Finite Group Databasebeta

← #14736788

Subgroups — #14736788

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#13079335C211yesmaximal, characteristic, complemented
2#13078676C211yesmaximal, characteristic
3#13077636C211yesmaximal, characteristic, complemented
4#13068189C211yesmaximal, characteristic, complemented
5#13068151C211yesmaximal, characteristic, complemented
6#13068137C211yesmaximal, characteristic, complemented
7#13068083C211yesmaximal, characteristic, complemented
8#13068072C211yesmaximal, characteristic, complemented
9#13068034C211yesmaximal, characteristic, complemented
10#13068018C211yesmaximal, characteristic, complemented
11#13067966C211yesmaximal, characteristic, complemented
12#13067366C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067309C211yesmaximal, characteristic, complemented
15C11×#3076C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18#10623008C2211yescharacteristic
19C11×#479—21no—
20C11×#478—21no—
21C11×#477C2211yescharacteristic
22C11×#476C2211yescharacteristic
23C11×#475C2211yescharacteristic
24C11×#474C2211yescharacteristic
25C11×#427—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C11×#416—21no—
28#10622851—21no—
29#10622701C2211yescharacteristic
30#10622698C2211yescharacteristic
31#10622694C2211yescharacteristic
32#10622691C2211yescharacteristic
33#10622662—21no—
34#10622662—21no—
35#10622640C2211yescharacteristic
36#10622639—21no—
37#10622639—21no—
38C4×#4325—21no—
39Q8×C11⋊C8C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622634C2211yescharacteristic
42#10622628C2211yescharacteristic
43C4×#4323—21no—
44#10622625—21no—
45#10622625—21no—
46#10622625C2211yescharacteristic
47#10622625C2211yescharacteristic
48#10622621C2211yescharacteristic
49#10622616—21no—
50#10622539—21no—
51#10622539C2211yescharacteristic
52#10622538C2211yescharacteristic
53C4×#4318—21no—
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×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C22×C8×C11—21no—
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C11×#117—21no—
85C11×#117D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×#4325—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4323—21no—
92#66983—21no—
93#66983—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C2×#4318D411yescharacteristic
97C2×#4318D411yescharacteristic
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⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113C11×#102—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117#66896—21no—
118C22⋊(C11⋊C8)—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)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19183—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
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—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—42no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4C2×D411yescharacteristic
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—41no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—41no—
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11#4111yescharacteristic
189C42×C11C2411yescharacteristic
190#4325—42no—
191#4325—42no—
192#4325—42no—
193#4323—42no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—41no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198#4318—22no—
199#4318—41no—
200#4318—42no—
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#3182—111no—
211#3106—111no—
212#3076D1111yescharacteristic, complemented
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#12111yescharacteristic
227C22×D11—41no—
228Q8×C11—21no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—81no—
232Q8×C11#13712yes—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11—42no—
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—21no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—81no—
250C2×C4×C11#12111yescharacteristic
251C2×C4×C11#12111yescharacteristic
252C2×C4×C11#12111yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—82no—
257C2×Dic11—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—81no—
263C4×D11—82no—
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#533C2×D1111yescharacteristic
276#532—111no—
277C4×#41C2×D1111yescharacteristic
278#500—111no—
279#492—111no—
280#487—111no—
281#486—111no—
282#482—221no—
283#479—21no—
284#478—21no—
285#477—111no—
286#477C2×D1111yescharacteristic
287#476—111no—
288#476C2×D1111yescharacteristic
289#475C2×D1111yescharacteristic
290#474C2×D1111yescharacteristic
291#468—221no—
292#468—221no—
293#460—111no—
294#459—111no—
295#449—221no—
296C8×Q8—111no—
297C8×Q8—111no—
298#440—221no—
299#440—221no—
300C4×SD16—221no—
301C4×D8—221no—
302#436—111no—
303#436—111no—
304#436—221no—
305#436—221no—
306#432—111no—
307#432—221no—
308#431—111no—
309#427—21no—
310C2×C4⋊C8C2×D1111yescharacteristic
311#416—21no—
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×C11C2×#12111yescharacteristic
333C2×D11—81no—
334C2×D11—81no—
335C2×D11—81no—
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×C11—81no—
345C4×C11C2×#13511yescharacteristic
346C4×C11C2×#13711yescharacteristic
347C4×C11#57511yescharacteristic
348C4×C11#57511yescharacteristic
349Dic11—81no—
350C2×#41—221no—
351C2×#41C22⋊D1111yescharacteristic
352C2×SD16—221no—
353C2×SD16—221no—
354C2×SD16—221no—
355C2×D8—221no—
356C2×M16—111no—
357C2×M16—111no—
358C2×M16—221no—
359C2×M16—221no—
360C22×C8—21no—
361C4⋊Q8—111no—
362C4⋊Q8C22×D1111yescharacteristic
363C4⋊Q8C22×D1111yescharacteristic
364#127—111no—
365#125—21no—
366#124—221no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369#121—221no—
370#121—221no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C22⋊D1111yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—221no—
378C4×D4—221no—
379C4×D4C22⋊D1111yescharacteristic
380C4×D4C22×D1111yescharacteristic
381#117—21no—
382#117—21no—
383#117C22⋊D1111yescharacteristic
384C2×C42—21no—
385C2×C42C22×D1111yescharacteristic
386#107—21no—
387#107—21no—
388#107—221no—
389#107—221no—
390#107—221no—
391#106—21no—
392#106—21no—
393#106—221no—
394C4⋊C8—21no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403#103—21no—
404#103—21no—
405#103—221no—
406#103—221no—
407#103—221no—
408#102—21no—
409#102—21no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—221no—
416C22⋊C8—221no—
417C22⋊C8—221no—
418C22⋊C8—221no—
419#97—111no—
420#97—111no—
421#97—221no—
422C4×C8—111no—
423C4×C8—111no—
424C4×C8—221no—
425C4×C8—221no—
426C4×C8—221no—
427C2×C11—41no—
428C2×C11—81no—
429C2×C11#303511yescharacteristic
430C2×C11#305611yescharacteristic
431C2×C11#306811yescharacteristic
432D11—161no—
433#41—22no—
434#41—41no—
435#41—882no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—221no—
439C2×Q8C2×C22⋊D1111yescharacteristic
440C2×D4—21no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—441no—
445C2×D4C2×C22⋊D1111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—441no—
450C22×C4D4×D1111yescharacteristic
451C22×C4#434111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453SD16—442no—
454SD16—442no—
455SD16—442no—
456D8—442no—
457M16—222no—
458M16—442no—
459M16—441no—
460M16—442no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—42no—
464C2×C8—111no—
465C2×C8—111no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4C2×C22⋊D1111yescharacteristic
483C4⋊C4C2×C22⋊D1111yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42D4×D1111yescharacteristic
495C42#434111yescharacteristic
496C42C2×C22⋊D1111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1918311yescharacteristic, complemented, Sylow
499C23—21no—
500C23—441no—
501C23#6699211yescharacteristic
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—81no—
506Q8—881no—
507Q8#6699512yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—441no—
512D4—441no—
513D4—441no—
514D4—441no—
515D4—881no—
516D4—882no—
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—41no—
530C2×C4—81no—
531C2×C4—441no—
532C2×C4—882no—
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—881no—
556C22—881no—
557C22—881no—
558C22C2×#6699211yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—81no—
568C4—881no—
569C4D11×#13511yescharacteristic
570C4#1062329911yescharacteristic
571C4C2×#6699511yescharacteristic
572C4#1062335311yescharacteristic
573C2—41no—
574C2—81no—
575C2—1761no—
576C2#1307806711yescharacteristic
577C2#1307824211yescharacteristic
578C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3076C2
socleC22×C11C2×#121
prime radical#13078676C2
hypercenter#3076D11
hypocenterC11#19183
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13079335C2semidirect
3. #13077636C2semidirect
4. #13068189C2semidirect
5. #13068151C2semidirect
6. #13068137C2semidirect
7. #13068083C2semidirect
8. #13068072C2semidirect
9. #13068034C2semidirect
10. #13068018C2semidirect
11. #13067966C2semidirect
12. #13067366C2semidirect
13. #13067326C2semidirect
14. #13067309C2semidirect
15. C11×#3076C2semidirect
212. #3076D11semidirect
498. C11#19183semidirect

Maximal subgroups

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

subgroupindex
#130793352
#130786762
#130776362
#130681892
#130681512
#130681372
#130680832
#130680722
#130680342
#130680182
#130679662
#130673662
#130673262
#130673092
C11×#30762
#1918311