Finite Group Databasebeta

← #14738899

Subgroups — #14738899

Order 2816.

594 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#13079972C211yesmaximal, characteristic
2#13079837C211yesmaximal, characteristic, complemented
3#13077620C211yesmaximal, characteristic, complemented
4#13068195C211yesmaximal, characteristic, complemented
5#13068188C211yesmaximal, characteristic, complemented
6#13068153C211yesmaximal, characteristic, complemented
7#13068146C211yesmaximal, characteristic, complemented
8#13068071C211yesmaximal, characteristic, complemented
9#13068064C211yesmaximal, characteristic, complemented
10#13068029C211yesmaximal, characteristic, complemented
11#13068022C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067321C211yesmaximal, characteristic, complemented
14#13067297C211yesmaximal, characteristic, complemented
15C11×#3141C211yesmaximal, characteristic, complemented
16C11×#532C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#489—21no—
20C11×#489—21no—
21C11×#487C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#486C2211yescharacteristic
25C11×#417—21no—
26C11×#417—21no—
27C4×C11×M16C2211yescharacteristic
28#10622741—21no—
29#10622740—21no—
30#10622707C2211yescharacteristic
31#10622704C2211yescharacteristic
32#10622704C2211yescharacteristic
33#10622702—21no—
34#10622700C2211yescharacteristic
35#10622697C2211yescharacteristic
36#10622697C2211yescharacteristic
37#10622693—21no—
38#10622688C2211yescharacteristic
39#10622685C2211yescharacteristic
40#10622655—21no—
41#10622652—21no—
42#10622629—21no—
43#10622622—21no—
44#10622584—21no—
45#10622580—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48#10622537C2211yescharacteristic
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—
68C22×Q8×C11—21no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8—21no—
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#127C2311yescharacteristic
78C11×#124—21no—
79C11×#121—21no—
80C11×#121—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4324—21no—
87C2×#4323—21no—
88#66983D411yescharacteristic
89#66982—21no—
90C4×C22⋊D11—21no—
91#66977D411yescharacteristic
92C2×#4318—21no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95#66929—21no—
96#66928D411yescharacteristic
97C4×D44C2311yescharacteristic
98#66925—21no—
99#66923D411yescharacteristic
100C4×Dic22C2311yescharacteristic
101C11×#103—21no—
102C11×#103—21no—
103C11×#103—21no—
104C11×#103—21no—
105C11×#102—21no—
106C11×#102—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
142#66867—21no—
143C4×C11⋊C8—21no—
144#19382—111nomaximal, Sylow
145C11×#41—42no—
146C11×#41—42no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—41no—
151C2×Q8×C11—82no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C2×C22⋊D11—21no—
162C2×D44C2×D411yescharacteristic
163C2×C4×D11—21no—
164C2×Dic22C2×D411yescharacteristic
165C11×M16—41no—
166C11×M16—41no—
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2×D411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C22⋊C4—41no—
180C11×C22⋊C4—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—
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206#4313—42no—
207C8×D11—42no—
208#3251—111no—
209#3238—111no—
210#3141D1111yescharacteristic, complemented
211#2969—111no—
212#1704—111no—
213#1703—111no—
214#1698—111no—
215#1697—111no—
216#1684—111no—
217#1683—111no—
218#1678—111no—
219#1677—111no—
220#1569—111no—
221#1553—111no—
222#1548—111no—
223C23×C11—41no—
224C23×C11#12111yescharacteristic
225C22×D11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—81no—
229Q8×C11—81no—
230Q8×C11—82no—
231D4×C11—41no—
232D4×C11—41no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—81no—
236D4×C11—82no—
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—82no—
246C2×C4×C11—82no—
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11#12111yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C22⋊D11—81no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257D44—21no—
258D44—21no—
259C4×D11—41no—
260C4×D11—41no—
261Dic22—21no—
262Dic22—21no—
263C8×C11—21no—
264C8×C11—21no—
265C8×C11—21no—
266C8×C11—21no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273#532C2×D1111yescharacteristic
274C2×C4⋊Q8C2×D1111yescharacteristic
275#529—111no—
276#501—221no—
277#489—21no—
278#489—21no—
279#489—221no—
280#487C2×D1111yescharacteristic
281#487C2×D1111yescharacteristic
282#486C2×D1111yescharacteristic
283#486C2×D1111yescharacteristic
284#483—221no—
285#480—221no—
286#478—221no—
287#477—111no—
288#477—111no—
289#476—111no—
290#476—111no—
291#475—111no—
292#474—111no—
293#469—221no—
294#468—221no—
295#463—221no—
296#460—111no—
297#459—111no—
298#446—111no—
299C8×Q8—111no—
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304#433—221no—
305#432—111no—
306#431—111no—
307#423—111no—
308#417—21no—
309#417—21no—
310#405—221no—
311C4×M16C2×D1111yescharacteristic
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—21no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11C2×#12111yescharacteristic
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—41no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#57511yescharacteristic
342C4×C11#57511yescharacteristic
343C4×C11#57711yescharacteristic
344C4×C11#57811yescharacteristic
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348C2×#41—21no—
349C22×Q8—21no—
350C2×SD16—221no—
351C2×D8—221no—
352C2×M16—221no—
353C2×M16—221no—
354C2×M16C22⋊D1111yescharacteristic
355C2×M16C22⋊D1111yescharacteristic
356C22×C8—221no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8C22×D1111yescharacteristic
361C4⋊Q8C22×D1111yescharacteristic
362C4⋊Q8C22×D1111yescharacteristic
363#127C22×D1111yescharacteristic
364#126—221no—
365#125—111no—
366#124—21no—
367#124—111no—
368#123—221no—
369C22⋊Q8—111no—
370#121—21no—
371#121—21no—
372#121—111no—
373C4×Q8—111no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—111no—
377C4×D4—221no—
378#117—221no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C42C22×D1111yescharacteristic
382#107—221no—
383#107—221no—
384#107—221no—
385#106—221no—
386#106—221no—
387#106—221no—
388C4⋊C8—111no—
389C4⋊C8—111no—
390C4⋊C8—111no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—111no—
394C4⋊C8—221no—
395C4⋊C8—221no—
396C4⋊C8—221no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—221no—
402#103—221no—
403#103—221no—
404#102—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417#97—221no—
418#97—221no—
419#97C22⋊D1111yescharacteristic
420#97C22⋊D1111yescharacteristic
421C4×C8—221no—
422C4×C8—221no—
423C4×C8C22×D1111yescharacteristic
424C4×C8C22×D1111yescharacteristic
425C2×C11—41no—
426C2×C11—161no—
427C2×C11#304011yescharacteristic
428C2×C11#306311yescharacteristic
429C2×C11#306811yescharacteristic
430D11—81no—
431#41—42no—
432#41—42no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—41no—
437C2×Q8—82no—
438C2×Q8—111no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—111no—
444C2×D4—221no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—221no—
448C22×C4D4×D1111yescharacteristic
449C22×C4#434111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451SD16—881no—
452D8—881no—
453M16—41no—
454M16—41no—
455M16—442no—
456M16—881no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—442no—
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C2×C22⋊D1111yescharacteristic
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1111yescharacteristic
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—111no—
477C4⋊C4—111no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C22⋊C4—221no—
488C22⋊C4—221no—
489C42—221no—
490C42D4×D1111yescharacteristic
491C42#434111yescharacteristic
492C42C2×C22⋊D1111yescharacteristic
493C42C23×D1111yescharacteristic
494C11#1938211yescharacteristic, complemented, Sylow
495C23—41no—
496C23—221no—
497C23#6699111yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502Q8—82no—
503Q8—221no—
504Q8—221no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4—82no—
511D4—221no—
512D4—221no—
513D4—881no—
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—82no—
523C2×C4—82no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4#6699111yescharacteristic
530C2×C4#6699111yescharacteristic
531C2×C4#6699111yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4C2×#434111yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—441no—
540C8—441no—
541C8—441no—
542C8—441no—
543C8—441no—
544C8—441no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—441no—
552C22—441no—
553C22—441no—
554C22C2×#6699111yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—441no—
563C4—441no—
564C4—441no—
565C4#1062330911yescharacteristic
566C4#1062331011yescharacteristic
567C4#1062335311yescharacteristic
568C4#1062335311yescharacteristic
569C2—41no—
570C2—161no—
571C2—881no—
572C2#1307810611yescharacteristic
573C2#1307830111yescharacteristic
574C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3141C2
socleC22×C11C2×#121
prime radical#13079972C2
hypercenter#3141D11
hypocenterC11#19382
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. #13079837C2semidirect
3. #13077620C2semidirect
4. #13068195C2semidirect
5. #13068188C2semidirect
6. #13068153C2semidirect
7. #13068146C2semidirect
8. #13068071C2semidirect
9. #13068064C2semidirect
10. #13068029C2semidirect
11. #13068022C2semidirect
12. #13067383C2semidirect
13. #13067321C2semidirect
14. #13067297C2semidirect
15. C11×#3141C2semidirect
210. #3141D11semidirect
494. C11#19382semidirect

Maximal subgroups

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

subgroupindex
#130799722
#130798372
#130776202
#130681952
#130681882
#130681532
#130681462
#130680712
#130680642
#130680292
#130680222
#130673832
#130673212
#130672972
C11×#31412
#1938211