Finite Group Databasebeta

← #14753829

Subgroups — #14753829

Order 2816.

1350 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×C4×Q8×D11C211yesmaximal, characteristic
2C2×#10622318C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13068701C212yesmaximal
5#13068620C212yesmaximal, complemented
6#13068619C212yesmaximal, 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×#66925—21no—
22C2×C42×D11—21no—
23C2×C42×D11C2211yescharacteristic
24C2×C4×Dic22—21no—
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#97C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2212yes—
30C2×(C2×D11)⋊C8C2212yes—
31C2×#66880C2212yes—
32C2×Dic11⋊C8C2212yes—
33#10622600C2212yes—
34#10622589C2212yes—
35C2×#66874C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37C4×Dic11⋊C4—21no—
38C2×#66867C2211yescharacteristic
39#10622318—24no—
40#10622280—21no—
41#10622263—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×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86C4⋊C4×D11—28no—
87C4⋊C4×D11—22no—
88C4⋊C4×D11C2×C414yes—
89#66940—28no—
90#66940—22no—
91#66940C2×C414yes—
92#66925—44no—
93C42×D11—28no—
94C42×D11C2×C414yes—
95C42×D11D414yes—
96C4×Dic22—22no—
97C4×Dic22—28no—
98C4×Dic22C2×C414yes—
99C11×#103—24no—
100C11×#97—22no—
101C11×#95—21no—
102#66899—24no—
103C11⋊#95—21no—
104C11⋊#95—22no—
105(C2×D11)⋊C8—24no—
106#66880—24no—
107Dic11⋊C8—24no—
108#66874—24no—
109#66867—22no—
110#20740—111nomaximal, Sylow
111C23×D11C2×D411yescharacteristic
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C2×Q8×C11#4114yes—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128Q8×D11—216no—
129Q8×D11—28no—
130Q8×D11—28no—
131C2×C4×D11—28no—
132C2×C4×D11—24no—
133C2×C4×D11—24no—
134C2×C4×D11—24no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×C4×D11C22⋊C414yes—
142C2×C4×D11C22⋊C414yes—
143C2×C4×D11C22×C412yes—
144C2×C4×D11C2×D412yes—
145C2×Dic22—28no—
146C2×Dic22—24no—
147C2×Dic22—21no—
148C2×Dic22—22no—
149C2×Dic22C22×C412yes—
150C2×Dic22#4114yes—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C22×C412yes—
159C42×C11—24no—
160C42×C11—42no—
161C42×C11C22×C412yes—
162C42×C11C2×D412yes—
163(C2×D11)⋊C4—44no—
164C4⋊Dic11—24no—
165C4⋊Dic11—21no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11C22×C412yes—
169Dic11⋊C4—24no—
170Dic11⋊C4—24no—
171Dic11⋊C4—24no—
172Dic11⋊C4—44no—
173Dic11⋊C4—44no—
174C4×Dic11—24no—
175C4×Dic11—24no—
176C4×Dic11—24no—
177C4×Dic11—42no—
178C4×Dic11C22⋊C414yes—
179C4×Dic11C22⋊C414yes—
180C4×Dic11C22×C412yes—
181C4×Dic11C2×D412yes—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C22×C4×Q8—111no—
186C2×#432—111no—
187#2285—111no—
188#1823—112no—
189#1803—112no—
190#1803—112no—
191#1787—112no—
192#1763—111no—
193#1763—111no—
194#1763—111no—
195#1763D1111yescharacteristic, complemented
196C23×C11C22×D411yescharacteristic
197C22×D11—22no—
198C22×D11—22no—
199C22×D11C2×C22⋊C412yes—
200C22×D11AGL(1,ℤ/8)12yes—
201C22×D11#13712yes—
202Q8×C11—22no—
203Q8×C11—24no—
204Q8×C11#11714yescomplemented
205C2×C4×C11—22no—
206C2×C4×C11—24no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11C2×C22⋊C412yes—
217C2×C4×C11C2×C22⋊C412yes—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4112yes—
221C2×C4×C11C2×#4112yes—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—22no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C412yes—
236C2×Dic11#13714yes—
237C4×D11—216no—
238C4×D11—28no—
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—24no—
242C4×D11—28no—
243C4×D11—48no—
244Dic22—216no—
245Dic22—22no—
246Dic22—24no—
247Dic22#11714yescomplemented
248C8×C11—42no—
249C11⋊C8—42no—
250C23×Q8—111no—
251C2×C4×Q8—111no—
252C2×C4×Q8—118no—
253C2×C4×Q8—111no—
254C2×C4×Q8—111no—
255C2×C4×Q8—221no—
256C2×C4×Q8—221no—
257C2×C4×Q8—224no—
258C2×C4×Q8C2×D1111yescharacteristic
259C2×#117—221no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—221no—
262C22×C42—111no—
263C22×C42—221no—
264#432—224no—
265C2×C4⋊C8—112no—
266C2×#103—112no—
267C2×#103—112no—
268C2×#103—112no—
269C2×#103C2×D1112yes—
270C2×C22⋊C8—112no—
271C2×#97—111no—
272C2×#97C2×D1111yescharacteristic
273#384—112no—
274#382—221no—
275#380—112no—
276#380—221no—
277C4×C4⋊C4—111no—
278C4×C4⋊C4—221no—
279C4×C4⋊C4C2×D1111yescharacteristic
280#340—112no—
281#340—112no—
282#340—112no—
283#340C2×D1112yes—
284C22×C11C22×C22⋊C411yescharacteristic
285C22×C11#52512yes—
286C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
287C22×C11C2×#13712yes—
288C22×C11C2×#13711yescharacteristic
289C2×D11—24no—
290C2×D11—24no—
291C2×D11—22no—
292C2×D11—22no—
293C2×D11#41714yes—
294C4×C11—22no—
295C4×C11—22no—
296C4×C11—24no—
297C4×C11—42no—
298C4×C11—82no—
299C4×C11C2×#11711yescharacteristic
300C4×C11C2×#11711yescharacteristic
301C4×C11#52512yes—
302Dic11—22no—
303Dic11—22no—
304Dic11—24no—
305Dic11—42no—
306Dic11—82no—
307Dic11#41914yes—
308C22×Q8—114no—
309C22×Q8—111no—
310C22×Q8—221no—
311C22×Q8—222no—
312C22×Q8—224no—
313C22×Q8—224no—
314C22×Q8C22×D1111yescharacteristic
315C23×C4—111no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—221no—
319C23×C4—221no—
320C22×C8—112no—
321C22×C8C22×D1112yes—
322C4×Q8—22no—
323C4×Q8—114no—
324C4×Q8—114no—
325C4×Q8—114no—
326C4×Q8—228no—
327C4×Q8—228no—
328C4×Q8—222no—
329C4×Q8—222no—
330C4×Q8—222no—
331C4×Q8C4×D1114yes—
332#117—444no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—111no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—228no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4C22×D1112yes—
346C2×C4⋊C4C22×D1111yescharacteristic
347C2×C22⋊C4—222no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—111no—
351C2×C42—111no—
352C2×C42—111no—
353C2×C42—114no—
354C2×C42—114no—
355C2×C42—228no—
356C2×C42—221no—
357C2×C42—221no—
358C2×C42—221no—
359C2×C42—221no—
360C2×C42C22×D1111yescharacteristic
361C4⋊C8—224no—
362#103—24no—
363#103—224no—
364#103—224no—
365#103—224no—
366C22⋊C8—224no—
367#97—22no—
368#97—222no—
369#95—21no—
370#95—222no—
371#95—221no—
372C2×C11#228011yescharacteristic
373C2×C11C2×#41911yescharacteristic
374C2×C11C2×#41711yescharacteristic
375C2×C11#311212yes—
376C2×C11#311312yes—
377D11—24no—
378C24—111no—
379C2×Q8—21no—
380C2×Q8—22no—
381C2×Q8—112no—
382C2×Q8—114no—
383C2×Q8—224no—
384C2×Q8—228no—
385C2×Q8—228no—
386C2×Q8—2216no—
387C2×Q8—228no—
388C2×Q8—222no—
389C2×Q8—221no—
390C2×Q8C2×C4×D1112yes—
391C2×Q8#433914yes—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—111no—
396C22×C4—111no—
397C22×C4—111no—
398C22×C4—114no—
399C22×C4—114no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—224no—
403C22×C4—224no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—228no—
407C22×C4—224no—
408C22×C4—221no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—442no—
414C22×C4—442no—
415C22×C4D4×D1111yescharacteristic
416C22×C4D4×D1111yescharacteristic
417C22×C4C23×D1111yescharacteristic
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C4⋊C4—24no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—112no—
429C4⋊C4—224no—
430C4⋊C4—224no—
431C4⋊C4—224no—
432C4⋊C4—224no—
433C4⋊C4—221no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—444no—
437C4⋊C4—444no—
438C4⋊C4C2×C4×D1112yes—
439C22⋊C4—444no—
440C42—24no—
441C42—42no—
442C42—114no—
443C42—114no—
444C42—112no—
445C42—112no—
446C42—224no—
447C42—224no—
448C42—224no—
449C42—442no—
450C42C2×C4×D1112yes—
451C42D4×D1112yes—
452C11#2074011yescharacteristic, complemented, Sylow
453C23—112no—
454C23—112no—
455C23—112no—
456C23—222no—
457C23—222no—
458C23C2×D4×D1111yescharacteristic
459Q8—22no—
460Q8—24no—
461Q8—114no—
462Q8—2216no—
463Q8—222no—
464Q8—224no—
465Q8#6692514yescomplemented
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—112no—
478C2×C4—114no—
479C2×C4—112no—
480C2×C4—112no—
481C2×C4—228no—
482C2×C4—228no—
483C2×C4—2216no—
484C2×C4—222no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—222no—
488C2×C4—224no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—222no—
493C2×C4—448no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4C22⋊C4×D1112yes—
500C2×C4C22⋊C4×D1112yes—
501C2×C4C22×C4×D1111yescharacteristic
502C2×C4C2×#433912yes—
503C2×C4C2×D4×D1111yescharacteristic
504C2×C4#41×D1112yes—
505C8—42no—
506C8—442no—
507C22—114no—
508C22—222no—
509C22—222no—
510C22—224no—
511C22—224no—
512C22C2×C22⋊C4×D1111yescharacteristic
513C22#1062307812yes—
514C22D11×AGL(1,ℤ/8)11yescharacteristic
515C22D11×#13712yes—
516C22D11×#13711yescharacteristic
517C4—22no—
518C4—22no—
519C4—24no—
520C4—42no—
521C4—82no—
522C4—114no—
523C4—222no—
524C4—222no—
525C4—224no—
526C4—442no—
527C4—882no—
528C4C2×#6692511yescharacteristic
529C4D11×#11711yescharacteristic
530C4#1062307812yes—
531C2—224no—
532C2#1307099711yescharacteristic
533C2D11×#41911yescharacteristic
534C2D11×#41711yescharacteristic
535C2#1307873612yes—
536C2#1307874412yes—
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#20740
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. #13068620C2semidirect
6. #13068619C2semidirect
8. #13068449C2semidirect
9. #13068447C2semidirect
10. #13068446C2semidirect
11. C11×#1763C2semidirect
16. C4×Q8×D11C4semidirect
195. #1763D11semidirect
204. Q8×C11#117semidirect
247. Dic22#117semidirect
452. C11#20740semidirect
465. Q8#66925semidirect

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
#130710202
#130687012
#130686202
#130686192
#130685492
#130684492
#130684472
#130684462
C11×#17632
#2074011