Finite Group Databasebeta

← #14765645

Subgroups — #14765645

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#13078529C211yesmaximal, characteristic
2#13077315C211yesmaximal, characteristic
3#13077180C211yesmaximal, characteristic, complemented
4#13069368C211yesmaximal, characteristic, complemented
5#13069363C211yesmaximal, characteristic, complemented
6#13069328C211yesmaximal, characteristic, complemented
7#13069321C211yesmaximal, characteristic, complemented
8#13069218C211yesmaximal, characteristic, complemented
9#13069218C211yesmaximal, characteristic, complemented
10#13068916C211yesmaximal, characteristic
11#13068892C211yesmaximal, characteristic, complemented
12#13068892C211yesmaximal, characteristic, complemented
13#13068820C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#1826C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17#10623322C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66960C2211yescharacteristic
21C11×#407C2211yescharacteristic
22C4×C11×C22⋊C4C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24#10622742C2211yescharacteristic
25C2×#66886C2211yescharacteristic
26C2×#66886C2211yescharacteristic
27#10622735C2211yescharacteristic
28#10622732C2211yescharacteristic
29#10622616C411yescharacteristic, complemented
30#10622616C411yescharacteristic, complemented
31#10622615C2211yescharacteristic
32#10622615C2211yescharacteristic
33#10622612—21no—
34#10622612—21no—
35#10622612C2211yescharacteristic
36#10622612C2211yescharacteristic
37#10622612C2211yescharacteristic
38#10622612C2211yescharacteristic
39#10622611C2211yescharacteristic
40#10622611C2211yescharacteristic
41#10622609C411yescharacteristic, complemented
42#10622609C411yescharacteristic, complemented
43#10622584C411yescharacteristic, complemented
44#10622583C411yescharacteristic, complemented
45#10622581C411yescharacteristic, complemented
46#10622580C411yescharacteristic, complemented
47C2×#66869C2211yescharacteristic
48C2×#66869C2211yescharacteristic
49#10622537—21no—
50#10622537—21no—
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622342—21no—
54#10622342—21no—
55#10622341—21no—
56#10622341—21no—
57C11×#339C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#339C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622196C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C11×#117—21no—
72C11×#117—21no—
73C11×#117C2×C411yescharacteristic
74C11×#117C2×C411yescharacteristic
75C11×#117C2311yescharacteristic
76C11×#117C2311yescharacteristic
77C2×C11×C4⋊C4C2×C411yescharacteristic
78C2×C11×C4⋊C4C2×C411yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84#67006—21no—
85#66983C2×C411yescharacteristic
86#66983C2×C411yescharacteristic
87#66982—21no—
88C4×C22⋊D11—21no—
89C4×C22⋊D11—21no—
90#66979C2311yescharacteristic
91#66977C2×C411yescharacteristic
92#66977C2×C411yescharacteristic
93C2×#4318—21no—
94C2×#4318—41no—
95C2×#4318—41no—
96C2×#4318—41no—
97C2×#4318—41no—
98C2×#4318D411yescharacteristic
99C2×#4318D411yescharacteristic
100C2×#4318D411yescharacteristic
101C2×#4318D411yescharacteristic
102C2×#4318C2311yescharacteristic
103C2×#4318C2311yescharacteristic
104C22×C11⋊C8—21no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66960—41no—
110#66960—41no—
111C2×#4313—21no—
112C2×C8×D11—21no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×#95—21no—
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)C2×C411yescharacteristic
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120#66886—41no—
121#66886—41no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127C8×Dic11—21no—
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66874C2×C411yescharacteristic
131#66874C2×C411yescharacteristic
132#66873C2×C411yescharacteristic
133#66873C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139#66872C2×C411yescharacteristic
140#66871C2×C411yescharacteristic
141#66871C2×C411yescharacteristic
142#66871C2×C411yescharacteristic
143#66871C2×C411yescharacteristic
144#66869—41no—
145#66869—41no—
146C4⋊(C11⋊C8)—21no—
147C4⋊(C11⋊C8)—21no—
148C4⋊(C11⋊C8)—21no—
149C4⋊(C11⋊C8)—21no—
150C4⋊(C11⋊C8)—21no—
151C4⋊(C11⋊C8)—21no—
152C4⋊(C11⋊C8)—21no—
153C4⋊(C11⋊C8)—21no—
154#66867—41no—
155C4×C11⋊C8—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×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11#4111yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—21no—
173C2×C22⋊D11—21no—
174C2×C22⋊D11—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—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C22×C411yescharacteristic
191C11×C4⋊C4C22×C411yescharacteristic
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—42no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C22⋊Dic11—21no—
208C22⋊Dic11—21no—
209C22⋊Dic11—21no—
210(C2×D11)⋊C4—21no—
211(C2×D11)⋊C4—21no—
212C4⋊Dic11C22×C411yescharacteristic
213C4⋊Dic11C22×C411yescharacteristic
214Dic11⋊C4—21no—
215Dic11⋊C4—21no—
216C4×Dic11—21no—
217#4318—21no—
218#4318—21no—
219#4318—21no—
220#4318—21no—
221#4318—41no—
222#4318—41no—
223#4318—41no—
224#4318—41no—
225#4318—42no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
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—42no—
237C2×C11⋊C8C22×C411yescharacteristic
238C2×C11⋊C8C22×C411yescharacteristic
239C2×C11⋊C8C22×C411yescharacteristic
240C2×C11⋊C8C22×C411yescharacteristic
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#1855—111no—
260#1826D1111yescharacteristic, complemented
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×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—81no—
291C2×C4×C11—81no—
292C2×C4×C11C4×D411yescharacteristic
293C2×C4×C11C4×D411yescharacteristic
294C2×C4×C11C23×C411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11H(5,𝔽2)11yescharacteristic
297C2×C4×C11H(5,𝔽2)11yescharacteristic
298C2×C4×C112−1+411yescharacteristic
299C2×C4×C112−1+411yescharacteristic
300C22⋊D11—41no—
301C22⋊D11—41no—
302C22⋊D11—81no—
303C22⋊D11—81no—
304C2×Dic11—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307D44—21no—
308D44—21no—
309C4×D11—41no—
310C4×D11—41no—
311Dic22—21no—
312Dic22—21no—
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×M16—111no—
328#525—111no—
329C2×#117C2×D1111yescharacteristic
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#407C2×D1111yescharacteristic
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#339C2×D1111yescharacteristic
371#339C2×D1111yescharacteristic
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—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—41no—
396C4×C11—41no—
397C4×C11—41no—
398C4×C11—41no—
399C4×C11—81no—
400C4×C11#52011yescharacteristic
401C4×C11#52011yescharacteristic
402C4×C11#53411yescharacteristic
403C4×C11#53611yescharacteristic
404Dic11—41no—
405Dic11—41no—
406Dic11—41no—
407C2×#41—111no—
408C23×C4C22×D1111yescharacteristic
409#131—441no—
410#131—441no—
411C2×M16—111no—
412C2×M16—111no—
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×M16—441no—
422C2×M16—441no—
423C2×M16C22×D1111yescharacteristic
424C2×M16C22×D1111yescharacteristic
425C22×C8—111no—
426C22×C8—111no—
427C22×C8—111no—
428C22×C8—111no—
429C22×C8—221no—
430C22×C8—221no—
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—21no—
440#117—21no—
441#117—111no—
442#117C4×D1111yescharacteristic
443#117C4×D1111yescharacteristic
444#117C22×D1111yescharacteristic
445#117C22×D1111yescharacteristic
446C2×C4⋊C4C4×D1111yescharacteristic
447C2×C4⋊C4C4×D1111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C42—21no—
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—21no—
484C22⋊C8—21no—
485C22⋊C8—111no—
486C22⋊C8—111no—
487C22⋊C8—111no—
488C22⋊C8—111no—
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#232211yescharacteristic
501C2×C11#295611yescharacteristic
502C2×C11#295711yescharacteristic
503D11—81no—
504C24#434111yescharacteristic
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—21no—
521C22×C4—21no—
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—221no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—442no—
538M16—441no—
539M16—441no—
540M16—441no—
541M16—441no—
542M16—442no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—111no—
546C2×C8—111no—
547C2×C8—111no—
548C2×C8—111no—
549C2×C8—111no—
550C2×C8—111no—
551C2×C8—111no—
552C2×C8—111no—
553C2×C8—221no—
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—442no—
564C2×C8—442no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—111no—
568C4⋊C4—111no—
569C4⋊C4—221no—
570C4⋊C4—221no—
571C4⋊C4C2×C4×D1111yescharacteristic
572C4⋊C4C2×C4×D1111yescharacteristic
573C4⋊C4C2×C4×D1111yescharacteristic
574C4⋊C4C2×C4×D1111yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—42no—
580C22⋊C4—221no—
581C22⋊C4—221no—
582C22⋊C4—221no—
583C22⋊C4—221no—
584C22⋊C4—221no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—221no—
594C11#2209711yescharacteristic, complemented, Sylow
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—221no—
600C23(C22⋊D11)⋊C411yescharacteristic
601C23(C22⋊D11)⋊C411yescharacteristic
602C23C2×#434111yescharacteristic
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—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4(C22⋊D11)⋊C411yescharacteristic
639C2×C4(C22⋊D11)⋊C411yescharacteristic
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4#6704211yescharacteristic
643C2×C4#6704211yescharacteristic
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—81no—
667C22—81no—
668C22—441no—
669C22—441no—
670C22—441no—
671C22C2×(C22⋊D11)⋊C411yescharacteristic
672C22#1062319611yescharacteristic
673C22#1062319611yescharacteristic
674C4—21no—
675C4—21no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—41no—
681C4—81no—
682C4—441no—
683C4—441no—
684C4—441no—
685C4#1062305411yescharacteristic
686C4#1062305411yescharacteristic
687C4#1062317911yescharacteristic
688C4#1062318411yescharacteristic
689C2—21no—
690C2—21no—
691C2—41no—
692C2—41no—
693C2—881no—
694C2#1307128211yescharacteristic
695C2#1307752211yescharacteristic
696C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1826C2
socleC22×C11C2×C4×D4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenter#1826D11
hypocenterC11#22097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. #13077180C2semidirect
4. #13069368C2semidirect
5. #13069363C2semidirect
6. #13069328C2semidirect
7. #13069321C2semidirect
8. #13069218C2semidirect
9. #13069218C2semidirect
11. #13068892C2semidirect
12. #13068892C2semidirect
13. #13068820C2semidirect
14. #13068400C2semidirect
15. C11×#1826C2semidirect
29. #10622616C4semidirect
30. #10622616C4semidirect
41. #10622609C4semidirect
42. #10622609C4semidirect
43. #10622584C4semidirect
44. #10622583C4semidirect
45. #10622581C4semidirect
46. #10622580C4semidirect
260. #1826D11semidirect
594. C11#22097semidirect

Maximal subgroups

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

subgroupindex
#130785292
#130773152
#130771802
#130693682
#130693632
#130693282
#130693212
#130692182
#130689162
#130688922
#130688202
#130684002
C11×#18262
#2209711