Finite Group Databasebeta

← #14739185

Subgroups — #14739185

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079531C211yesmaximal, characteristic, complemented
2#13078096C211yesmaximal, characteristic, complemented
3#13077727C211yesmaximal, characteristic, complemented
4#13068062C212yesmaximal, complemented
5#13068055C212yesmaximal, complemented
6#13067974C212yesmaximal, complemented
7#13067969C212yesmaximal, complemented
8#13067390C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10C2×#10622123C211yesmaximal, characteristic, complemented
11C11×#3035C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C11×#532C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C2×#67002—21no—
16C2×#66927C2211yescharacteristic
17C11×#464—21no—
18C11×#463—21no—
19C11×#462C2211yescharacteristic, complemented
20C11×#461C2211yescharacteristic, complemented
21C11×#460C2211yescharacteristic, complemented
22C11×#459C2211yescharacteristic, complemented
23C2×C11×C4⋊C8C2211yescharacteristic
24C11×#416—21no—
25#10622701C2212yes—
26#10622686C2212yes—
27#10622649—22no—
28#10622640—21no—
29#10622640C2212yes—
30Q8×C11⋊C8C2212yescomplemented
31#10622628—21no—
32#10622628—21no—
33#10622628—21no—
34#10622628C2212yes—
35D4×C11⋊C8—22no—
36D4×C11⋊C8C2212yescomplemented
37#10622614—21no—
38#10622538—21no—
39#10622538C2211yescharacteristic
40#10622537C2211yescharacteristic
41C2×C4⋊(C11⋊C8)—21no—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622185C2212yescomplemented
44#10622182C2212yescomplemented
45#10622123C2212yes—
46#10622123C2212yes—
47#10622117C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41—21no—
50C2×C11×#41D411yescharacteristic
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—21no—
54C11×#135—44no—
55C2×C11×Q16—21no—
56C2×C11×SD16—21no—
57C2×C11×SD16—21no—
58C2×C11×D8—21no—
59C22×C8×C11—21no—
60C11×C4⋊Q8C2311yescharacteristic
61C11×#127C2311yescharacteristic
62C11×#124—21no—
63C11×#121—21no—
64C11×#121—21no—
65C4×Q8×C11D411yescharacteristic
66C4×Q8×C11C2311yescharacteristic
67C4×D4×C11—21no—
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11D411yescharacteristic
72C4×D4×C11C2311yescharacteristic
73C11×#117—21no—
74C11×#117D411yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77#67002—44no—
78C2×#4325—22no—
79C2×#4323—22no—
80C2×#4323—22no—
81C2×#4323—22no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C22×C11⋊C8—22no—
85#66927—21no—
86#66927—21no—
87#66927—21no—
88#66927C2312yes—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2311yescharacteristic
91C11×C4⋊C8C2311yescharacteristic
92C11×#103—21no—
93C11×#103—21no—
94C11×#102—21no—
95C11×#102—21no—
96C22⋊(C11⋊C8)—22no—
97C22⋊(C11⋊C8)D412yes—
98#66873—22no—
99#66873—22no—
100#66873—22no—
101#66873—22no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—22no—
105C4⋊(C11⋊C8)D411yescharacteristic
106C4⋊(C11⋊C8)D411yescharacteristic
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109C4×C11⋊C8—22no—
110C4×C11⋊C8C2312yes—
111#19410—111nomaximal, Sylow
112C23×D11—41no—
113C11×#41—22no—
114C11×#41—42no—
115C11×#41—42no—
116C11×#41D814yescomplemented
117C2×Q8×C11—21no—
118C2×Q8×C11C2×D411yescharacteristic
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—41no—
124C2×D4×C11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—41no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11#4111yescharacteristic
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—41no—
136C2×D44—41no—
137C2×D44—41no—
138C2×D44—42no—
139C2×D44—42no—
140C2×D44—81no—
141C2×D44—81no—
142C2×D44—82no—
143C11×Q16—42no—
144C11×SD16—42no—
145C11×SD16—42no—
146C11×D8—42no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—42no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4C2×D411yescharacteristic
155C11×C4⋊C4C2×D411yescharacteristic
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C11×C22⋊C4—21no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11#4111yescharacteristic
167C42×C11C2411yescharacteristic
168#4325—44no—
169#4323—44no—
170#4323—82no—
171#4323—82no—
172#4318—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—81no—
176C2×C11⋊C8—82no—
177C2×C11⋊C8C2×D412yes—
178C2×C11⋊C8C2×D412yes—
179#3205—111no—
180#3038—111no—
181#3035D1111yescharacteristic, complemented
182#2988—111no—
183#1682—112no—
184#1681—112no—
185#1668—112no—
186#1667—112no—
187#1571—111no—
188#1547—111no—
189C2×#331—111no—
190C23×C11—21no—
191C23×C11—41no—
192C23×C11#12111yescharacteristic
193C22×D11—42no—
194C22×D11—82no—
195C22×D11—82no—
196C22×D11—82no—
197Q8×C11—21no—
198Q8×C11—41no—
199Q8×C11—41no—
200Q8×C11C2×D812yes—
201D4×C11—24no—
202D4×C11—21no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—81no—
208D4×C11—82no—
209D4×C11C2×D812yes—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—81no—
221C2×C4×C11—82no—
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11C2×D812yes—
226C2×C4×C11#13512yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230D44—42no—
231D44—42no—
232D44—42no—
233D44—42no—
234D44—82no—
235D44—82no—
236D44—82no—
237D44—82no—
238C8×C11—41no—
239C8×C11—41no—
240C11⋊C8—22no—
241C11⋊C8—22no—
242C11⋊C8—42no—
243C11⋊C8—42no—
244C2×AGL(1,ℤ/8)—221no—
245C2×#135—21no—
246#532C2×D1111yescharacteristic
247C2×#127—111no—
248C4×#41C2×D1111yescharacteristic
249#493—112no—
250#486—112no—
251#464—21no—
252#463—21no—
253#462C2×D1111yescharacteristic, complemented
254#461C2×D1111yescharacteristic, complemented
255#460—112no—
256#460—221no—
257#460C2×D1111yescharacteristic, complemented
258#459—112no—
259#459—221no—
260#459—221no—
261#459—221no—
262#459C2×D1111yescharacteristic, complemented
263#447—222no—
264C8×Q8—112no—
265C8×D4—112no—
266C8×D4—222no—
267#431—111no—
268#431—221no—
269#423—111no—
270C2×C4⋊C8—111no—
271C2×C4⋊C8—221no—
272C2×C4⋊C8C2×D1111yescharacteristic
273#418—221no—
274#416—21no—
275#335—112no—
276#335—112no—
277#332—112no—
278#331—112no—
279#331—112no—
280#331—112no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—22no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11#46612yes—
290C22×C11C2×#12111yescharacteristic
291C2×D11—82no—
292C2×D11—82no—
293C2×D11—82no—
294C2×D11—164no—
295C4×C11—21no—
296C4×C11—22no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—41no—
300C4×C11—41no—
301C4×C11—81no—
302C4×C11#46612yes—
303C4×C11C22×D811yescharacteristic
304C4×C11C2×#13511yescharacteristic
305C4×C11#57611yescharacteristic
306C4×C11#57711yescharacteristic
307C2×#41—21no—
308C2×#41C22⋊D1111yescharacteristic
309C22×D4—221no—
310C22×D4—221no—
311C22×D4—221no—
312AGL(1,ℤ/8)—444no—
313#135—44no—
314C2×Q16—21no—
315C2×SD16—21no—
316C2×SD16—21no—
317C2×SD16—222no—
318C2×D8—21no—
319C2×D8—222no—
320C2×D8—222no—
321C2×D8—222no—
322C2×M16—221no—
323C22×C8—21no—
324C22×C8—222no—
325C22×C8—221no—
326C4⋊Q8C22×D1111yescharacteristic
327#127—112no—
328#127—221no—
329#127—221no—
330#127—221no—
331#127C22×D1111yescharacteristic
332#124—21no—
333#121—21no—
334#121—21no—
335C4×Q8C22⋊D1111yescharacteristic
336C4×Q8C22×D1111yescharacteristic
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4—21no—
341C4×D4C22⋊D1111yescharacteristic
342C4×D4C22×D1111yescharacteristic
343#117—21no—
344#117C22⋊D1111yescharacteristic
345C2×C42—21no—
346C2×C42C22×D1111yescharacteristic
347C4⋊C8—21no—
348C4⋊C8—111no—
349C4⋊C8—111no—
350C4⋊C8—112no—
351C4⋊C8—112no—
352C4⋊C8—222no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355C4⋊C8C22×D1111yescharacteristic
356C4⋊C8C22×D1111yescharacteristic
357#103—21no—
358#103—21no—
359#102—21no—
360#102—21no—
361#102—222no—
362#102—222no—
363#102—222no—
364#102—222no—
365C22⋊C8—112no—
366C22⋊C8—222no—
367C4×C8—112no—
368C4×C8—222no—
369C2×C11—22no—
370C2×C11—42no—
371C2×C11—161no—
372C2×C11#304511yescharacteristic
373C2×C11C2×#46611yescharacteristic
374C2×C11#306811yescharacteristic
375D11—162no—
376C24—441no—
377#41—22no—
378#41—42no—
379#41—42no—
380#41#432314yescomplemented
381C2×Q8—21no—
382C2×Q8C2×C22⋊D1111yescharacteristic
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—222no—
389C2×D4—222no—
390C2×D4—222no—
391C2×D4—442no—
392C2×D4—441no—
393C2×D4—441no—
394C2×D4—441no—
395C2×D4—442no—
396C2×D4—881no—
397C2×D4—881no—
398C2×D4—882no—
399C2×D4C2×C22⋊D1111yescharacteristic
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—41no—
404C22×C4D4×D1111yescharacteristic
405C22×C4#434111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407Q16—42no—
408SD16—42no—
409SD16—42no—
410SD16—444no—
411D8—42no—
412D8—444no—
413D8—882no—
414D8—882no—
415M16—442no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—42no—
419C2×C8—112no—
420C2×C8—112no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—882no—
424C2×C8—881no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4C2×C22⋊D1111yescharacteristic
430C4⋊C4C2×C22⋊D1111yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42D4×D1111yescharacteristic
440C42#434111yescharacteristic
441C42C2×C22⋊D1111yescharacteristic
442C42C23×D1111yescharacteristic
443C11#1941011yescharacteristic, complemented, Sylow
444C23—21no—
445C23—41no—
446C23—442no—
447C23—882no—
448C23—882no—
449C23—882no—
450C23#6699211yescharacteristic
451Q8—21no—
452Q8—41no—
453Q8—41no—
454Q8C2×#432312yes—
455D4—24no—
456D4—21no—
457D4—41no—
458D4—41no—
459D4—41no—
460D4—41no—
461D4—81no—
462D4—82no—
463D4—442no—
464D4—442no—
465D4—442no—
466D4—442no—
467D4—882no—
468D4—882no—
469D4—882no—
470D4—882no—
471D4C2×#432312yes—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—24no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—81no—
483C2×C4—82no—
484C2×C4C2×#432312yes—
485C2×C4#6699211yescharacteristic
486C2×C4#6699211yescharacteristic
487C2×C4#6699211yescharacteristic
488C2×C4#6700312yes—
489C2×C4C2×D4×D1111yescharacteristic
490C2×C4C2×#434111yescharacteristic
491C2×C4C22×C22⋊D1111yescharacteristic
492C8—41no—
493C8—41no—
494C8—222no—
495C8—222no—
496C8—442no—
497C8—442no—
498C22—21no—
499C22—21no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—882no—
507C22—882no—
508C22—882no—
509C22—1764no—
510C22#1062265112yes—
511C22C2×#6699211yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—22no—
516C4—41no—
517C4—41no—
518C4—81no—
519C4#1062265112yes—
520C4#1062330011yescharacteristic
521C4#1062330111yescharacteristic
522C4C22×#432311yescharacteristic
523C4C2×#6700311yescharacteristic
524C2—22no—
525C2—42no—
526C2—161no—
527C2—1762no—
528C2#1307815311yescharacteristic
529C2C2×#1062265111yescharacteristic
530C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3035C2
socleC22×C11C2×#121
hypercenter#3035D11
hypocenterC11#19410
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. #13078096C2semidirect
3. #13077727C2semidirect
4. #13068062C2semidirect
5. #13068055C2semidirect
6. #13067974C2semidirect
7. #13067969C2semidirect
8. #13067390C2semidirect
9. #13067293C2semidirect
10. C2×#10622123C2semidirect
11. C11×#3035C2semidirect
19. C11×#462C22semidirect
20. C11×#461C22semidirect
21. C11×#460C22semidirect
22. C11×#459C22semidirect
30. Q8×C11⋊C8C22semidirect
36. D4×C11⋊C8C22semidirect
43. #10622185C22semidirect
44. #10622182C22semidirect
47. #10622117C22semidirect
48. #10622117C22semidirect
116. C11×#41D8semidirect
181. #3035D11semidirect
253. #462C2×D11semidirect
254. #461C2×D11semidirect
257. #460C2×D11semidirect
262. #459C2×D11semidirect
380. #41#4323semidirect
443. C11#19410semidirect

Maximal subgroups

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

subgroupindex
#130795312
#130780962
#130777272
#130680622
#130680552
#130679742
#130679692
#130673902
#130672932
C2×#106221232
C11×#30352
#1941011