Finite Group Databasebeta

← #14826965

Subgroups — #14826965

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073200C211yesmaximal, characteristic
2#13071676C211yesmaximal, characteristic, complemented
3#13070157C211yesmaximal, characteristic, complemented
4#13069929C211yesmaximal, characteristic
5#13069859C211yesmaximal, characteristic, complemented
6#13069472C211yesmaximal, characteristic
7#13069253C211yesmaximal, characteristic, complemented
8#13069240C211yesmaximal, characteristic
9#13069195C211yesmaximal, characteristic, complemented
10#13069172C211yesmaximal, characteristic, complemented
11#13068973C211yesmaximal, characteristic
12#13068973C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#2013C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66932—21no—
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#390C2211yescharacteristic
25#10622843C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622834C2211yescharacteristic
32#10622834C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622598—21no—
39#10622594—21no—
40#10622594—21no—
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622565—21no—
46#10622561—21no—
47#10622558—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622541C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C2×C11×SD16—22no—
63C2×C11×SD16—22no—
64C2×C11×SD16—22no—
65C2×C11×SD16—41no—
66C2×C11×SD16—41no—
67C2×C11×SD16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85Q8×Dic11—41no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11D411yescharacteristic
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66932—44no—
106C11×#103—22no—
107C11×#103—41no—
108#66899—22no—
109#66899—22no—
110#66899—41no—
111#66899—41no—
112#66896—22no—
113#66896—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66881—22no—
124Dic11⋊C8—41no—
125C8×Dic11—41no—
126#66872—41no—
127#27066—111nomaximal, Sylow
128C24×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11#4112yes—
140C2×Q8×C11#4112yes—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C11×SD16—44no—
162C11×SD16—44no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11#4112yes—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—81no—
175C42×C11—21no—
176C42×C11—21no—
177C22⋊Dic11—42no—
178C22⋊Dic11—42no—
179C22⋊Dic11—42no—
180C22⋊Dic11—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—41no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11SD1614yescomplemented
192C4⋊Dic11#4112yes—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—81no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210#2512—111no—
211#2365—111no—
212#2096—111no—
213#2055—111no—
214#2043—111no—
215#2013D1111yescharacteristic
216#1968—111no—
217#1927—111no—
218#1926—111no—
219#1919—111no—
220#1916—111no—
221#1880—111no—
222#1880—111no—
223#1803—111no—
224C4×#103—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11C22×D411yescharacteristic
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C2×SD1612yes—
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11C2×SD1612yes—
289C2×Dic11C2×SD1612yes—
290C8×C11—22no—
291C8×C11—41no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C22×SD16C2×D1111yescharacteristic
295C22×SD16C2×D1111yescharacteristic
296C2×C4⋊Q8C2×D1111yescharacteristic
297C2×#126—221no—
298C2×C4×Q8—111no—
299C2×C4×Q8—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×C4⋊C8—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103C2×D1111yescharacteristic
308C2×#103C2×D1111yescharacteristic
309C2×#102—111no—
310C2×#102—111no—
311C2×C4×C8—111no—
312#397—221no—
313#396—221no—
314#391—111no—
315#391—111no—
316#390—111no—
317#390—111no—
318#390C2×D1111yescharacteristic
319#389—111no—
320#389—221no—
321#388—221no—
322#387—221no—
323#387—221no—
324#384—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—221no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336C2×D1111yescharacteristic
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11#52511yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#55011yescharacteristic
347C22×C11C22×SD1611yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57711yescharacteristic
350C22×C11#57811yescharacteristic
351C4×C11—22no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—81no—
356C4×C11#52911yescharacteristic
357C4×C11#53811yescharacteristic
358C4×C11#55111yescharacteristic
359C4×C11#55311yescharacteristic
360Dic11—22no—
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364Dic11—42no—
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8C22×D1111yescharacteristic
369C22×Q8C22×D1111yescharacteristic
370C22×D4C22×D1111yescharacteristic
371C2×SD16—22no—
372C2×SD16—22no—
373C2×SD16—22no—
374C2×SD16—41no—
375C2×SD16—41no—
376C2×SD16—41no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383#126—444no—
384C4×Q8—222no—
385C4×Q8—222no—
386C4×Q8—441no—
387C4×Q8—441no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415#106—222no—
416#106—441no—
417C4⋊C8—441no—
418#103—22no—
419#103—41no—
420#103—222no—
421#103—222no—
422#103—441no—
423#103—441no—
424#102—222no—
425#102—441no—
426C4×C8—441no—
427#95—111no—
428#95—111no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436C2×C11—161no—
437C2×C11#246711yescharacteristic
438C2×C11#310311yescharacteristic
439C2×C11#312111yescharacteristic
440C2×C11#329811yescharacteristic
441C2×C11#330711yescharacteristic
442C2×C11#339211yescharacteristic
443C2×C11#340211yescharacteristic
444C24—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8#434112yes—
456C2×Q8#434112yes—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4D4×D1111yescharacteristic
475C22×C4D4×D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477SD16—44no—
478SD16—44no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8#434112yes—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—114no—
496C4⋊C4—112no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—441no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—881no—
510C22⋊C4—42no—
511C22⋊C4—81no—
512C22⋊C4—442no—
513C22⋊C4—442no—
514C22⋊C4—442no—
515C22⋊C4—881no—
516C42—21no—
517C42—21no—
518C42—221no—
519C42—221no—
520C42—221no—
521C42—221no—
522C42—442no—
523C42—442no—
524C42—442no—
525C42—442no—
526C11#2706611yescharacteristic, complemented, Sylow
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23C2×D4×D1111yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—112no—
562C2×C4—112no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—222no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4SD16×D1112yes—
586C2×C4C2×#434111yescharacteristic
587C2×C4C2×#434111yescharacteristic
588C2×C4C2×#434111yescharacteristic
589C2×C4#6703711yescharacteristic
590C2×C4#6703711yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C8—22no—
593C8—41no—
594C8—441no—
595C8—441no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22#1062311711yescharacteristic
604C22#1062314311yescharacteristic
605C22#1062324911yescharacteristic
606C22C2×SD16×D1111yescharacteristic
607C22#1062329311yescharacteristic
608C22#1062330811yescharacteristic
609C22#1062331011yescharacteristic
610C4—22no—
611C4—42no—
612C4—42no—
613C4—41no—
614C4—81no—
615C4—222no—
616C4—222no—
617C4—441no—
618C4—441no—
619C4—442no—
620C4—881no—
621C4—881no—
622C4—881no—
623C4#1062311811yescharacteristic
624C4#1062312411yescharacteristic
625C4#1062313111yescharacteristic
626C4#1062313211yescharacteristic
627C2—161no—
628C2#1307266211yescharacteristic
629C2#1307864211yescharacteristic
630C2#1307883811yescharacteristic
631C2#1308048411yescharacteristic
632C2#1308059911yescharacteristic
633C2#1308159411yescharacteristic
634C2#1308169211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2013C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2013D11
hypocenterC11#27066
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2013

Complements

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

NH ≅ G/Ntype
2. #13071676C2semidirect
3. #13070157C2semidirect
5. #13069859C2semidirect
7. #13069253C2semidirect
9. #13069195C2semidirect
10. #13069172C2semidirect
13. #13068619C2semidirect
14. #103×Dic11C2semidirect
191. C4⋊Dic11SD16semidirect
526. C11#27066semidirect

Maximal subgroups

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

subgroupindex
#130732002
#130716762
#130701572
#130699292
#130698592
#130694722
#130692532
#130692402
#130691952
#130691722
#130689732
#130686192
#103×Dic112
C11×#20132
#2706611