Finite Group Databasebeta

← #14737444

Subgroups — #14737444

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079942C211yesmaximal, characteristic
2#13079335C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068189C211yesmaximal, characteristic, complemented
5#13068151C211yesmaximal, characteristic, complemented
6#13068142C211yesmaximal, characteristic, complemented
7#13068090C211yesmaximal, characteristic, complemented
8#13068072C211yesmaximal, characteristic, complemented
9#13068034C211yesmaximal, characteristic, complemented
10#13068013C211yesmaximal, characteristic, complemented
11#13067959C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067276C211yesmaximal, characteristic, complemented
14#13067273C211yesmaximal, characteristic, complemented
15C11×#3233C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#499—21no—
20C11×#488—21no—
21C11×#485—21no—
22C11×#482—21no—
23C11×#477C2211yescharacteristic
24C11×#476C2211yescharacteristic
25C11×#475C2211yescharacteristic
26C11×#474C2211yescharacteristic
27C11×#431C2211yescharacteristic
28#10622701C2211yescharacteristic
29#10622698C2211yescharacteristic
30#10622694C2211yescharacteristic
31#10622691C2211yescharacteristic
32#10622679—21no—
33#10622670—21no—
34#10622662—21no—
35#10622662—21no—
36#10622661—21no—
37#10622651—21no—
38#10622640C2211yescharacteristic
39#10622639—21no—
40#10622639—21no—
41#10622637C2211yescharacteristic
42Q8×C11⋊C8C2211yescharacteristic
43#10622634C2211yescharacteristic
44#10622628C2211yescharacteristic
45#10622625—21no—
46#10622625C2211yescharacteristic
47#10622624—21no—
48D4×C11⋊C8C2211yescharacteristic
49#10622621C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622538C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×#4339—21no—
68C11×C4⋊Q8C2311yescharacteristic
69C11×C4⋊Q8C2311yescharacteristic
70C11×#126—21no—
71C11×#125—21no—
72C11×#125D411yescharacteristic
73C11×#124D411yescharacteristic
74C11×#123—21no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8D411yescharacteristic
78C11×#121D411yescharacteristic
79C4×Q8×C11—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11C2311yescharacteristic
82C4×D4×C11—21no—
83C4×D4×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117—21no—
86C2×C42×C11C2311yescharacteristic
87C2×#4325—21no—
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4323—21no—
91#66983—21no—
92#66983—21no—
93C2×#4318—21no—
94C2×#4318D411yescharacteristic
95C2×#4318D411yescharacteristic
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98#66928—21no—
99#66927C2311yescharacteristic
100C4×D44—21no—
101C4×D44—21no—
102#66922C2311yescharacteristic
103C11×#107—21no—
104C11×#107—21no—
105C11×#106—21no—
106C11×#106—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C4×C8×C11—21no—
115#66899—21no—
116#66899—21no—
117#66899—21no—
118#66896—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#66871—21no—
128#66871—21no—
129#66871—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19247—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C2×C22⋊D11—41no—
155#4339—82no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×C4×D11—41no—
160C2×Dic22—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—41no—
181C42×C11—21no—
182C42×C11—41no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187#4325—42no—
188#4325—42no—
189#4325—81no—
190#4323—81no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4—41no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195#4318—22no—
196#4318—41no—
197#4318—42no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3247—111no—
209#3233D1111yescharacteristic, complemented
210#3182—111no—
211#2969—111no—
212#1703—111no—
213#1697—111no—
214#1696—111no—
215#1686—111no—
216#1684—111no—
217#1678—111no—
218#1675—111no—
219#1665—111no—
220#1565—111no—
221#1543—111no—
222#1542—111no—
223C23×C11—21no—
224C23×C11#12111yescharacteristic
225C22×D11—41no—
226Q8×C11—21no—
227Q8×C11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—81no—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—81no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—82no—
253C2×Dic11—41no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—81no—
259C4×D11—82no—
260Dic22—81no—
261C8×C11—41no—
262C8×C11—41no—
263C11⋊C8—21no—
264C11⋊C8—21no—
265C11⋊C8—21no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8#13512yes—
271#533C2×D1111yescharacteristic
272#532—111no—
273#529C2×D1111yescharacteristic
274#500—111no—
275#499—21no—
276#492—111no—
277#488—21no—
278#487—111no—
279#486—111no—
280#485—21no—
281#482—21no—
282#478—221no—
283#477—111no—
284#477C2×D1111yescharacteristic
285#476—111no—
286#476C2×D1111yescharacteristic
287#475C2×D1111yescharacteristic
288#474C2×D1111yescharacteristic
289#468—221no—
290#468—221no—
291#466—221no—
292#465—221no—
293#463—221no—
294#460—111no—
295#459—111no—
296#446—111no—
297C8×Q8—111no—
298#440—221no—
299#440—221no—
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304#433—221no—
305#431—111no—
306#431C2×D1111yescharacteristic
307C2×C4⋊C8—111no—
308#405—221no—
309C4×M16—111no—
310#335—111no—
311#335—111no—
312#334—111no—
313#334—111no—
314#333—111no—
315#333—111no—
316#333—111no—
317#333—111no—
318#332—111no—
319#332—111no—
320#331—111no—
321#331—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11C2×#12111yescharacteristic
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11C2×#13511yescharacteristic
342C4×C11#57511yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57811yescharacteristic
345Dic11—81no—
346C2×#41—221no—
347C2×SD16—221no—
348C2×SD16—221no—
349C2×SD16—221no—
350C2×D8—221no—
351C2×M16—111no—
352C2×M16—111no—
353C2×M16—221no—
354C22×C8—221no—
355C22×C8—221no—
356C4⋊Q8—111no—
357C4⋊Q8C22×D1111yescharacteristic
358C4⋊Q8C22×D1111yescharacteristic
359#127—111no—
360#126—21no—
361#125—21no—
362#125C22⋊D1111yescharacteristic
363#124—221no—
364#124C22⋊D1111yescharacteristic
365#123—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8C22⋊D1111yescharacteristic
369#121—221no—
370#121—221no—
371#121C22⋊D1111yescharacteristic
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C22×D1111yescharacteristic
375C4×D4—21no—
376C4×D4—221no—
377C4×D4—221no—
378C4×D4C22×D1111yescharacteristic
379#117—21no—
380#117—21no—
381C2×C42C22×D1111yescharacteristic
382#107—21no—
383#107—21no—
384#107—221no—
385#107—221no—
386#107—221no—
387#106—21no—
388#106—21no—
389#106—221no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397C4⋊C8C22×D1111yescharacteristic
398C4⋊C8C22×D1111yescharacteristic
399#103—21no—
400#103—21no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—21no—
405#102—21no—
406#102—221no—
407#102—221no—
408#102—221no—
409#102—221no—
410#102—221no—
411C22⋊C8—21no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415#97—111no—
416#97—111no—
417#97—221no—
418C4×C8—21no—
419C4×C8—111no—
420C4×C8—111no—
421C4×C8—221no—
422C4×C8—221no—
423C2×C11—41no—
424C2×C11—81no—
425C2×C11#303511yescharacteristic
426C2×C11#306311yescharacteristic
427C2×C11#306811yescharacteristic
428D11—161no—
429#41—882no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—221no—
433C2×Q8C2×C22⋊D1111yescharacteristic
434C2×D4—21no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—221no—
438C2×D4—441no—
439C2×D4C2×C22⋊D1111yescharacteristic
440C22×C4—21no—
441C22×C4—441no—
442C22×C4D4×D1111yescharacteristic
443C22×C4#434111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445SD16—442no—
446SD16—442no—
447SD16—881no—
448D8—881no—
449M16—222no—
450M16—441no—
451M16—442no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—111no—
455C2×C8—111no—
456C2×C8—111no—
457C2×C8—111no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—442no—
463C2×C8—881no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4C2×C22⋊D1111yescharacteristic
477C4⋊C4C2×C22⋊D1111yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C42—21no—
487C42—41no—
488C42D4×D1111yescharacteristic
489C42#434111yescharacteristic
490C42C2×C22⋊D1111yescharacteristic
491C42C23×D1111yescharacteristic
492C11#1924711yescharacteristic, complemented, Sylow
493C23—21no—
494C23—441no—
495C23#6699211yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—881no—
502D4—21no—
503D4—21no—
504D4—81no—
505D4—441no—
506D4—441no—
507D4—441no—
508D4—441no—
509D4—881no—
510D4—882no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—441no—
524C2×C4—882no—
525C2×C4#6699211yescharacteristic
526C2×C4#6699211yescharacteristic
527C2×C4#6699211yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×#434111yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—41no—
532C8—41no—
533C8—112no—
534C8—221no—
535C8—221no—
536C8—221no—
537C8—441no—
538C8—441no—
539C8—441no—
540C8—441no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—881no—
548C22—881no—
549C22—881no—
550C22C2×#6699211yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—881no—
561C4D11×#13511yescharacteristic
562C4#1062329911yescharacteristic
563C4#1062336811yescharacteristic
564C4#1062336911yescharacteristic
565C2—41no—
566C2—81no—
567C2—1761no—
568C2#1307806711yescharacteristic
569C2#1307830311yescharacteristic
570C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3233C2
socleC22×C11C2×#121
prime radical#13079942C2
hypercenter#3233D11
hypocenterC11#19247
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3233

Complements

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

NH ≅ G/Ntype
2. #13079335C2semidirect
3. #13077621C2semidirect
4. #13068189C2semidirect
5. #13068151C2semidirect
6. #13068142C2semidirect
7. #13068090C2semidirect
8. #13068072C2semidirect
9. #13068034C2semidirect
10. #13068013C2semidirect
11. #13067959C2semidirect
12. #13067369C2semidirect
13. #13067276C2semidirect
14. #13067273C2semidirect
15. C11×#3233C2semidirect
209. #3233D11semidirect
492. C11#19247semidirect

Maximal subgroups

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

subgroupindex
#130799422
#130793352
#130776212
#130681892
#130681512
#130681422
#130680902
#130680722
#130680342
#130680132
#130679592
#130673692
#130672762
#130672732
C11×#32332
#1924711