Finite Group Databasebeta

← #14739304

Subgroups — #14739304

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079752C211yesmaximal, characteristic, complemented
2#13078676C211yesmaximal, characteristic
3#13077727C211yesmaximal, characteristic, complemented
4#13068062C211yesmaximal, characteristic, complemented
5#13068055C211yesmaximal, characteristic, complemented
6#13068034C211yesmaximal, characteristic, complemented
7#13068027C211yesmaximal, characteristic, complemented
8#13068018C211yesmaximal, characteristic, complemented
9#13068013C211yesmaximal, characteristic, complemented
10#13067996C211yesmaximal, characteristic, complemented
11#13067989C211yesmaximal, characteristic, complemented
12#13067397C211yesmaximal, characteristic, complemented
13#13067312C211yesmaximal, characteristic, complemented
14#13067273C211yesmaximal, characteristic, complemented
15C11×#3116C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#485—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#462C2211yescharacteristic
23C11×#461C2211yescharacteristic
24C11×#452—21no—
25C11×#441—21no—
26C11×#440—21no—
27C11×#432C2211yescharacteristic
28#10622851—21no—
29#10622701C2211yescharacteristic
30#10622701C2211yescharacteristic
31#10622692C2211yescharacteristic
32#10622691C2211yescharacteristic
33#10622679—21no—
34#10622679—21no—
35#10622640C2211yescharacteristic
36C4×#4325—21no—
37Q8×C11⋊C8C2211yescharacteristic
38Q8×C11⋊C8C2211yescharacteristic
39#10622634C2211yescharacteristic
40#10622628C2211yescharacteristic
41C4×#4323—21no—
42D4×C11⋊C8—21no—
43D4×C11⋊C8—21no—
44D4×C11⋊C8C2211yescharacteristic
45D4×C11⋊C8C2211yescharacteristic
46#10622621C2211yescharacteristic
47#10622616—21no—
48#10622616—21no—
49#10622616—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52#10622538C2211yescharacteristic
53C2×C4⋊(C11⋊C8)—21no—
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
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×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×#4323—21no—
91#66983—21no—
92#66983—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95C22×C11⋊C8—21no—
96#66928—21no—
97#66927C2311yescharacteristic
98C4×D44—21no—
99C4×D44—21no—
100#66922C2311yescharacteristic
101C11×#107—21no—
102C11×#106—21no—
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#103—21no—
106C11×#103—21no—
107C11×#103—21no—
108C11×#102—21no—
109C11×C22⋊C8—21no—
110C11×#97—21no—
111#66899—21no—
112#66896—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)D411yescharacteristic
117C22⋊(C11⋊C8)D411yescharacteristic
118#66873—21no—
119#66873—21no—
120#66873—21no—
121#66873—21no—
122#66873—21no—
123#66873—21no—
124#66872—21no—
125#66872—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)D411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19419—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#4323—42no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—41no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—81no—
202C2×C11⋊C8—81no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#3228—111no—
209#3116D1111yescharacteristic, complemented
210#3106—111no—
211#2988—111no—
212#1682—111no—
213#1681—111no—
214#1678—111no—
215#1677—111no—
216#1676—111no—
217#1675—111no—
218#1672—111no—
219#1671—111no—
220#1572—111no—
221#1551—111no—
222#1542—111no—
223C23×C11—21no—
224C23×C11#12111yescharacteristic
225C22×D11—41no—
226Q8×C11—21no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—81no—
230Q8×C11#13512yes—
231D4×C11—24no—
232D4×C11—21no—
233D4×C11#13512yes—
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—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—81no—
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C22⋊D11—82no—
255C2×Dic11—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—81no—
261C4×D11—82no—
262Dic22—81no—
263C8×C11—41no—
264C8×C11—41no—
265C11⋊C8—21no—
266C11⋊C8—21no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#533C2×D1111yescharacteristic
274#532—111no—
275C4×#41C2×D1111yescharacteristic
276#500—111no—
277#498—111no—
278#486—111no—
279#486—111no—
280#485—21no—
281#482—221no—
282#482—221no—
283#482—221no—
284#478—221no—
285#478—221no—
286#477—111no—
287#477C2×D1111yescharacteristic
288#476—111no—
289#476C2×D1111yescharacteristic
290#462C2×D1111yescharacteristic
291#461C2×D1111yescharacteristic
292#460—111no—
293#459—111no—
294#452—21no—
295#449—221no—
296C8×Q8—111no—
297C8×Q8—111no—
298#441—21no—
299#440—21no—
300C4×SD16—221no—
301C4×D8—221no—
302C8×D4—111no—
303C8×D4—111no—
304C8×D4—221no—
305C8×D4—221no—
306#432C2×D1111yescharacteristic
307#431—111no—
308#431—111no—
309#431—221no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—221no—
312#335—111no—
313#335—111no—
314#334—111no—
315#334—111no—
316#333—111no—
317#333—111no—
318#333—111no—
319#333—111no—
320#332—111no—
321#332—111no—
322#331—111no—
323#331—111no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—22no—
327C22×C11—21no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11C2×#12111yescharacteristic
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11C2×#13511yescharacteristic
344C4×C11C2×#13511yescharacteristic
345C4×C11#57711yescharacteristic
346C4×C11#57811yescharacteristic
347Dic11—81no—
348C2×#41—221no—
349C2×#41C22⋊D1111yescharacteristic
350C2×Q16—21no—
351C2×SD16—21no—
352C2×SD16—221no—
353C2×D8—221no—
354C22×C8—221no—
355C22×C8—221no—
356C22×C8—221no—
357C4⋊Q8—111no—
358C4⋊Q8C22×D1111yescharacteristic
359C4⋊Q8C22×D1111yescharacteristic
360#127—111no—
361#125—21no—
362#124—221no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365#121—221no—
366#121—221no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C22⋊D1111yescharacteristic
370C4×Q8C22×D1111yescharacteristic
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—221no—
374C4×D4—221no—
375C4×D4C22⋊D1111yescharacteristic
376C4×D4C22×D1111yescharacteristic
377#117—21no—
378#117—21no—
379#117C22⋊D1111yescharacteristic
380C2×C42—21no—
381C2×C42C22×D1111yescharacteristic
382#107—21no—
383#107—221no—
384#107—221no—
385#107—221no—
386#106—21no—
387#106—221no—
388#106—221no—
389#106—221no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—221no—
397C4⋊C8—221no—
398C4⋊C8—221no—
399C4⋊C8C22×D1111yescharacteristic
400C4⋊C8C22×D1111yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—221no—
405#102—21no—
406#102—221no—
407#102—221no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413C22⋊C8—21no—
414C22⋊C8—111no—
415C22⋊C8—111no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—21no—
420C4×C8—111no—
421C4×C8—111no—
422C4×C8—221no—
423C4×C8—221no—
424C4×C8—221no—
425C2×C11—41no—
426C2×C11—42no—
427C2×C11#304611yescharacteristic
428C2×C11#305011yescharacteristic
429C2×C11#306811yescharacteristic
430D11—161no—
431#41—22no—
432#41—22no—
433#41—882no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—221no—
437C2×Q8C2×C22⋊D1111yescharacteristic
438C2×D4—21no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—441no—
443C2×D4C2×C22⋊D1111yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—441no—
448C22×C4D4×D1111yescharacteristic
449C22×C4#434111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451Q16—42no—
452SD16—42no—
453SD16—442no—
454D8—442no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—111no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—881no—
466C2×C8—881no—
467C2×C8—881no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4C2×C22⋊D1111yescharacteristic
479C4⋊C4C2×C22⋊D1111yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42D4×D1111yescharacteristic
491C42#434111yescharacteristic
492C42C2×C22⋊D1111yescharacteristic
493C42C23×D1111yescharacteristic
494C11#1941911yescharacteristic, complemented, Sylow
495C23—21no—
496C23—441no—
497C23#6699211yescharacteristic
498Q8—21no—
499Q8—41no—
500Q8—41no—
501Q8—81no—
502Q8—881no—
503Q8#6700312yes—
504D4—24no—
505D4—21no—
506D4—441no—
507D4—441no—
508D4—441no—
509D4—441no—
510D4—881no—
511D4—882no—
512D4#6700312yes—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—81no—
527C2×C4—441no—
528C2×C4—882no—
529C2×C4#6699211yescharacteristic
530C2×C4#6699211yescharacteristic
531C2×C4#6699211yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4C2×#434111yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—41no—
536C8—41no—
537C8—221no—
538C8—221no—
539C8—221no—
540C8—221no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—881no—
552C22—881no—
553C22—881no—
554C22C2×#6699211yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—81no—
563C4—81no—
564C4—881no—
565C4#1062330911yescharacteristic
566C4#1062331011yescharacteristic
567C4C2×#6700311yescharacteristic
568C4C2×#6700311yescharacteristic
569C2—41no—
570C2—42no—
571C2—1761no—
572C2#1307817011yescharacteristic
573C2#1307819411yescharacteristic
574C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3116C2
socleC22×C11C2×#121
prime radical#13078676C2
hypercenter#3116D11
hypocenterC11#19419
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3116

Complements

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

NH ≅ G/Ntype
1. #13079752C2semidirect
3. #13077727C2semidirect
4. #13068062C2semidirect
5. #13068055C2semidirect
6. #13068034C2semidirect
7. #13068027C2semidirect
8. #13068018C2semidirect
9. #13068013C2semidirect
10. #13067996C2semidirect
11. #13067989C2semidirect
12. #13067397C2semidirect
13. #13067312C2semidirect
14. #13067273C2semidirect
15. C11×#3116C2semidirect
209. #3116D11semidirect
494. C11#19419semidirect

Maximal subgroups

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

subgroupindex
#130797522
#130786762
#130777272
#130680622
#130680552
#130680342
#130680272
#130680182
#130680132
#130679962
#130679892
#130673972
#130673122
#130672732
C11×#31162
#1941911