Finite Group Databasebeta

← #14719682

Subgroups — #14719682

Order 2816.

1210 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623035C211yesmaximal, characteristic
2#13077642C212yesmaximal, complemented
3#13066958C212yesmaximal, complemented
4#13066953C212yesmaximal, complemented
5#13066949C212yesmaximal, complemented
6#13066944C212yesmaximal, complemented
7#13066932C212yesmaximal, complemented
8C2×#10622166C211yesmaximal, characteristic, complemented
9C2×C11×#324C211yesmaximal, characteristic, complemented
10C22×#4339C411yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×C4×C22⋊D11C411yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C2×C4×C22⋊D11C2211yescharacteristic
16C2×#66979C411yescharacteristic
17#10623035—24no—
18#10623035—24no—
19C2×#66946C411yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66945C411yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×C4⋊C4×D11C411yescharacteristic
24C2×C4⋊C4×D11C2211yescharacteristic
25C2×#66940C411yescharacteristic
26C2×#66940C2211yescharacteristic
27C2×C11×C22⋊C8C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622724—24no—
30#10622343—24no—
31#10622339C2214yes—
32#10622332C2214yes—
33C11×#324C2212yes—
34C11×#324C2212yes—
35#10622166C2212yes—
36#10622166C2212yes—
37#10622107C2214yes—
38#10622106C2214yes—
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11C2×C411yescharacteristic
43C22×C22⋊D11C2×C411yescharacteristic
44C2×#4339—24no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—24no—
48C22×D44C2×C411yescharacteristic
49C22×C4×D11C2×C411yescharacteristic
50C22×C4×D11C2×C411yescharacteristic
51C22×C4×D11C2×C411yescharacteristic
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11C2311yescharacteristic
55C22×Dic22C2×C411yescharacteristic
56C22×C8×C11—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C22⋊Dic11C2×C411yescharacteristic
64C2×C22⋊Dic11C2×C411yescharacteristic
65C4×C22⋊D11—22no—
66C4×C22⋊D11—22no—
67C4×C22⋊D11—22no—
68C4×C22⋊D11—22no—
69C4×C22⋊D11—22no—
70C4×C22⋊D11—22no—
71C4×C22⋊D11D414yes—
72C4×C22⋊D11D414yes—
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2311yescharacteristic
77#66979—22no—
78#66979—22no—
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2311yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8—22no—
92C2×#4313—24no—
93#66946—24no—
94#66946—24no—
95#66945—24no—
96#66945—24no—
97C4⋊C4×D11—24no—
98C4⋊C4×D11—24no—
99#66940—24no—
100#66940—24no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8C2314yes—
103C22⋊(C11⋊C8)—22no—
104C22⋊(C11⋊C8)C2314yes—
105(C2×D11)⋊C8—24no—
106#66879—24no—
107Dic11⋊C8—24no—
108#17368—111nomaximal, Sylow
109C24×C11C22×C411yescharacteristic
110C23×D11C22×C411yescharacteristic
111C23×D11C22×C411yescharacteristic
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—81no—
118C22×C4×C11—81no—
119C22×C4×C11M1614yescomplemented
120C22×C4×C11C22×C411yescharacteristic
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×C11C2411yescharacteristic
128C2×C22⋊D11—21no—
129C2×C22⋊D11—21no—
130C2×C22⋊D11—22no—
131C2×C22⋊D11—22no—
132C2×C22⋊D11—22no—
133C2×C22⋊D11C22⋊C412yes—
134C2×C22⋊D11C22⋊C412yes—
135C2×C22⋊D11M1614yescomplemented
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142#4339—216no—
143#4339—216no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×C4×D11—22no—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—22no—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—81no—
157C2×C4×D11—81no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×C4×D11C2×D414yes—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×C8×C11—24no—
165C2×C8×C11—82no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C22⋊Dic11C22⋊C412yes—
173C22⋊Dic11C22⋊C412yes—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4—22no—
177(C2×D11)⋊C4C22⋊C414yes—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—22no—
183Dic11⋊C4C22⋊C414yes—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11C2×D414yes—
190C2×C11⋊C8—24no—
191C2×C11⋊C8—82no—
192#4313—84no—
193C2×#520—111no—
194#2973—112no—
195#1467—112no—
196#1465—112no—
197#1464—112no—
198#1463—112no—
199#1459—112no—
200C2×#324—111no—
201C2×#324D1111yescharacteristic, complemented
202C23×C11—41no—
203C23×C11—41no—
204C23×C11C2×C22⋊C411yescharacteristic
205C23×C11C2×C22⋊C411yescharacteristic
206C23×C11C2×M1612yes—
207C23×C11C2×M1612yes—
208C23×C11C23×C411yescharacteristic
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11C2×C22⋊C412yes—
218C22×D11C2×M1612yes—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
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×C11—81no—
234C2×C4×C11—81no—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×M1612yes—
237C2×C4×C11C2×M1612yes—
238C2×C4×C11C22×D412yes—
239C22⋊D11—24no—
240C22⋊D11—24no—
241C22⋊D11—24no—
242C22⋊D11—24no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11C2×C22⋊C412yes—
254C2×Dic11C2×C22⋊C412yes—
255C2×Dic11C2×C22⋊C412yes—
256C2×Dic11C2×M1612yes—
257D44—28no—
258C4×D11—28no—
259C4×D11—28no—
260C4×D11—44no—
261C4×D11—82no—
262C4×D11—82no—
263C4×D11—82no—
264Dic22—28no—
265C8×C11—44no—
266C11⋊C8—44no—
267C22×#41—111no—
268#520—224no—
269#520—224no—
270C2×C4×Q8—111no—
271C2×C4×Q8—111no—
272C2×C4×D4—111no—
273C2×C4×D4—111no—
274C2×C4×D4—111no—
275C2×C4×D4—111no—
276C2×C4×D4—111no—
277C2×C4×D4—111no—
278C2×#117—111no—
279C2×#117—111no—
280C2×#117—111no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4C2×D1111yescharacteristic
284#435—224no—
285#435—224no—
286#432—114no—
287#407—114no—
288C2×C22⋊C8—112no—
289C2×C22⋊C8C2×D1112yes—
290#324—112no—
291#324—112no—
292#324—114no—
293#324C2×D1112yes—
294#324C2×D1112yes—
295#323—114no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11#40712yes—
305C22×C11#40712yes—
306C22×C11C22×C22⋊C411yescharacteristic
307C22×C11C22×M1611yescharacteristic
308C22×C11C22×M1611yescharacteristic
309C2×D11—22no—
310C2×D11—22no—
311C2×D11—22no—
312C2×D11—22no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—41no—
317C2×D11—41no—
318C2×D11—42no—
319C4×C11—22no—
320C4×C11—22no—
321C4×C11—22no—
322C4×C11—22no—
323C4×C11—41no—
324C4×C11—41no—
325Dic11—22no—
326Dic11—22no—
327Dic11—22no—
328Dic11—22no—
329Dic11—41no—
330Dic11—41no—
331C2×#41—222no—
332C2×#41—222no—
333C2×#41—224no—
334C2×#41—224no—
335C22×Q8—111no—
336C22×D4—111no—
337C22×D4—111no—
338C22×D4—111no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4C4×D1111yescharacteristic
346C23×C4C4×D1111yescharacteristic
347C23×C4C22×D1111yescharacteristic
348C2×M16—224no—
349C22×C8—22no—
350C22×C8—222no—
351C4×Q8—224no—
352C4×Q8—224no—
353C4×D4—114no—
354C4×D4—114no—
355C4×D4—224no—
356C4×D4—222no—
357C4×D4—222no—
358C4×D4—224no—
359C4×D4—222no—
360C4×D4—222no—
361C4×D4—222no—
362C4×D4—222no—
363#117—224no—
364#117—224no—
365#117—222no—
366#117—222no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
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—224no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4C4×D1111yescharacteristic
378C2×C4⋊C4C4×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C22⋊C4—111no—
382C2×C22⋊C4—111no—
383C2×C22⋊C4—111no—
384C2×C22⋊C4—111no—
385C2×C22⋊C4—111no—
386C2×C22⋊C4—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C4⋊C8—224no—
394C22⋊C8—22no—
395C22⋊C8—114no—
396C22⋊C8—224no—
397C22⋊C8—222no—
398C22⋊C8C22×D1114yes—
399#97—224no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—22no—
403C2×C11—22no—
404C2×C11C2×#40711yescharacteristic
405C2×C11#288311yescharacteristic
406C2×C11#288911yescharacteristic
407D11—42no—
408D11—42no—
409C24—111no—
410C24—111no—
411C24C2×C4×D1111yescharacteristic
412#41—2216no—
413#41—2216no—
414C2×Q8—222no—
415C2×Q8—222no—
416C2×Q8—222no—
417C2×D4—112no—
418C2×D4—112no—
419C2×D4—114no—
420C2×D4—222no—
421C2×D4—222no—
422C2×D4—221no—
423C2×D4—221no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—111no—
438C22×C4—111no—
439C22×C4—114no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—881no—
452C22×C4—881no—
453C22×C4—881no—
454C22×C4—881no—
455C22×C4#431314yescomplemented
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4C2×C4×D1111yescharacteristic
459C22×C4C2×C4×D1111yescharacteristic
460C22×C4C2×C4×D1111yescharacteristic
461C22×C4D4×D1112yes—
462C22×C4D4×D1112yes—
463C22×C4C23×D1111yescharacteristic
464M16—884no—
465C2×C8—24no—
466C2×C8—82no—
467C2×C8—224no—
468C2×C8—882no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—114no—
474C4⋊C4—222no—
475C4⋊C4—222no—
476C4⋊C4—222no—
477C4⋊C4—222no—
478C4⋊C4—222no—
479C22⋊C4—112no—
480C22⋊C4—112no—
481C22⋊C4—114no—
482C22⋊C4—222no—
483C22⋊C4—222no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—222no—
487C42—114no—
488C42—222no—
489C42—222no—
490C42—222no—
491C42—222no—
492C42—222no—
493C11#1736811yescharacteristic, complemented, Sylow
494C23—41no—
495C23—41no—
496C23—112no—
497C23—112no—
498C23—221no—
499C23—221no—
500C23—221no—
501C23—221no—
502C23—441no—
503C23—441no—
504C23—441no—
505C23—441no—
506C23C22⋊C4×D1111yescharacteristic
507C23C22⋊C4×D1111yescharacteristic
508C23C2×#431312yes—
509C23M16×D1112yes—
510C23C22×C4×D1111yescharacteristic
511Q8—228no—
512D4—228no—
513D4—224no—
514D4—224no—
515D4—224no—
516D4—224no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—228no—
538C2×C4—228no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—444no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—882no—
551C2×C4—882no—
552C2×C4—882no—
553C2×C4C22⋊C4×D1112yes—
554C2×C4C2×#431312yes—
555C2×C4C2×#431312yes—
556C2×C4C2×D4×D1112yes—
557C8—44no—
558C8—444no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—222no—
568C22—222no—
569C22—222no—
570C22—222no—
571C22—442no—
572C22—442no—
573C22—442no—
574C22—442no—
575C22—441no—
576C22—441no—
577C22#1062233912yes—
578C22#1062233912yes—
579C22C2×C22⋊C4×D1111yescharacteristic
580C22C22×#431311yescharacteristic
581C22C2×M16×D1111yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—222no—
589C4—222no—
590C4—222no—
591C4—222no—
592C4—441no—
593C4—441no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—442no—
599C2—442no—
600C2C2×#1062233911yescharacteristic
601C2#1307707411yescharacteristic
602C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4339C4
cosocleC22×C4×C11C24
hypercenterC2×#324D11
hypocenterC11#17368
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13077642C2semidirect
3. #13066958C2semidirect
4. #13066953C2semidirect
5. #13066949C2semidirect
6. #13066944C2semidirect
7. #13066932C2semidirect
8. C2×#10622166C2semidirect
9. C2×C11×#324C2semidirect
119. C22×C4×C11M16semidirect
135. C2×C22⋊D11M16semidirect
201. C2×#324D11semidirect
455. C22×C4#4313semidirect
493. C11#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#106230352
#130776422
#130669582
#130669532
#130669492
#130669442
#130669322
C2×#106221662
C2×C11×#3242
#1736811