Finite Group Databasebeta

← #14810777

Subgroups — #14810777

Order 2816.

1100 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2C2×#10622684C211yesmaximal, characteristic
3C2×#10622688C211yesmaximal, characteristic
4#13069762C212yesmaximal, complemented
5#13069752C212yesmaximal, complemented
6#13069573C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal, complemented
9#13068974C212yesmaximal, complemented
10#13068449C211yesmaximal, characteristic, complemented
11C11×#2548C211yesmaximal, characteristic
12C2×C11×#127C2211yescharacteristic
13C2×C11×#124—21no—
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66997—21no—
16C22×#4324C2212yes—
17#10623098—24no—
18#10623098—24no—
19C2×#66942—21no—
20C2×#66942—21no—
21C2×#66940—21no—
22C2×#66923C2211yescharacteristic
23C2×#66923C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C11×#394—21no—
29C11×#394—21no—
30C11×#390—21no—
31C11×#390C2212yes—
32C11×#390C2212yes—
33C4×C11×C4⋊C4C2211yescharacteristic
34C2×#66896C2212yes—
35C2×#66896C2212yes—
36C2×#66896C2212yes—
37#10622688—24no—
38#10622684—24no—
39C2×#66874C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46#10622162C2212yes—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11C2312yes—
51C22×Dic22—21no—
52C22×Dic22C2311yescharacteristic
53C11×#127—22no—
54C11×#127—22no—
55C11×#124—44no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70#66997—28no—
71C2×#4324—24no—
72C2×#4324—24no—
73C2×#4324—24no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90#66942—28no—
91#66942—28no—
92#66940—28no—
93#66923—22no—
94#66923—22no—
95#66923—22no—
96#66923D414yes—
97#66922—22no—
98#66922—22no—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C4×Dic22—22no—
102C4×Dic22—22no—
103C4×Dic22—22no—
104C4×Dic22D414yes—
105C11×#95—21no—
106#66896—24no—
107#66896—24no—
108#66896—24no—
109#66874—24no—
110C4⋊(C11⋊C8)—22no—
111#66867—22no—
112#25944—111nomaximal, Sylow
113C24×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—41no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—82no—
128C22×C4×C11—22no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C2×Dic22—24no—
141C2×Dic22—21no—
142C2×Dic22—22no—
143C2×Dic22—42no—
144C2×Dic22—42no—
145C2×Dic22C2×D412yes—
146C2×Dic22#4114yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C22⋊C4—44no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—82no—
155C11×C22⋊C4—82no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—42no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163#4324—48no—
164C4⋊Dic11—24no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11C2×D412yes—
169C4⋊Dic11C2×D412yes—
170C4⋊Dic11C2×D412yes—
171Dic11⋊C4—24no—
172Dic11⋊C4—24no—
173Dic11⋊C4—24no—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176Dic11⋊C4—24no—
177Dic11⋊C4—24no—
178C4×Dic11—24no—
179C4×Dic11—24no—
180C4×Dic11—24no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×#557—111no—
188C2×#490—111no—
189C2×#460—111no—
190#2548D1111yescharacteristic
191#2025—112no—
192#2023—112no—
193#1989—111no—
194#1985—111no—
195#1880—112no—
196#1880—112no—
197#1763—111no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11C22×D411yescharacteristic
206Q8×C11—44no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—84no—
212D4×C11—84no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11#12012yes—
229C2×C4×C11#12012yes—
230C2×C4×C11AGL(1,ℤ/8)12yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4112yes—
234C2×C4×C112−1+412yes—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245Dic22—22no—
246Dic22—24no—
247Dic22—48no—
248Dic22#12414yescomplemented
249C11⋊C8—42no—
250C11⋊C8—42no—
251C22×SD16—112no—
252#557—224no—
253#557—224no—
254C2×C4⋊Q8—111no—
255C2×C4⋊Q8—221no—
256C2×#127C2×D1111yescharacteristic
257C2×#125—111no—
258C2×#125—111no—
259C2×#125—221no—
260C2×#125—221no—
261C2×#124—21no—
262C2×C4×Q8—111no—
263C2×C4×Q8—111no—
264C2×C4×Q8—111no—
265C2×C4×Q8—221no—
266C2×C4×Q8C2×D1111yescharacteristic
267#490—224no—
268#460—224no—
269C2×C4⋊C8—111no—
270C2×#103—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#97—111no—
275#394—21no—
276#394—21no—
277#390—21no—
278#390C2×D1112yes—
279#390C2×D1112yes—
280C4×C4⋊C4C2×D1111yescharacteristic
281#340—112no—
282#340—112no—
283#340—112no—
284#336—112no—
285#336—112no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11—82no—
292C22×C11—82no—
293C22×C11C2×#12011yescharacteristic
294C22×C11#54812yes—
295C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C11#57511yescharacteristic
297C22×C11#57712yes—
298C4×C11—22no—
299C4×C11—22no—
300C4×C11—22no—
301C4×C11—41no—
302C4×C11—41no—
303C4×C11—41no—
304C4×C11—82no—
305C4×C11C2×#12411yescharacteristic
306C4×C11#53611yescharacteristic
307C4×C11#54812yes—
308Dic11—24no—
309Dic11—42no—
310Dic11—42no—
311Dic11—42no—
312C22×Q8—111no—
313C22×Q8—221no—
314C22×Q8C22⋊D1111yescharacteristic
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C22×D1112yes—
318C2×SD16—224no—
319C2×SD16—224no—
320C2×SD16—224no—
321C22×C8—112no—
322C22×C8—112no—
323C4⋊Q8—222no—
324C4⋊Q8—222no—
325C4⋊Q8—228no—
326#127—22no—
327#127—22no—
328#125—114no—
329#125—222no—
330#125—222no—
331#125—228no—
332#125—228no—
333#125—222no—
334#124—44no—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×Q8—114no—
338C4×Q8—222no—
339C4×Q8—222no—
340C4×Q8—222no—
341C4×Q8—222no—
342C4×Q8—228no—
343C4×Q8—222no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C22⋊D1111yescharacteristic
356C2×C4⋊C4C22⋊D1111yescharacteristic
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C4⋊C4C22×D1112yes—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C42—21no—
364C2×C42—221no—
365C2×C42—221no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368C2×C42C22×D1111yescharacteristic
369C2×C42C22×D1111yescharacteristic
370C4⋊C8—222no—
371#103—224no—
372#102—224no—
373#102—224no—
374#102—224no—
375#97—222no—
376#95—21no—
377C2×C11—162no—
378C2×C11#243611yescharacteristic
379C2×C11#300611yescharacteristic
380C2×C11#301011yescharacteristic
381C2×C11#336812yes—
382C2×C11#337112yes—
383C24—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8—112no—
388C2×Q8—114no—
389C2×Q8—224no—
390C2×Q8—221no—
391C2×Q8—222no—
392C2×Q8—442no—
393C2×Q8—442no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—82no—
405C22×C4—22no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—221no—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417SD16—448no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—112no—
430C4⋊C4—112no—
431C4⋊C4—112no—
432C4⋊C4—224no—
433C4⋊C4—224no—
434C4⋊C4—224no—
435C4⋊C4—224no—
436C4⋊C4—224no—
437C4⋊C4—224no—
438C4⋊C4—224no—
439C4⋊C4—224no—
440C4⋊C4—221no—
441C4⋊C4—221no—
442C4⋊C4—221no—
443C22⋊C4—44no—
444C22⋊C4—44no—
445C22⋊C4—82no—
446C22⋊C4—82no—
447C42—21no—
448C42—21no—
449C42—21no—
450C42—21no—
451C42—42no—
452C42—224no—
453C42—224no—
454C42—224no—
455C42D4×D1112yes—
456C42D4×D1112yes—
457C11#2594411yescharacteristic, complemented, Sylow
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23—42no—
465C23C22×C22⋊D1111yescharacteristic
466Q8—44no—
467Q8—114no—
468Q8—222no—
469Q8—224no—
470Q8—448no—
471D4—42no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—84no—
476D4—84no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—222no—
493C2×C4—224no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—441no—
501C2×C4—442no—
502C2×C4#6698512yes—
503C2×C4#6699012yes—
504C2×C4#6699012yes—
505C2×C4C2×D4×D1111yescharacteristic
506C2×C4C2×D4×D1111yescharacteristic
507C2×C4#41×D1112yes—
508C2×C4#6704312yes—
509C8—442no—
510C8—442no—
511C22—82no—
512C22—82no—
513C22—82no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22C2×#6698511yescharacteristic
519C22C2×#6699011yescharacteristic
520C22#1062335311yescharacteristic
521C22#1062336212yes—
522C22#1062336712yes—
523C4—22no—
524C4—22no—
525C4—22no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—82no—
530C4—224no—
531C4—442no—
532C4—442no—
533C4—442no—
534C4D11×#12411yescharacteristic
535C4#1062320611yescharacteristic
536C4#1062320812yes—
537C2—162no—
538C2#1307227111yescharacteristic
539C2#1307786611yescharacteristic
540C2#1307790011yescharacteristic
541C2#1308134112yes—
542C2#1308137812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2548C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2548D11
hypocenterC11#25944
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
4. #13069762C2semidirect
5. #13069752C2semidirect
6. #13069573C2semidirect
7. #13069557C2semidirect
8. #13068974C2semidirect
9. #13068974C2semidirect
10. #13068449C2semidirect
248. Dic22#124semidirect
457. C11#25944semidirect

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106226842
C2×#106226882
#130697622
#130697522
#130695732
#130695572
#130689742
#130684492
C11×#25482
#2594411