Finite Group Databasebeta

← #14812575

Subgroups — #14812575

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×#10622608C211yesmaximal, characteristic
3#13072318C211yesmaximal, characteristic
4#13070098C211yesmaximal, characteristic, complemented
5#13070087C211yesmaximal, characteristic, complemented
6#13069949C211yesmaximal, characteristic, complemented
7#13069941C211yesmaximal, characteristic, complemented
8#13069351C211yesmaximal, characteristic, complemented
9#13069341C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic
11#13068803C211yesmaximal, characteristic
12#13068785C211yesmaximal, characteristic, complemented
13#13068647C211yesmaximal, characteristic
14#13068400C211yesmaximal, characteristic
15C11×#2439C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66931—21no—
21C2×#66922C2211yescharacteristic
22C11×#396—21no—
23C11×#393—21no—
24C11×#391—21no—
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#387—21no—
28C11×#382C2211yescharacteristic
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622691—24no—
34#10622608—24no—
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622563—21no—
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622274—21no—
52#10622269—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22—21no—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—41no—
67C11×#117—22no—
68C11×#117—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318Q814yescomplemented
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66931—44no—
104#66922—22no—
105#66922—41no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C22⋊(C11⋊C8)Q814yescomplemented
117#66872—22no—
118#66872—22no—
119#66872—22no—
120#66872—41no—
121#66871—22no—
122#66871—22no—
123#66871—22no—
124#66871—22no—
125#66871—41no—
126#66871D414yes—
127#66867—22no—
128C4×C11⋊C8—22no—
129#26074—111nomaximal, Sylow
130C24×C11C2×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×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×Q812yes—
148C22×C4×C11C2×Q812yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—81no—
157C2×Dic22—42no—
158C2×Dic22—42no—
159C2×Dic22—81no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—81no—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—81no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—42no—
180C22⋊Dic11—42no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—42no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11—81no—
192C4⋊Dic11C2×D412yes—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195#4318—28no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C2×D412yes—
203C2×C11⋊C8C2×Q812yes—
204C2×C11⋊C8C2×Q812yes—
205C2×C11⋊C8C2×Q812yes—
206C2×C11⋊C8C2×Q812yes—
207C2×C11⋊C8#4112yes—
208C2×#500—111no—
209C2×#428—111no—
210#2440—111no—
211#2439D1111yescharacteristic
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×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C4⋊Q812yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—84no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
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×C11—41no—
260C2×C4×C11C4⋊Q812yes—
261C2×C4×C11AGL(1,ℤ/8)12yes—
262C2×C4×C11#13712yes—
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C22×Q811yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C2×Dic11—22no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—84no—
282Dic22—84no—
283C11⋊C8—22no—
284C11⋊C8—22no—
285C11⋊C8—22no—
286C11⋊C8C22⋊Q814yescomplemented
287C22×M16—111no—
288C2×C4⋊Q8—111no—
289C2×C4⋊Q8C2×D1111yescharacteristic
290C2×C22⋊Q8—221no—
291C2×#117C2×D1111yescharacteristic
292C22×C4⋊C4—111no—
293#500—224no—
294#428—224no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#107—111no—
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—21no—
310#395—221no—
311#393—21no—
312#391—21no—
313#389—111no—
314#389—111no—
315#389C2×D1111yescharacteristic
316#389C2×D1111yescharacteristic
317#387—21no—
318#385—221no—
319#384—111no—
320#382C2×D1111yescharacteristic
321#380—111no—
322#380C2×D1111yescharacteristic
323C4×C22⋊C4C2×D1111yescharacteristic
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×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4⋊Q811yescharacteristic
340C22×C11D4211yescharacteristic
341C22×C11#54711yescharacteristic
342C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C11C2×#13711yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57811yescharacteristic
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—22no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11C2×C22⋊Q811yescharacteristic
356C4×C11#54411yescharacteristic
357C4×C11D4×Q811yescharacteristic
358C4×C11#55411yescharacteristic
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—21no—
364C22×Q8—221no—
365C23×C4—221no—
366C23×C4C22×D1111yescharacteristic
367C2×M16—114no—
368C2×M16—222no—
369C2×M16—222no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8—111no—
374C4⋊Q8—22no—
375C4⋊Q8—41no—
376C4⋊Q8—222no—
377C4⋊Q8—441no—
378C22⋊Q8—444no—
379#117—22no—
380#117—41no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—222no—
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—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4C22⋊D1111yescharacteristic
404C2×C22⋊C4C22⋊D1111yescharacteristic
405C2×C42—21no—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408#107—114no—
409#107—222no—
410#107—222no—
411#107—222no—
412#107—222no—
413#107—441no—
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—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95C22⋊D1111yescharacteristic
430#95C22⋊D1111yescharacteristic
431C2×C11—42no—
432C2×C11#244011yescharacteristic
433C2×C11#316411yescharacteristic
434C2×C11#316511yescharacteristic
435C2×C11#326411yescharacteristic
436C2×C11#327011yescharacteristic
437C2×C11#335311yescharacteristic
438C2×C11#335711yescharacteristic
439C24C2×C22⋊D1111yescharacteristic
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—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4—881no—
461C22×C4Q8×D1112yes—
462C22×C4Q8×D1112yes—
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469M16—228no—
470C2×C8—112no—
471C2×C8—112no—
472C2×C8—112no—
473C2×C8—112no—
474C2×C8—112no—
475C2×C8—112no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
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—81no—
492C4⋊C4—112no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—442no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—881no—
506C4⋊C4D4×D1112yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C22⋊C4—81no—
511C22⋊C4—442no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C11#2607411yescharacteristic, complemented, Sylow
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23#6699712yes—
525C23C22×C22⋊D1111yescharacteristic
526Q8—84no—
527Q8—884no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—222no—
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—884no—
569C2×C4#6699712yes—
570C2×C4#6700212yes—
571C2×C4#6700412yes—
572C2×C4C2×D4×D1111yescharacteristic
573C2×C4#6703711yescharacteristic
574C2×C4C2×Q8×D1111yescharacteristic
575C2×C4C2×Q8×D1111yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#6704311yescharacteristic
578C8—114no—
579C8—222no—
580C8—222no—
581C8—222no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22D4×C22⋊D1111yescharacteristic
590C22C2×#6699711yescharacteristic
591C22C2×#6700211yescharacteristic
592C22C2×#6700411yescharacteristic
593C22#1062335511yescharacteristic
594C22#1062336611yescharacteristic
595C22#1062336911yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4—81no—
605C4—442no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4#1062315411yescharacteristic
610C4D11×C22⋊Q811yescharacteristic
611C4#1062316311yescharacteristic
612C4#1062316711yescharacteristic
613C2—42no—
614C2#1307231511yescharacteristic
615C2#1307915011yescharacteristic
616C2#1307916311yescharacteristic
617C2#1308009711yescharacteristic
618C2#1308018211yescharacteristic
619C2#1308119411yescharacteristic
620C2#1308123611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2439C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2439D11
hypocenterC11#26074
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2439

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
4. #13070098C2semidirect
5. #13070087C2semidirect
6. #13069949C2semidirect
7. #13069941C2semidirect
8. #13069351C2semidirect
9. #13069341C2semidirect
12. #13068785C2semidirect
98. C2×#4318Q8semidirect
116. C22⋊(C11⋊C8)Q8semidirect
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×#106226082
#130723182
#130700982
#130700872
#130699492
#130699412
#130693512
#130693412
#130688152
#130688032
#130687852
#130686472
#130684002
C11×#24392
#2607411