Finite Group Databasebeta

← #14812566

Subgroups — #14812566

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×#10622494C211yesmaximal, characteristic
2#13072314C211yesmaximal, characteristic
3#13072303C211yesmaximal, characteristic
4#13070100C211yesmaximal, characteristic, complemented
5#13070090C211yesmaximal, characteristic, complemented
6#13069946C211yesmaximal, characteristic, complemented
7#13069941C211yesmaximal, characteristic, complemented
8#13069355C211yesmaximal, characteristic, complemented
9#13069344C211yesmaximal, characteristic, complemented
10#13068812C211yesmaximal, characteristic
11#13068802C211yesmaximal, characteristic
12#13068783C211yesmaximal, characteristic, complemented
13#13068650C211yesmaximal, characteristic
14#13068399C211yesmaximal, characteristic
15C2×C11×#500C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×#66999—21no—
19C22×#4313C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C11×#500—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#107C2211yescharacteristic
26C2×C11×#107C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622844—21no—
29#10622843—21no—
30#10622842—21no—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35#10622607—21no—
36#10622602—21no—
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622597—21no—
42#10622591—21no—
43#10622590C2211yescharacteristic
44#10622589C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C4×(C2×D11)⋊C4C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622494—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—21no—
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—41no—
70C11×C4⋊Q8—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78#66999—44no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×#4313—22no—
100C2×#4313—22no—
101C2×#4313Q814yescomplemented
102#66945—22no—
103#66945—41no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—41no—
106C11×#107—22no—
107C11×#107—22no—
108C11×#107—22no—
109C11×#107D414yes—
110C4×C8×C11—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121(C2×D11)⋊C8Q814yescomplemented
122#66881—22no—
123#66881—22no—
124#66879—22no—
125#66872—22no—
126#66872—41no—
127#66871—22no—
128#66871—41no—
129#26074—111nomaximal, Sylow
130C23×D11C2×D411yescharacteristic
131C2×Q8×C11—42no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C2×Q8×C11—42no—
135C2×Q8×C11—81no—
136C2×Q8×C11—81no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×C4×D11C2×Q812yes—
159C2×C4×D11C2×Q812yes—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C2×D412yes—
163C2×C8×C11C2×Q812yes—
164C2×C8×C11C2×Q812yes—
165C2×C8×C11#4112yes—
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—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4C2×D412yes—
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—21no—
191C4⋊Dic11—42no—
192C4⋊Dic11—81no—
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⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C2×Q812yes—
206C2×C11⋊C8C2×Q812yes—
207#4313—28no—
208C2×#500D1111yescharacteristic, complemented
209C2×#428—111no—
210#2440—111no—
211#2439—111no—
212#2085—111no—
213#2083—111no—
214#2058—111no—
215#2057—111no—
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—
232Q8×C11—84no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
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×C11—41no—
249C2×C4×C11AGL(1,ℤ/8)12yes—
250C2×C4×C11#13712yes—
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×Q811yescharacteristic
253C2×C4×C11C22×Q811yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C2×Dic11—21no—
258C2×Dic11—21no—
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×Dic11—41no—
277C2×Dic11C4⋊Q812yes—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—84no—
283C8×C11—22no—
284C8×C11C22⋊Q814yescomplemented
285C11⋊C8—22no—
286C11⋊C8—22no—
287C22×M16—111no—
288C2×C4⋊Q8C2×D1111yescharacteristic
289C2×C4⋊Q8C2×D1111yescharacteristic
290C2×C22⋊Q8—221no—
291C2×#117—111no—
292C22×C4⋊C4—111no—
293#500—24no—
294#428—224no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107C2×D1111yescharacteristic
298C2×#107C2×D1111yescharacteristic
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×C8C2×D1111yescharacteristic
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#389—111no—
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#340—111no—
329#340—111no—
330#336—111no—
331#336—111no—
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—42no—
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—81no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—21no—
364C22×Q8—21no—
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—22no—
376C4⋊Q8—41no—
377C4⋊Q8—41no—
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—22no—
410#107—22no—
411#107—222no—
412#107—441no—
413#107C22⋊D1114yes—
414#106—222no—
415#106—222no—
416#106—222no—
417#106—441no—
418C22⋊C8—114no—
419#97—222no—
420C4×C8—22no—
421#95—111no—
422#95—111no—
423#95—221no—
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—42no—
443C2×Q8—42no—
444C2×Q8—81no—
445C2×Q8—81no—
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—112no—
473C2×C8—112no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8Q8×D1112yes—
479C2×C8Q8×D1112yes—
480C2×C8#434312yes—
481C2×C8C2×C22⋊D1112yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—881no—
504C4⋊C4—881no—
505C4⋊C4C2×C22⋊D1112yes—
506C4⋊C4C2×C22⋊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—84no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
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—221no—
556C2×C4—221no—
557C2×C4—441no—
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×C4#6703711yescharacteristic
573C2×C4C2×Q8×D1111yescharacteristic
574C2×C4C2×Q8×D1111yescharacteristic
575C2×C4C2×#434311yescharacteristic
576C2×C4#6704011yescharacteristic
577C2×C4C22×C22⋊D1111yescharacteristic
578C8—22no—
579C8—222no—
580C8—222no—
581C8#6699914yescomplemented
582C22—222no—
583C22—222no—
584C22—222no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22D11×C4⋊Q811yescharacteristic
590C22#1062325711yescharacteristic
591C22C2×#6696411yescharacteristic
592C22#1062328811yescharacteristic
593C22C2×#6697111yescharacteristic
594C22#1062329711yescharacteristic
595C22D4×C22⋊D1111yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—42no—
600C4—81no—
601C4—81no—
602C4—222no—
603C4—441no—
604C4—441no—
605C4—881no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4#1062326011yescharacteristic
610C4#1062326111yescharacteristic
611C4C2×#6699911yescharacteristic
612C4Q8×C22⋊D1111yescharacteristic
613C2—442no—
614C2#1307231411yescharacteristic
615C2#1307914911yescharacteristic
616C2#1307915911yescharacteristic
617C2#1308009611yescharacteristic
618C2#1308018611yescharacteristic
619C2#1308119911yescharacteristic
620C2#1308124111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#500C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#500D11
hypocenterC11#26074
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
4. #13070100C2semidirect
5. #13070090C2semidirect
6. #13069946C2semidirect
7. #13069941C2semidirect
8. #13069355C2semidirect
9. #13069344C2semidirect
12. #13068783C2semidirect
15. C2×C11×#500C2semidirect
101. C2×#4313Q8semidirect
121. (C2×D11)⋊C8Q8semidirect
208. C2×#500D11semidirect
284. C8×C11C22⋊Q8semidirect
517. C11#26074semidirect
581. C8#66999semidirect

Maximal subgroups

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

subgroupindex
C2×#106224942
#130723142
#130723032
#130701002
#130700902
#130699462
#130699412
#130693552
#130693442
#130688122
#130688022
#130687832
#130686502
#130683992
C2×C11×#5002
#2607411