Finite Group Databasebeta

← #14757018

Subgroups — #14757018

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077412C211yesmaximal, characteristic
2#13077263C211yesmaximal, characteristic, complemented
3#13077043C211yesmaximal, 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#104×Dic11C211yesmaximal, characteristic, complemented
13#13068420C211yesmaximal, characteristic, complemented
14#13068363C211yesmaximal, 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×#66879C2211yescharacteristic
37#10622611C2211yescharacteristic
38#10622610C2211yescharacteristic
39C42×Dic11C2211yescharacteristic
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#10622332—21no—
52#10622332—21no—
53#10622321—21no—
54D11×#97—21no—
55#10622302—21no—
56C4×#4313—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×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×#4318C2311yescharacteristic
95C2×#4318C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66960—22no—
99#66960—22no—
100#66954—22no—
101#66954—22no—
102C2×#4313—21no—
103C2×#4313—21no—
104C2×C8×D11—21no—
105C2×C8×D11—21no—
106#66946C2×C411yescharacteristic
107#66946C2×C411yescharacteristic
108#66940C2×C411yescharacteristic
109#66940C2×C411yescharacteristic
110(C22⋊D11)⋊C4—21no—
111(C22⋊D11)⋊C4—21no—
112#66925—21no—
113C42×D11—21no—
114C11×#108—22no—
115C11×#104—22no—
116C11×#103C2×C411yescharacteristic
117C11×#103C2×C411yescharacteristic
118C11×#102C2×C411yescharacteristic
119C11×#102C2×C411yescharacteristic
120C11×C22⋊C8—21no—
121C11×C22⋊C8—21no—
122C11×#97—21no—
123C4×C8×C11—21no—
124#66901—22no—
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
139#66879D411yescharacteristic
140#66879D411yescharacteristic
141#66879D411yescharacteristic
142#66879D411yescharacteristic
143Dic11⋊C8—21no—
144Dic11⋊C8—21no—
145Dic11⋊C8—21no—
146Dic11⋊C8—21no—
147C8×Dic11—21no—
148C8×Dic11—21no—
149#66872C2×C411yescharacteristic
150#66872C2×C411yescharacteristic
151#66871C2×C411yescharacteristic
152#66871C2×C411yescharacteristic
153#66869—22no—
154#66867—21no—
155C4×C11⋊C8—21no—
156#21139—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×Dic11—42no—
225C4×Dic11—42no—
226C4×Dic11C22×C411yescharacteristic
227C4×Dic11C22×C411yescharacteristic
228C4×Dic11C2×D411yescharacteristic
229C4×Dic11C2×D411yescharacteristic
230#4318—21no—
231#4318—21no—
232#4318—21no—
233#4318#4112yes—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8C22×C411yescharacteristic
241C2×C11⋊C8C22×C411yescharacteristic
242C2×C11⋊C8C2×D411yescharacteristic
243C2×C11⋊C8C2×D411yescharacteristic
244#4313—24no—
245#4313—24no—
246C8×D11—24no—
247C8×D11—24no—
248#2943—111no—
249#2923—111no—
250#2875—111no—
251#1929—111no—
252#1929D1111yescharacteristic, complemented
253#1922—111no—
254#1922—111no—
255#1876—111no—
256#1876—111no—
257#1866—111no—
258#1866—111no—
259#1778—111no—
260C4×#104—111no—
261C4×#104—111no—
262#1745—111no—
263C23×C11—21no—
264C23×C11C2×#4111yescharacteristic
265C22×D11—21no—
266Q8×C11—21no—
267Q8×C11—21no—
268D4×C11—21no—
269D4×C11—21no—
270D4×C11—41no—
271D4×C11—41no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11C23×C411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C22⋊D11—22no—
287C22⋊D11—22no—
288C2×Dic11—21no—
289C2×Dic11—22no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—81no—
297C2×Dic11—81no—
298C2×Dic11C4×D411yescharacteristic
299C2×Dic11C4×D411yescharacteristic
300C2×Dic11C4×D411yescharacteristic
301C2×Dic11C4×D411yescharacteristic
302D44—21no—
303D44#11712yes—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—81no—
307C4×D11—81no—
308Dic22—21no—
309Dic22#11712yes—
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—21no—
313C8×C11—22no—
314C8×C11—21no—
315C8×C11—41no—
316C11⋊C8—21no—
317C11⋊C8—21no—
318C11⋊C8—21no—
319C11⋊C8—22no—
320C11⋊C8—21no—
321C11⋊C8—41no—
322C2×#135—111no—
323C2×#131—111no—
324C2×#131—111no—
325C4×#41—111no—
326C4×#41—111no—
327#442—111no—
328#442—111no—
329#441—111no—
330#441—111no—
331#440—111no—
332#440—111no—
333#440—111no—
334#440—111no—
335#433—221no—
336#433—221no—
337#432—221no—
338#432—221no—
339C2×#108—111no—
340C2×#108C2×D1111yescharacteristic
341#427—111no—
342#424—111no—
343#424—111no—
344C2×#104—111no—
345C2×#104—111no—
346C2×#104—111no—
347C2×#104C2×D1111yescharacteristic
348#416—111no—
349#416C2×D1111yescharacteristic
350#408—111no—
351#408C2×D1111yescharacteristic
352#405—111no—
353#405—221no—
354#405—221no—
355#405C2×D1111yescharacteristic
356C4×M16—111no—
357C4×M16—111no—
358C4×M16—221no—
359C2×#97—111no—
360C2×#97—111no—
361C2×#97—221no—
362C43—111no—
363#341—111no—
364#341—111no—
365#339—111no—
366#339—111no—
367#339—111no—
368#339C2×D1111yescharacteristic
369#336—111no—
370#336—111no—
371#336—111no—
372#336C2×D1111yescharacteristic
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11C2×C4×D411yescharacteristic
379C22×C11#52911yescharacteristic
380C22×C11#52911yescharacteristic
381C2×D11—22no—
382C2×D11—41no—
383C2×D11—41no—
384C4×C11—42no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11C2×#11711yescharacteristic
389C4×C11C4×#4111yescharacteristic
390C4×C11#52511yescharacteristic
391C4×C11#52511yescharacteristic
392Dic11—21no—
393Dic11—21no—
394Dic11—21no—
395Dic11—21no—
396Dic11—22no—
397Dic11—42no—
398Dic11—41no—
399Dic11—41no—
400C2×#41—111no—
401C2×#41C22×D1111yescharacteristic
402#135—222no—
403#135—222no—
404C2×Q16—111no—
405C2×SD16—111no—
406C2×SD16—111no—
407C2×D8—111no—
408#131—222no—
409#131—222no—
410#131—222no—
411#131—222no—
412C2×M16—111no—
413C2×M16—111no—
414C2×M16—221no—
415C2×M16—221no—
416C2×M16C22×D1111yescharacteristic
417C2×M16C22×D1111yescharacteristic
418C22×C8—111no—
419C22×C8—111no—
420C22×C8—221no—
421C22×C8—221no—
422C22×C8C22×D1111yescharacteristic
423C22×C8C22×D1111yescharacteristic
424C4×Q8—111no—
425C4×Q8—111no—
426C4×Q8—111no—
427C4×Q8—111no—
428C4×D4—111no—
429C4×D4—111no—
430C4×D4—111no—
431C4×D4—111no—
432C4×D4—221no—
433C4×D4—221no—
434C4×D4—221no—
435C4×D4—221no—
436#117—111no—
437#117—221no—
438#117—221no—
439#117C22×D1111yescharacteristic
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447#108—22no—
448#108—222no—
449#107—111no—
450#107—111no—
451#106—111no—
452#106—111no—
453C4⋊C8—221no—
454C4⋊C8—221no—
455C4⋊C8—221no—
456C4⋊C8—221no—
457#104—22no—
458#104—222no—
459#104—222no—
460#104—222no—
461#103—111no—
462#103—111no—
463#103C4×D1111yescharacteristic
464#103C4×D1111yescharacteristic
465#102—111no—
466#102—111no—
467#102C4×D1111yescharacteristic
468#102C4×D1111yescharacteristic
469C22⋊C8—21no—
470C22⋊C8—21no—
471C22⋊C8—221no—
472C22⋊C8—221no—
473#97—21no—
474#97—111no—
475#97—111no—
476#97—111no—
477#97—111no—
478#97—111no—
479#97—111no—
480#97—111no—
481#97—111no—
482#97—221no—
483#97—221no—
484#97—221no—
485C4×C8—21no—
486C4×C8—221no—
487C4×C8—221no—
488C4×C8—221no—
489C2×C11—21no—
490C2×C11—21no—
491C2×C11—81no—
492C2×C11#229011yescharacteristic
493C2×C11#295611yescharacteristic
494C2×C11#295611yescharacteristic
495D11—42no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—112no—
501#41—112no—
502#41—221no—
503#41—221no—
504C2×Q8—111no—
505C2×Q8C2×C4×D1111yescharacteristic
506C2×D4—21no—
507C2×D4—111no—
508C2×D4—221no—
509C2×D4C2×C4×D1111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4C23×D1111yescharacteristic
521Q16—222no—
522SD16—222no—
523SD16—222no—
524D8—222no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—112no—
529M16—224no—
530M16—224no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16#434112yes—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—111no—
542C2×C8—111no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—224no—
546C2×C8—224no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8C2×C4×D1111yescharacteristic
554C2×C8C2×C4×D1111yescharacteristic
555C2×C8D4×D1111yescharacteristic
556C2×C8D4×D1111yescharacteristic
557C4⋊C4—111no—
558C4⋊C4—111no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4C2×C4×D1111yescharacteristic
564C4⋊C4C2×C4×D1111yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—221no—
567C22⋊C4—221no—
568C22⋊C4—221no—
569C22⋊C4—221no—
570C22⋊C4—221no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—111no—
575C42—111no—
576C42—111no—
577C42—111no—
578C42—221no—
579C42—221no—
580C42—221no—
581C42—221no—
582C42—221no—
583C42—221no—
584C42—221no—
585C42—442no—
586C42—442no—
587C11#2113911yescharacteristic, complemented, Sylow
588C23—21no—
589C23—221no—
590C23#41×D1111yescharacteristic
591Q8—21no—
592Q8—21no—
593Q8—112no—
594Q8—221no—
595D4—21no—
596D4—21no—
597D4—41no—
598D4—41no—
599D4—112no—
600D4—222no—
601D4—222no—
602D4—221no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—111no—
612C2×C4—111no—
613C2×C4—111no—
614C2×C4—111no—
615C2×C4—221no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—881no—
626C2×C4—881no—
627C2×C4—881no—
628C2×C4—881no—
629C2×C4C22×C4×D1111yescharacteristic
630C2×C4C2×D4×D1111yescharacteristic
631C2×C4C2×#434111yescharacteristic
632C2×C4#41×D1111yescharacteristic
633C2×C4#41×D1111yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C8—21no—
636C8—21no—
637C8—22no—
638C8—21no—
639C8—21no—
640C8—41no—
641C8—221no—
642C8—221no—
643C8—221no—
644C8—221no—
645C8—222no—
646C8—441no—
647C22—21no—
648C22—21no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—222no—
653C22—441no—
654C22—441no—
655C22C4×D4×D1111yescharacteristic
656C22#1062321111yescharacteristic
657C22#1062323711yescharacteristic
658C4—42no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—221no—
663C4—221no—
664C4—221no—
665C4—221no—
666C4—222no—
667C4—442no—
668C4—441no—
669C4—441no—
670C4D11×#11711yescharacteristic
671C4C4×#434111yescharacteristic
672C4#1062313711yescharacteristic
673C4#1062318711yescharacteristic
674C2—21no—
675C2—21no—
676C2—81no—
677C2—442no—
678C2#1307105811yescharacteristic
679C2#1307752111yescharacteristic
680C2#1307752411yescharacteristic
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#21139
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. #13077263C2semidirect
3. #13077043C2semidirect
4. #13069266C2semidirect
5. #13069215C2semidirect
6. #13069213C2semidirect
9. #13068894C2semidirect
10. #13068888C2semidirect
11. #13068524C2semidirect
12. #104×Dic11C2semidirect
13. #13068420C2semidirect
14. #13068363C2semidirect
15. C11×#1929C2semidirect
41. #10622430C4semidirect
42. #10622430C4semidirect
43. #10622402C4semidirect
44. #10622402C4semidirect
45. #10622398C4semidirect
46. #10622398C4semidirect
47. #10622370C4semidirect
48. #10622370C4semidirect
252. #1929D11semidirect
587. C11#21139semidirect

Maximal subgroups

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

subgroupindex
#130774122
#130772632
#130770432
#130692662
#130692152
#130692132
#130689462
#130689402
#130688942
#130688882
#130685242
#104×Dic112
#130684202
#130683632
C11×#19292
#2113911