Finite Group Databasebeta

← #14722281

Subgroups — #14722281

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082523C211yesmaximal, characteristic
2#13077725C211yesmaximal, characteristic, complemented
3#13077284C211yesmaximal, characteristic, complemented
4#13067318C212yesmaximal, complemented
5#13067313C212yesmaximal, complemented
6#13067302C211yesmaximal, characteristic, complemented
7#13067279C212yesmaximal, complemented
8#13067265C211yesmaximal, characteristic, complemented
9#13067262C212yesmaximal, complemented
10C2×#10622120C211yesmaximal, characteristic, complemented
11C11×#1547C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13#10623364—21no—
14#10623358—21no—
15#10623259C2212yes—
16#10623247C2212yes—
17#10623213—22no—
18#10623149C414yes—
19#10623129—22no—
20#10623094C412yes—
21#10623086—21no—
22#10623074C412yes—
23#10623073—21no—
24C4×#4339C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#423C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622742—21no—
29#10622735—21no—
30C8×C22⋊D11—22no—
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622453—22no—
34#10622448C2212yes—
35#10622447—21no—
36#10622446C2212yes—
37#10622446C2212yes—
38D11×C4⋊C8C2212yes—
39#10622443—21no—
40C11×#332C2212yes—
41C11×#331C2212yes—
42#10622185C2211yescharacteristic
43#10622185C2211yescharacteristic
44#10622182C2211yescharacteristic
45#10622182C2211yescharacteristic
46#10622124C2212yes—
47#10622124C2212yes—
48#10622120C2212yes—
49#10622120C2212yes—
50C2×C11×#41—21no—
51C2×#4341—22no—
52C2×#4339D411yescharacteristic
53C22×Dic22—21no—
54C2×C11×M16—21no—
55C22×C8×C11—21no—
56C11×C4⋊Q8C2311yescharacteristic
57C11×#127C2311yescharacteristic
58C11×#124—21no—
59C11×#121—21no—
60C11×#121C2×C412yes—
61C4×D4×C11—21no—
62C4×D4×C11C2×C412yes—
63C2×C42×C11C2311yescharacteristic
64#66999—22no—
65Q8×Dic11—22no—
66#66992—24no—
67#66991—22no—
68#66991C2×C414yes—
69#66989—22no—
70D4×Dic11—24no—
71D4×Dic11—22no—
72D4×Dic11C2×C414yes—
73#66983—22no—
74C4×C22⋊D11C2×C412yes—
75C4×C22⋊D11D412yes—
76#66979—22no—
77#66979D411yescharacteristic
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11C2×C412yes—
81#66977—22no—
82C22×C11⋊C8—21no—
83C2×C8×D11—22no—
84#66950—22no—
85#66945C2×C414yes—
86#66943C2×C414yes—
87#66940—22no—
88#66939—24no—
89#66938—24no—
90#66932—24no—
91#66931—24no—
92C4×D44C2×C411yescharacteristic
93C4×D44D411yescharacteristic
94#66925D412yes—
95C42×D11C2312yes—
96#66922—21no—
97#66922—21no—
98#66922C2×C412yes—
99#66922C2312yes—
100C4×Dic22C2×C411yescharacteristic
101C4×Dic22D411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2312yes—
106C22⋊(C11⋊C8)—21no—
107(C2×D11)⋊C8—22no—
108(C2×D11)⋊C8—22no—
109(C2×D11)⋊C8—22no—
110#66879—22no—
111Dic11⋊C8—22no—
112C8×Dic11—22no—
113C8×Dic11—22no—
114C4⋊(C11⋊C8)—21no—
115C4⋊(C11⋊C8)C2311yescharacteristic
116C4⋊(C11⋊C8)C2311yescharacteristic
117C4⋊(C11⋊C8)C2311yescharacteristic
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4×C11⋊C8—21no—
120#17727—111nomaximal, Sylow
121C11×#41—42no—
122C11×#41—42no—
123C2×Q8×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11C22×C412yes—
128C22×C4×C11—22no—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C2×C22⋊D11—24no—
133C2×C22⋊D11C22⋊C412yes—
134C22×Dic11—24no—
135C22×Dic11—22no—
136#4341—82no—
137#4341—82no—
138#4339—22no—
139#4339—22no—
140C2×D44C22⋊C411yescharacteristic
141C2×C4×D11C22×C412yes—
142C2×C4×D11C2×D412yes—
143C2×C4×D11C2×D412yes—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—81no—
147C2×Dic22—81no—
148C2×Dic22C22⋊C411yescharacteristic
149C11×M16—42no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—81no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4C22×C412yes—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C42×C11C22×C411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2411yescharacteristic
161C22⋊Dic11—24no—
162C22⋊Dic11—24no—
163C22⋊Dic11C22⋊C412yes—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4C22⋊C412yes—
166(C2×D11)⋊C4C22⋊C412yes—
167C4⋊Dic11—24no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11C22⋊C411yescharacteristic
172C4⋊Dic11C22⋊C411yescharacteristic
173C4⋊Dic11C22×C414yes—
174Dic11⋊C4—24no—
175Dic11⋊C4C22⋊C412yes—
176Dic11⋊C4C22⋊C412yes—
177C4×Dic11—24no—
178C4×Dic11C22×C412yes—
179C4×Dic11C2×D412yes—
180C4×Dic11C2×D412yes—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—42no—
186C8×D11—82no—
187#3511—111no—
188#2988—111no—
189#2925—111no—
190#1553—112no—
191#1552—112no—
192#1549—111no—
193#1547D1111yescharacteristic, complemented
194#1544—112no—
195#1540—112no—
196#1540—111no—
197C2×#332—111no—
198C23×C11—22no—
199C23×C11C2×C22⋊C411yescharacteristic
200C22×D11C2×C22⋊C412yes—
201Q8×C11—41no—
202Q8×C11—41no—
203D4×C11—42no—
204D4×C11—44no—
205D4×C11—41no—
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—44no—
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11C2×C22⋊C411yescharacteristic
216C2×C4×C11C2×C22⋊C411yescharacteristic
217C2×C4×C11#13512yes—
218C2×C4×C11#13512yes—
219C2×C4×C11C23×C411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C22⋊D11—24no—
223C22⋊D11—84no—
224C2×Dic11—24no—
225C2×Dic11—84no—
226C2×Dic11—82no—
227C2×Dic11C2×C22⋊C412yes—
228C2×Dic11C2×C22⋊C412yes—
229C2×Dic11C2×C22⋊C412yes—
230D44—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—42no—
236Dic22—22no—
237Dic22—42no—
238Dic22—42no—
239Dic22—82no—
240C8×C11—42no—
241C8×C11—42no—
242C11⋊C8—41no—
243C11⋊C8—41no—
244C11⋊C8—41no—
245C11⋊C8—41no—
246#556—221no—
247#555—112no—
248#554—112no—
249#553—114no—
250#548—222no—
251#547—221no—
252#542—222no—
253#537—221no—
254#533—112no—
255#532—112no—
256#532C2×D1111yescharacteristic
257C2×C4⋊Q8—111no—
258#520—221no—
259C4×#41—111no—
260C8×Q8—221no—
261C8×D4—221no—
262C8×D4—222no—
263#433—222no—
264#432—112no—
265#431—111no—
266#431—112no—
267#431—112no—
268#423C2×D1111yescharacteristic
269C2×C4⋊C8—111no—
270C2×C4⋊C8—112no—
271C2×C4⋊C8C2×D1111yescharacteristic
272#408—221no—
273#405—221no—
274#332—111no—
275#332—111no—
276#332—112no—
277#332—112no—
278#332—112no—
279#332—112no—
280#332C2×D1112yes—
281#331—111no—
282#331—111no—
283#331C2×D1112yes—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11#41612yes—
290C22×C11C22×C22⋊C411yescharacteristic
291C2×D11—22no—
292C2×D11—22no—
293C2×D11—22no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—42no—
298C4×C11#41612yes—
299C4×C11C2×#13511yescharacteristic
300C4×C11C2×#13511yescharacteristic
301C4×C11#57611yescharacteristic
302C4×C11#57711yescharacteristic
303Dic11—22no—
304Dic11—22no—
305Dic11—22no—
306Dic11—44no—
307C2×#41—21no—
308C2×#41—111no—
309C2×#41—222no—
310C22×Q8—221no—
311C2×M16—21no—
312C22×C8—21no—
313C22×C8—222no—
314C22×C8—221no—
315C4⋊Q8—112no—
316C4⋊Q8—112no—
317C4⋊Q8—221no—
318C4⋊Q8—221no—
319C4⋊Q8C22×D1111yescharacteristic
320#127C22×D1111yescharacteristic
321#126—224no—
322#125—114no—
323#124—21no—
324#124—222no—
325#124—224no—
326#123—224no—
327C22⋊Q8—224no—
328C22⋊Q8—222no—
329C22⋊Q8—222no—
330C22⋊Q8—222no—
331#121—21no—
332#121—114no—
333#121—222no—
334#121—222no—
335#121—224no—
336#121C4×D1112yes—
337C4×Q8—111no—
338C4×Q8—111no—
339C4×Q8—222no—
340C4×Q8—222no—
341C4×D4—21no—
342C4×D4—112no—
343C4×D4—112no—
344C4×D4—114no—
345C4×D4—111no—
346C4×D4—111no—
347C4×D4—222no—
348C4×D4—224no—
349C4×D4C4×D1112yes—
350#117—111no—
351#117—112no—
352#117—114no—
353#117—222no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—221no—
357C2×C42—112no—
358C2×C42C22×D1111yescharacteristic
359C4⋊C8—21no—
360C4⋊C8—21no—
361C4⋊C8—111no—
362C4⋊C8—111no—
363C4⋊C8—111no—
364C4⋊C8—111no—
365C4⋊C8—222no—
366C4⋊C8—221no—
367C4⋊C8C22×D1112yes—
368C4⋊C8C22×D1112yes—
369C22⋊C8—222no—
370C22⋊C8—222no—
371C22⋊C8—222no—
372C22⋊C8—221no—
373#97—222no—
374C4×C8—222no—
375C4×C8—222no—
376C4×C8—221no—
377C2×C11—22no—
378C2×C11—82no—
379C2×C11#288911yescharacteristic
380C2×C11C2×#41611yescharacteristic
381C2×C11#289711yescharacteristic
382D11—42no—
383#41—42no—
384#41—42no—
385#41—222no—
386#41—222no—
387#41—882no—
388#41—882no—
389C2×Q8—21no—
390C2×Q8—111no—
391C2×Q8—222no—
392C2×Q8—222no—
393C2×Q8—881no—
394C2×Q8—881no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—112no—
399C2×D4—111no—
400C2×D4—224no—
401C2×D4C2×C4×D1112yes—
402C22×C4—22no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—224no—
407C22×C4—222no—
408C22×C4C2×C4×D1111yescharacteristic
409C22×C4D4×D1111yescharacteristic
410C22×C4D4×D1111yescharacteristic
411M16—42no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—81no—
415C2×C8—221no—
416C2×C8—221no—
417C2×C8—221no—
418C2×C8—221no—
419C2×C8—442no—
420C2×C8—882no—
421C4⋊C4—21no—
422C4⋊C4—111no—
423C4⋊C4—111no—
424C4⋊C4—112no—
425C4⋊C4—112no—
426C4⋊C4—114no—
427C4⋊C4—224no—
428C4⋊C4—224no—
429C4⋊C4—222no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C4⋊C4C2×C4×D1112yes—
433C22⋊C4—22no—
434C22⋊C4—22no—
435C22⋊C4—112no—
436C22⋊C4—112no—
437C22⋊C4—112no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C22⋊C4—224no—
441C42—112no—
442C42—112no—
443C42—112no—
444C42—224no—
445C42C2×C4×D1111yescharacteristic
446C42D4×D1111yescharacteristic
447C42D4×D1111yescharacteristic
448C42C23×D1111yescharacteristic
449C11#1772711yescharacteristic, complemented, Sylow
450C23—22no—
451C23—112no—
452C23C22⋊C4×D1111yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—222no—
456Q8—442no—
457Q8—442no—
458Q8—882no—
459D4—42no—
460D4—44no—
461D4—41no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—224no—
466D4—222no—
467D4—884no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—44no—
473C2×C4—112no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—222no—
479C2×C4—222no—
480C2×C4—224no—
481C2×C4—442no—
482C2×C4—884no—
483C2×C4—882no—
484C2×C4C22⋊C4×D1111yescharacteristic
485C2×C4C22⋊C4×D1111yescharacteristic
486C2×C4C22⋊C4×D1111yescharacteristic
487C2×C4#6696512yes—
488C2×C4#6696912yes—
489C2×C4C22×C4×D1111yescharacteristic
490C2×C4C2×D4×D1111yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C8—42no—
493C8—42no—
494C8—441no—
495C8—441no—
496C8—441no—
497C8—441no—
498C22—21no—
499C22—21no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—222no—
504C22—222no—
505C22—222no—
506C22#1062238512yes—
507C22C2×C22⋊C4×D1111yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—42no—
512C4—222no—
513C4—222no—
514C4—222no—
515C4—444no—
516C4#1062238512yes—
517C4C2×#6696511yescharacteristic
518C4C2×#6696911yescharacteristic
519C4#1062330511yescharacteristic
520C4#1062330911yescharacteristic
521C2—22no—
522C2—82no—
523C2—442no—
524C2#1307709711yescharacteristic
525C2C2×#1062238511yescharacteristic
526C2#1307714011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1547C2
socleC22×C11C22×C22⋊C4
prime radical#13082523C2
cosocleC42×C11C24
hypercenter#1547D11
hypocenterC11#17727
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
2. #13077725C2semidirect
3. #13077284C2semidirect
4. #13067318C2semidirect
5. #13067313C2semidirect
6. #13067302C2semidirect
7. #13067279C2semidirect
8. #13067265C2semidirect
9. #13067262C2semidirect
10. C2×#10622120C2semidirect
11. C11×#1547C2semidirect
193. #1547D11semidirect
449. C11#17727semidirect

Maximal subgroups

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

subgroupindex
#130825232
#130777252
#130772842
#130673182
#130673132
#130673022
#130672792
#130672652
#130672622
C2×#106221202
C11×#15472
#1772711