Finite Group Databasebeta

← #14731035

Subgroups — #14731035

Order 2816.

1024 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#13079757C211yesmaximal, characteristic, complemented
2C2×#10622683C211yesmaximal, characteristic, complemented
3#13078103C211yesmaximal, characteristic, complemented
4#13067816C214yesmaximal, complemented
5#13067802C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067071C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic, complemented
9C11×#3508C211yesmaximal, characteristic
10C11×#559—21no—
11C11×#559C2212yes—
12C11×#550—21no—
13C11×#550C2212yes—
14C11×#546—22no—
15C11×#546—22no—
16C11×#540—22no—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532—21no—
20C11×#532—21no—
21C2×C11×#127C2211yescharacteristic
22C11×#518—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#67004—21no—
25C2×#66922C2211yescharacteristic
26C2×#66896—22no—
27#10622694—21no—
28#10622692—21no—
29#10622683—22no—
30#10622683C2214yes—
31#10622656—22no—
32#10622644—21no—
33#10622644C2212yescomplemented
34#10622633C2214yescomplemented
35#10622632—21no—
36#10622632C2212yescomplemented
37#10622617—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622182C2214yes—
42Q8⋊(C11⋊C8)C2212yescomplemented
43Q8⋊(C11⋊C8)C2214yescomplemented
44D4⋊(C11⋊C8)C2212yescomplemented
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D412yes—
51C22×Dic22—21no—
52C11×C4⋊Q8D411yescharacteristic
53C11×C4⋊Q8D411yescharacteristic
54C11×#127—22no—
55C11×#127—21no—
56C11×#127—21no—
57C11×#127D412yes—
58C11×#127C2312yes—
59C11×#125—21no—
60C11×#124—22no—
61C11×#124—22no—
62C11×#124—22no—
63C11×#123—24no—
64C11×#123—24no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8D412yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—22no—
70C11×#121—24no—
71C11×#121—24no—
72C11×#121—22no—
73C11×#120—24no—
74C4×Q8×C11—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2312yes—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11D411yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117—21no—
90C11×#117D411yescharacteristic
91C2×C11×C22⋊C4—24no—
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—24no—
106#66896—28no—
107C22⋊(C11⋊C8)—21no—
108#66874—22no—
109#66874—22no—
110#66872—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#18634—111nomaximal, Sylow
118C24×C11—22no—
119C11×#41—22no—
120C11×#41—22no—
121C11×#41—84no—
122C11×#41—84no—
123C2×Q8×C11—21no—
124C2×Q8×C11C2×D412yes—
125C2×Q8×C11C2×D411yescharacteristic
126C2×D4×C11—21no—
127C2×D4×C11—24no—
128C2×D4×C11—24no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—44no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—82no—
138C2×D4×C11C2×D411yescharacteristic
139C2×D4×C11C2×D414yes—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×Dic11—41no—
149C2×Dic22—22no—
150C2×Dic22—41no—
151C2×Dic22—42no—
152C2×Dic22—42no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C2×D412yes—
161C11×C4⋊C4C2×D411yescharacteristic
162C11×C4⋊C4C2×D411yescharacteristic
163C11×C22⋊C4—24no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—21no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—21no—
170C11×C22⋊C4—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—22no—
175C42×C11C2×D411yescharacteristic
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2411yescharacteristic
179#4326—44no—
180#4324—44no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—41no—
184C4⋊Dic11—41no—
185#4318—42no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—42no—
190#3508D1111yescharacteristic
191#3229—111no—
192C2×#486—111no—
193#3039—111no—
194#1642—114no—
195#1640—114no—
196#1545—111no—
197#1493—111no—
198#1476—111no—
199C23×C11—24no—
200C23×C11—21no—
201C23×C11—44no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11#12011yescharacteristic
205Q8×C11—21no—
206Q8×C11—21no—
207Q8×C11—24no—
208Q8×C11—42no—
209D4×C11—21no—
210D4×C11—21no—
211D4×C11—44no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—44no—
216D4×C11—44no—
217D4×C11—44no—
218D4×C11—82no—
219D4×C11—84no—
220D4×C11—84no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—84no—
232C2×C4×C11—84no—
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11#12011yescharacteristic
236C2×C4×C11#13512yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×Dic11—42no—
242C2×Dic11—82no—
243Dic22—42no—
244Dic22—42no—
245Dic22—82no—
246C11⋊C8—42no—
247C11⋊C8—42no—
248C11⋊C8—42no—
249C2×#137—221no—
250#559—21no—
251#559C2×D1112yes—
252#550—21no—
253#550C2×D1112yes—
254#546—22no—
255#546—22no—
256#540—22no—
257#535—21no—
258#533C2×D1111yescharacteristic
259#532—21no—
260#532—21no—
261C2×C4⋊Q8—111no—
262C2×#127C2×D1111yescharacteristic
263#518—21no—
264C4×#41C2×D1111yescharacteristic
265#498—221no—
266#487—221no—
267#486—114no—
268#486—222no—
269#483—222no—
270#475—114no—
271#462—112no—
272#462—221no—
273#461—112no—
274#461—221no—
275#431—111no—
276#423—111no—
277#419—221no—
278C2×#102—222no—
279C2×C4×C8—111no—
280#331—114no—
281Q8⋊C8—112no—
282Q8⋊C8—114no—
283D4⋊C8—112no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—41no—
287C22×C11—44no—
288C22×C11—41no—
289C22×C11—44no—
290C22×C11—41no—
291C22×C11—44no—
292C22×C11—164no—
293C22×C11#44912yes—
294C22×C11C2×#12011yescharacteristic
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11—42no—
300C4×C11—41no—
301C4×C11—42no—
302C4×C11#44912yes—
303C4×C11#45512yes—
304C4×C11C2×#13511yescharacteristic
305C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C11#57712yes—
307Dic11—82no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41C22⋊D1111yescharacteristic
311C22×Q8—221no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4C22⋊D1112yes—
315#137—444no—
316C2×Q16—222no—
317C2×SD16—222no—
318C2×M16—221no—
319C22×C8—221no—
320C4⋊Q8—112no—
321C4⋊Q8—221no—
322C4⋊Q8—221no—
323C4⋊Q8—221no—
324C4⋊Q8C22⋊D1111yescharacteristic
325C4⋊Q8C22⋊D1111yescharacteristic
326#127—22no—
327#127—21no—
328#127—21no—
329#127C22⋊D1112yes—
330#127C22×D1112yes—
331#125—21no—
332#124—22no—
333#124—22no—
334#124—22no—
335#123—24no—
336#123—24no—
337C22⋊Q8—21no—
338C22⋊Q8C22⋊D1112yes—
339#121—22no—
340#121—22no—
341#121—22no—
342#121—24no—
343#121—24no—
344#121—22no—
345#120—24no—
346C4×Q8—21no—
347C4×Q8C22⋊D1111yescharacteristic
348C4×Q8C22×D1111yescharacteristic
349C4×Q8C22×D1112yes—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4C22⋊D1111yescharacteristic
359C4×D4C22×D1111yescharacteristic
360#117—21no—
361#117—21no—
362#117C22⋊D1111yescharacteristic
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C22⋊C4—24no—
366C2×C42—21no—
367C2×C42C22×D1111yescharacteristic
368#106—224no—
369C4⋊C8—112no—
370C4⋊C8—112no—
371C4⋊C8—221no—
372#103—224no—
373#103—222no—
374#103—222no—
375#102—228no—
376C22⋊C8—221no—
377C4×C8—112no—
378C4×C8—221no—
379C4×C8—221no—
380C2×C11—22no—
381C2×C11—81no—
382C2×C11—84no—
383C2×C11C2×#44911yescharacteristic
384C2×C11#300911yescharacteristic
385C2×C11C2×#45511yescharacteristic
386C24—22no—
387#41—22no—
388#41—22no—
389#41—84no—
390#41—84no—
391C2×Q8—21no—
392C2×Q8—222no—
393C2×Q8—441no—
394C2×Q8—442no—
395C2×Q8—442no—
396C2×Q8C2×C22⋊D1112yes—
397C2×Q8C2×C22⋊D1111yescharacteristic
398C2×D4—21no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—44no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4—82no—
410C2×D4C2×C22⋊D1111yescharacteristic
411C2×D4C2×C22⋊D1114yes—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—441no—
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C2×C22⋊D1111yescharacteristic
420C22×C4C2×C22⋊D1111yescharacteristic
421Q16—444no—
422SD16—444no—
423M16—442no—
424C2×C8—222no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—442no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—222no—
436C4⋊C4—222no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4C2×C22⋊D1111yescharacteristic
440C4⋊C4C2×C22⋊D1111yescharacteristic
441C4⋊C4C2×C22⋊D1112yes—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—21no—
447C22⋊C4—22no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—22no—
454C42C2×C22⋊D1111yescharacteristic
455C42C2×C22⋊D1111yescharacteristic
456C42C2×C22⋊D1111yescharacteristic
457C42C23×D1111yescharacteristic
458C11#1863411yescharacteristic, complemented, Sylow
459C23—24no—
460C23—21no—
461C23—44no—
462C23—82no—
463C23—82no—
464C23#6700611yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—24no—
468Q8—42no—
469Q8—442no—
470Q8—442no—
471Q8—882no—
472D4—21no—
473D4—21no—
474D4—44no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—44no—
479D4—44no—
480D4—44no—
481D4—82no—
482D4—84no—
483D4—84no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—84no—
495C2×C4—84no—
496C2×C4—442no—
497C2×C4—882no—
498C2×C4#6700212yes—
499C2×C4#6700312yes—
500C2×C4#6700611yescharacteristic
501C2×C4#6700611yescharacteristic
502C2×C4#6700611yescharacteristic
503C2×C4C22×C22⋊D1111yescharacteristic
504C2×C4C22×C22⋊D1111yescharacteristic
505C2×C4C22×C22⋊D1111yescharacteristic
506C8—442no—
507C8—442no—
508C8—442no—
509C22—21no—
510C22—21no—
511C22—41no—
512C22—44no—
513C22—41no—
514C22—44no—
515C22—41no—
516C22—44no—
517C22—164no—
518C22#1062285112yes—
519C22C2×#6700611yescharacteristic
520C4—21no—
521C4—21no—
522C4—41no—
523C4—41no—
524C4—42no—
525C4—41no—
526C4—42no—
527C4—882no—
528C4#1062285112yes—
529C4#1062285512yes—
530C4C2×#6700211yescharacteristic
531C4C2×#6700311yescharacteristic
532C4#1062336712yes—
533C2—22no—
534C2—84no—
535C2—81no—
536C2C2×#1062285111yescharacteristic
537C2#1307789311yescharacteristic
538C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3508C2
socleC22×C11C2×#120
hypercenter#3508D11
hypocenterC11#18634
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #13079757C2semidirect
2. C2×#10622683C2semidirect
3. #13078103C2semidirect
4. #13067816C2semidirect
5. #13067802C2semidirect
6. #13067284C2semidirect
7. #13067071C2semidirect
8. #13066998C2semidirect
33. #10622644C22semidirect
34. #10622633C22semidirect
36. #10622632C22semidirect
42. Q8⋊(C11⋊C8)C22semidirect
43. Q8⋊(C11⋊C8)C22semidirect
44. D4⋊(C11⋊C8)C22semidirect
458. C11#18634semidirect

Maximal subgroups

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

subgroupindex
#130797572
C2×#106226832
#130781032
#130678162
#130678022
#130672842
#130670712
#130669982
C11×#35082
#1863411