Finite Group Databasebeta

← #14759703

Subgroups — #14759703

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
1H(5,𝔽2)×Dic11C211yesmaximal, characteristic
2#137×Dic11C212yesmaximal, complemented
3#13071329C211yesmaximal, characteristic, complemented
4#13069005C211yesmaximal, characteristic, complemented
5#13068987C212yesmaximal, complemented
6#13068844C212yesmaximal, complemented
7#13068828C211yesmaximal, characteristic, complemented
8#13068570C211yesmaximal, characteristic
9#13068428C212yesmaximal, complemented
10#100×Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#455C211yesmaximal, characteristic
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C2×C11×#137C2212yes—
14C2×C11×#124C2211yescharacteristic
15#10623358—22no—
16#10623358C2212yes—
17#41×Dic11—22no—
18#41×Dic11C2212yes—
19C2×Q8×Dic11C2211yescharacteristic, complemented
20#10623329—22no—
21#10623329—22no—
22#10623329C2211yescharacteristic
23C2×D4×Dic11—22no—
24C2×D4×Dic11—22no—
25C2×D4×Dic11C2211yescharacteristic
26C11×#455C418yescomplemented
27C2×C11×#104C2212yes—
28C2×C11×#100C2211yescharacteristic
29C2×#66901C2212yes—
30#10622845C2212yes—
31#10622843C2211yescharacteristic, complemented
32#10622838C2212yescomplemented
33#10622834C2211yescharacteristic
34C2×#66897C2211yescharacteristic
35#10622797—22no—
36Q16×Dic11—22no—
37#10622777—22no—
38SD16×Dic11—22no—
39#10622734C2212yescomplemented
40M16×Dic11C2212yescomplemented
41#10622564—22no—
42#10622563—22no—
43#10622548C2211yescharacteristic, complemented
44#10622545C2211yescharacteristic, complemented
45#10622193C2212yescomplemented
46#10622192C2212yescomplemented
47#10622161C2212yescomplemented
48C11×H(5,𝔽2)—24no—
49C11×H(5,𝔽2)—22no—
50C11×H(5,𝔽2)C2×C414yes—
51C2×C11×#41—22no—
52C2×C11×#41C2312yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11C2311yescharacteristic
57C23×Dic11—22no—
58C23×Dic11D412yes—
59C11×#137—24no—
60C11×#137C2×C418yescomplemented
61C2×C11×Q16—22no—
62C2×C11×SD16—22no—
63C2×C11×M16C2312yes—
64C11×#124—22no—
65C11×#124C2×C414yescomplemented
66C2×C11×C22⋊C4—22no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11D412yes—
73Q8×Dic11—22no—
74Q8×Dic11—22no—
75Q8×Dic11—22no—
76Q8×Dic11D412yes—
77Q8×Dic11D412yes—
78D4×Dic11—24no—
79D4×Dic11—24no—
80D4×Dic11—24no—
81D4×Dic11—24no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—24no—
85D4×Dic11—22no—
86D4×Dic11—22no—
87D4×Dic11—22no—
88D4×Dic11—22no—
89D4×Dic11—22no—
90D4×Dic11D412yes—
91D4×Dic11D412yes—
92#66979—24no—
93#66979—22no—
94#66979—22no—
95#66979C2312yes—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×#4318C2312yes—
108C11×#104C2×C418yescomplemented
109C11×#100C2×C414yescomplemented
110#66901—24no—
111#66899—22no—
112#66899—22no—
113#66899—22no—
114#66897—22no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—22no—
119#66882—22no—
120#66881—22no—
121#66879—22no—
122C8×Dic11—22no—
123#21474—111nomaximal, Sylow
124C24×C11—22no—
125C24×C11C2×D412yes—
126C11×#41—28no—
127C11×#41—28no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41C22×C414yes—
131C11×#41#4114yes—
132C2×Q8×C11—21no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11C22×C412yescomplemented
136C2×Q8×C11C2×D412yes—
137C2×D4×C11—24no—
138C2×D4×C11—28no—
139C2×D4×C11—28no—
140C2×D4×C11—28no—
141C2×D4×C11—22no—
142C2×D4×C11—28no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11C22×C412yes—
146C2×D4×C11C2×D412yes—
147C2×D4×C11#4112yes—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—82no—
163C22×Dic11—84no—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C11×Q16—28no—
168C11×SD16—28no—
169C11×M16—22no—
170C11×M16C22×C414yescomplemented
171C2×C8×C11—22no—
172C11×C22⋊C4—28no—
173C42×C11—21no—
174C42×C11C22×C412yescomplemented
175C22⋊Dic11—24no—
176C22⋊Dic11—24no—
177C22⋊Dic11—24no—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C22⋊Dic11—22no—
181C22⋊Dic11—82no—
182C4⋊Dic11—24no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11—41no—
188C4⋊Dic11—41no—
189C4⋊Dic11—82no—
190C4⋊Dic11C2×D412yes—
191C4⋊Dic11C2×D412yes—
192C4×Dic11—24no—
193C4×Dic11—22no—
194C4×Dic11—22no—
195C4×Dic11—22no—
196C4×Dic11—22no—
197C4×Dic11—42no—
198C4×Dic11C2×D412yes—
199C4×Dic11C2×D412yes—
200#4318—22no—
201#4318—22no—
202C2×C11⋊C8—22no—
203C4×H(5,𝔽2)—111no—
204C2×#455D1111yescharacteristic
205C4×#137—112no—
206#2326—111no—
207#1885—111no—
208#1882—112no—
209#1859—112no—
210#1856—111no—
211#1792—111no—
212#1759—112no—
213C4×#100—111no—
214C23×C11—28no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11—82no—
221C23×C11—82no—
222C23×C11C4×D414yes—
223C23×C11C22×D411yescharacteristic
224Q8×C11—22no—
225Q8×C11—24no—
226Q8×C11—42no—
227Q8×C11C4×D414yes—
228D4×C11—216no—
229D4×C11—24no—
230D4×C11—24no—
231D4×C11—24no—
232D4×C11—22no—
233D4×C11—24no—
234D4×C11C4×D414yes—
235C2×C4×C11—28no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C22×D412yes—
247C2×C4×C11C2×#4112yes—
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—44no—
255C2×Dic11—44no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—82no—
263C2×Dic11—82no—
264C2×Dic11—82no—
265C2×Dic11—84no—
266C2×Dic11—82no—
267C2×Dic11#12011yescharacteristic
268C2×Dic11#12012yes—
269C2×Dic11#12011yescharacteristic
270C8×C11—24no—
271C11⋊C8—42no—
272C2×H(5,𝔽2)C2×D1111yescharacteristic
273C2×#137C2×D1112yes—
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×Q8—111no—
283C2×C4×D4—111no—
284C2×C4×D4—222no—
285C2×C4×D4—222no—
286#455Dic1118yescomplemented
287#441—222no—
288#440—222no—
289C4×Q16—222no—
290C4×SD16—222no—
291#428—112no—
292C2×#104—112no—
293C2×#104C2×D1112yes—
294#419—112no—
295#417—112no—
296C2×#100—111no—
297C2×#100C2×D1111yescharacteristic
298C4×M16—112no—
299#391—111no—
300#390—111no—
301#388—222no—
302#385—222no—
303#384—111no—
304#376—111no—
305#343—112no—
306#339—112no—
307#339—112no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—44no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—82no—
318C22×C11—88no—
319C22×C11C2×C4×D411yescharacteristic
320C22×C11C2×#12011yescharacteristic
321C22×C11#52511yescharacteristic
322C4×C11—24no—
323C4×C11—42no—
324C4×C11—42no—
325C4×C11C2×C4×D412yes—
326C4×C11#52512yes—
327Dic11—21no—
328Dic11—21no—
329Dic11—22no—
330Dic11—42no—
331Dic11—42no—
332Dic11—42no—
333Dic11—81no—
334Dic11—81no—
335H(5,𝔽2)—24no—
336H(5,𝔽2)—22no—
337H(5,𝔽2)C2×Dic1114yes—
338C2×#41—22no—
339C2×#41C22×D1112yes—
340C22×Q8C22×D1111yescharacteristic
341C22×D4—22no—
342C22×D4—22no—
343C22×D4C22×D1111yescharacteristic
344C23×C4—112no—
345C23×C4—222no—
346#137—24no—
347#137C2×Dic1118yescomplemented
348C2×Q16—22no—
349C2×SD16—22no—
350C2×M16—112no—
351C2×M16C22×D1112yes—
352#124—22no—
353#124C2×Dic1114yescomplemented
354C4×Q8—112no—
355C4×Q8—112no—
356C4×Q8—222no—
357C4×Q8—222no—
358C4×Q8—222no—
359C4×D4—112no—
360C4×D4—112no—
361C4×D4—222no—
362C4×D4—222no—
363C4×D4—222no—
364C4×D4—222no—
365C4×D4—222no—
366C4×D4—224no—
367C4×D4—222no—
368C4×D4—224no—
369C4×D4—224no—
370C4×D4—224no—
371C4×D4—224no—
372C4×D4—222no—
373#117—112no—
374#117—222no—
375#117—222no—
376#117—224no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—222no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—222no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—222no—
392C2×C42—222no—
393C2×C42—221no—
394C2×C42C22×D1111yescharacteristic
395#107—222no—
396#106—222no—
397#104—224no—
398#104C2×Dic1118yescomplemented
399#103—222no—
400#103—222no—
401#103—222no—
402#102—222no—
403#100—222no—
404#100C2×Dic1114yescomplemented
405#97—222no—
406C4×C8—222no—
407#95—221no—
408#95—221no—
409#95—222no—
410C2×C11—21no—
411C2×C11—21no—
412C2×C11—44no—
413C2×C11—44no—
414C2×C11C4×#12011yescharacteristic
415C2×C11#301911yescharacteristic
416C2×C11#302211yescharacteristic
417C24—22no—
418C24D4×D1112yes—
419#41—28no—
420#41—28no—
421#41—22no—
422#41—22no—
423#41#434114yes—
424#41C22×Dic1114yes—
425C2×Q8—21no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8D4×D1112yes—
429C2×Q8C22×Dic1112yescomplemented
430C2×D4—24no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—22no—
435C2×D4—28no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4D4×D1112yes—
439C2×D4#434112yes—
440C2×D4C22×Dic1112yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—112no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—224no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—882no—
458C22×C4—884no—
459C22×C4C23×D1111yescharacteristic
460Q16—28no—
461SD16—28no—
462M16—22no—
463M16—222no—
464M16—222no—
465M16C22×Dic1114yescomplemented
466C2×C8—22no—
467C2×C8—222no—
468C4⋊C4—112no—
469C4⋊C4—112no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—224no—
473C4⋊C4—222no—
474C4⋊C4—222no—
475C4⋊C4—441no—
476C4⋊C4—441no—
477C4⋊C4—882no—
478C22⋊C4—28no—
479C22⋊C4—224no—
480C22⋊C4—222no—
481C22⋊C4—222no—
482C22⋊C4—224no—
483C22⋊C4—224no—
484C22⋊C4—222no—
485C22⋊C4—882no—
486C42—21no—
487C42—112no—
488C42—112no—
489C42—222no—
490C42—222no—
491C42—224no—
492C42—222no—
493C42—222no—
494C42—442no—
495C42C22×Dic1112yescomplemented
496C11#2147411yescharacteristic, complemented, Sylow
497C23—28no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—42no—
502C23—42no—
503C23—82no—
504C23—82no—
505C23D4×Dic1114yes—
506C23C2×D4×D1111yescharacteristic
507Q8—22no—
508Q8—24no—
509Q8—42no—
510Q8D4×Dic1114yes—
511D4—216no—
512D4—24no—
513D4—24no—
514D4—24no—
515D4—22no—
516D4—24no—
517D4D4×Dic1114yes—
518C2×C4—28no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—111no—
529C2×C4—112no—
530C2×C4—111no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—444no—
537C2×C4—444no—
538C2×C4—442no—
539C2×C4—441no—
540C2×C4—442no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—882no—
545C2×C4—882no—
546C2×C4—884no—
547C2×C4—882no—
548C2×C4—882no—
549C2×C4C2×D4×D1112yes—
550C2×C4C2×#434112yes—
551C2×C4C2×#434111yescharacteristic
552C2×C4C23×Dic1111yescharacteristic
553C8—24no—
554C8—442no—
555C22—21no—
556C22—21no—
557C22—24no—
558C22—24no—
559C22—44no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—82no—
565C22—88no—
566C22#1062311711yescharacteristic
567C22D11×#12011yescharacteristic
568C22C2×D4×Dic1111yescharacteristic
569C4—24no—
570C4—42no—
571C4—42no—
572C4—221no—
573C4—221no—
574C4—222no—
575C4—442no—
576C4—442no—
577C4—442no—
578C4—881no—
579C4—881no—
580C4#1062311712yes—
581C4C2×D4×Dic1112yes—
582C2—21no—
583C2—21no—
584C2—44no—
585C2—44no—
586C2#120×Dic1111yescharacteristic
587C2#1307797411yescharacteristic
588C2#1307799111yescharacteristic
subgroupG/H
centerC22D11×#120
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#455C2
socleC22×C11C2×#120
prime radicalC2×C11×H(5,𝔽2)C22
cosocleC22×C4×C11C24
hypercenterC2×#455D11
hypocenterC11#21474
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#455

Complements

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

NH ≅ G/Ntype
2. #137×Dic11C2semidirect
3. #13071329C2semidirect
4. #13069005C2semidirect
5. #13068987C2semidirect
6. #13068844C2semidirect
7. #13068828C2semidirect
9. #13068428C2semidirect
10. #100×Dic11C2semidirect
19. C2×Q8×Dic11C22semidirect
26. C11×#455C4semidirect
31. #10622843C22semidirect
32. #10622838C22semidirect
39. #10622734C22semidirect
40. M16×Dic11C22semidirect
43. #10622548C22semidirect
44. #10622545C22semidirect
45. #10622193C22semidirect
46. #10622192C22semidirect
47. #10622161C22semidirect
60. C11×#137C2×C4semidirect
65. C11×#124C2×C4semidirect
108. C11×#104C2×C4semidirect
109. C11×#100C2×C4semidirect
135. C2×Q8×C11C22×C4semidirect
170. C11×M16C22×C4semidirect
174. C42×C11C22×C4semidirect
286. #455Dic11semidirect
347. #137C2×Dic11semidirect
353. #124C2×Dic11semidirect
398. #104C2×Dic11semidirect
404. #100C2×Dic11semidirect
429. C2×Q8C22×Dic11semidirect
465. M16C22×Dic11semidirect
495. C42C22×Dic11semidirect
496. C11#21474semidirect

Maximal subgroups

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

subgroupindex
H(5,𝔽2)×Dic112
#137×Dic112
#130713292
#130690052
#130689872
#130688442
#130688282
#130685702
#130684282
#100×Dic112
C2×C11×#4552
#2147411