Finite Group Databasebeta

← #14736796

Subgroups — #14736796

Order 2816.

614 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#13079330C211yesmaximal, characteristic, complemented
2#13078404C211yesmaximal, characteristic, complemented
3#13077636C211yesmaximal, characteristic, complemented
4#13068193C211yesmaximal, characteristic, complemented
5#13068147C211yesmaximal, characteristic, complemented
6#13068137C211yesmaximal, characteristic, complemented
7#13068079C211yesmaximal, characteristic, complemented
8#13068076C211yesmaximal, characteristic, complemented
9#13068030C211yesmaximal, characteristic, complemented
10#13068018C211yesmaximal, characteristic, complemented
11#13067962C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067324C211yesmaximal, characteristic, complemented
14#13067311C211yesmaximal, characteristic, complemented
15C11×#3106C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#482—21no—
20C11×#477C2211yescharacteristic
21C11×#476C2211yescharacteristic
22C11×#460C2211yescharacteristic
23C11×#459C2211yescharacteristic
24C11×#449—21no—
25C4×C11×SD16—21no—
26C4×C11×D8—21no—
27C11×#431C2211yescharacteristic
28#10622846—21no—
29#10622706C2211yescharacteristic
30#10622691C2211yescharacteristic
31#10622689C2211yescharacteristic
32#10622683C2211yescharacteristic
33#10622655—21no—
34#10622655—21no—
35Q8×C11⋊C8C2211yescharacteristic
36Q8×C11⋊C8C2211yescharacteristic
37#10622635—21no—
38#10622634C2211yescharacteristic
39#10622633C2211yescharacteristic
40#10622631—21no—
41#10622631—21no—
42#10622625—21no—
43#10622625—21no—
44#10622625C2211yescharacteristic
45#10622625C2211yescharacteristic
46#10622622—21no—
47#10622621C2211yescharacteristic
48#10622620C2211yescharacteristic
49#10622611—21no—
50#10622539—21no—
51#10622539C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C4×#4318—21no—
54C4×#4318C2211yescharacteristic
55#10622184C2211yescharacteristic
56#10622184C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×D8—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×#127C2311yescharacteristic
73C11×#124—21no—
74C11×#121—21no—
75C11×#121—21no—
76C4×Q8×C11D411yescharacteristic
77C4×Q8×C11C2311yescharacteristic
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4324—21no—
89C2×#4324—21no—
90#66979—21no—
91#66977—21no—
92#66977—21no—
93C2×#4318—21no—
94C2×#4318—21no—
95C2×#4318D411yescharacteristic
96C2×#4318D411yescharacteristic
97C22×C11⋊C8—21no—
98#66923—21no—
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22—21no—
103C11×#107—21no—
104C11×#106—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103—21no—
108C11×#102—21no—
109C11×#102—21no—
110C11×#102—21no—
111C11×C22⋊C8—21no—
112C4×C8×C11—21no—
113#66899—21no—
114#66899—21no—
115#66896—21no—
116#66896—21no—
117#66896—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122#66874—21no—
123#66874—21no—
124#66872—21no—
125#66872—21no—
126#66871—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#19183—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
147C11×#41—82no—
148C2×Q8×C11—21no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C2×D4×C11C2×D411yescharacteristic
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—41no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C2×Dic22—21no—
164C2×Dic22—21no—
165C11×SD16—42no—
166C11×D8—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⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—41no—
179C11×C22⋊C4—41no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11C2×D411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187C22⋊Dic11—41no—
188#4324—42no—
189#4324—42no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194Dic11⋊C4—41no—
195Dic11⋊C4—41no—
196C4×Dic11—41no—
197#4318—22no—
198#4318—41no—
199#4318—42no—
200#4318—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3182—111no—
211#3106D1111yescharacteristic
212#3076—111no—
213#2971—111no—
214#1703—111no—
215#1697—111no—
216#1695—111no—
217#1685—111no—
218#1684—111no—
219#1678—111no—
220#1676—111no—
221#1666—111no—
222#1565—111no—
223#1554—111no—
224#1551—111no—
225C23×C11—21no—
226C23×C11—41no—
227C23×C11#12111yescharacteristic
228Q8×C11—21no—
229Q8×C11—81no—
230Q8×C11#13712yes—
231D4×C11—21no—
232D4×C11—21no—
233D4×C11—42no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—81no—
239D4×C11—82no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—81no—
253C2×C4×C11—82no—
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×Dic11—41no—
261C2×Dic11—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—81no—
265C8×C11—41no—
266C8×C11—41no—
267C11⋊C8—21no—
268C11⋊C8—21no—
269C11⋊C8—21no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8#13512yes—
275#533—111no—
276#532C2×D1111yescharacteristic
277C4×#41C2×D1111yescharacteristic
278#500—111no—
279#492—111no—
280#487—111no—
281#486—111no—
282#482—21no—
283#479—221no—
284#478—221no—
285#477—111no—
286#477C2×D1111yescharacteristic
287#476—111no—
288#476C2×D1111yescharacteristic
289#475—111no—
290#474—111no—
291#468—221no—
292#468—221no—
293#460C2×D1111yescharacteristic
294#459C2×D1111yescharacteristic
295#449—21no—
296C8×Q8—111no—
297C8×Q8—111no—
298#440—221no—
299#440—221no—
300C4×SD16—21no—
301C4×D8—21no—
302#436—111no—
303#436—111no—
304#436—221no—
305#436—221no—
306#432—111no—
307#432—221no—
308#431C2×D1111yescharacteristic
309#427—221no—
310C2×C4⋊C8—111no—
311#416—221no—
312C4×M16—111no—
313C4×M16—221no—
314#335—111no—
315#335—111no—
316#334—111no—
317#334—111no—
318#333—111no—
319#333—111no—
320#333—111no—
321#333—111no—
322#332—111no—
323#332—111no—
324#331—111no—
325#331—111no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11C2×#12111yescharacteristic
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—22no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11C2×#13511yescharacteristic
345C4×C11C2×#13711yescharacteristic
346C4×C11#57511yescharacteristic
347C4×C11#57511yescharacteristic
348Dic11—81no—
349Dic11—81no—
350C2×#41—21no—
351C2×#41C22⋊D1111yescharacteristic
352C2×SD16—21no—
353C2×SD16—221no—
354C2×SD16—221no—
355C2×D8—21no—
356C2×M16—111no—
357C2×M16—111no—
358C2×M16—221no—
359C2×M16—221no—
360C22×C8—221no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8C22×D1111yescharacteristic
364#127C22×D1111yescharacteristic
365#125—221no—
366#124—21no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369#121—21no—
370#121—21no—
371C4×Q8—221no—
372C4×Q8—221no—
373C4×Q8C22⋊D1111yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C22⋊D1111yescharacteristic
380C4×D4C22×D1111yescharacteristic
381#117—21no—
382#117—221no—
383#117C22⋊D1111yescharacteristic
384C2×C42—21no—
385C2×C42C22×D1111yescharacteristic
386#107—21no—
387#107—221no—
388#107—221no—
389#107—221no—
390#107—221no—
391#106—21no—
392#106—221no—
393#106—221no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403#103—21no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—21no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—111no—
420#97—111no—
421#97—221no—
422C4×C8—21no—
423C4×C8—111no—
424C4×C8—111no—
425C4×C8—221no—
426C4×C8—221no—
427C2×C11—41no—
428C2×C11—81no—
429C2×C11—161no—
430C2×C11#303511yescharacteristic
431C2×C11#305611yescharacteristic
432C2×C11#306811yescharacteristic
433#41—22no—
434#41—41no—
435#41—82no—
436C2×Q8—21no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8C2×C22⋊D1111yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—41no—
445C2×D4C2×C22⋊D1111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—41no—
450C22×C4D4×D1111yescharacteristic
451C22×C4#434111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453SD16—42no—
454SD16—442no—
455SD16—442no—
456D8—42no—
457M16—222no—
458M16—442no—
459M16—441no—
460M16—442no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—111no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—442no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4C2×C22⋊D1111yescharacteristic
483C4⋊C4C2×C22⋊D1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—441no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—441no—
494C42D4×D1111yescharacteristic
495C42#434111yescharacteristic
496C42C2×C22⋊D1111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1918311yescharacteristic, complemented, Sylow
499C23—21no—
500C23—41no—
501C23#6699211yescharacteristic
502Q8—21no—
503Q8—81no—
504Q8—441no—
505Q8—441no—
506Q8—881no—
507Q8#6700412yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—81no—
530C2×C4—82no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4#6699211yescharacteristic
534C2×C4#6699211yescharacteristic
535C2×C4#6699211yescharacteristic
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4C2×#434111yescharacteristic
538C2×C4C22×C22⋊D1111yescharacteristic
539C8—41no—
540C8—41no—
541C8—112no—
542C8—221no—
543C8—221no—
544C8—221no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8—441no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22C2×#6699211yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—881no—
568C4—881no—
569C4D11×#13511yescharacteristic
570C4#1062329911yescharacteristic
571C4#1062335311yescharacteristic
572C4C2×#6700411yescharacteristic
573C2—41no—
574C2—81no—
575C2—161no—
576C2#1307806711yescharacteristic
577C2#1307824811yescharacteristic
578C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3106C2
socleC22×C11C2×#121
hypercenter#3106D11
hypocenterC11#19183
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #13079330C2semidirect
2. #13078404C2semidirect
3. #13077636C2semidirect
4. #13068193C2semidirect
5. #13068147C2semidirect
6. #13068137C2semidirect
7. #13068079C2semidirect
8. #13068076C2semidirect
9. #13068030C2semidirect
10. #13068018C2semidirect
11. #13067962C2semidirect
12. #13067369C2semidirect
13. #13067324C2semidirect
14. #13067311C2semidirect
498. C11#19183semidirect

Maximal subgroups

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

subgroupindex
#130793302
#130784042
#130776362
#130681932
#130681472
#130681372
#130680792
#130680762
#130680302
#130680182
#130679622
#130673692
#130673242
#130673112
C11×#31062
#1918311