Finite Group Databasebeta

← #14737519

Subgroups — #14737519

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079953C211yesmaximal, characteristic, complemented
2#13079330C211yesmaximal, characteristic, complemented
3#13077621C211yesmaximal, characteristic, complemented
4#13068182C211yesmaximal, characteristic, complemented
5#13068172C211yesmaximal, characteristic, complemented
6#13068127C211yesmaximal, characteristic, complemented
7#13068079C211yesmaximal, characteristic, complemented
8#13068051C211yesmaximal, characteristic, complemented
9#13068041C211yesmaximal, characteristic, complemented
10#13068008C211yesmaximal, characteristic, complemented
11#13067962C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067280C211yesmaximal, characteristic, complemented
14#13067265C211yesmaximal, characteristic, complemented
15C11×#3212C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C11×#529C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#495—21no—
20C11×#488—21no—
21C11×#462C2211yescharacteristic
22C11×#461C2211yescharacteristic
23C11×#460C2211yescharacteristic
24C11×#459C2211yescharacteristic
25C11×#452—21no—
26C11×#449—21no—
27C11×#431C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622691C2211yescharacteristic
30#10622689C2211yescharacteristic
31#10622683C2211yescharacteristic
32#10622676—21no—
33#10622667—21no—
34#10622664—21no—
35#10622655—21no—
36#10622655—21no—
37#10622654—21no—
38#10622644C2211yescharacteristic
39#10622637C2211yescharacteristic
40Q8×C11⋊C8C2211yescharacteristic
41#10622633C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622631—21no—
44#10622631—21no—
45#10622625—21no—
46#10622625C2211yescharacteristic
47#10622624—21no—
48D4×C11⋊C8C2211yescharacteristic
49#10622620C2211yescharacteristic
50#10622613—21no—
51#10622610—21no—
52#10622538C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622182C2211yescharacteristic
58#10622182C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×Q16—21no—
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×D8—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×#127C2311yescharacteristic
74C11×#126—21no—
75C11×#125D411yescharacteristic
76C11×#124—21no—
77C11×#124D411yescharacteristic
78C11×#123—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×#121—21no—
81C11×#121—21no—
82C11×#121D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×D4×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C2×C42×C11C2311yescharacteristic
90C2×#4326—21no—
91C2×#4324—21no—
92C2×#4324—21no—
93C2×#4324—21no—
94#66979—21no—
95#66977—21no—
96#66977—21no—
97C2×#4318—21no—
98C2×#4318D411yescharacteristic
99C2×#4318D411yescharacteristic
100C22×C11⋊C8—21no—
101C22×C11⋊C8—21no—
102#66923—21no—
103#66922C2311yescharacteristic
104#66922C2311yescharacteristic
105C4×Dic22—21no—
106C4×Dic22—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C4×C8×C11—21no—
115#66899—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#66874—21no—
125#66874—21no—
126#66872—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#19252—111nomaximal, Sylow
145C11×#41—81no—
146C11×#41—81no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11C2×D411yescharacteristic
155C22×C4×C11—21no—
156C22×C4×C11—41no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4111yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C11×Q16—81no—
163C11×SD16—81no—
164C11×SD16—81no—
165C11×D8—81no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
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⋊C4C2×D411yescharacteristic
175C11×C4⋊C4C2×D411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—41no—
182C11×C22⋊C4—41no—
183C42×C11—21no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11#4111yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—81no—
190#4324—42no—
191#4324—42no—
192#4324—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199C4×Dic11—41no—
200#4318—22no—
201#4318—41no—
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3248—111no—
214#3212D1111yescharacteristic
215#3182—111no—
216#2969—111no—
217#1702—111no—
218#1700—111no—
219#1693—111no—
220#1685—111no—
221#1681—111no—
222#1679—111no—
223#1674—111no—
224#1666—111no—
225#1565—111no—
226#1544—111no—
227#1540—111no—
228C23×C11—21no—
229C23×C11—41no—
230C23×C11#12111yescharacteristic
231Q8×C11—21no—
232Q8×C11—21no—
233Q8×C11—41no—
234Q8×C11—41no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—81no—
242D4×C11—81no—
243D4×C11—82no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—82no—
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×Dic11—41no—
263C2×Dic11—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8#13512yes—
278#533—111no—
279#532C2×D1111yescharacteristic
280#529C2×D1111yescharacteristic
281#500—111no—
282#495—21no—
283#492—111no—
284#488—21no—
285#487—111no—
286#486—111no—
287#479—221no—
288#475—111no—
289#474—111no—
290#468—221no—
291#468—221no—
292#467—221no—
293#465—221no—
294#464—221no—
295#462—111no—
296#462C2×D1111yescharacteristic
297#461—111no—
298#461C2×D1111yescharacteristic
299#460C2×D1111yescharacteristic
300#459C2×D1111yescharacteristic
301#452—21no—
302#449—21no—
303#446—111no—
304C8×Q8—111no—
305#440—221no—
306#440—221no—
307#436—111no—
308#436—221no—
309#435—221no—
310C8×D4—111no—
311#433—221no—
312#431—111no—
313#431C2×D1111yescharacteristic
314C2×C4⋊C8—111no—
315#405—221no—
316C4×M16—111no—
317#335—111no—
318#335—111no—
319#334—111no—
320#334—111no—
321#332—111no—
322#332—111no—
323#332—111no—
324#332—111no—
325#332—111no—
326#332—111no—
327#331—111no—
328#331—111no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11C2×#12111yescharacteristic
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—81no—
347C4×C11C2×#13511yescharacteristic
348C4×C11#57511yescharacteristic
349C4×C11#57611yescharacteristic
350C4×C11#57711yescharacteristic
351Dic11—81no—
352Dic11—81no—
353C2×#41—21no—
354C2×Q16—21no—
355C2×Q16—221no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—221no—
359C2×SD16—221no—
360C2×SD16—221no—
361C2×D8—21no—
362C2×M16—111no—
363C2×M16—111no—
364C2×M16—221no—
365C22×C8—221no—
366C22×C8—221no—
367C4⋊Q8—111no—
368C4⋊Q8—111no—
369C4⋊Q8C22×D1111yescharacteristic
370#127C22×D1111yescharacteristic
371#126—21no—
372#125—221no—
373#125C22⋊D1111yescharacteristic
374#124—21no—
375#124C22⋊D1111yescharacteristic
376#123—21no—
377C22⋊Q8—221no—
378C22⋊Q8—221no—
379C22⋊Q8C22⋊D1111yescharacteristic
380#121—21no—
381#121—21no—
382#121C22⋊D1111yescharacteristic
383C4×Q8—221no—
384C4×Q8—221no—
385C4×Q8C22×D1111yescharacteristic
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389C4×D4C22×D1111yescharacteristic
390#117—21no—
391#117—221no—
392C2×C42C22×D1111yescharacteristic
393#107—221no—
394#107—221no—
395#107—221no—
396#106—221no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—221no—
402C4⋊C8—221no—
403C4⋊C8—221no—
404C4⋊C8C22×D1111yescharacteristic
405C4⋊C8C22×D1111yescharacteristic
406#103—21no—
407#103—21no—
408#103—221no—
409#103—221no—
410#103—221no—
411#103—221no—
412#103—221no—
413#102—21no—
414#102—21no—
415#102—221no—
416#102—221no—
417#102—221no—
418C22⋊C8—21no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422#97—111no—
423#97—111no—
424#97—221no—
425C4×C8—21no—
426C4×C8—111no—
427C4×C8—111no—
428C4×C8—221no—
429C4×C8—221no—
430C2×C11—41no—
431C2×C11—81no—
432C2×C11—161no—
433C2×C11#303511yescharacteristic
434C2×C11#306211yescharacteristic
435C2×C11#306911yescharacteristic
436#41—81no—
437#41—81no—
438C2×Q8—21no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8C2×C22⋊D1111yescharacteristic
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4C2×C22⋊D1111yescharacteristic
448C22×C4—21no—
449C22×C4—41no—
450C22×C4D4×D1111yescharacteristic
451C22×C4#434111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453Q16—81no—
454Q16—881no—
455SD16—81no—
456SD16—81no—
457SD16—442no—
458SD16—442no—
459SD16—881no—
460D8—81no—
461M16—222no—
462M16—442no—
463M16—441no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—111no—
467C2×C8—111no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—442no—
475C2×C8—881no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—441no—
487C4⋊C4—441no—
488C4⋊C4C2×C22⋊D1111yescharacteristic
489C4⋊C4C2×C22⋊D1111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—441no—
498C42—21no—
499C42—441no—
500C42D4×D1111yescharacteristic
501C42#434111yescharacteristic
502C42C2×C22⋊D1111yescharacteristic
503C42C23×D1111yescharacteristic
504C11#1925211yescharacteristic, complemented, Sylow
505C23—21no—
506C23—41no—
507C23#6699211yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515Q8—441no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4#6699211yescharacteristic
540C2×C4#6699211yescharacteristic
541C2×C4#6699211yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C8—41no—
546C8—41no—
547C8—112no—
548C8—221no—
549C8—221no—
550C8—221no—
551C8—441no—
552C8—441no—
553C8—441no—
554C8—441no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#6699211yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—881no—
574C4—881no—
575C4D11×#13511yescharacteristic
576C4#1062329911yescharacteristic
577C4#1062336611yescharacteristic
578C4#1062336711yescharacteristic
579C2—41no—
580C2—81no—
581C2—161no—
582C2#1307806711yescharacteristic
583C2#1307829211yescharacteristic
584C2#1307835511yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3212C2
socleC22×C11C2×#121
hypercenter#3212D11
hypocenterC11#19252
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3212

Complements

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

NH ≅ G/Ntype
1. #13079953C2semidirect
2. #13079330C2semidirect
3. #13077621C2semidirect
4. #13068182C2semidirect
5. #13068172C2semidirect
6. #13068127C2semidirect
7. #13068079C2semidirect
8. #13068051C2semidirect
9. #13068041C2semidirect
10. #13068008C2semidirect
11. #13067962C2semidirect
12. #13067369C2semidirect
13. #13067280C2semidirect
14. #13067265C2semidirect
504. C11#19252semidirect

Maximal subgroups

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

subgroupindex
#130799532
#130793302
#130776212
#130681822
#130681722
#130681272
#130680792
#130680512
#130680412
#130680082
#130679622
#130673692
#130672802
#130672652
C11×#32122
#1925211