Finite Group Databasebeta

← #14736792

Subgroups — #14736792

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#13079334C211yesmaximal, characteristic, complemented
2#13078676C211yesmaximal, characteristic
3#13078404C211yesmaximal, characteristic, complemented
4#13068191C211yesmaximal, characteristic, complemented
5#13068149C211yesmaximal, characteristic, complemented
6#13068139C211yesmaximal, characteristic, complemented
7#13068081C211yesmaximal, characteristic, complemented
8#13068074C211yesmaximal, characteristic, complemented
9#13068032C211yesmaximal, characteristic, complemented
10#13068020C211yesmaximal, characteristic, complemented
11#13067964C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067327C211yesmaximal, characteristic, complemented
14#13067312C211yesmaximal, characteristic, complemented
15C11×#2971C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623008C2211yescharacteristic
18#10623001C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C8×Q8×C11C2211yescharacteristic
21C11×#436—21no—
22C11×#436—21no—
23C11×#436C2211yescharacteristic
24C11×#436C2211yescharacteristic
25C11×#432—21no—
26C11×#432C2211yescharacteristic
27C4×C11×M16—21no—
28C4×C11×M16C2211yescharacteristic
29#10622851—21no—
30#10622846—21no—
31#10622747—21no—
32#10622747—21no—
33#10622640C2211yescharacteristic
34C4×#4325—21no—
35#10622635—21no—
36#10622634C2211yescharacteristic
37#10622634C2211yescharacteristic
38#10622633C2211yescharacteristic
39#10622628C2211yescharacteristic
40C4×#4323—21no—
41#10622622—21no—
42#10622621C2211yescharacteristic
43#10622621C2211yescharacteristic
44#10622620C2211yescharacteristic
45#10622616—21no—
46#10622611—21no—
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622323—21no—
50#10622323—21no—
51#10622307C2211yescharacteristic
52#10622306C2211yescharacteristic
53#10622295C2211yescharacteristic
54#10622294C2211yescharacteristic
55#10622123C2211yescharacteristic
56#10622123C2211yescharacteristic
57#10622120C2211yescharacteristic
58#10622120C2211yescharacteristic
59#10622119C2211yescharacteristic
60#10622119C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C2×C11×M16—21no—
70C2×C11×M16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C4×Q8×C11D411yescharacteristic
74C4×Q8×C11C2311yescharacteristic
75C4×D4×C11—21no—
76C4×D4×C11—21no—
77C4×D4×C11D411yescharacteristic
78C4×D4×C11C2311yescharacteristic
79C11×#117—21no—
80C11×#117D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4325—21no—
84C2×#4323—21no—
85#66983—21no—
86#66983—21no—
87#66979—21no—
88#66977—21no—
89#66977—21no—
90C22×C11⋊C8—21no—
91C2×#4314—21no—
92C2×#4314—21no—
93#66928—21no—
94#66927C2311yescharacteristic
95C4×D44—21no—
96C4×D44—21no—
97#66923—21no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100#66922C2311yescharacteristic
101C4×Dic22—21no—
102C4×Dic22—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C11×C22⋊C8—21no—
110C11×#97—21no—
111C11×#97D411yescharacteristic
112C11×#97D411yescharacteristic
113C4×C8×C11—21no—
114C4×C8×C11—21no—
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66896—21no—
121#66896—21no—
122#66896—21no—
123C22⋊(C11⋊C8)—21no—
124#66885—21no—
125#66885—21no—
126#66882—21no—
127#66882—21no—
128#66880—21no—
129#66880—21no—
130#66873—21no—
131#66873—21no—
132#66872—21no—
133#66872—21no—
134#66872—21no—
135#66871—21no—
136#66871—21no—
137#66871—21no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8—21no—
144#19183—111nomaximal, Sylow
145C11×#41—22no—
146C11×#41—41no—
147C2×Q8×C11C2×D411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—41no—
157#4339—82no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×C4×D11—41no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C11×M16—22no—
166C11×M16—41no—
167C11×M16—42no—
168C11×M16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4C2×D411yescharacteristic
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11#4111yescharacteristic
188C42×C11C2411yescharacteristic
189C22⋊Dic11—41no—
190#4325—42no—
191#4323—42no—
192(C2×D11)⋊C4—41no—
193(C2×D11)⋊C4—41no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200Dic11⋊C4—41no—
201Dic11⋊C4—41no—
202C4×Dic11—41no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
208#4314—42no—
209#4314—42no—
210#3182—111no—
211#3106—111no—
212#3076—111no—
213#2971D1111yescharacteristic, complemented
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#13712yes—
230D4×C11—21no—
231D4×C11—21no—
232D4×C11—42no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—81no—
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—82no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255D44—41no—
256D44—41no—
257D44—41no—
258D44—41no—
259D44—81no—
260C4×D11—82no—
261Dic22—41no—
262Dic22—41no—
263Dic22—81no—
264Dic22—81no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—41no—
269C8×C11—41no—
270C8×C11#13512yes—
271C11⋊C8—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275#533—111no—
276#532—111no—
277C4×#41C2×D1111yescharacteristic
278#500—111no—
279#492—111no—
280#487—111no—
281#486—111no—
282#482—221no—
283#479—221no—
284#478—221no—
285#477—111no—
286#477—111no—
287#476—111no—
288#476—111no—
289#475—111no—
290#474—111no—
291#468—221no—
292#468—221no—
293#460—111no—
294#459—111no—
295#449—221no—
296C8×Q8C2×D1111yescharacteristic
297C8×Q8C2×D1111yescharacteristic
298#440—221no—
299#440—221no—
300C4×SD16—221no—
301C4×D8—221no—
302#436—21no—
303#436—21no—
304#436C2×D1111yescharacteristic
305#436C2×D1111yescharacteristic
306#432—21no—
307#432C2×D1111yescharacteristic
308#431—111no—
309#427—221no—
310C2×C4⋊C8—111no—
311#416—221no—
312C4×M16—21no—
313C4×M16C2×D1111yescharacteristic
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×C11C2×#13511yescharacteristic
344C4×C11C2×#13711yescharacteristic
345C4×C11#57511yescharacteristic
346C4×C11#57511yescharacteristic
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350C2×#41—221no—
351C2×#41D4411yescharacteristic
352C2×SD16—221no—
353C2×SD16—221no—
354C2×SD16—221no—
355C2×D8—221no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16C22⋊D1111yescharacteristic
359C2×M16C22⋊D1111yescharacteristic
360C22×C8—221no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363C4⋊Q8—111no—
364#127—111no—
365#125—221no—
366#124—221no—
367C22⋊Q8—221no—
368C22⋊Q8—221no—
369#121—221no—
370#121—221no—
371C4×Q8—221no—
372C4×Q8—221no—
373C4×Q8D4411yescharacteristic
374C4×Q8C22×D1111yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—221no—
378C4×D4—221no—
379C4×D4D4411yescharacteristic
380C4×D4C22×D1111yescharacteristic
381#117—21no—
382#117—221no—
383#117D4411yescharacteristic
384C2×C42—21no—
385C2×C42C22×D1111yescharacteristic
386#107—221no—
387#107—221no—
388#107—221no—
389#107—221no—
390#107—221no—
391#106—221no—
392#106—221no—
393#106—221no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—221no—
401C4⋊C8C22×D1111yescharacteristic
402C4⋊C8C22×D1111yescharacteristic
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#102—221no—
409#102—221no—
410#102—221no—
411#102—221no—
412#102—221no—
413#102—221no—
414#102—221no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—221no—
419#97—21no—
420#97C22⋊D1111yescharacteristic
421#97C22⋊D1111yescharacteristic
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—221no—
425C4×C8C22×D1111yescharacteristic
426C4×C8C22×D1111yescharacteristic
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—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8C2×D4411yescharacteristic
440C2×D4—21no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—441no—
445C2×D4C2×D4411yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—441no—
450C22×C4C2×D4411yescharacteristic
451C22×C4#433911yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453SD16—442no—
454SD16—442no—
455SD16—442no—
456D8—442no—
457M16—22no—
458M16—41no—
459M16—42no—
460M16—42no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—442no—
468C2×C8C2×C22⋊D1111yescharacteristic
469C2×C8C2×C22⋊D1111yescharacteristic
470C2×C8C2×C22⋊D1111yescharacteristic
471C2×C8C2×C22⋊D1111yescharacteristic
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4C2×D4411yescharacteristic
483C4⋊C4C2×D4411yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—441no—
494C42C2×D4411yescharacteristic
495C42#433911yescharacteristic
496C42C2×C22⋊D1111yescharacteristic
497C42C23×D1111yescharacteristic
498C11#1918311yescharacteristic, complemented, Sylow
499C23—21no—
500C23—441no—
501C23#6698311yescharacteristic
502Q8—21no—
503Q8—441no—
504Q8—441no—
505Q8—881no—
506Q8—881no—
507Q8#6696212yes—
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—81no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—882no—
533C2×C4#6698311yescharacteristic
534C2×C4#6698311yescharacteristic
535C2×C4#6698311yescharacteristic
536C2×C4C22×D4411yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4C22×C22⋊D1111yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—441no—
545C8—441no—
546C8—441no—
547C8—441no—
548C8#6700312yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22C2×#6698311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—881no—
567C4—881no—
568C4—881no—
569C4C2×#6696211yescharacteristic
570C4#1062327911yescharacteristic
571C4C2×#6700311yescharacteristic
572C4#1062335311yescharacteristic
573C2—41no—
574C2—81no—
575C2—1761no—
576C2#1307807111yescharacteristic
577C2#1307824611yescharacteristic
578C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2971C2
socleC22×C11C2×#121
prime radical#13078676C2
hypercenter#2971D11
hypocenterC11#19183
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #13079334C2semidirect
3. #13078404C2semidirect
4. #13068191C2semidirect
5. #13068149C2semidirect
6. #13068139C2semidirect
7. #13068081C2semidirect
8. #13068074C2semidirect
9. #13068032C2semidirect
10. #13068020C2semidirect
11. #13067964C2semidirect
12. #13067368C2semidirect
13. #13067327C2semidirect
14. #13067312C2semidirect
15. C11×#2971C2semidirect
213. #2971D11semidirect
498. C11#19183semidirect

Maximal subgroups

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

subgroupindex
#130793342
#130786762
#130784042
#130681912
#130681492
#130681392
#130680812
#130680742
#130680322
#130680202
#130679642
#130673682
#130673272
#130673122
C11×#29712
#1918311