Finite Group Databasebeta

← #14719684

Subgroups — #14719684

Order 2816.

1210 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623077C211yesmaximal, characteristic
2#13077645C211yesmaximal, characteristic, complemented
3#13066959C212yesmaximal, complemented
4#13066952C212yesmaximal, complemented
5#13066948C212yesmaximal, complemented
6#13066945C212yesmaximal, complemented
7#13066932C212yesmaximal, complemented
8C2×#10622107C212yesmaximal, complemented
9C11×#2973C211yesmaximal, characteristic, complemented
10C22×#4341C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11C2211yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C22×Dic11⋊C4C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17#10623077—24no—
18#10623077—24no—
19C2×C4⋊C4×D11C411yescharacteristic
20C2×#66940C411yescharacteristic
21C2×(C22⋊D11)⋊C4C411yescharacteristic
22C2×(C22⋊D11)⋊C4C411yescharacteristic
23C2×#66930C411yescharacteristic
24C2×#66930C411yescharacteristic
25C2×#66925C2211yescharacteristic
26C2×C4×Dic22C2211yescharacteristic
27C11×#435—24no—
28C11×#432C2212yes—
29C11×#407C2212yes—
30C2×C11×C22⋊C8C2212yes—
31#10622820C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622624—24no—
34#10622539C2212yes—
35#10622107C2214yes—
36#10622107C2214yes—
37#10622107C2214yes—
38#10622106C2214yes—
39C22×D4×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11C2×C411yescharacteristic
43C22×C22⋊D11C2×C411yescharacteristic
44C23×Dic11C2×C411yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C23×Dic11C2×C411yescharacteristic
47C23×Dic11C2×C411yescharacteristic
48C2×#4341—24no—
49C2×#4341—24no—
50C2×#4341—24no—
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C22×Dic22C2×C411yescharacteristic
55C2×C11×M16—22no—
56C22×C8×C11—22no—
57C4×D4×C11D414yes—
58C4×D4×C11D414yes—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C22⋊C4C2×C411yescharacteristic
61C2×C11×C22⋊C4C2×C411yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11C2×C411yescharacteristic
64C2×C22⋊Dic11C2×C411yescharacteristic
65D4×Dic11—24no—
66C4×C22⋊D11—22no—
67C4×C22⋊D11—22no—
68C4×C22⋊D11—22no—
69C4×C22⋊D11—22no—
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×(C2×D11)⋊C4C2311yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2311yescharacteristic
83C2×Dic11⋊C4C2311yescharacteristic
84C2×Dic11⋊C4C2311yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×#4318—22no—
91C22×C11⋊C8—22no—
92C4⋊C4×D11—24no—
93#66940—24no—
94(C22⋊D11)⋊C4—24no—
95(C22⋊D11)⋊C4—24no—
96#66930—24no—
97#66930—24no—
98#66925—22no—
99#66925—22no—
100C4×Dic22—22no—
101C4×Dic22—22no—
102C11×C4⋊C8—22no—
103C11×C22⋊C8—22no—
104C11×C22⋊C8—22no—
105C11×C22⋊C8C2314yes—
106C11×#97—22no—
107C22⋊(C11⋊C8)—22no—
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)C2314yes—
110C4⋊(C11⋊C8)—22no—
111#66867—22no—
112#17368—111nomaximal, Sylow
113C24×C11C22×C411yescharacteristic
114C24×C11C22×C411yescharacteristic
115C23×D11C22×C411yescharacteristic
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11C22⋊C414yes—
119C22×C4×C11—81no—
120C22×C4×C11—81no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C22×C411yescharacteristic
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—22no—
131C2×C22⋊D11—22no—
132C2×C22⋊D11—22no—
133C2×C22⋊D11—22no—
134C2×C22⋊D11—22no—
135C2×C22⋊D11M1614yescomplemented
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—81no—
144C22×Dic11—81no—
145C22×Dic11M1614yescomplemented
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153#4341—232no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—81no—
160C2×C4×D11—81no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C11×M16—82no—
165C2×C8×C11—24no—
166C2×C8×C11—82no—
167C11×C4⋊C4C22⋊C414yes—
168C11×C22⋊C4C22⋊C414yes—
169C11×C22⋊C4C22⋊C414yes—
170C42×C11C2×D412yes—
171C42×C11C2×D412yes—
172C22⋊Dic11—22no—
173C22⋊Dic11—22no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—21no—
176(C2×D11)⋊C4—21no—
177C4⋊Dic11—22no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183Dic11⋊C4—21no—
184Dic11⋊C4—21no—
185Dic11⋊C4—21no—
186Dic11⋊C4—21no—
187Dic11⋊C4—21no—
188Dic11⋊C4—21no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194#4318—82no—
195C2×C11⋊C8—24no—
196C2×C11⋊C8—82no—
197C2×#520—111no—
198#2973—111no—
199#2973D1111yescharacteristic, complemented
200#1467—112no—
201#1465—112no—
202#1464—112no—
203#1463—112no—
204#1459—112no—
205C2×#324—112no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11C2×C22⋊C412yes—
213C23×C11C2×C22⋊C412yes—
214C23×C11C2×M1612yes—
215C23×C11C2×M1612yes—
216C23×C11C23×C411yescharacteristic
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11C2×M1612yes—
222D4×C11—28no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C2×C22⋊C412yes—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×C22⋊C412yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C22⋊D11—28no—
240C22⋊D11—28no—
241C2×Dic11—28no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—28no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—82no—
258C2×Dic11—82no—
259C2×Dic11C2×M1612yes—
260C2×Dic11C2×M1612yes—
261C2×Dic11C2×M1612yes—
262C4×D11—28no—
263C4×D11—82no—
264C4×D11—82no—
265Dic22—28no—
266C8×C11—44no—
267C11⋊C8—44no—
268C22×#41—111no—
269#520—224no—
270#520—224no—
271C2×C4×Q8—111no—
272C2×C4×Q8—111no—
273C2×C4×D4—111no—
274C2×C4×D4—111no—
275C2×C4×D4—111no—
276C2×C4×D4—111no—
277C2×C4×D4—111no—
278C2×C4×D4C2×D1111yescharacteristic
279C2×#117—111no—
280C2×#117—111no—
281C2×#117—111no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—111no—
285#435—24no—
286#435—224no—
287#432—112no—
288#432C2×D1112yes—
289#407—112no—
290#407C2×D1112yes—
291C2×C22⋊C8—112no—
292C2×C22⋊C8C2×D1112yes—
293#324—114no—
294#324—114no—
295#324—114no—
296#323—114no—
297C22×C11—21no—
298C22×C11—22no—
299C22×C11—21no—
300C22×C11—22no—
301C22×C11—22no—
302C22×C11—22no—
303C22×C11—22no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11#40714yes—
309C22×C11C22×C22⋊C411yescharacteristic
310C22×C11C22×M1611yescharacteristic
311C22×C11C22×M1611yescharacteristic
312C2×D11—22no—
313C2×D11—42no—
314C2×D11—41no—
315C2×D11—41no—
316C2×D11—42no—
317C4×C11—22no—
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—22no—
323Dic11—22no—
324Dic11—22no—
325Dic11—22no—
326Dic11—41no—
327Dic11—41no—
328Dic11—41no—
329Dic11—41no—
330C2×#41—224no—
331C2×#41—224no—
332C2×#41—224no—
333C22×Q8—111no—
334C22×D4—111no—
335C22×D4—111no—
336C22×D4C4×D1111yescharacteristic
337C23×C4—111no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4C22×D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C2×M16—22no—
347C2×M16—222no—
348C22×C8—22no—
349C22×C8—222no—
350C4×Q8—224no—
351C4×Q8—222no—
352C4×Q8—222no—
353C4×D4—224no—
354C4×D4—222no—
355C4×D4—222no—
356C4×D4—222no—
357C4×D4—222no—
358C4×D4—224no—
359C4×D4—224no—
360C4×D4D4414yes—
361C4×D4C22⋊D1114yes—
362#117—224no—
363#117—224no—
364#117—222no—
365#117—222no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4C4×D1111yescharacteristic
381C2×C22⋊C4—111no—
382C2×C22⋊C4—111no—
383C2×C22⋊C4—111no—
384C2×C22⋊C4—111no—
385C2×C22⋊C4C4×D1111yescharacteristic
386C2×C22⋊C4C4×D1111yescharacteristic
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42C22×D1111yescharacteristic
393C4⋊C8—22no—
394C4⋊C8—222no—
395C22⋊C8—22no—
396C22⋊C8—22no—
397C22⋊C8—114no—
398C22⋊C8—222no—
399C22⋊C8—222no—
400C22⋊C8C22×D1114yes—
401#97—22no—
402#97—222no—
403C2×C11—21no—
404C2×C11—21no—
405C2×C11—24no—
406C2×C11—42no—
407C2×C11C2×#40711yescharacteristic
408C2×C11#288311yescharacteristic
409C2×C11#288911yescharacteristic
410D11—42no—
411C24—111no—
412C24C2×C4×D1111yescharacteristic
413C24C2×C4×D1111yescharacteristic
414#41—2232no—
415C2×Q8—222no—
416C2×Q8—222no—
417C2×Q8—222no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—114no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4(C2×D11)⋊C414yes—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4—114no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—881no—
450C22×C4—881no—
451C22×C4—881no—
452C22×C4—881no—
453C22×C4C2×C4×D1111yescharacteristic
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×D4412yes—
458C22×C4C2×D4412yes—
459C22×C4C2×C22⋊D1112yes—
460C22×C4C2×C22⋊D1112yes—
461C22×C4C23×D1111yescharacteristic
462M16—82no—
463M16—882no—
464C2×C8—24no—
465C2×C8—82no—
466C2×C8—224no—
467C2×C8—882no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—222no—
472C4⋊C4—222no—
473C4⋊C4—222no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4(C2×D11)⋊C414yes—
481C22⋊C4—222no—
482C22⋊C4—222no—
483C22⋊C4—222no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4(C2×D11)⋊C414yes—
487C22⋊C4(C2×D11)⋊C414yes—
488C42—222no—
489C42—222no—
490C42—222no—
491C42—222no—
492C42—222no—
493C42C2×D4412yes—
494C42C2×C22⋊D1112yes—
495C11#1736811yescharacteristic, complemented, Sylow
496C23—21no—
497C23—21no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—112no—
503C23—221no—
504C23—221no—
505C23—441no—
506C23—441no—
507C23M16×D1112yes—
508C23M16×D1112yes—
509C23C2×(C2×D11)⋊C412yes—
510C23C2×(C2×D11)⋊C412yes—
511C23C22×C4×D1111yescharacteristic
512Q8—228no—
513D4—28no—
514D4—228no—
515D4—228no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—112no—
529C2×C4—228no—
530C2×C4—228no—
531C2×C4—228no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—882no—
547C2×C4—882no—
548C2×C4—882no—
549C2×C4—882no—
550C2×C4C2×(C2×D11)⋊C412yes—
551C2×C4C2×(C2×D11)⋊C412yes—
552C2×C4C2×(C2×D11)⋊C412yes—
553C2×C4C2×(C2×D11)⋊C412yes—
554C2×C4C22×D4411yescharacteristic
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—44no—
557C8—444no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—222no—
570C22—442no—
571C22—442no—
572C22—441no—
573C22—441no—
574C22#1062273914yes—
575C22C2×M16×D1111yescharacteristic
576C22C2×M16×D1111yescharacteristic
577C22C22×(C2×D11)⋊C411yescharacteristic
578C4—22no—
579C4—21no—
580C4—21no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—222no—
585C4—222no—
586C4—222no—
587C4—441no—
588C4—441no—
589C4—441no—
590C4—441no—
591C2—21no—
592C2—21no—
593C2—24no—
594C2—42no—
595C2—442no—
596C2C2×#1062273911yescharacteristic
597C2#1307707611yescharacteristic
598C2#1307709811yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2973C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#2973D11
hypocenterC11#17368
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13077645C2semidirect
3. #13066959C2semidirect
4. #13066952C2semidirect
5. #13066948C2semidirect
6. #13066945C2semidirect
7. #13066932C2semidirect
8. C2×#10622107C2semidirect
9. C11×#2973C2semidirect
135. C2×C22⋊D11M16semidirect
145. C22×Dic11M16semidirect
199. #2973D11semidirect
495. C11#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#106230772
#130776452
#130669592
#130669522
#130669482
#130669452
#130669322
C2×#106221072
C11×#29732
#1736811