Finite Group Databasebeta

← #14775320

Subgroups — #14775320

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622616C211yesmaximal, characteristic
2#13071630C211yesmaximal, characteristic
3#13069351C211yesmaximal, characteristic, complemented
4#13069298C211yesmaximal, characteristic, complemented
5#13069243C211yesmaximal, characteristic, complemented
6#13069201C211yesmaximal, characteristic, complemented
7#13069184C211yesmaximal, characteristic, complemented
8#13069052C211yesmaximal, characteristic
9#13068876C211yesmaximal, characteristic, complemented
10#13068808C211yesmaximal, characteristic, complemented
11C4×#66872C211yesmaximal, characteristic, complemented
12#13068444C211yesmaximal, characteristic, complemented
13#13068400C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C11×#2347C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×(C22⋊D11)⋊C4—21no—
21C2×C4×D44C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#388—21no—
26C11×#383—21no—
27C11×#380C2211yescharacteristic
28C4×C11×C4⋊C4—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622616C418yescomplemented
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622571—21no—
43#10622552C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48#10622283—21no—
49#10622281—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C11×#117—22no—
66C11×#117C2×C414yescomplemented
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82#66983—22no—
83#66983C2×C414yes—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—41no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—41no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103(C22⋊D11)⋊C4—44no—
104C4×D44—22no—
105C4×D44—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—
115C22⋊(C11⋊C8)C2×C414yescomplemented
116#66873—22no—
117#66873—41no—
118#66873C2×C414yescomplemented
119#66873C2×C414yescomplemented
120#66872—22no—
121#66872—41no—
122#66872C2×C414yescomplemented
123#66871C2×C414yescomplemented
124#66867—41no—
125C4×C11⋊C8—22no—
126#22944—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
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×C11C22×C412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—24no—
146C2×C22⋊D11—42no—
147C2×C22⋊D11—42no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—81no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44C22×C412yes—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—81no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4C22×C412yes—
172C11×C4⋊C4C22×C412yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—41no—
176C11×C22⋊C4—81no—
177C42×C11—24no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—81no—
183C42×C11—81no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11C22×C412yes—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—42no—
196C4×Dic11—42no—
197#4318—44no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
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⋊C8C22×C412yes—
208C2×C11⋊C8C22×C412yes—
209C2×C11⋊C8#4112yes—
210C2×#482—111no—
211#2361—111no—
212#2347D1111yescharacteristic, complemented
213#1943—111no—
214#1934—111no—
215#1926—111no—
216#1920—111no—
217#1918—111no—
218#1895—111no—
219#1864—111no—
220#1853—111no—
221C4×#106—111no—
222#1762—111no—
223#1753—111no—
224#1736—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C4×D412yes—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
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—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11C4×D412yes—
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C22⋊D11—48no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—84no—
288D44—22no—
289D44—22no—
290D44—41no—
291D44—41no—
292C4×D11—84no—
293C11⋊C8—22no—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C22×M16—111no—
298C2×#121—111no—
299C2×C4×D4—111no—
300C2×C4×D4—221no—
301C2×#117C2×D1111yescharacteristic
302C22×C4⋊C4—111no—
303#482—118no—
304C2×#107—111no—
305C2×#106—111no—
306C2×#106—111no—
307C2×#106—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C22⋊C8—111no—
313C2×#97—111no—
314C2×C4×C8—111no—
315#390—111no—
316#389—111no—
317#389C2×D1111yescharacteristic
318#389C2×D1111yescharacteristic
319#388—21no—
320#388—21no—
321#388—221no—
322#386—221no—
323#385—221no—
324#383—21no—
325#380C2×D1111yescharacteristic
326C4×C4⋊C4—21no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4C2×D1111yescharacteristic
329C4×C4⋊C4C2×D1111yescharacteristic
330C4×C22⋊C4C2×D1111yescharacteristic
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#336—111no—
340#336—111no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11C2×C4×D411yescharacteristic
349C22×C11#54611yescharacteristic
350C22×C11#54711yescharacteristic
351C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C11#57511yescharacteristic
353C22×C11#57711yescharacteristic
354C22×C11#57711yescharacteristic
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C4×C11—22no—
363C4×C11—22no—
364C4×C11—41no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—41no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11C4×#4111yescharacteristic
372C4×C11#52011yescharacteristic
373C4×C11#55111yescharacteristic
374C4×C11#55211yescharacteristic
375Dic11—42no—
376Dic11—42no—
377Dic11—81no—
378C22×D4—111no—
379C22×D4—221no—
380C23×C4—221no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C2×M16—222no—
384C2×M16—222no—
385C2×M16—441no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8—111no—
389C22×C8—111no—
390#121—114no—
391#121—222no—
392C4×D4—222no—
393C4×D4—441no—
394C4×D4—444no—
395#117—22no—
396#117C4×D1114yescomplemented
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—441no—
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4C22⋊D1111yescharacteristic
417C2×C22⋊C4C22⋊D1111yescharacteristic
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1111yescharacteristic
424#107—114no—
425#106—114no—
426#106—222no—
427#106—441no—
428#102—114no—
429#102—114no—
430#102—222no—
431#102—441no—
432C22⋊C8—114no—
433#97—441no—
434C4×C8—222no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—221no—
441#95—221no—
442#95C22⋊D1111yescharacteristic
443#95C22⋊D1111yescharacteristic
444C2×C11—42no—
445C2×C11#235911yescharacteristic
446C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
447C2×C11#295211yescharacteristic
448C2×C11#332411yescharacteristic
449C2×C11#332611yescharacteristic
450C2×C11#334511yescharacteristic
451C2×C11#335011yescharacteristic
452D11—82no—
453C24—221no—
454C24C2×C22⋊D1111yescharacteristic
455C2×D4—112no—
456C2×D4—224no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—442no—
463C2×D4—442no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—881no—
480C22×C4—881no—
481C22×C4C2×C4×D1112yes—
482C22×C4#433912yes—
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489M16—444no—
490C2×C8—112no—
491C2×C8—112no—
492C2×C8—112no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4C2×C4×D1112yes—
519C4⋊C4C2×C4×D1112yes—
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—41no—
523C22⋊C4—81no—
524C22⋊C4—224no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—881no—
528C42—24no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—81no—
534C42—81no—
535C42—442no—
536C11#2294411yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—222no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23C4×C22⋊D1112yes—
551C23C22×C22⋊D1111yescharacteristic
552D4—222no—
553D4—222no—
554D4—448no—
555D4—441no—
556D4—441no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—884no—
596C2×C4—884no—
597C2×C4C4×C22⋊D1112yes—
598C2×C4#6700212yes—
599C2×C4C22×C4×D1111yescharacteristic
600C2×C4C2×#433911yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#6704211yescharacteristic
604C2×C4#6704311yescharacteristic
605C8—222no—
606C8—222no—
607C8—222no—
608C8—441no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—442no—
617C22—442no—
618C22—442no—
619C22—881no—
620C22—881no—
621C22—881no—
622C22—881no—
623C22C2×C4×C22⋊D1111yescharacteristic
624C22C2×#6700211yescharacteristic
625C22#1062335311yescharacteristic
626C22#1062335511yescharacteristic
627C22#1062336011yescharacteristic
628C22#1062336711yescharacteristic
629C22#1062336811yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—42no—
636C4—42no—
637C4—81no—
638C4—81no—
639C4—442no—
640C4—442no—
641C4—881no—
642C4#1062305311yescharacteristic
643C4#1062305411yescharacteristic
644C4#1062305811yescharacteristic
645C4#1062306211yescharacteristic
646C2—42no—
647C2—882no—
648C2#1307160811yescharacteristic
649C2C4×#6700211yescharacteristic
650C2#1307749711yescharacteristic
651C2#1308084111yescharacteristic
652C2#1308086311yescharacteristic
653C2#1308108011yescharacteristic
654C2#1308116111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2347C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#2347D11
hypocenterC11#22944
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2347

Complements

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

NH ≅ G/Ntype
3. #13069351C2semidirect
4. #13069298C2semidirect
5. #13069243C2semidirect
6. #13069201C2semidirect
7. #13069184C2semidirect
9. #13068876C2semidirect
10. #13068808C2semidirect
11. C4×#66872C2semidirect
12. #13068444C2semidirect
13. #13068400C2semidirect
14. #13068337C2semidirect
15. C11×#2347C2semidirect
33. #10622616C4semidirect
66. C11×#117C2×C4semidirect
115. C22⋊(C11⋊C8)C2×C4semidirect
118. #66873C2×C4semidirect
119. #66873C2×C4semidirect
122. #66872C2×C4semidirect
123. #66871C2×C4semidirect
212. #2347D11semidirect
396. #117C4×D11semidirect
536. C11#22944semidirect

Maximal subgroups

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

subgroupindex
C2×#106226162
#130716302
#130693512
#130692982
#130692432
#130692012
#130691842
#130690522
#130688762
#130688082
C4×#668722
#130684442
#130684002
#130683372
C11×#23472
#2294411