Finite Group Databasebeta

← #14758990

Subgroups — #14758990

Order 2816.

1230 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×#10623111C211yesmaximal, characteristic
2C2×D11×#97C211yesmaximal, characteristic, complemented
3#13071020C211yesmaximal, characteristic, complemented
4#13069583C212yesmaximal, complemented
5#13069429C212yesmaximal, complemented
6#13069043C212yesmaximal
7#13069036C212yesmaximal, complemented
8#13068446C211yesmaximal, characteristic, complemented
9#13068444C211yesmaximal, characteristic, complemented
10#13068442C211yesmaximal, characteristic, complemented
11C11×#1763C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C2211yescharacteristic
14C2×#66999C2211yescharacteristic
15C22×C8×D11C2212yes—
16#10623111—24no—
17#10623111C418yescomplemented
18C2×#66951—21no—
19C2×#66948C2211yescharacteristic
20C2×#66947—21no—
21C2×#66943C2211yescharacteristic
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×#66925—21no—
25C2×#66925—21no—
26C2×C42×D11C2211yescharacteristic
27C2×C11×#103C2212yes—
28C2×C11×#97C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66899C2212yes—
31C2×#66885C2212yes—
32C2×#66879C2212yes—
33#10622600C2212yes—
34#10622589C2212yes—
35C2×#66873C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37C4×Dic11⋊C4—21no—
38C2×#66867C2211yescharacteristic
39D11×#97—24no—
40#10622280—21no—
41#10622263—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D44—21no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C4×D11D411yescharacteristic
51C22×C4×D11D411yescharacteristic
52C22×C4×D11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C4×Q8×C11—22no—
55C4×Q8×C11C2×C414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62#67000—22no—
63#67000C2×C414yes—
64#66999—22no—
65#66999C2×C414yes—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84C2×C8×D11—24no—
85C2×C8×D11—24no—
86C2×C8×D11—24no—
87#66951—28no—
88#66948—22no—
89#66948C2×C414yes—
90#66947—28no—
91#66943—22no—
92#66943C2×C414yes—
93C4×D44—28no—
94C4×D44—22no—
95C4×D44C2×C414yes—
96#66925—28no—
97#66925—44no—
98C42×D11C2×C414yes—
99C42×D11D414yes—
100C11×#103—24no—
101C11×#97—22no—
102C11×#95—21no—
103#66899—24no—
104C11⋊#95—21no—
105C11⋊#95—22no—
106#66885—24no—
107#66879—24no—
108#66873—24no—
109#66867—22no—
110#21406—111nomaximal, Sylow
111C23×D11—21no—
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11C22×C412yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C2×D44—24no—
129C2×D44—21no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44C22×C412yes—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—24no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—42no—
141C2×C4×D11—44no—
142C2×C4×D11C22⋊C414yes—
143C2×C4×D11C22⋊C414yes—
144C2×C4×D11C22×C412yes—
145C2×C4×D11C2×D412yes—
146C2×C8×C11—22no—
147C2×C8×C11—22no—
148C2×C8×C11#4114yes—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C22×C412yes—
154C42×C11—24no—
155C42×C11—42no—
156C42×C11C22×C412yes—
157C42×C11C2×D412yes—
158(C2×D11)⋊C4—24no—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
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—44no—
172Dic11⋊C4—44no—
173C4×Dic11—42no—
174C4×Dic11C22⋊C414yes—
175C4×Dic11C22⋊C414yes—
176C4×Dic11C22×C412yes—
177C4×Dic11C2×D412yes—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8#4114yes—
181C8×D11—216no—
182C2×#529—111no—
183C22×#97—111no—
184#2285—111no—
185#1992—112no—
186#1959—112no—
187#1893—112no—
188#1892—112no—
189#1763—111no—
190#1763D1111yescharacteristic, complemented
191#1762—111no—
192#1762—111no—
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—42no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—42no—
201C22×D11C2×C22⋊C412yes—
202C22×D11AGL(1,ℤ/8)12yes—
203C22×D11#13712yes—
204Q8×C11—22no—
205Q8×C11—22no—
206Q8×C11—42no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—42no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11C2×C22⋊C412yes—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4112yes—
223C2×C4×C11C2×#4112yes—
224C2×Dic11—22no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11C2×C22⋊C412yes—
234C2×Dic11C2×C22⋊C412yes—
235C2×Dic11C2×C22⋊C412yes—
236D44—22no—
237D44—22no—
238D44—48no—
239D44—42no—
240C4×D11—28no—
241C4×D11—22no—
242C4×D11—22no—
243C4×D11—24no—
244C4×D11—44no—
245C4×D11—48no—
246C8×C11—24no—
247C11⋊C8—24no—
248C23×C8—112no—
249#529—118no—
250#529—224no—
251C2×#126—221no—
252C2×#125—111no—
253C2×#124—111no—
254C2×#123—221no—
255C2×C22⋊Q8—111no—
256C2×#121—111no—
257C2×C4×Q8C2×D1111yescharacteristic
258C2×C4×D4—111no—
259C2×C4×D4—221no—
260C2×#117—221no—
261C2×#117—221no—
262C22×C42—111no—
263C2×#103—112no—
264C2×#103C2×D1112yes—
265C2×#102—112no—
266C2×#102—112no—
267C2×#97—112no—
268C2×#97—111no—
269C2×#97—224no—
270C2×#97C2×D1111yescharacteristic
271#384—112no—
272#382—221no—
273#380—112no—
274#380—221no—
275C4×C4⋊C4—111no—
276C4×C4⋊C4—221no—
277C4×C4⋊C4C2×D1111yescharacteristic
278#340—112no—
279#340—112no—
280#340—112no—
281#340C2×D1112yes—
282C22×C11C22×C22⋊C411yescharacteristic
283C22×C11#53212yes—
284C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C22×C11#57512yes—
287C2×D11—22no—
288C2×D11—24no—
289C2×D11—24no—
290C2×D11—22no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—82no—
295C2×D11—82no—
296C2×D11#41714yes—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—82no—
302C4×C11C4×#4111yescharacteristic
303C4×C11C4×#4111yescharacteristic
304C4×C11#52512yes—
305Dic11—22no—
306Dic11—22no—
307Dic11—22no—
308Dic11—42no—
309Dic11—82no—
310C22×Q8C22×D1111yescharacteristic
311C22×D4—111no—
312C22×D4—221no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—221no—
317C22×C8—112no—
318C22×C8—224no—
319C22×C8—224no—
320C22×C8—224no—
321C22×C8C22×D1112yes—
322#126—228no—
323#125—114no—
324#125—222no—
325#124—114no—
326#124—222no—
327#123—228no—
328C22⋊Q8—114no—
329C22⋊Q8—222no—
330#121—114no—
331#121—222no—
332C4×Q8—22no—
333C4×Q8C4×D1114yes—
334C4×D4—114no—
335C4×D4—228no—
336C4×D4—222no—
337#117—228no—
338#117—444no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—111no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4C22×D1112yes—
348C2×C4⋊C4C22×D1111yescharacteristic
349C2×C22⋊C4—221no—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—222no—
355C2×C42—21no—
356C2×C42—21no—
357C2×C42—111no—
358C2×C42—111no—
359C2×C42—111no—
360C2×C42—114no—
361C2×C42—114no—
362C2×C42—221no—
363C2×C42C22×D1111yescharacteristic
364#103—24no—
365#103—224no—
366#102—224no—
367#102—224no—
368#97—22no—
369#97—224no—
370#97—222no—
371#95—21no—
372#95—222no—
373#95—221no—
374C2×C11#229711yescharacteristic
375C2×C11C2×#41711yescharacteristic
376C2×C11#289611yescharacteristic
377C2×C11#318012yes—
378C2×C11#318112yes—
379D11—24no—
380D11—82no—
381C24—111no—
382C24—221no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8C2×C4×D1112yes—
387C2×D4—112no—
388C2×D4—224no—
389C2×D4—222no—
390C2×D4—221no—
391C2×D4—222no—
392C2×D4—442no—
393C2×D4—442no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—111no—
398C22×C4—111no—
399C22×C4—111no—
400C22×C4—114no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—114no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—221no—
409C22×C4—224no—
410C22×C4—222no—
411C22×C4—442no—
412C22×C4—444no—
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4C23×D1111yescharacteristic
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—114no—
419C2×C8—2216no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8#433914yes—
423C4⋊C4—24no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—112no—
428C4⋊C4—224no—
429C4⋊C4—224no—
430C4⋊C4—224no—
431C4⋊C4—221no—
432C4⋊C4—222no—
433C4⋊C4—222no—
434C4⋊C4—444no—
435C4⋊C4—444no—
436C4⋊C4C2×C4×D1112yes—
437C22⋊C4—224no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C22⋊C4—224no—
441C22⋊C4—224no—
442C22⋊C4—444no—
443C42—24no—
444C42—42no—
445C42—114no—
446C42—114no—
447C42—112no—
448C42—112no—
449C42—442no—
450C42C2×C4×D1112yes—
451C42D4×D1112yes—
452C11#2140611yescharacteristic, complemented, Sylow
453C23—112no—
454C23—112no—
455C23—112no—
456C23—222no—
457C23—222no—
458C23—222no—
459C23—441no—
460C23—441no—
461C23—442no—
462C23—442no—
463C23C2×D4×D1111yescharacteristic
464Q8—22no—
465Q8—22no—
466Q8—42no—
467D4—222no—
468D4—222no—
469D4—448no—
470D4—442no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—112no—
483C2×C4—112no—
484C2×C4—112no—
485C2×C4—228no—
486C2×C4—221no—
487C2×C4—221no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—222no—
494C2×C4—444no—
495C2×C4—448no—
496C2×C4—442no—
497C2×C4—442no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4C22⋊C4×D1112yes—
501C2×C4C22⋊C4×D1112yes—
502C2×C4C22×C4×D1111yescharacteristic
503C2×C4C2×#433912yes—
504C2×C4C2×D4×D1111yescharacteristic
505C2×C4#41×D1112yes—
506C8—24no—
507C8—224no—
508C22—114no—
509C22—224no—
510C22—224no—
511C22—222no—
512C22—222no—
513C22—442no—
514C22—442no—
515C22—442no—
516C22—882no—
517C22—882no—
518C22C2×C22⋊C4×D1111yescharacteristic
519C22#1062307912yes—
520C22D11×AGL(1,ℤ/8)11yescharacteristic
521C22D11×#13711yescharacteristic
522C22#1062330812yes—
523C4—22no—
524C4—22no—
525C4—42no—
526C4—42no—
527C4—82no—
528C4—222no—
529C4—222no—
530C4—222no—
531C4—442no—
532C4—882no—
533C4C4×#433911yescharacteristic
534C4#1062305311yescharacteristic
535C4#1062307812yes—
536C2—224no—
537C2—882no—
538C2#1307110211yescharacteristic
539C2D11×#41711yescharacteristic
540C2#1307713411yescharacteristic
541C2#1307931012yes—
542C2#1307932312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#21406
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
2. C2×D11×#97C2semidirect
3. #13071020C2semidirect
4. #13069583C2semidirect
5. #13069429C2semidirect
7. #13069036C2semidirect
8. #13068446C2semidirect
9. #13068444C2semidirect
10. #13068442C2semidirect
11. C11×#1763C2semidirect
17. #10623111C4semidirect
190. #1763D11semidirect
452. C11#21406semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
C2×D11×#972
#130710202
#130695832
#130694292
#130690432
#130690362
#130684462
#130684442
#130684422
C11×#17632
#2140611