Finite Group Databasebeta

← #14722264

Subgroups — #14722264

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082523C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic, complemented
3#13077281C211yesmaximal, characteristic, complemented
4#13067323C212yesmaximal, complemented
5#13067308C212yesmaximal, complemented
6#13067296C211yesmaximal, characteristic, complemented
7#13067293C211yesmaximal, characteristic, complemented
8#13067275C212yesmaximal, complemented
9#13067272C212yesmaximal, complemented
10C2×#10622119C211yesmaximal, characteristic, complemented
11C11×#1540C211yesmaximal, characteristic, complemented
12C11×#532C2211yescharacteristic
13#10623364—21no—
14#10623358—21no—
15#10623259C2212yes—
16#10623247C2212yes—
17#10623213—22no—
18#10623149—22no—
19#10623129C414yes—
20#10623094—21no—
21#10623086C412yes—
22#10623074—21no—
23#10623073C412yes—
24C4×#4339C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28#10622723—21no—
29#10622714—21no—
30#10622537C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622453—22no—
33#10622448C2212yes—
34#10622446C2212yes—
35#10622446C2212yes—
36D11×C4⋊C8C2212yes—
37(C22⋊D11)⋊C8—22no—
38C8×D44—21no—
39C8×Dic22—21no—
40C11×#332C2211yescharacteristic
41C11×#332C2211yescharacteristic
42C11×#331C2211yescharacteristic
43C11×#331C2211yescharacteristic
44#10622185C2212yes—
45#10622182C2212yes—
46#10622119C2212yes—
47#10622119C2212yes—
48#10622119C2212yes—
49#10622119C2212yes—
50C2×C11×#41—21no—
51C2×#4341C2×C414yes—
52C2×#4339D411yescharacteristic
53C22×Dic22C2×C412yes—
54C22×C8×C11—21no—
55C11×C4⋊Q8C2311yescharacteristic
56C11×#127C2311yescharacteristic
57C11×#124—21no—
58C11×#121—21no—
59C11×#121C2×C412yes—
60C4×D4×C11—21no—
61C4×D4×C11C2×C412yes—
62C2×C42×C11C2311yescharacteristic
63#66999—22no—
64Q8×Dic11—22no—
65#66992—24no—
66#66991—22no—
67#66991—22no—
68#66989C2×C414yes—
69D4×Dic11—24no—
70D4×Dic11—22no—
71D4×Dic11—22no—
72#66983—22no—
73C4×C22⋊D11C2×C412yes—
74C4×C22⋊D11D412yes—
75#66979—22no—
76#66979D411yescharacteristic
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80#66977—22no—
81C2×#4318—21no—
82C22×C11⋊C8—21no—
83C2×C8×D11—22no—
84#66950C2×C414yes—
85#66945—22no—
86#66943—22no—
87#66940C2×C414yes—
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⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8—21no—
108C4×C8×C11—21no—
109(C2×D11)⋊C8—22no—
110(C2×D11)⋊C8—22no—
111(C2×D11)⋊C8—22no—
112#66879—22no—
113Dic11⋊C8—22no—
114C8×Dic11—22no—
115C8×Dic11—22no—
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)—21no—
118C4⋊(C11⋊C8)C2312yes—
119C4⋊(C11⋊C8)C2312yes—
120#17726—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—84no—
137#4339—22no—
138#4339—22no—
139C2×D44C22⋊C411yescharacteristic
140C2×C4×D11C22×C412yes—
141C2×C4×D11C2×D412yes—
142C2×C4×D11C2×D412yes—
143C2×Dic22—22no—
144C2×Dic22—82no—
145C2×Dic22C22⋊C411yescharacteristic
146C2×Dic22C22×C414yes—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—42no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4C22×C412yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C42×C11C22×C411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2411yescharacteristic
160C22⋊Dic11—24no—
161C22⋊Dic11—24no—
162C22⋊Dic11C22⋊C412yes—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4C22⋊C412yes—
165(C2×D11)⋊C4C22⋊C412yes—
166C4⋊Dic11—24no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—22no—
171C4⋊Dic11C22⋊C411yescharacteristic
172C4⋊Dic11C22⋊C411yescharacteristic
173Dic11⋊C4—24no—
174Dic11⋊C4C22⋊C412yes—
175Dic11⋊C4C22⋊C412yes—
176C4×Dic11—24no—
177C4×Dic11C22×C412yes—
178C4×Dic11C2×D412yes—
179C4×Dic11C2×D412yes—
180#4318—42no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—81no—
184C8×D11—82no—
185#3511—111no—
186#2988—111no—
187#2925—111no—
188#1554—112no—
189#1551—112no—
190#1548—111no—
191#1547—111no—
192#1543—112no—
193#1542—112no—
194C2×#333—111no—
195#1540D1111yescharacteristic, complemented
196C23×C11—22no—
197C23×C11C2×C22⋊C411yescharacteristic
198C22×D11C2×C22⋊C412yes—
199Q8×C11—41no—
200Q8×C11—41no—
201D4×C11—42no—
202D4×C11—44no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—41no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—44no—
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C2×C22⋊C411yescharacteristic
215C2×C4×C11#13512yes—
216C2×C4×C11#13512yes—
217C2×C4×C11C23×C411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—24no—
221C22⋊D11—84no—
222C2×Dic11—24no—
223C2×Dic11—84no—
224C2×Dic11—82no—
225C2×Dic11C2×C22⋊C412yes—
226C2×Dic11C2×C22⋊C412yes—
227C2×Dic11C2×C22⋊C412yes—
228D44—22no—
229C4×D11—22no—
230C4×D11—22no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—42no—
234Dic22—22no—
235Dic22—44no—
236Dic22—82no—
237C8×C11—41no—
238C8×C11—41no—
239C8×C11—41no—
240C8×C11—41no—
241C11⋊C8—42no—
242C11⋊C8—42no—
243#556—112no—
244#555—221no—
245#554—221no—
246#553—222no—
247#548—114no—
248#547—112no—
249#542—222no—
250#537—221no—
251#533—112no—
252#532—112no—
253#532C2×D1111yescharacteristic
254C2×C4⋊Q8—111no—
255#520—221no—
256C4×#41—111no—
257C8×Q8—221no—
258C8×D4—221no—
259C8×D4—222no—
260#433—222no—
261#432—112no—
262#431—112no—
263#431—112no—
264#431C2×D1111yescharacteristic
265#423—111no—
266C2×C4⋊C8—111no—
267C2×C4⋊C8—112no—
268C2×C4⋊C8C2×D1111yescharacteristic
269#408—221no—
270#405—221no—
271#333—112no—
272#333—112no—
273#333—112no—
274#333—112no—
275#332—112no—
276#332C2×D1111yescharacteristic
277#332C2×D1111yescharacteristic
278#331—112no—
279#331C2×D1111yescharacteristic
280#331C2×D1111yescharacteristic
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11#41612yes—
287C22×C11C22×C22⋊C411yescharacteristic
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—22no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11#41612yes—
296C4×C11C2×#13511yescharacteristic
297C4×C11C2×#13511yescharacteristic
298C4×C11#57711yescharacteristic
299C4×C11#57811yescharacteristic
300Dic11—22no—
301Dic11—22no—
302Dic11—22no—
303Dic11—44no—
304C2×#41—21no—
305C2×#41—111no—
306C2×#41—114no—
307C22×Q8—112no—
308C2×M16—221no—
309C22×C8—21no—
310C22×C8—222no—
311C22×C8—221no—
312C4⋊Q8—112no—
313C4⋊Q8—112no—
314C4⋊Q8—221no—
315C4⋊Q8—221no—
316C4⋊Q8C22×D1111yescharacteristic
317#127C22×D1111yescharacteristic
318#126—224no—
319#125—222no—
320#124—21no—
321#124—114no—
322#124—224no—
323#123—224no—
324C22⋊Q8—114no—
325C22⋊Q8—224no—
326C22⋊Q8—222no—
327C22⋊Q8—222no—
328#121—21no—
329#121—222no—
330#121—222no—
331#121—222no—
332#121—224no—
333#121C4×D1112yes—
334C4×Q8—111no—
335C4×Q8—111no—
336C4×Q8—114no—
337C4×Q8—222no—
338C4×D4—21no—
339C4×D4—112no—
340C4×D4—112no—
341C4×D4—111no—
342C4×D4—111no—
343C4×D4—222no—
344C4×D4—222no—
345C4×D4—224no—
346C4×D4C4×D1112yes—
347#117—111no—
348#117—112no—
349#117—222no—
350#117—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—221no—
354C2×C42—112no—
355C2×C42C22×D1111yescharacteristic
356C4⋊C8—21no—
357C4⋊C8—112no—
358C4⋊C8—112no—
359C4⋊C8—222no—
360C4⋊C8—221no—
361C4⋊C8—221no—
362C4⋊C8C22×D1111yescharacteristic
363C4⋊C8C22×D1111yescharacteristic
364C4⋊C8C22×D1111yescharacteristic
365C4⋊C8C22×D1111yescharacteristic
366C22⋊C8—21no—
367C22⋊C8—222no—
368C22⋊C8—222no—
369C22⋊C8—222no—
370#97—222no—
371C4×C8—21no—
372C4×C8—222no—
373C4×C8—222no—
374C2×C11—22no—
375C2×C11—82no—
376C2×C11#288811yescharacteristic
377C2×C11C2×#41611yescharacteristic
378C2×C11#289811yescharacteristic
379D11—42no—
380#41—42no—
381#41—42no—
382#41—222no—
383#41—222no—
384#41—884no—
385C2×Q8—21no—
386C2×Q8—111no—
387C2×Q8—114no—
388C2×Q8—222no—
389C2×Q8—882no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—112no—
394C2×D4—111no—
395C2×D4—224no—
396C2×D4C2×C4×D1112yes—
397C22×C4—22no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—224no—
402C22×C4—222no—
403C22×C4C2×C4×D1111yescharacteristic
404C22×C4D4×D1111yescharacteristic
405C22×C4D4×D1111yescharacteristic
406M16—442no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—42no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—882no—
415C2×C8—881no—
416C4⋊C4—21no—
417C4⋊C4—111no—
418C4⋊C4—111no—
419C4⋊C4—112no—
420C4⋊C4—112no—
421C4⋊C4—224no—
422C4⋊C4—224no—
423C4⋊C4—222no—
424C4⋊C4—222no—
425C4⋊C4—222no—
426C4⋊C4—222no—
427C4⋊C4C2×C4×D1112yes—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—112no—
431C22⋊C4—112no—
432C22⋊C4—112no—
433C22⋊C4—224no—
434C22⋊C4—224no—
435C22⋊C4—224no—
436C42—112no—
437C42—112no—
438C42—112no—
439C42—224no—
440C42C2×C4×D1111yescharacteristic
441C42D4×D1111yescharacteristic
442C42D4×D1111yescharacteristic
443C42C23×D1111yescharacteristic
444C11#1772611yescharacteristic, complemented, Sylow
445C23—22no—
446C23—112no—
447C23C22⋊C4×D1111yescharacteristic
448Q8—41no—
449Q8—41no—
450Q8—222no—
451Q8—444no—
452Q8—882no—
453D4—42no—
454D4—44no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—41no—
459D4—224no—
460D4—222no—
461D4—884no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—112no—
468C2×C4—112no—
469C2×C4—112no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—224no—
475C2×C4—442no—
476C2×C4—884no—
477C2×C4—882no—
478C2×C4C22⋊C4×D1111yescharacteristic
479C2×C4C22⋊C4×D1111yescharacteristic
480C2×C4C22⋊C4×D1111yescharacteristic
481C2×C4#6696512yes—
482C2×C4#6696912yes—
483C2×C4C22×C4×D1111yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×D4×D1111yescharacteristic
486C8—41no—
487C8—41no—
488C8—41no—
489C8—41no—
490C8—442no—
491C8—442no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22—222no—
498C22—222no—
499C22—222no—
500C22#1062238512yes—
501C22C2×C22⋊C4×D1111yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—42no—
506C4—222no—
507C4—222no—
508C4—222no—
509C4—444no—
510C4#1062238512yes—
511C4C2×#6696511yescharacteristic
512C4C2×#6696911yescharacteristic
513C4#1062330111yescharacteristic
514C4#1062330211yescharacteristic
515C2—22no—
516C2—82no—
517C2—442no—
518C2#1307709311yescharacteristic
519C2C2×#1062238511yescharacteristic
520C2#1307714511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1540C2
socleC22×C11C22×C22⋊C4
prime radical#13082523C2
cosocleC42×C11C24
hypercenter#1540D11
hypocenterC11#17726
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #13077724C2semidirect
3. #13077281C2semidirect
4. #13067323C2semidirect
5. #13067308C2semidirect
6. #13067296C2semidirect
7. #13067293C2semidirect
8. #13067275C2semidirect
9. #13067272C2semidirect
10. C2×#10622119C2semidirect
11. C11×#1540C2semidirect
195. #1540D11semidirect
444. C11#17726semidirect

Maximal subgroups

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

subgroupindex
#130825232
#130777242
#130772812
#130673232
#130673082
#130672962
#130672932
#130672752
#130672722
C2×#106221192
C11×#15402
#1772611