Finite Group Databasebeta

← #14739183

Subgroups — #14739183

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#13078092C211yesmaximal, characteristic, complemented
2#13078065C211yesmaximal, characteristic, complemented
3#13077724C211yesmaximal, characteristic, complemented
4#13068057C212yesmaximal, complemented
5#13068050C212yesmaximal, complemented
6#13067973C212yesmaximal, complemented
7#13067968C212yesmaximal, complemented
8#13067391C211yesmaximal, characteristic, complemented
9#13067293C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3205C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×#67003—21no—
15C2×#66985—21no—
16C4×#4339C2211yescharacteristic
17C11×#493C2212yes—
18C11×#486C2212yes—
19C11×#459—21no—
20C11×#459—21no—
21C11×#447—22no—
22C11×#431C2211yescharacteristic
23#10622846—21no—
24#10622828—21no—
25#10622703C2211yescharacteristic, complemented
26#10622696C2211yescharacteristic, complemented
27#10622688—21no—
28#10622688C2212yes—
29#10622688C2211yescharacteristic, complemented
30#10622685—21no—
31#10622685C2212yes—
32#10622685C2211yescharacteristic, complemented
33#10622670—21no—
34#10622667—21no—
35#10622537C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622446—21no—
39D11×C4⋊C8—21no—
40(C22⋊D11)⋊C8—22no—
41C8×D44C2212yescomplemented
42C8×Dic22C2212yescomplemented
43#10622185C2212yescomplemented
44#10622182C2212yes—
45#10622182C2212yes—
46#10622182C2212yescomplemented
47#10622096C2212yescomplemented
48#10622096C2212yescomplemented
49C2×C11×#41—21no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C2×#4339D411yescharacteristic
54C2×C11×D8—22no—
55C2×C11×D8—22no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127C2311yescharacteristic
61C11×#127C2312yes—
62C11×#124—21no—
63C11×#121—21no—
64C11×#121—21no—
65C4×D4×C11—21no—
66C4×D4×C11—21no—
67C2×C42×C11C2311yescharacteristic
68#67003—44no—
69C2×#4326—21no—
70C2×#4325—21no—
71C2×#4324—22no—
72C2×#4324—21no—
73#66985—44no—
74C2×#4323—22no—
75C2×#4323—21no—
76C4×C22⋊D11—21no—
77C4×C22⋊D11—21no—
78#66979D411yescharacteristic
79C2×#4318—21no—
80C22×C11⋊C8—21no—
81C22×C11⋊C8—21no—
82C2×C8×D11—22no—
83C4×D44D411yescharacteristic
84C4×D44C2311yescharacteristic
85#66925—21no—
86C42×D11—21no—
87C4×Dic22D411yescharacteristic
88C4×Dic22C2311yescharacteristic
89C11×C4⋊C8D411yescharacteristic
90C11×C4⋊C8D411yescharacteristic
91C11×#102—22no—
92C11×#102—22no—
93C11×C22⋊C8D412yes—
94C4×C8×C11C2312yes—
95#66899—21no—
96#66899—21no—
97#66896—22no—
98#66896—22no—
99#66896—21no—
100#66896—21no—
101(C2×D11)⋊C8—22no—
102Dic11⋊C8—22no—
103C8×Dic11—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4⋊(C11⋊C8)C2312yes—
111#19410—111nomaximal, Sylow
112C24×C11—41no—
113C11×#41—42no—
114C11×#41—42no—
115C2×Q8×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—22no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—42no—
127C2×D4×C11—42no—
128C2×D4×C11—81no—
129C2×D4×C11—81no—
130C2×D4×C11—82no—
131C22×C4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C2×C22⋊D11—21no—
136#4339—22no—
137#4339D814yescomplemented
138C2×D44C2×D411yescharacteristic
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×Dic22C2×D411yescharacteristic
143C11×D8—82no—
144C11×D8—82no—
145C2×C8×C11C2×D412yes—
146C2×C8×C11C2×D412yes—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155C22⋊Dic11—21no—
156#4326—42no—
157#4325—42no—
158#4324—44no—
159#4324—42no—
160#4323—44no—
161#4323—42no—
162(C2×D11)⋊C4—21no—
163(C2×D11)⋊C4—21no—
164C4⋊Dic11C2×D411yescharacteristic
165C4⋊Dic11C2×D411yescharacteristic
166Dic11⋊C4—21no—
167Dic11⋊C4—21no—
168C4×Dic11—21no—
169C4×Dic11—21no—
170C4×Dic11—21no—
171#4318—42no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—42no—
177C2×C11⋊C8—81no—
178C8×D11—82no—
179#3205D1111yescharacteristic, complemented
180#3038—111no—
181#3035—111no—
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—41no—
191C23×C11—42no—
192C23×C11—82no—
193C23×C11—82no—
194C23×C11—82no—
195C23×C11#12111yescharacteristic
196C22×D11—21no—
197Q8×C11—41no—
198Q8×C11—41no—
199D4×C11—42no—
200D4×C11—41no—
201D4×C11—42no—
202D4×C11—41no—
203D4×C11—41no—
204D4×C11—42no—
205D4×C11—41no—
206D4×C11—42no—
207D4×C11—81no—
208D4×C11—82no—
209D4×C11—82no—
210D4×C11—82no—
211D4×C11—82no—
212D4×C11—82no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—82no—
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11C2×D812yes—
222C2×C4×C11#13512yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C22⋊D11—24no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—21no—
230D44—21no—
231D44C2×D812yes—
232C4×D11—24no—
233C4×D11—41no—
234C4×D11—41no—
235C4×D11—81no—
236Dic22—21no—
237Dic22C2×D812yes—
238C8×C11—22no—
239C8×C11—22no—
240C11⋊C8—41no—
241C11⋊C8—41no—
242C11⋊C8—42no—
243C11⋊C8—42no—
244C2×AGL(1,ℤ/8)—221no—
245C2×#135—221no—
246#532C2×D1111yescharacteristic
247C2×#127C2×D1111yescharacteristic
248C4×#41—111no—
249#493C2×D1112yes—
250#486C2×D1112yes—
251#464—221no—
252#463—221no—
253#462—111no—
254#461—111no—
255#460—111no—
256#460—112no—
257#460—221no—
258#459—21no—
259#459—21no—
260#459—111no—
261#459—112no—
262#459—221no—
263#447—22no—
264C8×Q8—112no—
265C8×D4—112no—
266C8×D4—222no—
267#431—221no—
268#431C2×D1111yescharacteristic
269#423—111no—
270C2×C4⋊C8—111no—
271C2×C4⋊C8—111no—
272C2×C4⋊C8—221no—
273#418—221no—
274#416—221no—
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—82no—
284C22×C11—81no—
285C22×C11—81no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—81no—
289C22×C11—164no—
290C22×C11#46612yes—
291C22×C11C2×#12111yescharacteristic
292C2×D11—22no—
293C2×D11—41no—
294C2×D11—41no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—81no—
299C4×C11#46612yes—
300C4×C11C22×D811yescharacteristic
301C4×C11C2×#13511yescharacteristic
302C4×C11#57611yescharacteristic
303C4×C11#57711yescharacteristic
304Dic11—22no—
305Dic11—41no—
306Dic11—41no—
307C2×#41—21no—
308C2×#41—111no—
309C22×D4—21no—
310C22×D4—21no—
311C22×D4—21no—
312AGL(1,ℤ/8)—444no—
313#135—444no—
314C2×Q16—221no—
315C2×SD16—221no—
316C2×SD16—222no—
317C2×SD16—221no—
318C2×D8—22no—
319C2×D8—22no—
320C2×D8—221no—
321C2×D8—222no—
322C2×M16—221no—
323C22×C8—221no—
324C22×C8—221no—
325C22×C8—222no—
326C4⋊Q8C22×D1111yescharacteristic
327#127—21no—
328#127—21no—
329#127—21no—
330#127C22×D1112yes—
331#127C22×D1111yescharacteristic
332#124—21no—
333#121—21no—
334#121—21no—
335C4×Q8—111no—
336C4×Q8—111no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—111no—
340C4×D4—111no—
341C4×D4—221no—
342C4×D4—221no—
343#117—111no—
344#117—221no—
345C2×C42—221no—
346C2×C42C22×D1111yescharacteristic
347C4⋊C8—112no—
348C4⋊C8—111no—
349C4⋊C8—111no—
350C4⋊C8—112no—
351C4⋊C8—222no—
352C4⋊C8—221no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355C4⋊C8C22⋊D1111yescharacteristic
356C4⋊C8C22⋊D1111yescharacteristic
357#103—221no—
358#103—221no—
359#102—22no—
360#102—22no—
361#102—221no—
362#102—221no—
363#102—222no—
364#102—222no—
365C22⋊C8—222no—
366C22⋊C8C22⋊D1112yes—
367C4×C8—222no—
368C4×C8C22×D1112yes—
369C2×C11—22no—
370C2×C11—161no—
371C2×C11—162no—
372C2×C11#304511yescharacteristic
373C2×C11C2×#46611yescharacteristic
374C2×C11#306811yescharacteristic
375D11—42no—
376C24—41no—
377#41—42no—
378#41—42no—
379#41—114no—
380#41—222no—
381C2×Q8—21no—
382C2×Q8—111no—
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—41no—
390C2×D4—42no—
391C2×D4—42no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—81no—
396C2×D4—81no—
397C2×D4—82no—
398C2×D4—111no—
399C2×D4—221no—
400C22×C4—41no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—221no—
404C22×C4D4×D1111yescharacteristic
405C22×C4#434111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407Q16—442no—
408SD16—442no—
409SD16—444no—
410SD16—442no—
411D8—82no—
412D8—82no—
413D8—442no—
414D8—444no—
415M16—442no—
416C2×C8—222no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—222no—
420C2×C8—442no—
421C2×C8—882no—
422C2×C8—881no—
423C2×C8C2×C22⋊D1112yes—
424C2×C8C2×C22⋊D1112yes—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—111no—
428C4⋊C4—111no—
429C4⋊C4—221no—
430C4⋊C4—221no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—221no—
434C22⋊C4—221no—
435C22⋊C4—221no—
436C42—221no—
437C42—221no—
438C42—221no—
439C42D4×D1111yescharacteristic
440C42#434111yescharacteristic
441C42C2×C22⋊D1111yescharacteristic
442C42C23×D1111yescharacteristic
443C11#1941011yescharacteristic, complemented, Sylow
444C23—41no—
445C23—42no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—221no—
450C23#6699111yescharacteristic
451Q8—41no—
452Q8—41no—
453Q8—112no—
454Q8—221no—
455D4—42no—
456D4—41no—
457D4—42no—
458D4—41no—
459D4—41no—
460D4—42no—
461D4—41no—
462D4—42no—
463D4—81no—
464D4—82no—
465D4—82no—
466D4—82no—
467D4—82no—
468D4—82no—
469D4—112no—
470D4—224no—
471D4—221no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—221no—
478C2×C4—224no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—881no—
484C2×C4D8×D1112yes—
485C2×C4#6696512yes—
486C2×C4#6699111yescharacteristic
487C2×C4#6699111yescharacteristic
488C2×C4#6699111yescharacteristic
489C2×C4C2×D4×D1111yescharacteristic
490C2×C4C2×#434111yescharacteristic
491C2×C4C22×C22⋊D1111yescharacteristic
492C8—22no—
493C8—22no—
494C8—441no—
495C8—441no—
496C8—442no—
497C8—442no—
498C22—21no—
499C22—21no—
500C22—82no—
501C22—81no—
502C22—82no—
503C22—81no—
504C22—81no—
505C22—82no—
506C22—164no—
507C22—222no—
508C22—441no—
509C22—441no—
510C22#1062277012yes—
511C22C2×#6699111yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—81no—
516C4—222no—
517C4—441no—
518C4—441no—
519C4#1062277012yes—
520C4C2×D8×D1111yescharacteristic
521C4C2×#6696511yescharacteristic
522C4#1062336611yescharacteristic
523C4#1062336711yescharacteristic
524C2—22no—
525C2—162no—
526C2—161no—
527C2—442no—
528C2#1307815111yescharacteristic
529C2C2×#1062277011yescharacteristic
530C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3205C2
socleC22×C11C2×#121
hypercenter#3205D11
hypocenterC11#19410
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13078092C2semidirect
2. #13078065C2semidirect
3. #13077724C2semidirect
4. #13068057C2semidirect
5. #13068050C2semidirect
6. #13067973C2semidirect
7. #13067968C2semidirect
8. #13067391C2semidirect
9. #13067293C2semidirect
10. C2×#10622182C2semidirect
11. C11×#3205C2semidirect
25. #10622703C22semidirect
26. #10622696C22semidirect
29. #10622688C22semidirect
32. #10622685C22semidirect
41. C8×D44C22semidirect
42. C8×Dic22C22semidirect
43. #10622185C22semidirect
46. #10622182C22semidirect
47. #10622096C22semidirect
48. #10622096C22semidirect
137. #4339D8semidirect
179. #3205D11semidirect
443. C11#19410semidirect

Maximal subgroups

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

subgroupindex
#130780922
#130780652
#130777242
#130680572
#130680502
#130679732
#130679682
#130673912
#130672932
C2×#106221822
C11×#32052
#1941011