Finite Group Databasebeta

← #14753836

Subgroups — #14753836

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2C2×#10622318C211yesmaximal, characteristic
3#13071012C211yesmaximal, characteristic
4#13068705C212yesmaximal
5#13068630C212yesmaximal, complemented
6#13068629C212yesmaximal, complemented
7#13068549C212yesmaximal
8#13068449C211yesmaximal, characteristic, complemented
9#13068447C211yesmaximal, characteristic, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C11×#1763C211yesmaximal, characteristic, complemented
12C22×Q8×D11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C4×Q8×D11—24no—
16C4×Q8×D11C418yescomplemented
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×#66940—21no—
20C2×#66940C2211yescharacteristic
21C2×C42×D11—21no—
22C2×C42×D11C2211yescharacteristic
23C2×C4×Dic22—21no—
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×#103C2212yes—
26C2×C11×#97C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66880C2212yes—
31C2×Dic11⋊C8C2212yes—
32#10622600C2212yes—
33#10622590C2212yes—
34C2×#66874C2212yes—
35C4×(C2×D11)⋊C4—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622545—21no—
38C2×#66867C2211yescharacteristic
39#10622318—24no—
40#10622277—21no—
41#10622264—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C2×Q8×D11—24no—
48C2×Q8×D11—22no—
49C2×Q8×D11—24no—
50C2×Q8×D11C2×C414yes—
51C22×C4×D11—21no—
52C22×C4×D11—21no—
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×Dic22—21no—
57C22×Dic22C2311yescharacteristic
58C22×C8×C11C2312yes—
59C4×Q8×C11—22no—
60C4×Q8×C11C2×C414yes—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67Q8×Dic11—22no—
68Q8×Dic11C2×C414yes—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C4⋊C4×D11—28no—
85C4⋊C4×D11—22no—
86C4⋊C4×D11C2×C414yes—
87#66940—28no—
88#66940—22no—
89#66940C2×C414yes—
90C42×D11—28no—
91C42×D11C2×C414yes—
92C42×D11D414yes—
93C4×Dic22—22no—
94C4×Dic22—28no—
95C4×Dic22C2×C414yes—
96C11×#103—24no—
97C11×#97—22no—
98C11×#95—21no—
99#66899—24no—
100C11⋊#95—21no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104(C2×D11)⋊C8—24no—
105#66880—24no—
106Dic11⋊C8—24no—
107#66874—24no—
108#66867—22no—
109#20741—111nomaximal, Sylow
110C23×D11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11C22×C412yes—
114C2×Q8×C11#4114yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127Q8×D11—216no—
128Q8×D11—28no—
129Q8×D11—28no—
130C2×C4×D11—28no—
131C2×C4×D11—24no—
132C2×C4×D11—24no—
133C2×C4×D11—24no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—41no—
137C2×C4×D11—41no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11C22⋊C414yes—
141C2×C4×D11C22⋊C414yes—
142C2×C4×D11C22×C412yes—
143C2×C4×D11C2×D412yes—
144C2×Dic22—28no—
145C2×Dic22—24no—
146C2×Dic22—21no—
147C2×Dic22—22no—
148C2×Dic22C22×C412yes—
149C2×Dic22#4114yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4C22×C412yes—
158C42×C11—24no—
159C42×C11—42no—
160C42×C11C22×C412yes—
161C42×C11C2×D412yes—
162(C2×D11)⋊C4—44no—
163C4⋊Dic11—24no—
164C4⋊Dic11—21no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11C22×C412yes—
168Dic11⋊C4—24no—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171C4×Dic11—24no—
172C4×Dic11—24no—
173C4×Dic11—24no—
174C4×Dic11—42no—
175C4×Dic11C22⋊C414yes—
176C4×Dic11C22⋊C414yes—
177C4×Dic11C22×C412yes—
178C4×Dic11C2×D412yes—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C22×C4×Q8—111no—
183C2×#432—111no—
184#2283—111no—
185#1824—112no—
186#1805—112no—
187#1805—112no—
188#1787—112no—
189#1763—111no—
190#1763—111no—
191#1763—111no—
192#1763D1111yescharacteristic, complemented
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—21no—
196C22×D11—21no—
197C22×D11C2×C22⋊C412yes—
198C22×D11#13714yes—
199Q8×C11—22no—
200Q8×C11—24no—
201Q8×C11#11714yes—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—22no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C2×C22⋊C412yes—
214C2×C4×C11C2×C22⋊C412yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C2×#4112yes—
218C2×C4×C11C2×#4112yes—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—24no—
222C2×Dic11—22no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225C2×Dic11—22no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11C2×C22⋊C412yes—
232C2×Dic11C2×C22⋊C412yes—
233C2×Dic11C2×C22⋊C412yes—
234C4×D11—216no—
235C4×D11—28no—
236C4×D11—22no—
237C4×D11—22no—
238C4×D11—24no—
239C4×D11—44no—
240C4×D11—48no—
241Dic22—216no—
242Dic22—22no—
243Dic22—24no—
244Dic22#11714yes—
245C8×C11—42no—
246C11⋊C8—42no—
247C23×Q8—111no—
248C2×C4×Q8—111no—
249C2×C4×Q8—118no—
250C2×C4×Q8—111no—
251C2×C4×Q8—111no—
252C2×C4×Q8—221no—
253C2×C4×Q8—221no—
254C2×C4×Q8—224no—
255C2×C4×Q8C2×D1111yescharacteristic
256C22×C4⋊C4—111no—
257C22×C4⋊C4—221no—
258C22×C42—111no—
259C22×C42—221no—
260#432—224no—
261C2×C4⋊C8—112no—
262C2×#103—112no—
263C2×#103—112no—
264C2×#103—112no—
265C2×#103C2×D1112yes—
266C2×C22⋊C8—112no—
267C2×#97—111no—
268C2×#97C2×D1111yescharacteristic
269#383—221no—
270#382—112no—
271#381—221no—
272#380—112no—
273C4×C4⋊C4—111no—
274C4×C4⋊C4C2×D1111yescharacteristic
275C4×C22⋊C4—221no—
276#376—221no—
277#340—112no—
278#340—112no—
279#340—112no—
280#340C2×D1112yes—
281C22×C11C22×C22⋊C411yescharacteristic
282C22×C11#52512yes—
283C22×C11C2×#13712yes—
284C22×C11#57511yescharacteristic
285C22×C11#57511yescharacteristic
286C2×D11—24no—
287C2×D11—24no—
288C2×D11—22no—
289C2×D11—22no—
290C2×D11#41914yes—
291C4×C11—22no—
292C4×C11—22no—
293C4×C11—24no—
294C4×C11—42no—
295C4×C11—82no—
296C4×C11C2×#11711yescharacteristic
297C4×C11C2×#11711yescharacteristic
298C4×C11#52512yes—
299Dic11—22no—
300Dic11—22no—
301Dic11—22no—
302Dic11—24no—
303Dic11—42no—
304Dic11—82no—
305C22×Q8—114no—
306C22×Q8—111no—
307C22×Q8—221no—
308C22×Q8—222no—
309C22×Q8—224no—
310C22×Q8—224no—
311C22×Q8C22×D1111yescharacteristic
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—221no—
316C23×C4—221no—
317C22×C8—112no—
318C22×C8C22×D1112yes—
319C4×Q8—22no—
320C4×Q8—114no—
321C4×Q8—114no—
322C4×Q8—114no—
323C4×Q8—228no—
324C4×Q8—228no—
325C4×Q8—222no—
326C4×Q8—222no—
327C4×Q8—222no—
328C4×Q8C4×D1114yes—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—228no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4C22×D1112yes—
340C2×C4⋊C4C22×D1111yescharacteristic
341C2×C22⋊C4—222no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—111no—
345C2×C42—111no—
346C2×C42—111no—
347C2×C42—114no—
348C2×C42—114no—
349C2×C42—228no—
350C2×C42—221no—
351C2×C42—221no—
352C2×C42—221no—
353C2×C42—221no—
354C2×C42C22×D1111yescharacteristic
355C4⋊C8—224no—
356#103—24no—
357#103—224no—
358#103—224no—
359#103—224no—
360C22⋊C8—224no—
361#97—22no—
362#97—222no—
363#95—21no—
364#95—222no—
365#95—222no—
366#95—222no—
367#95—221no—
368C2×C11#228011yescharacteristic
369C2×C11C2×#41911yescharacteristic
370C2×C11#289611yescharacteristic
371C2×C11#311712yes—
372C2×C11#311712yes—
373D11—24no—
374C24—111no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—112no—
378C2×Q8—114no—
379C2×Q8—224no—
380C2×Q8—228no—
381C2×Q8—228no—
382C2×Q8—2216no—
383C2×Q8—228no—
384C2×Q8—222no—
385C2×Q8—221no—
386C2×Q8C2×C4×D1112yes—
387C2×Q8#433914yes—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—111no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—114no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—114no—
398C22×C4—224no—
399C22×C4—224no—
400C22×C4—228no—
401C22×C4—224no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4—222no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4—442no—
410C22×C4—442no—
411C22×C4D4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4C23×D1111yescharacteristic
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—222no—
420C4⋊C4—24no—
421C4⋊C4—21no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—112no—
425C4⋊C4—224no—
426C4⋊C4—224no—
427C4⋊C4—224no—
428C4⋊C4—224no—
429C4⋊C4—221no—
430C4⋊C4—222no—
431C4⋊C4—222no—
432C4⋊C4C2×C4×D1112yes—
433C22⋊C4—444no—
434C42—24no—
435C42—42no—
436C42—114no—
437C42—114no—
438C42—112no—
439C42—112no—
440C42—224no—
441C42—224no—
442C42—224no—
443C42—442no—
444C42C2×C4×D1112yes—
445C42D4×D1112yes—
446C11#2074111yescharacteristic, complemented, Sylow
447C23—112no—
448C23—114no—
449C23—221no—
450C23—221no—
451C23—222no—
452C23C2×D4×D1111yescharacteristic
453Q8—22no—
454Q8—24no—
455Q8—114no—
456Q8—2216no—
457Q8—222no—
458Q8—224no—
459Q8#6692514yes—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—112no—
472C2×C4—112no—
473C2×C4—112no—
474C2×C4—228no—
475C2×C4—2216no—
476C2×C4—222no—
477C2×C4—221no—
478C2×C4—222no—
479C2×C4—221no—
480C2×C4—222no—
481C2×C4—224no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—224no—
485C2×C4—222no—
486C2×C4—444no—
487C2×C4—448no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4C22⋊C4×D1112yes—
494C2×C4C22⋊C4×D1112yes—
495C2×C4C22×C4×D1111yescharacteristic
496C2×C4C2×#433912yes—
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4#41×D1112yes—
499C8—42no—
500C8—442no—
501C22—114no—
502C22—224no—
503C22—224no—
504C22—222no—
505C22—222no—
506C22C2×C22⋊C4×D1111yescharacteristic
507C22#1062307812yes—
508C22#1062330411yescharacteristic
509C22D11×#13712yes—
510C22#1062330811yescharacteristic
511C4—22no—
512C4—22no—
513C4—24no—
514C4—42no—
515C4—82no—
516C4—222no—
517C4—222no—
518C4—222no—
519C4—224no—
520C4—442no—
521C4—882no—
522C4C2×#6692511yescharacteristic
523C4D11×#11711yescharacteristic
524C4#1062307812yes—
525C2—224no—
526C2#1307099711yescharacteristic
527C2D11×#41911yescharacteristic
528C2#1307713211yescharacteristic
529C2#1307878512yes—
530C2#1307879112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#20741
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
5. #13068630C2semidirect
6. #13068629C2semidirect
8. #13068449C2semidirect
9. #13068447C2semidirect
10. #13068446C2semidirect
11. C11×#1763C2semidirect
16. C4×Q8×D11C4semidirect
192. #1763D11semidirect
446. C11#20741semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
C2×#106223182
#130710122
#130687052
#130686302
#130686292
#130685492
#130684492
#130684472
#130684462
C11×#17632
#2074111