Finite Group Databasebeta

← #14736236

Subgroups — #14736236

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic, complemented
2#13078676C211yesmaximal, characteristic
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068072C211yesmaximal, characteristic, complemented
5#13068065C211yesmaximal, characteristic, complemented
6#13068062C211yesmaximal, characteristic, complemented
7#13068055C211yesmaximal, characteristic, complemented
8#13067996C211yesmaximal, characteristic, complemented
9#13067989C211yesmaximal, characteristic, complemented
10#13067966C211yesmaximal, characteristic, complemented
11#13067959C211yesmaximal, characteristic, complemented
12#13067362C211yesmaximal, characteristic, complemented
13#13067281C211yesmaximal, characteristic, complemented
14#13067276C211yesmaximal, characteristic, complemented
15C11×#3107C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#485—21no—
20C11×#475C2211yescharacteristic
21C11×#474C2211yescharacteristic
22C11×#462C2211yescharacteristic
23C11×#461C2211yescharacteristic
24C11×#452—21no—
25C4×C11×Q16—21no—
26C4×C11×SD16—21no—
27C11×#431C2211yescharacteristic
28#10622851—21no—
29#10622701C2211yescharacteristic
30#10622698C2211yescharacteristic
31#10622694C2211yescharacteristic
32#10622692C2211yescharacteristic
33#10622661—21no—
34#10622661—21no—
35#10622640C2211yescharacteristic
36C4×#4325—21no—
37C4×#4325—21no—
38C4×#4325—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622628C2211yescharacteristic
43C4×#4323—21no—
44D4×C11⋊C8—21no—
45D4×C11⋊C8—21no—
46D4×C11⋊C8C2211yescharacteristic
47D4×C11⋊C8C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622616—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#125—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11D411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117—21no—
86C11×#117D411yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4323—21no—
93#66983—21no—
94#66983—21no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8D411yescharacteristic
98C22×C11⋊C8D411yescharacteristic
99#66928—21no—
100#66927C2311yescharacteristic
101C4×D44—21no—
102C4×D44—21no—
103#66922C2311yescharacteristic
104C11×#107—21no—
105C11×#106—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×C22⋊C8—21no—
113C4×C8×C11—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66873—21no—
123#66873—21no—
124#66873—21no—
125#66873—21no—
126#66872—21no—
127#66872—21no—
128#66872—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4×C11⋊C8—21no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8D411yescharacteristic
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19127—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—22no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4111yescharacteristic
158C2×C22⋊D11—41no—
159#4339—82no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×C4×D11—41no—
164C2×Dic22—21no—
165C11×Q16—42no—
166C11×SD16—42no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—41no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—41no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191#4325—42no—
192#4325—42no—
193#4325—42no—
194#4323—42no—
195(C2×D11)⋊C4—41no—
196(C2×D11)⋊C4—41no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—41no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8—42no—
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211#3167—111no—
212#3107D1111yescharacteristic, complemented
213#3106—111no—
214C8×#41—111no—
215#1684—111no—
216#1683—111no—
217#1682—111no—
218#1681—111no—
219#1672—111no—
220#1671—111no—
221#1666—111no—
222#1665—111no—
223#1564—111no—
224#1544—111no—
225#1543—111no—
226C23×C11—21no—
227C23×C11#12111yescharacteristic
228C22×D11—41no—
229Q8×C11—21no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11#13512yes—
235D4×C11—24no—
236D4×C11—21no—
237D4×C11#13512yes—
238C2×C4×C11—24no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C22⋊D11—82no—
259C2×Dic11—41no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—81no—
265C4×D11—82no—
266Dic22—81no—
267C8×C11—41no—
268C8×C11—41no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8#13512yes—
277#533C2×D1111yescharacteristic
278#532—111no—
279C4×#41C2×D1111yescharacteristic
280#498—111no—
281#492—111no—
282#487—111no—
283#486—111no—
284#485—21no—
285#482—221no—
286#477—111no—
287#476—111no—
288#475C2×D1111yescharacteristic
289#474C2×D1111yescharacteristic
290#465—221no—
291#465—221no—
292#462C2×D1111yescharacteristic
293#461C2×D1111yescharacteristic
294#460—111no—
295#459—111no—
296#452—21no—
297#449—221no—
298C8×Q8—111no—
299C8×Q8—111no—
300C4×Q16—21no—
301C4×SD16—21no—
302C4×SD16—221no—
303C4×SD16—221no—
304C4×SD16—221no—
305C4×D8—221no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—221no—
309C8×D4—221no—
310#431—111no—
311#431—111no—
312#431—221no—
313#431C2×D1111yescharacteristic
314C2×C4×C8—111no—
315C2×C4×C8—221no—
316#335—111no—
317#335—111no—
318#334—111no—
319#334—111no—
320#333—111no—
321#333—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#331—111no—
327#331—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—22no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11C2×#12111yescharacteristic
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—22no—
341C4×C11—21no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11#47112yes—
347C4×C11C2×#13511yescharacteristic
348C4×C11C2×#13511yescharacteristic
349C4×C11C2×#13511yescharacteristic
350C4×C11#57511yescharacteristic
351Dic11—81no—
352C2×#41—221no—
353C2×#41C22⋊D1111yescharacteristic
354C2×Q16—21no—
355C2×SD16—21no—
356C2×SD16—221no—
357C2×SD16—221no—
358C2×SD16—221no—
359C2×D8—221no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8—221no—
363C22×C8—221no—
364C4⋊Q8—111no—
365C4⋊Q8C22×D1111yescharacteristic
366C4⋊Q8C22×D1111yescharacteristic
367#127—111no—
368#125—21no—
369#124—221no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—221no—
373#121—221no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C22⋊D1111yescharacteristic
377C4×Q8C22×D1111yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—221no—
381C4×D4—221no—
382C4×D4C22⋊D1111yescharacteristic
383C4×D4C22×D1111yescharacteristic
384#117—21no—
385#117—21no—
386#117C22⋊D1111yescharacteristic
387C2×C42—21no—
388C2×C42C22×D1111yescharacteristic
389#107—21no—
390#107—221no—
391#106—21no—
392#106—221no—
393#106—221no—
394#106—221no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—221no—
407#103—221no—
408#103—221no—
409#102—21no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—21no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419C22⋊C8—221no—
420C4×C8—21no—
421C4×C8—111no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C4×C8—221no—
427C4×C8—221no—
428C4×C8—221no—
429C2×C11—41no—
430C2×C11—42no—
431C2×C11#303511yescharacteristic
432C2×C11#305011yescharacteristic
433C2×C11C2×#47111yescharacteristic
434D11—161no—
435#41—22no—
436#41—22no—
437#41—882no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—221no—
441C2×Q8C2×C22⋊D1111yescharacteristic
442C2×D4—21no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—441no—
447C2×D4C2×C22⋊D1111yescharacteristic
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—441no—
452C22×C4D4×D1111yescharacteristic
453C22×C4#434111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455Q16—42no—
456SD16—42no—
457SD16—442no—
458SD16—442no—
459SD16—442no—
460D8—442no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—222no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—442no—
473C2×C8—441no—
474C2×C8—442no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4C2×C22⋊D1111yescharacteristic
486C4⋊C4C2×C22⋊D1111yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—41no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—41no—
497C42D4×D1111yescharacteristic
498C42#434111yescharacteristic
499C42C2×C22⋊D1111yescharacteristic
500C42C23×D1111yescharacteristic
501C11#1912711yescharacteristic, complemented, Sylow
502C23—21no—
503C23—441no—
504C23#6699211yescharacteristic
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—881no—
511Q8#6700312yes—
512D4—24no—
513D4—21no—
514D4—441no—
515D4—441no—
516D4—441no—
517D4—441no—
518D4—881no—
519D4—882no—
520D4#6700312yes—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—441no—
536C2×C4—882no—
537C2×C4#6699211yescharacteristic
538C2×C4#6699211yescharacteristic
539C2×C4#6699211yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C8—41no—
544C8—41no—
545C8—112no—
546C8—221no—
547C8—221no—
548C8—221no—
549C8—441no—
550C8—441no—
551C8—441no—
552C8—441no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22C2×#6699211yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—881no—
572C4#1062281612yes—
573C4D11×#13511yescharacteristic
574C4#1062329911yescharacteristic
575C4C2×#6700311yescharacteristic
576C4C2×#6700311yescharacteristic
577C2—41no—
578C2—42no—
579C2—1761no—
580C2#1307806711yescharacteristic
581C2#1307819411yescharacteristic
582C2C2×#1062281611yescharacteristic
subgroupG/H
centerC2×C4#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3107C2
socleC22×C11C2×#121
prime radical#13078676C2
hypercenter#3107D11
hypocenterC11#19127
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #13079176C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13068072C2semidirect
5. #13068065C2semidirect
6. #13068062C2semidirect
7. #13068055C2semidirect
8. #13067996C2semidirect
9. #13067989C2semidirect
10. #13067966C2semidirect
11. #13067959C2semidirect
12. #13067362C2semidirect
13. #13067281C2semidirect
14. #13067276C2semidirect
15. C11×#3107C2semidirect
212. #3107D11semidirect
501. C11#19127semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130786762
#41×C11⋊C82
#130680722
#130680652
#130680622
#130680552
#130679962
#130679892
#130679662
#130679592
#130673622
#130672812
#130672762
C11×#31072
#1912711