Finite Group Databasebeta

← #14759700

Subgroups — #14759700

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67037C211yesmaximal, characteristic
2C2×#10622674C211yesmaximal, characteristic
3C4×#66995C212yesmaximal, complemented
4#13069005C211yesmaximal, characteristic, complemented
5#13068988C212yesmaximal, complemented
6#13068841C212yesmaximal, complemented
7#13068825C211yesmaximal, characteristic, complemented
8#13068569C211yesmaximal, characteristic
9#13068427C212yesmaximal, complemented
10C4×#66897C211yesmaximal, characteristic, complemented
11C11×#2326C211yesmaximal, characteristic, complemented
12C2×#67037C2211yescharacteristic
13C2×C11×#124C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic, complemented
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66995C2212yes—
17#10623329C2211yescharacteristic
18C2×C4×C22⋊D11—22no—
19#10623077—22no—
20#10623076—22no—
21C4×D4×D11—22no—
22C4×#4341—22no—
23#10623035C2212yes—
24#10623017—22no—
25C4×#4339C2212yes—
26C11×#391C2211yescharacteristic, complemented
27C11×#390C2211yescharacteristic
28C11×#388—22no—
29C11×#385—22no—
30C11×#384C2211yescharacteristic, complemented
31C11×#376C2211yescharacteristic, complemented
32#10622838C2212yescomplemented
33C2×#66897C2211yescharacteristic
34C2×#66897C2211yescharacteristic
35#10622674C418yescomplemented
36#10622643—22no—
37C4×#4326—22no—
38#10622639—22no—
39C4×#4325—22no—
40#10622579C2212yes—
41#10622577C2212yescomplemented
42C2×#66869C2212yes—
43C2×#66869C2212yes—
44C4×#4318C2212yescomplemented
45#10622168C2212yescomplemented
46#10622161C2212yescomplemented
47#10622161C2212yescomplemented
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11D412yes—
51C22×C22⋊D11—22no—
52#67037—22no—
53#67037—24no—
54#67037C2×C414yes—
55C2×#4341—22no—
56C2×D4×D11—22no—
57C2×#4339C2312yes—
58C22×C4×D11—22no—
59C11×#124—22no—
60C11×#124C2×C414yescomplemented
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C11×C22⋊C4D412yes—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—22no—
77C2×#4326—22no—
78#66995—24no—
79#66995C2×C418yescomplemented
80C2×#4325—22no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83C4×C22⋊D11—24no—
84C4×C22⋊D11—24no—
85C4×C22⋊D11—22no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—24no—
88C2×(C2×D11)⋊C4—22no—
89#66979C2312yes—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—22no—
92C2×#4318C2312yes—
93C2×#4318C2312yes—
94#66946—22no—
95#66945—22no—
96C4⋊C4×D11—22no—
97#66940—22no—
98(C22⋊D11)⋊C4—24no—
99(C22⋊D11)⋊C4—24no—
100C22⋊C4×D11—24no—
101#66930—24no—
102C4×D44D412yes—
103C4×D44D412yes—
104#66925—22no—
105C42×D11—22no—
106C4×Dic22D412yes—
107C4×Dic22D412yes—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—22no—
111#66899—22no—
112#66899—22no—
113#66897—22no—
114#66897C2×C414yescomplemented
115#66874—22no—
116#66873—22no—
117#66872—22no—
118#66871—22no—
119#66869—24no—
120#66869C2×C418yescomplemented
121#66867—22no—
122C4×C11⋊C8—22no—
123#21474—111nomaximal, Sylow
124C24×C11C2×D412yes—
125C23×D11—22no—
126C2×Q8×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11C22×C412yescomplemented
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11C22×C412yes—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—82no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C2×C22⋊D11—24no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152#4341—28no—
153#4341—28no—
154D4×D11—28no—
155D4×D11—28no—
156#4339—22no—
157#4339—22no—
158#4339C22×C414yes—
159#4339#4114yes—
160C2×D44C2×D412yes—
161C2×C4×D11—24no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—84no—
166C2×Dic22C2×D412yes—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C4⋊C4—82no—
172C11×C22⋊C4—28no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—82no—
175C42×C11—21no—
176C42×C11—22no—
177C42×C11—42no—
178C42×C11C22×C412yescomplemented
179C42×C11C2×D412yes—
180C42×C11C2×D412yes—
181C22⋊Dic11—24no—
182C22⋊Dic11—22no—
183#4326—28no—
184#4325—28no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—22no—
188C4⋊Dic11C2×D412yes—
189C4⋊Dic11C2×D412yes—
190Dic11⋊C4—24no—
191Dic11⋊C4—22no—
192Dic11⋊C4—22no—
193C4×Dic11—24no—
194C4×Dic11—22no—
195C4×Dic11—22no—
196C4×Dic11—22no—
197#4318—22no—
198#4318—22no—
199#4318—22no—
200#4318C22×C414yescomplemented
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C4×H(5,𝔽2)—111no—
204C2×#455—111no—
205C4×#137—112no—
206#2326D1111yescharacteristic, complemented
207#1885—111no—
208#1882—112no—
209#1859—112no—
210#1856—111no—
211#1792—111no—
212#1759—112no—
213C4×#100—111no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11C4×D414yes—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—28no—
222C22×D11—82no—
223C22×D11—82no—
224Q8×C11—24no—
225Q8×C11—42no—
226D4×C11—24no—
227D4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—44no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—82no—
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11#12012yes—
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11C23×C411yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4112yes—
252C22⋊D11—216no—
253C22⋊D11—24no—
254C22⋊D11—24no—
255C2×Dic11—28no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—82no—
260C2×Dic11—82no—
261D44—22no—
262D44C4×D414yes—
263C4×D11—24no—
264C4×D11—24no—
265C4×D11—44no—
266C4×D11—82no—
267C4×D11—84no—
268Dic22—22no—
269Dic22C4×D414yes—
270C11⋊C8—24no—
271C11⋊C8—42no—
272C2×H(5,𝔽2)—111no—
273C2×#137—112no—
274C2×#124C2×D1111yescharacteristic
275#520—112no—
276#520—222no—
277#518—111no—
278#518—222no—
279#518—222no—
280C4×#41—112no—
281C4×#41—222no—
282C2×C4×Q8C2×D1111yescharacteristic, complemented
283C2×C4×D4—222no—
284C2×C4×D4—222no—
285C2×C4×D4C2×D1111yescharacteristic
286#455—118no—
287#441—222no—
288#440—222no—
289C4×Q16—222no—
290C4×SD16—222no—
291#428—112no—
292C2×#104—112no—
293C2×#104—112no—
294#419—112no—
295#417—112no—
296C2×#100—111no—
297C2×#100—111no—
298C4×M16—112no—
299#391C2×D1111yescharacteristic, complemented
300#390C2×D1111yescharacteristic
301#388—22no—
302#385—22no—
303#384C2×D1111yescharacteristic, complemented
304#376C2×D1111yescharacteristic, complemented
305#343—112no—
306#339—112no—
307#339—112no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—24no—
311C22×C11—44no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—82no—
315C22×C11C2×C4×D411yescharacteristic
316C22×C11C2×#12011yescharacteristic
317C22×C11#52511yescharacteristic
318C2×D11—24no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—88no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11C2×C4×D412yes—
331C4×C11#52512yes—
332Dic11—24no—
333Dic11—42no—
334Dic11—42no—
335H(5,𝔽2)—114no—
336H(5,𝔽2)—224no—
337H(5,𝔽2)—222no—
338C2×#41—112no—
339C2×#41—222no—
340C22×Q8C22×D1111yescharacteristic
341C22×D4—222no—
342C22×D4—222no—
343C22×D4C22×D1111yescharacteristic
344C23×C4—222no—
345C23×C4C22⋊D1112yes—
346#137—118no—
347#137—224no—
348C2×Q16—222no—
349C2×SD16—222no—
350C2×M16—112no—
351C2×M16—112no—
352#124—22no—
353#124C4×D1114yescomplemented
354C4×Q8—22no—
355C4×Q8—22no—
356C4×Q8—112no—
357C4×Q8—112no—
358C4×Q8—222no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—112no—
362C4×D4—112no—
363C4×D4—224no—
364C4×D4—224no—
365C4×D4—222no—
366C4×D4—222no—
367C4×D4—222no—
368C4×D4—224no—
369C4×D4—224no—
370C4×D4—222no—
371C4×D4—224no—
372C4×D4—222no—
373#117—112no—
374#117—224no—
375#117—222no—
376#117—222no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4C22⋊D1112yes—
389C2×C42—21no—
390C2×C42—222no—
391C2×C42—222no—
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394C2×C42C22×D1111yescharacteristic
395#107—222no—
396#106—222no—
397#104—118no—
398#104—224no—
399#103—222no—
400#103—222no—
401#103—222no—
402#102—222no—
403#100—114no—
404#100—222no—
405#97—222no—
406C4×C8—222no—
407#95—21no—
408#95—21no—
409#95—22no—
410C2×C11—21no—
411C2×C11—21no—
412C2×C11—44no—
413C2×C11C4×#12011yescharacteristic
414C2×C11#301911yescharacteristic
415C2×C11#302211yescharacteristic
416D11—44no—
417C24—222no—
418C24C2×C22⋊D1112yes—
419#41—114no—
420#41—114no—
421#41—228no—
422#41—228no—
423#41—222no—
424#41—222no—
425C2×Q8—21no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—112no—
429C2×Q8C2×C4×D1112yescomplemented
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—112no—
433C2×D4—228no—
434C2×D4—228no—
435C2×D4—224no—
436C2×D4—228no—
437C2×D4—228no—
438C2×D4—222no—
439C2×D4C2×C4×D1112yes—
440C2×D4#433912yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—82no—
448C22×C4—224no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—884no—
456C22×C4C2×C22⋊D1112yes—
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C23×D1111yescharacteristic
460Q16—228no—
461SD16—228no—
462M16—114no—
463M16—222no—
464M16—222no—
465M16—222no—
466C2×C8—222no—
467C2×C8—222no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—82no—
473C4⋊C4—112no—
474C4⋊C4—112no—
475C4⋊C4—224no—
476C4⋊C4—222no—
477C4⋊C4—222no—
478C22⋊C4—28no—
479C22⋊C4—24no—
480C22⋊C4—82no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C22⋊C4—222no—
484C22⋊C4—222no—
485C22⋊C4—222no—
486C42—21no—
487C42—22no—
488C42—42no—
489C42—224no—
490C42—222no—
491C42—222no—
492C42—222no—
493C42C2×C4×D1112yescomplemented
494C42D4×D1112yes—
495C42D4×D1112yes—
496C11#2147411yescharacteristic, complemented, Sylow
497C23—22no—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—228no—
502C23—222no—
503C23—882no—
504C23—882no—
505C23C4×C22⋊D1114yes—
506C23C22×C22⋊D1111yescharacteristic
507Q8—24no—
508Q8—42no—
509Q8—114no—
510Q8—222no—
511D4—24no—
512D4—24no—
513D4—114no—
514D4—2216no—
515D4—224no—
516D4—224no—
517D4—222no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—44no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—228no—
536C2×C4—222no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—444no—
542C2×C4—882no—
543C2×C4—884no—
544C2×C4—882no—
545C2×C4—882no—
546C2×C4#6699012yes—
547C2×C4#6699011yescharacteristic
548C2×C4#6699011yescharacteristic
549C2×C4C22×C4×D1111yescharacteristic
550C2×C4C2×#433911yescharacteristic
551C2×C4C2×D4×D1112yes—
552C2×C4#41×D1112yes—
553C8—224no—
554C8—442no—
555C22—21no—
556C22—21no—
557C22—24no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—82no—
562C22—224no—
563C22—442no—
564C22—442no—
565C22—888no—
566C22C2×C4×C22⋊D1111yescharacteristic
567C22C2×#6699011yescharacteristic
568C22#1062335911yescharacteristic
569C4—21no—
570C4—21no—
571C4—22no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—81no—
576C4—81no—
577C4—224no—
578C4—442no—
579C4—442no—
580C4C4×D4×D1112yes—
581C4#1062307812yes—
582C2—21no—
583C2—21no—
584C2—44no—
585C2—444no—
586C2C4×#6699011yescharacteristic
587C2#1307797211yescharacteristic
588C2#1307799411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2326C2
socleC22×C11C2×#120
prime radicalC2×#67037C22
cosocleC22×C4×C11C24
hypercenter#2326D11
hypocenterC11#21474
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2326

Complements

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

NH ≅ G/Ntype
3. C4×#66995C2semidirect
4. #13069005C2semidirect
5. #13068988C2semidirect
6. #13068841C2semidirect
7. #13068825C2semidirect
9. #13068427C2semidirect
10. C4×#66897C2semidirect
11. C11×#2326C2semidirect
14. C2×C4×Q8×C11C22semidirect
26. C11×#391C22semidirect
30. C11×#384C22semidirect
31. C11×#376C22semidirect
32. #10622838C22semidirect
35. #10622674C4semidirect
41. #10622577C22semidirect
44. C4×#4318C22semidirect
45. #10622168C22semidirect
46. #10622161C22semidirect
47. #10622161C22semidirect
60. C11×#124C2×C4semidirect
79. #66995C2×C4semidirect
114. #66897C2×C4semidirect
120. #66869C2×C4semidirect
129. C2×Q8×C11C22×C4semidirect
178. C42×C11C22×C4semidirect
200. #4318C22×C4semidirect
206. #2326D11semidirect
282. C2×C4×Q8C2×D11semidirect
299. #391C2×D11semidirect
303. #384C2×D11semidirect
304. #376C2×D11semidirect
353. #124C4×D11semidirect
429. C2×Q8C2×C4×D11semidirect
493. C42C2×C4×D11semidirect
496. C11#21474semidirect

Maximal subgroups

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

subgroupindex
C4×#670372
C2×#106226742
C4×#669952
#130690052
#130689882
#130688412
#130688252
#130685692
#130684272
C4×#668972
C11×#23262
#2147411