Finite Group Databasebeta

← #14755150

Subgroups — #14755150

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×#66962C211yesmaximal, characteristic
2C2×C4×#4339C211yesmaximal, characteristic
3C2×#10622746C211yesmaximal, characteristic
4C2×#10622733C211yesmaximal, characteristic, complemented
5C2×#10622542C211yesmaximal, characteristic, complemented
6#13068956C214yesmaximal, complemented
7#13068949C214yesmaximal, complemented
8#13068336C211yesmaximal, characteristic, complemented
9C11×#1728C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×C4×C22⋊D11—22no—
16C2×#66979C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C2×#66962—24no—
19C2×#66962—24no—
20C2×#66962C418yescomplemented
21C22×Dic44C2212yes—
22C22×#4314C2212yes—
23C4×#4339—24no—
24C4×#4339—24no—
25C2×C4×D44C2212yes—
26C2×#66925—21no—
27C2×C42×D11—21no—
28C2×C4×Dic22C2212yes—
29C2×C11⋊#95—22no—
30#10622746—24no—
31#10622733—24no—
32C2×#66885C2212yes—
33C2×#66880C2214yes—
34C2×#66880C2212yes—
35#10622542—21no—
36#10622542—21no—
37#10622542C2214yes—
38C11×#336C2214yes—
39#10622189C2214yes—
40C23×C4×C11D412yes—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C23×Dic11—21no—
44C23×Dic11—21no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339C2×C414yes—
49C2×#4339D414yes—
50C2×#4339D414yes—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×C4×D11—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×Dic22C2×C414yescomplemented
61C22×Dic22C2312yes—
62C22×Dic22C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16C2×C414yescomplemented
69C22×C8×C11C2312yes—
70C22×C8×C11C2312yes—
71C2×C42×C11—22no—
72C2×C42×C11—22no—
73C2×C42×C11D411yescharacteristic
74C2×C42×C11D411yescharacteristic
75C2×C42×C11C2312yes—
76C2×C22⋊Dic11—21no—
77C4×C22⋊D11—216no—
78C2×(C2×D11)⋊C4—22no—
79#66979—22no—
80#66979D414yes—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2312yes—
85C2×C4⋊Dic11C2312yes—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—21no—
89#66962—232no—
90C2×Dic44—24no—
91C2×Dic44—24no—
92C2×Dic44C2×C418yescomplemented
93C2×#4314—24no—
94C2×#4314—24no—
95C2×#4314C2×C418yescomplemented
96C4×D44—24no—
97C4×D44—24no—
98#66925—28no—
99C42×D11—28no—
100C4×Dic22—24no—
101C4×Dic22—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104#66885—24no—
105#66880—24no—
106#66880—28no—
107#20927—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—42no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11#4112yes—
121C22×C4×C11#4112yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11—24no—
124C2×C22⋊D11—24no—
125C2×C22⋊D11—24no—
126C22×Dic11—24no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—44no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11—42no—
135#4339—28no—
136#4339—28no—
137#4339—28no—
138#4339C22⋊C4116yes—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44C22×C412yes—
143C2×D44C2×D412yes—
144C2×D44C2×D412yes—
145C2×C4×D11—28no—
146C2×C4×D11—24no—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—44no—
150C2×C4×D11—44no—
151C2×Dic22—28no—
152C2×Dic22—28no—
153C2×Dic22—24no—
154C2×Dic22—21no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—42no—
163C2×Dic22—44no—
164C2×Dic22—42no—
165C2×Dic22—44no—
166C2×Dic22C22×C414yes—
167C2×Dic22C22×C412yes—
168C2×Dic22C2×D412yes—
169C2×Dic22C2×D412yes—
170C11×M16—28no—
171C11×M16—44no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11C22×C414yes—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181C42×C11—22no—
182C22⋊Dic11—24no—
183(C2×D11)⋊C4—28no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11—42no—
188C4⋊Dic11C2×D414yes—
189Dic11⋊C4—28no—
190C4×Dic11—28no—
191C4×Dic11—24no—
192Dic44—216no—
193#4314—216no—
194C22×#137—111no—
195C2×C4×#41—111no—
196C2×#417—111no—
197C2×#419—111no—
198C2×#391—111no—
199#1878—114no—
200#1877—114no—
201#1736—111no—
202#1728D1111yescharacteristic, complemented
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—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—48no—
220C2×C4×C11C2×C22⋊C414yes—
221C2×C4×C11C4×D412yes—
222C2×C4×C11C4×D414yes—
223C2×C4×C11#12012yes—
224C2×C4×C11#12114yes—
225C2×C4×C11#12112yes—
226C2×C4×C11#12314yes—
227C2×C4×C11#13714yescomplemented
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C22⋊D11—216no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—48no—
245C2×Dic11—42no—
246C2×Dic11—44no—
247C2×Dic11—84no—
248D44—22no—
249D44—22no—
250D44—22no—
251D44C2×C22⋊C414yes—
252C4×D11—216no—
253C4×D11—416no—
254Dic22—22no—
255Dic22—22no—
256Dic22—22no—
257Dic22—24no—
258Dic22—24no—
259Dic22—42no—
260Dic22—42no—
261Dic22—48no—
262Dic22C2×C22⋊C414yes—
263C8×C11—24no—
264C8×C11—42no—
265C22×#41—111no—
266C23×Q8—111no—
267C2×#137—118no—
268C2×#137—224no—
269C2×#137—224no—
270C22×Q16—112no—
271C22×SD16—112no—
272C22×M16C2×D1111yescharacteristic
273C22×M16C2×D1111yescharacteristic
274C4×#41—224no—
275C4×#41—224no—
276C2×C4×Q8—112no—
277C2×C4×D4—112no—
278C2×C4×D4—222no—
279C2×#117—111no—
280C2×#117—221no—
281C22×C4⋊C4—111no—
282C22×C42—221no—
283C22×C42C2×D1111yescharacteristic
284#419—224no—
285#417—224no—
286C2×#103—114no—
287C2×#103—112no—
288C2×#102—112no—
289#391—114no—
290#391—221no—
291#391—221no—
292C2×#95—222no—
293#340—114no—
294#336C2×D1114yes—
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—24no—
311C4×C11—42no—
312C4×C11#38614yes—
313C4×C11C22×C22⋊C411yescharacteristic
314C4×C11C2×C4×D411yescharacteristic
315C4×C11C2×#12111yescharacteristic
316C4×C11C2×#12311yescharacteristic
317Dic11—24no—
318Dic11—44no—
319Dic11—44no—
320Dic11—82no—
321C2×#41—114no—
322C2×#41—114no—
323C2×#41—114no—
324C2×#41—222no—
325C2×#41—222no—
326C2×#41—222no—
327C22×Q8—114no—
328C22×Q8—111no—
329C22×Q8—112no—
330C22×Q8—221no—
331C22×Q8—222no—
332C22×Q8—222no—
333C22×Q8—222no—
334C22×Q8—222no—
335C22×Q8—222no—
336C22×D4—111no—
337C22×D4—221no—
338C23×C4—221no—
339C23×C4—221no—
340C23×C4—222no—
341C23×C4—221no—
342C23×C4D4412yes—
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—22no—
355C2×M16—22no—
356C2×M16C4×D1114yescomplemented
357C22×C8C22×D1112yes—
358C22×C8C22×D1112yes—
359C4×Q8—224no—
360C4×Q8—224no—
361C4×D4—224no—
362C4×D4—224no—
363C4×D4—2216no—
364#117—114no—
365#117—228no—
366#117—222no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—222no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—228no—
378C2×C42—221no—
379C2×C42—222no—
380C2×C42D4411yescharacteristic
381C2×C42D4411yescharacteristic
382C2×C42C22×D1112yes—
383#103—228no—
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—
396C24C2×D4411yescharacteristic
397#41—1116no—
398#41—228no—
399#41—228no—
400#41—228no—
401C2×Q8—112no—
402C2×Q8—114no—
403C2×Q8—112no—
404C2×Q8—112no—
405C2×Q8—224no—
406C2×Q8—221no—
407C2×Q8—222no—
408C2×Q8—221no—
409C2×Q8—221no—
410C2×Q8—228no—
411C2×Q8—228no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8—222no—
416C2×Q8—442no—
417C2×Q8—444no—
418C2×Q8—444no—
419C2×Q8—442no—
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—24no—
431C22×C4—42no—
432C22×C4—228no—
433C22×C4—221no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—444no—
442C22×C4—442no—
443C22×C4—442no—
444C22×C4—444no—
445C22×C4—444no—
446C22×C4—442no—
447C22×C4C2×C4×D1112yes—
448C22×C4C2×D4412yes—
449C22×C4C2×D4412yes—
450C22×C4C2×D4411yescharacteristic
451C22×C4#433912yes—
452C22×C4D4×D1112yes—
453C22×C4D4×D1112yes—
454C22×C4D4×D1112yes—
455C22×C4#434312yes—
456C22×C4C23×D1111yescharacteristic
457Q16—2216no—
458SD16—2216no—
459M16—28no—
460M16—44no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8C2×C4×D1114yes—
467C4⋊C4—114no—
468C4⋊C4—228no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—442no—
473C22⋊C4—228no—
474C22⋊C4—224no—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—228no—
480C42—224no—
481C11#2092711yescharacteristic, complemented, Sylow
482C23—22no—
483C23—22no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—442no—
488C23—442no—
489C23C4×D4412yes—
490C23#6693512yes—
491C23#6694812yes—
492C23C22×D4411yescharacteristic
493Q8—114no—
494Q8—222no—
495Q8—222no—
496Q8—222no—
497Q8—224no—
498Q8—224no—
499Q8—442no—
500Q8—442no—
501Q8—448no—
502D4—114no—
503D4—2216no—
504D4—222no—
505D4—222no—
506D4—222no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—48no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—2216no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—4416no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—448no—
525C2×C4—444no—
526C2×C4—442no—
527C2×C4—884no—
528C2×C4C4×D4412yes—
529C2×C4C22⋊C4×D1114yes—
530C2×C4#6693512yes—
531C2×C4#6693714yes—
532C2×C4#6694614yes—
533C2×C4#6694714yes—
534C2×C4#6694812yes—
535C2×C4#6696214yescomplemented
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434311yescharacteristic
542C8—24no—
543C8—42no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—224no—
549C22—442no—
550C22—442no—
551C22—444no—
552C22—444no—
553C22#1062227814yes—
554C22C2×C4×D4411yescharacteristic
555C22C2×#6693511yescharacteristic
556C22C2×#6694811yescharacteristic
557C22C2×#6696212yes—
558C22#1062327912yes—
559C4—24no—
560C4—42no—
561C4—224no—
562C4—444no—
563C4—444no—
564C4—882no—
565C4#1062227814yes—
566C4C2×C22⋊C4×D1111yescharacteristic
567C4C2×#6693711yescharacteristic
568C4C2×#6694611yescharacteristic
569C4C2×#6694711yescharacteristic
570C2—24no—
571C2—444no—
572C2C2×#1062227811yescharacteristic
573C2C4×#6696212yes—
574C2#1307787812yes—
575C2#1307810411yescharacteristic
576C2#1307811111yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1728C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1728D11
hypocenterC11#20927
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
4. C2×#10622733C2semidirect
5. C2×#10622542C2semidirect
6. #13068956C2semidirect
7. #13068949C2semidirect
8. #13068336C2semidirect
9. C11×#1728C2semidirect
20. C2×#66962C4semidirect
60. C22×Dic22C2×C4semidirect
68. C2×C11×M16C2×C4semidirect
92. C2×Dic44C2×C4semidirect
95. C2×#4314C2×C4semidirect
202. #1728D11semidirect
227. C2×C4×C11#137semidirect
356. C2×M16C4×D11semidirect
481. C11#20927semidirect
535. C2×C4#66962semidirect

Maximal subgroups

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

subgroupindex
C22×#669622
C2×C4×#43392
C2×#106227462
C2×#106227332
C2×#106225422
#130689562
#130689492
#130683362
C11×#17282
#2092711