Finite Group Databasebeta

← #14765406

Subgroups — #14765406

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622422C211yesmaximal, characteristic
2#13071154C211yesmaximal, characteristic
3D11×#389C211yesmaximal, characteristic
4#13069349C211yesmaximal, characteristic, complemented
5#13069346C211yesmaximal, characteristic, complemented
6#13069295C211yesmaximal, characteristic, complemented
7#13069211C211yesmaximal, characteristic, complemented
8#13069207C211yesmaximal, characteristic, complemented
9#13068920C211yesmaximal, characteristic
10#13068872C211yesmaximal, characteristic, complemented
11#13068868C211yesmaximal, characteristic, complemented
12#13068805C211yesmaximal, characteristic
13#13068705C211yesmaximal, characteristic
14C4×(C2×D11)⋊C8C211yesmaximal, characteristic
15C11×#1933C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×C4⋊C4×D11—21no—
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622585—21no—
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622422C418yescomplemented
44#10622281—21no—
45#10622279—21no—
46D11×#95—21no—
47#10622268—21no—
48#10622262—21no—
49#10622260—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73#66999—22no—
74#66999C2×C414yes—
75Q8×Dic11—41no—
76Q8×Dic11—41no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C4⋊C4×D11—22no—
99C4⋊C4×D11—41no—
100C4⋊C4×D11—41no—
101C4⋊C4×D11—44no—
102C4⋊C4×D11C2×C414yes—
103C42×D11—41no—
104C42×D11—41no—
105C11×#103—41no—
106C11×#103C2×C414yescomplemented
107C4×C8×C11—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111#66899—41no—
112#66899C2×C414yescomplemented
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119(C2×D11)⋊C8—22no—
120(C2×D11)⋊C8C2×C414yes—
121#66882—41no—
122#66882C2×C414yescomplemented
123#66871—41no—
124#66871C2×C414yescomplemented
125C4×C11⋊C8—41no—
126#22079—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C22×C412yes—
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—24no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—41no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11Q1614yes—
164C2×C4×D11C22×C412yes—
165C2×C4×D11#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4C22×C412yes—
179C42×C11—21no—
180C42×C11—21no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—42no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11C22×C412yes—
192C4⋊Dic11C22×C412yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—41no—
202C4×Dic11—41no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C22×C412yes—
211C2×#484—111no—
212C4×C22⋊Q8—111no—
213C2×#389—111no—
214#1942—111no—
215#1942—111no—
216#1933—111no—
217#1933D1111yescharacteristic, complemented
218#1921—111no—
219#1921—111no—
220#1872—111no—
221#1863—111no—
222#1863—111no—
223#1852—111no—
224#1824—111no—
225C4×C22⋊C8—111no—
226C23×C11C22×D411yescharacteristic
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11C4×D412yes—
232C22×D11C2×Q1612yes—
233C22×D11#13512yes—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—41no—
237Q8×C11—41no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
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×C11C2×Q1612yes—
255C2×C4×C11AGL(1,ℤ/8)12yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
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×Dic11C4×D412yes—
282C2×Dic11C2×Q1612yes—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—22no—
287C4×D11—44no—
288C4×D11—44no—
289C4×D11—48no—
290C4×D11—84no—
291C8×C11—22no—
292C8×C11—41no—
293C11⋊C8—22no—
294C11⋊C8—41no—
295C2×C22⋊Q8—111no—
296C2×C4×Q8—111no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—111no—
299C22×C4⋊C4—221no—
300C22×C42—111no—
301#484—118no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#107—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103C2×D1111yescharacteristic
309C2×#103C2×D1111yescharacteristic
310C2×C22⋊C8—111no—
311C2×C22⋊C8—111no—
312C2×C4×C8—111no—
313C2×C4×C8C2×D1111yescharacteristic
314#391C2×D1111yescharacteristic
315#389—111no—
316#389—111no—
317#389—111no—
318#389—111no—
319#389—221no—
320#389—221no—
321#389C2×D1111yescharacteristic
322#387—221no—
323#385—221no—
324#380—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—221no—
327C4×C22⋊C4—221no—
328C2×#95—221no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340C2×D1111yescharacteristic
336#340C2×D1111yescharacteristic
337#336—111no—
338#336—111no—
339C22×C11C2×C4×D411yescharacteristic
340C22×C11#53411yescharacteristic
341C22×C11#53611yescharacteristic
342C22×C11C22×Q1611yescharacteristic
343C22×C11C2×#13511yescharacteristic
344C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C11#57511yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11—22no—
352C2×D11C4×Q1614yes—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11#52011yescharacteristic
360C4×C11#52011yescharacteristic
361C4×C11#53911yescharacteristic
362C4×C11#53911yescharacteristic
363Dic11—22no—
364Dic11—22no—
365Dic11—41no—
366Dic11—42no—
367Dic11—42no—
368Dic11—81no—
369Dic11—81no—
370C22×Q8C22×D1111yescharacteristic
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—111no—
374C23×C4—221no—
375C23×C4—221no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C22⋊Q8—114no—
381C22⋊Q8—222no—
382C4×Q8—441no—
383C4×Q8—441no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—441no—
400C2×C4⋊C4—441no—
401C2×C4⋊C4—444no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42—441no—
413C2×C42—441no—
414C2×C42C22×D1111yescharacteristic
415#107—114no—
416#107—114no—
417#107—441no—
418#107—441no—
419#103—41no—
420#103—114no—
421#103—441no—
422#103C4×D1114yescomplemented
423C22⋊C8—114no—
424C22⋊C8—222no—
425C4×C8—41no—
426C4×C8—441no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436C2×C11#232211yescharacteristic
437C2×C11C2×C4×Q1611yescharacteristic
438C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
439C2×C11#318811yescharacteristic
440C2×C11#318911yescharacteristic
441C2×C11#323011yescharacteristic
442C2×C11#323211yescharacteristic
443D11—24no—
444C24—111no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×C4×D1112yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—114no—
460C22×C4—111no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—222no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4—441no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—112no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8C2×C4×D1112yes—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—112no—
502C4⋊C4—112no—
503C4⋊C4—224no—
504C4⋊C4—224no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4C2×C4×D1112yes—
518C22⋊C4—224no—
519C22⋊C4—442no—
520C42—21no—
521C42—21no—
522C42—221no—
523C42—221no—
524C42—441no—
525C42—441no—
526C42—442no—
527C42—442no—
528C11#2207911yescharacteristic, complemented, Sylow
529C23—112no—
530C23—112no—
531C23—112no—
532C23—221no—
533C23—221no—
534C23—221no—
535C23—221no—
536C23C2×D4×D1111yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
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—41no—
557C2×C4—112no—
558C2×C4—112no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—221no—
572C2×C4—444no—
573C2×C4—444no—
574C2×C4—448no—
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×C4—884no—
586C2×C4#6696712yes—
587C2×C4Q16×D1112yes—
588C2×C4C22×C4×D1111yescharacteristic
589C2×C4#6703711yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#6704211yescharacteristic
592C2×C4#6704311yescharacteristic
593C2×C4#6704311yescharacteristic
594C8—22no—
595C8—41no—
596C8—222no—
597C8—441no—
598C22—114no—
599C22—222no—
600C22—222no—
601C22—222no—
602C22—222no—
603C22—222no—
604C22—222no—
605C22C4×D4×D1111yescharacteristic
606C22#1062313611yescharacteristic
607C22#1062320611yescharacteristic
608C22C2×#6696711yescharacteristic
609C22C2×Q16×D1111yescharacteristic
610C22D11×#13511yescharacteristic
611C22#1062329911yescharacteristic
612C4—22no—
613C4—22no—
614C4—42no—
615C4—42no—
616C4—81no—
617C4—81no—
618C4—222no—
619C4—222no—
620C4—441no—
621C4—442no—
622C4—442no—
623C4—881no—
624C4—881no—
625C4#1062305411yescharacteristic
626C4#1062307711yescharacteristic
627C4#1062319111yescharacteristic
628C4#1062323811yescharacteristic
629C2—224no—
630C2#1307128611yescharacteristic
631C2C4×Q16×D1111yescharacteristic
632C2C4×#6696711yescharacteristic
633C2#1307938211yescharacteristic
634C2#1307938711yescharacteristic
635C2#1307976311yescharacteristic
636C2#1307977911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1933C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1933D11
hypocenterC11#22079
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1933

Complements

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

NH ≅ G/Ntype
4. #13069349C2semidirect
5. #13069346C2semidirect
6. #13069295C2semidirect
7. #13069211C2semidirect
8. #13069207C2semidirect
10. #13068872C2semidirect
11. #13068868C2semidirect
15. C11×#1933C2semidirect
43. #10622422C4semidirect
106. C11×#103C2×C4semidirect
112. #66899C2×C4semidirect
122. #66882C2×C4semidirect
124. #66871C2×C4semidirect
217. #1933D11semidirect
422. #103C4×D11semidirect
528. C11#22079semidirect

Maximal subgroups

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

subgroupindex
C2×#106224222
#130711542
D11×#3892
#130693492
#130693462
#130692952
#130692112
#130692072
#130689202
#130688722
#130688682
#130688052
#130687052
C4×(C2×D11)⋊C82
C11×#19332
#2207911