Finite Group Databasebeta

← #14757005

Subgroups — #14757005

Order 2816.

772 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077417C211yesmaximal, characteristic
2#13077256C211yesmaximal, characteristic, complemented
3#131×Dic11C211yesmaximal, characteristic, complemented
4#13069267C211yesmaximal, characteristic, complemented
5#13069261C211yesmaximal, characteristic, complemented
6#13069216C211yesmaximal, characteristic, complemented
7#13069214C211yesmaximal, characteristic, complemented
8#13068945C211yesmaximal, characteristic
9#13068891C211yesmaximal, characteristic, complemented
10#13068889C211yesmaximal, characteristic, complemented
11#13068521C211yesmaximal, characteristic, complemented
12#13068428C211yesmaximal, characteristic, complemented
13#13068428C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1876C211yesmaximal, characteristic
16C2×C11×#135C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18#41×Dic11C2211yescharacteristic
19#41×Dic11C2211yescharacteristic
20C2×#67001C2211yescharacteristic
21C2×C11×#104C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23C11×#408C2211yescharacteristic
24C2×#66901C2211yescharacteristic
25C2×#66901C2211yescharacteristic
26#10622847C2211yescharacteristic
27#10622846C2211yescharacteristic
28#10622846C2211yescharacteristic
29#10622797C411yescharacteristic, complemented
30#10622797C411yescharacteristic, complemented
31#10622777C411yescharacteristic, complemented
32#10622777C411yescharacteristic, complemented
33#10622777C411yescharacteristic, complemented
34#10622777C411yescharacteristic, complemented
35#10622765C411yescharacteristic, complemented
36#10622765C411yescharacteristic, complemented
37C2×#66886C2211yescharacteristic
38C2×#66886C2211yescharacteristic
39#10622735—21no—
40#10622735C2211yescharacteristic
41#10622732C2211yescharacteristic
42M16×Dic11—21no—
43M16×Dic11C2211yescharacteristic
44M16×Dic11C2211yescharacteristic
45#10622719C2211yescharacteristic
46#10622715C2211yescharacteristic
47#10622714—21no—
48#10622714C2211yescharacteristic
49C2×#66879C2211yescharacteristic
50C2×C8×Dic11—21no—
51C2×C8×Dic11C2211yescharacteristic
52#10622545C2211yescharacteristic
53#10622333—21no—
54#10622333—21no—
55#10622331—21no—
56#10622331—21no—
57C11×#341C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622193C2211yescharacteristic
60#10622193C2211yescharacteristic
61#10622190C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622162C2211yescharacteristic
65#10622161C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×C11×#41C2311yescharacteristic
69C11×#135—22no—
70C11×#135—22no—
71C2×C11×Q16C2×C411yescharacteristic
72C2×C11×SD16C2×C411yescharacteristic
73C2×C11×SD16C2×C411yescharacteristic
74C2×C11×D8C2×C411yescharacteristic
75C11×#131—22no—
76C11×#131—22no—
77C2×C11×M16—21no—
78C2×C11×M16C2311yescharacteristic
79C2×C11×M16C2311yescharacteristic
80C22×C8×C11—21no—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84#67001—22no—
85#67001—22no—
86Q8×Dic11C2×C411yescharacteristic
87Q8×Dic11C2×C411yescharacteristic
88Q8×Dic11C2×C411yescharacteristic
89Q8×Dic11C2×C411yescharacteristic
90D4×Dic11—21no—
91D4×Dic11—21no—
92D4×Dic11—21no—
93D4×Dic11—21no—
94D4×Dic11C2×C411yescharacteristic
95D4×Dic11C2×C411yescharacteristic
96D4×Dic11C2×C411yescharacteristic
97D4×Dic11C2×C411yescharacteristic
98#66979—21no—
99#66979—21no—
100#66979C2311yescharacteristic
101#66979C2311yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×#4318—21no—
107C2×#4318C2311yescharacteristic
108C2×#4318C2311yescharacteristic
109C22×C11⋊C8—21no—
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C11×#104—22no—
113C11×#104—22no—
114C11×C22⋊C8—21no—
115C11×C22⋊C8—21no—
116#66901—22no—
117#66901—22no—
118#66899C2×C411yescharacteristic
119#66899C2×C411yescharacteristic
120#66899C2×C411yescharacteristic
121#66899C2×C411yescharacteristic
122#66896C2×C411yescharacteristic
123#66896C2×C411yescharacteristic
124#66896C2×C411yescharacteristic
125#66896C2×C411yescharacteristic
126C11⋊#95—21no—
127C11⋊#95—21no—
128C22⋊(C11⋊C8)—21no—
129C22⋊(C11⋊C8)—21no—
130#66886—22no—
131#66886—22no—
132#66882C2×C411yescharacteristic
133#66882C2×C411yescharacteristic
134#66881C2×C411yescharacteristic
135#66881C2×C411yescharacteristic
136#66879—21no—
137#66879—21no—
138#66879—21no—
139#66879—21no—
140#66879C2×C411yescharacteristic
141#66879C2×C411yescharacteristic
142#66879C2×C411yescharacteristic
143#66879C2×C411yescharacteristic
144Dic11⋊C8—21no—
145Dic11⋊C8—21no—
146Dic11⋊C8—21no—
147Dic11⋊C8—21no—
148C8×Dic11—21no—
149C8×Dic11—21no—
150C8×Dic11—21no—
151C8×Dic11—21no—
152C8×Dic11D411yescharacteristic
153C8×Dic11D411yescharacteristic
154C8×Dic11D411yescharacteristic
155C8×Dic11D411yescharacteristic
156#21138—111nomaximal, Sylow
157C11×#41—21no—
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C11×#41—21no—
162C11×#41—21no—
163C11×#41#4112yes—
164C11×#41#4112yes—
165C2×Q8×C11C22×C411yescharacteristic
166C2×Q8×C11C22×C411yescharacteristic
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11C22×C411yescharacteristic
170C2×D4×C11C22×C411yescharacteristic
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C2411yescharacteristic
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11#4111yescharacteristic
181C22×Dic11#4111yescharacteristic
182C11×Q16—22no—
183C11×SD16—22no—
184C11×SD16—22no—
185C11×D8—22no—
186C11×M16—24no—
187C11×M16—21no—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16#4112yes—
191C2×C8×C11—24no—
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×C11C22×C411yescharacteristic
199C2×C8×C11C22×C411yescharacteristic
200C2×C8×C11C2×D411yescharacteristic
201C2×C8×C11C2×D411yescharacteristic
202C42×C11—21no—
203C42×C11—21no—
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—21no—
207C22⋊Dic11—21no—
208C22⋊Dic11—21no—
209C22⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11C22×C411yescharacteristic
215C4⋊Dic11C22×C411yescharacteristic
216C4⋊Dic11C22×C411yescharacteristic
217C4⋊Dic11C22×C411yescharacteristic
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11C22×C411yescharacteristic
227C4×Dic11C22×C411yescharacteristic
228C4×Dic11C2×D411yescharacteristic
229C4×Dic11C2×D411yescharacteristic
230#4318—24no—
231#4318—21no—
232#4318—21no—
233#4318—21no—
234#4318#4112yes—
235C2×C11⋊C8—24no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8C22×C411yescharacteristic
243C2×C11⋊C8C22×C411yescharacteristic
244C2×C11⋊C8C2×D411yescharacteristic
245C2×C11⋊C8C2×D411yescharacteristic
246#2943—111no—
247#2922—111no—
248C4×#131—111no—
249#1929—111no—
250#1929—111no—
251#1922—111no—
252#1922—111no—
253#1876—111no—
254#1876D1111yescharacteristic
255#1866—111no—
256#1866—111no—
257#1778—111no—
258#1759—111no—
259#1759—111no—
260#1746—111no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11C2×#4111yescharacteristic
264Q8×C11—21no—
265Q8×C11—21no—
266Q8×C11—21no—
267Q8×C11#11712yes—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—21no—
271D4×C11—21no—
272D4×C11—21no—
273D4×C11—41no—
274D4×C11—41no—
275D4×C11#11712yes—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—21no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11C23×C411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11—42no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11C4×D411yescharacteristic
305C2×Dic11C4×D411yescharacteristic
306C2×Dic11C4×D411yescharacteristic
307C2×Dic11C4×D411yescharacteristic
308C8×C11—21no—
309C8×C11—21no—
310C8×C11—21no—
311C8×C11—22no—
312C8×C11—21no—
313C8×C11—41no—
314C11⋊C8—21no—
315C11⋊C8—21no—
316C11⋊C8—21no—
317C11⋊C8—22no—
318C11⋊C8—21no—
319C11⋊C8—41no—
320C2×#135C2×D1111yescharacteristic
321C2×#131—111no—
322C2×#131C2×D1111yescharacteristic
323C4×#41—111no—
324C4×#41—111no—
325#442—111no—
326#442—111no—
327#441—111no—
328#441—111no—
329#440—111no—
330#440—111no—
331#440—111no—
332#440—111no—
333#433—221no—
334#433—221no—
335#431—221no—
336#431—221no—
337C2×#108—111no—
338C2×#108—111no—
339#427—111no—
340#424—111no—
341#424—111no—
342C2×#104—111no—
343C2×#104—111no—
344C2×#104C2×D1111yescharacteristic
345C2×#104C2×D1111yescharacteristic
346#416—111no—
347#416—111no—
348#408—111no—
349#408C2×D1111yescharacteristic
350#405—111no—
351#405—111no—
352#405—221no—
353#405—221no—
354C4×M16—111no—
355C4×M16—111no—
356C4×M16—221no—
357C2×#97—111no—
358C2×C4×C8—111no—
359C2×C4×C8—221no—
360#376—111no—
361#341—111no—
362#341C2×D1111yescharacteristic
363#339—111no—
364#339—111no—
365#339—111no—
366#339—111no—
367#336—111no—
368#336—111no—
369#336—111no—
370#336C2×D1111yescharacteristic
371C22×C11—21no—
372C22×C11—21no—
373C22×C11—22no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11C2×C4×D411yescharacteristic
380C22×C11#52911yescharacteristic
381C22×C11#52911yescharacteristic
382C4×C11—22no—
383C4×C11—41no—
384C4×C11—81no—
385C4×C11C2×#11711yescharacteristic
386C4×C11C4×#4111yescharacteristic
387C4×C11#52511yescharacteristic
388C4×C11#52511yescharacteristic
389Dic11—21no—
390Dic11—21no—
391Dic11—21no—
392Dic11—21no—
393Dic11—41no—
394Dic11—41no—
395Dic11—41no—
396Dic11—41no—
397Dic11—81no—
398C2×#41C22×D1111yescharacteristic
399C2×#41C22×D1111yescharacteristic
400#135—22no—
401#135—22no—
402C2×Q16C4×D1111yescharacteristic
403C2×SD16C4×D1111yescharacteristic
404C2×SD16C4×D1111yescharacteristic
405C2×D8C4×D1111yescharacteristic
406#131—22no—
407#131—22no—
408#131—222no—
409#131—222no—
410C2×M16—21no—
411C2×M16—111no—
412C2×M16—111no—
413C2×M16—221no—
414C2×M16C22×D1111yescharacteristic
415C2×M16C22×D1111yescharacteristic
416C22×C8—21no—
417C22×C8—111no—
418C22×C8—111no—
419C22×C8—221no—
420C22×C8C22×D1111yescharacteristic
421C22×C8C22×D1111yescharacteristic
422C4×Q8—111no—
423C4×Q8—111no—
424C4×Q8—111no—
425C4×Q8—111no—
426C4×D4—111no—
427C4×D4—111no—
428C4×D4—111no—
429C4×D4—111no—
430C4×D4—221no—
431C4×D4—221no—
432C4×D4—221no—
433C4×D4—221no—
434#117—111no—
435#117—111no—
436#117—221no—
437#117—221no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#108—222no—
444#108—222no—
445#107—111no—
446#107—111no—
447#106—111no—
448#106—111no—
449C4⋊C8—221no—
450C4⋊C8—221no—
451C4⋊C8—221no—
452C4⋊C8—221no—
453#104—22no—
454#104—22no—
455#104—222no—
456#104—222no—
457#103—111no—
458#103—111no—
459#103—111no—
460#103—111no—
461#102—111no—
462#102—111no—
463#102—111no—
464#102—111no—
465C22⋊C8—21no—
466C22⋊C8—21no—
467C22⋊C8—221no—
468C22⋊C8—221no—
469#97—111no—
470#97—111no—
471#97—111no—
472#97—111no—
473#97—221no—
474#97—221no—
475#97—221no—
476#97—221no—
477C4×C8—111no—
478C4×C8—111no—
479C4×C8—111no—
480C4×C8—111no—
481C4×C8—221no—
482C4×C8—221no—
483C4×C8—221no—
484C4×C8—221no—
485#95—221no—
486#95—221no—
487C2×C11—21no—
488C2×C11—21no—
489C2×C11—42no—
490C2×C11—81no—
491C2×C11#229011yescharacteristic
492C2×C11#295511yescharacteristic
493C2×C11#295511yescharacteristic
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41#434112yes—
501#41#434112yes—
502C2×Q8C2×C4×D1111yescharacteristic
503C2×Q8C2×C4×D1111yescharacteristic
504C2×D4—21no—
505C2×D4—21no—
506C2×D4C2×C4×D1111yescharacteristic
507C2×D4C2×C4×D1111yescharacteristic
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4C23×D1111yescharacteristic
519Q16—22no—
520SD16—22no—
521SD16—22no—
522D8—22no—
523M16—24no—
524M16—21no—
525M16—21no—
526M16—21no—
527M16—112no—
528M16—224no—
529M16—221no—
530M16—221no—
531M16—221no—
532M16#434112yes—
533C2×C8—24no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—111no—
541C2×C8—111no—
542C2×C8—111no—
543C2×C8—111no—
544C2×C8—224no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8C2×C4×D1111yescharacteristic
552C2×C8C2×C4×D1111yescharacteristic
553C2×C8D4×D1111yescharacteristic
554C2×C8D4×D1111yescharacteristic
555C4⋊C4—111no—
556C4⋊C4—111no—
557C4⋊C4—111no—
558C4⋊C4—111no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C22⋊C4—221no—
564C22⋊C4—221no—
565C22⋊C4—221no—
566C22⋊C4—221no—
567C22⋊C4—221no—
568C22⋊C4—221no—
569C42—21no—
570C42—21no—
571C42—111no—
572C42—111no—
573C42—111no—
574C42—111no—
575C42—221no—
576C42—221no—
577C42—221no—
578C42—221no—
579C42—221no—
580C42—221no—
581C42—221no—
582C42—221no—
583C11#2113811yescharacteristic, complemented, Sylow
584C23—21no—
585C23—21no—
586C23#41×D1111yescharacteristic
587Q8—21no—
588Q8—21no—
589Q8—21no—
590Q8#6693012yes—
591D4—22no—
592D4—22no—
593D4—21no—
594D4—21no—
595D4—21no—
596D4—41no—
597D4—41no—
598D4#6693012yes—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—111no—
609C2×C4—111no—
610C2×C4—111no—
611C2×C4—111no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4C22×C4×D1111yescharacteristic
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4C2×#434111yescharacteristic
628C2×C4C2×#434111yescharacteristic
629C2×C4C2×#434111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C8—21no—
632C8—21no—
633C8—21no—
634C8—22no—
635C8—21no—
636C8—41no—
637C8—221no—
638C8—221no—
639C8—221no—
640C8—221no—
641C8—222no—
642C8—441no—
643C22—21no—
644C22—21no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C4×D4×D1111yescharacteristic
652C22#1062313111yescharacteristic
653C22#1062318011yescharacteristic
654C4—22no—
655C4—41no—
656C4—81no—
657C4—221no—
658C4—221no—
659C4—221no—
660C4—221no—
661C4—441no—
662C4—441no—
663C4—441no—
664C4—441no—
665C4—881no—
666C4C2×#6693011yescharacteristic
667C4C4×#434111yescharacteristic
668C4#1062311711yescharacteristic
669C4#1062313711yescharacteristic
670C2—21no—
671C2—21no—
672C2—42no—
673C2—81no—
674C2#1307105611yescharacteristic
675C2#1307751411yescharacteristic
676C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1876C2
socleC22×C11C2×C4×D4
prime radicalC2×C11×#135C22
cosocleC22×C4×C11C24
hypercenter#1876D11
hypocenterC11#21138
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1876

Complements

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

NH ≅ G/Ntype
2. #13077256C2semidirect
3. #131×Dic11C2semidirect
4. #13069267C2semidirect
5. #13069261C2semidirect
6. #13069216C2semidirect
7. #13069214C2semidirect
9. #13068891C2semidirect
10. #13068889C2semidirect
11. #13068521C2semidirect
12. #13068428C2semidirect
13. #13068428C2semidirect
14. #13068366C2semidirect
29. #10622797C4semidirect
30. #10622797C4semidirect
31. #10622777C4semidirect
32. #10622777C4semidirect
33. #10622777C4semidirect
34. #10622777C4semidirect
35. #10622765C4semidirect
36. #10622765C4semidirect
583. C11#21138semidirect

Maximal subgroups

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

subgroupindex
#130774172
#130772562
#131×Dic112
#130692672
#130692612
#130692162
#130692142
#130689452
#130688912
#130688892
#130685212
#130684282
#130683662
C11×#18762
#2113811