Finite Group Databasebeta

← #14729961

Subgroups — #14729961

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078998C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13078431C211yesmaximal, characteristic, complemented
4#13067788C212yesmaximal, complemented
5#13067781C212yesmaximal, complemented
6#13067774C212yesmaximal, complemented
7#13067767C212yesmaximal, complemented
8#13067354C211yesmaximal, characteristic, complemented
9#13067055C211yesmaximal, characteristic, complemented
10#13067055C211yesmaximal, characteristic, complemented
11C11×#3482C211yesmaximal, characteristic
12C11×#557C2211yescharacteristic
13C11×#556—21no—
14C11×#556C2211yescharacteristic
15C11×#552—22no—
16C11×#552—21no—
17D4×Q8×C11C2211yescharacteristic
18C11×#548—21no—
19C11×#547—21no—
20C11×#547C2211yescharacteristic
21C11×#533—21no—
22C11×#533C2211yescharacteristic
23C11×#529—21no—
24C11×#529—22no—
25C4×C11×#41—21no—
26C4×C11×#41C2211yescharacteristic
27C4×C11×#41C2211yescharacteristic
28C2×C4×Q8×C11—21no—
29C2×#66922C2211yescharacteristic
30#10622845—21no—
31#10622845—21no—
32#10622706C2212yes—
33#10622706C2212yes—
34#10622682—22no—
35#10622634C2212yes—
36#10622634C2212yes—
37#10622633—21no—
38#10622633—21no—
39#10622621C2212yes—
40#10622621C2212yes—
41#10622620—21no—
42#10622620—21no—
43#10622617—22no—
44#10622608—21no—
45#10622608—21no—
46#10622537C2211yescharacteristic
47#10622537C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49#10622185C2212yes—
50#10622185C2212yes—
51Q8⋊(C11⋊C8)C2212yes—
52Q8⋊(C11⋊C8)C2212yes—
53D4⋊(C11⋊C8)C2212yes—
54D4⋊(C11⋊C8)C2212yes—
55C2×C11×#41—21no—
56C2×C11×#41D411yescharacteristic
57C2×C11×#41D411yescharacteristic
58C22×Q8×C11—21no—
59C22×Dic22—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#126—22no—
65C11×#126—22no—
66C11×#126—22no—
67C11×#125—22no—
68C11×#125—22no—
69C11×#125—21no—
70C11×#125D412yes—
71C11×#124—22no—
72C11×#124—21no—
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—22no—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—21no—
83C11×#121—22no—
84C11×#121—21no—
85C4×Q8×C11—22no—
86C4×Q8×C11—22no—
87C4×Q8×C11—21no—
88C4×Q8×C11—21no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11D411yescharacteristic
93C4×Q8×C11D411yescharacteristic
94C4×Q8×C11C2311yescharacteristic
95C4×Q8×C11C2311yescharacteristic
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11—21no—
99C4×D4×C11—21no—
100C4×D4×C11—21no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11D411yescharacteristic
104C4×D4×C11D411yescharacteristic
105C4×D4×C11C2311yescharacteristic
106C4×D4×C11C2311yescharacteristic
107C11×#117—22no—
108C11×#117—22no—
109C11×#117—21no—
110C11×#117—21no—
111C11×#117—21no—
112C11×#117D411yescharacteristic
113C11×#117D411yescharacteristic
114C11×#117D412yes—
115C2×C11×C4⋊C4—22no—
116C2×C11×C4⋊C4—21no—
117C2×C42×C11—22no—
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11—21no—
123C2×#4318—21no—
124C2×#4318—21no—
125C2×#4318—21no—
126#66922—21no—
127#66922—21no—
128#66922—21no—
129#66922C2312yes—
130#66899—22no—
131#66899—22no—
132#66896—22no—
133#66896—22no—
134#66874—24no—
135#66874—24no—
136#66872—22no—
137#66872—22no—
138#66871—22no—
139#66871—22no—
140C4⋊(C11⋊C8)—21no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)C2312yes—
143C4⋊(C11⋊C8)C2312yes—
144#66867—21no—
145C4×C11⋊C8C2312yes—
146#18538—111nomaximal, Sylow
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—42no—
152C11×#41—42no—
153C2×Q8×C11—22no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11—42no—
157C2×Q8×C11—42no—
158C2×Q8×C11C2×D411yescharacteristic
159C2×Q8×C11C2×D411yescharacteristic
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11C2×D411yescharacteristic
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×Dic11—41no—
177C2×Dic22—22no—
178C2×Dic22—44no—
179C2×Dic22—41no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
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—22no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4C2×D411yescharacteristic
195C11×C4⋊C4C2×D411yescharacteristic
196C11×C4⋊C4C2×D411yescharacteristic
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D412yes—
199C11×C4⋊C4C2×D412yes—
200C11×C22⋊C4—22no—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—21no—
205C11×C22⋊C4—21no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—21no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—21no—
211C42×C11—22no—
212C42×C11—22no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—21no—
216C42×C11—22no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11C2×D411yescharacteristic
221C42×C11C2×D411yescharacteristic
222C42×C11C2×D411yescharacteristic
223C42×C11C2411yescharacteristic
224C4⋊Dic11—22no—
225C4⋊Dic11—22no—
226C4⋊Dic11—41no—
227C4⋊Dic11—41no—
228#4318—42no—
229#4318—42no—
230#4318—42no—
231C2×C11⋊C8—22no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8—22no—
234#3482D1111yescharacteristic
235#3139—111no—
236#3079—111no—
237#3079—111no—
238#1638—112no—
239#1637—112no—
240#1636—112no—
241#1635—112no—
242#1561—111no—
243#1489—111no—
244#1489—111no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11#12011yescharacteristic
248Q8×C11—21no—
249Q8×C11—21no—
250Q8×C11—21no—
251Q8×C11—44no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—41no—
255Q8×C11—41no—
256Q8×C11#13712yes—
257D4×C11—21no—
258D4×C11—21no—
259D4×C11—21no—
260D4×C11—42no—
261D4×C11—42no—
262D4×C11—44no—
263D4×C11#13712yes—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—44no—
280C2×C4×C11—44no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
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—44no—
296Dic22—82no—
297C11⋊C8—42no—
298C11⋊C8—42no—
299C11⋊C8—42no—
300#557C2×D1111yescharacteristic
301#556—21no—
302#556C2×D1111yescharacteristic
303#552—22no—
304#552—21no—
305D4×Q8C2×D1111yescharacteristic
306#548—21no—
307#547—21no—
308#547C2×D1111yescharacteristic
309#533—21no—
310#533C2×D1111yescharacteristic
311C2×C4⋊Q8—111no—
312#529—21no—
313#529—22no—
314C4×#41—21no—
315C4×#41C2×D1111yescharacteristic
316C4×#41C2×D1111yescharacteristic
317C2×C4×Q8—21no—
318#491—222no—
319#487—112no—
320#487—112no—
321#477—112no—
322#477—112no—
323#476—112no—
324#476—112no—
325#475—221no—
326#475—221no—
327#474—221no—
328#474—221no—
329#428—221no—
330#428—221no—
331#423—111no—
332#423—111no—
333#419—222no—
334#417—221no—
335#417—221no—
336C4×M16—111no—
337#332—112no—
338#332—112no—
339Q8⋊C8—112no—
340Q8⋊C8—112no—
341D4⋊C8—112no—
342D4⋊C8—112no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—22no—
346C22×C11—21no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11C2×#12011yescharacteristic
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—22no—
356C4×C11—21no—
357C4×C11—41no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11#45412yes—
365C4×C11C2×#13711yescharacteristic
366C4×C11C2×#13711yescharacteristic
367C4×C11#57511yescharacteristic
368C4×C11#57511yescharacteristic
369Dic11—82no—
370C2×#41—21no—
371C2×#41C22⋊D1111yescharacteristic
372C2×#41C22⋊D1111yescharacteristic
373C22×Q8—21no—
374C22×Q8—221no—
375C2×M16—221no—
376C2×M16—221no—
377C2×M16—221no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8—112no—
381C4⋊Q8—221no—
382C4⋊Q8—221no—
383C4⋊Q8—221no—
384C4⋊Q8C22×D1111yescharacteristic
385C4⋊Q8C22×D1111yescharacteristic
386#126—22no—
387#126—22no—
388#126—22no—
389#125—22no—
390#125—22no—
391#125—21no—
392#125C22⋊D1112yes—
393#124—22no—
394#124—21no—
395#123—22no—
396#123—22no—
397#123—22no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—22no—
404C22⋊Q8—21no—
405#121—22no—
406#121—21no—
407C4×Q8—22no—
408C4×Q8—22no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8C22⋊D1111yescharacteristic
415C4×Q8C22⋊D1111yescharacteristic
416C4×Q8C22×D1111yescharacteristic
417C4×Q8C22×D1111yescharacteristic
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4C22⋊D1111yescharacteristic
426C4×D4C22⋊D1111yescharacteristic
427C4×D4C22×D1111yescharacteristic
428C4×D4C22×D1111yescharacteristic
429#117—22no—
430#117—22no—
431#117—21no—
432#117—21no—
433#117—21no—
434#117C22⋊D1111yescharacteristic
435#117C22⋊D1111yescharacteristic
436#117C22⋊D1112yes—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C42—22no—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C22×D1111yescharacteristic
445#107—222no—
446#107—222no—
447#106—222no—
448#106—222no—
449C4⋊C8—112no—
450C4⋊C8—112no—
451C4⋊C8—221no—
452C4⋊C8—221no—
453#103—222no—
454#103—222no—
455#103—224no—
456#103—224no—
457#102—222no—
458#102—222no—
459#97—221no—
460C4×C8—112no—
461C2×C11—41no—
462C2×C11—42no—
463C2×C11—81no—
464C2×C11#300711yescharacteristic
465C2×C11#300711yescharacteristic
466C2×C11C2×#45411yescharacteristic
467#41—22no—
468#41—22no—
469#41—41no—
470#41—41no—
471#41—42no—
472#41—42no—
473C2×Q8—22no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—222no—
479C2×Q8—444no—
480C2×Q8—441no—
481C2×Q8C2×C22⋊D1111yescharacteristic
482C2×Q8C2×C22⋊D1111yescharacteristic
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×C22⋊D1111yescharacteristic
487C2×D4C2×C22⋊D1111yescharacteristic
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—441no—
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500M16—442no—
501M16—442no—
502M16—442no—
503C2×C8—222no—
504C2×C8—222no—
505C2×C8—222no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4—441no—
523C4⋊C4—441no—
524C4⋊C4C2×C22⋊D1112yes—
525C4⋊C4C2×C22⋊D1112yes—
526C4⋊C4C2×C22⋊D1111yescharacteristic
527C4⋊C4C2×C22⋊D1111yescharacteristic
528C4⋊C4C2×C22⋊D1111yescharacteristic
529C4⋊C4C2×C22⋊D1111yescharacteristic
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—22no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C42—22no—
542C42—22no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—22no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42C2×C22⋊D1111yescharacteristic
551C42C2×C22⋊D1111yescharacteristic
552C42C2×C22⋊D1111yescharacteristic
553C42C23×D1111yescharacteristic
554C11#1853811yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23#6700611yescharacteristic
558Q8—21no—
559Q8—21no—
560Q8—21no—
561Q8—44no—
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—444no—
567Q8—882no—
568Q8#6700412yes—
569D4—21no—
570D4—21no—
571D4—21no—
572D4—42no—
573D4—42no—
574D4—44no—
575D4#6700412yes—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—442no—
600C2×C4—882no—
601C2×C4#6700611yescharacteristic
602C2×C4#6700611yescharacteristic
603C2×C4#6700611yescharacteristic
604C2×C4C22×C22⋊D1111yescharacteristic
605C2×C4C22×C22⋊D1111yescharacteristic
606C2×C4C22×C22⋊D1111yescharacteristic
607C8—442no—
608C8—442no—
609C8—442no—
610C22—21no—
611C22—21no—
612C22—22no—
613C22—21no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22C2×#6700611yescharacteristic
620C4—21no—
621C4—21no—
622C4—22no—
623C4—21no—
624C4—41no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—882no—
632C4#1062285812yes—
633C4#1062335311yescharacteristic
634C4#1062335311yescharacteristic
635C4C2×#6700411yescharacteristic
636C4C2×#6700411yescharacteristic
637C2—41no—
638C2—42no—
639C2—81no—
640C2#1307787611yescharacteristic
641C2#1307787611yescharacteristic
642C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3482C2
socleC22×C11C2×#120
hypercenter#3482D11
hypocenterC11#18538
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #13078998C2semidirect
2. #13078431C2semidirect
3. #13078431C2semidirect
4. #13067788C2semidirect
5. #13067781C2semidirect
6. #13067774C2semidirect
7. #13067767C2semidirect
8. #13067354C2semidirect
9. #13067055C2semidirect
10. #13067055C2semidirect
554. C11#18538semidirect

Maximal subgroups

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

subgroupindex
#130789982
#130784312
#130677882
#130677812
#130677742
#130677672
#130673542
#130670552
C11×#34822
#1853811