Finite Group Databasebeta

← #14769945

Subgroups — #14769945

Order 2816.

1106 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623042C211yesmaximal, characteristic
2#13077348C212yesmaximal
3#13069603C212yesmaximal, complemented
4#13069083C212yesmaximal, complemented
5#13069082C212yesmaximal, complemented
6#13068695C211yesmaximal, characteristic, complemented
7#13068611C211yesmaximal, characteristic, complemented
8#13068411C211yesmaximal, characteristic, complemented
9C2×#10622168C211yesmaximal, characteristic, complemented
10D11×#343C211yesmaximal, characteristic, complemented
11C11×#1821C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×C4×C22⋊D11C412yes—
14C2×C4×C22⋊D11C2211yescharacteristic
15C2×#66977C412yes—
16C2×#66977C2211yescharacteristic
17C22×#4318C2212yes—
18C2×M16×D11C2212yes—
19#10623042—22no—
20#10623042—22no—
21#10623042—22no—
22#10623042—22no—
23C2×#66950C2211yescharacteristic
24C2×#66949C412yes—
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×#66942C412yes—
27C2×#66941C2211yescharacteristic
28C2×#66940C2211yescharacteristic
29C11×#407C2212yes—
30C2×#66888C2212yes—
31C2×#66888C2212yes—
32#10622739C2212yes—
33#10622731C2212yes—
34M16×Dic11C2212yes—
35#10622343—22no—
36#10622342—22no—
37#10622341—22no—
38(C22⋊D11)⋊C8—22no—
39C11×#343C2212yes—
40C11×#343C2211yescharacteristic
41C11×#343C2211yescharacteristic
42#10622192C2212yes—
43#10622192C2212yes—
44#10622168C2212yes—
45#10622168C2211yescharacteristic
46#10622168C2211yescharacteristic
47C23×C4×C11C2×C412yes—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11C2×C411yescharacteristic
50C22×C4×D11C2×C412yes—
51C22×C4×D11C2311yescharacteristic
52C22×Dic22C2×C412yes—
53C22×Dic22C2311yescharacteristic
54C2×C11×M16C2312yes—
55C2×C11×M16C2312yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4C2×C412yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C22⋊Dic11C2×C412yes—
62C2×C22⋊Dic11C2×C411yescharacteristic
63C4×C22⋊D11—22no—
64C4×C22⋊D11—22no—
65C4×C22⋊D11—22no—
66C4×C22⋊D11—22no—
67C4×C22⋊D11D412yes—
68C4×C22⋊D11D412yes—
69C4×C22⋊D11D412yes—
70C4×C22⋊D11D412yes—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×C4⋊Dic11C2×C412yes—
74C2×C4⋊Dic11C2311yescharacteristic
75#66977—22no—
76#66977—22no—
77#66977—24no—
78#66977—24no—
79C2×Dic11⋊C4C2×C412yes—
80C2×Dic11⋊C4C2×C412yes—
81C2×Dic11⋊C4C2×C412yes—
82C2×Dic11⋊C4C2×C412yes—
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×C4×Dic11C2×C412yes—
85C2×C4×Dic11C2311yescharacteristic
86C2×#4318—22no—
87C2×#4318—24no—
88C2×#4318—42no—
89C2×#4318C2312yes—
90C2×#4318C2312yes—
91C22×C11⋊C8—22no—
92M16×D11—24no—
93M16×D11—42no—
94C2×#4313—22no—
95C2×C8×D11—22no—
96#66950—22no—
97#66950—22no—
98#66949—24no—
99#66949—24no—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—22no—
102#66942—24no—
103#66942—24no—
104#66941—22no—
105#66941—22no—
106#66940—22no—
107#66940—22no—
108C11×C22⋊C8—22no—
109C11×C22⋊C8—22no—
110#66888—24no—
111#66888—42no—
112(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8—22no—
114#66879—22no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117C8×Dic11—22no—
118#22481—111nomaximal, Sylow
119C24×C11C22×C411yescharacteristic
120C23×D11C22×C411yescharacteristic
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—82no—
127C22×C4×C11C22×C411yescharacteristic
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2411yescharacteristic
133C2×C22⋊D11—24no—
134C2×C22⋊D11C22⋊C411yescharacteristic
135C2×C22⋊D11C22⋊C411yescharacteristic
136C2×C22⋊D11C22⋊C411yescharacteristic
137C2×C22⋊D11C22⋊C411yescharacteristic
138C22×Dic11C22×C412yes—
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C412yes—
142C22×Dic11C22×C411yescharacteristic
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—82no—
149C2×C4×D11C2×D412yes—
150C2×C4×D11C2×D412yes—
151C2×Dic22—24no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—82no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C22⋊Dic11—22no—
167C22⋊Dic11—22no—
168C22⋊Dic11C22⋊C412yes—
169C22⋊Dic11C22⋊C412yes—
170(C2×D11)⋊C4—22no—
171(C2×D11)⋊C4—22no—
172(C2×D11)⋊C4C22⋊C412yes—
173(C2×D11)⋊C4C22⋊C412yes—
174C4⋊Dic11—24no—
175C4⋊Dic11—22no—
176Dic11⋊C4—24no—
177Dic11⋊C4—22no—
178Dic11⋊C4—22no—
179Dic11⋊C4—24no—
180Dic11⋊C4—24no—
181Dic11⋊C4C22⋊C412yes—
182Dic11⋊C4C22⋊C412yes—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11C2×D412yes—
186C4×Dic11C2×D412yes—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—44no—
191#4318#4114yes—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—44no—
195#4313—44no—
196C8×D11—44no—
197C2×#554—111no—
198D4×M16—112no—
199#1997—112no—
200#1901—112no—
201#1901—112no—
202#1821—111no—
203#1821D1111yescharacteristic, complemented
204#1801—111no—
205C4×#101—111no—
206C2×#343—111no—
207C2×#343—111no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—22no—
211C23×C11—41no—
212C23×C11C2×C22⋊C411yescharacteristic
213C23×C11C2×C22⋊C411yescharacteristic
214C23×C11C23×C411yescharacteristic
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—22no—
218C22×D11—41no—
219C22×D11C2×C22⋊C411yescharacteristic
220C22×D11C2×C22⋊C411yescharacteristic
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—82no—
232C2×C4×C11—82no—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2×#4112yes—
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C22⋊D11—22no—
239C22⋊D11—22no—
240C22⋊D11—22no—
241C22⋊D11#10114yescomplemented
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—41no—
250C2×Dic11—42no—
251C2×Dic11C2×C22⋊C411yescharacteristic
252C2×Dic11C2×C22⋊C412yes—
253C2×Dic11C2×C22⋊C412yes—
254C2×Dic11C2×C22⋊C411yescharacteristic
255C4×D11—22no—
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—22no—
259C4×D11—82no—
260C4×D11—82no—
261Dic22—42no—
262Dic22—42no—
263Dic22—84no—
264C8×C11—42no—
265C8×C11—42no—
266C11⋊C8—24no—
267C11⋊C8—42no—
268C22×M16—112no—
269C22×M16—112no—
270#554—222no—
271#554—222no—
272#554—222no—
273#554—222no—
274C2×C4⋊Q8—111no—
275C2×#125—112no—
276C2×C22⋊Q8—111no—
277C2×C22⋊Q8—112no—
278C2×C22⋊Q8—111no—
279C2×C22⋊Q8—112no—
280C2×C4×Q8—111no—
281C2×C4×D4—111no—
282C2×C4×D4—112no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4C2×D1111yescharacteristic
285#436—222no—
286#435—222no—
287#435—222no—
288C8×D4—222no—
289#423—112no—
290C2×#101—112no—
291C2×#101—112no—
292#407—112no—
293#407C2×D1112yes—
294C4×M16—112no—
295#343—112no—
296#343—112no—
297#343—111no—
298#343—112no—
299#343—111no—
300#343C2×D1111yescharacteristic
301#343C2×D1111yescharacteristic
302#343C2×D1112yes—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11C2×#10112yes—
313C22×C11C22×C22⋊C411yescharacteristic
314C22×C11C4×#4111yescharacteristic
315C22×C11#52011yescharacteristic
316C2×D11—21no—
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—21no—
320C2×D11—21no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11C2×#10112yes—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11#54612yes—
328C4×C11#54712yes—
329Dic11—22no—
330Dic11—21no—
331Dic11—22no—
332Dic11—42no—
333Dic11—42no—
334Dic11C2×#10112yes—
335C22×Q8—112no—
336C22×Q8—111no—
337C22×D4—111no—
338C23×C4—111no—
339C23×C4—112no—
340C23×C4C4×D1112yes—
341C23×C4C22×D1111yescharacteristic
342C2×M16—112no—
343C2×M16—112no—
344C2×M16—222no—
345C2×M16—222no—
346C2×M16—224no—
347C2×M16—224no—
348C2×M16—442no—
349C2×M16—442no—
350C2×M16C22×D1112yes—
351C2×M16C22×D1112yes—
352C22×C8—222no—
353C22×C8—222no—
354C4⋊Q8—222no—
355C4⋊Q8—222no—
356#125—224no—
357#125—224no—
358C22⋊Q8—224no—
359C22⋊Q8—224no—
360C22⋊Q8—224no—
361C22⋊Q8—224no—
362C22⋊Q8—222no—
363C22⋊Q8—222no—
364C22⋊Q8—222no—
365C22⋊Q8—222no—
366C4×Q8—222no—
367C4×Q8—222no—
368C4×D4—112no—
369C4×D4—112no—
370C4×D4—112no—
371C4×D4—112no—
372C4×D4—222no—
373C4×D4—222no—
374C4×D4—222no—
375C4×D4—222no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—112no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—112no—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4C4×D1112yes—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—111no—
391C2×C22⋊C4—111no—
392C2×C22⋊C4—112no—
393C2×C22⋊C4—112no—
394C2×C42—111no—
395C2×C42—112no—
396C4⋊C8—222no—
397C4⋊C8—222no—
398#101—224no—
399#101—442no—
400C22⋊C8—22no—
401C22⋊C8—22no—
402C22⋊C8—222no—
403C22⋊C8—222no—
404#97—222no—
405C4×C8—222no—
406C2×C11—21no—
407C2×C11—21no—
408C2×C11—22no—
409C2×C11—41no—
410C2×C11#233911yescharacteristic
411C2×C11C22×#10111yescharacteristic
412C2×C11#288811yescharacteristic
413D11—22no—
414D11—41no—
415C24—111no—
416C24C2×C4×D1111yescharacteristic
417C2×Q8—224no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—882no—
423C2×D4—111no—
424C2×D4—111no—
425C2×D4—111no—
426C2×D4—111no—
427C2×D4—224no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—82no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—882no—
447C22×C4C2×C4×D1111yescharacteristic
448C22×C4C2×C4×D1112yes—
449C22×C4C2×C4×D1112yes—
450C22×C4D4×D1112yes—
451C22×C4D4×D1112yes—
452C22×C4C23×D1111yescharacteristic
453M16—22no—
454M16—22no—
455M16—22no—
456M16—22no—
457M16—114no—
458M16—222no—
459M16—222no—
460M16—222no—
461M16—444no—
462M16—444no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—222no—
466C2×C8—222no—
467C2×C8—444no—
468C2×C8—444no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—112no—
473C4⋊C4—112no—
474C4⋊C4—224no—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C4⋊C4—224no—
478C4⋊C4—224no—
479C4⋊C4—224no—
480C4⋊C4—222no—
481C22⋊C4—112no—
482C22⋊C4—112no—
483C22⋊C4—112no—
484C22⋊C4—112no—
485C22⋊C4—222no—
486C22⋊C4—222no—
487C22⋊C4—222no—
488C22⋊C4—222no—
489C42—112no—
490C42—112no—
491C42—222no—
492C42—222no—
493C11#2248111yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496C23—22no—
497C23—41no—
498C23—111no—
499C23—111no—
500C23—222no—
501C23—221no—
502C23—221no—
503C23—441no—
504C23C22⋊C4×D1111yescharacteristic
505C23C22⋊C4×D1111yescharacteristic
506C23C22×C4×D1111yescharacteristic
507Q8—442no—
508Q8—442no—
509Q8—884no—
510D4—114no—
511D4—222no—
512D4—222no—
513D4—222no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—222no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—441no—
542C2×C4—442no—
543C2×C4—882no—
544C2×C4—882no—
545C2×C4C22⋊C4×D1112yes—
546C2×C4C2×D4×D1112yes—
547C2×C4#41×D1112yes—
548C2×C4#6704211yescharacteristic
549C2×C4#6704311yescharacteristic
550C8—42no—
551C8—42no—
552C8—224no—
553C8—442no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—42no—
562C22—42no—
563C22—112no—
564C22—221no—
565C22—221no—
566C22—221no—
567C22—221no—
568C22—221no—
569C22—442no—
570C22—442no—
571C22D11×#10112yes—
572C22C2×C22⋊C4×D1111yescharacteristic
573C22#1062305311yescharacteristic
574C22#1062305411yescharacteristic
575C4—22no—
576C4—42no—
577C4—42no—
578C4—112no—
579C4—222no—
580C4—221no—
581C4—222no—
582C4—442no—
583C4—442no—
584C4#1062318512yes—
585C4#1062318612yes—
586C2—21no—
587C2—21no—
588C2—22no—
589C2—41no—
590C2—222no—
591C2—441no—
592C2#1307144011yescharacteristic
593C2C2×D11×#10111yescharacteristic
594C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1821C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1821D11
hypocenterC11#22481
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #13069603C2semidirect
4. #13069083C2semidirect
5. #13069082C2semidirect
6. #13068695C2semidirect
7. #13068611C2semidirect
8. #13068411C2semidirect
9. C2×#10622168C2semidirect
10. D11×#343C2semidirect
11. C11×#1821C2semidirect
203. #1821D11semidirect
241. C22⋊D11#101semidirect
493. C11#22481semidirect

Maximal subgroups

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

subgroupindex
C2×#106230422
#130773482
#130696032
#130690832
#130690822
#130686952
#130686112
#130684112
C2×#106221682
D11×#3432
C11×#18212
#2248111