Finite Group Databasebeta

← #14763532

Subgroups — #14763532

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2C2×#10622448C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic
4#13069587C212yesmaximal, complemented
5#13069434C212yesmaximal, complemented
6#13068927C212yesmaximal
7#13068925C212yesmaximal
8#13068622C211yesmaximal, characteristic, complemented
9#13068621C211yesmaximal, characteristic, complemented
10#13068618C211yesmaximal, characteristic, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2211yescharacteristic
14C2×#66997C2211yescharacteristic
15#10623109—24no—
16#10623109C418yescomplemented
17C2×#66950C2211yescharacteristic
18C2×#66949—21no—
19C2×#66945C2212yes—
20C2×#66942—21no—
21C2×#66941C2211yescharacteristic
22C2×#66925—21no—
23C2×C42×D11C2211yescharacteristic
24C2×C4×Dic22—21no—
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C11×#384C2211yescharacteristic
29C2×#66899C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66880C2212yes—
32C2×#66879C2212yes—
33#10622600—21no—
34#10622600—21no—
35#10622590C2212yes—
36C4⋊C4×Dic11—21no—
37C4⋊C4×Dic11—21no—
38C2×#66874C2212yes—
39#10622548C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622448—24no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×Dic22—21no—
51C22×Dic22C2311yescharacteristic
52C22×C8×C11C2312yes—
53C4×Q8×C11—22no—
54C4×Q8×C11C2×C414yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62#66999—22no—
63#66999C2×C414yes—
64#66997—22no—
65#66997C2×C414yes—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85#66950—22no—
86#66950C2×C414yes—
87#66949—28no—
88#66945—42no—
89#66945—42no—
90#66942—28no—
91#66941—22no—
92#66941C2×C414yes—
93#66925—28no—
94C42×D11C2×C414yes—
95C42×D11D414yes—
96C4×Dic22—22no—
97C4×Dic22—28no—
98C4×Dic22C2×C414yes—
99C11×C4⋊C8—22no—
100C11×#103—42no—
101#66899—42no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104(C2×D11)⋊C8—24no—
105#66880—42no—
106#66879—24no—
107#66874—42no—
108C4⋊(C11⋊C8)—22no—
109#21870—111nomaximal, Sylow
110C23×D11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11C22×C412yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C2×C4×D11—22no—
130C2×C4×D11—22no—
131C2×C4×D11—21no—
132C2×C4×D11—21no—
133C2×C4×D11—21no—
134C2×C4×D11—21no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C4×D11C22⋊C414yes—
138C2×C4×D11C22⋊C414yes—
139C2×C4×D11C22×C412yes—
140C2×C4×D11C2×D412yes—
141C2×Dic22—24no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C2×Dic22C22×C412yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4C22×C412yes—
160C42×C11—24no—
161C42×C11C22×C412yes—
162C42×C11C2×D412yes—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—44no—
166C4⋊Dic11—24no—
167C4⋊Dic11—21no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—42no—
171C4⋊Dic11—42no—
172C4⋊Dic11C22×C412yes—
173Dic11⋊C4—24no—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176Dic11⋊C4—24no—
177Dic11⋊C4—24no—
178C4×Dic11—24no—
179C4×Dic11—44no—
180C4×Dic11C22⋊C414yes—
181C4×Dic11C22⋊C414yes—
182C4×Dic11C22×C412yes—
183C4×Dic11C2×D412yes—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×#533—111no—
188C2×#432—111no—
189#2285—111no—
190#1993—112no—
191#1960—112no—
192#1873—112no—
193#1873—112no—
194#1803—111no—
195#1803—111no—
196#1803—111no—
197#1803D1111yescharacteristic, complemented
198C23×C11C22×D411yescharacteristic
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—21no—
204C22×D11—21no—
205C22×D11C2×C22⋊C412yes—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—41no—
209Q8×C11—41no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11C2×C22⋊C412yes—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11#13712yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11H(5,𝔽2)11yescharacteristic
228C2×C4×C11H(5,𝔽2)11yescharacteristic
229C2×C4×C112−1+411yescharacteristic
230C2×C4×C112−1+411yescharacteristic
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11C2×C22⋊C412yes—
247C2×Dic11C2×C22⋊C412yes—
248C2×Dic11C2×C22⋊C412yes—
249C4×D11—22no—
250C4×D11—22no—
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—28no—
254C4×D11—44no—
255Dic22—22no—
256Dic22—22no—
257Dic22—48no—
258Dic22—41no—
259Dic22—41no—
260C8×C11—42no—
261C11⋊C8—42no—
262#533—118no—
263#533—224no—
264C2×C4⋊Q8—111no—
265C2×C4⋊Q8—111no—
266C2×#125—221no—
267C2×C22⋊Q8—111no—
268C2×C22⋊Q8—111no—
269C2×C22⋊Q8—221no—
270C2×C4×Q8—111no—
271C2×C4×Q8—221no—
272C2×C4×Q8C2×D1111yescharacteristic
273C2×#117—112no—
274C2×#117—221no—
275C22×C42—111no—
276#432—224no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#103—112no—
280C2×#103—112no—
281C2×#103—112no—
282C2×#103C2×D1112yes—
283C2×C22⋊C8—112no—
284C2×#97—112no—
285#384—111no—
286#384C2×D1111yescharacteristic
287#382—112no—
288#380—221no—
289#380—221no—
290C4×C4⋊C4—221no—
291C4×C4⋊C4—221no—
292#340—112no—
293#340—112no—
294#340—112no—
295#340C2×D1112yes—
296C22×C11C22×C22⋊C411yescharacteristic
297C22×C11#53511yescharacteristic
298C22×C11#53611yescharacteristic
299C22×C11C2×#13711yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C22×C11#57511yescharacteristic
302C22×C11#57511yescharacteristic
303C2×D11—22no—
304C2×D11—22no—
305C2×D11—22no—
306C2×D11—41no—
307C2×D11—41no—
308C2×D11—41no—
309C2×D11—41no—
310C4×C11—22no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11—82no—
314C4×C11#41914yes—
315C4×C11#52011yescharacteristic
316C4×C11#52011yescharacteristic
317C4×C11#53711yescharacteristic
318C4×C11#53711yescharacteristic
319Dic11—22no—
320Dic11—22no—
321Dic11—22no—
322Dic11—42no—
323Dic11—42no—
324Dic11—82no—
325C22×Q8—111no—
326C22×Q8—221no—
327C22×Q8C22×D1111yescharacteristic
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—111no—
331C22×C8—112no—
332C22×C8C22×D1112yes—
333C4⋊Q8—114no—
334C4⋊Q8—114no—
335C4⋊Q8—222no—
336C4⋊Q8—222no—
337#125—228no—
338C22⋊Q8—114no—
339C22⋊Q8—114no—
340C22⋊Q8—222no—
341C22⋊Q8—228no—
342C22⋊Q8—222no—
343C4×Q8—22no—
344C4×Q8—114no—
345C4×Q8—228no—
346C4×Q8—222no—
347C4×Q8C4×D1114yes—
348#117—228no—
349#117—442no—
350#117—442no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4C22×D1112yes—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C42—21no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—114no—
374C2×C42—114no—
375C2×C42—221no—
376C2×C42—222no—
377C2×C42C22×D1111yescharacteristic
378C4⋊C8—22no—
379C4⋊C8—222no—
380#103—42no—
381#103—442no—
382#103—442no—
383#103—442no—
384C22⋊C8—224no—
385#97—224no—
386#95—222no—
387#95—222no—
388C2×C11#231111yescharacteristic
389C2×C11C2×#41911yescharacteristic
390C2×C11#289611yescharacteristic
391C2×C11#321611yescharacteristic
392C2×C11#321611yescharacteristic
393C2×C11#323711yescharacteristic
394C2×C11#323711yescharacteristic
395D11—42no—
396C24—111no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—112no—
403C2×Q8—224no—
404C2×Q8—221no—
405C2×Q8—221no—
406C2×Q8—221no—
407C2×Q8—221no—
408C2×Q8—221no—
409C2×Q8—442no—
410C2×Q8—442no—
411C2×Q8C2×C4×D1112yes—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—114no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—114no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—222no—
431C22×C4—441no—
432C22×C4—441no—
433C22×C4D4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—42no—
447C4⋊C4—42no—
448C4⋊C4—112no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—221no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—442no—
459C4⋊C4—442no—
460C4⋊C4C2×C4×D1112yes—
461C22⋊C4—224no—
462C22⋊C4—224no—
463C22⋊C4—444no—
464C42—24no—
465C42—114no—
466C42—114no—
467C42—112no—
468C42—112no—
469C42—224no—
470C42—444no—
471C42C2×C4×D1112yes—
472C42D4×D1112yes—
473C11#2187011yescharacteristic, complemented, Sylow
474C23—112no—
475C23—221no—
476C23—221no—
477C23—221no—
478C23—221no—
479C23—221no—
480C23—221no—
481C23C2×D4×D1111yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—222no—
487Q8—222no—
488Q8—448no—
489Q8—441no—
490Q8—441no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—112no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—228no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—444no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4C22⋊C4×D1112yes—
527C2×C4C22⋊C4×D1112yes—
528C2×C4#6696812yes—
529C2×C4#6697112yes—
530C2×C4C22×C4×D1111yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4#6703711yescharacteristic
533C2×C4#6704011yescharacteristic
534C2×C4#6704211yescharacteristic
535C2×C4#6704311yescharacteristic
536C8—42no—
537C8—442no—
538C22—222no—
539C22—222no—
540C22—222no—
541C22—441no—
542C22—441no—
543C22—441no—
544C22—441no—
545C22C2×C22⋊C4×D1111yescharacteristic
546C22#1062313811yescharacteristic
547C22#1062315911yescharacteristic
548C22C2×#6696811yescharacteristic
549C22C2×#6697111yescharacteristic
550C22#1062330411yescharacteristic
551C22#1062330811yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—82no—
556C4—222no—
557C4—222no—
558C4—222no—
559C4—442no—
560C4—442no—
561C4—882no—
562C4#1062241514yes—
563C4#1062303511yescharacteristic
564C4#1062305411yescharacteristic
565C4#1062313911yescharacteristic
566C4#1062316011yescharacteristic
567C2—442no—
568C2#1307120511yescharacteristic
569C2C2×#1062241511yescharacteristic
570C2#1307713211yescharacteristic
571C2#1307962511yescharacteristic
572C2#1307962611yescharacteristic
573C2#1307982811yescharacteristic
574C2#1307982911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#21870
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #13069587C2semidirect
5. #13069434C2semidirect
8. #13068622C2semidirect
9. #13068621C2semidirect
10. #13068618C2semidirect
11. C11×#1803C2semidirect
16. #10623109C4semidirect
197. #1803D11semidirect
473. C11#21870semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
C2×#106224482
#130710212
#130695872
#130694342
#130689272
#130689252
#130686222
#130686212
#130686182
C11×#18032
#2187011