Finite Group Databasebeta

← #14729950

Subgroups — #14729950

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078992C211yesmaximal, characteristic, complemented
2#13078096C211yesmaximal, characteristic, complemented
3#13078096C211yesmaximal, characteristic, complemented
4#13067726C212yesmaximal, complemented
5#13067719C212yesmaximal, complemented
6#13067712C212yesmaximal, complemented
7#13067705C212yesmaximal, complemented
8#13067354C211yesmaximal, characteristic, complemented
9#13067055C211yesmaximal, characteristic, complemented
10#13067055C211yesmaximal, characteristic, complemented
11C11×#3482C211yesmaximal, characteristic, complemented
12C11×#557C2211yescharacteristic, complemented
13C11×#556—21no—
14C11×#556C2211yescharacteristic, complemented
15C11×#552—22no—
16C11×#552—21no—
17D4×Q8×C11C2211yescharacteristic, complemented
18C11×#548—21no—
19C11×#547—21no—
20C11×#547C2211yescharacteristic, complemented
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×#67002—21no—
30C2×#67002—21no—
31C2×#66927C2211yescharacteristic
32#10622701C2212yes—
33#10622701C2212yes—
34#10622680—22no—
35#10622640—21no—
36#10622640—21no—
37#10622640C2212yes—
38#10622640C2212yes—
39#10622628—21no—
40#10622628—21no—
41#10622628C2212yes—
42#10622628C2212yes—
43#10622614—21no—
44#10622614—21no—
45#10622614—22no—
46#10622537C2211yescharacteristic
47#10622537C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49#10622185C2212yescomplemented
50#10622185C2212yescomplemented
51Q8⋊(C11⋊C8)C2212yescomplemented
52Q8⋊(C11⋊C8)C2212yescomplemented
53D4⋊(C11⋊C8)C2212yescomplemented
54D4⋊(C11⋊C8)C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41D411yescharacteristic
57C2×C11×#41D411yescharacteristic
58C22×Q8×C11—21no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8C2311yescharacteristic
65C11×C4⋊Q8C2311yescharacteristic
66C11×#126—22no—
67C11×#126—22no—
68C11×#126—22no—
69C11×#125—22no—
70C11×#125—22no—
71C11×#125—21no—
72C11×#125D412yes—
73C11×#124—22no—
74C11×#124—21no—
75C11×#123—22no—
76C11×#123—22no—
77C11×#123—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—21no—
85C11×#121—22no—
86C11×#121—21no—
87C4×Q8×C11—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—21no—
90C4×Q8×C11—21no—
91C4×Q8×C11—21no—
92C4×Q8×C11—21no—
93C4×Q8×C11—21no—
94C4×Q8×C11D411yescharacteristic
95C4×Q8×C11D411yescharacteristic
96C4×Q8×C11C2311yescharacteristic
97C4×Q8×C11C2311yescharacteristic
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—21no—
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
109C11×#117—22no—
110C11×#117—22no—
111C11×#117—21no—
112C11×#117—21no—
113C11×#117—21no—
114C11×#117D411yescharacteristic
115C11×#117D411yescharacteristic
116C11×#117D412yes—
117C2×C11×C4⋊C4—22no—
118C2×C11×C4⋊C4—21no—
119C2×C42×C11—22no—
120C2×C42×C11—21no—
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123#67002—44no—
124#67002—44no—
125C2×#4325—22no—
126C2×#4325—22no—
127C2×#4323—22no—
128C2×#4323—22no—
129C2×#4318—21no—
130C2×#4318—21no—
131C2×#4318—21no—
132#66927—21no—
133#66927—21no—
134#66927—21no—
135#66927C2312yes—
136#66873—22no—
137#66873—22no—
138#66873—22no—
139#66873—22no—
140#66873—24no—
141#66873—24no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)—21no—
144C4⋊(C11⋊C8)C2312yes—
145C4⋊(C11⋊C8)C2312yes—
146#66867—21no—
147C4×C11⋊C8C2312yes—
148#18537—111nomaximal, Sylow
149C23×D11—41no—
150C11×#41—22no—
151C11×#41—22no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—42no—
155C11×#41—42no—
156C2×Q8×C11—22no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—42no—
160C2×Q8×C11—42no—
161C2×Q8×C11C2×D411yescharacteristic
162C2×Q8×C11C2×D411yescharacteristic
163C2×D4×C11—22no—
164C2×D4×C11—21no—
165C2×D4×C11—21no—
166C2×D4×C11C2×D411yescharacteristic
167C2×D4×C11C2×D411yescharacteristic
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C2×D44—22no—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44—42no—
183C2×D44—42no—
184C2×D44—42no—
185C2×D44—42no—
186C2×D44—44no—
187C2×D44—41no—
188C2×D44—41no—
189C2×D44—41no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C4⋊C4C2×D411yescharacteristic
207C11×C4⋊C4C2×D411yescharacteristic
208C11×C4⋊C4C2×D412yes—
209C11×C4⋊C4C2×D412yes—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—22no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—22no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—22no—
217C11×C22⋊C4—21no—
218C11×C22⋊C4—21no—
219C11×C22⋊C4—21no—
220C11×C22⋊C4—21no—
221C42×C11—22no—
222C42×C11—22no—
223C42×C11—21no—
224C42×C11—21no—
225C42×C11—21no—
226C42×C11—22no—
227C42×C11—21no—
228C42×C11—21no—
229C42×C11—21no—
230C42×C11C2×D411yescharacteristic
231C42×C11C2×D411yescharacteristic
232C42×C11C2×D411yescharacteristic
233C42×C11C2411yescharacteristic
234#4325—44no—
235#4325—44no—
236#4323—44no—
237#4323—44no—
238#4318—42no—
239#4318—42no—
240#4318—42no—
241C2×C11⋊C8—22no—
242C2×C11⋊C8—22no—
243C2×C11⋊C8—22no—
244#3482D1111yescharacteristic, complemented
245#3138—111no—
246#3038—111no—
247#3038—111no—
248#1628—112no—
249#1627—112no—
250#1626—112no—
251#1625—112no—
252#1561—111no—
253#1489—111no—
254#1489—111no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11#12011yescharacteristic
258C22×D11—42no—
259C22×D11—82no—
260C22×D11—82no—
261C22×D11—82no—
262Q8×C11—21no—
263Q8×C11—21no—
264Q8×C11—21no—
265Q8×C11—44no—
266Q8×C11—41no—
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11AGL(1,ℤ/8)12yescomplemented
271D4×C11—21no—
272D4×C11—21no—
273D4×C11—21no—
274D4×C11—42no—
275D4×C11—42no—
276D4×C11—44no—
277D4×C11AGL(1,ℤ/8)12yescomplemented
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—22no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—44no—
294C2×C4×C11—44no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11#12011yescharacteristic
302C2×C4×C11#12011yescharacteristic
303C2×C4×C11#12011yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307D44—44no—
308D44—42no—
309D44—42no—
310D44—42no—
311D44—42no—
312D44—82no—
313D44—82no—
314D44—82no—
315C11⋊C8—42no—
316C11⋊C8—42no—
317C11⋊C8—42no—
318C2×AGL(1,ℤ/8)—221no—
319C2×AGL(1,ℤ/8)—221no—
320#557C2×D1111yescharacteristic, complemented
321#556—21no—
322#556C2×D1111yescharacteristic, complemented
323#552—22no—
324#552—21no—
325D4×Q8C2×D1111yescharacteristic, complemented
326#548—21no—
327#547—21no—
328#547C2×D1111yescharacteristic, complemented
329#533—21no—
330#533C2×D1111yescharacteristic
331C2×#127—111no—
332#529—21no—
333#529—22no—
334C4×#41—21no—
335C4×#41C2×D1111yescharacteristic
336C4×#41C2×D1111yescharacteristic
337C2×C4×Q8—21no—
338#490—222no—
339#486—112no—
340#486—112no—
341#460—112no—
342#460—112no—
343#460—221no—
344#460—221no—
345#459—112no—
346#459—112no—
347#459—221no—
348#459—221no—
349#423—111no—
350#423—111no—
351#418—222no—
352#418—221no—
353#418—221no—
354C4×M16—111no—
355#332—112no—
356#332—112no—
357Q8⋊C8—112no—
358Q8⋊C8—112no—
359D4⋊C8—112no—
360D4⋊C8—112no—
361C22×C11—21no—
362C22×C11—21no—
363C22×C11—22no—
364C22×C11—21no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11C2×#12011yescharacteristic
371C2×D11—82no—
372C2×D11—82no—
373C2×D11—82no—
374C2×D11—164no—
375C4×C11—21no—
376C4×C11—21no—
377C4×C11—22no—
378C4×C11—21no—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11#45412yes—
387C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
388C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
389C4×C11#57511yescharacteristic
390C4×C11#57511yescharacteristic
391C2×#41—21no—
392C2×#41C22⋊D1111yescharacteristic
393C2×#41C22⋊D1111yescharacteristic
394C22×Q8—21no—
395C22×D4—221no—
396C22×D4—221no—
397C22×D4—221no—
398AGL(1,ℤ/8)—444no—
399AGL(1,ℤ/8)—444no—
400C2×SD16—222no—
401C2×SD16—222no—
402C2×D8—222no—
403C2×D8—222no—
404C2×M16—221no—
405C2×M16—221no—
406C2×M16—221no—
407C4⋊Q8—21no—
408C4⋊Q8—21no—
409C4⋊Q8C22×D1111yescharacteristic
410C4⋊Q8C22×D1111yescharacteristic
411#127—112no—
412#127—221no—
413#127—221no—
414#127—221no—
415#126—22no—
416#126—22no—
417#126—22no—
418#125—22no—
419#125—22no—
420#125—21no—
421#125C22⋊D1112yes—
422#124—22no—
423#124—21no—
424#123—22no—
425#123—22no—
426#123—22no—
427C22⋊Q8—22no—
428C22⋊Q8—21no—
429C22⋊Q8—21no—
430C22⋊Q8—21no—
431C22⋊Q8—21no—
432C22⋊Q8—22no—
433C22⋊Q8—21no—
434#121—22no—
435#121—21no—
436C4×Q8—22no—
437C4×Q8—22no—
438C4×Q8—21no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8—21no—
443C4×Q8C22⋊D1111yescharacteristic
444C4×Q8C22⋊D1111yescharacteristic
445C4×Q8C22×D1111yescharacteristic
446C4×Q8C22×D1111yescharacteristic
447C4×D4—22no—
448C4×D4—22no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4—21no—
453C4×D4—21no—
454C4×D4C22⋊D1111yescharacteristic
455C4×D4C22⋊D1111yescharacteristic
456C4×D4C22×D1111yescharacteristic
457C4×D4C22×D1111yescharacteristic
458#117—22no—
459#117—22no—
460#117—21no—
461#117—21no—
462#117—21no—
463#117C22⋊D1111yescharacteristic
464#117C22⋊D1111yescharacteristic
465#117C22⋊D1112yes—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—21no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C22×D1111yescharacteristic
472C4⋊C8—112no—
473C4⋊C8—112no—
474C4⋊C8—221no—
475C4⋊C8—221no—
476#102—222no—
477#102—222no—
478#102—222no—
479#102—222no—
480#102—224no—
481#102—224no—
482#97—221no—
483C4×C8—112no—
484C2×C11—41no—
485C2×C11—42no—
486C2×C11—81no—
487C2×C11#300611yescharacteristic
488C2×C11#300611yescharacteristic
489C2×C11C2×#45411yescharacteristic
490D11—162no—
491C24—441no—
492#41—22no—
493#41—22no—
494#41—41no—
495#41—41no—
496#41—42no—
497#41—42no—
498C2×Q8—22no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8C2×C22⋊D1111yescharacteristic
504C2×Q8C2×C22⋊D1111yescharacteristic
505C2×D4—22no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—222no—
509C2×D4—222no—
510C2×D4—222no—
511C2×D4—442no—
512C2×D4—442no—
513C2×D4—442no—
514C2×D4—442no—
515C2×D4—444no—
516C2×D4—441no—
517C2×D4—441no—
518C2×D4—441no—
519C2×D4C2×C22⋊D1111yescharacteristic
520C2×D4C2×C22⋊D1111yescharacteristic
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4C2×C22⋊D1111yescharacteristic
530C22×C4C2×C22⋊D1111yescharacteristic
531C22×C4C2×C22⋊D1111yescharacteristic
532SD16—444no—
533SD16—444no—
534D8—444no—
535D8—444no—
536M16—442no—
537M16—442no—
538M16—442no—
539C2×C8—222no—
540C2×C8—222no—
541C2×C8—222no—
542C4⋊C4—22no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4C2×C22⋊D1111yescharacteristic
557C4⋊C4C2×C22⋊D1111yescharacteristic
558C4⋊C4C2×C22⋊D1111yescharacteristic
559C4⋊C4C2×C22⋊D1111yescharacteristic
560C4⋊C4C2×C22⋊D1112yes—
561C4⋊C4C2×C22⋊D1112yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—22no—
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—21no—
572C22⋊C4—21no—
573C42—22no—
574C42—22no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—22no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42C2×C22⋊D1111yescharacteristic
583C42C2×C22⋊D1111yescharacteristic
584C42C2×C22⋊D1111yescharacteristic
585C42C23×D1111yescharacteristic
586C11#1853711yescharacteristic, complemented, Sylow
587C23—21no—
588C23—21no—
589C23—442no—
590C23—882no—
591C23—882no—
592C23—882no—
593C23#6700611yescharacteristic
594Q8—21no—
595Q8—21no—
596Q8—21no—
597Q8—44no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8#6700212yescomplemented
603D4—21no—
604D4—21no—
605D4—21no—
606D4—42no—
607D4—42no—
608D4—44no—
609D4—444no—
610D4—442no—
611D4—442no—
612D4—442no—
613D4—442no—
614D4—882no—
615D4—882no—
616D4—882no—
617D4#6700212yescomplemented
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4#6700611yescharacteristic
642C2×C4#6700611yescharacteristic
643C2×C4#6700611yescharacteristic
644C2×C4C22×C22⋊D1111yescharacteristic
645C2×C4C22×C22⋊D1111yescharacteristic
646C2×C4C22×C22⋊D1111yescharacteristic
647C8—442no—
648C8—442no—
649C8—442no—
650C22—21no—
651C22—21no—
652C22—22no—
653C22—21no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—882no—
660C22—882no—
661C22—882no—
662C22—1764no—
663C22C2×#6700611yescharacteristic
664C4—21no—
665C4—21no—
666C4—22no—
667C4—21no—
668C4—41no—
669C4—41no—
670C4—42no—
671C4—42no—
672C4—41no—
673C4—41no—
674C4—41no—
675C4#1062285812yes—
676C4C2×#6700211yescharacteristic
677C4C2×#6700211yescharacteristic
678C4#1062335311yescharacteristic
679C4#1062335311yescharacteristic
680C2—41no—
681C2—42no—
682C2—81no—
683C2—1762no—
684C2#1307786811yescharacteristic
685C2#1307786811yescharacteristic
686C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3482C2
socleC22×C11C2×#120
hypercenter#3482D11
hypocenterC11#18537
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. #13078992C2semidirect
2. #13078096C2semidirect
3. #13078096C2semidirect
4. #13067726C2semidirect
5. #13067719C2semidirect
6. #13067712C2semidirect
7. #13067705C2semidirect
8. #13067354C2semidirect
9. #13067055C2semidirect
10. #13067055C2semidirect
11. C11×#3482C2semidirect
12. C11×#557C22semidirect
14. C11×#556C22semidirect
17. D4×Q8×C11C22semidirect
20. C11×#547C22semidirect
49. #10622185C22semidirect
50. #10622185C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
53. D4⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
244. #3482D11semidirect
270. Q8×C11AGL(1,ℤ/8)semidirect
277. D4×C11AGL(1,ℤ/8)semidirect
320. #557C2×D11semidirect
322. #556C2×D11semidirect
325. D4×Q8C2×D11semidirect
328. #547C2×D11semidirect
586. C11#18537semidirect
602. Q8#67002semidirect
617. D4#67002semidirect

Maximal subgroups

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

subgroupindex
#130789922
#130780962
#130677262
#130677192
#130677122
#130677052
#130673542
#130670552
C11×#34822
#1853711