Finite Group Databasebeta

← #14807982

Subgroups — #14807982

Order 2816.

1092 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079009C211yesmaximal, characteristic, complemented
2#13078431C211yesmaximal, characteristic, complemented
3#13077012C211yesmaximal, characteristic, complemented
4#13069837C214yesmaximal, complemented
5#13069606C211yesmaximal, characteristic, complemented
6#13069445C211yesmaximal, characteristic, complemented
7#13068842C214yesmaximal, complemented
8C4×#66901C211yesmaximal, characteristic, complemented
9C11×#3511C211yesmaximal, characteristic
10C11×#556—21no—
11C11×#555—21no—
12C11×#554—21no—
13C11×#553—22no—
14C11×#548—22no—
15C11×#547—21no—
16C11×#542—22no—
17C11×#537C2212yes—
18C11×#533—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520C2212yes—
23C4×C11×#41C2211yescharacteristic
24C2×#66997—22no—
25C2×#66922C2211yescharacteristic
26C2×#66901C2212yes—
27C2×#66901C2214yes—
28#10622845C2212yes—
29#10622845C2214yes—
30#10622694—21no—
31#10622683—21no—
32#10622668—22no—
33#10622634—21no—
34#10622633—21no—
35#10622621—21no—
36#10622620—21no—
37#10622608C2212yes—
38#10622589—22no—
39#10622589C2214yes—
40C42×Dic11C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622170C2212yes—
44#10622168C2214yes—
45C2×C11×#41—22no—
46C2×C11×#41C2311yescharacteristic
47C2×C11×#41C2312yes—
48C22×Q8×C11D412yes—
49C22×Dic22—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8D411yescharacteristic
55C11×#127D411yescharacteristic
56C11×#126—24no—
57C11×#125—22no—
58C11×#124—22no—
59C11×#124—24no—
60C11×#124D412yes—
61C11×#123—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—24no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—21no—
70C11×#121—21no—
71C11×#121—24no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11D411yescharacteristic
75C4×Q8×C11D411yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11—24no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11D411yescharacteristic
84C4×D4×C11D411yescharacteristic
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—21no—
88C11×#117C2311yescharacteristic
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94#66997—48no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2312yes—
97C2×Dic11⋊C4—28no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2312yes—
101C2×#4318C2312yes—
102C2×#4318C2312yes—
103#66922—21no—
104#66922—21no—
105#66922—21no—
106#66922—21no—
107#66901—24no—
108#66901—28no—
109#66899—22no—
110#66899—24no—
111#66896—22no—
112#66896—24no—
113#66872—22no—
114#66871—22no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)—21no—
117#66867—21no—
118C4×C11⋊C8—21no—
119#25666—111nomaximal, Sylow
120C11×#41—24no—
121C11×#41—22no—
122C11×#41—24no—
123C11×#41—22no—
124C11×#41—84no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11—44no—
128C2×Q8×C11C2×D412yes—
129C2×Q8×C11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11C2×D412yes—
136C2×D4×C11C2×D411yescharacteristic
137C22×C4×C11—24no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—22no—
147C22×Dic11—22no—
148C2×Dic22—44no—
149C2×Dic22—41no—
150C2×Dic22—41no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C4⋊C4C2×D411yescharacteristic
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—21no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—21no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C42×C11—24no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—41no—
182C4⋊Dic11—41no—
183Dic11⋊C4—416no—
184C4×Dic11—24no—
185C4×Dic11—24no—
186C4×Dic11—22no—
187C4×Dic11#4114yescomplemented
188#4318—24no—
189#4318—22no—
190#4318—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193#3511D1111yescharacteristic
194#3141—111no—
195#3079—111no—
196#2868—111no—
197#2039—114no—
198#1997—111no—
199#1962—111no—
200#1859—114no—
201C4×#104—111no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11C22×D411yescharacteristic
205Q8×C11—21no—
206Q8×C11—21no—
207Q8×C11—24no—
208Q8×C11—44no—
209Q8×C11—82no—
210D4×C11—21no—
211D4×C11—21no—
212D4×C11—24no—
213D4×C11—44no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—84no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—24no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—84no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4112yes—
239C2×C4×C112−1+412yes—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—44no—
244C2×Dic11—42no—
245Dic22—82no—
246Dic22—82no—
247C11⋊C8—42no—
248C11⋊C8—42no—
249#556—21no—
250#555—21no—
251#554—21no—
252#553—22no—
253#548—22no—
254#547—21no—
255#542—22no—
256#537C2×D1112yes—
257#533—21no—
258#532—21no—
259#532C2×D1111yescharacteristic
260C2×C4⋊Q8—111no—
261C2×C4⋊Q8—222no—
262C2×C4⋊Q8C2×D1111yescharacteristic
263#520C2×D1112yes—
264C4×#41C2×D1111yescharacteristic
265#489—222no—
266#487—221no—
267#486—221no—
268#477—221no—
269#476—221no—
270#475—221no—
271#474—221no—
272#428—112no—
273#423—111no—
274C2×#104—114no—
275C2×#104—112no—
276#417—112no—
277#417—114no—
278C4×M16—111no—
279#384—114no—
280#384—222no—
281C43—111no—
282#343—114no—
283#339—112no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—42no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—42no—
290C22×C11—41no—
291C22×C11—42no—
292C22×C11C2×#12011yescharacteristic
293C22×C11#54812yes—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—42no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—44no—
300C4×C11—41no—
301C4×C11#45312yes—
302C4×C11#45612yes—
303C4×C11#53211yescharacteristic
304C4×C11#53611yescharacteristic
305C4×C11#54712yes—
306Dic11—28no—
307Dic11—82no—
308C2×#41—22no—
309C2×#41C22×D1111yescharacteristic
310C2×#41C22×D1112yes—
311C22×Q8—221no—
312C22×Q8C22⋊D1112yes—
313C2×M16—112no—
314C2×M16—112no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—221no—
320C4⋊Q8—221no—
321C4⋊Q8—221no—
322C4⋊Q8—221no—
323C4⋊Q8—448no—
324C4⋊Q8C22⋊D1111yescharacteristic
325#127C22⋊D1111yescharacteristic
326#126—24no—
327#125—22no—
328#124—22no—
329#124—24no—
330#124C22⋊D1112yes—
331#123—24no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336#121—22no—
337#121—22no—
338#121—22no—
339#121—21no—
340#121—21no—
341#121—24no—
342C4×Q8—22no—
343C4×Q8—22no—
344C4×Q8C22⋊D1111yescharacteristic
345C4×Q8C22⋊D1111yescharacteristic
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—24no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4C22⋊D1111yescharacteristic
354C4×D4C22⋊D1111yescharacteristic
355#117—22no—
356#117—22no—
357#117—21no—
358#117C22×D1111yescharacteristic
359C2×C4⋊C4—22no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—228no—
363C2×C4⋊C4C22⋊D1112yes—
364C2×C4⋊C4C22×D1112yes—
365C2×C42—21no—
366C2×C42—112no—
367C2×C42—221no—
368C2×C42—221no—
369C2×C42C22×D1111yescharacteristic
370#107—222no—
371#106—222no—
372C4⋊C8—221no—
373C4⋊C8—221no—
374#104—228no—
375#104—224no—
376#103—222no—
377#103—224no—
378#102—222no—
379#102—224no—
380#97—221no—
381C4×C8—221no—
382C2×C11—22no—
383C2×C11—81no—
384C2×C11—82no—
385C2×C11#243211yescharacteristic
386C2×C11C2×#45311yescharacteristic
387C2×C11C2×#45611yescharacteristic
388#41—22no—
389#41—24no—
390#41—22no—
391#41—24no—
392#41—84no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—44no—
396C2×Q8—444no—
397C2×Q8—441no—
398C2×Q8—441no—
399C2×Q8C2×C22⋊D1112yes—
400C2×Q8C2×C22⋊D1111yescharacteristic
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4C2×C22⋊D1112yes—
407C2×D4C2×C22⋊D1111yescharacteristic
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C2×C22⋊D1114yes—
418C22×C4C23×D1111yescharacteristic
419M16—222no—
420M16—224no—
421M16—222no—
422C2×C8—222no—
423C2×C8—222no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—4416no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4C2×C22⋊D1111yescharacteristic
440C4⋊C4C2×C22⋊D1111yescharacteristic
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—21no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C42—24no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—114no—
454C42—224no—
455C42—224no—
456C42—222no—
457C42C2×C22⋊D1111yescharacteristic
458C42C2×C22⋊D1111yescharacteristic
459C42C2×C22⋊D1111yescharacteristic
460C42C2×C22⋊D1111yescharacteristic
461C11#2566611yescharacteristic, complemented, Sylow
462C23—21no—
463C23—22no—
464C23C22×C22⋊D1111yescharacteristic
465Q8—24no—
466Q8—21no—
467Q8—21no—
468Q8—44no—
469Q8—82no—
470Q8—882no—
471Q8—882no—
472D4—24no—
473D4—21no—
474D4—21no—
475D4—42no—
476D4—44no—
477D4—42no—
478D4—42no—
479D4—84no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—84no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—444no—
498C2×C4—442no—
499C2×C4#6700611yescharacteristic
500C2×C4#6700611yescharacteristic
501C2×C4#6700611yescharacteristic
502C2×C4#6700611yescharacteristic
503C2×C4#41×D1112yes—
504C2×C4#6704312yes—
505C2×C4C22×C22⋊D1111yescharacteristic
506C2×C4C22×C22⋊D1111yescharacteristic
507C8—442no—
508C8—442no—
509C22—21no—
510C22—21no—
511C22—41no—
512C22—42no—
513C22—41no—
514C22—42no—
515C22—41no—
516C22—42no—
517C22#1062336212yes—
518C22C2×#6700611yescharacteristic
519C4—21no—
520C4—21no—
521C4—41no—
522C4—42no—
523C4—41no—
524C4—44no—
525C4—41no—
526C4—228no—
527C4—882no—
528C4#1062285412yes—
529C4#1062285912yes—
530C4#1062335512yes—
531C4#1062335611yescharacteristic
532C4#1062336311yescharacteristic
533C2—22no—
534C2—81no—
535C2—82no—
536C2#1307224011yescharacteristic
537C2C2×#1062285411yescharacteristic
538C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C2×#120
hypercenter#3511D11
hypocenterC11#25666
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13079009C2semidirect
2. #13078431C2semidirect
3. #13077012C2semidirect
4. #13069837C2semidirect
5. #13069606C2semidirect
6. #13069445C2semidirect
7. #13068842C2semidirect
8. C4×#66901C2semidirect
187. C4×Dic11#41semidirect
461. C11#25666semidirect

Maximal subgroups

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

subgroupindex
#130790092
#130784312
#130770122
#130698372
#130696062
#130694452
#130688422
C4×#669012
C11×#35112
#2566611