Finite Group Databasebeta

← #14812571

Subgroups — #14812571

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2C2×#10622494C211yesmaximal, characteristic
3#13072320C211yesmaximal, characteristic
4#13072303C211yesmaximal, characteristic
5#13070102C211yesmaximal, characteristic, complemented
6#13070090C211yesmaximal, characteristic, complemented
7#13069950C211yesmaximal, characteristic, complemented
8#13069353C211yesmaximal, characteristic, complemented
9#13069341C211yesmaximal, characteristic, complemented
10#13068816C211yesmaximal, characteristic
11#13068802C211yesmaximal, characteristic
12#13068783C211yesmaximal, characteristic, complemented
13#13068648C211yesmaximal, characteristic
14#13068396C211yesmaximal, characteristic
15C11×#2057C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66949—21no—
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622844—21no—
26#10622843—21no—
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31#10622691—24no—
32#10622607—21no—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622592—21no—
37#10622591—21no—
38#10622590C2211yescharacteristic
39#10622589C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×(C2×D11)⋊C4C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622494—24no—
51#10622281—21no—
52#10622270—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×Dic22—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4D411yescharacteristic
80C2×(C2×D11)⋊C4D411yescharacteristic
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313Q814yescomplemented
99#66949—44no—
100#66945—22no—
101#66945—41no—
102C4⋊C4×D11—22no—
103C4⋊C4×D11—41no—
104#66922—22no—
105#66922—41no—
106C11×#107—22no—
107C11×#107—41no—
108C11×#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118(C2×D11)⋊C8Q814yescomplemented
119#66881—22no—
120#66881—41no—
121#66879—22no—
122#66872—22no—
123#66872—22no—
124#66871—22no—
125#66871—22no—
126#66871—22no—
127#66871D414yes—
128C4×C11⋊C8—22no—
129#26074—111nomaximal, Sylow
130C23×D11C2×D411yescharacteristic
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—81no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—81no—
155C2×C4×D11C2×Q812yes—
156C2×C4×D11C2×Q812yes—
157C2×Dic22—42no—
158C2×Dic22—42no—
159C2×Dic22—81no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C2×Q812yes—
165C2×C8×C11C2×Q812yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4C2×D412yes—
176C42×C11—21no—
177C42×C11—21no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—81no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—42no—
191C4⋊Dic11—81no—
192C4⋊Dic11C2×D412yes—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—81no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C2×D412yes—
204C2×C11⋊C8C2×Q812yes—
205C2×C11⋊C8C2×Q812yes—
206C2×C11⋊C8#4112yes—
207#4313—28no—
208C2×#500—111no—
209C2×#428—111no—
210#2440—111no—
211#2439—111no—
212#2085—111no—
213#2083—111no—
214#2058—111no—
215#2057D1111yescharacteristic, complemented
216#1943—111no—
217#1941—111no—
218#1854—111no—
219#1852—111no—
220#1847—111no—
221#1809—111no—
222#1753—111no—
223C23×C11C22×D411yescharacteristic
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11C4⋊Q812yes—
231Q8×C11—84no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11AGL(1,ℤ/8)12yes—
249C2×C4×C11#13712yes—
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×Q811yescharacteristic
252C2×C4×C11C22×Q811yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11C4⋊Q812yes—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—84no—
282Dic22—84no—
283C8×C11—22no—
284C8×C11—22no—
285C11⋊C8—22no—
286C11⋊C8C22⋊Q814yescomplemented
287C22×M16—111no—
288C2×C4⋊Q8—111no—
289C2×C4⋊Q8C2×D1111yescharacteristic
290C2×C22⋊Q8—221no—
291C2×#117—111no—
292C22×C4⋊C4—111no—
293#500—224no—
294#428—224no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#107C2×D1111yescharacteristic
300C2×#107C2×D1111yescharacteristic
301C2×#106—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×#106—111no—
305C2×C22⋊C8—111no—
306C2×#97—111no—
307C2×C4×C8—111no—
308#398—221no—
309#396—221no—
310#395—221no—
311#393—221no—
312#391—221no—
313#389—111no—
314#389—111no—
315#389—111no—
316#389C2×D1111yescharacteristic
317#387—221no—
318#385—221no—
319#384—111no—
320#382—111no—
321#380—111no—
322#380—111no—
323C4×C22⋊C4—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#336—111no—
331#336C2×D1111yescharacteristic
332C22×C11C2×C4⋊Q811yescharacteristic
333C22×C11D4211yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57611yescharacteristic
338C22×C11#57811yescharacteristic
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11C2×C22⋊Q811yescharacteristic
353C4×C11#54411yescharacteristic
354C4×C11D4×Q811yescharacteristic
355C4×C11#55411yescharacteristic
356Dic11—22no—
357Dic11—41no—
358Dic11—41no—
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—21no—
364C22×Q8—221no—
365C23×C4—111no—
366C23×C4—221no—
367C2×M16—114no—
368C2×M16—222no—
369C2×M16—222no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C4⋊Q8—22no—
375C4⋊Q8—41no—
376C4⋊Q8—222no—
377C4⋊Q8—441no—
378C22⋊Q8—444no—
379#117—222no—
380#117—441no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—441no—
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—111no—
401C2×C22⋊C4—111no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C42—111no—
406C2×C42—221no—
407C2×C42C22×D1111yescharacteristic
408#107—22no—
409#107—41no—
410#107—114no—
411#107—222no—
412#107—222no—
413#107—222no—
414#106—222no—
415#106—222no—
416#106—222no—
417#106—441no—
418C22⋊C8—114no—
419#97—222no—
420C4×C8—222no—
421#95—21no—
422#95—111no—
423#95—111no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431C2×C11#244011yescharacteristic
432C2×C11#316411yescharacteristic
433C2×C11#316511yescharacteristic
434C2×C11#326411yescharacteristic
435C2×C11#327011yescharacteristic
436C2×C11#335311yescharacteristic
437C2×C11#335711yescharacteristic
438D11—42no—
439C24—111no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—81no—
443C2×Q8—442no—
444C2×Q8—442no—
445C2×Q8—881no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—111no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—881no—
466C22×C4D4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469M16—228no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—112no—
475C2×C8—112no—
476C2×C8—112no—
477C2×C8—112no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8Q8×D1112yes—
481C2×C8Q8×D1112yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—112no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—881no—
505C4⋊C4—881no—
506C4⋊C4D4×D1112yes—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C22⋊C4—442no—
510C22⋊C4—442no—
511C22⋊C4—881no—
512C42—21no—
513C42—21no—
514C42—221no—
515C42—221no—
516C42—442no—
517C11#2607411yescharacteristic, complemented, Sylow
518C23—112no—
519C23—221no—
520C23—221no—
521C23—221no—
522C23—221no—
523C23—221no—
524C23—221no—
525C23C2×D4×D1111yescharacteristic
526Q8—84no—
527Q8—884no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—112no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—222no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—884no—
570C2×C4#6696412yes—
571C2×C4#6697112yes—
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4#6703711yescharacteristic
574C2×C4C2×Q8×D1111yescharacteristic
575C2×C4C2×Q8×D1111yescharacteristic
576C2×C4#6704011yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C8—22no—
579C8—22no—
580C8—114no—
581C8—222no—
582C22—222no—
583C22—222no—
584C22—222no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22#1062312111yescharacteristic
590C22#1062316211yescharacteristic
591C22D11×C4⋊Q811yescharacteristic
592C22C2×#6696411yescharacteristic
593C22C2×#6697111yescharacteristic
594C22#1062330511yescharacteristic
595C22#1062331011yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—222no—
603C4—442no—
604C4—441no—
605C4—441no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4D11×C22⋊Q811yescharacteristic
610C4#1062316711yescharacteristic
611C4#1062325811yescharacteristic
612C4#1062326011yescharacteristic
613C2—442no—
614C2#1307231111yescharacteristic
615C2#1307915111yescharacteristic
616C2#1307915911yescharacteristic
617C2#1308008911yescharacteristic
618C2#1308019011yescharacteristic
619C2#1308119711yescharacteristic
620C2#1308123911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2057C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2057D11
hypocenterC11#26074
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
5. #13070102C2semidirect
6. #13070090C2semidirect
7. #13069950C2semidirect
8. #13069353C2semidirect
9. #13069341C2semidirect
12. #13068783C2semidirect
15. C11×#2057C2semidirect
98. C2×#4313Q8semidirect
118. (C2×D11)⋊C8Q8semidirect
215. #2057D11semidirect
286. C11⋊C8C22⋊Q8semidirect
517. C11#26074semidirect

Maximal subgroups

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

subgroupindex
C2×#106226912
C2×#106224942
#130723202
#130723032
#130701022
#130700902
#130699502
#130693532
#130693412
#130688162
#130688022
#130687832
#130686482
#130683962
C11×#20572
#2607411