Finite Group Databasebeta

← #14730419

Subgroups — #14730419

Order 2816.

962 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#13079631C211yesmaximal, characteristic
2#13078992C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic, complemented
4#13067726C212yesmaximal, complemented
5#13067719C212yesmaximal, complemented
6#13067712C212yesmaximal, complemented
7#13067712C212yesmaximal, complemented
8#13067316C211yesmaximal, characteristic, complemented
9#13067063C211yesmaximal, characteristic, complemented
10#13067029C211yesmaximal, characteristic, complemented
11C11×#3523C211yesmaximal, characteristic, complemented
12C11×#557—21no—
13C11×#557C2211yescharacteristic, complemented
14C11×#557C2211yescharacteristic, complemented
15C11×#556—21no—
16C11×#556C2211yescharacteristic, complemented
17C11×#552—22no—
18C11×#552—21no—
19D4×Q8×C11—21no—
20D4×Q8×C11C2211yescharacteristic, complemented
21C11×#541—22no—
22C11×#541—21no—
23C11×#533—21no—
24C11×#533C2211yescharacteristic
25C11×#529—21no—
26C11×#529C2211yescharacteristic
27C11×#519—21no—
28C2×C4×Q8×C11C2211yescharacteristic
29C22×#4325—21no—
30C2×#66927C2211yescharacteristic
31#10622701C2212yes—
32#10622701C2212yes—
33#10622680—21no—
34#10622680—22no—
35#10622671—21no—
36#10622659—21no—
37#10622649—21no—
38#10622640—21no—
39#10622640—21no—
40#10622640C2212yes—
41#10622640C2212yes—
42#10622640C2212yes—
43#10622628C2212yes—
44#10622614—22no—
45C2×#66873—21no—
46#10622539C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49#10622185C2212yescomplemented
50#10622185C2212yescomplemented
51Q8⋊(C11⋊C8)C2212yescomplemented
52Q8⋊(C11⋊C8)C2212yescomplemented
53Q8⋊(C11⋊C8)C2212yescomplemented
54D4⋊(C11⋊C8)C2212yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11D411yescharacteristic
57C22×D44—21no—
58C22×D44—21no—
59C22×D44—21no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—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×#126—22no—
70C11×#126—21no—
71C11×#125—22no—
72C11×#125—22no—
73C11×#125—22no—
74C11×#125—21no—
75C11×#125—22no—
76C11×#125—22no—
77C11×#125—21no—
78C11×#125D411yescharacteristic
79C11×#125D412yes—
80C11×#124—21no—
81C11×#124D411yescharacteristic
82C11×#123—22no—
83C11×#123—21no—
84C11×C22⋊Q8—22no—
85C11×C22⋊Q8—22no—
86C11×C22⋊Q8—21no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8—21no—
89C11×C22⋊Q8—21no—
90C11×C22⋊Q8—22no—
91C11×C22⋊Q8D411yescharacteristic
92C11×#121D411yescharacteristic
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11—21no—
98C4×Q8×C11—21no—
99C4×Q8×C11—21no—
100C4×Q8×C11—21no—
101C4×Q8×C11—21no—
102C4×Q8×C11—21no—
103C4×Q8×C11—21no—
104C4×Q8×C11D411yescharacteristic
105C4×Q8×C11D411yescharacteristic
106C4×Q8×C11C2311yescharacteristic
107C4×Q8×C11C2311yescharacteristic
108C4×Q8×C11C2311yescharacteristic
109C4×D4×C11—22no—
110C4×D4×C11—21no—
111C4×D4×C11—21no—
112C4×D4×C11C2311yescharacteristic
113C11×#117—22no—
114C11×#117—22no—
115C11×#117—22no—
116C11×#117—21no—
117C11×#117—21no—
118C11×#117D412yes—
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4D411yescharacteristic
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123C2×#4325—22no—
124C2×#4325—22no—
125C2×#4325—22no—
126C2×#4325—44no—
127C2×#4323—22no—
128C2×#4318—21no—
129C22×C11⋊C8—21no—
130#66927—21no—
131#66927—21no—
132#66927—21no—
133#66927C2312yes—
134C22⋊(C11⋊C8)—21no—
135#66873—22no—
136#66873—22no—
137#66873—24no—
138#66873—24no—
139#66873—22no—
140#66873—22no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)C2312yes—
143C4⋊(C11⋊C8)C2312yes—
144#66867—21no—
145#66867—21no—
146C4×C11⋊C8C2312yes—
147#18580—111nomaximal, Sylow
148C23×D11—41no—
149C2×Q8×C11—22no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—22no—
154C2×Q8×C11—41no—
155C2×Q8×C11—42no—
156C2×Q8×C11—42no—
157C2×Q8×C11C2×D411yescharacteristic
158C2×Q8×C11C2×D411yescharacteristic
159C2×Q8×C11C2×D411yescharacteristic
160C2×D4×C11—21no—
161C2×D4×C11C2×D411yescharacteristic
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C2×D44—22no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44—42no—
173C2×D44—44no—
174C2×D44—42no—
175C2×D44—41no—
176C2×D44—41no—
177C2×D44—41no—
178C2×D44—82no—
179C11×C4⋊C4—22no—
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—22no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4C2×D411yescharacteristic
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D412yes—
203C11×C4⋊C4C2×D412yes—
204C11×C4⋊C4C2×D411yescharacteristic
205C11×C4⋊C4C2×D411yescharacteristic
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—22no—
209C11×C22⋊C4—21no—
210C11×C22⋊C4—22no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C42×C11—22no—
216C42×C11—22no—
217C42×C11—22no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—22no—
221C42×C11—21no—
222C42×C11—21no—
223C42×C11—21no—
224C42×C11C2×D411yescharacteristic
225C42×C11C2×D411yescharacteristic
226C42×C11C2×D411yescharacteristic
227C42×C11C2411yescharacteristic
228#4325—44no—
229#4325—44no—
230#4325—82no—
231#4323—82no—
232#4318—42no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—22no—
235C2×C11⋊C8—22no—
236C2×C11⋊C8—42no—
237#3523D1111yescharacteristic, complemented
238#3217—111no—
239#3138—111no—
240C2×#460—111no—
241#1628—112no—
242#1627—112no—
243#1626—112no—
244#1626—112no—
245#1552—111no—
246#1491—111no—
247#1483—111no—
248C23×C11—21no—
249C23×C11#12011yescharacteristic
250C22×D11—42no—
251C22×D11—82no—
252C22×D11—82no—
253C22×D11—82no—
254Q8×C11—21no—
255Q8×C11—21no—
256Q8×C11—21no—
257Q8×C11—22no—
258Q8×C11—42no—
259Q8×C11—44no—
260Q8×C11—41no—
261Q8×C11—41no—
262Q8×C11—42no—
263Q8×C11AGL(1,ℤ/8)12yes—
264D4×C11—22no—
265D4×C11—42no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—22no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—22no—
279C2×C4×C11—42no—
280C2×C4×C11—44no—
281C2×C4×C11—42no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11#12011yescharacteristic
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290D44—44no—
291D44—42no—
292D44—42no—
293D44—42no—
294D44—42no—
295D44—82no—
296D44—82no—
297D44—82no—
298C11⋊C8—42no—
299C11⋊C8—42no—
300C11⋊C8—42no—
301C22×SD16—221no—
302#557—21no—
303#557C2×D1111yescharacteristic, complemented
304#557C2×D1111yescharacteristic, complemented
305#556—21no—
306#556C2×D1111yescharacteristic, complemented
307#552—22no—
308#552—21no—
309D4×Q8—21no—
310D4×Q8C2×D1111yescharacteristic, complemented
311#541—22no—
312#541—21no—
313#533—21no—
314#533C2×D1111yescharacteristic
315C2×#127—111no—
316#529—21no—
317#529C2×D1111yescharacteristic
318#519—21no—
319C2×C4×Q8C2×D1111yescharacteristic
320#496—221no—
321#490—222no—
322#490—221no—
323#486—112no—
324#486—112no—
325#460—112no—
326#460—112no—
327#460—112no—
328#460—221no—
329#460—221no—
330#459—112no—
331#450—221no—
332#447—221no—
333#432—111no—
334C2×C4⋊C8—111no—
335#418—222no—
336C2×#102—221no—
337C4×M16—111no—
338#332—112no—
339#332—112no—
340Q8⋊C8—112no—
341Q8⋊C8—112no—
342Q8⋊C8—112no—
343D4⋊C8—112no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11#45412yes—
350C22×C11C2×#12011yescharacteristic
351C2×D11—82no—
352C2×D11—82no—
353C2×D11—82no—
354C2×D11—164no—
355C4×C11—21no—
356C4×C11—22no—
357C4×C11—21no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—42no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C4×C11#57511yescharacteristic
370C4×C11#57712yes—
371C22×Q8—21no—
372C22×Q8C22⋊D1111yescharacteristic
373C22×D4—221no—
374C22×D4—221no—
375C22×D4—221no—
376C2×SD16—222no—
377C2×SD16—222no—
378C2×SD16—222no—
379C2×SD16—444no—
380C2×D8—222no—
381C2×M16—221no—
382C22×C8—221no—
383C4⋊Q8—22no—
384C4⋊Q8—21no—
385C4⋊Q8—21no—
386C4⋊Q8—21no—
387C4⋊Q8C22×D1111yescharacteristic
388C4⋊Q8C22×D1111yescharacteristic
389#127—112no—
390#127—221no—
391#127—221no—
392#127—221no—
393#126—22no—
394#126—22no—
395#126—22no—
396#126—22no—
397#126—21no—
398#125—22no—
399#125—22no—
400#125—22no—
401#125—21no—
402#125—22no—
403#125—22no—
404#125—21no—
405#125C22⋊D1111yescharacteristic
406#125C22⋊D1112yes—
407#124—21no—
408#124C22⋊D1111yescharacteristic
409#123—22no—
410#123—21no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—22no—
418C22⋊Q8C22⋊D1111yescharacteristic
419#121C22⋊D1111yescharacteristic
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8C22⋊D1111yescharacteristic
432C4×Q8C22⋊D1111yescharacteristic
433C4×Q8C22×D1111yescharacteristic
434C4×Q8C22×D1111yescharacteristic
435C4×Q8C22×D1111yescharacteristic
436C4×D4—22no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4C22×D1111yescharacteristic
440#117—22no—
441#117—22no—
442#117—22no—
443#117—21no—
444#117—21no—
445#117C22⋊D1112yes—
446C2×C4⋊C4—21no—
447C2×C4⋊C4C22⋊D1111yescharacteristic
448C2×C42—21no—
449C2×C42C22×D1111yescharacteristic
450C4⋊C8—112no—
451C4⋊C8—112no—
452C4⋊C8—221no—
453#102—222no—
454#102—222no—
455#102—224no—
456#102—224no—
457#102—222no—
458#102—222no—
459C22⋊C8—221no—
460#97—221no—
461#97—221no—
462C4×C8—112no—
463C2×C11—22no—
464C2×C11—81no—
465C2×C11#300611yescharacteristic
466C2×C11#301011yescharacteristic
467C2×C11C2×#45411yescharacteristic
468D11—162no—
469C24—441no—
470C2×Q8—22no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—41no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8C2×C22⋊D1111yescharacteristic
479C2×Q8C2×C22⋊D1111yescharacteristic
480C2×Q8C2×C22⋊D1111yescharacteristic
481C2×D4—21no—
482C2×D4—222no—
483C2×D4—222no—
484C2×D4—222no—
485C2×D4—442no—
486C2×D4—444no—
487C2×D4—442no—
488C2×D4—441no—
489C2×D4—441no—
490C2×D4—441no—
491C2×D4—882no—
492C2×D4C2×C22⋊D1111yescharacteristic
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500SD16—444no—
501SD16—444no—
502SD16—882no—
503D8—882no—
504M16—442no—
505C2×C8—222no—
506C2×C8—222no—
507C2×C8—222no—
508C2×C8—442no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4C2×C22⋊D1111yescharacteristic
531C4⋊C4C2×C22⋊D1111yescharacteristic
532C4⋊C4C2×C22⋊D1112yes—
533C4⋊C4C2×C22⋊D1112yes—
534C4⋊C4C2×C22⋊D1111yescharacteristic
535C4⋊C4C2×C22⋊D1111yescharacteristic
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—22no—
541C22⋊C4—21no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—21no—
549C42—21no—
550C42—22no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42C2×C22⋊D1111yescharacteristic
555C42C2×C22⋊D1111yescharacteristic
556C42C2×C22⋊D1111yescharacteristic
557C42C23×D1111yescharacteristic
558C11#1858011yescharacteristic, complemented, Sylow
559C23—21no—
560C23—442no—
561C23—882no—
562C23—882no—
563C23—882no—
564C23#6700611yescharacteristic
565Q8—21no—
566Q8—21no—
567Q8—21no—
568Q8—22no—
569Q8—42no—
570Q8—44no—
571Q8—41no—
572Q8—41no—
573Q8—42no—
574Q8#6700212yes—
575D4—22no—
576D4—42no—
577D4—444no—
578D4—442no—
579D4—442no—
580D4—442no—
581D4—442no—
582D4—882no—
583D4—882no—
584D4—882no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—42no—
599C2×C4—44no—
600C2×C4—42no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4#6700611yescharacteristic
604C2×C4#6700611yescharacteristic
605C2×C4#6700611yescharacteristic
606C2×C4C22×C22⋊D1111yescharacteristic
607C2×C4C22×C22⋊D1111yescharacteristic
608C2×C4C22×C22⋊D1111yescharacteristic
609C8—442no—
610C8—442no—
611C8—442no—
612C22—21no—
613C22—21no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—882no—
618C22—882no—
619C22—882no—
620C22—1764no—
621C22#1062285812yes—
622C22C2×#6700611yescharacteristic
623C4—21no—
624C4—22no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4C2×#6700211yescharacteristic
637C4#1062335311yescharacteristic
638C4#1062336812yes—
639C2—22no—
640C2—81no—
641C2—1762no—
642C2#1307786811yescharacteristic
643C2#1307790211yescharacteristic
644C2C2×#1062285811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3523C2
socleC22×C11C2×#120
prime radical#13079631C2
hypercenter#3523D11
hypocenterC11#18580
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3523

Complements

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

NH ≅ G/Ntype
2. #13078992C2semidirect
3. C2×#10622640C2semidirect
4. #13067726C2semidirect
5. #13067719C2semidirect
6. #13067712C2semidirect
7. #13067712C2semidirect
8. #13067316C2semidirect
9. #13067063C2semidirect
10. #13067029C2semidirect
11. C11×#3523C2semidirect
13. C11×#557C22semidirect
14. C11×#557C22semidirect
16. C11×#556C22semidirect
20. D4×Q8×C11C22semidirect
49. #10622185C22semidirect
50. #10622185C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
53. Q8⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
237. #3523D11semidirect
303. #557C2×D11semidirect
304. #557C2×D11semidirect
306. #556C2×D11semidirect
310. D4×Q8C2×D11semidirect
558. C11#18580semidirect

Maximal subgroups

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

subgroupindex
#130796312
#130789922
C2×#106226402
#130677262
#130677192
#130677122
#130673162
#130670632
#130670292
C11×#35232
#1858011