Finite Group Databasebeta

← #14719937

Subgroups — #14719937

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623093C211yesmaximal, characteristic
2#13077645C211yesmaximal, characteristic, complemented
3#13066977C212yesmaximal, complemented
4#13066975C212yesmaximal, complemented
5#13066965C212yesmaximal, complemented
6#13066962C212yesmaximal, complemented
7#13066956C212yesmaximal, complemented
8#13066948C212yesmaximal, complemented
9C11×#2973C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66993C411yescharacteristic
12C2×#66991C411yescharacteristic
13C2×#66983C2211yescharacteristic
14C2×#66983C2211yescharacteristic
15C2×#66982C2211yescharacteristic
16C2×#66982C2211yescharacteristic
17#10623093—24no—
18#10623093—24no—
19C2×#66948C411yescharacteristic
20C2×#66943C411yescharacteristic
21C2×#66937C411yescharacteristic
22C2×#66937C411yescharacteristic
23C2×#66936C411yescharacteristic
24C2×#66936C411yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×#66925C2211yescharacteristic
27C11×#435—24no—
28C11×#432C2212yes—
29C11×#407C2212yes—
30C2×C11×C22⋊C8C2212yes—
31#10622820C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622624—24no—
34#10622539C2212yes—
35#10622107C2214yes—
36#10622106C2214yes—
37#10622106C2214yes—
38#10622106C2214yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11C2×C411yescharacteristic
43C22×C22⋊D11C2×C411yescharacteristic
44C22×C22⋊D11C2×C411yescharacteristic
45C22×C22⋊D11C2×C411yescharacteristic
46C22×C22⋊D11C2×C411yescharacteristic
47C22×C22⋊D11C2×C411yescharacteristic
48C22×D44C2×C411yescharacteristic
49C22×D44C2×C411yescharacteristic
50C22×D44C2×C411yescharacteristic
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C2×C11×M16—22no—
55C22×C8×C11—22no—
56C4×D4×C11D414yes—
57C4×D4×C11D414yes—
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C22⋊C4C2×C411yescharacteristic
60C2×C11×C22⋊C4C2×C411yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11C2×C411yescharacteristic
63C2×C22⋊Dic11C2×C411yescharacteristic
64#66993—24no—
65#66991—24no—
66#66983—22no—
67#66983—22no—
68#66983—22no—
69#66983—22no—
70#66982—22no—
71#66982—22no—
72#66982—22no—
73#66982—22no—
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2311yescharacteristic
78C2×(C2×D11)⋊C4C2311yescharacteristic
79C2×(C2×D11)⋊C4C2311yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4⋊Dic11C2×C411yescharacteristic
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2311yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×#4318—22no—
89C22×C11⋊C8—22no—
90#66948—24no—
91#66943—24no—
92#66937—24no—
93#66937—24no—
94#66936—24no—
95#66936—24no—
96C4×D44—22no—
97C4×D44—22no—
98#66925—22no—
99#66925—22no—
100C11×C4⋊C8—22no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8C2314yes—
104C11×#97—22no—
105C22⋊(C11⋊C8)—22no—
106C22⋊(C11⋊C8)—22no—
107C22⋊(C11⋊C8)C2314yes—
108C4⋊(C11⋊C8)—22no—
109#66867—22no—
110#17408—111nomaximal, Sylow
111C24×C11C22×C411yescharacteristic
112C24×C11C22×C411yescharacteristic
113C23×D11C22×C411yescharacteristic
114C23×D11C22×C411yescharacteristic
115C23×D11C22×C411yescharacteristic
116C2×D4×C11—42no—
117C2×D4×C11C22⋊C414yes—
118C22×C4×C11—81no—
119C22×C4×C11—81no—
120C22×C4×C11C22×C411yescharacteristic
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2411yescharacteristic
129C2×C22⋊D11—22no—
130C2×C22⋊D11—22no—
131C2×C22⋊D11—22no—
132C2×C22⋊D11—22no—
133C2×C22⋊D11—22no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11—81no—
136C2×C22⋊D11—81no—
137C2×C22⋊D11—81no—
138C2×C22⋊D11—81no—
139C2×C22⋊D11—81no—
140C2×C22⋊D11—81no—
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
143C22×Dic11C22×C411yescharacteristic
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—42no—
150C2×D44—81no—
151C2×D44—81no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—42no—
156C2×C4×D11—81no—
157C2×C4×D11—81no—
158C11×M16—82no—
159C2×C8×C11—24no—
160C2×C8×C11—82no—
161C11×C4⋊C4C22⋊C414yes—
162C11×C22⋊C4C22⋊C414yes—
163C11×C22⋊C4C22⋊C414yes—
164C42×C11C2×D412yes—
165C42×C11C2×D412yes—
166C22⋊Dic11—22no—
167C22⋊Dic11—22no—
168(C2×D11)⋊C4—22no—
169(C2×D11)⋊C4—22no—
170(C2×D11)⋊C4—22no—
171(C2×D11)⋊C4—21no—
172(C2×D11)⋊C4—21no—
173(C2×D11)⋊C4—21no—
174(C2×D11)⋊C4—21no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185C4×Dic11—22no—
186#4318—82no—
187C2×C11⋊C8—24no—
188C2×C11⋊C8—82no—
189C2×#540—111no—
190#2973—111no—
191#2973D1111yescharacteristic, complemented
192#1471—112no—
193#1471—112no—
194#1468—112no—
195#1468—112no—
196#1466—112no—
197#1464—112no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11C2×C22⋊C412yes—
205C23×C11C2×C22⋊C412yes—
206C23×C11C23×C411yescharacteristic
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219D4×C11—44no—
220C2×C4×C11—22no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11C2×C22⋊C412yes—
230C2×C4×C11C2×C22⋊C412yes—
231C2×C4×C11C2×C22⋊C412yes—
232C2×C4×C11C2×C22⋊C412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C22⋊D11—82no—
236C22⋊D11—82no—
237C22⋊D11—82no—
238C22⋊D11—82no—
239C22⋊D11—82no—
240C22⋊D11—82no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—22no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251D44—44no—
252D44—82no—
253D44—82no—
254C4×D11—44no—
255C4×D11—82no—
256C4×D11—82no—
257C8×C11—44no—
258C11⋊C8—44no—
259#540—224no—
260#540—224no—
261C2×#127—111no—
262C2×#125—111no—
263C2×#123—111no—
264C2×#123—111no—
265C2×#123—111no—
266C2×#123—111no—
267C2×#121—111no—
268C2×#121—111no—
269C2×#121—111no—
270C2×#121—111no—
271C2×#121—111no—
272C2×#121—111no—
273C2×C4×D4—111no—
274C2×C4×D4C2×D1111yescharacteristic
275C2×#117—111no—
276#435—24no—
277#435—224no—
278#432—112no—
279#432C2×D1112yes—
280#407—112no—
281#407C2×D1112yes—
282C2×C22⋊C8—112no—
283C2×C22⋊C8C2×D1112yes—
284#324—114no—
285#323—114no—
286#323—114no—
287#323—114no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11#56812yes—
300C2×D11—41no—
301C2×D11—41no—
302C2×D11—41no—
303C2×D11—41no—
304C2×D11—41no—
305C2×D11—41no—
306C2×D11—41no—
307C2×D11—41no—
308C2×D11—41no—
309C2×D11—82no—
310C2×D11—82no—
311C2×D11—82no—
312C4×C11—22no—
313C4×C11—21no—
314C4×C11—21no—
315C4×C11—22no—
316C4×C11—22no—
317C4×C11—22no—
318Dic11—41no—
319Dic11—41no—
320Dic11—41no—
321Dic11—41no—
322Dic11—41no—
323C22×D4—111no—
324C22×D4—111no—
325C22×D4—111no—
326C22×D4—111no—
327C22×D4—111no—
328C22×D4—111no—
329C22×D4—111no—
330C22×D4—111no—
331C22×D4—111no—
332C22×D4C4×D1111yescharacteristic
333C23×C4—111no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C2×M16—22no—
339C2×M16—222no—
340C22×C8—22no—
341C22×C8—222no—
342#127—224no—
343#125—224no—
344#123—222no—
345#123—222no—
346#123—222no—
347#123—222no—
348#123—224no—
349#123—224no—
350#121—224no—
351#121—222no—
352#121—222no—
353#121—222no—
354#121—222no—
355#121—224no—
356#121—224no—
357#121—224no—
358C4×D4—222no—
359C4×D4—222no—
360C4×D4D4414yes—
361C4×D4C22⋊D1114yes—
362#117—222no—
363#117—222no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4C4×D1111yescharacteristic
372C2×C22⋊C4—111no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—111no—
375C2×C22⋊C4—111no—
376C2×C22⋊C4—111no—
377C2×C22⋊C4—111no—
378C2×C22⋊C4—111no—
379C2×C22⋊C4—111no—
380C2×C22⋊C4C4×D1111yescharacteristic
381C2×C22⋊C4C4×D1111yescharacteristic
382C2×C42—111no—
383C2×C42C22×D1111yescharacteristic
384C4⋊C8—22no—
385C4⋊C8—222no—
386C22⋊C8—22no—
387C22⋊C8—22no—
388C22⋊C8—114no—
389C22⋊C8—222no—
390C22⋊C8—222no—
391C22⋊C8C22×D1114yes—
392#97—22no—
393#97—222no—
394C2×C11—22no—
395C2×C11—42no—
396C2×C11—42no—
397C2×C11#287911yescharacteristic
398C2×C11#288311yescharacteristic
399C2×C11#288811yescharacteristic
400D11—81no—
401D11—81no—
402D11—81no—
403C24—111no—
404C24—111no—
405C24—111no—
406C24C2×C4×D1111yescharacteristic
407C24C2×C4×D1111yescharacteristic
408C2×D4—42no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—222no—
418C2×D4—442no—
419C2×D4—881no—
420C2×D4—881no—
421C2×D4—881no—
422C2×D4—881no—
423C2×D4—881no—
424C2×D4—881no—
425C2×D4—881no—
426C2×D4—881no—
427C2×D4(C2×D11)⋊C414yes—
428C22×C4—81no—
429C22×C4—81no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—442no—
439C22×C4—881no—
440C22×C4—881no—
441C22×C4C2×C4×D1111yescharacteristic
442C22×C4C2×C4×D1111yescharacteristic
443C22×C4C2×C4×D1111yescharacteristic
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4C2×D4412yes—
446C22×C4C2×D4412yes—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C23×D1111yescharacteristic
450M16—82no—
451M16—882no—
452C2×C8—24no—
453C2×C8—82no—
454C2×C8—224no—
455C2×C8—882no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—222no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4(C2×D11)⋊C414yes—
465C22⋊C4—222no—
466C22⋊C4—222no—
467C22⋊C4—222no—
468C22⋊C4—222no—
469C22⋊C4—222no—
470C22⋊C4—221no—
471C22⋊C4—221no—
472C22⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C22⋊C4(C2×D11)⋊C414yes—
477C22⋊C4(C2×D11)⋊C414yes—
478C42—222no—
479C42C2×D4412yes—
480C42C2×C22⋊D1112yes—
481C11#1740811yescharacteristic, complemented, Sylow
482C23—22no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23—222no—
492C23—222no—
493C23—222no—
494C23—441no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23C2×(C2×D11)⋊C412yes—
501C23C2×(C2×D11)⋊C412yes—
502C23C22×C4×D1111yescharacteristic
503D4—44no—
504D4—444no—
505D4—882no—
506D4—882no—
507D4—882no—
508D4—882no—
509D4—882no—
510D4—882no—
511D4—882no—
512D4—882no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—222no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—444no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—882no—
534C2×C4—882no—
535C2×C4C2×(C2×D11)⋊C412yes—
536C2×C4C2×(C2×D11)⋊C412yes—
537C2×C4C2×(C2×D11)⋊C412yes—
538C2×C4C2×(C2×D11)⋊C412yes—
539C2×C4C22×D4411yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—44no—
542C8—444no—
543C22—21no—
544C22—21no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—82no—
552C22—82no—
553C22—441no—
554C22—441no—
555C22—441no—
556C22—441no—
557C22—441no—
558C22—441no—
559C22—441no—
560C22—441no—
561C22—441no—
562C22—882no—
563C22—882no—
564C22—882no—
565C22#1062327612yes—
566C22C22×(C2×D11)⋊C411yescharacteristic
567C4—22no—
568C4—21no—
569C4—21no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—441no—
574C4—441no—
575C4—441no—
576C4—441no—
577C4—441no—
578C2—22no—
579C2—42no—
580C2—42no—
581C2—881no—
582C2—881no—
583C2—881no—
584C2#1307706011yescharacteristic
585C2#1307707611yescharacteristic
586C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2973C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623093C2
cosocleC22×C4×C11C24
hypercenter#2973D11
hypocenterC11#17408
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13077645C2semidirect
3. #13066977C2semidirect
4. #13066975C2semidirect
5. #13066965C2semidirect
6. #13066962C2semidirect
7. #13066956C2semidirect
8. #13066948C2semidirect
9. C11×#2973C2semidirect
191. #2973D11semidirect
481. C11#17408semidirect

Maximal subgroups

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

subgroupindex
C2×#106230932
#130776452
#130669772
#130669752
#130669652
#130669622
#130669562
#130669482
C11×#29732
#1740811