Finite Group Databasebeta

← #14725540

Subgroups — #14725540

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079172C211yesmaximal, characteristic
2#13077558C211yesmaximal, characteristic, complemented
3#13077361C211yesmaximal, characteristic
4#13067504C211yesmaximal, characteristic, complemented
5#13067503C211yesmaximal, characteristic, complemented
6#13067458C211yesmaximal, characteristic, complemented
7#13067454C211yesmaximal, characteristic, complemented
8#13067453C211yesmaximal, characteristic, complemented
9#13067419C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic, complemented
11D11×#334C211yesmaximal, characteristic, complemented
12#13067017C211yesmaximal, characteristic, complemented
13#13067013C211yesmaximal, characteristic
14#13066895C211yesmaximal, characteristic, complemented
15C11×#1583C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17#10623109C2211yescharacteristic
18#10623079C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C11×#436C2211yescharacteristic
22#10622788C411yescharacteristic
23#10622784C411yescharacteristic
24#10622740—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic
27C4×#4324C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622477C411yescharacteristic
30#10622468C411yescharacteristic
31#10622452—21no—
32#10622451C2211yescharacteristic
33D11×C4⋊C8C2211yescharacteristic
34D11×C4⋊C8C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622441—21no—
37#10622420C411yescharacteristic
38#10622405C411yescharacteristic
39#10622391C411yescharacteristic
40#10622373C411yescharacteristic
41#10622343—21no—
42#10622340—21no—
43C4×#4314C2211yescharacteristic
44#10622302—21no—
45C4×#4313C2211yescharacteristic
46C8×D44C2211yescharacteristic
47#10622298C2211yescharacteristic
48C4×C8×D11C2211yescharacteristic
49#10622292—21no—
50#10622292C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622118C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
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×#4313D411yescharacteristic
84C2×#4313D411yescharacteristic
85C2×C8×D11—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88C2×C8×D11C2×C411yescharacteristic
89C2×C8×D11C2×C411yescharacteristic
90#66950C2×C411yescharacteristic
91#66949—21no—
92#66948C2×C411yescharacteristic
93#66942—21no—
94#66941C2×C411yescharacteristic
95#66941C2×C411yescharacteristic
96#66938—21no—
97#66937—21no—
98C4×D44C2311yescharacteristic
99#66925—21no—
100C42×D11C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22C2311yescharacteristic
103C11×#106C2×C411yescharacteristic
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×C22⋊C8—21no—
110C4×C8×C11—21no—
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114#66899C2×C411yescharacteristic
115#66896C2×C411yescharacteristic
116C22⋊(C11⋊C8)—21no—
117#66885C2×C411yescharacteristic
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66881C2×C411yescharacteristic
122#66880C2×C411yescharacteristic
123#66879—21no—
124#66879D411yescharacteristic
125#66879D411yescharacteristic
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131C8×Dic11—21no—
132C8×Dic11C2×C411yescharacteristic
133C8×Dic11C2×C411yescharacteristic
134#66874C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141#66867—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18067—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—41no—
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—41no—
207#4313—22no—
208#4313—42no—
209#4313SD1614yescomplemented
210C8×D11—22no—
211C8×D11—41no—
212C8×D11—42no—
213C8×D11—42no—
214C8×D11—42no—
215#3167—111no—
216#2962—111no—
217#2935—111no—
218#1590—111no—
219#1590—111no—
220#1583—111no—
221#1583D1111yescharacteristic, complemented
222#1582—111no—
223#1582—111no—
224C8×SD16—111no—
225C8×SD16—111no—
226C2×#334—111no—
227#1481—111no—
228#1480—111no—
229C8×M16—111no—
230C23×C11—21no—
231C22×D11—21no—
232C22×D11C4×D411yescharacteristic
233Q8×C11—21no—
234Q8×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C22⋊D11—42no—
246C22⋊D11—42no—
247C22⋊D11—81no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11C4×D411yescharacteristic
252C2×Dic11C4×D411yescharacteristic
253C2×Dic11C4×D411yescharacteristic
254D44—21no—
255D44—21no—
256D44—42no—
257C4×D11—21no—
258C4×D11—21no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11C2×SD1612yes—
263C4×D11#13512yes—
264Dic22—21no—
265Dic22—21no—
266Dic22—42no—
267Dic22—81no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C8×C11C2×SD1612yes—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8#13112yescomplemented
281C11⋊C8C2×SD1612yes—
282C2×#131—221no—
283#533—111no—
284#532—111no—
285#498—111no—
286#492—111no—
287#487—111no—
288#486—111no—
289#465—111no—
290#465—111no—
291#465—111no—
292#465—111no—
293#446—111no—
294#446—111no—
295#446—221no—
296#446—221no—
297C8×Q8—111no—
298C8×Q8C2×D1111yescharacteristic
299C4×SD16—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×SD16C2×D1111yescharacteristic
303#436—111no—
304#436C2×D1111yescharacteristic
305#435—221no—
306#435—221no—
307C8×D4—111no—
308C8×D4—111no—
309#431—111no—
310#424—221no—
311C2×C4⋊C8—111no—
312C2×C4⋊C8—111no—
313#408—221no—
314#405—221no—
315C4×M16—111no—
316C2×C4×C8—111no—
317#334—111no—
318#334—111no—
319#334—111no—
320#334C2×D1111yescharacteristic
321Q8⋊C8—111no—
322Q8⋊C8—111no—
323Q8⋊C8—111no—
324Q8⋊C8C2×D1111yescharacteristic
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8C2×D1111yescharacteristic
329#322—111no—
330#322C2×D1111yescharacteristic
331C82—111no—
332C82—111no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×C4×D411yescharacteristic
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—41no—
340C2×D11—41no—
341C2×D11—41no—
342C2×D11C4×SD1612yes—
343C4×C11—21no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11C2×#13111yescharacteristic
348C4×C11#56811yescharacteristic
349C4×C11C22×SD1611yescharacteristic
350C4×C11C2×#13511yescharacteristic
351Dic11—21no—
352Dic11—21no—
353Dic11—41no—
354Dic11—41no—
355Dic11—41no—
356Dic11C4×SD1612yes—
357C2×#41—221no—
358C2×SD16—111no—
359C2×SD16—111no—
360C2×SD16—111no—
361C2×SD16C4×D1111yescharacteristic
362#131—444no—
363C2×M16—21no—
364C2×M16—111no—
365C2×M16—111no—
366C2×M16—221no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C4⋊Q8—111no—
374C4⋊Q8—111no—
375C4⋊Q8—111no—
376#127—111no—
377#125—221no—
378#124—221no—
379C22⋊Q8—111no—
380C22⋊Q8—111no—
381C22⋊Q8—221no—
382#121—111no—
383#121—111no—
384#121—221no—
385C4×Q8—111no—
386C4×Q8—221no—
387C4×Q8C22×D1111yescharacteristic
388C4×D4—111no—
389C4×D4—221no—
390C4×D4C22×D1111yescharacteristic
391#117—221no—
392C2×C42—111no—
393#106—111no—
394#106—111no—
395#106—111no—
396#106C4×D1111yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8C22×D1111yescharacteristic
407C4⋊C8C22×D1111yescharacteristic
408#103—111no—
409#103—111no—
410#103—111no—
411#103C4×D1111yescharacteristic
412#102—111no—
413#102—111no—
414#102—111no—
415#102C4×D1111yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421#97—111no—
422#97—111no—
423#97—221no—
424#97—221no—
425C4×C8—21no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—221no—
432C4×C8C22×D1111yescharacteristic
433C4×C8C22×D1111yescharacteristic
434C4×C8C22×D1111yescharacteristic
435C2×C11—81no—
436C2×C11#293511yescharacteristic
437C2×C11C2×C4×SD1611yescharacteristic
438C2×C11#295711yescharacteristic
439D11—22no—
440D11—81no—
441#41—442no—
442#41—442no—
443C2×Q8—111no—
444C2×Q8—221no—
445C2×Q8—221no—
446C2×Q8C2×C4×D1111yescharacteristic
447C2×D4—111no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4C2×C4×D1111yescharacteristic
453C22×C4—21no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—221no—
458SD16—41no—
459SD16—222no—
460SD16—222no—
461SD16—441no—
462M16—42no—
463M16—114no—
464M16—222no—
465M16—442no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—111no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—222no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—441no—
478C2×C8—442no—
479C2×C8—442no—
480C2×C8—442no—
481C2×C8—442no—
482C2×C8C2×C4×D1111yescharacteristic
483C2×C8C2×C4×D1111yescharacteristic
484C2×C8D4×D1111yescharacteristic
485C2×C8D4×D1111yescharacteristic
486C4⋊C4—21no—
487C4⋊C4—111no—
488C4⋊C4—111no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4C2×C4×D1111yescharacteristic
497C4⋊C4C2×C4×D1111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C42—21no—
505C42—111no—
506C42—111no—
507C42—111no—
508C42—221no—
509C42C23×D1111yescharacteristic
510C11#1806711yescharacteristic, complemented, Sylow
511C23—21no—
512C23—111no—
513C23—221no—
514Q8—21no—
515Q8—21no—
516Q8—221no—
517Q8—221no—
518Q8—442no—
519Q8—881no—
520D4—21no—
521D4—21no—
522D4—221no—
523D4—221no—
524D4—442no—
525D4—442no—
526D4—442no—
527D4—881no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—111no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—111no—
537C2×C4—111no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4C22×C4×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—112no—
556C8—112no—
557C8—221no—
558C8—221no—
559C8—441no—
560C8—441no—
561C8—441no—
562C8SD16×D1112yes—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—112no—
567C22—221no—
568C22—221no—
569C22—441no—
570C22—441no—
571C22—441no—
572C22C4×D4×D1111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—112no—
578C4—221no—
579C4—221no—
580C4—441no—
581C4—441no—
582C4—441no—
583C4#1062327611yescharacteristic
584C4D11×#13111yescharacteristic
585C4C2×SD16×D1111yescharacteristic
586C4D11×#13511yescharacteristic
587C2—81no—
588C2—222no—
589C2—881no—
590C2#1307735711yescharacteristic
591C2C4×SD16×D1111yescharacteristic
592C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1583C2
socleC22×C11C2×C4×D4
prime radical#10623079C22
cosocleC42×C11C24
hypercenter#1583D11
hypocenterC11#18067
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. #13077558C2semidirect
4. #13067504C2semidirect
5. #13067503C2semidirect
6. #13067458C2semidirect
7. #13067454C2semidirect
8. #13067453C2semidirect
9. #13067419C2semidirect
10. C8×#4325C2semidirect
11. D11×#334C2semidirect
12. #13067017C2semidirect
14. #13066895C2semidirect
15. C11×#1583C2semidirect
209. #4313SD16semidirect
221. #1583D11semidirect
280. C11⋊C8#131semidirect
510. C11#18067semidirect

Maximal subgroups

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

subgroupindex
#130791722
#130775582
#130773612
#130675042
#130675032
#130674582
#130674542
#130674532
#130674192
C8×#43252
D11×#3342
#130670172
#130670132
#130668952
C11×#15832
#1806711