Finite Group Databasebeta

← #14812635

Subgroups — #14812635

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622678C211yesmaximal, characteristic, complemented
2C2×#10622608C211yesmaximal, characteristic
3#13072318C211yesmaximal, characteristic
4#13070093C211yesmaximal, characteristic, complemented
5#13070087C211yesmaximal, characteristic, complemented
6#13069951C211yesmaximal, characteristic, complemented
7#13069949C211yesmaximal, characteristic, complemented
8#13069351C211yesmaximal, characteristic, complemented
9#13069346C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic
11#13068808C211yesmaximal, characteristic
12#13068772C211yesmaximal, characteristic, complemented
13#13068647C211yesmaximal, characteristic
14#13068400C211yesmaximal, characteristic
15C11×#2441C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×#66931—21no—
21C2×#66922C2211yescharacteristic
22C11×#399—21no—
23C11×#396—21no—
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#387—21no—
28C11×#384C2211yescharacteristic
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622678—24no—
34#10622608—24no—
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
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
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C11×#125—22no—
65C11×#125—41no—
66C11×#117—22no—
67C11×#117—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×#4318—22no—
99C2×#4318—22no—
100C2×#4318Q814yescomplemented
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66931—44no—
106#66922—22no—
107#66922—41no—
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—22no—
121#66872—41no—
122#66872—41no—
123#66871—22no—
124#66871—22no—
125#66871—22no—
126#66871D414yes—
127#66867—22no—
128C4×C11⋊C8—22no—
129#26078—111nomaximal, Sylow
130C24×C11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×Q812yes—
145C22×C4×C11C2×Q812yes—
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—81no—
154C2×Dic22—42no—
155C2×Dic22—42no—
156C2×Dic22—81no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—81no—
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×#501—111no—
209C2×#428—111no—
210#2441D1111yescharacteristic
211#2440—111no—
212#2084—111no—
213#2083—111no—
214#2059—111no—
215#2058—111no—
216#1943—111no—
217#1942—111no—
218#1854—111no—
219#1853—111no—
220#1844—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
231C2×C4×C11—21no—
232C2×C4×C11—21no—
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—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
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×C11C4⋊Q812yes—
260C2×C4×C11AGL(1,ℤ/8)12yes—
261C2×C4×C11#13712yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×Q811yescharacteristic
264C2×C4×C11C22×Q811yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—22no—
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×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—84no—
281Dic22—84no—
282C11⋊C8—22no—
283C11⋊C8—22no—
284C11⋊C8—22no—
285C11⋊C8C22⋊Q814yescomplemented
286C22×M16—111no—
287C2×C4⋊Q8—111no—
288C2×#125C2×D1111yescharacteristic
289C2×C22⋊Q8—221no—
290C2×#117C2×D1111yescharacteristic
291C22×C4⋊C4—111no—
292#501—224no—
293#428—224no—
294C2×#107—111no—
295C2×#107—111no—
296C2×#107—111no—
297C2×#107—111no—
298C2×#106—111no—
299C2×#106—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×#106—111no—
304C2×C22⋊C8—111no—
305C2×#97—111no—
306C2×C4×C8—111no—
307#399—21no—
308#398—221no—
309#396—21no—
310#395—221no—
311#389—21no—
312#389—111no—
313#389—111no—
314#389C2×D1111yescharacteristic
315#389C2×D1111yescharacteristic
316#387—21no—
317#385—221no—
318#384—111no—
319#384C2×D1111yescharacteristic
320#380—111no—
321#380C2×D1111yescharacteristic
322C4×C22⋊C4C2×D1111yescharacteristic
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#336—111no—
330#336—111no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×C4⋊Q811yescharacteristic
339C22×C11D4211yescharacteristic
340C22×C11#54711yescharacteristic
341C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57711yescharacteristic
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11C2×C22⋊Q811yescharacteristic
355C4×C11#54411yescharacteristic
356C4×C11D4×Q811yescharacteristic
357C4×C11#55411yescharacteristic
358Dic11—42no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8—221no—
363C23×C4—221no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—114no—
366C2×M16—222no—
367C2×M16—222no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—111no—
372C4⋊Q8—222no—
373C4⋊Q8—441no—
374#125—22no—
375#125—41no—
376C22⋊Q8—444no—
377#117—22no—
378#117—41no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—441no—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4C22⋊D1111yescharacteristic
405C2×C22⋊C4C22⋊D1111yescharacteristic
406C2×C42—21no—
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1111yescharacteristic
409#107—114no—
410#107—222no—
411#107—222no—
412#107—222no—
413#106—222no—
414#106—222no—
415#106—222no—
416#106—222no—
417#106—441no—
418#106—441no—
419C22⋊C8—114no—
420#97—222no—
421C4×C8—222no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95C22⋊D1111yescharacteristic
429#95C22⋊D1111yescharacteristic
430C2×C11—42no—
431C2×C11#244011yescharacteristic
432C2×C11#316311yescharacteristic
433C2×C11#316511yescharacteristic
434C2×C11#327211yescharacteristic
435C2×C11#327811yescharacteristic
436C2×C11#334411yescharacteristic
437C2×C11#334511yescharacteristic
438C24C2×C22⋊D1111yescharacteristic
439C2×Q8—442no—
440C2×Q8—442no—
441C2×Q8—881no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4—881no—
457C22×C4Q8×D1112yes—
458C22×C4Q8×D1112yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465M16—228no—
466C2×C8—112no—
467C2×C8—112no—
468C2×C8—112no—
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—112no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—81no—
490C4⋊C4—81no—
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⋊C4D4×D1112yes—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—42no—
509C22⋊C4—81no—
510C22⋊C4—442no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—42no—
516C11#2607811yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#6699712yes—
524C23C22×C22⋊D1111yescharacteristic
525Q8—884no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
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—222no—
555C2×C4—441no—
556C2×C4—441no—
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—884no—
567C2×C4#6699712yes—
568C2×C4#6700212yes—
569C2×C4#6700412yes—
570C2×C4C2×D4×D1111yescharacteristic
571C2×C4#6703711yescharacteristic
572C2×C4C2×Q8×D1111yescharacteristic
573C2×C4C2×Q8×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#6704311yescharacteristic
576C8—114no—
577C8—222no—
578C8—222no—
579C8—222no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22D4×C22⋊D1111yescharacteristic
588C22C2×#6699711yescharacteristic
589C22C2×#6700211yescharacteristic
590C22C2×#6700411yescharacteristic
591C22#1062335511yescharacteristic
592C22#1062336711yescharacteristic
593C22#1062336811yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—42no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—442no—
604C4—881no—
605C4—881no—
606C4—881no—
607C4#1062315411yescharacteristic
608C4D11×C22⋊Q811yescharacteristic
609C4#1062316311yescharacteristic
610C4#1062316711yescharacteristic
611C2—42no—
612C2#1307231511yescharacteristic
613C2#1307914211yescharacteristic
614C2#1307916311yescharacteristic
615C2#1308021611yescharacteristic
616C2#1308028211yescharacteristic
617C2#1308107111yescharacteristic
618C2#1308108011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2441C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2441D11
hypocenterC11#26078
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
1. C2×#10622678C2semidirect
4. #13070093C2semidirect
5. #13070087C2semidirect
6. #13069951C2semidirect
7. #13069949C2semidirect
8. #13069351C2semidirect
9. #13069346C2semidirect
12. #13068772C2semidirect
100. C2×#4318Q8semidirect
116. C22⋊(C11⋊C8)Q8semidirect
285. C11⋊C8C22⋊Q8semidirect
516. C11#26078semidirect

Maximal subgroups

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

subgroupindex
C2×#106226782
C2×#106226082
#130723182
#130700932
#130700872
#130699512
#130699492
#130693512
#130693462
#130688152
#130688082
#130687722
#130686472
#130684002
C11×#24412
#2607811