Finite Group Databasebeta

← #14722174

Subgroups — #14722174

Order 2816.

972 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic
3D11×#431C211yesmaximal, characteristic
4#13067313C214yesmaximal, complemented
5#13067302C211yesmaximal, characteristic, complemented
6#13067300C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067279C214yesmaximal, complemented
9C11×#1546C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13#10623259—21no—
14#10623259—21no—
15#10623259—21no—
16#10623259—21no—
17#10623259C412yes—
18#10623259C412yes—
19#10623259C2212yes—
20#10623259C2212yes—
21C2×#66950—21no—
22C2×#66945C412yes—
23C2×#66943C412yes—
24C2×#66940—21no—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29#10622739—21no—
30M16×Dic11—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622448—21no—
34#10622448C2212yes—
35#10622446—21no—
36#10622446C2212yes—
37#10622446C2212yes—
38D11×C4⋊C8C2212yes—
39D11×C22⋊C8—21no—
40#10622331—21no—
41#10622298—21no—
42C4×C8×D11—21no—
43C11×#332C2214yescomplemented
44#10622185C2214yescomplemented
45#10622124C2214yescomplemented
46#10622120C2214yescomplemented
47C22×Q8×C11—21no—
48C22×C4×D11C2×C411yescharacteristic
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×Dic22—21no—
52C2×C11×M16—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2×C412yes—
56C11×C4⋊Q8C2312yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C42×C11C2311yescharacteristic
60#66999—22no—
61#66999—22no—
62#66999—22no—
63#66999—22no—
64Q8×Dic11—22no—
65Q8×Dic11—22no—
66Q8×Dic11—22no—
67Q8×Dic11—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11C2×C412yes—
72C2×Dic11⋊C4—22no—
73C2×C4×Dic11—22no—
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×#4318—21no—
78C2×C8×D11—22no—
79#66950—22no—
80#66950—22no—
81#66950—22no—
82#66950—22no—
83#66945—22no—
84#66945—22no—
85#66945C2×C414yes—
86#66945C2×C414yes—
87#66943—22no—
88#66943—22no—
89#66943C2×C414yes—
90#66943C2×C414yes—
91#66940—22no—
92#66940—22no—
93#66940—22no—
94#66940—22no—
95C42×D11C2×C411yescharacteristic
96C42×D11C2×C411yescharacteristic
97C42×D11D411yescharacteristic
98C42×D11D411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11C2311yescharacteristic
102C42×D11C2311yescharacteristic
103#66922—21no—
104#66922—21no—
105#66922C2×C412yes—
106#66922C2312yes—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2312yes—
109C11×C4⋊C8C2312yes—
110C11×C22⋊C8—21no—
111C4×C8×C11—21no—
112C22⋊(C11⋊C8)—21no—
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116#66879—22no—
117Dic11⋊C8—22no—
118C8×Dic11—22no—
119C8×Dic11—22no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123C4×C11⋊C8—21no—
124#17715—111nomaximal, Sylow
125C23×D11C22⋊C411yescharacteristic
126C2×Q8×C11—22no—
127C2×Q8×C11—22no—
128C2×Q8×C11—42no—
129C2×Q8×C11—42no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×Dic11—22no—
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137C22×Dic11C22⋊C411yescharacteristic
138C2×C4×D11—24no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—42no—
142C2×C4×D11C22⋊C411yescharacteristic
143C2×C4×D11C22⋊C411yescharacteristic
144C2×C4×D11C22⋊C411yescharacteristic
145C2×C4×D11C22⋊C411yescharacteristic
146C2×C4×D11C22⋊C411yescharacteristic
147C2×C4×D11C22⋊C411yescharacteristic
148C2×C4×D11C22×C411yescharacteristic
149C2×C4×D11C22×C411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×C4×D11C2×D411yescharacteristic
152C2×C4×D11C2×D411yescharacteristic
153C2×C4×D11C2×D411yescharacteristic
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—44no—
157C11×M16—42no—
158C2×C8×C11—22no—
159C2×C8×C11—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C22×C414yes—
164C42×C11C22×C411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C42×C11C2411yescharacteristic
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—24no—
170C4⋊Dic11—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11C22×C414yes—
176Dic11⋊C4—24no—
177Dic11⋊C4—24no—
178C4×Dic11—24no—
179C4×Dic11—24no—
180C4×Dic11C22⋊C411yescharacteristic
181C4×Dic11C22⋊C411yescharacteristic
182C4×Dic11C22⋊C411yescharacteristic
183C4×Dic11C22⋊C411yescharacteristic
184C4×Dic11C22⋊C411yescharacteristic
185C4×Dic11C22⋊C411yescharacteristic
186C4×Dic11C22×C411yescharacteristic
187C4×Dic11C22×C411yescharacteristic
188C4×Dic11C2×D411yescharacteristic
189C4×Dic11C2×D411yescharacteristic
190C4×Dic11C2×D411yescharacteristic
191C4×Dic11C2×D411yescharacteristic
192#4318—42no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C8×D11—44no—
196C2×#533—111no—
197#2920—111no—
198C2×#431—111no—
199#1552—114no—
200#1549—111no—
201#1549—111no—
202#1546—111no—
203#1546D1111yescharacteristic, complemented
204#1544—114no—
205C23×C11C2×C22⋊C411yescharacteristic
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—41no—
209C22×D11C2×C22⋊C411yescharacteristic
210C22×D11C2×C22⋊C411yescharacteristic
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—44no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—44no—
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11#13512yes—
222C2×C4×C11#13512yes—
223C2×C4×C11C23×C411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—41no—
230C2×Dic11—44no—
231C2×Dic11C2×C22⋊C411yescharacteristic
232C2×Dic11C2×C22⋊C411yescharacteristic
233C2×Dic11C2×C22⋊C411yescharacteristic
234C2×Dic11C2×C22⋊C411yescharacteristic
235C2×Dic11C2×C22⋊C411yescharacteristic
236C2×Dic11C2×C22⋊C411yescharacteristic
237C4×D11—22no—
238C4×D11—21no—
239C4×D11—21no—
240C4×D11—21no—
241C4×D11—21no—
242C4×D11—22no—
243C4×D11—22no—
244C4×D11—22no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—22no—
248C4×D11—41no—
249C4×D11—41no—
250C4×D11#10114yes—
251Dic22—44no—
252Dic22—44no—
253C8×C11—42no—
254C8×C11—42no—
255C11⋊C8—42no—
256C11⋊C8—42no—
257#533—112no—
258#533—112no—
259#533—112no—
260#533—112no—
261#533—221no—
262#533—221no—
263#533—221no—
264#533—221no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8C2×D1111yescharacteristic
267C2×#125—112no—
268C2×C22⋊Q8—221no—
269C2×C22⋊Q8—221no—
270C2×C4×Q8—221no—
271C2×C4×Q8—221no—
272C2×#117—112no—
273C22×C42—111no—
274#432—112no—
275#432—221no—
276#431—111no—
277#431—112no—
278#431—112no—
279#431—221no—
280#431—221no—
281#431—221no—
282#431C2×D1111yescharacteristic
283#423—111no—
284#423C2×D1111yescharacteristic
285C2×C4⋊C8—112no—
286#407—221no—
287C2×C22⋊C8—221no—
288C4×M16—221no—
289C2×C4×C8—221no—
290#332—114no—
291#332—114no—
292#332—114no—
293#332C2×D1114yescomplemented
294C22×C11—21no—
295C22×C11—21no—
296C22×C11#41612yes—
297C22×C11C22×C22⋊C411yescharacteristic
298C2×D11—21no—
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—21no—
302C2×D11—21no—
303C2×D11—44no—
304C2×D11C2×#10112yes—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—44no—
308C4×C11C2×#10112yes—
309C4×C11#41612yes—
310C4×C11C2×#13511yescharacteristic
311C4×C11C2×#13511yescharacteristic
312C4×C11#57512yes—
313Dic11—21no—
314Dic11—21no—
315Dic11—21no—
316Dic11—21no—
317Dic11—21no—
318Dic11—44no—
319Dic11C2×#10112yes—
320C22×Q8—21no—
321C22×Q8—221no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—111no—
325C2×M16—21no—
326C2×M16—221no—
327C22×C8—222no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—112no—
331C4⋊Q8—112no—
332C4⋊Q8—221no—
333C4⋊Q8—221no—
334C4⋊Q8C4×D1112yes—
335C4⋊Q8C22×D1112yes—
336#125—114no—
337#125—114no—
338#125—222no—
339#125—222no—
340C22⋊Q8—222no—
341C22⋊Q8—222no—
342C22⋊Q8—222no—
343C22⋊Q8—222no—
344C22⋊Q8—222no—
345C22⋊Q8—222no—
346C22⋊Q8—222no—
347C22⋊Q8—222no—
348C4×Q8—222no—
349C4×Q8—222no—
350C4×Q8—222no—
351C4×Q8—222no—
352C4×Q8—222no—
353C4×Q8—222no—
354C4×Q8—222no—
355C4×Q8—222no—
356#117—114no—
357#117—114no—
358#117—222no—
359#117—222no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4C4×D1112yes—
366C2×C22⋊C4—222no—
367C2×C42—111no—
368C2×C42—111no—
369C2×C42—111no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—222no—
379C2×C42C22×D1111yescharacteristic
380C4⋊C8—21no—
381C4⋊C8—112no—
382C4⋊C8—112no—
383C4⋊C8—222no—
384C4⋊C8—221no—
385C4⋊C8C22×D1112yes—
386C4⋊C8C22×D1112yes—
387C22⋊C8—21no—
388C22⋊C8—222no—
389C22⋊C8—222no—
390C22⋊C8—222no—
391C22⋊C8—221no—
392#97—222no—
393C4×C8—21no—
394C4×C8—222no—
395C4×C8—222no—
396C4×C8—221no—
397C2×C11—22no—
398C2×C11C22×#10111yescharacteristic
399C2×C11C2×#41611yescharacteristic
400C2×C11#289611yescharacteristic
401D11—22no—
402D11—41no—
403C24—111no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—42no—
407C2×Q8—42no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—444no—
411C22×C4—22no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—224no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—442no—
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4D4×D1111yescharacteristic
435M16—42no—
436M16—442no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—444no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—114no—
446C4⋊C4—224no—
447C4⋊C4—224no—
448C4⋊C4—224no—
449C4⋊C4—224no—
450C4⋊C4—222no—
451C4⋊C4—222no—
452C4⋊C4—222no—
453C4⋊C4C2×C4×D1114yes—
454C22⋊C4—224no—
455C22⋊C4—224no—
456C42—111no—
457C42—111no—
458C42—111no—
459C42—111no—
460C42—111no—
461C42—111no—
462C42—111no—
463C42—111no—
464C42—111no—
465C42—111no—
466C42—111no—
467C42—111no—
468C42—224no—
469C42—224no—
470C42C2×C4×D1111yescharacteristic
471C42D4×D1111yescharacteristic
472C42D4×D1111yescharacteristic
473C42C23×D1111yescharacteristic
474C11#1771511yescharacteristic, complemented, Sylow
475C23—111no—
476C23—111no—
477C23—222no—
478C23—222no—
479C23—441no—
480C23C22⋊C4×D1111yescharacteristic
481Q8—42no—
482Q8—42no—
483Q8—44no—
484Q8—444no—
485Q8—444no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—44no—
490C2×C4—111no—
491C2×C4—114no—
492C2×C4—111no—
493C2×C4—111no—
494C2×C4—111no—
495C2×C4—111no—
496C2×C4—111no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—444no—
515C2×C4C22⋊C4×D1111yescharacteristic
516C2×C4C22⋊C4×D1111yescharacteristic
517C2×C4C22⋊C4×D1111yescharacteristic
518C2×C4#6696512yes—
519C2×C4#6696912yes—
520C2×C4C22×C4×D1111yescharacteristic
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C8—42no—
524C8—42no—
525C8—442no—
526C8—442no—
527C22—21no—
528C22—21no—
529C22—112no—
530C22—221no—
531C22—221no—
532C22—221no—
533C22—221no—
534C22—221no—
535C22—444no—
536C22#1062238512yes—
537C22C2×C22⋊C4×D1111yescharacteristic
538C4—21no—
539C4—21no—
540C4—44no—
541C4—112no—
542C4—221no—
543C4—221no—
544C4—221no—
545C4—221no—
546C4—221no—
547C4—444no—
548C4D11×#10112yes—
549C4#1062238512yes—
550C4C2×#6696511yescharacteristic
551C4C2×#6696911yescharacteristic
552C4#1062330812yes—
553C2—22no—
554C2—222no—
555C2—441no—
556C2C2×D11×#10111yescharacteristic
557C2C2×#1062238511yescharacteristic
558C2#1307713411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1546D11
hypocenterC11#17715
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
4. #13067313C2semidirect
5. #13067302C2semidirect
6. #13067300C2semidirect
7. #13067288C2semidirect
8. #13067279C2semidirect
9. C11×#1546C2semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
203. #1546D11semidirect
293. #332C2×D11semidirect
474. C11#17715semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130772482
D11×#4312
#130673132
#130673022
#130673002
#130672882
#130672792
C11×#15462
#1771511