Finite Group Databasebeta

← #14757007

Subgroups — #14757007

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#13077412C211yesmaximal, characteristic
2#13077256C211yesmaximal, characteristic, complemented
3#13077038C211yesmaximal, characteristic, complemented
4#13069266C211yesmaximal, characteristic, complemented
5#13069215C211yesmaximal, characteristic, complemented
6#13069213C211yesmaximal, characteristic, complemented
7#13068946C211yesmaximal, characteristic
8#13068940C211yesmaximal, characteristic
9#13068894C211yesmaximal, characteristic, complemented
10#13068888C211yesmaximal, characteristic, complemented
11#13068524C211yesmaximal, characteristic, complemented
12#13068428C211yesmaximal, characteristic, complemented
13#13068425C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1929C211yesmaximal, characteristic, complemented
16#41×Dic11C2211yescharacteristic
17C2×#67003C2211yescharacteristic
18C2×#66960C2211yescharacteristic
19C2×#66954C2211yescharacteristic
20#10623053C2211yescharacteristic
21C2×C11×#108C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23C11×#416C2211yescharacteristic
24C11×#408C2211yescharacteristic
25C11×#405C2211yescharacteristic
26C2×#66901C2211yescharacteristic
27#10622847C2211yescharacteristic
28C2×#66889C2211yescharacteristic
29#10622732C2211yescharacteristic
30M16×Dic11C2211yescharacteristic
31M16×Dic11C2211yescharacteristic
32#10622726C2211yescharacteristic
33C2×#66883C2211yescharacteristic
34#10622715C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622611C2211yescharacteristic
38#10622610C2211yescharacteristic
39#10622545C2211yescharacteristic
40C2×#66869C2211yescharacteristic
41#10622430C411yescharacteristic, complemented
42#10622430C411yescharacteristic, complemented
43#10622402C411yescharacteristic, complemented
44#10622402C411yescharacteristic, complemented
45#10622398C411yescharacteristic, complemented
46#10622398C411yescharacteristic, complemented
47#10622370C411yescharacteristic, complemented
48#10622370C411yescharacteristic, complemented
49#10622333—21no—
50#10622333—21no—
51#10622331—21no—
52#10622331—21no—
53#10622321—21no—
54#10622320—21no—
55#10622302—21no—
56C4×C8×D11—21no—
57C11×#339C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622162C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75#67003—22no—
76#67003—22no—
77Q8×Dic11C2×C411yescharacteristic
78Q8×Dic11C2×C411yescharacteristic
79C2×#4326C2×C411yescharacteristic
80C2×#4325C2×C411yescharacteristic
81D4×Dic11—21no—
82D4×Dic11—21no—
83D4×Dic11C2×C411yescharacteristic
84D4×Dic11C2×C411yescharacteristic
85C2×#4324C2×C411yescharacteristic
86C2×#4323C2×C411yescharacteristic
87#66979—21no—
88#66979C2311yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×#4318C2311yescharacteristic
93C2×#4318C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66960—22no—
97#66960—22no—
98#66954—22no—
99#66954—22no—
100C2×#4313—21no—
101C2×#4313—21no—
102C2×C8×D11—21no—
103C2×C8×D11—21no—
104#66946C2×C411yescharacteristic
105#66946C2×C411yescharacteristic
106#66940C2×C411yescharacteristic
107#66940C2×C411yescharacteristic
108(C22⋊D11)⋊C4—21no—
109(C22⋊D11)⋊C4—21no—
110#66925—21no—
111C42×D11—21no—
112C11×#108—22no—
113C11×#104—22no—
114C11×#103C2×C411yescharacteristic
115C11×#103C2×C411yescharacteristic
116C11×#102C2×C411yescharacteristic
117C11×#102C2×C411yescharacteristic
118C11×C22⋊C8—21no—
119C11×C22⋊C8—21no—
120C11×#97—21no—
121C4×C8×C11—21no—
122#66901—22no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C22⋊(C11⋊C8)—21no—
126C22⋊(C11⋊C8)—21no—
127#66889—22no—
128#66885C2×C411yescharacteristic
129#66885C2×C411yescharacteristic
130#66883—22no—
131#66880C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66879—21no—
134#66879—21no—
135#66879C2×C411yescharacteristic
136#66879C2×C411yescharacteristic
137#66879C2×C411yescharacteristic
138#66879C2×C411yescharacteristic
139Dic11⋊C8—21no—
140Dic11⋊C8—21no—
141Dic11⋊C8—21no—
142Dic11⋊C8—21no—
143C8×Dic11—21no—
144C8×Dic11—21no—
145C8×Dic11D411yescharacteristic
146C8×Dic11D411yescharacteristic
147C8×Dic11D411yescharacteristic
148C8×Dic11D411yescharacteristic
149#66872C2×C411yescharacteristic
150#66872C2×C411yescharacteristic
151#66871C2×C411yescharacteristic
152#66871C2×C411yescharacteristic
153#66869—22no—
154#66867—21no—
155C4×C11⋊C8—21no—
156#21138—111nomaximal, Sylow
157C11×#41—21no—
158C11×#41—21no—
159C11×#41—21no—
160C11×#41—21no—
161C2×Q8×C11C22×C411yescharacteristic
162C2×D4×C11—21no—
163C2×D4×C11C22×C411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11#4111yescharacteristic
172C22×Dic11#4111yescharacteristic
173#4339—21no—
174#4339—21no—
175#4339#4112yes—
176#4339#4112yes—
177C2×D44C22×C411yescharacteristic
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×Dic22C22×C411yescharacteristic
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16#4112yes—
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×C11C22×C411yescharacteristic
193C2×C8×C11C22×C411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C2×C8×C11C2×D411yescharacteristic
196C11×C4⋊C4C22×C411yescharacteristic
197C11×C4⋊C4C22×C411yescharacteristic
198C11×C22⋊C4—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C22⋊Dic11—21no—
203C22⋊Dic11—21no—
204C22⋊Dic11—21no—
205#4326—22no—
206#4325—22no—
207#4324—22no—
208#4323—22no—
209(C2×D11)⋊C4—21no—
210(C2×D11)⋊C4—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11C22×C411yescharacteristic
214C4⋊Dic11C22×C411yescharacteristic
215Dic11⋊C4—21no—
216Dic11⋊C4—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11C22×C411yescharacteristic
225C4×Dic11C22×C411yescharacteristic
226C4×Dic11C2×D411yescharacteristic
227C4×Dic11C2×D411yescharacteristic
228#4318—21no—
229#4318—21no—
230#4318—21no—
231#4318#4112yes—
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⋊C8C22×C411yescharacteristic
239C2×C11⋊C8C22×C411yescharacteristic
240C2×C11⋊C8C2×D411yescharacteristic
241C2×C11⋊C8C2×D411yescharacteristic
242#4313—24no—
243#4313—24no—
244C8×D11—24no—
245C8×D11—24no—
246#2943—111no—
247#2922—111no—
248C4×#131—111no—
249#1929—111no—
250#1929D1111yescharacteristic, complemented
251#1922—111no—
252#1922—111no—
253#1876—111no—
254#1876—111no—
255#1866—111no—
256#1866—111no—
257#1778—111no—
258#1759—111no—
259#1759—111no—
260#1746—111no—
261C23×C11—21no—
262C23×C11C2×#4111yescharacteristic
263C22×D11—21no—
264Q8×C11—21no—
265Q8×C11—21no—
266D4×C11—21no—
267D4×C11—21no—
268D4×C11—41no—
269D4×C11—41no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C22⋊D11—22no—
285C22⋊D11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11C4×D411yescharacteristic
297C2×Dic11C4×D411yescharacteristic
298C2×Dic11C4×D411yescharacteristic
299C2×Dic11C4×D411yescharacteristic
300D44—21no—
301D44#11712yes—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—42no—
305C4×D11—42no—
306Dic22—21no—
307Dic22#11712yes—
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×#135—111no—
321C2×#131—111no—
322C2×#131—111no—
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×#108C2×D1111yescharacteristic
339#427—111no—
340#424—111no—
341#424—111no—
342C2×#104—111no—
343C2×#104—111no—
344C2×#104—111no—
345C2×#104C2×D1111yescharacteristic
346#416—111no—
347#416C2×D1111yescharacteristic
348#408—111no—
349#408C2×D1111yescharacteristic
350#405—111no—
351#405—221no—
352#405—221no—
353#405C2×D1111yescharacteristic
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#341—111no—
363#339—111no—
364#339—111no—
365#339—111no—
366#339C2×D1111yescharacteristic
367#336—111no—
368#336—111no—
369#336—111no—
370#336C2×D1111yescharacteristic
371C22×C11—21no—
372C22×C11—21no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11C2×C4×D411yescharacteristic
377C22×C11#52911yescharacteristic
378C22×C11#52911yescharacteristic
379C2×D11—22no—
380C2×D11—41no—
381C2×D11—41no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—81no—
386C4×C11C2×#11711yescharacteristic
387C4×C11C4×#4111yescharacteristic
388C4×C11#52511yescharacteristic
389C4×C11#52511yescharacteristic
390Dic11—21no—
391Dic11—21no—
392Dic11—21no—
393Dic11—21no—
394Dic11—22no—
395Dic11—41no—
396Dic11—41no—
397Dic11—81no—
398C2×#41—111no—
399C2×#41C22×D1111yescharacteristic
400#135—222no—
401#135—222no—
402C2×Q16—111no—
403C2×SD16—111no—
404C2×SD16—111no—
405C2×D8—111no—
406#131—222no—
407#131—222no—
408#131—222no—
409#131—222no—
410C2×M16—111no—
411C2×M16—111no—
412C2×M16—221no—
413C2×M16—221no—
414C2×M16C22×D1111yescharacteristic
415C2×M16C22×D1111yescharacteristic
416C22×C8—111no—
417C22×C8—111no—
418C22×C8—221no—
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—221no—
436#117—221no—
437#117C22×D1111yescharacteristic
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#108—22no—
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—222no—
455#104—222no—
456#104—222no—
457#103—111no—
458#103—111no—
459#103C4×D1111yescharacteristic
460#103C4×D1111yescharacteristic
461#102—111no—
462#102—111no—
463#102C4×D1111yescharacteristic
464#102C4×D1111yescharacteristic
465C22⋊C8—21no—
466C22⋊C8—21no—
467C22⋊C8—221no—
468C22⋊C8—221no—
469#97—21no—
470#97—111no—
471#97—111no—
472#97—111no—
473#97—111no—
474#97—221no—
475#97—221no—
476#97—221no—
477C4×C8—21no—
478C4×C8—111no—
479C4×C8—111no—
480C4×C8—111no—
481C4×C8—111no—
482C4×C8—221no—
483C4×C8—221no—
484C4×C8—221no—
485#95—221no—
486#95—221no—
487C2×C11—21no—
488C2×C11—21no—
489C2×C11—81no—
490C2×C11#229011yescharacteristic
491C2×C11#295511yescharacteristic
492C2×C11#295511yescharacteristic
493D11—42no—
494#41—21no—
495#41—21no—
496#41—21no—
497#41—21no—
498#41—112no—
499#41—112no—
500#41—221no—
501#41—221no—
502C2×Q8—111no—
503C2×Q8C2×C4×D1111yescharacteristic
504C2×D4—21no—
505C2×D4—111no—
506C2×D4—221no—
507C2×D4C2×C4×D1111yescharacteristic
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4C23×D1111yescharacteristic
519Q16—222no—
520SD16—222no—
521SD16—222no—
522D8—222no—
523M16—21no—
524M16—21no—
525M16—21no—
526M16—112no—
527M16—224no—
528M16—224no—
529M16—221no—
530M16—221no—
531M16—221no—
532M16#434112yes—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—111no—
540C2×C8—111no—
541C2×C8—111no—
542C2×C8—111no—
543C2×C8—224no—
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—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4C2×C4×D1111yescharacteristic
562C4⋊C4C2×C4×D1111yescharacteristic
563C22⋊C4—21no—
564C22⋊C4—221no—
565C22⋊C4—221no—
566C22⋊C4—221no—
567C22⋊C4—221no—
568C22⋊C4—221no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—111no—
573C42—111no—
574C42—111no—
575C42—111no—
576C42—221no—
577C42—221no—
578C42—221no—
579C42—221no—
580C42—221no—
581C42—221no—
582C42—221no—
583C11#2113811yescharacteristic, complemented, Sylow
584C23—21no—
585C23—221no—
586C23#41×D1111yescharacteristic
587Q8—21no—
588Q8—21no—
589Q8—112no—
590Q8—221no—
591D4—21no—
592D4—21no—
593D4—41no—
594D4—41no—
595D4—112no—
596D4—222no—
597D4—222no—
598D4—221no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—111no—
608C2×C4—111no—
609C2×C4—111no—
610C2×C4—111no—
611C2×C4—221no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—441no—
619C2×C4—441no—
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×C4#41×D1111yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C8—21no—
632C8—21no—
633C8—22no—
634C8—21no—
635C8—21no—
636C8—41no—
637C8—221no—
638C8—221no—
639C8—221no—
640C8—221no—
641C8—222no—
642C8—441no—
643C22—21no—
644C22—21no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—222no—
649C22—441no—
650C22—441no—
651C22C4×D4×D1111yescharacteristic
652C22#1062321111yescharacteristic
653C22#1062323711yescharacteristic
654C4—41no—
655C4—41no—
656C4—41no—
657C4—81no—
658C4—221no—
659C4—221no—
660C4—221no—
661C4—221no—
662C4—222no—
663C4—441no—
664C4—441no—
665C4—881no—
666C4D11×#11711yescharacteristic
667C4C4×#434111yescharacteristic
668C4#1062313711yescharacteristic
669C4#1062318711yescharacteristic
670C2—21no—
671C2—21no—
672C2—81no—
673C2—442no—
674C2#1307105811yescharacteristic
675C2#1307751411yescharacteristic
676C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1929C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenter#1929D11
hypocenterC11#21138
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1929

Complements

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

NH ≅ G/Ntype
2. #13077256C2semidirect
3. #13077038C2semidirect
4. #13069266C2semidirect
5. #13069215C2semidirect
6. #13069213C2semidirect
9. #13068894C2semidirect
10. #13068888C2semidirect
11. #13068524C2semidirect
12. #13068428C2semidirect
13. #13068425C2semidirect
14. #13068366C2semidirect
15. C11×#1929C2semidirect
41. #10622430C4semidirect
42. #10622430C4semidirect
43. #10622402C4semidirect
44. #10622402C4semidirect
45. #10622398C4semidirect
46. #10622398C4semidirect
47. #10622370C4semidirect
48. #10622370C4semidirect
250. #1929D11semidirect
583. C11#21138semidirect

Maximal subgroups

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

subgroupindex
#130774122
#130772562
#130770382
#130692662
#130692152
#130692132
#130689462
#130689402
#130688942
#130688882
#130685242
#130684282
#130684252
#130683662
C11×#19292
#2113811