Finite Group Databasebeta

← #14730496

Subgroups — #14730496

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079640C211yesmaximal, characteristic, complemented
2#13079163C211yesmaximal, characteristic, complemented
3C2×#10622620C211yesmaximal, characteristic, complemented
4#13067900C212yesmaximal, complemented
5#13067886C212yesmaximal, complemented
6#13067865C212yesmaximal, complemented
7#13067851C212yesmaximal, complemented
8#13067316C211yesmaximal, characteristic, complemented
9#13067059C211yesmaximal, characteristic, complemented
10#13067029C211yesmaximal, characteristic, complemented
11C11×#3520C211yesmaximal, characteristic
12C11×#556C2211yescharacteristic
13C11×#554—21no—
14C11×#552—21no—
15C11×#551—22no—
16D4×Q8×C11C2211yescharacteristic
17C11×#548—21no—
18C11×#547C2211yescharacteristic
19C11×#547C2211yescharacteristic
20C11×#546—21no—
21C11×#542—21no—
22C11×#539—22no—
23C11×#533C2211yescharacteristic
24C11×#529C2211yescharacteristic
25C11×#525—21no—
26C2×C11×C22⋊Q8—21no—
27C11×#520—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C2×#66922C2211yescharacteristic
30C2×#66896—21no—
31#10622692C2212yescomplemented
32#10622691C2212yescomplemented
33#10622682—21no—
34#10622678—22no—
35#10622673—21no—
36#10622663—21no—
37#10622653—21no—
38#10622644C2212yescomplemented
39#10622632C2212yescomplemented
40#10622620—21no—
41#10622620—21no—
42#10622620C2212yes—
43#10622620C2212yes—
44#10622608—22no—
45C2×#66871—21no—
46#10622539C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49#10622185C2212yescomplemented
50#10622185C2212yescomplemented
51Q8⋊(C11⋊C8)C2212yescomplemented
52D4⋊(C11⋊C8)C2212yes—
53D4⋊(C11⋊C8)C2212yes—
54D4⋊(C11⋊C8)C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×D4×C11D411yescharacteristic
59C23×C4×C11—21no—
60C22×Dic22—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#126—22no—
65C11×#126—22no—
66C11×#126—21no—
67C11×#125—22no—
68C11×#125D411yescharacteristic
69C11×#125D412yes—
70C11×#124—22no—
71C11×#124—21no—
72C11×#124D411yescharacteristic
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—21no—
76C11×#123—22no—
77C11×#123—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8D411yescharacteristic
89C11×#121—22no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121D411yescharacteristic
93C11×#120—22no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11C2311yescharacteristic
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11D411yescharacteristic
106C4×D4×C11D411yescharacteristic
107C4×D4×C11C2311yescharacteristic
108C4×D4×C11C2311yescharacteristic
109C4×D4×C11C2311yescharacteristic
110C11×#117—22no—
111C11×#117—21no—
112C11×#117—21no—
113C11×#117D412yes—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—21no—
120C2×C42×C11C2311yescharacteristic
121C2×#4326—22no—
122C2×#4324—22no—
123C2×C4⋊Dic11—21no—
124C2×C4⋊Dic11—21no—
125C2×#4318—21no—
126C22×C11⋊C8—21no—
127#66922—21no—
128#66922—21no—
129#66922—21no—
130#66922C2312yes—
131#66896—22no—
132#66896—22no—
133C22⋊(C11⋊C8)—21no—
134#66874—22no—
135#66874—22no—
136#66872—24no—
137#66871—22no—
138#66871—22no—
139#66871—24no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)C2312yes—
142C4⋊(C11⋊C8)C2312yes—
143#66867—21no—
144#66867—21no—
145C4×C11⋊C8C2312yes—
146#18587—111nomaximal, Sylow
147C24×C11—21no—
148C11×#41—42no—
149C11×#41—42no—
150C11×#41—82no—
151C2×Q8×C11—22no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—82no—
155C2×Q8×C11C2×D411yescharacteristic
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—21no—
159C2×D4×C11—22no—
160C2×D4×C11—21no—
161C2×D4×C11—41no—
162C2×D4×C11C2×D411yescharacteristic
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11C2×D411yescharacteristic
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—82no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×Dic11—41no—
179C2×Dic22—22no—
180C2×Dic22—41no—
181C2×Dic22—82no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D412yes—
198C11×C4⋊C4C2×D412yes—
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—21no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11—21no—
219C42×C11C2×D411yescharacteristic
220C42×C11C2×D411yescharacteristic
221C42×C11C2×D411yescharacteristic
222C42×C11C2411yescharacteristic
223#4326—82no—
224#4324—82no—
225C4⋊Dic11—22no—
226C4⋊Dic11—22no—
227C4⋊Dic11—41no—
228C4⋊Dic11—41no—
229#4318—24no—
230C2×C11⋊C8—22no—
231C2×C11⋊C8—22no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8—42no—
234#3520D1111yescharacteristic
235#3218—111no—
236#3165—111no—
237C2×#474—111no—
238#1654—112no—
239#1652—112no—
240#1649—112no—
241#1647—112no—
242#1552—111no—
243#1490—111no—
244#1483—111no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—42no—
249C23×C11—42no—
250C23×C11—81no—
251C23×C11#12011yescharacteristic
252Q8×C11—22no—
253Q8×C11—41no—
254Q8×C11—41no—
255Q8×C11—42no—
256Q8×C11—82no—
257D4×C11—21no—
258D4×C11—21no—
259D4×C11—21no—
260D4×C11—22no—
261D4×C11—42no—
262D4×C11—44no—
263D4×C11—42no—
264D4×C11—82no—
265D4×C11#13712yes—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—44no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—81no—
283C2×C4×C11—81no—
284C2×C4×C11—81no—
285C2×C4×C11—82no—
286C2×C4×C11—82no—
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11#12011yescharacteristic
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×C4×C11C22×D411yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×Dic11—42no—
294C2×Dic11—82no—
295Dic22—42no—
296Dic22—42no—
297Dic22—82no—
298C11⋊C8—24no—
299C11⋊C8—42no—
300C11⋊C8—42no—
301#556C2×D1111yescharacteristic
302#554—21no—
303#552—21no—
304#551—22no—
305D4×Q8C2×D1111yescharacteristic
306#548—21no—
307#547C2×D1111yescharacteristic
308#547C2×D1111yescharacteristic
309#546—21no—
310#542—21no—
311#539—22no—
312#533C2×D1111yescharacteristic
313C2×C4⋊Q8—111no—
314#529C2×D1111yescharacteristic
315#525—21no—
316C2×C22⋊Q8—21no—
317#520—21no—
318C2×C4×D4C2×D1111yescharacteristic
319#501—222no—
320#500—112no—
321#498—112no—
322#497—221no—
323#491—221no—
324#474—112no—
325#474—112no—
326#474—221no—
327#474—221no—
328#462—112no—
329#461—112no—
330#451—221no—
331#448—221no—
332#432—111no—
333#428—222no—
334C2×#107—221no—
335C2×C4⋊C8—111no—
336C2×#102—221no—
337C4×M16—111no—
338#332—112no—
339#332—112no—
340Q8⋊C8—112no—
341D4⋊C8—112no—
342D4⋊C8—112no—
343D4⋊C8—112no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—22no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—84no—
356C22×C11#45612yes—
357C22×C11C2×#12011yescharacteristic
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11C2×#13711yescharacteristic
370C4×C11#57511yescharacteristic
371C4×C11#57612yes—
372Dic11—82no—
373C2×#41—21no—
374C2×#41—21no—
375C22×Q8—21no—
376C22×Q8—221no—
377C22×D4C22⋊D1111yescharacteristic
378C23×C4—21no—
379C2×Q16—222no—
380C2×SD16—222no—
381C2×M16—221no—
382C22×C8—221no—
383C4⋊Q8—21no—
384C4⋊Q8—112no—
385C4⋊Q8—221no—
386C4⋊Q8—221no—
387C4⋊Q8—221no—
388C4⋊Q8C22×D1111yescharacteristic
389C4⋊Q8C22×D1111yescharacteristic
390#126—22no—
391#126—22no—
392#126—21no—
393#125—22no—
394#125C22⋊D1111yescharacteristic
395#125C22⋊D1112yes—
396#124—22no—
397#124—21no—
398#124C22⋊D1111yescharacteristic
399#123—22no—
400#123—22no—
401#123—21no—
402#123—22no—
403#123—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414C22⋊Q8C22⋊D1111yescharacteristic
415#121—22no—
416#121—21no—
417#121—21no—
418#121C22⋊D1111yescharacteristic
419#120—22no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—21no—
423C4×Q8C22×D1111yescharacteristic
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—21no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4C22⋊D1111yescharacteristic
432C4×D4C22⋊D1111yescharacteristic
433C4×D4C22×D1111yescharacteristic
434C4×D4C22×D1111yescharacteristic
435C4×D4C22×D1111yescharacteristic
436#117—22no—
437#117—21no—
438#117—21no—
439#117C22⋊D1112yes—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4C22⋊D1111yescharacteristic
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C42C22×D1111yescharacteristic
449#107—222no—
450#107—222no—
451#107—224no—
452#106—224no—
453C4⋊C8—112no—
454C4⋊C8—112no—
455C4⋊C8—221no—
456#103—222no—
457#103—222no—
458#102—222no—
459#102—222no—
460C22⋊C8—221no—
461#97—221no—
462#97—221no—
463C4×C8—112no—
464C2×C11—22no—
465C2×C11—42no—
466C2×C11—81no—
467C2×C11—81no—
468C2×C11#300711yescharacteristic
469C2×C11#300811yescharacteristic
470C2×C11C2×#45611yescharacteristic
471C24—21no—
472#41—42no—
473#41—42no—
474#41—82no—
475C2×Q8—22no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—82no—
479C2×Q8—222no—
480C2×Q8—441no—
481C2×Q8—882no—
482C2×Q8C2×C22⋊D1111yescharacteristic
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—21no—
486C2×D4—22no—
487C2×D4—21no—
488C2×D4—41no—
489C2×D4C2×C22⋊D1111yescharacteristic
490C2×D4C2×C22⋊D1111yescharacteristic
491C2×D4C2×C22⋊D1111yescharacteristic
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—82no—
502C22×C4—441no—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506Q16—882no—
507SD16—882no—
508M16—224no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—222no—
512C2×C8—442no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—441no—
529C4⋊C4—441no—
530C4⋊C4C2×C22⋊D1111yescharacteristic
531C4⋊C4C2×C22⋊D1111yescharacteristic
532C4⋊C4C2×C22⋊D1112yes—
533C4⋊C4C2×C22⋊D1111yescharacteristic
534C4⋊C4C2×C22⋊D1111yescharacteristic
535C4⋊C4C2×C22⋊D1112yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C42—22no—
552C42—22no—
553C42—21no—
554C42C2×C22⋊D1111yescharacteristic
555C42C2×C22⋊D1111yescharacteristic
556C42C2×C22⋊D1111yescharacteristic
557C42C23×D1111yescharacteristic
558C11#1858711yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—42no—
563C23—42no—
564C23—81no—
565C23#6700611yescharacteristic
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—42no—
570Q8—82no—
571Q8—442no—
572Q8—442no—
573Q8—882no—
574D4—21no—
575D4—21no—
576D4—21no—
577D4—22no—
578D4—42no—
579D4—44no—
580D4—42no—
581D4—82no—
582D4#6700412yes—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—44no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—81no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—442no—
605C2×C4—882no—
606C2×C4#6700611yescharacteristic
607C2×C4#6700611yescharacteristic
608C2×C4#6700611yescharacteristic
609C2×C4C22×C22⋊D1111yescharacteristic
610C2×C4C22×C22⋊D1111yescharacteristic
611C2×C4C22×C22⋊D1111yescharacteristic
612C8—224no—
613C8—442no—
614C8—442no—
615C22—21no—
616C22—21no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—84no—
627C22#1062285912yes—
628C22C2×#6700611yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—42no—
635C4—41no—
636C4—41no—
637C4—42no—
638C4—41no—
639C4—41no—
640C4—882no—
641C4#1062335311yescharacteristic
642C4C2×#6700411yescharacteristic
643C4#1062336612yes—
644C2—22no—
645C2—42no—
646C2—81no—
647C2—81no—
648C2#1307787611yescharacteristic
649C2#1307788411yescharacteristic
650C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3520C2
socleC22×C11C2×#120
hypercenter#3520D11
hypocenterC11#18587
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #13079640C2semidirect
2. #13079163C2semidirect
3. C2×#10622620C2semidirect
4. #13067900C2semidirect
5. #13067886C2semidirect
6. #13067865C2semidirect
7. #13067851C2semidirect
8. #13067316C2semidirect
9. #13067059C2semidirect
10. #13067029C2semidirect
31. #10622692C22semidirect
32. #10622691C22semidirect
38. #10622644C22semidirect
39. #10622632C22semidirect
49. #10622185C22semidirect
50. #10622185C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
558. C11#18587semidirect

Maximal subgroups

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

subgroupindex
#130796402
#130791632
C2×#106226202
#130679002
#130678862
#130678652
#130678512
#130673162
#130670592
#130670292
C11×#35202
#1858711