Finite Group Databasebeta

← #14757016

Subgroups — #14757016

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#13077417C211yesmaximal, characteristic
2#13077263C211yesmaximal, characteristic, complemented
3#13077042C211yesmaximal, 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#104×Dic11C211yesmaximal, characteristic, complemented
13#104×Dic11C211yesmaximal, characteristic, complemented
14#13068363C211yesmaximal, 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×#66879—21no—
50C2×#66879C2211yescharacteristic
51C2×#66879C2211yescharacteristic
52C42×Dic11C2211yescharacteristic
53#10622333—21no—
54#10622333—21no—
55#10622332—21no—
56#10622332—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×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×#4318—21no—
109C2×#4318C2311yescharacteristic
110C2×#4318C2311yescharacteristic
111C22×C11⋊C8—21no—
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C11×#104—22no—
115C11×#104—22no—
116C11×C22⋊C8—21no—
117C11×C22⋊C8—21no—
118#66901—22no—
119#66901—22no—
120#66899C2×C411yescharacteristic
121#66899C2×C411yescharacteristic
122#66899C2×C411yescharacteristic
123#66899C2×C411yescharacteristic
124#66896C2×C411yescharacteristic
125#66896C2×C411yescharacteristic
126#66896C2×C411yescharacteristic
127#66896C2×C411yescharacteristic
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
144#66879D411yescharacteristic
145#66879D411yescharacteristic
146#66879D411yescharacteristic
147#66879D411yescharacteristic
148Dic11⋊C8—21no—
149Dic11⋊C8—21no—
150Dic11⋊C8—21no—
151Dic11⋊C8—21no—
152C8×Dic11—21no—
153C8×Dic11—21no—
154C8×Dic11—21no—
155C8×Dic11—21no—
156#21139—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×Dic11—42no—
227C4×Dic11—42no—
228C4×Dic11C22×C411yescharacteristic
229C4×Dic11C22×C411yescharacteristic
230C4×Dic11C2×D411yescharacteristic
231C4×Dic11C2×D411yescharacteristic
232#4318—24no—
233#4318—21no—
234#4318—21no—
235#4318—21no—
236#4318#4112yes—
237C2×C11⋊C8—24no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C411yescharacteristic
245C2×C11⋊C8C22×C411yescharacteristic
246C2×C11⋊C8C2×D411yescharacteristic
247C2×C11⋊C8C2×D411yescharacteristic
248#2943—111no—
249#2923—111no—
250#2875—111no—
251#1929—111no—
252#1929—111no—
253#1922—111no—
254#1922—111no—
255#1876—111no—
256#1876D1111yescharacteristic
257#1866—111no—
258#1866—111no—
259#1778—111no—
260C4×#104—111no—
261C4×#104—111no—
262#1745—111no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11C2×#4111yescharacteristic
266Q8×C11—21no—
267Q8×C11—21no—
268Q8×C11—21no—
269Q8×C11#11712yes—
270D4×C11—22no—
271D4×C11—22no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—21no—
275D4×C11—41no—
276D4×C11—41no—
277D4×C11#11712yes—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—21no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11C23×C411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×Dic11—22no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—81no—
303C2×Dic11—81no—
304C2×Dic11—81no—
305C2×Dic11—81no—
306C2×Dic11C4×D411yescharacteristic
307C2×Dic11C4×D411yescharacteristic
308C2×Dic11C4×D411yescharacteristic
309C2×Dic11C4×D411yescharacteristic
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×#135C2×D1111yescharacteristic
323C2×#131—111no—
324C2×#131C2×D1111yescharacteristic
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×#108—111no—
341#427—111no—
342#424—111no—
343#424—111no—
344C2×#104—111no—
345C2×#104—111no—
346C2×#104C2×D1111yescharacteristic
347C2×#104C2×D1111yescharacteristic
348#416—111no—
349#416—111no—
350#408—111no—
351#408C2×D1111yescharacteristic
352#405—111no—
353#405—111no—
354#405—221no—
355#405—221no—
356C4×M16—111no—
357C4×M16—111no—
358C4×M16—221no—
359C2×#97—111no—
360C2×#97—111no—
361C2×#97—221no—
362C43—111no—
363#341—111no—
364#341C2×D1111yescharacteristic
365#339—111no—
366#339—111no—
367#339—111no—
368#339—111no—
369#336—111no—
370#336—111no—
371#336—111no—
372#336C2×D1111yescharacteristic
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11C2×C4×D411yescharacteristic
382C22×C11#52911yescharacteristic
383C22×C11#52911yescharacteristic
384C4×C11—22no—
385C4×C11—42no—
386C4×C11—41no—
387C4×C11C2×#11711yescharacteristic
388C4×C11C4×#4111yescharacteristic
389C4×C11#52511yescharacteristic
390C4×C11#52511yescharacteristic
391Dic11—21no—
392Dic11—21no—
393Dic11—21no—
394Dic11—21no—
395Dic11—42no—
396Dic11—41no—
397Dic11—41no—
398Dic11—41no—
399Dic11—41no—
400C2×#41C22×D1111yescharacteristic
401C2×#41C22×D1111yescharacteristic
402#135—22no—
403#135—22no—
404C2×Q16C4×D1111yescharacteristic
405C2×SD16C4×D1111yescharacteristic
406C2×SD16C4×D1111yescharacteristic
407C2×D8C4×D1111yescharacteristic
408#131—22no—
409#131—22no—
410#131—222no—
411#131—222no—
412C2×M16—21no—
413C2×M16—111no—
414C2×M16—111no—
415C2×M16—221no—
416C2×M16C22×D1111yescharacteristic
417C2×M16C22×D1111yescharacteristic
418C22×C8—21no—
419C22×C8—111no—
420C22×C8—111no—
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—111no—
438#117—221no—
439#117—221no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447#108—222no—
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—22no—
459#104—222no—
460#104—222no—
461#103—111no—
462#103—111no—
463#103—111no—
464#103—111no—
465#102—111no—
466#102—111no—
467#102—111no—
468#102—111no—
469C22⋊C8—21no—
470C22⋊C8—21no—
471C22⋊C8—221no—
472C22⋊C8—221no—
473#97—111no—
474#97—111no—
475#97—111no—
476#97—111no—
477#97—111no—
478#97—111no—
479#97—111no—
480#97—111no—
481#97—221no—
482#97—221no—
483#97—221no—
484#97—221no—
485C4×C8—221no—
486C4×C8—221no—
487C4×C8—221no—
488C4×C8—221no—
489C2×C11—21no—
490C2×C11—21no—
491C2×C11—42no—
492C2×C11—81no—
493C2×C11#229011yescharacteristic
494C2×C11#295611yescharacteristic
495C2×C11#295611yescharacteristic
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—21no—
501#41—21no—
502#41#434112yes—
503#41#434112yes—
504C2×Q8C2×C4×D1111yescharacteristic
505C2×Q8C2×C4×D1111yescharacteristic
506C2×D4—21no—
507C2×D4—21no—
508C2×D4C2×C4×D1111yescharacteristic
509C2×D4C2×C4×D1111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4C23×D1111yescharacteristic
521Q16—22no—
522SD16—22no—
523SD16—22no—
524D8—22no—
525M16—24no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—112no—
530M16—224no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16#434112yes—
535C2×C8—24no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—111no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—111no—
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—111no—
560C4⋊C4—111no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C22⋊C4—221no—
566C22⋊C4—221no—
567C22⋊C4—221no—
568C22⋊C4—221no—
569C22⋊C4—221no—
570C22⋊C4—221no—
571C42—21no—
572C42—21no—
573C42—111no—
574C42—111no—
575C42—111no—
576C42—111no—
577C42—221no—
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—21no—
590C23#41×D1111yescharacteristic
591Q8—21no—
592Q8—21no—
593Q8—21no—
594Q8#6693012yes—
595D4—22no—
596D4—22no—
597D4—21no—
598D4—21no—
599D4—21no—
600D4—41no—
601D4—41no—
602D4#6693012yes—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—111no—
613C2×C4—111no—
614C2×C4—111no—
615C2×C4—111no—
616C2×C4—222no—
617C2×C4—221no—
618C2×C4—221no—
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×C4C2×#434111yescharacteristic
633C2×C4C2×#434111yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C8—21no—
636C8—21no—
637C8—21no—
638C8—22no—
639C8—21no—
640C8—41no—
641C8—221no—
642C8—221no—
643C8—221no—
644C8—221no—
645C8—222no—
646C8—441no—
647C22—21no—
648C22—21no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22C4×D4×D1111yescharacteristic
656C22#1062313111yescharacteristic
657C22#1062318011yescharacteristic
658C4—22no—
659C4—42no—
660C4—41no—
661C4—221no—
662C4—221no—
663C4—221no—
664C4—221no—
665C4—442no—
666C4—441no—
667C4—441no—
668C4—441no—
669C4—441no—
670C4C2×#6693011yescharacteristic
671C4C4×#434111yescharacteristic
672C4#1062311711yescharacteristic
673C4#1062313711yescharacteristic
674C2—21no—
675C2—21no—
676C2—42no—
677C2—81no—
678C2#1307105611yescharacteristic
679C2#1307752111yescharacteristic
680C2#1307752411yescharacteristic
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#21139
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. #13077263C2semidirect
3. #13077042C2semidirect
4. #13069267C2semidirect
5. #13069261C2semidirect
6. #13069216C2semidirect
7. #13069214C2semidirect
9. #13068891C2semidirect
10. #13068889C2semidirect
11. #13068521C2semidirect
12. #104×Dic11C2semidirect
13. #104×Dic11C2semidirect
14. #13068363C2semidirect
29. #10622797C4semidirect
30. #10622797C4semidirect
31. #10622777C4semidirect
32. #10622777C4semidirect
33. #10622777C4semidirect
34. #10622777C4semidirect
35. #10622765C4semidirect
36. #10622765C4semidirect
587. C11#21139semidirect

Maximal subgroups

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

subgroupindex
#130774172
#130772632
#130770422
#130692672
#130692612
#130692162
#130692142
#130689452
#130688912
#130688892
#130685212
#104×Dic112
#130683632
C11×#18762
#2113911