Finite Group Databasebeta

← #14759006

Subgroups — #14759006

Order 2816.

1434 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2C2×D11×#97C211yesmaximal, characteristic, complemented
3#13071012C211yesmaximal, characteristic, complemented
4#13069587C212yesmaximal, complemented
5#13069438C212yesmaximal, complemented
6#13069043C212yesmaximal, complemented
7#13069041C212yesmaximal, complemented
8#13068444C211yesmaximal, characteristic, complemented
9#13068442C211yesmaximal, characteristic, complemented
10#13068441C211yesmaximal, characteristic, complemented
11C11×#1762C211yesmaximal, characteristic, complemented
12C22×#4339—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66993C2211yescharacteristic
15C2×#66991C2211yescharacteristic
16C2×C4×C22⋊D11—21no—
17C22×C8×D11C2212yes—
18#10623079—24no—
19#10623079C418yescomplemented
20C2×#66948C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×#66938—21no—
23C2×#66937—21no—
24C2×C4×D44C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#97C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66896C2212yes—
30C2×#66885C2212yes—
31C2×#66879C2212yes—
32#10622600C2212yes—
33#10622590C2212yes—
34C2×#66873C2212yes—
35C4×(C2×D11)⋊C4—21no—
36C4×C4⋊Dic11C2211yescharacteristic
37#10622545—21no—
38C2×#66867C2211yescharacteristic
39D11×#97—24no—
40#10622277—21no—
41#10622264—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C22×C22⋊D11—21no—
49C22×C22⋊D11—21no—
50C22×C22⋊D11—21no—
51C2×#4339—28no—
52C2×#4339—48no—
53C22×D44—21no—
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×Dic22—21no—
60C22×C8×C11C2312yes—
61C4×D4×C11—22no—
62C4×D4×C11C2×C414yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—21no—
69#66993—22no—
70#66993C2×C414yes—
71#66991—22no—
72#66991C2×C414yes—
73C4×C22⋊D11—28no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—22no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C2×C8×D11—24no—
86C2×C8×D11—24no—
87C2×C8×D11—24no—
88#66948—22no—
89#66948C2×C414yes—
90#66941—22no—
91#66941C2×C414yes—
92#66938—28no—
93#66937—28no—
94C4×D44—22no—
95C4×D44C2×C414yes—
96C42×D11C2×C414yes—
97C42×D11D414yes—
98C11×#102—24no—
99C11×#97—22no—
100C11×#95—21no—
101#66896—24no—
102C11⋊#95—21no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106#66885—24no—
107#66879—24no—
108#66873—24no—
109#66867—22no—
110#21408—111nomaximal, Sylow
111C24×C11—21no—
112C23×D11—21no—
113C23×D11C2×D411yescharacteristic
114C2×D4×C11—21no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11C22×C412yes—
118C22×C4×C11—21no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—44no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2411yescharacteristic
125C2×C22⋊D11—24no—
126C2×C22⋊D11—24no—
127C2×C22⋊D11—24no—
128C2×C22⋊D11—44no—
129C2×C22⋊D11—42no—
130C2×C22⋊D11—42no—
131C2×C22⋊D11—44no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137#4339—432no—
138C2×D44—24no—
139C2×D44—21no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—44no—
143C2×D44C22×C412yes—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×C4×D11—44no—
151C2×C4×D11C22⋊C414yes—
152C2×C4×D11C22⋊C414yes—
153C2×C4×D11C22×C412yes—
154C2×C4×D11C2×D412yes—
155C2×Dic22—24no—
156C2×Dic22—44no—
157C2×C8×C11—22no—
158C2×C8×C11—22no—
159C2×C8×C11#4114yescomplemented
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C22×C412yes—
164C11×C22⋊C4—24no—
165C42×C11—42no—
166C42×C11C22×C412yes—
167C42×C11C2×D412yes—
168C22⋊Dic11—24no—
169(C2×D11)⋊C4—24no—
170(C2×D11)⋊C4—24no—
171(C2×D11)⋊C4—44no—
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11C22×C412yes—
176Dic11⋊C4—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#4114yescomplemented
185C8×D11—216no—
186C2×#532—111no—
187C22×#97—111no—
188#2283—111no—
189#1993—112no—
190#1961—112no—
191#1893—112no—
192#1893—112no—
193#1762—111no—
194#1762—111no—
195#1762—111no—
196#1762D1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—21no—
205C22×D11—21no—
206C22×D11—22no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11C2×C22⋊C412yes—
212C22×D11AGL(1,ℤ/8)14yes—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—42no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11C2×C22⋊C412yes—
227C2×C4×C11C23×C411yescharacteristic
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C2×#4112yes—
230C2×C4×C11C2×#4112yes—
231C22⋊D11—48no—
232C22⋊D11—48no—
233C22⋊D11—48no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—22no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11C2×C22⋊C412yes—
244C2×Dic11C2×C22⋊C412yes—
245C2×Dic11C2×C22⋊C412yes—
246D44—22no—
247D44—22no—
248D44—48no—
249D44—42no—
250C4×D11—28no—
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—24no—
254C4×D11—44no—
255C4×D11—48no—
256Dic22—48no—
257C8×C11—24no—
258C11⋊C8—24no—
259C22×#41—221no—
260C23×C8—112no—
261#532—118no—
262#532—224no—
263C2×C4⋊Q8—111no—
264C2×#127—111no—
265C2×#124—221no—
266C2×#121—111no—
267C2×#121—111no—
268C2×#121—221no—
269C2×C4×D4—111no—
270C2×C4×D4—221no—
271C2×C4×D4C2×D1111yescharacteristic
272C22×C42—111no—
273C2×#102—112no—
274C2×#102—112no—
275C2×#102—112no—
276C2×#102C2×D1112yes—
277C2×#97—112no—
278C2×#97—111no—
279C2×#97—224no—
280C2×#97C2×D1111yescharacteristic
281#383—221no—
282#382—112no—
283#381—221no—
284#380—112no—
285C4×C4⋊C4—111no—
286C4×C4⋊C4C2×D1111yescharacteristic
287C4×C22⋊C4—221no—
288#376—221no—
289#340—112no—
290#340—112no—
291#340—112no—
292#340C2×D1112yes—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11C22×C22⋊C411yescharacteristic
299C22×C11#53212yes—
300C22×C11C2×AGL(1,ℤ/8)12yes—
301C22×C11#57511yescharacteristic
302C22×C11#57511yescharacteristic
303C2×D11—22no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—22no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11#41814yes—
313C4×C11—22no—
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—82no—
317C4×C11C4×#4111yescharacteristic
318C4×C11C4×#4111yescharacteristic
319C4×C11#52512yes—
320Dic11—22no—
321Dic11—22no—
322Dic11—22no—
323Dic11—42no—
324Dic11—82no—
325C2×#41—228no—
326C2×#41—448no—
327C22×Q8—221no—
328C22×D4—111no—
329C22×D4—221no—
330C22×D4—221no—
331C22×D4—221no—
332C22×D4—221no—
333C22×D4C22×D1111yescharacteristic
334C23×C4—21no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—111no—
338C23×C4—221no—
339C22×C8—112no—
340C22×C8—224no—
341C22×C8—224no—
342C22×C8—224no—
343C22×C8C22×D1112yes—
344C4⋊Q8—114no—
345C4⋊Q8—222no—
346#127—114no—
347#127—222no—
348#124—228no—
349#121—114no—
350#121—114no—
351#121—228no—
352#121—222no—
353#121—222no—
354C4×D4—22no—
355C4×D4—114no—
356C4×D4—228no—
357C4×D4—222no—
358C4×D4C4×D1114yes—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1112yes—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—221no—
366C2×C22⋊C4—221no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C42—21no—
370C2×C42—111no—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—114no—
374C2×C42—114no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377#102—24no—
378#102—224no—
379#102—224no—
380#102—224no—
381#97—22no—
382#97—224no—
383#97—222no—
384#95—21no—
385#95—222no—
386#95—222no—
387#95—222no—
388#95—221no—
389C2×C11—82no—
390C2×C11#229711yescharacteristic
391C2×C11C2×#41811yescharacteristic
392C2×C11#289611yescharacteristic
393C2×C11#318012yes—
394C2×C11#318012yes—
395D11—24no—
396D11—82no—
397C24—21no—
398C24—111no—
399C24—221no—
400#41—4432no—
401C2×Q8—224no—
402C2×Q8—444no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—112no—
407C2×D4—224no—
408C2×D4—224no—
409C2×D4—224no—
410C2×D4—224no—
411C2×D4—222no—
412C2×D4—221no—
413C2×D4—222no—
414C2×D4—444no—
415C2×D4—444no—
416C2×D4—442no—
417C2×D4—442no—
418C2×D4—444no—
419C2×D4C2×C4×D1112yes—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—114no—
428C22×C4—112no—
429C22×C4—112no—
430C22×C4—114no—
431C22×C4—224no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—221no—
435C22×C4—224no—
436C22×C4—222no—
437C22×C4—441no—
438C22×C4—441no—
439C22×C4—444no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—114no—
446C2×C8—2216no—
447C2×C8—222no—
448C2×C8—222no—
449C2×C8#433914yescomplemented
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—112no—
454C4⋊C4—224no—
455C4⋊C4—221no—
456C4⋊C4—222no—
457C4⋊C4—222no—
458C4⋊C4C2×C4×D1112yes—
459C22⋊C4—24no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C22⋊C4—224no—
463C22⋊C4—444no—
464C42—42no—
465C42—114no—
466C42—114no—
467C42—112no—
468C42—112no—
469C42—442no—
470C42C2×C4×D1112yes—
471C42D4×D1112yes—
472C11#2140811yescharacteristic, complemented, Sylow
473C23—22no—
474C23—42no—
475C23—41no—
476C23—41no—
477C23—42no—
478C23—112no—
479C23—114no—
480C23—221no—
481C23—221no—
482C23—222no—
483C23—222no—
484C23—442no—
485C23—441no—
486C23—441no—
487C23—442no—
488C23C2×D4×D1111yescharacteristic
489Q8—448no—
490D4—22no—
491D4—22no—
492D4—42no—
493D4—222no—
494D4—222no—
495D4—448no—
496D4—448no—
497D4—448no—
498D4—448no—
499D4—442no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—48no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—112no—
510C2×C4—112no—
511C2×C4—112no—
512C2×C4—228no—
513C2×C4—222no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—224no—
520C2×C4—222no—
521C2×C4—444no—
522C2×C4—448no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4C22⋊C4×D1112yes—
528C2×C4C22⋊C4×D1112yes—
529C2×C4C22×C4×D1111yescharacteristic
530C2×C4C2×#433912yes—
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4#41×D1112yes—
533C8—24no—
534C8—224no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—82no—
539C22—82no—
540C22—114no—
541C22—224no—
542C22—224no—
543C22—222no—
544C22—222no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—882no—
549C22—882no—
550C22C2×C22⋊C4×D1111yescharacteristic
551C22#1062307912yes—
552C22D11×AGL(1,ℤ/8)12yes—
553C22#1062330411yescharacteristic
554C22#1062330811yescharacteristic
555C4—22no—
556C4—22no—
557C4—42no—
558C4—82no—
559C4—222no—
560C4—222no—
561C4—222no—
562C4—442no—
563C4—882no—
564C4C4×#433911yescharacteristic
565C4#1062305311yescharacteristic
566C4#1062307812yes—
567C2—82no—
568C2—224no—
569C2—882no—
570C2#1307110211yescharacteristic
571C2D11×#41811yescharacteristic
572C2#1307713211yescharacteristic
573C2#1307931012yes—
574C2#1307931212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1762C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
cosocleC22×C4×C11C24
hypercenter#1762D11
hypocenterC11#21408
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×D11×#97C2semidirect
3. #13071012C2semidirect
4. #13069587C2semidirect
5. #13069438C2semidirect
6. #13069043C2semidirect
7. #13069041C2semidirect
8. #13068444C2semidirect
9. #13068442C2semidirect
10. #13068441C2semidirect
11. C11×#1762C2semidirect
19. #10623079C4semidirect
159. C2×C8×C11#41semidirect
184. C2×C11⋊C8#41semidirect
196. #1762D11semidirect
449. C2×C8#4339semidirect
472. C11#21408semidirect

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×D11×#972
#130710122
#130695872
#130694382
#130690432
#130690412
#130684442
#130684422
#130684412
C11×#17622
#2140811