—
212C22⋊Dic11—21no—
213C22⋊Dic11—21no—
214(C2×D11)⋊C4—21no—
215(C2×D11)⋊C4—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11C22×C411yescharacteristic
219C4⋊Dic11C22×C411yescharacteristic
220C4⋊Dic11C22×C411yescharacteristic
221C4⋊Dic11C22×C411yescharacteristic
222C4⋊Dic11C22×C411yescharacteristic
223C4⋊Dic11C22×C411yescharacteristic
224Dic11⋊C4—21no—
225Dic11⋊C4—21no—
226C4×Dic11—21no—
227C4×Dic11—21no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231#4318—21no—
232#4318—21no—
233#4318—21no—
234#4318—21no—
235#4318—21no—
236#4318—21no—
237#4318—21no—
238#4318—21no—
239#4318—42no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—42no—
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#1855—111no—
260#1826—111no—
261#1753D1111yescharacteristic, complemented
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×C11—22no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11C4×D411yescharacteristic
287C2×C4×C11C4×D411yescharacteristic
288C2×C4×C11C23×C411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C112−1+411yescharacteristic
293C2×C4×C112−1+411yescharacteristic
294C22⋊D11—41no—
295C22⋊D11—41no—
296C22⋊D11—81no—
297C22⋊D11—81no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—21no—
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—21no—
318C8×C11—21no—
319C8×C11—21no—
320C8×C11—21no—
321C11⋊C8—41no—
322C11⋊C8—41no—
323C11⋊C8—41no—
324C11⋊C8—41no—
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×#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×#104—111no—
356C2×#104—111no—
357#416—111no—
358#416—111no—
359#408—111no—
360#407—111no—
361C2×C22⋊C8C2×D1111yescharacteristic
362#405—111no—
363C2×#97C2×D1111yescharacteristic
364C2×C4×C8C2×D1111yescharacteristic
365C4×C22⋊C4C2×D1111yescharacteristic
366#341—111no—
367#341—111no—
368#339—111no—
369#339—111no—
370#339—111no—
371#339—111no—
372#339—111no—
373#339—111no—
374#336C2×D1111yescharacteristic
375#336C2×D1111yescharacteristic
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—42no—
395C4×C11—81no—
396C4×C11#52011yescharacteristic
397C4×C11#52011yescharacteristic
398C4×C11#53411yescharacteristic
399C4×C11#53611yescharacteristic
400Dic11—41no—
401Dic11—41no—
402Dic11—41no—
403Dic11—41no—
404Dic11—41no—
405Dic11—41no—
406Dic11—41no—
407C2×#41—111no—
408C23×C4C22×D1111yescharacteristic
409#131—441no—
410#131—441no—
411C2×M16—41no—
412C2×M16—41no—
413C2×M16—111no—
414C2×M16—111no—
415C2×M16—111no—
416C2×M16—111no—
417C2×M16—221no—
418C2×M16—221no—
419C2×M16—441no—
420C2×M16—441no—
421C2×M16D4411yescharacteristic
422C2×M16D4411yescharacteristic
423C2×M16D4411yescharacteristic
424C2×M16D4411yescharacteristic
425C22×C8—221no—
426C22×C8—221no—
427C22×C8C22×D1111yescharacteristic
428C22×C8C22×D1111yescharacteristic
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—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—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—221no—
484C22⋊C8—221no—
485C22⋊C8—221no—
486C22⋊C8—221no—
487C22⋊C8C4×D1111yescharacteristic
488C22⋊C8C4×D1111yescharacteristic
489C22⋊C8C4×D1111yescharacteristic
490C22⋊C8C4×D1111yescharacteristic
491#97—41no—
492#97—221no—
493C4×C8—41no—
494C4×C8—221no—
495#95—21no—
496C2×C11—21no—
497C2×C11—21no—
498C2×C11—41no—
499C2×C11—41no—
500C2×C11#232211yescharacteristic
501C2×C11#295611yescharacteristic
502C2×C11#295711yescharacteristic
503D11—81no—
504C24#433911yescharacteristic
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—21no—
519C22×C4—21no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4C2×C4×D1111yescharacteristic
524C22×C4C2×C4×D1111yescharacteristic
525C22×C4C2×D4411yescharacteristic
526C22×C4C2×D4411yescharacteristic
527C22×C4#433911yescharacteristic
528C22×C4C23×D1111yescharacteristic
529M16—41no—
530M16—41no—
531M16—41no—
532M16—41no—
533M16—221no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—221no—
538M16—221no—
539M16—221no—
540M16—221no—
541M16—442no—
542M16—442no—
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—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—442no—
556C2×C8—442no—
557C2×C8C2×C4×D1111yescharacteristic
558C2×C8C2×C4×D1111yescharacteristic
559C2×C8C2×C4×D1111yescharacteristic
560C2×C8C2×C4×D1111yescharacteristic
561C2×C8C2×D4411yescharacteristic
562C2×C8C2×D4411yescharacteristic
563C2×C8C2×D4411yescharacteristic
564C2×C8C2×D4411yescharacteristic
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—42no—
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—221no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—221no—
590C42—221no—
591C42—221no—
592C42—221no—
593C42—221no—
594C11#2209711yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—221no—
600C23C4×D4411yescharacteristic
601C23C4×D4411yescharacteristic
602C23C2×#433911yescharacteristic
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—22no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—881no—
637C2×C4—881no—
638C2×C4C4×D4411yescharacteristic
639C2×C4C4×D4411yescharacteristic
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C22×D4411yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4#6704311yescharacteristic
645C2×C4#6704311yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—21no—
651C8—21no—
652C8—21no—
653C8—21no—
654C8—441no—
655C8—441no—
656C8—441no—
657C8—441no—
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×C4×D4411yescharacteristic
672C22#1062309511yescharacteristic
673C22#1062309511yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—81no—
678C4—441no—
679C4—441no—
680C4—441no—
681C4—441no—
682C4—441no—
683C4—441no—
684C4—441no—
685C4#1062302411yescharacteristic
686C4#1062305711yescharacteristic
687C4#1062307711yescharacteristic
688C4#1062307711yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—881no—
694C2#1307128711yescharacteristic
695C2#1307752711yescharacteristic
696C2#1307753411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC22×C11C2×C4×D4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×M16 ◁ #1753

Complements

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

NH ≅ G/Ntype
3. #13077179C2semidirect
4. #13069369C2semidirect
5. #13069364C2semidirect
6. #13069327C2semidirect
7. #13069320C2semidirect
8. #13069216C2semidirect
9. #13069216C2semidirect
11. #13068894C2semidirect
12. #13068894C2semidirect
13. #13068823C2semidirect
14. #13068716C2semidirect
15. C11×#1753C2semidirect
49. #10622350C4semidirect
50. #10622350C4semidirect
51. #10622349C4semidirect
52. #10622348C4semidirect
53. #10622336C4semidirect
54. #10622336C4semidirect
55. #10622335C4semidirect
56. #10622334C4semidirect
261. #1753D11semidirect
594. C11#22097semidirect

Maximal subgroups

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

subgroupindex
#130785312
#130773192
#130771792
#130693692
#130693642
#130693272
#130693202
#130692162
#130689162
#130688942
#130688232
#130687162
C11×#17532
#2209711