Finite Group Databasebeta

← #14759702

Subgroups — #14759702

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
1C2×#10622855C211yesmaximal, characteristic
2C4×#67004C212yesmaximal, complemented
3#13071328C211yesmaximal, characteristic, complemented
4#13069004C211yesmaximal, characteristic, complemented
5#13068985C212yesmaximal, complemented
6#13068842C212yesmaximal, complemented
7#13068826C211yesmaximal, characteristic, complemented
8#13068570C211yesmaximal, characteristic
9#13068426C212yesmaximal, complemented
10C4×#66897C211yesmaximal, characteristic, complemented
11C4×C11×H(5,𝔽2)C211yesmaximal, characteristic
12C2×C11×H(5,𝔽2)C2211yescharacteristic
13C11×#520—22no—
14C11×#520C2212yes—
15C11×#518—22no—
16C11×#518—22no—
17C11×#518C2211yescharacteristic
18C4×C11×#41—22no—
19C4×C11×#41C2212yes—
20C2×C4×D4×C11—22no—
21C2×C4×D4×C11—22no—
22C2×C4×D4×C11C2211yescharacteristic
23C2×#67004C2212yes—
24C2×#66989C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic, complemented
26#10622855C418yescomplemented
27C2×#66901C2212yes—
28C2×#66901C2212yes—
29#10622845C2212yes—
30#10622834C2211yescharacteristic
31C2×#66897C2211yescharacteristic
32C2×#66897C2211yescharacteristic
33#10622823—22no—
34#10622643—22no—
35C4×#4326—22no—
36#10622631—22no—
37C4×#4324—22no—
38#10622617C2212yescomplemented
39#10622608C2212yescomplemented
40#10622589C2211yescharacteristic, complemented
41#10622587C2211yescharacteristic, complemented
42#10622557—22no—
43#10622545C2211yescharacteristic, complemented
44C4×#4318C2212yescomplemented
45#10622170C2212yescomplemented
46#10622170C2212yescomplemented
47#10622168C2212yescomplemented
48C11×H(5,𝔽2)—24no—
49C11×H(5,𝔽2)—22no—
50C11×H(5,𝔽2)C2×C414yes—
51C2×C11×#41—22no—
52C2×C11×#41C2312yes—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11C2311yescharacteristic
56C23×C4×C11—22no—
57C23×C4×C11D412yes—
58C22×Dic22C2311yescharacteristic
59C4×Q8×C11—22no—
60C4×Q8×C11D412yes—
61C4×Q8×C11D412yes—
62C4×D4×C11—24no—
63C4×D4×C11—24no—
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—24no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11D412yes—
75C4×D4×C11D412yes—
76C11×#117—24no—
77C11×#117—22no—
78C11×#117—22no—
79C11×#117C2312yes—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4D412yes—
87C2×C42×C11—22no—
88C2×C42×C11—22no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92#67004—24no—
93#67004C2×C418yescomplemented
94C2×#4326—22no—
95#66989—22no—
96#66989C2×C414yescomplemented
97C2×#4324—22no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—22no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C2×#4318C2312yes—
105C2×#4318C2312yes—
106C4×Dic22—22no—
107C4×Dic22—22no—
108#66901—24no—
109#66901C2×C418yescomplemented
110#66899—22no—
111#66897—22no—
112#66897C2×C414yescomplemented
113#66896—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—22no—
117#66874—22no—
118#66874—22no—
119#66872—22no—
120#66871—22no—
121#66867—22no—
122C4×C11⋊C8—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×C11C2×D412yes—
133C2×D4×C11—24no—
134C2×D4×C11—28no—
135C2×D4×C11—28no—
136C2×D4×C11—28no—
137C2×D4×C11—22no—
138C2×D4×C11—28no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11C22×C412yes—
142C2×D4×C11C2×D412yes—
143C2×D4×C11#4112yes—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—82no—
154C22×C4×C11—84no—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—21no—
166C2×Dic22C22×C412yescomplemented
167C11×C4⋊C4—24no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4C2×D412yes—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—24no—
179C42×C11—24no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11C2×D412yes—
184C42×C11C2×D412yes—
185C22⋊Dic11—28no—
186C22⋊Dic11—82no—
187#4326—28no—
188#4324—28no—
189C4⋊Dic11—22no—
190Dic11⋊C4—41no—
191Dic11⋊C4—41no—
192Dic11⋊C4—82no—
193C4×Dic11—21no—
194C4×Dic11—22no—
195C4×Dic11—42no—
196C4×Dic11C22×C412yescomplemented
197#4318—22no—
198#4318—22no—
199#4318—22no—
200#4318C22×C414yescomplemented
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C4×H(5,𝔽2)D1111yescharacteristic
204C2×#455—111no—
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×C11C4×D414yes—
226D4×C11—216no—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—24no—
230D4×C11—22no—
231D4×C11—24no—
232D4×C11C4×D414yes—
233C2×C4×C11—28no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—44no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—82no—
246C2×C4×C11—82no—
247C2×C4×C11—82no—
248C2×C4×C11—84no—
249C2×C4×C11—82no—
250C2×C4×C11#12012yes—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D412yes—
255C2×C4×C11C2×#4112yes—
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—42no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268Dic22—24no—
269Dic22—42no—
270C11⋊C8—24no—
271C11⋊C8—42no—
272C2×H(5,𝔽2)C2×D1111yescharacteristic
273C2×#137—112no—
274C2×#124—111no—
275#520—22no—
276#520C2×D1112yes—
277#518—22no—
278#518—22no—
279#518C2×D1111yescharacteristic
280C4×#41—22no—
281C4×#41C2×D1112yes—
282C2×C4×Q8—111no—
283C2×C4×D4—22no—
284C2×C4×D4—22no—
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#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—21no—
323C4×C11—21no—
324C4×C11—22no—
325C4×C11—24no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11C2×C4×D412yes—
330C4×C11#52512yes—
331Dic11—42no—
332Dic11—42no—
333Dic11—81no—
334Dic11—81no—
335H(5,𝔽2)—24no—
336H(5,𝔽2)—22no—
337H(5,𝔽2)C4×D1114yes—
338C2×#41—22no—
339C2×#41C22×D1112yes—
340C22×Q8—111no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4C22×D1111yescharacteristic
344C23×C4—22no—
345C23×C4C22⋊D1112yes—
346#137—118no—
347#137—224no—
348C2×Q16—222no—
349C2×SD16—222no—
350C2×M16—112no—
351C2×M16—112no—
352#124—114no—
353#124—222no—
354C4×Q8—22no—
355C4×Q8—222no—
356C4×Q8—222no—
357C4×Q8C22⋊D1112yes—
358C4×Q8C22⋊D1112yes—
359C4×D4—24no—
360C4×D4—24no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—24no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4C22⋊D1112yes—
372C4×D4C22⋊D1112yes—
373#117—24no—
374#117—22no—
375#117—22no—
376#117C22×D1112yes—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4C22⋊D1112yes—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—221no—
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—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—
418C24C2×C22⋊D1112yes—
419#41—28no—
420#41—28no—
421#41—22no—
422#41—22no—
423#41C2×C4×D1114yes—
424#41#433914yes—
425C2×Q8—112no—
426C2×Q8—221no—
427C2×Q8—222no—
428C2×Q8—222no—
429C2×Q8C2×C22⋊D1112yes—
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×D4C2×C4×D1112yes—
439C2×D4#433912yes—
440C2×D4C2×C22⋊D1112yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—82no—
451C22×C4—84no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
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—24no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—222no—
473C4⋊C4—441no—
474C4⋊C4—441no—
475C4⋊C4—882no—
476C4⋊C4C2×C22⋊D1112yes—
477C4⋊C4C2×C22⋊D1112yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—24no—
484C22⋊C4—228no—
485C22⋊C4—882no—
486C42—24no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—112no—
491C42—221no—
492C42—222no—
493C42—442no—
494C42C2×C22⋊D1112yes—
495C42C2×C22⋊D1112yes—
496C11#2147411yescharacteristic, complemented, Sylow
497C23—28no—
498C23—22no—
499C23—22no—
500C23—22no—
501C23—42no—
502C23—42no—
503C23—82no—
504C23—82no—
505C23C4×C22⋊D1114yes—
506C23C22×C22⋊D1111yescharacteristic
507Q8—22no—
508Q8—224no—
509Q8—442no—
510Q8C4×C22⋊D1114yes—
511D4—216no—
512D4—24no—
513D4—24no—
514D4—24no—
515D4—24no—
516D4—22no—
517D4C4×C22⋊D1114yes—
518C2×C4—28no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—84no—
534C2×C4—82no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—442no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4#6700611yescharacteristic
547C2×C4#6700612yes—
548C2×C4#6700611yescharacteristic
549C2×C4C22×C4×D1111yescharacteristic
550C2×C4C2×#433912yes—
551C2×C4C2×#433911yescharacteristic
552C2×C4C22×C22⋊D1112yes—
553C8—224no—
554C8—442no—
555C22—21no—
556C22—21no—
557C22—24no—
558C22—24no—
559C22—44no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—82no—
565C22—88no—
566C22C2×C4×C22⋊D1111yescharacteristic
567C22#1062332211yescharacteristic
568C22C2×#6700611yescharacteristic
569C4—24no—
570C4—21no—
571C4—21no—
572C4—22no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—442no—
577C4—442no—
578C4—881no—
579C4—881no—
580C4C2×C4×C22⋊D1112yes—
581C4#1062332212yes—
582C2—21no—
583C2—21no—
584C2—44no—
585C2—44no—
586C2C4×#6700611yescharacteristic
587C2#1307797311yescharacteristic
588C2#1307799511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×H(5,𝔽2)C2
socleC22×C11C2×#120
prime radicalC2×C11×H(5,𝔽2)C22
cosocleC22×C4×C11C24
hypercenterC4×H(5,𝔽2)D11
hypocenterC11#21474
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
2. C4×#67004C2semidirect
3. #13071328C2semidirect
4. #13069004C2semidirect
5. #13068985C2semidirect
6. #13068842C2semidirect
7. #13068826C2semidirect
9. #13068426C2semidirect
10. C4×#66897C2semidirect
25. C2×C4×Dic22C22semidirect
26. #10622855C4semidirect
38. #10622617C22semidirect
39. #10622608C22semidirect
40. #10622589C22semidirect
41. #10622587C22semidirect
43. #10622545C22semidirect
44. C4×#4318C22semidirect
45. #10622170C22semidirect
46. #10622170C22semidirect
47. #10622168C22semidirect
93. #67004C2×C4semidirect
96. #66989C2×C4semidirect
109. #66901C2×C4semidirect
112. #66897C2×C4semidirect
166. C2×Dic22C22×C4semidirect
196. C4×Dic11C22×C4semidirect
200. #4318C22×C4semidirect
496. C11#21474semidirect

Maximal subgroups

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

subgroupindex
C2×#106228552
C4×#670042
#130713282
#130690042
#130689852
#130688422
#130688262
#130685702
#130684262
C4×#668972
C4×C11×H(5,𝔽2)2
#2147411