Finite Group Databasebeta

← #14755147

Subgroups — #14755147

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10623053C211yesmaximal, characteristic
3C2×#10622746C211yesmaximal, characteristic
4C2×#10622843C211yesmaximal, characteristic, complemented
5#13068954C214yesmaximal, complemented
6#13068947C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C2×C11×#419C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×#4326C2212yes—
15C2×#66995—24no—
16C2×#66995—24no—
17C2×#66995C418yescomplemented
18C22×#4325C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22#10623053—24no—
23#10623053—24no—
24C2×#66946C2212yes—
25C2×#66940C2212yes—
26C2×(C22⋊D11)⋊C4—22no—
27C2×#66925—21no—
28C2×C42×D11—21no—
29C11×#419—24no—
30C2×C11×#103C2214yes—
31#10622843—21no—
32#10622843—21no—
33#10622843C2214yes—
34C2×C11⋊#95—22no—
35#10622746—24no—
36C2×#66885C2212yes—
37C2×#66880C2212yes—
38#10622188C2214yes—
39#10622167C2214yes—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11C2×C414yescomplemented
47C22×Q8×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C23×Dic11—21no—
52C23×Dic11D412yes—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339C2×C414yes—
57C2×#4339D414yes—
58C2×#4339D414yes—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—22no—
62C22×Dic22C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C22×C8×C11C2312yes—
67C11×#117—22no—
68C11×#117D414yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×#4326—24no—
73C2×#4326—24no—
74C2×#4326C2×C418yescomplemented
75#66995—232no—
76C2×#4325—24no—
77C2×#4325—24no—
78C2×#4325C2×C418yescomplemented
79C2×(C2×D11)⋊C4—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2312yes—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11C2312yes—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318C2×C414yescomplemented
94C22×C11⋊C8C2312yes—
95#66946—24no—
96#66946—24no—
97#66940—24no—
98#66940—24no—
99(C22⋊D11)⋊C4—216no—
100#66925—28no—
101C42×D11—28no—
102C11×#103—28no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105#66885—24no—
106#66880—24no—
107#20927—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11—21no—
110C2×Q8×C11—24no—
111C2×Q8×C11—22no—
112C2×Q8×C11—28no—
113C2×Q8×C11—28no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11—44no—
121C2×Q8×C11—44no—
122C2×Q8×C11C22×C414yes—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—42no—
144C22×Dic11—44no—
145C22×Dic11—42no—
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D412yes—
148#4339—28no—
149#4339—28no—
150#4339—28no—
151#4339C22⋊C4116yes—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22×C412yes—
156C2×D44C2×D412yes—
157C2×D44C2×D412yes—
158C2×C4×D11—28no—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—44no—
163C2×C4×D11—44no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22C22×C412yes—
168C2×Dic22C2×D412yes—
169C2×Dic22C2×D412yes—
170C11×M16—44no—
171C2×C8×C11—22no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4C2×D414yes—
176C11×C22⋊C4—24no—
177C42×C11—24no—
178#4326—216no—
179#4325—216no—
180(C2×D11)⋊C4—28no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—42no—
184Dic11⋊C4—28no—
185C4×Dic11—28no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—22no—
190#4318—28no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C22×C414yes—
194C22×#137—111no—
195C2×C4×#41—111no—
196C2×#417—111no—
197C2×#419D1111yescharacteristic, complemented
198C2×#391—111no—
199#1878—114no—
200#1877—114no—
201#1736—111no—
202#1728—111no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11C4×D412yes—
206C23×C11#12012yes—
207C23×C11#12112yes—
208C23×C11C22×D411yescharacteristic
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—42no—
213C22×D11—42no—
214Q8×C11—24no—
215Q8×C11—24no—
216Q8×C11—42no—
217Q8×C11—42no—
218Q8×C11—48no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—48no—
226C2×C4×C11C2×C22⋊C414yes—
227C2×C4×C11C4×D412yes—
228C2×C4×C11C4×D414yes—
229C2×C4×C11#12012yes—
230C2×C4×C11#12112yes—
231C2×C4×C11#12114yes—
232C2×C4×C11#12314yes—
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—216no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—48no—
249C2×Dic11—42no—
250C2×Dic11—44no—
251C2×Dic11—84no—
252C2×Dic11#13714yescomplemented
253D44—22no—
254D44—22no—
255D44—22no—
256D44C2×C22⋊C414yes—
257C4×D11—216no—
258C4×D11—416no—
259Dic22—22no—
260Dic22—22no—
261Dic22—22no—
262Dic22C2×C22⋊C414yes—
263C8×C11—42no—
264C11⋊C8—24no—
265C22×#41—111no—
266C23×Q8C2×D1111yescharacteristic
267C2×#137—118no—
268C2×#137—224no—
269C2×#137—224no—
270C22×Q16—112no—
271C22×SD16—112no—
272C22×M16—111no—
273C22×M16C2×D1111yescharacteristic
274C4×#41—224no—
275C4×#41—224no—
276C2×C4×Q8—112no—
277C2×C4×D4—112no—
278C2×C4×D4—222no—
279C2×#117—221no—
280C2×#117C2×D1111yescharacteristic
281C22×C4⋊C4—111no—
282C22×C42—111no—
283C22×C42—221no—
284#419—24no—
285#417—224no—
286C2×#103—112no—
287C2×#103C2×D1114yes—
288C2×#102—112no—
289#391—114no—
290#391—221no—
291#391—221no—
292C2×#95—222no—
293#340—114no—
294#336—114no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11#38614yes—
300C22×C11C2×C4×D411yescharacteristic
301C22×C11C2×#12011yescharacteristic
302C22×C11C2×#12111yescharacteristic
303C22×C11C2×#13712yes—
304C22×C11#57512yes—
305C2×D11—24no—
306C2×D11—44no—
307C2×D11—44no—
308C2×D11—42no—
309C2×D11—42no—
310C4×C11—44no—
311C4×C11—44no—
312C4×C11#38614yes—
313C4×C11C22×C22⋊C411yescharacteristic
314C4×C11C2×C4×D411yescharacteristic
315C4×C11C2×#12111yescharacteristic
316C4×C11C2×#12311yescharacteristic
317Dic11—24no—
318Dic11—24no—
319Dic11—42no—
320Dic11—82no—
321C2×#41—114no—
322C2×#41—114no—
323C2×#41—114no—
324C2×#41—222no—
325C2×#41—222no—
326C2×#41—222no—
327C22×Q8—21no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—111no—
334C22×Q8C4×D1114yescomplemented
335C22×Q8C22×D1112yes—
336C22×D4—111no—
337C22×D4—221no—
338C23×C4—21no—
339C23×C4—112no—
340C23×C4—222no—
341C23×C4—221no—
342C23×C4—221no—
343C23×C4C22×D1111yescharacteristic
344#137—2232no—
345C2×Q16—118no—
346C2×Q16—224no—
347C2×Q16—224no—
348C2×SD16—118no—
349C2×SD16—224no—
350C2×SD16—224no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—22no—
354C2×M16—114no—
355C2×M16—222no—
356C2×M16—222no—
357C22×C8—112no—
358C22×C8C22×D1112yes—
359C4×Q8—224no—
360C4×Q8—224no—
361C4×D4—2216no—
362C4×D4—224no—
363C4×D4—224no—
364#117—22no—
365#117—228no—
366#117C22⋊D1114yes—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22×D1112yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—222no—
375C2×C42—21no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—112no—
379C2×C42—228no—
380C2×C42—222no—
381C2×C42—222no—
382C2×C42—222no—
383#103—28no—
384#103—224no—
385#102—224no—
386#95—224no—
387#95—224no—
388C2×C11—24no—
389C2×C11C2×#38611yescharacteristic
390C2×C11C4×#13712yes—
391C2×C11#300712yes—
392C2×C11#303911yescharacteristic
393C2×C11#304011yescharacteristic
394D11—44no—
395C24—221no—
396C24D4×D1111yescharacteristic
397#41—1116no—
398#41—228no—
399#41—228no—
400#41—228no—
401C2×Q8—24no—
402C2×Q8—22no—
403C2×Q8—28no—
404C2×Q8—28no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—44no—
410C2×Q8—42no—
411C2×Q8—42no—
412C2×Q8—44no—
413C2×Q8—112no—
414C2×Q8—112no—
415C2×Q8—112no—
416C2×Q8—221no—
417C2×Q8—221no—
418C2×Q8—221no—
419C2×Q8C2×C4×D1114yes—
420C2×D4—112no—
421C2×D4—112no—
422C2×D4—112no—
423C2×D4—224no—
424C2×D4—224no—
425C2×D4—224no—
426C2×D4—221no—
427C2×D4—221no—
428C2×D4—221no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—228no—
437C22×C4—224no—
438C22×C4—221no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—222no—
444C22×C4—444no—
445C22×C4—444no—
446C22×C4—442no—
447C22×C4—444no—
448C22×C4—442no—
449C22×C4C2×C4×D1112yes—
450C22×C4#433912yes—
451C22×C4D4×D1112yes—
452C22×C4D4×D1112yes—
453C22×C4D4×D1111yescharacteristic
454C22×C4#434112yes—
455C22×C4C2×C22⋊D1112yes—
456C22×C4C23×D1111yescharacteristic
457Q16—2216no—
458SD16—2216no—
459M16—44no—
460M16—228no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—114no—
465C2×C8—222no—
466C2×C8—222no—
467C4⋊C4—22no—
468C4⋊C4—228no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—442no—
472C4⋊C4C2×C22⋊D1114yes—
473C22⋊C4—24no—
474C22⋊C4—228no—
475C42—24no—
476C42—228no—
477C42—222no—
478C42—222no—
479C42—222no—
480C42—222no—
481C11#2092711yescharacteristic, complemented, Sylow
482C23—22no—
483C23—22no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—442no—
488C23—442no—
489C23(C22⋊D11)⋊C412yes—
490C23#6693712yes—
491C23#6699012yes—
492C23C2×D4×D1111yescharacteristic
493Q8—24no—
494Q8—24no—
495Q8—42no—
496Q8—42no—
497Q8—48no—
498Q8—114no—
499Q8—222no—
500Q8—222no—
501Q8—222no—
502D4—114no—
503D4—2216no—
504D4—222no—
505D4—222no—
506D4—222no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—48no—
514C2×C4—114no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—2216no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—4416no—
525C2×C4—448no—
526C2×C4—442no—
527C2×C4—444no—
528C2×C4—884no—
529C2×C4C22⋊C4×D1114yes—
530C2×C4(C22⋊D11)⋊C412yes—
531C2×C4#6693614yes—
532C2×C4#6693712yes—
533C2×C4C4×C22⋊D1114yes—
534C2×C4#6699012yes—
535C2×C4#6699114yes—
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×#434111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C8—42no—
543C8—224no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—224no—
549C22—442no—
550C22—442no—
551C22—444no—
552C22—444no—
553C22#1062256914yes—
554C22C2×(C22⋊D11)⋊C411yescharacteristic
555C22C2×#6693711yescharacteristic
556C22D11×#13712yes—
557C22#1062330812yes—
558C22C2×#6699011yescharacteristic
559C4—44no—
560C4—44no—
561C4—224no—
562C4—224no—
563C4—442no—
564C4—882no—
565C4#1062256914yes—
566C4C2×C22⋊C4×D1111yescharacteristic
567C4C2×#6693611yescharacteristic
568C4C2×C4×C22⋊D1111yescharacteristic
569C4C2×#6699111yescharacteristic
570C2—24no—
571C2—444no—
572C2C2×#1062256911yescharacteristic
573C2#1307743112yes—
574C2#1307787212yes—
575C2#1307810211yescharacteristic
576C2#1307811311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#419D11
hypocenterC11#20927
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
4. C2×#10622843C2semidirect
5. #13068954C2semidirect
6. #13068947C2semidirect
7. #13068337C2semidirect
8. #13068309C2semidirect
9. C2×C11×#419C2semidirect
17. C2×#66995C4semidirect
46. C22×Q8×C11C2×C4semidirect
74. C2×#4326C2×C4semidirect
78. C2×#4325C2×C4semidirect
93. C2×#4318C2×C4semidirect
197. C2×#419D11semidirect
252. C2×Dic11#137semidirect
334. C22×Q8C4×D11semidirect
481. C11#20927semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106230532
C2×#106227462
C2×#106228432
#130689542
#130689472
#130683372
#130683092
C2×C11×#4192
#2092711