Finite Group Databasebeta

← #14754643

Subgroups — #14754643

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081817C211yesmaximal, characteristic
2#13077205C211yesmaximal, characteristic, complemented
3C22×#66869C211yesmaximal, characteristic
4#13077133C211yesmaximal, characteristic
5#13068848C214yesmaximal, complemented
6#13068841C214yesmaximal, complemented
7#13068355C211yesmaximal, characteristic, complemented
8C2×#10622161C211yesmaximal, characteristic, complemented
9C11×#2285C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17#10623054—22no—
18#10623053—22no—
19#10623052—21no—
20D11×#117—22no—
21#10623047—21no—
22#10623035C2214yes—
23#10623017—22no—
24C4×#4339—22no—
25C11×#384C2212yescomplemented
26C11×#382C2212yescomplemented
27C11×#380—22no—
28C4×C11×C4⋊C4—22no—
29#10622617—21no—
30#10622615—22no—
31#10622614—21no—
32#10622611—22no—
33#10622608—22no—
34#10622579C2214yes—
35#10622577C2214yescomplemented
36C2×#66869C418yescomplemented
37C2×#66869C2212yes—
38C2×#66869C2212yes—
39#10622168C2214yescomplemented
40#10622161C2212yescomplemented
41#10622161C2212yescomplemented
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339C2×C414yes—
50C2×#4339D412yes—
51C2×#4339Q814yes—
52C2×#4339C2312yes—
53C22×D44D411yescharacteristic
54C22×C4×D11—21no—
55C22×Dic22D411yescharacteristic
56C11×#117—21no—
57C11×#117—21no—
58C11×#117—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117—21no—
62C11×#117—21no—
63C11×#117—21no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4D412yes—
69C2×C42×C11—21no—
70C2×C42×C11—22no—
71C2×C42×C11—21no—
72C2×C42×C11C2×C414yescomplemented
73C2×C42×C11D412yes—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C4×C22⋊D11—28no—
78#66979—21no—
79#66979—21no—
80#66979D412yes—
81#66979C2312yes—
82C2×C4⋊Dic11D412yes—
83C2×C4×Dic11—21no—
84C2×#4318—21no—
85C2×#4318—22no—
86C2×#4318—21no—
87C2×#4318—22no—
88C2×#4318—22no—
89C2×#4318C2×C414yescomplemented
90C2×#4318C2312yes—
91C2×#4318C2312yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94#66946—24no—
95#66945—24no—
96C4⋊C4×D11—24no—
97#66940—24no—
98(C22⋊D11)⋊C4—28no—
99C22⋊C4×D11—24no—
100#66930—24no—
101C4×D44—24no—
102#66925—24no—
103C42×D11—24no—
104C4×Dic22—24no—
105C11×#95—24no—
106#66874—24no—
107#66873—24no—
108#66872—24no—
109#66871—24no—
110#66869C2×C418yescomplemented
111#66869C2×C418yescomplemented
112#20863—111nomaximal, Sylow
113C24×C11C2×D411yescharacteristic
114C23×D11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—24no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—44no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D414yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×Q812yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—24no—
132C2×C22⋊D11—22no—
133C2×C22⋊D11—24no—
134C2×C22⋊D11—22no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137#4339—24no—
138#4339—24no—
139#4339—24no—
140#4339—24no—
141#4339—24no—
142#4339—22no—
143#4339—22no—
144#4339C4⋊C418yescomplemented
145#4339C22×C414yes—
146#4339C2×Q814yes—
147C2×D44—21no—
148C2×D44—22no—
149C2×D44C4⋊C414yescomplemented
150C2×D44C2×D412yes—
151C2×C4×D11—28no—
152C2×C4×D11—24no—
153C2×C4×D11—22no—
154C2×C4×D11—24no—
155C2×C4×D11—22no—
156C2×Dic22—21no—
157C2×Dic22—22no—
158C2×Dic22C4⋊C414yescomplemented
159C2×Dic22C2×D412yes—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—48no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C42×C11—24no—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—41no—
175C42×C11—41no—
176C42×C11C22×C412yes—
177C42×C11C22×C412yes—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180(C2×D11)⋊C4—28no—
181C4⋊Dic11—22no—
182C4⋊Dic11C2×D414yes—
183Dic11⋊C4—28no—
184C4×Dic11—28no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187#4318—24no—
188#4318—22no—
189#4318—22no—
190#4318—22no—
191#4318—42no—
192#4318C22×C414yes—
193C2×C11⋊C8—24no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—42no—
197#3428—111no—
198#2911—111no—
199C22×#104—111no—
200#2896—111no—
201#2285D1111yescharacteristic, complemented
202#1860—114no—
203#1859—114no—
204#1742—111no—
205C2×#339—111no—
206C23×C11—42no—
207C23×C11C4×D412yes—
208C23×C11#12011yescharacteristic
209C23×C11#12011yescharacteristic
210C23×C11C22⋊Q812yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—24no—
214C22×D11—82no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—48no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
222C2×C4×C11—44no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C4⋊C412yes—
225C2×C4×C11C2×C4⋊C412yes—
226C2×C4×C11C4×D412yes—
227C2×C4×C11C4×D412yes—
228C2×C4×C11C4×D412yes—
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11C22⋊Q812yes—
232C2×C4×C11C22⋊Q812yes—
233C2×C4×C11C22⋊Q812yes—
234C2×C4×C11#12312yes—
235C2×C4×C11#12312yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C22⋊D11—24no—
243C22⋊D11—24no—
244C22⋊D11—28no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—82no—
249D44—22no—
250D44—24no—
251D44C2×C4⋊C414yes—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—28no—
255C4×D11—88no—
256Dic22—22no—
257Dic22—24no—
258Dic22C2×C4⋊C414yes—
259C11⋊C8—24no—
260C11⋊C8—42no—
261C22×#41—111no—
262C22×M16—111no—
263C22×M16—111no—
264#520—114no—
265#520—222no—
266#519—221no—
267#518—221no—
268#518—222no—
269C4×#41—222no—
270C4×#41—222no—
271C2×#117—111no—
272C2×#117—222no—
273C2×#117C2×D1111yescharacteristic
274C2×#117C2×D1111yescharacteristic
275C22×C42C2×D1111yescharacteristic
276#428—114no—
277#428—222no—
278#427—222no—
279C2×#104—112no—
280C2×#104—112no—
281C2×#104—118no—
282#419—221no—
283#418—221no—
284#417—114no—
285#416—222no—
286#384C2×D1112yescomplemented
287#382C2×D1112yescomplemented
288#380—22no—
289C4×C4⋊C4—22no—
290#343—114no—
291#339—112no—
292#339—112no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11#38512yes—
299C22×C11#38512yes—
300C22×C11C2×C4×D411yescharacteristic
301C22×C11C2×#12011yescharacteristic
302C22×C11C2×C22⋊Q811yescharacteristic
303C2×D11—24no—
304C2×D11—44no—
305C2×D11—84no—
306C4×C11—24no—
307C4×C11—42no—
308C4×C11—44no—
309C4×C11—82no—
310C4×C11#38512yes—
311C4×C11#38512yes—
312C4×C11C22×C4⋊C411yescharacteristic
313C4×C11C2×C4×D411yescharacteristic
314C4×C11C2×C22⋊Q811yescharacteristic
315C4×C11C2×#12311yescharacteristic
316Dic11—24no—
317Dic11—44no—
318C2×#41—114no—
319C2×#41—112no—
320C2×#41—114no—
321C2×#41—112no—
322C2×#41—222no—
323C2×#41—221no—
324C2×#41—222no—
325C2×#41—221no—
326C22×Q8—111no—
327C22×D4—111no—
328C22×D4—221no—
329C23×C4—21no—
330C23×C4—221no—
331C23×C4C22×D1111yescharacteristic
332C2×M16—114no—
333C2×M16—112no—
334C2×M16—112no—
335C2×M16—221no—
336C2×M16—222no—
337C2×M16—221no—
338C2×M16—222no—
339C2×M16—222no—
340C22×C8—221no—
341C22×C8—221no—
342C4×Q8—224no—
343C4×Q8—224no—
344C4×D4—224no—
345C4×D4—228no—
346C4×D4—224no—
347C4×D4—228no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—112no—
357#117—112no—
358#117—224no—
359#117—224no—
360#117—224no—
361#117—221no—
362#117—221no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4C22×D1112yes—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—224no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4C22⋊D1112yes—
372C2×C42—22no—
373C2×C42—21no—
374C2×C42—21no—
375C2×C42—224no—
376C2×C42—221no—
377C2×C42C4×D1114yescomplemented
378C2×C42C22⋊D1112yes—
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381#107—224no—
382#106—224no—
383#104—118no—
384#104—118no—
385#103—224no—
386#102—224no—
387#95—24no—
388C2×C11—21no—
389C2×C11—22no—
390C2×C11—21no—
391C2×C11—22no—
392C2×C11C2×#38511yescharacteristic
393C2×C11#301812yes—
394D11—44no—
395C24—221no—
396C24C2×C22⋊D1111yescharacteristic
397#41—118no—
398#41—114no—
399#41—114no—
400#41—224no—
401#41—224no—
402#41—224no—
403#41—224no—
404#41—224no—
405#41—222no—
406#41—222no—
407C2×Q8—114no—
408C2×Q8—112no—
409C2×Q8—222no—
410C2×Q8—221no—
411C2×D4—114no—
412C2×D4—112no—
413C2×D4—224no—
414C2×D4—222no—
415C2×D4—224no—
416C2×D4—222no—
417C2×D4—222no—
418C2×D4—221no—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—228no—
425C22×C4—221no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4C2×C4×D1112yes—
432C22×C4#433912yes—
433C22×C4D4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435C22×C4D4×D1111yescharacteristic
436C22×C4D4×D1111yescharacteristic
437C22×C4Q8×D1112yes—
438C22×C4#434312yes—
439C22×C4C2×C22⋊D1114yes—
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C23×D1111yescharacteristic
442M16—114no—
443M16—224no—
444M16—222no—
445M16—222no—
446M16—222no—
447M16—442no—
448C2×C8—224no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—442no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—48no—
457C4⋊C4—114no—
458C4⋊C4—228no—
459C4⋊C4—222no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—228no—
465C22⋊C4—222no—
466C22⋊C4—222no—
467C42—24no—
468C42—22no—
469C42—22no—
470C42—21no—
471C42—21no—
472C42—41no—
473C42—41no—
474C42—228no—
475C42—222no—
476C42—222no—
477C42C2×C4×D1112yes—
478C42C2×C4×D1112yes—
479C11#2086311yescharacteristic, complemented, Sylow
480C23—42no—
481C23—222no—
482C23—224no—
483C23—882no—
484C23C4×C22⋊D1112yes—
485C23#6699011yescharacteristic
486C23#6699011yescharacteristic
487C23#6699912yes—
488C23C22×C22⋊D1111yescharacteristic
489Q8—114no—
490Q8—222no—
491Q8—224no—
492D4—114no—
493D4—224no—
494D4—224no—
495D4—228no—
496D4—222no—
497D4—224no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—48no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—228no—
512C2×C4—224no—
513C2×C4—888no—
514C2×C4—882no—
515C2×C4C4⋊C4×D1112yes—
516C2×C4C4⋊C4×D1112yes—
517C2×C4#6694612yes—
518C2×C4#6694612yes—
519C2×C4#6694712yes—
520C2×C4#6694712yes—
521C2×C4#6694912yes—
522C2×C4#6694912yes—
523C2×C4C4×C22⋊D1112yes—
524C2×C4#6699011yescharacteristic
525C2×C4#6699011yescharacteristic
526C2×C4#6699912yes—
527C2×C4C22×C4×D1111yescharacteristic
528C2×C4C2×#433911yescharacteristic
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4C2×D4×D1111yescharacteristic
531C2×C4C2×Q8×D1111yescharacteristic
532C2×C4C2×#434311yescharacteristic
533C8—224no—
534C8—442no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—42no—
539C22—42no—
540C22—224no—
541C22—444no—
542C22—884no—
543C22#1062260212yes—
544C22#1062260212yes—
545C22C2×C4×C22⋊D1111yescharacteristic
546C22C2×#6699011yescharacteristic
547C22C2×#6699911yescharacteristic
548C4—24no—
549C4—42no—
550C4—44no—
551C4—82no—
552C4—224no—
553C4—444no—
554C4#1062260212yes—
555C4#1062260212yes—
556C4C2×C4⋊C4×D1111yescharacteristic
557C4C2×#6694611yescharacteristic
558C4C2×#6694711yescharacteristic
559C4C2×#6694911yescharacteristic
560C2—21no—
561C2—22no—
562C2—21no—
563C2—22no—
564C2—444no—
565C2C2×#1062260211yescharacteristic
566C2#1307796412yes—
subgroupG/H
centerC2×C4#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2285C2
socleC22×C11C2×#120
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#2285D11
hypocenterC11#20863
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #13077205C2semidirect
5. #13068848C2semidirect
6. #13068841C2semidirect
7. #13068355C2semidirect
8. C2×#10622161C2semidirect
9. C11×#2285C2semidirect
25. C11×#384C22semidirect
26. C11×#382C22semidirect
35. #10622577C22semidirect
36. C2×#66869C4semidirect
39. #10622168C22semidirect
40. #10622161C22semidirect
41. #10622161C22semidirect
72. C2×C42×C11C2×C4semidirect
89. C2×#4318C2×C4semidirect
110. #66869C2×C4semidirect
111. #66869C2×C4semidirect
144. #4339C4⋊C4semidirect
149. C2×D44C4⋊C4semidirect
158. C2×Dic22C4⋊C4semidirect
201. #2285D11semidirect
286. #384C2×D11semidirect
287. #382C2×D11semidirect
377. C2×C42C4×D11semidirect
479. C11#20863semidirect

Maximal subgroups

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

subgroupindex
#130818172
#130772052
C22×#668692
#130771332
#130688482
#130688412
#130683552
C2×#106221612
C11×#22852
#2086311