Finite Group Databasebeta

← #14737442

Subgroups — #14737442

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#13079936C211yesmaximal, characteristic
2#13079795C211yesmaximal, characteristic, complemented
3#13077620C211yesmaximal, characteristic, complemented
4#13068188C211yesmaximal, characteristic, complemented
5#13068146C211yesmaximal, characteristic, complemented
6#13068141C211yesmaximal, characteristic, complemented
7#13068085C211yesmaximal, characteristic, complemented
8#13068071C211yesmaximal, characteristic, complemented
9#13068029C211yesmaximal, characteristic, complemented
10#13068012C211yesmaximal, characteristic, complemented
11#13067954C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067278C211yesmaximal, characteristic, complemented
14#13067273C211yesmaximal, characteristic, complemented
15C11×#3182C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#500C2211yescharacteristic
20C11×#492C2211yescharacteristic
21C11×#487C2211yescharacteristic
22C11×#486C2211yescharacteristic
23C11×#468—21no—
24C11×#468—21no—
25C11×#440—21no—
26C11×#440—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622740—21no—
30#10622707C2211yescharacteristic
31#10622704C2211yescharacteristic
32#10622704C2211yescharacteristic
33#10622700C2211yescharacteristic
34#10622697C2211yescharacteristic
35#10622697C2211yescharacteristic
36#10622688C2211yescharacteristic
37#10622685C2211yescharacteristic
38#10622681—21no—
39#10622677—21no—
40#10622654—21no—
41#10622651—21no—
42#10622629—21no—
43#10622622—21no—
44#10622616—21no—
45#10622609—21no—
46#10622538C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622322—21no—
50#10622321—21no—
51#10622301C2211yescharacteristic
52C8×D44C2211yescharacteristic
53#10622292C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622184C2211yescharacteristic
60#10622184C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×#127C2311yescharacteristic
76C11×#125—21no—
77C11×#124—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C11×#117—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4324—21no—
89C2×#4323—21no—
90#66983D411yescharacteristic
91#66982—21no—
92C4×C22⋊D11—21no—
93#66977D411yescharacteristic
94C22×C11⋊C8—21no—
95C2×#4313—21no—
96C2×C8×D11—21no—
97#66929—21no—
98#66928D411yescharacteristic
99C4×D44C2311yescharacteristic
100#66925—21no—
101#66923D411yescharacteristic
102C4×Dic22C2311yescharacteristic
103C11×#107—21no—
104C11×#107—21no—
105C11×#103—21no—
106C11×#103—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×#97D411yescharacteristic
110C11×#97D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119#66879—21no—
120Dic11⋊C8—21no—
121Dic11⋊C8—21no—
122C8×Dic11—21no—
123#66874—21no—
124#66874—21no—
125#66874—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66872—21no—
130#66872—21no—
131#66872—21no—
132#66871—21no—
133#66871—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8—21no—
143C4×C11⋊C8—21no—
144#19247—111nomaximal, Sylow
145C11×#41—82no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—41no—
153C22×C4×C11—41no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×C22⋊D11—21no—
158C2×D44C2×D411yescharacteristic
159C2×C4×D11—21no—
160C2×Dic22C2×D411yescharacteristic
161C11×SD16—42no—
162C11×SD16—42no—
163C11×M16—22no—
164C11×M16—41no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
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×C22⋊C4—41no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—41no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—21no—
186#4324—81no—
187#4323—81no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11C2×D411yescharacteristic
193C4⋊Dic11C2×D411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—21no—
196Dic11⋊C4—21no—
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—81no—
206#4313—42no—
207C8×D11—42no—
208#3247—111no—
209#3233—111no—
210#3182D1111yescharacteristic, complemented
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—41no—
224C23×C11#12111yescharacteristic
225C22×D11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—81no—
229Q8×C11—81no—
230D4×C11—41no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—81no—
235D4×C11—82no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—82no—
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C22⋊D11—81no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255D44—21no—
256D44—21no—
257C4×D11—41no—
258C4×D11—41no—
259Dic22—21no—
260Dic22—21no—
261C8×C11—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11#13512yes—
265C11⋊C8—41no—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271#533C2×D1111yescharacteristic
272#532C2×D1111yescharacteristic
273#529—111no—
274#500C2×D1111yescharacteristic
275#499—221no—
276#492C2×D1111yescharacteristic
277#488—221no—
278#487C2×D1111yescharacteristic
279#486C2×D1111yescharacteristic
280#485—221no—
281#482—221no—
282#478—221no—
283#477—111no—
284#477—111no—
285#476—111no—
286#476—111no—
287#475—111no—
288#474—111no—
289#468—21no—
290#468—21no—
291#466—221no—
292#465—221no—
293#463—221no—
294#460—111no—
295#459—111no—
296#446—111no—
297C8×Q8—111no—
298#440—21no—
299#440—21no—
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304#433—221no—
305#431—111no—
306#431—111no—
307C2×C4⋊C8—111no—
308#405—221no—
309C4×M16C2×D1111yescharacteristic
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—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11C2×#12111yescharacteristic
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C2×#13511yescharacteristic
340C4×C11#57511yescharacteristic
341C4×C11#57711yescharacteristic
342C4×C11#57811yescharacteristic
343Dic11—41no—
344Dic11—41no—
345Dic11—41no—
346C2×#41—21no—
347C2×SD16—21no—
348C2×SD16—21no—
349C2×SD16—221no—
350C2×D8—221no—
351C2×M16—221no—
352C2×M16C22⋊D1111yescharacteristic
353C2×M16C22⋊D1111yescharacteristic
354C22×C8—221no—
355C22×C8—221no—
356C4⋊Q8C22×D1111yescharacteristic
357C4⋊Q8C22×D1111yescharacteristic
358C4⋊Q8C22×D1111yescharacteristic
359#127C22×D1111yescharacteristic
360#126—221no—
361#125—21no—
362#125—111no—
363#124—21no—
364#124—111no—
365#123—221no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—111no—
369#121—21no—
370#121—21no—
371#121—111no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—111no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—111no—
378C4×D4—221no—
379#117—21no—
380#117—221no—
381C2×C42C22×D1111yescharacteristic
382#107—21no—
383#107—21no—
384#107—221no—
385#107—221no—
386#107—221no—
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—
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—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415#97—221no—
416#97C22⋊D1111yescharacteristic
417#97C22⋊D1111yescharacteristic
418C4×C8—221no—
419C4×C8—221no—
420C4×C8—221no—
421C4×C8C22×D1111yescharacteristic
422C4×C8C22×D1111yescharacteristic
423C2×C11—41no—
424C2×C11—161no—
425C2×C11#303511yescharacteristic
426C2×C11#306311yescharacteristic
427C2×C11#306811yescharacteristic
428D11—81no—
429#41—82no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—111no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—111no—
439C2×D4—221no—
440C22×C4—41no—
441C22×C4—221no—
442C22×C4D4×D1111yescharacteristic
443C22×C4#434111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445SD16—42no—
446SD16—42no—
447SD16—881no—
448D8—881no—
449M16—22no—
450M16—41no—
451M16—442no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—442no—
459C2×C8—881no—
460C2×C8C2×C22⋊D1111yescharacteristic
461C2×C8C2×C22⋊D1111yescharacteristic
462C2×C8C2×C22⋊D1111yescharacteristic
463C2×C8C2×C22⋊D1111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—111no—
473C4⋊C4—111no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—221no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C42—41no—
487C42—221no—
488C42D4×D1111yescharacteristic
489C42#434111yescharacteristic
490C42C2×C22⋊D1111yescharacteristic
491C42C23×D1111yescharacteristic
492C11#1924711yescharacteristic, complemented, Sylow
493C23—41no—
494C23—221no—
495C23#6699111yescharacteristic
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500Q8—221no—
501Q8—221no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—82no—
508D4—221no—
509D4—221no—
510D4—881no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—82no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4#6699111yescharacteristic
526C2×C4#6699111yescharacteristic
527C2×C4#6699111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×#434111yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—441no—
535C8—441no—
536C8—441no—
537C8—441no—
538C8—441no—
539C8—441no—
540C8#6700312yes—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—441no—
548C22—441no—
549C22—441no—
550C22C2×#6699111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4—441no—
559C4—441no—
560C4—441no—
561C4#1062330911yescharacteristic
562C4#1062331011yescharacteristic
563C4C2×#6700311yescharacteristic
564C4#1062335311yescharacteristic
565C2—41no—
566C2—161no—
567C2—881no—
568C2#1307806511yescharacteristic
569C2#1307830111yescharacteristic
570C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3182C2
socleC22×C11C2×#121
prime radical#13079936C2
hypercenter#3182D11
hypocenterC11#19247
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
2. #13079795C2semidirect
3. #13077620C2semidirect
4. #13068188C2semidirect
5. #13068146C2semidirect
6. #13068141C2semidirect
7. #13068085C2semidirect
8. #13068071C2semidirect
9. #13068029C2semidirect
10. #13068012C2semidirect
11. #13067954C2semidirect
12. #13067368C2semidirect
13. #13067278C2semidirect
14. #13067273C2semidirect
15. C11×#3182C2semidirect
210. #3182D11semidirect
492. C11#19247semidirect

Maximal subgroups

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

subgroupindex
#130799362
#130797952
#130776202
#130681882
#130681462
#130681412
#130680852
#130680712
#130680292
#130680122
#130679542
#130673682
#130672782
#130672732
C11×#31822
#1924711