Finite Group Databasebeta

← #14787689

Subgroups — #14787689

Order 2816.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4#13073532C211yesmaximal, characteristic
5#13069811C212yesmaximal, complemented
6#13069618C212yesmaximal, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13069409C211yesmaximal, characteristic, complemented
9#13068932C212yesmaximal, complemented
10#13068810C212yesmaximal, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C2212yes—
14C22×#4325C2211yescharacteristic
15#10623110—24no—
16#10623110—24no—
17C2×#66949—22no—
18C2×#66948—21no—
19C2×#66948C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×C4×D44—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×#66923—21no—
25C2×#66922C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#103C2212yes—
28C11×#384C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×#66881C2212yes—
34C4×#4325—24no—
35#10622604—22no—
36#10622600—21no—
37#10622600C2212yes—
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622455—24no—
42C11×#340C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D44—22no—
47C22×D44D411yescharacteristic
48C22×D44C2311yescharacteristic
49C22×C4×D11—22no—
50C22×C4×D11—21no—
51C22×C4×D11C2312yes—
52C22×Dic22—21no—
53C22×C8×C11C2312yes—
54C4×Q8×C11—22no—
55C4×Q8×C11D414yescomplemented
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C42×C11—21no—
62C2×C42×C11C2311yescharacteristic
63#66999—24no—
64#66999—24no—
65C2×#4325—22no—
66C2×#4325—22no—
67C2×#4325—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4D412yes—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81#66949—216no—
82#66948—24no—
83#66948—42no—
84#66948—44no—
85C4⋊C4×D11—24no—
86C4⋊C4×D11—24no—
87C4×D44—28no—
88C4×D44—22no—
89C4×D44—22no—
90C4×D44—22no—
91C4×D44—22no—
92#66923—28no—
93#66922—22no—
94#66922D414yescomplemented
95C11×C4⋊C8—22no—
96C11×#103—42no—
97#66899—22no—
98C11⋊#95—22no—
99#66885—24no—
100(C2×D11)⋊C8—24no—
101(C2×D11)⋊C8—42no—
102#66881—24no—
103#66873—22no—
104#66872—22no—
105C4×C11⋊C8—22no—
106#24118—111nomaximal, Sylow
107C23×D11—21no—
108C23×D11C2×D412yes—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—21no—
114C2×Q8×C11C2×D412yes—
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—22no—
122C22×Dic11—21no—
123C22×Dic11C2×D412yes—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—44no—
132C2×D44—44no—
133C2×D44—82no—
134C2×D44SD1614yescomplemented
135C2×D44#4112yes—
136C2×C4×D11—28no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C4×D11—82no—
147C2×C4×D11—82no—
148C2×Dic22—24no—
149C2×Dic22—81no—
150C2×Dic22—81no—
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⋊C4—42no—
159C11×C4⋊C4—81no—
160C11×C4⋊C4C2×D412yes—
161C42×C11—24no—
162C42×C11C2×D412yes—
163C42×C11C2×D412yes—
164#4325—28no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—44no—
168(C2×D11)⋊C4—44no—
169(C2×D11)⋊C4—42no—
170C4⋊Dic11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11C2×D414yes—
176Dic11⋊C4—28no—
177Dic11⋊C4—28no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8#4112yes—
184C2×#554—111no—
185C2×#476—111no—
186C2×C4×SD16—111no—
187#2537—111no—
188#2035—112no—
189#2000—112no—
190#1990—111no—
191#1954—111no—
192#1874—112no—
193#1853—112no—
194#1803D1111yescharacteristic, complemented
195C23×C11C22×D411yescharacteristic
196C22×D11—22no—
197C22×D11—22no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11C2×SD1614yes—
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—41no—
213Q8×C11—41no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11#12012yes—
226C2×C4×C11#12012yes—
227C2×C4×C11C2×SD1612yes—
228C2×C4×C11#13712yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C112−1+411yescharacteristic
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244D44—22no—
245D44—22no—
246D44—28no—
247D44—41no—
248D44—41no—
249D44—88no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—42no—
253C4×D11—42no—
254C4×D11—88no—
255C4×D11—84no—
256Dic22—84no—
257C8×C11—42no—
258C11⋊C8—22no—
259C11⋊C8—41no—
260C22×SD16—111no—
261#554—224no—
262#554—224no—
263C2×C4⋊Q8—111no—
264C2×#125—221no—
265C2×C22⋊Q8—112no—
266C2×C22⋊Q8—222no—
267C2×#121—112no—
268C2×#121—221no—
269C2×C4×Q8C2×D1111yescharacteristic
270C2×C4×D4—111no—
271C2×C4×D4—111no—
272C2×C4×D4—221no—
273C22×C4⋊C4—112no—
274#476—224no—
275C4×SD16—224no—
276C2×#106—112no—
277C2×#106—111no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#103—111no—
280C2×#103C2×D1112yes—
281C2×#102—112no—
282C2×#102—111no—
283C2×C22⋊C8—112no—
284C2×C22⋊C8—112no—
285C2×C4×C8—111no—
286#394—222no—
287#384C2×D1111yescharacteristic
288#380—112no—
289#380—221no—
290#340—112no—
291#340—112no—
292#340C2×D1112yes—
293C22×C11C2×#12011yescharacteristic
294C22×C11#54611yescharacteristic
295C22×C11#54711yescharacteristic
296C22×C11C22×SD1611yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C22×C11#57611yescharacteristic
299C22×C11#57711yescharacteristic
300C2×D11—24no—
301C2×D11—24no—
302C2×D11—24no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—81no—
311C2×D11—81no—
312C2×D11—81no—
313C2×D11—81no—
314C4×C11—22no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—82no—
318C4×C11#44814yes—
319C4×C11#52511yescharacteristic
320C4×C11#53711yescharacteristic
321C4×C11#54811yescharacteristic
322C4×C11#55011yescharacteristic
323Dic11—42no—
324Dic11—44no—
325Dic11—81no—
326C22×Q8—221no—
327C22×Q8C22×D1111yescharacteristic
328C22×D4—111no—
329C22×D4—111no—
330C22×D4—222no—
331C23×C4—112no—
332C23×C4—222no—
333C23×C4—221no—
334C2×SD16—222no—
335C2×SD16—222no—
336C2×SD16—222no—
337C22×C8—111no—
338C22×C8—111no—
339C22×C8C22×D1112yes—
340C4⋊Q8—114no—
341C4⋊Q8—222no—
342#125—228no—
343C22⋊Q8—2216no—
344C22⋊Q8—224no—
345C22⋊Q8—224no—
346#121—224no—
347#121—442no—
348#121—444no—
349C4×Q8—22no—
350C4×Q8D4414yescomplemented
351C4×D4—228no—
352C4×D4—222no—
353C4×D4—222no—
354C4×D4—222no—
355C4×D4—222no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—224no—
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—112no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—221no—
374C2×C42—21no—
375C2×C42C22×D1111yescharacteristic
376#106—224no—
377#106—222no—
378C4⋊C8—22no—
379#103—42no—
380#103—222no—
381#102—224no—
382#102—222no—
383C22⋊C8—224no—
384C22⋊C8—442no—
385C4×C8—222no—
386#95—222no—
387C2×C11#240711yescharacteristic
388C2×C11C2×#44811yescharacteristic
389C2×C11#301211yescharacteristic
390C2×C11#329511yescharacteristic
391C2×C11#333111yescharacteristic
392C2×C11#333511yescharacteristic
393C2×C11#335711yescharacteristic
394D11—44no—
395D11—82no—
396C24—112no—
397C24—221no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—224no—
404C2×Q8—881no—
405C2×Q8—881no—
406C2×Q8C2×D4412yes—
407C2×D4—114no—
408C2×D4—112no—
409C2×D4—222no—
410C2×D4—222no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—221no—
416C2×D4—444no—
417C2×D4—444no—
418C2×D4—882no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—112no—
423C22×C4—228no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—221no—
432C22×C4—442no—
433C22×C4—442no—
434C22×C4—442no—
435C22×C4—882no—
436C22×C4—882no—
437C22×C4D4×D1111yescharacteristic
438C22×C4D4×D1111yescharacteristic
439C22×C4C23×D1111yescharacteristic
440SD16—228no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—112no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C4⋊C4—24no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—42no—
455C4⋊C4—81no—
456C4⋊C4—114no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—222no—
460C4⋊C4—224no—
461C4⋊C4—222no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4C2×D4412yes—
465C22⋊C4—228no—
466C22⋊C4—224no—
467C22⋊C4—444no—
468C22⋊C4—444no—
469C22⋊C4—442no—
470C42—24no—
471C42C2×D4412yes—
472C42D4×D1112yes—
473C11#2411811yescharacteristic, complemented, Sylow
474C23—114no—
475C23—222no—
476C23—222no—
477C23—222no—
478C23—222no—
479C23—222no—
480C23—222no—
481C23—222no—
482C23—441no—
483C23—441no—
484C23—441no—
485C23—441no—
486C23—441no—
487C23—441no—
488C23C2×D4×D1111yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—884no—
494D4—222no—
495D4—222no—
496D4—228no—
497D4—441no—
498D4—441no—
499D4—888no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—888no—
525C2×C4—884no—
526C2×C4#6693512yes—
527C2×C4#6693512yes—
528C2×C4SD16×D1112yes—
529C2×C4#6697112yes—
530C2×C4C22×D4411yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4#6703711yescharacteristic
533C2×C4#6704011yescharacteristic
534C2×C4#41×D1111yescharacteristic
535C2×C4#41×D1111yescharacteristic
536C8—42no—
537C8—222no—
538C8—441no—
539C22—224no—
540C22—224no—
541C22—224no—
542C22—442no—
543C22—442no—
544C22—442no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—881no—
553C22C2×#6693511yescharacteristic
554C22#1062314311yescharacteristic
555C22#1062316211yescharacteristic
556C22C2×SD16×D1111yescharacteristic
557C22C2×#6697111yescharacteristic
558C22#1062330511yescharacteristic
559C22#1062330911yescharacteristic
560C4—22no—
561C4—42no—
562C4—42no—
563C4—82no—
564C4—442no—
565C4—444no—
566C4—881no—
567C4#1062241914yes—
568C4#1062304111yescharacteristic
569C4#1062305511yescharacteristic
570C4#1062313011yescharacteristic
571C4#1062316411yescharacteristic
572C2—444no—
573C2—882no—
574C2#1307196211yescharacteristic
575C2C2×#1062241911yescharacteristic
576C2#1307792211yescharacteristic
577C2#1308044311yescharacteristic
578C2#1308093511yescharacteristic
579C2#1308097611yescharacteristic
580C2#1308123911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radical#13073532C2
hypercenter#1803D11
hypocenterC11#24118
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
2. C2×#10622455C2semidirect
3. C2×C4×#4325C2semidirect
5. #13069811C2semidirect
6. #13069618C2semidirect
7. #13069576C2semidirect
8. #13069409C2semidirect
9. #13068932C2semidirect
10. #13068810C2semidirect
11. C11×#1803C2semidirect
55. C4×Q8×C11D4semidirect
94. #66922D4semidirect
134. C2×D44SD16semidirect
194. #1803D11semidirect
350. C4×Q8D44semidirect
473. C11#24118semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106224552
C2×C4×#43252
#130735322
#130698112
#130696182
#130695762
#130694092
#130689322
#130688102
C11×#18032
#2411811