Finite Group Databasebeta

← #14763231

Subgroups — #14763231

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic
3#13077247C211yesmaximal, characteristic
4#13069606C211yesmaximal, characteristic, complemented
5#13069605C211yesmaximal, characteristic, complemented
6#13069604C211yesmaximal, characteristic, complemented
7#13069603C214yesmaximal, complemented
8#13068695C214yesmaximal
9C11×#1997C211yesmaximal, characteristic, complemented
10C22×Q8×D11C412yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997C412yes—
13D11×C4⋊Q8—21no—
14D11×C4⋊Q8—21no—
15D11×C4⋊Q8—21no—
16D11×C4⋊Q8—21no—
17D11×C4⋊Q8—21no—
18D11×C4⋊Q8—21no—
19D11×C4⋊Q8—21no—
20D11×C4⋊Q8—21no—
21C2×C4⋊C4×D11C412yes—
22C2×C4⋊C4×D11C2212yes—
23C2×#66941C412yes—
24C2×#66941C2212yes—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#423C2211yescharacteristic
28C4×C11×M16C2211yescharacteristic
29#10622739C2212yes—
30#10622739C2212yes—
31#10622731C2212yes—
32M16×Dic11C2212yes—
33#10622537C2211yescharacteristic
34C4×#4318C2211yescharacteristic
35#10622448—21no—
36#10622448—21no—
37#10622446—21no—
38#10622446—21no—
39#10622318—21no—
40#10622318—21no—
41#10622298—21no—
42#10622298—21no—
43C11×#343C2214yes—
44#10622192C2214yes—
45#10622192C2214yes—
46#10622168C2214yes—
47C22×Q8×C11C2×C412yes—
48C2×Q8×D11—22no—
49C2×Q8×D11—22no—
50C2×Q8×D11—22no—
51C2×Q8×D11—22no—
52C2×Q8×D11—48no—
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C414yes—
56C22×C4×D11C2311yescharacteristic
57C22×Dic22C2×C412yes—
58C22×Dic22C2×C414yes—
59C2×C11×M16C2312yes—
60C2×C11×M16C2312yes—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C2×C11×C4⋊C4C2×C412yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2311yescharacteristic
68#66997—22no—
69#66997—22no—
70#66997—22no—
71#66997—22no—
72C2×C4⋊Dic11C2×C412yes—
73C2×C4⋊Dic11C2312yes—
74C2×Dic11⋊C4C2×C414yes—
75C2×Dic11⋊C4C2×C414yes—
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11C2×C411yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×#4318C2312yes—
80C2×#4318C2312yes—
81C4⋊C4×D11—22no—
82C4⋊C4×D11—22no—
83C4⋊C4×D11—22no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11—22no—
86C4⋊C4×D11—22no—
87C4⋊C4×D11—22no—
88C4⋊C4×D11—22no—
89#66941—22no—
90#66941—22no—
91#66941—22no—
92#66941—22no—
93#66941—22no—
94#66941—22no—
95#66941—22no—
96#66941—22no—
97C42×D11D411yescharacteristic
98C42×D11D411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11D411yescharacteristic
105#66922—21no—
106#66922—21no—
107#66922—21no—
108#66922—21no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×#97—21no—
112C4×C8×C11—21no—
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117#66879—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120C8×Dic11—22no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)—21no—
123#66867—21no—
124C4×C11⋊C8—21no—
125#21829—111nomaximal, Sylow
126C23×D11C22×C411yescharacteristic
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—44no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C414yes—
133C22×C4×C11C2411yescharacteristic
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C414yes—
138Q8×D11—48no—
139Q8×D11—48no—
140Q8×D11—48no—
141Q8×D11—48no—
142C2×C4×D11—24no—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—48no—
149C2×C4×D11C22⋊C411yescharacteristic
150C2×C4×D11C22⋊C411yescharacteristic
151C2×C4×D11C22⋊C411yescharacteristic
152C2×C4×D11C22⋊C411yescharacteristic
153C2×C4×D11C22⋊C411yescharacteristic
154C2×C4×D11C22⋊C411yescharacteristic
155C2×C4×D11C22⋊C411yescharacteristic
156C2×C4×D11C22⋊C411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C2×C4×D11C2×D411yescharacteristic
159C2×C4×D11C2×D411yescharacteristic
160C2×C4×D11C2×D411yescharacteristic
161C2×Dic22—24no—
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—44no—
166C2×Dic22—48no—
167C11×M16—22no—
168C11×M16—24no—
169C11×M16—22no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C42×C11C2×D411yescharacteristic
177C42×C11C2×D411yescharacteristic
178C42×C11C2×D411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184Dic11⋊C4—24no—
185Dic11⋊C4—24no—
186Dic11⋊C4—24no—
187Dic11⋊C4—24no—
188C4×Dic11C22⋊C411yescharacteristic
189C4×Dic11C22⋊C411yescharacteristic
190C4×Dic11C22⋊C411yescharacteristic
191C4×Dic11C22⋊C411yescharacteristic
192C4×Dic11C22⋊C411yescharacteristic
193C4×Dic11C22⋊C411yescharacteristic
194C4×Dic11C22⋊C411yescharacteristic
195C4×Dic11C22⋊C411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200#4318—24no—
201#4318—22no—
202#4318—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C22×C4⋊Q8—111no—
206#2920—111no—
207#2920—111no—
208#1997—111no—
209#1997—111no—
210#1997—114no—
211#1997—111no—
212#1997D1111yescharacteristic, complemented
213#1821—114no—
214C23×C11C23×C411yescharacteristic
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11C2×C22⋊C411yescharacteristic
219C22×D11C2×C22⋊C411yescharacteristic
220Q8×C11—44no—
221Q8×C11—44no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—44no—
226C2×C4×C11C2×C22⋊C411yescharacteristic
227C2×C4×C11C2×C22⋊C411yescharacteristic
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C112−1+412yes—
233C2×C4×C112−1+412yes—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—44no—
239C2×Dic11C2×C22⋊C411yescharacteristic
240C2×Dic11C2×C22⋊C411yescharacteristic
241C2×Dic11C2×C22⋊C411yescharacteristic
242C2×Dic11C2×C22⋊C411yescharacteristic
243C2×Dic11C2×C22⋊C411yescharacteristic
244C2×Dic11C2×C22⋊C411yescharacteristic
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—21no—
248C4×D11—21no—
249C4×D11—22no—
250C4×D11—22no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—22no—
257C4×D11—48no—
258C4×D11—48no—
259C4×D11#10014yes—
260C4×D11#10114yes—
261Dic22—48no—
262Dic22—44no—
263Dic22—44no—
264Dic22—48no—
265C8×C11—42no—
266C8×C11—42no—
267C11⋊C8—42no—
268C11⋊C8—42no—
269C23×Q8—112no—
270C2×C4⋊Q8—112no—
271C2×C4⋊Q8—112no—
272C2×C4⋊Q8—112no—
273C2×C4⋊Q8—111no—
274C2×C4⋊Q8—221no—
275C2×C4⋊Q8—221no—
276C2×C4⋊Q8—221no—
277C2×C4⋊Q8—221no—
278C2×C4⋊Q8—221no—
279C2×C4⋊Q8—221no—
280C2×C4⋊Q8—221no—
281C2×C4⋊Q8—221no—
282C2×C4⋊Q8C2×D1111yescharacteristic
283C22×C4⋊C4—112no—
284C22×C4⋊C4—112no—
285C22×C42—111no—
286#432—221no—
287#432—221no—
288#432—221no—
289#432—221no—
290#431—221no—
291#431—221no—
292#431—221no—
293#431—221no—
294#423—112no—
295#423—111no—
296#423C2×D1111yescharacteristic
297#407—112no—
298#407—112no—
299C4×M16—112no—
300C4×M16—111no—
301C4×M16C2×D1111yescharacteristic
302#343—114no—
303#343—114no—
304#343—114no—
305#343C2×D1114yes—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11C22×C22⋊C411yescharacteristic
309C22×C11#51912yes—
310C2×D11—28no—
311C2×D11—21no—
312C2×D11—21no—
313C2×D11—21no—
314C2×D11—21no—
315C2×D11C2×#10012yes—
316C2×D11C2×#10112yes—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—44no—
320C4×C11C2×#10012yes—
321C4×C11C2×#10112yes—
322C4×C11#53611yescharacteristic
323C4×C11#53612yes—
324C4×C11#53611yescharacteristic
325Dic11—21no—
326Dic11—21no—
327Dic11—21no—
328Dic11—21no—
329Dic11—44no—
330Dic11C2×#10012yes—
331Dic11C2×#10112yes—
332C22×Q8—114no—
333C22×Q8—112no—
334C22×Q8—222no—
335C22×Q8—222no—
336C22×Q8—222no—
337C22×Q8—222no—
338C22×Q8—448no—
339C22×Q8C4×D1112yes—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—114no—
344C2×M16—112no—
345C2×M16—112no—
346C2×M16C22×D1112yes—
347C2×M16C22×D1112yes—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—222no—
353C4⋊Q8—222no—
354C4⋊Q8—222no—
355C4⋊Q8—222no—
356C4⋊Q8—222no—
357C4⋊Q8—222no—
358C4⋊Q8—222no—
359C4⋊Q8—222no—
360C4⋊Q8—222no—
361C4⋊Q8—222no—
362C4⋊Q8—222no—
363C4⋊Q8—222no—
364C4⋊Q8—221no—
365C4⋊Q8—221no—
366C4⋊Q8—221no—
367C4⋊Q8—221no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4C4×D1112yes—
381C2×C4⋊C4C22×D1112yes—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42C22×D1111yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—222no—
397C4⋊C8—222no—
398C4⋊C8—221no—
399C4⋊C8—221no—
400C22⋊C8—222no—
401C22⋊C8—222no—
402C22⋊C8—222no—
403C22⋊C8—222no—
404#97—21no—
405#97—222no—
406#97—221no—
407C4×C8—21no—
408C4×C8—222no—
409C4×C8—221no—
410C2×C11—22no—
411C2×C11#231011yescharacteristic
412C2×C11C22×#10011yescharacteristic
413C2×C11C22×#10111yescharacteristic
414D11—22no—
415D11—22no—
416C24—111no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—44no—
420C2×Q8—224no—
421C2×Q8—224no—
422C2×Q8—222no—
423C2×Q8—222no—
424C2×Q8—444no—
425C2×Q8—448no—
426C2×Q8—448no—
427C2×Q8—448no—
428C2×Q8—448no—
429C2×Q8—448no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—114no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—448no—
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×C4×D1114yes—
456C22×C4C23×D1111yescharacteristic
457M16—22no—
458M16—22no—
459M16—24no—
460M16—224no—
461M16—222no—
462M16—222no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—222no—
466C2×C8—222no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C4⋊C4—222no—
478C4⋊C4—222no—
479C42—111no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—111no—
484C42—111no—
485C42—111no—
486C42—111no—
487C42—111no—
488C42—111no—
489C42—111no—
490C42—111no—
491C42D4×D1111yescharacteristic
492C42D4×D1111yescharacteristic
493C42D4×D1111yescharacteristic
494C42D4×D1111yescharacteristic
495C11#2182911yescharacteristic, complemented, Sylow
496C23—111no—
497C23—111no—
498C23—222no—
499C23—222no—
500C23—222no—
501C23C22×C4×D1111yescharacteristic
502Q8—44no—
503Q8—44no—
504Q8—444no—
505Q8—448no—
506Q8—448no—
507Q8—444no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—111no—
513C2×C4—111no—
514C2×C4—114no—
515C2×C4—114no—
516C2×C4—111no—
517C2×C4—111no—
518C2×C4—111no—
519C2×C4—111no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—224no—
536C2×C4—448no—
537C2×C4—448no—
538C2×C4—444no—
539C2×C4C22⋊C4×D1111yescharacteristic
540C2×C4C22⋊C4×D1111yescharacteristic
541C2×C4C22⋊C4×D1111yescharacteristic
542C2×C4C22⋊C4×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4#6704012yes—
546C2×C4#6704312yes—
547C8—42no—
548C8—42no—
549C8—442no—
550C8—442no—
551C22—21no—
552C22—21no—
553C22—112no—
554C22—112no—
555C22—228no—
556C22—221no—
557C22—221no—
558C22—221no—
559C22—221no—
560C22C2×C22⋊C4×D1111yescharacteristic
561C22#1062310312yes—
562C4—21no—
563C4—21no—
564C4—44no—
565C4—112no—
566C4—112no—
567C4—221no—
568C4—221no—
569C4—221no—
570C4—221no—
571C4—444no—
572C4D11×#10012yes—
573C4D11×#10112yes—
574C4#1062315912yes—
575C4#1062320611yescharacteristic
576C4#1062325511yescharacteristic
577C2—22no—
578C2—222no—
579C2—222no—
580C2#1307119911yescharacteristic
581C2C2×D11×#10011yescharacteristic
582C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1997C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22×C4
cosocleC22×C4×C11C24
hypercenter#1997D11
hypocenterC11#21829
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. #13069606C2semidirect
5. #13069605C2semidirect
6. #13069604C2semidirect
7. #13069603C2semidirect
9. C11×#1997C2semidirect
212. #1997D11semidirect
495. C11#21829semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130772482
#130772472
#130696062
#130696052
#130696042
#130696032
#130686952
C11×#19972
#2182911