Finite Group Databasebeta

← #14730274

Subgroups — #14730274

Order 2816.

980 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079999C211yesmaximal, characteristic, complemented
2#13079073C211yesmaximal, characteristic, complemented
3#13078676C211yesmaximal, characteristic
4#13067756C212yesmaximal, complemented
5#13067750C212yesmaximal, complemented
6#13067694C212yesmaximal, complemented
7#13067688C212yesmaximal, complemented
8#13067297C211yesmaximal, characteristic, complemented
9#13067055C211yesmaximal, characteristic, complemented
10#13067037C211yesmaximal, characteristic, complemented
11C11×#3503C211yesmaximal, characteristic, complemented
12Q82×C11C2212yes—
13C11×#557—21no—
14C11×#554—22no—
15C11×#554C2212yes—
16D4×Q8×C11—22no—
17D4×Q8×C11—21no—
18C11×#544—22no—
19C11×#544—21no—
20C11×#533—21no—
21C11×#533C2211yescharacteristic
22C2×C11×C4⋊Q8—21no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520—21no—
25C4×C11×#41C2211yescharacteristic
26C2×#66995—22no—
27#10623008C2211yescharacteristic
28#10622851—21no—
29#10622705C2212yes—
30#10622700—21no—
31#10622699—22no—
32#10622698C2212yes—
33#10622696—21no—
34#10622662—22no—
35#10622640C2211yescharacteristic
36#10622640C2212yes—
37C4×#4325—21no—
38#10622634C2211yescharacteristic
39#10622634C2212yes—
40#10622628C2211yescharacteristic
41C4×#4323—21no—
42#10622621C2211yescharacteristic
43#10622616—21no—
44#10622538C2211yescharacteristic
45#10622537C2211yescharacteristic
46C4×#4318C2211yescharacteristic
47#10622184C2212yes—
48#10622184C2212yes—
49Q8⋊(C11⋊C8)C2212yes—
50Q8⋊(C11⋊C8)C2212yes—
51Q8⋊(C11⋊C8)C2212yes—
52D4⋊(C11⋊C8)C2212yes—
53C2×C11×#41D411yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11D412yes—
56C2×#4339—21no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—24no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8D412yes—
65C11×C4⋊Q8D411yescharacteristic
66C11×C4⋊Q8D411yescharacteristic
67C11×C4⋊Q8C2312yes—
68C11×#125—22no—
69C11×#125—24no—
70C11×#125—22no—
71C11×#125—21no—
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—24no—
75C11×C22⋊Q8—22no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8D412yes—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11D411yescharacteristic
84C4×Q8×C11C2311yescharacteristic
85C4×Q8×C11C2312yes—
86C4×D4×C11—24no—
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11D411yescharacteristic
91C4×D4×C11C2311yescharacteristic
92C11×#117—22no—
93C11×#117—21no—
94C11×#117—21no—
95C11×#117D411yescharacteristic
96C2×C11×C4⋊C4—22no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4—22no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×#4326—24no—
103#66995—48no—
104C2×#4325—24no—
105C2×#4325—21no—
106C2×#4325—22no—
107C2×#4323—21no—
108#66983—21no—
109#66983—21no—
110C2×#4318—21no—
111C2×#4318—21no—
112#66928—21no—
113#66927C2311yescharacteristic
114C4×D44—21no—
115C4×D44—21no—
116#66922C2311yescharacteristic
117#66899—21no—
118#66899—22no—
119#66896—21no—
120C22⋊(C11⋊C8)—21no—
121#66873—21no—
122#66873—21no—
123#66873—22no—
124#66872—21no—
125#66871—21no—
126#66871—22no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)C2312yes—
129C4⋊(C11⋊C8)C2311yescharacteristic
130C4⋊(C11⋊C8)C2311yescharacteristic
131#66867—21no—
132C4×C11⋊C8—21no—
133C4×C11⋊C8C2312yes—
134#18567—111nomaximal, Sylow
135C11×#41—22no—
136C11×#41—22no—
137C2×Q8×C11—24no—
138C2×Q8×C11—22no—
139C2×Q8×C11—21no—
140C2×Q8×C11—44no—
141C2×Q8×C11—84no—
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×D411yescharacteristic
144C2×Q8×C11C2×D414yes—
145C2×D4×C11—21no—
146C2×D4×C11C2×D411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C2×C22⋊D11—41no—
156#4339—44no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×C4×D11—41no—
161C2×Dic22—21no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—24no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C42×C11—24no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—22no—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2411yescharacteristic
194#4326—48no—
195#4325—48no—
196#4325—42no—
197#4325—82no—
198#4323—42no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203#4318—24no—
204#4318—81no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—22no—
209#3503D1111yescharacteristic, complemented
210#3254—111no—
211#3152—111no—
212#3106—111no—
213#1633—112no—
214#1632—112no—
215#1623—112no—
216#1622—112no—
217#1548—111no—
218#1489—111no—
219#1485—111no—
220C23×C11—21no—
221C23×C11#12011yescharacteristic
222C22×D11—41no—
223Q8×C11—21no—
224Q8×C11—22no—
225Q8×C11—22no—
226Q8×C11—44no—
227Q8×C11—44no—
228Q8×C11—42no—
229Q8×C11—84no—
230Q8×C11#13712yescomplemented
231D4×C11—24no—
232D4×C11—21no—
233D4×C11#13712yescomplemented
234C2×C4×C11—24no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—82no—
250C2×C4×C11—84no—
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C22⋊D11—82no—
258C2×Dic11—41no—
259D44—42no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—41no—
264C4×D11—82no—
265Dic22—42no—
266C11⋊C8—24no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—42no—
270C2×#137—222no—
271Q82C2×D1112yes—
272#557—21no—
273#554—22no—
274#554C2×D1112yes—
275D4×Q8—22no—
276D4×Q8—21no—
277#544—22no—
278#544—21no—
279#533—21no—
280#533C2×D1111yescharacteristic
281#532—111no—
282C2×C4⋊Q8—21no—
283C2×C4⋊Q8C2×D1111yescharacteristic
284#520—21no—
285C4×#41C2×D1111yescharacteristic
286#497—222no—
287#494—112no—
288#492—112no—
289#482—221no—
290#477—111no—
291#477—112no—
292#476—111no—
293#474—221no—
294#468—222no—
295#461—221no—
296#460—111no—
297#460—112no—
298#459—111no—
299#449—221no—
300C4×SD16—221no—
301C4×D8—221no—
302#431—111no—
303#423—111no—
304C4×M16—111no—
305#333—112no—
306#333—112no—
307Q8⋊C8—112no—
308Q8⋊C8—112no—
309Q8⋊C8—112no—
310D4⋊C8—112no—
311C22×C11—21no—
312C22×C11—22no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11C2×#12011yescharacteristic
318C2×D11—81no—
319C2×D11—81no—
320C2×D11—81no—
321C4×C11—21no—
322C4×C11—22no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—41no—
326C4×C11—42no—
327C4×C11—41no—
328C4×C11—44no—
329C4×C11—42no—
330C4×C11#45312yes—
331C4×C11C2×#13711yescharacteristic
332C4×C11C2×#13711yescharacteristic
333C4×C11#57711yescharacteristic
334C4×C11#57811yescharacteristic
335Dic11—81no—
336C2×#41—221no—
337C2×#41C22⋊D1111yescharacteristic
338C22×Q8—22no—
339C22×Q8C22⋊D1112yes—
340#137—448no—
341C2×Q16—224no—
342C2×SD16—224no—
343C2×SD16—221no—
344C2×SD16—222no—
345C2×D8—221no—
346C2×M16—221no—
347C2×M16—221no—
348C4⋊Q8—22no—
349C4⋊Q8—22no—
350C4⋊Q8—24no—
351C4⋊Q8—22no—
352C4⋊Q8—22no—
353C4⋊Q8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—111no—
356C4⋊Q8C22⋊D1112yes—
357C4⋊Q8C22⋊D1111yescharacteristic
358C4⋊Q8C22⋊D1111yescharacteristic
359C4⋊Q8C22×D1112yes—
360#127—111no—
361#125—22no—
362#125—24no—
363#125—22no—
364#125—21no—
365#124—221no—
366C22⋊Q8—22no—
367C22⋊Q8—24no—
368C22⋊Q8—24no—
369C22⋊Q8—22no—
370C22⋊Q8—24no—
371C22⋊Q8—21no—
372C22⋊Q8C22⋊D1112yes—
373#121—221no—
374#121—221no—
375C4×Q8—22no—
376C4×Q8—22no—
377C4×Q8—22no—
378C4×Q8—21no—
379C4×Q8C22⋊D1111yescharacteristic
380C4×Q8C22×D1111yescharacteristic
381C4×Q8C22×D1112yes—
382C4×D4—24no—
383C4×D4—22no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—221no—
387C4×D4—221no—
388C4×D4C22⋊D1111yescharacteristic
389C4×D4C22×D1111yescharacteristic
390#117—22no—
391#117—21no—
392#117—21no—
393#117C22⋊D1111yescharacteristic
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C42—21no—
399C2×C42C22×D1111yescharacteristic
400#107—221no—
401#107—222no—
402#106—221no—
403C4⋊C8—112no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—221no—
407#103—221no—
408#103—222no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—222no—
413C22⋊C8—221no—
414#97—221no—
415C4×C8—112no—
416C4×C8—221no—
417C2×C11—41no—
418C2×C11—42no—
419C2×C11#300411yescharacteristic
420C2×C11#301311yescharacteristic
421C2×C11C2×#45311yescharacteristic
422D11—161no—
423#41—22no—
424#41—22no—
425#41—444no—
426C2×Q8—24no—
427C2×Q8—22no—
428C2×Q8—21no—
429C2×Q8—44no—
430C2×Q8—84no—
431C2×Q8—221no—
432C2×Q8C2×C22⋊D1112yes—
433C2×Q8C2×C22⋊D1111yescharacteristic
434C2×Q8C2×C22⋊D1114yes—
435C2×D4—21no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—221no—
439C2×D4—441no—
440C2×D4C2×C22⋊D1111yescharacteristic
441C22×C4—21no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—441no—
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450Q16—448no—
451SD16—448no—
452SD16—442no—
453SD16—882no—
454D8—442no—
455M16—224no—
456M16—881no—
457C2×C8—222no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—222no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4C2×C22⋊D1111yescharacteristic
479C4⋊C4C2×C22⋊D1112yes—
480C4⋊C4C2×C22⋊D1111yescharacteristic
481C22⋊C4—24no—
482C22⋊C4—22no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C42—24no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—22no—
493C42C2×C22⋊D1111yescharacteristic
494C42C2×C22⋊D1111yescharacteristic
495C42C2×C22⋊D1111yescharacteristic
496C42C23×D1111yescharacteristic
497C11#1856711yescharacteristic, complemented, Sylow
498C23—21no—
499C23—441no—
500C23#6700611yescharacteristic
501Q8—21no—
502Q8—22no—
503Q8—22no—
504Q8—44no—
505Q8—44no—
506Q8—42no—
507Q8—84no—
508Q8—442no—
509Q8#6699512yescomplemented
510D4—24no—
511D4—21no—
512D4—442no—
513D4—441no—
514D4—441no—
515D4—441no—
516D4—441no—
517D4—882no—
518D4#6699512yescomplemented
519C2×C4—24no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—84no—
536C2×C4—441no—
537C2×C4—882no—
538C2×C4#6700611yescharacteristic
539C2×C4#6700611yescharacteristic
540C2×C4#6700611yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C2×C4C22×C22⋊D1111yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C8—224no—
545C8—441no—
546C8—441no—
547C8—442no—
548C22—21no—
549C22—22no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22C2×#6700611yescharacteristic
558C4—21no—
559C4—22no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—42no—
564C4—41no—
565C4—44no—
566C4—42no—
567C4—881no—
568C4#1062285412yes—
569C4C2×#6699511yescharacteristic
570C4C2×#6699511yescharacteristic
571C4#1062336811yescharacteristic
572C4#1062336911yescharacteristic
573C2—41no—
574C2—42no—
575C2—1761no—
576C2#1307785011yescharacteristic
577C2#1307793111yescharacteristic
578C2C2×#1062285411yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radical#13078676C2
hypercenter#3503D11
hypocenterC11#18567
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13079999C2semidirect
2. #13079073C2semidirect
4. #13067756C2semidirect
5. #13067750C2semidirect
6. #13067694C2semidirect
7. #13067688C2semidirect
8. #13067297C2semidirect
9. #13067055C2semidirect
10. #13067037C2semidirect
11. C11×#3503C2semidirect
209. #3503D11semidirect
230. Q8×C11#137semidirect
233. D4×C11#137semidirect
497. C11#18567semidirect
509. Q8#66995semidirect
518. D4#66995semidirect

Maximal subgroups

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

subgroupindex
#130799992
#130790732
#130786762
#130677562
#130677502
#130676942
#130676882
#130672972
#130670552
#130670372
C11×#35032
#1856711