Finite Group Databasebeta

← #14754644

Subgroups — #14754644

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#13077205C211yesmaximal, characteristic, complemented
2C22×#66901C211yesmaximal, characteristic
3#13077135C211yesmaximal, characteristic
4#13071019C211yesmaximal, characteristic, complemented
5#13068849C214yesmaximal, complemented
6#13068842C214yesmaximal, complemented
7#13068355C211yesmaximal, characteristic, complemented
8C2×#10622170C211yesmaximal, characteristic, complemented
9C11×#3428C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C11×#520—22no—
12C11×#520C2214yes—
13C11×#519—21no—
14C11×#518—21no—
15C11×#518—22no—
16C4×C11×#41—22no—
17C4×C11×#41—22no—
18C2×C11×#117—22no—
19C2×C11×#117C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C2×#66901C418yescomplemented
26C2×#66901C2212yes—
27C2×#66901C2212yes—
28#10622846—22no—
29#10622845C2214yes—
30#10622838—21no—
31#10622828—21no—
32#10622611—22no—
33#10622608C2214yescomplemented
34#10622590C2212yescomplemented
35#10622589C2212yescomplemented
36#10622577—22no—
37#10622555—22no—
38C4×Dic11⋊C4—22no—
39#10622170C2212yescomplemented
40#10622170C2212yescomplemented
41#10622168C2214yescomplemented
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41C2×C414yes—
47C2×C11×#41D412yes—
48C2×C11×#41Q814yes—
49C2×C11×#41C2312yes—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C23×Dic11—21no—
56C4×Q8×C11—24no—
57C4×Q8×C11—24no—
58C4×D4×C11—28no—
59C4×D4×C11—24no—
60C4×D4×C11—24no—
61C4×D4×C11—28no—
62C11×#117—24no—
63C11×#117—24no—
64C11×#117—21no—
65C11×#117—21no—
66C11×#117—21no—
67C11×#117—21no—
68C11×#117—21no—
69C11×#117—21no—
70C11×#117—24no—
71C11×#117D412yes—
72C11×#117C2312yes—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4D412yes—
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4D412yes—
79C2×C42×C11—24no—
80C2×C42×C11—21no—
81C2×C42×C11D412yes—
82C2×C22⋊Dic11—21no—
83#66979—21no—
84#66979—21no—
85#66979—21no—
86#66979—21no—
87C2×C4⋊Dic11C2312yes—
88C2×Dic11⋊C4—24no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11C2×C414yescomplemented
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×#4318—21no—
96C2×#4318—22no—
97C2×#4318—21no—
98C2×#4318—22no—
99C2×#4318—22no—
100C2×#4318C2×C414yescomplemented
101C2×#4318C2312yes—
102C2×#4318C2312yes—
103C22×C11⋊C8—21no—
104C22×C11⋊C8—21no—
105#66901C2×C418yescomplemented
106#66901C2×C418yescomplemented
107#66899—24no—
108#66896—24no—
109C11⋊#95—24no—
110#66872—24no—
111#66871—24no—
112#20863—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11C2×D411yescharacteristic
115C11×#41—24no—
116C11×#41—24no—
117C11×#41—24no—
118C11×#41—24no—
119C11×#41—24no—
120C11×#41—22no—
121C11×#41—22no—
122C11×#41C4⋊C418yescomplemented
123C11×#41C22×C414yes—
124C11×#41C2×Q814yes—
125C2×Q8×C11—21no—
126C2×Q8×C11—22no—
127C2×Q8×C11C4⋊C414yescomplemented
128C2×Q8×C11C2×D412yes—
129C2×D4×C11—24no—
130C2×D4×C11—22no—
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11C4⋊C414yescomplemented
136C2×D4×C11C2×D412yes—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—28no—
143C22×C4×C11—22no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×Q812yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—24no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—44no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4C2×D414yes—
165C11×C22⋊C4—28no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C42×C11—28no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—22no—
174C42×C11—22no—
175C22⋊Dic11—41no—
176C22⋊Dic11—41no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179Dic11⋊C4—48no—
180C4×Dic11—24no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183C4×Dic11—41no—
184C4×Dic11—41no—
185C4×Dic11C22×C412yes—
186C4×Dic11C22×C412yes—
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#3428D1111yescharacteristic
198#2911—111no—
199C22×#104—111no—
200#2896—111no—
201#2285—111no—
202#1860—114no—
203#1859—114no—
204#1742—111no—
205C2×#339—111no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—42no—
209C23×C11—82no—
210C23×C11C4×D412yes—
211C23×C11#12011yescharacteristic
212C23×C11#12011yescharacteristic
213C23×C11C22⋊Q812yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—22no—
216Q8×C11—24no—
217Q8×C11C2×C4⋊C414yes—
218D4×C11—24no—
219D4×C11—24no—
220D4×C11—28no—
221D4×C11—22no—
222D4×C11—24no—
223D4×C11C2×C4⋊C414yes—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—28no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—44no—
232C2×C4×C11—82no—
233C2×C4×C11—88no—
234C2×C4×C11C2×C4⋊C412yes—
235C2×C4×C11C2×C4⋊C412yes—
236C2×C4×C11C4×D412yes—
237C2×C4×C11C4×D412yes—
238C2×C4×C11C4×D412yes—
239C2×C4×C11#12011yescharacteristic
240C2×C4×C11#12011yescharacteristic
241C2×C4×C11C22⋊Q812yes—
242C2×C4×C11C22⋊Q812yes—
243C2×C4×C11C22⋊Q812yes—
244C2×C4×C11#12312yes—
245C2×C4×C11#12312yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×Q811yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—48no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259C11⋊C8—24no—
260C11⋊C8—42no—
261C22×#41C2×D1111yescharacteristic
262C22×M16—111no—
263C22×M16—111no—
264#520—22no—
265#520C2×D1114yes—
266#519—21no—
267#518—21no—
268#518—22no—
269C4×#41—22no—
270C4×#41—22no—
271C2×#117—22no—
272C2×#117—111no—
273C2×#117C2×D1111yescharacteristic
274C2×#117C2×D1111yescharacteristic
275C22×C42—111no—
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#384—112no—
287#382—112no—
288#380—222no—
289C4×C4⋊C4—222no—
290#343—114no—
291#339—112no—
292#339—112no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11—42no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—84no—
301C22×C11#38512yes—
302C22×C11#38512yes—
303C22×C11C2×C4×D411yescharacteristic
304C22×C11C2×#12011yescharacteristic
305C22×C11C2×C22⋊Q811yescharacteristic
306C4×C11—24no—
307C4×C11—44no—
308C4×C11—44no—
309C4×C11#38512yes—
310C4×C11#38512yes—
311C4×C11C22×C4⋊C411yescharacteristic
312C4×C11C2×C4×D411yescharacteristic
313C4×C11C2×C22⋊Q811yescharacteristic
314C4×C11C2×#12311yescharacteristic
315Dic11—24no—
316Dic11—42no—
317Dic11—82no—
318C2×#41—22no—
319C2×#41—22no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41Dic2214yes—
323C2×#41C4×D1114yes—
324C2×#41C22⋊D1112yes—
325C2×#41C22×D1112yes—
326C22×Q8C22⋊D1111yescharacteristic
327C22×D4—21no—
328C22×D4C22⋊D1111yescharacteristic
329C23×C4—21no—
330C23×C4—221no—
331C23×C4C22×D1111yescharacteristic
332C2×M16—114no—
333C2×M16—112no—
334C2×M16—112no—
335C2×M16—222no—
336C2×M16—221no—
337C2×M16—221no—
338C2×M16—222no—
339C2×M16—222no—
340C22×C8—221no—
341C22×C8—221no—
342C4×Q8—24no—
343C4×Q8—24no—
344C4×D4—28no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—28no—
348#117—24no—
349#117—24no—
350#117—21no—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—24no—
357#117—221no—
358#117—221no—
359#117—221no—
360#117—221no—
361#117C22⋊D1112yes—
362#117C22×D1112yes—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—224no—
366C2×C4⋊C4C22⋊D1112yes—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4C22⋊D1112yes—
372C2×C42—24no—
373C2×C42—21no—
374C2×C42—114no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—222no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42C22⋊D1112yes—
381#107—224no—
382#106—224no—
383#104—118no—
384#104—118no—
385#103—224no—
386#102—224no—
387#95—224no—
388C2×C11—21no—
389C2×C11—22no—
390C2×C11—21no—
391C2×C11—22no—
392C2×C11—44no—
393C2×C11C2×#38511yescharacteristic
394C2×C11#301812yes—
395C24—21no—
396C24C2×C22⋊D1111yescharacteristic
397#41—24no—
398#41—24no—
399#41—24no—
400#41—24no—
401#41—24no—
402#41—22no—
403#41—22no—
404#41Dic11⋊C418yescomplemented
405#41C2×Dic2214yes—
406#41C2×C4×D1114yes—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8Dic11⋊C414yescomplemented
410C2×Q8C2×C22⋊D1112yes—
411C2×D4—24no—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4Dic11⋊C414yescomplemented
418C2×D4C2×C22⋊D1112yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—28no—
425C22×C4—22no—
426C22×C4—221no—
427C22×C4—224no—
428C22×C4—221no—
429C22×C4—222no—
430C22×C4—444no—
431C22×C4C2×Dic2212yes—
432C22×C4C2×C4×D1112yes—
433C22×C4#433912yes—
434C22×C4#433912yes—
435C22×C4C2×C22⋊D1114yes—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
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—28no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—448no—
459C4⋊C4C2×C22⋊D1114yes—
460C22⋊C4—28no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—441no—
466C22⋊C4—441no—
467C42—28no—
468C42—22no—
469C42—22no—
470C42—22no—
471C42—22no—
472C42—112no—
473C42—112no—
474C42—224no—
475C42—221no—
476C42—221no—
477C42—441no—
478C42—441no—
479C11#2086311yescharacteristic, complemented, Sylow
480C23—22no—
481C23—24no—
482C23—42no—
483C23—82no—
484C23#6697712yes—
485C23C4×C22⋊D1112yes—
486C23#6700611yescharacteristic
487C23#6700611yescharacteristic
488C23C22×C22⋊D1111yescharacteristic
489Q8—22no—
490Q8—24no—
491Q8C2×Dic11⋊C414yes—
492D4—24no—
493D4—24no—
494D4—28no—
495D4—22no—
496D4—24no—
497D4C2×Dic11⋊C414yes—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—44no—
506C2×C4—82no—
507C2×C4—88no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—448no—
512C2×C4—442no—
513C2×C4—444no—
514C2×C4—442no—
515C2×C4C2×Dic11⋊C412yes—
516C2×C4C2×Dic11⋊C412yes—
517C2×C4#6697712yes—
518C2×C4#6697712yes—
519C2×C4#6697712yes—
520C2×C4C4×C22⋊D1112yes—
521C2×C4C4×C22⋊D1112yes—
522C2×C4C4×C22⋊D1112yes—
523C2×C4#6698212yes—
524C2×C4#6698212yes—
525C2×C4#6700611yescharacteristic
526C2×C4#6700611yescharacteristic
527C2×C4C22×Dic2211yescharacteristic
528C2×C4C22×C4×D1111yescharacteristic
529C2×C4C2×#433911yescharacteristic
530C2×C4C2×#433911yescharacteristic
531C2×C4C22×C22⋊D1111yescharacteristic
532C2×C4C22×C22⋊D1111yescharacteristic
533C8—224no—
534C8—442no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—24no—
539C22—42no—
540C22—42no—
541C22—44no—
542C22—84no—
543C22#1062282312yes—
544C22#1062282312yes—
545C22C2×#6697711yescharacteristic
546C22C2×C4×C22⋊D1111yescharacteristic
547C22C2×#6700611yescharacteristic
548C4—24no—
549C4—44no—
550C4—44no—
551C4—224no—
552C4—442no—
553C4—882no—
554C4#1062282312yes—
555C4#1062282312yes—
556C4C22×Dic11⋊C411yescharacteristic
557C4C2×#6697711yescharacteristic
558C4C2×C4×C22⋊D1111yescharacteristic
559C4C2×#6698211yescharacteristic
560C2—21no—
561C2—22no—
562C2—21no—
563C2—22no—
564C2—44no—
565C2C2×#1062282311yescharacteristic
566C2#1307796512yes—
subgroupG/H
centerC2×C4#67006
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3428C2
socleC22×C11C2×#120
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#3428D11
hypocenterC11#20863
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #13077205C2semidirect
4. #13071019C2semidirect
5. #13068849C2semidirect
6. #13068842C2semidirect
7. #13068355C2semidirect
8. C2×#10622170C2semidirect
25. C2×#66901C4semidirect
33. #10622608C22semidirect
34. #10622590C22semidirect
35. #10622589C22semidirect
39. #10622170C22semidirect
40. #10622170C22semidirect
41. #10622168C22semidirect
92. C2×C4×Dic11C2×C4semidirect
100. C2×#4318C2×C4semidirect
105. #66901C2×C4semidirect
106. #66901C2×C4semidirect
122. C11×#41C4⋊C4semidirect
127. C2×Q8×C11C4⋊C4semidirect
135. C2×D4×C11C4⋊C4semidirect
404. #41Dic11⋊C4semidirect
409. C2×Q8Dic11⋊C4semidirect
417. C2×D4Dic11⋊C4semidirect
479. C11#20863semidirect

Maximal subgroups

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

subgroupindex
#130772052
C22×#669012
#130771352
#130710192
#130688492
#130688422
#130683552
C2×#106221702
C11×#34282
#2086311