Finite Group Databasebeta

← #14731053

Subgroups — #14731053

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079734C211yesmaximal, characteristic, complemented
2C2×#10622694C211yesmaximal, characteristic, complemented
3#13078103C211yesmaximal, characteristic, complemented
4#13067844C214yesmaximal, complemented
5#13067830C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067067C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3511C211yesmaximal, characteristic
10C11×#556—21no—
11C11×#555C2212yes—
12C11×#554C2212yes—
13C11×#553—22no—
14C11×#548—22no—
15C11×#547—21no—
16C11×#542—22no—
17C11×#537—21no—
18C11×#533—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#67004—21no—
25C2×#66922C2211yescharacteristic
26C2×#66899—22no—
27#10622694—22no—
28#10622694C2214yes—
29#10622691—21no—
30#10622683—21no—
31#10622646—22no—
32#10622644—21no—
33#10622644C2212yes—
34#10622632—21no—
35#10622632C2212yes—
36#10622620C2214yes—
37#10622617—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622184C2214yes—
42Q8⋊(C11⋊C8)C2212yes—
43D4⋊(C11⋊C8)C2214yes—
44D4⋊(C11⋊C8)C2212yes—
45C2×C11×#41—22no—
46C2×C11×#41—21no—
47C2×C11×#41D411yescharacteristic
48C22×Q8×C11D412yes—
49C22×Dic22—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8D412yes—
53C11×C4⋊Q8D411yescharacteristic
54C11×C4⋊Q8C2312yes—
55C11×#127D411yescharacteristic
56C11×#126—24no—
57C11×#125—22no—
58C11×#124—22no—
59C11×#124—24no—
60C11×#124—21no—
61C11×#123—24no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—24no—
66C11×#121—22no—
67C11×#121—24no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—21no—
71C11×#121D412yes—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11D411yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C4×D4×C11—22no—
77C4×D4×C11—24no—
78C4×D4×C11—22no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C4×D4×C11C2312yes—
85C11×#117—22no—
86C11×#117—22no—
87C11×#117—21no—
88C11×#117D411yescharacteristic
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94#67004—44no—
95C2×#4326—22no—
96C2×#4324—22no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×#4318—21no—
100C22×C11⋊C8—21no—
101#66922—21no—
102#66922—21no—
103#66922—21no—
104#66922C2312yes—
105#66899—28no—
106#66896—24no—
107C22⋊(C11⋊C8)—21no—
108#66874—22no—
109#66874—22no—
110#66871—24no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)C2312yes—
113C4⋊(C11⋊C8)C2312yes—
114C4×C11⋊C8—21no—
115C4×C11⋊C8—21no—
116C4×C11⋊C8C2312yes—
117#18636—111nomaximal, Sylow
118C11×#41—22no—
119C11×#41—22no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—84no—
123C2×Q8×C11—21no—
124C2×Q8×C11—22no—
125C2×Q8×C11—44no—
126C2×Q8×C11C2×D411yescharacteristic
127C2×Q8×C11C2×D414yes—
128C2×D4×C11—21no—
129C2×D4×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11C2×D412yes—
134C2×D4×C11C2×D411yescharacteristic
135C22×C4×C11—24no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×Dic11—41no—
145C2×Dic22—22no—
146C2×Dic22—41no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D411yescharacteristic
160C11×C4⋊C4C2×D411yescharacteristic
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—21no—
165C11×C22⋊C4—21no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—22no—
169C42×C11—24no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2×D411yescharacteristic
176C42×C11C2411yescharacteristic
177#4326—44no—
178#4324—44no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—41no—
182C4⋊Dic11—41no—
183#4318—42no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—42no—
188#3511D1111yescharacteristic
189#3226—111no—
190C2×#487—111no—
191#3039—111no—
192#1646—114no—
193#1644—114no—
194#1548—111no—
195#1492—111no—
196#1476—111no—
197C23×C11—21no—
198C23×C11—22no—
199C23×C11#12011yescharacteristic
200Q8×C11—21no—
201Q8×C11—21no—
202Q8×C11—44no—
203Q8×C11—42no—
204Q8×C11—44no—
205D4×C11—21no—
206D4×C11—21no—
207D4×C11—24no—
208D4×C11—42no—
209D4×C11—44no—
210D4×C11—42no—
211D4×C11—42no—
212D4×C11—84no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—24no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—82no—
226C2×C4×C11—84no—
227C2×C4×C11#12011yescharacteristic
228C2×C4×C11#12011yescharacteristic
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#13512yes—
231C2×C4×C11AGL(1,ℤ/8)12yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×Dic11—42no—
236C2×Dic11—82no—
237Dic22—42no—
238Dic22—42no—
239Dic22—82no—
240C11⋊C8—42no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243C2×#137—221no—
244#556—21no—
245#555C2×D1112yes—
246#554C2×D1112yes—
247#553—22no—
248#548—22no—
249#547—21no—
250#542—22no—
251#537—21no—
252#533—21no—
253#532—21no—
254#532C2×D1111yescharacteristic
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8C2×D1111yescharacteristic
257#520—21no—
258C4×#41C2×D1111yescharacteristic
259#500—221no—
260#487—114no—
261#487—222no—
262#486—221no—
263#480—222no—
264#474—114no—
265#462—112no—
266#462—221no—
267#461—112no—
268#461—221no—
269#431—111no—
270#423—111no—
271#419—221no—
272C2×#103—222no—
273C2×C4×C8—111no—
274#333—114no—
275Q8⋊C8—112no—
276D4⋊C8—114no—
277D4⋊C8—112no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—41no—
281C22×C11—42no—
282C22×C11—41no—
283C22×C11—42no—
284C22×C11—41no—
285C22×C11—42no—
286C22×C11#44912yes—
287C22×C11C2×#12011yescharacteristic
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—41no—
291C4×C11—42no—
292C4×C11—41no—
293C4×C11—41no—
294C4×C11—44no—
295C4×C11#44912yes—
296C4×C11#45512yes—
297C4×C11C2×#13511yescharacteristic
298C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C11#57812yes—
300Dic11—82no—
301C2×#41—22no—
302C2×#41—21no—
303C2×#41C22⋊D1111yescharacteristic
304C22×Q8—221no—
305C22×Q8C22⋊D1112yes—
306#137—444no—
307C2×Q16—222no—
308C2×SD16—222no—
309C2×M16—221no—
310C22×C8—221no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—112no—
314C4⋊Q8—221no—
315C4⋊Q8—221no—
316C4⋊Q8—221no—
317C4⋊Q8C22⋊D1112yes—
318C4⋊Q8C22⋊D1111yescharacteristic
319C4⋊Q8C22×D1112yes—
320#127C22⋊D1111yescharacteristic
321#126—24no—
322#125—22no—
323#124—22no—
324#124—24no—
325#124—21no—
326#123—24no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331#121—22no—
332#121—24no—
333#121—22no—
334#121—22no—
335#121—21no—
336#121C22⋊D1112yes—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8C22⋊D1111yescharacteristic
340C4×Q8C22×D1111yescharacteristic
341C4×D4—22no—
342C4×D4—24no—
343C4×D4—22no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—21no—
347C4×D4C22⋊D1111yescharacteristic
348C4×D4C22×D1111yescharacteristic
349C4×D4C22×D1112yes—
350#117—22no—
351#117—22no—
352#117—21no—
353#117C22⋊D1111yescharacteristic
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C42—21no—
360C2×C42C22×D1111yescharacteristic
361#107—224no—
362C4⋊C8—112no—
363C4⋊C8—112no—
364C4⋊C8—221no—
365#103—228no—
366#103—222no—
367#103—222no—
368#102—224no—
369C22⋊C8—221no—
370C4×C8—112no—
371C4×C8—221no—
372C4×C8—221no—
373C2×C11—22no—
374C2×C11—81no—
375C2×C11—82no—
376C2×C11C2×#44911yescharacteristic
377C2×C11#301111yescharacteristic
378C2×C11C2×#45511yescharacteristic
379#41—22no—
380#41—22no—
381#41—42no—
382#41—42no—
383#41—84no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—44no—
387C2×Q8—222no—
388C2×Q8—441no—
389C2×Q8—442no—
390C2×Q8—442no—
391C2×Q8C2×C22⋊D1111yescharacteristic
392C2×Q8C2×C22⋊D1114yes—
393C2×D4—21no—
394C2×D4—22no—
395C2×D4—24no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4C2×C22⋊D1112yes—
399C2×D4C2×C22⋊D1111yescharacteristic
400C22×C4—24no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—441no—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C2×C22⋊D1111yescharacteristic
409C22×C4C2×C22⋊D1111yescharacteristic
410Q16—444no—
411SD16—444no—
412M16—442no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—442no—
417C4⋊C4—24no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—222no—
427C4⋊C4—222no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4C2×C22⋊D1111yescharacteristic
431C4⋊C4C2×C22⋊D1111yescharacteristic
432C4⋊C4C2×C22⋊D1112yes—
433C22⋊C4—24no—
434C22⋊C4—24no—
435C22⋊C4—24no—
436C22⋊C4—21no—
437C22⋊C4—21no—
438C22⋊C4—22no—
439C22⋊C4—21no—
440C22⋊C4—22no—
441C42—24no—
442C42—21no—
443C42—21no—
444C42—21no—
445C42C2×C22⋊D1111yescharacteristic
446C42C2×C22⋊D1111yescharacteristic
447C42C2×C22⋊D1111yescharacteristic
448C42C23×D1111yescharacteristic
449C11#1863611yescharacteristic, complemented, Sylow
450C23—21no—
451C23—22no—
452C23#6700611yescharacteristic
453Q8—21no—
454Q8—21no—
455Q8—44no—
456Q8—42no—
457Q8—44no—
458Q8—442no—
459Q8—442no—
460Q8—882no—
461D4—21no—
462D4—21no—
463D4—24no—
464D4—42no—
465D4—44no—
466D4—42no—
467D4—42no—
468D4—84no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—24no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—82no—
482C2×C4—84no—
483C2×C4—442no—
484C2×C4—882no—
485C2×C4#6700212yes—
486C2×C4#6700312yes—
487C2×C4#6700611yescharacteristic
488C2×C4#6700611yescharacteristic
489C2×C4#6700611yescharacteristic
490C2×C4C22×C22⋊D1111yescharacteristic
491C2×C4C22×C22⋊D1111yescharacteristic
492C2×C4C22×C22⋊D1111yescharacteristic
493C8—442no—
494C8—442no—
495C8—442no—
496C22—21no—
497C22—21no—
498C22—41no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22#1062285112yes—
505C22C2×#6700611yescharacteristic
506C4—21no—
507C4—21no—
508C4—41no—
509C4—42no—
510C4—41no—
511C4—41no—
512C4—44no—
513C4—882no—
514C4#1062285112yes—
515C4#1062285512yes—
516C4C2×#6700211yescharacteristic
517C4C2×#6700311yescharacteristic
518C4#1062336912yes—
519C2—22no—
520C2—81no—
521C2—82no—
522C2C2×#1062285111yescharacteristic
523C2#1307791111yescharacteristic
524C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3511C2
socleC22×C11C2×#120
hypercenter#3511D11
hypocenterC11#18636
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #13079734C2semidirect
2. C2×#10622694C2semidirect
3. #13078103C2semidirect
4. #13067844C2semidirect
5. #13067830C2semidirect
6. #13067297C2semidirect
7. #13067067C2semidirect
8. #13066998C2semidirect
449. C11#18636semidirect

Maximal subgroups

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

subgroupindex
#130797342
C2×#106226942
#130781032
#130678442
#130678302
#130672972
#130670672
#130669982
C11×#35112
#1863611