Finite Group Databasebeta

← #14757383

Subgroups — #14757383

Order 2816.

1718 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2C2×#10622742C211yesmaximal, characteristic, complemented
3C2×#10622723C211yesmaximal, characteristic, complemented
4C2×#10622739C211yesmaximal, characteristic, complemented
5C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
6C2×#10622610C211yesmaximal, characteristic, complemented
7#13069413C214yesmaximal, complemented
8#13069409C214yesmaximal, complemented
9C2×C11×#424C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×C4×D11C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C23×C11⋊C8C2211yescharacteristic
17#10623055—24no—
18#10623055—24no—
19C2×#66950C412yes—
20C2×#66948C412yes—
21C2×#66939C412yes—
22C2×#66935C412yes—
23C2×C4×D44C2214yes—
24C11×#424—24no—
25C2×C11×C4⋊C8C2214yescomplemented
26#10622742—24no—
27#10622739—24no—
28#10622723—24no—
29C2×(C2×D11)⋊C8—24no—
30C2×(C2×D11)⋊C8C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×(C2×D11)⋊C8C2214yes—
33C2×(C2×D11)⋊C8C2214yescomplemented
34C2×(C2×D11)⋊C8C2212yescomplemented
35C2×(C2×D11)⋊C8C2212yescomplemented
36#10622610—24no—
37C2×#66867C2212yescomplemented
38C2×C4×C11⋊C8C2212yescomplemented
39C24×D11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11C2×C412yes—
42C23×Dic11C2×C411yescharacteristic
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339—22no—
49C22×D44C2×C411yescharacteristic
50C22×D44C2×C414yes—
51C22×C4×D11—22no—
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11C2×C412yes—
58C22×C4×D11C2312yes—
59C22×C4×D11C2312yes—
60C22×Dic22C2×C411yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C11×#117D414yes—
70C11×#117D414yes—
71C2×C11×C4⋊C4C2×C412yes—
72C2×C11×C22⋊C4C2×C412yes—
73C2×C42×C11C2312yes—
74C2×(C2×D11)⋊C4C2×C414yes—
75C2×(C2×D11)⋊C4C2×C414yes—
76C2×C4⋊Dic11C2×C414yes—
77C2×#4318—22no—
78C2×#4318—22no—
79C2×#4318D414yescomplemented
80C22×C11⋊C8—22no—
81C22×C11⋊C8—22no—
82C22×C11⋊C8D414yescomplemented
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2311yescharacteristic
86#66950—28no—
87#66948—28no—
88#66939—28no—
89#66935—28no—
90C4×D44—28no—
91C4×D44—28no—
92C11×C4⋊C8—28no—
93(C2×D11)⋊C8—24no—
94(C2×D11)⋊C8—24no—
95(C2×D11)⋊C8—28no—
96(C2×D11)⋊C8—28no—
97(C2×D11)⋊C8—24no—
98(C2×D11)⋊C8—24no—
99#66867—24no—
100C4×C11⋊C8—24no—
101#21191—111nomaximal, Sylow
102C24×C11C22×C411yescharacteristic
103C23×D11—22no—
104C23×D11—24no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—42no—
108C23×D11C22×C412yes—
109C23×D11C22×C412yes—
110C22×C4×C11C22×C414yes—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4112yes—
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—24no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—24no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11C22×C412yes—
126C22×Dic11C22×C412yes—
127#4339—44no—
128#4339—44no—
129#4339—44no—
130#4339—44no—
131C2×D44—28no—
132C2×D44—28no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—44no—
137C2×C4×D11—24no—
138C2×C4×D11—24no—
139C2×C4×D11—24no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—44no—
153C2×C4×D11—44no—
154C2×C4×D11—44no—
155C2×C4×D11—44no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C11×M16—44no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—44no—
167C11×C4⋊C4C22⋊C418yes—
168C11×C22⋊C4C22⋊C418yes—
169C42×C11C2×D414yes—
170C42×C11C2×D414yes—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173C4⋊Dic11—28no—
174#4318—28no—
175C2×C11⋊C8—28no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8C2×D412yes—
183C2×C11⋊C8C2×D412yes—
184C2×C11⋊C8C2×D414yes—
185C2×#525—111no—
186C2×#424D1111yescharacteristic, complemented
187C2×#408—111no—
188C2×#408—111no—
189C2×#407—111no—
190C22×C22⋊C8—111no—
191C2×#405—111no—
192#1955—114no—
193#1954—114no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11C2×C22⋊C412yes—
197C23×C11C4×D412yes—
198C23×C11C4×D412yes—
199C23×C11C23×C411yescharacteristic
200C22×D11—28no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—48no—
213C22×D11—48no—
214C22×D11—44no—
215C22×D11—44no—
216C22×D11#13114yes—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11C2×C22⋊C418yes—
220C2×C4×C11C2×C22⋊C412yes—
221C2×C4×C11C4×D412yes—
222C2×C4×C11C4×D412yes—
223C2×C4×C11#12114yes—
224C2×C4×C11#12114yes—
225C2×C4×C11#12414yes—
226C2×C4×C11#12714yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C22⋊D11—48no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—44no—
241D44—416no—
242D44—44no—
243C4×D11—42no—
244C4×D11—42no—
245C4×D11—42no—
246C4×D11—42no—
247C4×D11—42no—
248C4×D11—42no—
249C4×D11—42no—
250C4×D11—42no—
251C4×D11—48no—
252Dic22—44no—
253C8×C11—42no—
254C8×C11—42no—
255C11⋊C8—22no—
256C11⋊C8—22no—
257C11⋊C8—24no—
258C22×#41—111no—
259C24×C4—111no—
260C22×M16—111no—
261C22×M16C2×D1111yescharacteristic
262C23×C8—111no—
263C23×C8C2×D1111yescharacteristic
264#525—224no—
265#525—224no—
266C2×#123—112no—
267C2×C22⋊Q8—112no—
268C2×#121—112no—
269C2×#120—112no—
270C2×C4×D4—114no—
271C2×#117C2×D1111yescharacteristic
272#424—24no—
273C2×C4⋊C8C2×D1114yescomplemented
274#408—224no—
275#408—224no—
276#407—224no—
277C2×C22⋊C8—112no—
278C2×C22⋊C8—112no—
279C2×C22⋊C8—114no—
280C2×C22⋊C8—112no—
281C2×C22⋊C8—114no—
282C2×C22⋊C8—112no—
283C2×C22⋊C8—224no—
284#405—224no—
285C2×#97—112no—
286C2×C4×C8—112no—
287C22×C11—24no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—24no—
291C22×C11#39014yes—
292C22×C11C22×C22⋊C411yescharacteristic
293C22×C11C2×C4×D411yescharacteristic
294C22×C11C2×C4×D411yescharacteristic
295C22×C11C2×#13112yes—
296C22×C11#56812yes—
297C2×D11—24no—
298C2×D11—24no—
299C2×D11—24no—
300C2×D11—416no—
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—44no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—44no—
309C2×D11—42no—
310C4×C11—28no—
311C4×C11#39014yes—
312C4×C11C2×#12111yescharacteristic
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12411yescharacteristic
315C4×C11C2×#12711yescharacteristic
316Dic11—42no—
317Dic11—42no—
318C25—111no—
319C2×#41—222no—
320C2×#41—222no—
321C2×#41—222no—
322C2×#41—222no—
323C2×#41—222no—
324C2×#41—222no—
325C22×Q8—111no—
326C22×D4—112no—
327C22×D4—111no—
328C22×D4—114no—
329C23×C4—111no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4—222no—
334C23×C4—222no—
335C23×C4—222no—
336C23×C4—222no—
337C23×C4—222no—
338C23×C4—222no—
339C23×C4C22×D1111yescharacteristic
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—22no—
343C2×M16—114no—
344C2×M16—222no—
345C2×M16—222no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—114no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—112no—
353C22×C8—222no—
354C22×C8—222no—
355C22×C8C22×D1112yes—
356C22×C8C22×D1112yes—
357#123—228no—
358C22⋊Q8—228no—
359#121—228no—
360#120—228no—
361C4×D4—228no—
362C4×D4—228no—
363#117D4414yes—
364#117C22⋊D1114yes—
365C2×C4⋊C4—114no—
366C2×C4⋊C4C4×D1112yes—
367C2×C22⋊C4—114no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4C4×D1112yes—
370C2×C42C22×D1112yes—
371C4⋊C8—28no—
372C22⋊C8—224no—
373C22⋊C8—224no—
374C22⋊C8—228no—
375C22⋊C8—228no—
376C22⋊C8—224no—
377C22⋊C8—224no—
378#97—224no—
379C4×C8—224no—
380C2×C11—24no—
381C2×C11C2×#39011yescharacteristic
382C2×C11#288012yes—
383C2×C11#292911yescharacteristic
384C2×C11#293011yescharacteristic
385C2×C11#293312yes—
386D11—44no—
387D11—82no—
388C24—112no—
389C24—112no—
390C24—224no—
391C24—222no—
392C24—222no—
393C24—222no—
394C24—442no—
395C24C2×C4×D1111yescharacteristic
396#41—444no—
397#41—444no—
398#41—444no—
399#41—444no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×Q8—222no—
403C2×D4—228no—
404C2×D4—224no—
405C2×D4—224no—
406C2×D4—224no—
407C2×D4—222no—
408C2×D4—222no—
409C2×D4—228no—
410C2×D4—222no—
411C2×D4—444no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—444no—
433C22×C4—444no—
434C22×C4—444no—
435C22×C4—444no—
436C22×C4C2×C4×D1114yes—
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×D4412yes—
439C22×C4D4×D1112yes—
440C22×C4D4×D1112yes—
441C22×C4#434312yes—
442C22×C4#434312yes—
443C22×C4C2×C22⋊D1112yes—
444C22×C4C23×D1111yescharacteristic
445M16—44no—
446M16—228no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—44no—
454C2×C8—112no—
455C2×C8—112no—
456C2×C8—114no—
457C2×C8—228no—
458C2×C8—221no—
459C2×C8—222no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—222no—
464C4⋊C4—228no—
465C4⋊C4(C2×D11)⋊C418yes—
466C22⋊C4—228no—
467C22⋊C4—228no—
468C22⋊C4(C2×D11)⋊C418yes—
469C42C2×D4414yes—
470C42C2×C22⋊D1114yes—
471C11#2119111yescharacteristic, complemented, Sylow
472C23—22no—
473C23—22no—
474C23—114no—
475C23—228no—
476C23—222no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23—222no—
481C23—222no—
482C23—224no—
483C23—224no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—448no—
488C23—448no—
489C23—444no—
490C23—444no—
491C23#6694612yes—
492C23#6694612yes—
493C23C2×(C2×D11)⋊C412yes—
494C23C22×C4×D1111yescharacteristic
495Q8—444no—
496D4—4416no—
497D4—448no—
498D4—444no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—444no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—448no—
517C2×C4#6694612yes—
518C2×C4#6694612yes—
519C2×C4#6694814yes—
520C2×C4#6694814yes—
521C2×C4C2×(C2×D11)⋊C418yes—
522C2×C4C2×(C2×D11)⋊C412yes—
523C2×C4#6699314yes—
524C2×C4#6700014yes—
525C2×C4C22×D4411yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434311yescharacteristic
529C2×C4C2×#434311yescharacteristic
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—42no—
532C8—42no—
533C8—222no—
534C8—222no—
535C8—224no—
536C22—22no—
537C22—22no—
538C22—24no—
539C22—24no—
540C22—224no—
541C22—224no—
542C22—224no—
543C22—4416no—
544C22—442no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—442no—
550C22—444no—
551C22—444no—
552C22—442no—
553C22#1062260114yes—
554C22C2×#6694611yescharacteristic
555C22C2×#6694611yescharacteristic
556C22D11×#13112yes—
557C22#1062328112yes—
558C22C22×(C2×D11)⋊C411yescharacteristic
559C4—28no—
560C4—442no—
561C4—442no—
562C4#1062260114yes—
563C4C2×#6694811yescharacteristic
564C4C2×#6694811yescharacteristic
565C4C2×#6699311yescharacteristic
566C4C2×#6700011yescharacteristic
567C2—24no—
568C2—444no—
569C2—882no—
570C2C2×#1062260111yescharacteristic
571C2#1307706312yes—
572C2#1307730911yescharacteristic
573C2#1307731811yescharacteristic
574C2#1307734012yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#424C2
prime radicalC2×#10623055C2
cosocleC22×C4×C11C24
hypercenterC2×#424D11
hypocenterC11#21191
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. C2×#10622742C2semidirect
3. C2×#10622723C2semidirect
4. C2×#10622739C2semidirect
5. C22×(C2×D11)⋊C8C2semidirect
6. C2×#10622610C2semidirect
7. #13069413C2semidirect
8. #13069409C2semidirect
9. C2×C11×#424C2semidirect
25. C2×C11×C4⋊C8C22semidirect
33. C2×(C2×D11)⋊C8C22semidirect
34. C2×(C2×D11)⋊C8C22semidirect
35. C2×(C2×D11)⋊C8C22semidirect
37. C2×#66867C22semidirect
38. C2×C4×C11⋊C8C22semidirect
79. C2×#4318D4semidirect
82. C22×C11⋊C8D4semidirect
186. C2×#424D11semidirect
273. C2×C4⋊C8C2×D11semidirect
471. C11#21191semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×#106227422
C2×#106227232
C2×#106227392
C22×(C2×D11)⋊C82
C2×#106226102
#130694132
#130694092
C2×C11×#4242
#2119111