Finite Group Databasebeta

← #14730408

Subgroups — #14730408

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079834C211yesmaximal, characteristic, complemented
2#13078998C211yesmaximal, characteristic, complemented
3C2×#10622621C211yesmaximal, characteristic, complemented
4#13067788C212yesmaximal, complemented
5#13067781C212yesmaximal, complemented
6#13067767C212yesmaximal, complemented
7#13067767C212yesmaximal, 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#10622706C2212yescomplemented
32#10622706C2212yescomplemented
33#10622682—22no—
34#10622678—21no—
35#10622668—21no—
36#10622656—21no—
37#10622646—21no—
38#10622634C2212yescomplemented
39#10622621—21no—
40#10622621—21no—
41#10622621C2212yes—
42#10622621C2212yes—
43#10622621C2212yescomplemented
44#10622617—22no—
45C2×#66872—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×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×#4318—21no—
124C22×C11⋊C8—21no—
125#66922—21no—
126#66922—21no—
127#66922—21no—
128#66922C2312yes—
129#66899—22no—
130#66896—22no—
131#66896—22no—
132#66896—22no—
133C22⋊(C11⋊C8)—21no—
134#66874—24no—
135#66874—24no—
136#66872—22no—
137#66872—22no—
138#66872—22no—
139#66871—22no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)C2312yes—
142C4⋊(C11⋊C8)C2312yes—
143#66867—21no—
144#66867—21no—
145C4×C11⋊C8C2312yes—
146#18579—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—44no—
181C2×Dic22—41no—
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×D411yescharacteristic
198C11×C4⋊C4C2×D411yescharacteristic
199C11×C4⋊C4C2×D412yes—
200C11×C4⋊C4C2×D412yes—
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
223C4⋊Dic11—22no—
224C4⋊Dic11—22no—
225C4⋊Dic11—41no—
226C4⋊Dic11—41no—
227#4318—42no—
228C2×C11⋊C8—22no—
229C2×C11⋊C8—22no—
230C2×C11⋊C8—22no—
231C2×C11⋊C8—42no—
232#3520D1111yescharacteristic
233#3238—111no—
234#3139—111no—
235C2×#476—111no—
236#1638—112no—
237#1637—112no—
238#1635—112no—
239#1635—112no—
240#1552—111no—
241#1490—111no—
242#1483—111no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—81no—
249C23×C11#12011yescharacteristic
250Q8×C11—22no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—42no—
254Q8×C11—82no—
255D4×C11—21no—
256D4×C11—21no—
257D4×C11—21no—
258D4×C11—22no—
259D4×C11—42no—
260D4×C11—44no—
261D4×C11—42no—
262D4×C11—82no—
263D4×C11#13712yes—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—44no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11—81no—
281C2×C4×C11—81no—
282C2×C4×C11—81no—
283C2×C4×C11—82no—
284C2×C4×C11—82no—
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C22×D411yescharacteristic
291C2×Dic11—42no—
292C2×Dic11—82no—
293Dic22—44no—
294Dic22—82no—
295C11⋊C8—42no—
296C11⋊C8—42no—
297C11⋊C8—42no—
298#556C2×D1111yescharacteristic
299#554—21no—
300#552—21no—
301#551—22no—
302D4×Q8C2×D1111yescharacteristic
303#548—21no—
304#547C2×D1111yescharacteristic
305#547C2×D1111yescharacteristic
306#546—21no—
307#542—21no—
308#539—22no—
309#533C2×D1111yescharacteristic
310C2×C4⋊Q8—111no—
311#529C2×D1111yescharacteristic
312#525—21no—
313C2×C22⋊Q8—21no—
314#520—21no—
315C2×C4×D4C2×D1111yescharacteristic
316#501—221no—
317#491—222no—
318#489—221no—
319#487—112no—
320#487—112no—
321#483—221no—
322#480—221no—
323#477—112no—
324#476—112no—
325#476—112no—
326#476—112no—
327#476—221no—
328#476—221no—
329#432—111no—
330C2×#106—221no—
331C2×C4⋊C8—111no—
332#419—222no—
333C2×#102—221no—
334C4×M16—111no—
335#332—112no—
336#332—112no—
337Q8⋊C8—112no—
338D4⋊C8—112no—
339D4⋊C8—112no—
340D4⋊C8—112no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—22no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—84no—
353C22×C11#45412yes—
354C22×C11C2×#12011yescharacteristic
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11C2×#13711yescharacteristic
367C4×C11#57511yescharacteristic
368C4×C11#57712yes—
369Dic11—82no—
370C2×#41—21no—
371C2×#41—21no—
372C22×Q8—21no—
373C22×Q8—221no—
374C22×D4C22⋊D1111yescharacteristic
375C23×C4—21no—
376C2×M16—221no—
377C22×C8—221no—
378C4⋊Q8—21no—
379C4⋊Q8—112no—
380C4⋊Q8—221no—
381C4⋊Q8—221no—
382C4⋊Q8—221no—
383C4⋊Q8C22×D1111yescharacteristic
384C4⋊Q8C22×D1111yescharacteristic
385#126—22no—
386#126—22no—
387#126—21no—
388#125—22no—
389#125C22⋊D1111yescharacteristic
390#125C22⋊D1112yes—
391#124—22no—
392#124—21no—
393#124C22⋊D1111yescharacteristic
394#123—22no—
395#123—22no—
396#123—21no—
397#123—22no—
398#123—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—22no—
408C22⋊Q8—21no—
409C22⋊Q8C22⋊D1111yescharacteristic
410#121—22no—
411#121—21no—
412#121—21no—
413#121C22⋊D1111yescharacteristic
414#120—22no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8C22×D1111yescharacteristic
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4C22⋊D1111yescharacteristic
427C4×D4C22⋊D1111yescharacteristic
428C4×D4C22×D1111yescharacteristic
429C4×D4C22×D1111yescharacteristic
430C4×D4C22×D1111yescharacteristic
431#117—22no—
432#117—21no—
433#117—21no—
434#117C22⋊D1112yes—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4C22⋊D1111yescharacteristic
441C2×C22⋊C4—22no—
442C2×C22⋊C4—21no—
443C2×C42C22×D1111yescharacteristic
444#107—222no—
445#106—222no—
446#106—222no—
447#106—222no—
448C4⋊C8—112no—
449C4⋊C8—112no—
450C4⋊C8—221no—
451#103—222no—
452#103—224no—
453#103—224no—
454#102—222no—
455#102—222no—
456#102—222no—
457C22⋊C8—221no—
458#97—221no—
459#97—221no—
460C4×C8—112no—
461C2×C11—22no—
462C2×C11—42no—
463C2×C11—81no—
464C2×C11—81no—
465C2×C11#300711yescharacteristic
466C2×C11#300911yescharacteristic
467C2×C11C2×#45411yescharacteristic
468C24—21no—
469#41—42no—
470#41—42no—
471#41—82no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—82no—
476C2×Q8—222no—
477C2×Q8—444no—
478C2×Q8—441no—
479C2×Q8C2×C22⋊D1111yescharacteristic
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4C2×C22⋊D1111yescharacteristic
487C2×D4C2×C22⋊D1111yescharacteristic
488C2×D4C2×C22⋊D1111yescharacteristic
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—82no—
499C22×C4—441no—
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503M16—442no—
504C2×C8—222no—
505C2×C8—222no—
506C2×C8—222no—
507C2×C8—442no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—441no—
524C4⋊C4—441no—
525C4⋊C4C2×C22⋊D1112yes—
526C4⋊C4C2×C22⋊D1112yes—
527C4⋊C4C2×C22⋊D1111yescharacteristic
528C4⋊C4C2×C22⋊D1111yescharacteristic
529C4⋊C4C2×C22⋊D1111yescharacteristic
530C4⋊C4C2×C22⋊D1111yescharacteristic
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—21no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C42—22no—
547C42—22no—
548C42—21no—
549C42C2×C22⋊D1111yescharacteristic
550C42C2×C22⋊D1111yescharacteristic
551C42C2×C22⋊D1111yescharacteristic
552C42C23×D1111yescharacteristic
553C11#1857911yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—21no—
557C23—42no—
558C23—42no—
559C23—81no—
560C23#6700611yescharacteristic
561Q8—22no—
562Q8—41no—
563Q8—41no—
564Q8—42no—
565Q8—82no—
566Q8—444no—
567Q8—882no—
568D4—21no—
569D4—21no—
570D4—21no—
571D4—22no—
572D4—42no—
573D4—44no—
574D4—42no—
575D4—82no—
576D4#6700412yes—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—44no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—442no—
599C2×C4—882no—
600C2×C4#6700611yescharacteristic
601C2×C4#6700611yescharacteristic
602C2×C4#6700611yescharacteristic
603C2×C4C22×C22⋊D1111yescharacteristic
604C2×C4C22×C22⋊D1111yescharacteristic
605C2×C4C22×C22⋊D1111yescharacteristic
606C8—442no—
607C8—442no—
608C8—442no—
609C22—21no—
610C22—21no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—84no—
621C22#1062285812yes—
622C22C2×#6700611yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—41no—
631C4—42no—
632C4—41no—
633C4—41no—
634C4—882no—
635C4#1062335311yescharacteristic
636C4C2×#6700411yescharacteristic
637C4#1062336712yes—
638C2—22no—
639C2—42no—
640C2—81no—
641C2—81no—
642C2#1307787611yescharacteristic
643C2#1307789311yescharacteristic
644C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3520C2
socleC22×C11C2×#120
hypercenter#3520D11
hypocenterC11#18579
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. #13079834C2semidirect
2. #13078998C2semidirect
3. C2×#10622621C2semidirect
4. #13067788C2semidirect
5. #13067781C2semidirect
6. #13067767C2semidirect
7. #13067767C2semidirect
8. #13067316C2semidirect
9. #13067059C2semidirect
10. #13067029C2semidirect
31. #10622706C22semidirect
32. #10622706C22semidirect
38. #10622634C22semidirect
43. #10622621C22semidirect
49. #10622185C22semidirect
50. #10622185C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
553. C11#18579semidirect

Maximal subgroups

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

subgroupindex
#130798342
#130789982
C2×#106226212
#130677882
#130677812
#130677672
#130673162
#130670592
#130670292
C11×#35202
#1857911