Finite Group Databasebeta

← #14724293

Subgroups — #14724293

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079172C211yesmaximal, characteristic
2#13077547C211yesmaximal, characteristic, complemented
3#13077325C211yesmaximal, characteristic
4#13067508C211yesmaximal, characteristic, complemented
5#13067506C211yesmaximal, characteristic, complemented
6#13067504C211yesmaximal, characteristic, complemented
7#13067419C211yesmaximal, characteristic, complemented
8SD16×C11⋊C8C211yesmaximal, characteristic, complemented
9#13067415C211yesmaximal, characteristic, complemented
10#13067413C211yesmaximal, characteristic, complemented
11#13067370C211yesmaximal, characteristic, complemented
12#13067069C211yesmaximal, characteristic, complemented
13#13067065C211yesmaximal, characteristic
14C82×D11C211yesmaximal, characteristic, complemented
15C11×#1590C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17#10623109C2211yescharacteristic
18#10623079C2211yescharacteristic
19C11×#446C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C11×#436C2211yescharacteristic
22#10622788C411yescharacteristic
23#10622784C411yescharacteristic
24#10622741—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622477C411yescharacteristic
30#10622468C411yescharacteristic
31#10622452—21no—
32#10622450C2211yescharacteristic
33#10622450C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622443—21no—
36#10622443C2211yescharacteristic
37#10622420C411yescharacteristic
38#10622405C411yescharacteristic
39#10622391C411yescharacteristic
40#10622373C411yescharacteristic
41#10622340—21no—
42(C22⋊D11)⋊C8—21no—
43#10622321—21no—
44#10622314—21no—
45C4×#4314C2211yescharacteristic
46#10622301C2211yescharacteristic
47C4×C8×D11C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49C4×C8×D11C2211yescharacteristic
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64C8×C11⋊C8C2211yescharacteristic
65C8×C11⋊C8C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×SD16C2×C411yescharacteristic
69C2×C11×M16—21no—
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11C2311yescharacteristic
72#66999C2×C411yescharacteristic
73#66997C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80#66960—44no—
81C2×#4314C2×C411yescharacteristic
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—21no—
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11C2×C411yescharacteristic
88C2×C8×D11C2×C411yescharacteristic
89C2×C8×D11D411yescharacteristic
90C2×C8×D11D411yescharacteristic
91#66950C2×C411yescharacteristic
92#66949—21no—
93#66948C2×C411yescharacteristic
94#66942—21no—
95#66941C2×C411yescharacteristic
96#66941C2×C411yescharacteristic
97#66938—21no—
98#66937—21no—
99C4×D44C2311yescharacteristic
100#66925—21no—
101C42×D11C2311yescharacteristic
102C4×Dic22—21no—
103C4×Dic22C2311yescharacteristic
104C11×#106C2×C411yescharacteristic
105C11×C4⋊C8—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×C22⋊C8—21no—
111C11×#97—21no—
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115#66899C2×C411yescharacteristic
116#66896C2×C411yescharacteristic
117C22⋊(C11⋊C8)—21no—
118#66885C2×C411yescharacteristic
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66881C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879—21no—
124Dic11⋊C8—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128C8×Dic11—21no—
129C8×Dic11—21no—
130C8×Dic11C2×C411yescharacteristic
131C8×Dic11C2×C411yescharacteristic
132C8×Dic11D411yescharacteristic
133C8×Dic11D411yescharacteristic
134#66874C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#17957—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152#4339—42no—
153#4339—42no—
154C2×D44—21no—
155C2×D44C22×C411yescharacteristic
156C2×C4×D11—21no—
157C2×C4×D11C22×C411yescharacteristic
158C2×C4×D11C2×D411yescharacteristic
159C2×C4×D11#4111yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22C22×C411yescharacteristic
163C11×SD16—22no—
164C11×M16—42no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C22×C411yescharacteristic
169C2×C8×C11C22×C411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2×D411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C22⋊C4—21no—
176C42×C11—21no—
177C42×C11C2411yescharacteristic
178C22⋊Dic11—21no—
179#4325—22no—
180#4324—22no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C411yescharacteristic
187C4⋊Dic11C22×C411yescharacteristic
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11C22×C411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11#4111yescharacteristic
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—42no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206#4314—22no—
207#4313—42no—
208#4313—42no—
209#4313—42no—
210C8×D11—24no—
211C8×D11—22no—
212C8×D11—22no—
213C8×D11—22no—
214C8×D11—42no—
215C8×D11SD1614yescomplemented
216#3167—111no—
217#2960—111no—
218#2931—111no—
219#1590—111no—
220#1590—111no—
221#1590—111no—
222#1590D1111yescharacteristic, complemented
223C8×SD16—111no—
224C8×SD16—111no—
225C8×SD16—111no—
226C8×SD16—111no—
227#1566—111no—
228#1493—111no—
229#1492—111no—
230C2×C82—111no—
231C23×C11—21no—
232C22×D11—21no—
233C22×D11C4×D411yescharacteristic
234Q8×C11—21no—
235Q8×C11—21no—
236D4×C11—21no—
237D4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—42no—
247C22⋊D11—42no—
248C22⋊D11—42no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11C4×D411yescharacteristic
253C2×Dic11C4×D411yescharacteristic
254C2×Dic11C4×D411yescharacteristic
255D44—21no—
256D44—21no—
257D44—42no—
258C4×D11—21no—
259C4×D11—21no—
260C4×D11—22no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11C2×SD1612yes—
264C4×D11#13512yes—
265Dic22—21no—
266Dic22—21no—
267Dic22—42no—
268Dic22—42no—
269C8×C11—22no—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11#13112yescomplemented
275C8×C11C2×SD1612yes—
276C11⋊C8—22no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8#13112yescomplemented
282C11⋊C8C2×SD1612yes—
283C2×#131—221no—
284#533—111no—
285#532—111no—
286#498—111no—
287#492—111no—
288#487—111no—
289#486—111no—
290#465—111no—
291#465—111no—
292#465—111no—
293#465—111no—
294#446—111no—
295#446—221no—
296#446C2×D1111yescharacteristic
297C8×Q8—111no—
298C8×Q8—111no—
299C8×Q8—221no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×SD16—111no—
303C4×SD16C2×D1111yescharacteristic
304#436—111no—
305#436—221no—
306#436C2×D1111yescharacteristic
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—221no—
310#424—221no—
311#423—111no—
312#423—111no—
313#408—221no—
314#405—221no—
315C2×C4×C8—111no—
316C2×C4×C8—111no—
317C2×C4×C8—111no—
318#334—111no—
319#334—111no—
320#334—111no—
321#334C2×D1111yescharacteristic
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325Q8⋊C8C2×D1111yescharacteristic
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8C2×D1111yescharacteristic
330C82—111no—
331C82—111no—
332C82—111no—
333C82C2×D1111yescharacteristic
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11C2×C4×D411yescharacteristic
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11C4×SD1612yes—
344C4×C11—21no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11C2×#13111yescharacteristic
349C4×C11C2×#13111yescharacteristic
350C4×C11C22×SD1611yescharacteristic
351C4×C11C2×#13511yescharacteristic
352Dic11—21no—
353Dic11—41no—
354Dic11—41no—
355Dic11—41no—
356Dic11C4×SD1612yes—
357Dic11#44312yes—
358C2×#41—221no—
359C2×SD16—111no—
360C2×SD16—111no—
361C2×SD16—111no—
362C2×SD16C4×D1111yescharacteristic
363#131—444no—
364C2×M16—21no—
365C2×M16—221no—
366C2×M16—221no—
367C2×M16—221no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C4⋊Q8—111no—
376C4⋊Q8—111no—
377C4⋊Q8—111no—
378#127—111no—
379#125—221no—
380#124—221no—
381C22⋊Q8—111no—
382C22⋊Q8—111no—
383C22⋊Q8—221no—
384#121—111no—
385#121—111no—
386#121—221no—
387C4×Q8—111no—
388C4×Q8—221no—
389C4×Q8C22×D1111yescharacteristic
390C4×D4—111no—
391C4×D4—221no—
392C4×D4C22×D1111yescharacteristic
393#117—221no—
394C2×C42—111no—
395#106—111no—
396#106—111no—
397#106—111no—
398#106C4×D1111yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8C22×D1111yescharacteristic
408C4⋊C8C22×D1111yescharacteristic
409#103—111no—
410#103—111no—
411#103—111no—
412#103C4×D1111yescharacteristic
413#102—111no—
414#102—111no—
415#102—111no—
416#102C4×D1111yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421#97—21no—
422#97—221no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—111no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—221no—
431C4×C8—221no—
432C4×C8—221no—
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C2×C11—81no—
437C2×C11#293111yescharacteristic
438C2×C11C2×C4×SD1611yescharacteristic
439C2×C11C2×#44311yescharacteristic
440D11—22no—
441D11—81no—
442#41—442no—
443#41—442no—
444C2×Q8—111no—
445C2×Q8—221no—
446C2×Q8—221no—
447C2×Q8C2×C4×D1111yescharacteristic
448C2×D4—111no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4C2×C4×D1111yescharacteristic
454C22×C4—21no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—221no—
459SD16—22no—
460SD16—222no—
461SD16—222no—
462SD16—222no—
463M16—42no—
464M16—442no—
465M16—442no—
466M16—442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—114no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—224no—
478C2×C8—221no—
479C2×C8—222no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—442no—
483C2×C8—442no—
484C2×C8C2×C4×D1111yescharacteristic
485C2×C8C2×C4×D1111yescharacteristic
486C2×C8D4×D1111yescharacteristic
487C2×C8D4×D1111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—111no—
490C4⋊C4—111no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4C2×C4×D1111yescharacteristic
499C4⋊C4C2×C4×D1111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C42—21no—
507C42—111no—
508C42—111no—
509C42—111no—
510C42—221no—
511C42C23×D1111yescharacteristic
512C11#1795711yescharacteristic, complemented, Sylow
513C23—21no—
514C23—111no—
515C23—221no—
516Q8—21no—
517Q8—21no—
518Q8—221no—
519Q8—221no—
520Q8—442no—
521Q8—442no—
522D4—21no—
523D4—21no—
524D4—221no—
525D4—221no—
526D4—442no—
527D4—442no—
528D4—442no—
529D4—442no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—111no—
536C2×C4—111no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—111no—
540C2×C4—222no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4C22×C4×D1111yescharacteristic
549C2×C4C2×D4×D1111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C8—22no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—112no—
557C8—112no—
558C8—222no—
559C8—221no—
560C8—221no—
561C8—441no—
562C8—441no—
563C8#6696012yescomplemented
564C8SD16×D1112yes—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—112no—
569C22—221no—
570C22—221no—
571C22—441no—
572C22—441no—
573C22—441no—
574C22C4×D4×D1111yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—112no—
580C4—112no—
581C4—221no—
582C4—441no—
583C4—441no—
584C4—441no—
585C4C2×#6696011yescharacteristic
586C4D11×#13111yescharacteristic
587C4C2×SD16×D1111yescharacteristic
588C4D11×#13511yescharacteristic
589C2—81no—
590C2—222no—
591C2—881no—
592C2#1307732511yescharacteristic
593C2C4×SD16×D1111yescharacteristic
594C2D11×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1590C2
socleC22×C11C2×C4×D4
prime radical#10623079C22
cosocleC42×C11C24
hypercenter#1590D11
hypocenterC11#17957
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #13077547C2semidirect
4. #13067508C2semidirect
5. #13067506C2semidirect
6. #13067504C2semidirect
7. #13067419C2semidirect
8. SD16×C11⋊C8C2semidirect
9. #13067415C2semidirect
10. #13067413C2semidirect
11. #13067370C2semidirect
12. #13067069C2semidirect
14. C82×D11C2semidirect
15. C11×#1590C2semidirect
215. C8×D11SD16semidirect
222. #1590D11semidirect
274. C8×C11#131semidirect
281. C11⋊C8#131semidirect
512. C11#17957semidirect
563. C8#66960semidirect

Maximal subgroups

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

subgroupindex
#130791722
#130775472
#130773252
#130675082
#130675062
#130675042
#130674192
SD16×C11⋊C82
#130674152
#130674132
#130673702
#130670692
#130670652
C82×D112
C11×#15902
#1795711