Finite Group Databasebeta

← #14765412

Subgroups — #14765412

Order 2816.

908 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622648C211yesmaximal, characteristic
2#13071099C211yesmaximal, characteristic, complemented
3#13069346C211yesmaximal, characteristic, complemented
4#13069341C211yesmaximal, characteristic, complemented
5#13069302C211yesmaximal, characteristic, complemented
6#13069302C211yesmaximal, characteristic, complemented
7#13069208C211yesmaximal, characteristic, complemented
8#13069194C211yesmaximal, characteristic, complemented
9#13068939C211yesmaximal, characteristic
10#13068877C211yesmaximal, characteristic, complemented
11#13068863C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068708C211yesmaximal, characteristic, complemented
14C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
15C4×C11×#121C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#386—21no—
26C11×#380C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622823—21no—
34#10622823—21no—
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622648C418yescomplemented
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C4×Dic11⋊C4—21no—
43C4×Dic11⋊C4—21no—
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C11×#121—22no—
67C11×#121C2×C414yes—
68C4×D4×C11—41no—
69C4×D4×C11—41no—
70C4×D4×C11—44no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11—41no—
82C2×C42×C11—41no—
83C2×C42×C11D411yescharacteristic
84C2×C42×C11D411yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89#66979—22no—
90#66979—41no—
91#66979—41no—
92#66979C2×C414yescomplemented
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C11×#95—21no—
108C11×#95—21no—
109C11×#95—21no—
110#66896—41no—
111#66896—41no—
112#66896C2×C414yescomplemented
113#66896C2×C414yescomplemented
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—22no—
119C22⋊(C11⋊C8)C2×C414yescomplemented
120#66872—41no—
121#66872C2×C414yescomplemented
122#66871—41no—
123#66871C2×C414yescomplemented
124C4×C11⋊C8—41no—
125C4×C11⋊C8—41no—
126#22080—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C2×D4×C11—24no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11C22×C412yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4112yes—
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4C22×C412yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—42no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—41no—
183C42×C11—41no—
184C42×C11—42no—
185C22⋊Dic11—24no—
186C22⋊Dic11—42no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22×C412yes—
194C4⋊Dic11C22×C412yes—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199C4×Dic11—24no—
200C4×Dic11—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8C22×C412yes—
212C2×C11⋊C8C22×C412yes—
213C2×#482—111no—
214C4×#121D1111yescharacteristic
215#2296—111no—
216#1942—111no—
217#1941—111no—
218#1934—111no—
219#1934—111no—
220#1921—111no—
221#1919—111no—
222#1875—111no—
223#1864—111no—
224#1862—111no—
225#1854—111no—
226#1825—111no—
227C4×C22⋊C8—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—22no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11C4×D412yes—
242C23×C11C22×D411yescharacteristic
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—48no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—44no—
265C2×C4×C11—44no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—84no—
275C2×C4×C11C4×D412yes—
276C2×C4×C11#13512yes—
277C2×C4×C11#13512yes—
278C2×C4×C11AGL(1,ℤ/8)12yes—
279C2×C4×C11C23×C411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C112−1+411yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C11⋊C8—22no—
298C11⋊C8—22no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C2×#121C2×D1111yescharacteristic
302C2×C4×D4—21no—
303C2×C4×D4C2×D1111yescharacteristic
304C2×#117—111no—
305C2×#117—111no—
306C22×C42C2×D1111yescharacteristic
307#482—118no—
308C2×#107—111no—
309C2×#107—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8—111no—
318C2×C4×C8—111no—
319C2×C4×C8—111no—
320#390C2×D1111yescharacteristic
321#389—111no—
322#389—111no—
323#389—111no—
324#389—111no—
325#389C2×D1111yescharacteristic
326#388—21no—
327#386—21no—
328#385—221no—
329#385—221no—
330#380C2×D1111yescharacteristic
331C4×C4⋊C4—221no—
332C4×C4⋊C4—221no—
333C4×C4⋊C4C2×D1111yescharacteristic
334C4×C22⋊C4—21no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#336—111no—
344#336—111no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11C2×C4×D411yescharacteristic
360C22×C11#53411yescharacteristic
361C22×C11#53611yescharacteristic
362C22×C11C2×#13511yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11#57511yescharacteristic
366C4×C11—22no—
367C4×C11—22no—
368C4×C11—22no—
369C4×C11—22no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52011yescharacteristic
375C4×C11#52011yescharacteristic
376C4×C11#53911yescharacteristic
377C4×C11#53911yescharacteristic
378Dic11—42no—
379Dic11—42no—
380Dic11—81no—
381Dic11—81no—
382C22×D4—21no—
383C22×D4C22×D1111yescharacteristic
384C23×C4—21no—
385C23×C4C22⋊D1111yescharacteristic
386C23×C4C22⋊D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C22×C8—111no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8—111no—
392#121—22no—
393#121C4×D1114yes—
394C4×D4—41no—
395C4×D4—41no—
396C4×D4—44no—
397#117—114no—
398#117—222no—
399#117—441no—
400#117—441no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—21no—
421C2×C42—41no—
422C2×C42—41no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42C22⋊D1111yescharacteristic
426C2×C42C22⋊D1111yescharacteristic
427C2×C42C22×D1111yescharacteristic
428C2×C42C22×D1111yescharacteristic
429#107—114no—
430#107—441no—
431#106—114no—
432#106—441no—
433#102—114no—
434#102—114no—
435#102—441no—
436#102—441no—
437C22⋊C8—114no—
438C22⋊C8—222no—
439C4×C8—441no—
440C4×C8—441no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11—42no—
449C2×C11—82no—
450C2×C11#232211yescharacteristic
451C2×C11C4×#13511yescharacteristic
452C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
453C2×C11#318811yescharacteristic
454C2×C11#319111yescharacteristic
455C2×C11#322811yescharacteristic
456C2×C11#323311yescharacteristic
457C24—21no—
458C24C2×C22⋊D1111yescharacteristic
459C2×D4—24no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4C2×C4×D1112yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4C2×C4×D1112yes—
489C22×C4#433912yes—
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496C2×C8—112no—
497C2×C8—112no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—42no—
514C4⋊C4—112no—
515C4⋊C4—112no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4C2×C4×D1112yes—
527C22⋊C4—24no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—224no—
533C22⋊C4—442no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—41no—
539C42—41no—
540C42—42no—
541C42—224no—
542C42—442no—
543C11#2208011yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23C4×C22⋊D1112yes—
558C23C22×C22⋊D1111yescharacteristic
559D4—22no—
560D4—22no—
561D4—48no—
562D4—41no—
563D4—41no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—84no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4C4×C22⋊D1112yes—
604C2×C4#6698512yes—
605C2×C4#6700312yes—
606C2×C4#6700312yes—
607C2×C4C22×C4×D1111yescharacteristic
608C2×C4C2×#433911yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#6703711yescharacteristic
611C2×C4#6704311yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—222no—
614C8—222no—
615C8—441no—
616C8—441no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×C4×C22⋊D1111yescharacteristic
632C22C2×#6698511yescharacteristic
633C22#1062333511yescharacteristic
634C22C2×#6700311yescharacteristic
635C22C2×#6700311yescharacteristic
636C22#1062335311yescharacteristic
637C22#1062335611yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—22no—
642C4—41no—
643C4—42no—
644C4—81no—
645C4—81no—
646C4—442no—
647C4—442no—
648C4—881no—
649C4—881no—
650C4#1062307711yescharacteristic
651C4#1062307711yescharacteristic
652C4#1062309511yescharacteristic
653C4#1062309511yescharacteristic
654C2—42no—
655C2—82no—
656C2#1307128111yescharacteristic
657C2C4×#6700311yescharacteristic
658C2C4×#6698511yescharacteristic
659C2#1307938111yescharacteristic
660C2#1307940411yescharacteristic
661C2#1307974811yescharacteristic
662C2#1307979111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenterC4×#121D11
hypocenterC11#22080
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. #13071099C2semidirect
3. #13069346C2semidirect
4. #13069341C2semidirect
5. #13069302C2semidirect
6. #13069302C2semidirect
7. #13069208C2semidirect
8. #13069194C2semidirect
10. #13068877C2semidirect
11. #13068863C2semidirect
12. #13068813C2semidirect
13. #13068708C2semidirect
14. C4×C22⋊(C11⋊C8)C2semidirect
37. #10622648C4semidirect
92. #66979C2×C4semidirect
112. #66896C2×C4semidirect
113. #66896C2×C4semidirect
119. C22⋊(C11⋊C8)C2×C4semidirect
121. #66872C2×C4semidirect
123. #66871C2×C4semidirect
543. C11#22080semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
#130710992
#130693462
#130693412
#130693022
#130692082
#130691942
#130689392
#130688772
#130688632
#130688132
#130687082
C4×C22⋊(C11⋊C8)2
C4×C11×#1212
#2208011