Finite Group Databasebeta

← #14763737

Subgroups — #14763737

Order 2816.

1118 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623222C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic, complemented
3#13071012C211yesmaximal, characteristic, complemented
4#13069574C211yesmaximal, characteristic, complemented
5#13069548C211yesmaximal, characteristic, complemented
6#13069546C211yesmaximal, characteristic, complemented
7#13069053C212yesmaximal
8#13069048C212yesmaximal, complemented
9#13068630C212yesmaximal, complemented
10#13068625C212yesmaximal, complemented
11C11×#1989C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13C22×#4313C2212yes—
14#10623222—24no—
15#10623222C418yescomplemented
16C2×#66951—21no—
17C2×#66950C2211yescharacteristic
18C2×#66948C2211yescharacteristic
19C2×#66947—21no—
20C2×#66946—21no—
21C2×#66946C2211yescharacteristic
22C2×#66945—21no—
23C2×#66940C2211yescharacteristic
24C2×#66928C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66885C2212yes—
29C2×#66880C2212yes—
30C2×Dic11⋊C8C2212yes—
31#10622600C2212yes—
32#10622590C2212yes—
33C2×#66874C2212yes—
34C2×#66873C2212yes—
35C4×(C2×D11)⋊C4—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622545—21no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622450—24no—
40#10622277—21no—
41#10622264—21no—
42C11×#340C2212yes—
43C11×#340C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D44—21no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×C4×D11D411yescharacteristic
50C22×C4×D11D411yescharacteristic
51C22×C4×D11C2311yescharacteristic
52C22×Dic22C2311yescharacteristic
53C22×C8×C11C2312yes—
54C11×#125—22no—
55C11×#125C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11—21no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C22×C11⋊C8C2312yes—
78C2×#4313—24no—
79C2×#4313—42no—
80C2×#4313—42no—
81#66951—28no—
82#66950—22no—
83#66950C2×C414yes—
84#66948—22no—
85#66948C2×C414yes—
86#66947—28no—
87#66946—28no—
88#66946—22no—
89#66946C2×C414yes—
90#66945—28no—
91#66940—22no—
92#66940C2×C414yes—
93#66928—22no—
94#66928C2×C414yes—
95C42×D11C2×C414yes—
96C42×D11D414yes—
97C11×C4⋊C8—22no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103#66885—42no—
104#66880—42no—
105Dic11⋊C8—24no—
106#66874—42no—
107#66873—42no—
108C4⋊(C11⋊C8)—22no—
109#21895—111nomaximal, Sylow
110C23×D11—21no—
111C23×D11C2×D411yescharacteristic
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123C2×D44—24no—
124C2×D44—21no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—42no—
128C2×D44—42no—
129C2×D44C22×C412yes—
130C2×C4×D11—24no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11—42no—
136C2×C4×D11—44no—
137C2×C4×D11C22⋊C414yes—
138C2×C4×D11C22⋊C414yes—
139C2×C4×D11C22×C412yes—
140C2×C4×D11C2×D412yes—
141C2×Dic22—21no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22C22×C412yes—
145C2×C8×C11—22no—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4C22×C412yes—
155C11×C4⋊C4C22×C412yes—
156C42×C11—42no—
157C42×C11C22×C412yes—
158C42×C11C2×D412yes—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—44no—
165C4⋊Dic11—24no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168Dic11⋊C4—24no—
169C4×Dic11—24no—
170C4×Dic11—42no—
171C4×Dic11C22⋊C414yes—
172C4×Dic11C22⋊C414yes—
173C4×Dic11C22×C412yes—
174C4×Dic11C2×D412yes—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178#4313—48no—
179C2×#529—111no—
180C2×#423—111no—
181#2283—111no—
182#1989—111no—
183#1989D1111yescharacteristic, complemented
184#1983—111no—
185#1983—111no—
186#1895—112no—
187#1894—112no—
188#1805—112no—
189#1804—112no—
190C23×C11C22×D411yescharacteristic
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—21no—
194C22×D11—21no—
195C22×D11—22no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11C2×C22⋊C412yes—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11C2×C22⋊C412yes—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11H(5,𝔽2)12yes—
217C2×C4×C112−1+412yes—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—21no—
221C2×Dic11—21no—
222C2×Dic11—22no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11C2×C22⋊C412yes—
228C2×Dic11C2×C22⋊C412yes—
229C2×Dic11C2×C22⋊C412yes—
230D44—24no—
231D44—48no—
232D44—41no—
233D44—41no—
234C4×D11—24no—
235C4×D11—22no—
236C4×D11—22no—
237C4×D11—44no—
238C4×D11—44no—
239C4×D11—48no—
240Dic22—24no—
241Dic22—41no—
242Dic22—41no—
243C8×C11—42no—
244C11⋊C8—42no—
245C22×M16—112no—
246#529—118no—
247#529—224no—
248C2×#126—221no—
249C2×#125C2×D1111yescharacteristic
250C2×#124—111no—
251C2×#123—221no—
252C2×C22⋊Q8—111no—
253C2×#121—111no—
254C2×C4×Q8—111no—
255C2×C4×D4—111no—
256C2×C4×D4—221no—
257C2×#117—221no—
258C22×C42—111no—
259#423—224no—
260C2×C4⋊C8—112no—
261C2×C4⋊C8—111no—
262C2×C4⋊C8C2×D1111yescharacteristic
263C2×#103—112no—
264C2×#103—112no—
265C2×#102—112no—
266C2×#102—112no—
267#383—221no—
268#382—112no—
269#381—221no—
270#380—112no—
271C4×C4⋊C4—111no—
272C4×C4⋊C4C2×D1111yescharacteristic
273C4×C22⋊C4—221no—
274#376—221no—
275#340—112no—
276#340—112no—
277#340C2×D1112yes—
278#340C2×D1112yes—
279C22×C11C22×C22⋊C411yescharacteristic
280C22×C11#53712yes—
281C22×C11#57512yes—
282C22×C11#57511yescharacteristic
283C22×C11#57511yescharacteristic
284C2×D11—22no—
285C2×D11—22no—
286C2×D11—22no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—42no—
292C2×D11—82no—
293C2×D11—82no—
294C4×C11—22no—
295C4×C11—22no—
296C4×C11—42no—
297C4×C11—42no—
298C4×C11—82no—
299C4×C11#52012yes—
300C4×C11#53511yescharacteristic
301C4×C11#53611yescharacteristic
302Dic11—22no—
303Dic11—22no—
304Dic11—22no—
305Dic11—42no—
306Dic11—82no—
307C22×Q8—111no—
308C22×D4—111no—
309C22×D4—221no—
310C23×C4—111no—
311C23×C4—111no—
312C23×C4—111no—
313C23×C4—221no—
314C2×M16—224no—
315C2×M16—442no—
316C2×M16—442no—
317C22×C8—112no—
318C22×C8C22×D1112yes—
319#126—228no—
320#125—22no—
321#125C4×D1114yes—
322#124—114no—
323#124—222no—
324#123—228no—
325C22⋊Q8—114no—
326C22⋊Q8—222no—
327#121—114no—
328#121—222no—
329C4×Q8—114no—
330C4×Q8—222no—
331C4×D4—114no—
332C4×D4—222no—
333C4×D4—228no—
334#117—228no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4C22×D1112yes—
341C2×C4⋊C4C22×D1111yescharacteristic
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C22⋊C4—221no—
344C2×C22⋊C4—221no—
345C2×C22⋊C4—221no—
346C2×C22⋊C4—221no—
347C2×C22⋊C4—221no—
348C2×C22⋊C4—222no—
349C2×C42—21no—
350C2×C42—111no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—114no—
354C2×C42—114no—
355C2×C42—221no—
356C2×C42—221no—
357C2×C42C22×D1111yescharacteristic
358C4⋊C8—22no—
359C4⋊C8—224no—
360C4⋊C8—222no—
361#103—442no—
362#103—442no—
363#102—442no—
364#102—442no—
365#95—21no—
366#95—222no—
367#95—222no—
368#95—222no—
369#95—221no—
370C2×C11#231111yescharacteristic
371C2×C11#289611yescharacteristic
372C2×C11#289611yescharacteristic
373C2×C11#325612yes—
374C2×C11#325612yes—
375D11—42no—
376D11—82no—
377C24—111no—
378C24—221no—
379C2×Q8—112no—
380C2×Q8—221no—
381C2×Q8—222no—
382C2×Q8—222no—
383C2×D4—112no—
384C2×D4—224no—
385C2×D4—221no—
386C2×D4—222no—
387C2×D4—222no—
388C2×D4—442no—
389C2×D4—442no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—111no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—114no—
399C22×C4—114no—
400C22×C4—224no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—442no—
406C22×C4—441no—
407C22×C4—441no—
408C22×C4—444no—
409C22×C4D4×D1111yescharacteristic
410C22×C4D4×D1111yescharacteristic
411C22×C4C23×D1111yescharacteristic
412M16—448no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—222no—
417C2×C8—222no—
418C2×C8—222no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C4⋊C4—222no—
428C4⋊C4—222no—
429C4⋊C4C2×C4×D1112yes—
430C4⋊C4C2×C4×D1112yes—
431C22⋊C4—224no—
432C22⋊C4—224no—
433C22⋊C4—224no—
434C22⋊C4—224no—
435C22⋊C4—224no—
436C22⋊C4—444no—
437C42—42no—
438C42—114no—
439C42—114no—
440C42—112no—
441C42—112no—
442C42—224no—
443C42—442no—
444C42C2×C4×D1112yes—
445C42D4×D1112yes—
446C11#2189511yescharacteristic, complemented, Sylow
447C23—112no—
448C23—222no—
449C23—221no—
450C23—221no—
451C23—222no—
452C23—222no—
453C23—442no—
454C23—441no—
455C23—441no—
456C23—442no—
457C23C2×D4×D1111yescharacteristic
458Q8—224no—
459Q8—441no—
460Q8—441no—
461D4—224no—
462D4—448no—
463D4—441no—
464D4—441no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—112no—
479C2×C4—222no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—224no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—444no—
488C2×C4—444no—
489C2×C4—448no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4C22⋊C4×D1112yes—
495C2×C4C22⋊C4×D1112yes—
496C2×C4C22×C4×D1111yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4#6704012yes—
499C2×C4#6704212yes—
500C8—42no—
501C8—442no—
502C22—222no—
503C22—222no—
504C22—222no—
505C22—442no—
506C22—442no—
507C22—442no—
508C22—442no—
509C22—442no—
510C22—882no—
511C22—882no—
512C22C2×C22⋊C4×D1111yescharacteristic
513C22#1062316012yes—
514C22#1062329912yes—
515C22#1062330411yescharacteristic
516C22#1062330811yescharacteristic
517C4—22no—
518C4—22no—
519C4—42no—
520C4—42no—
521C4—82no—
522C4—222no—
523C4—222no—
524C4—222no—
525C4—442no—
526C4—882no—
527C4#1062310512yes—
528C4#1062320511yescharacteristic
529C4#1062325511yescharacteristic
530C2—442no—
531C2—882no—
532C2#1307120711yescharacteristic
533C2#1307713111yescharacteristic
534C2#1307713211yescharacteristic
535C2#1308001612yes—
536C2#1308001912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1989D11
hypocenterC11#21895
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
2. C2×#10622450C2semidirect
3. #13071012C2semidirect
4. #13069574C2semidirect
5. #13069548C2semidirect
6. #13069546C2semidirect
8. #13069048C2semidirect
9. #13068630C2semidirect
10. #13068625C2semidirect
11. C11×#1989C2semidirect
15. #10623222C4semidirect
183. #1989D11semidirect
446. C11#21895semidirect

Maximal subgroups

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

subgroupindex
C2×#106232222
C2×#106224502
#130710122
#130695742
#130695482
#130695462
#130690532
#130690482
#130686302
#130686252
C11×#19892
#2189511