Finite Group Databasebeta

← #14719674

Subgroups — #14719674

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623017C211yesmaximal, characteristic
2#13077642C212yesmaximal, complemented
3#13066955C212yesmaximal, complemented
4#13066951C212yesmaximal, complemented
5#13066947C212yesmaximal, complemented
6#13066941C212yesmaximal, complemented
7#13066932C212yesmaximal, complemented
8C2×#10622163C211yesmaximal, characteristic, complemented
9C2×C11×#323C211yesmaximal, characteristic, complemented
10C23×C22⋊D11C411yescharacteristic
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic11C411yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×C4×C22⋊D11C411yescharacteristic
15C2×C4×C22⋊D11C2211yescharacteristic
16C2×C4×C22⋊D11C2211yescharacteristic
17#10623017—24no—
18#10623017—24no—
19C2×(C22⋊D11)⋊C4C411yescharacteristic
20C2×(C22⋊D11)⋊C4C411yescharacteristic
21C2×(C22⋊D11)⋊C4C2211yescharacteristic
22C2×(C22⋊D11)⋊C4C2211yescharacteristic
23C2×C22⋊C4×D11C411yescharacteristic
24C2×C22⋊C4×D11C2211yescharacteristic
25C2×#66930C411yescharacteristic
26C2×#66930C2211yescharacteristic
27C2×C11×C22⋊C8C2212yescomplemented
28C2×C22⋊(C11⋊C8)C2212yescomplemented
29#10622724—24no—
30#10622343—24no—
31#10622339C2214yescomplemented
32#10622332C2214yescomplemented
33C11×#323C2212yes—
34C11×#323C2212yescomplemented
35#10622163C2212yes—
36#10622163C2212yescomplemented
37#10622107C2214yescomplemented
38#10622106C2214yescomplemented
39C25×C11C2×C411yescharacteristic
40C24×D11C2×C411yescharacteristic
41C23×C4×C11C2×C411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—24no—
44C22×C22⋊D11—22no—
45C22×C22⋊D11—22no—
46C22×C22⋊D11—24no—
47C22×C22⋊D11C2×C411yescharacteristic
48C22×C22⋊D11C2×C411yescharacteristic
49C22×C22⋊D11C2×C411yescharacteristic
50C22×C22⋊D11C2×C411yescharacteristic
51C23×Dic11C2×C411yescharacteristic
52C23×Dic11C2×C411yescharacteristic
53C23×Dic11C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×C8×C11—22no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2×C411yescharacteristic
63C2×C11×C22⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11C2×C411yescharacteristic
68C2×C22⋊Dic11C2×C411yescharacteristic
69C2×C22⋊Dic11C2×C411yescharacteristic
70C2×C22⋊Dic11C2×C411yescharacteristic
71C4×C22⋊D11—22no—
72C4×C22⋊D11—22no—
73C4×C22⋊D11—22no—
74C4×C22⋊D11—22no—
75C4×C22⋊D11—22no—
76C4×C22⋊D11—22no—
77C4×C22⋊D11D414yes—
78C4×C22⋊D11D414yes—
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2311yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2311yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2×C411yescharacteristic
89C2×C4×Dic11C2×C411yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8—22no—
92C2×#4313—24no—
93(C22⋊D11)⋊C4—24no—
94(C22⋊D11)⋊C4—24no—
95(C22⋊D11)⋊C4—24no—
96(C22⋊D11)⋊C4—24no—
97C22⋊C4×D11—24no—
98C22⋊C4×D11—24no—
99#66930—24no—
100#66930—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#17367—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—81no—
113C24×C11—81no—
114C24×C11M1614yescomplemented
115C24×C11C22×C411yescharacteristic
116C24×C11C22×C411yescharacteristic
117C24×C11C22×C411yescharacteristic
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—22no—
121C23×D11—81no—
122C23×D11—81no—
123C23×D11C22×C411yescharacteristic
124C23×D11C22×C411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—81no—
128C22×C4×C11—81no—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—216no—
136C2×C22⋊D11—216no—
137C2×C22⋊D11—22no—
138C2×C22⋊D11—22no—
139C2×C22⋊D11—21no—
140C2×C22⋊D11—21no—
141C2×C22⋊D11—22no—
142C2×C22⋊D11—22no—
143C2×C22⋊D11—22no—
144C2×C22⋊D11—22no—
145C2×C22⋊D11—22no—
146C2×C22⋊D11—22no—
147C2×C22⋊D11—22no—
148C2×C22⋊D11C22⋊C412yes—
149C2×C22⋊D11C22⋊C412yes—
150C2×C22⋊D11M1614yescomplemented
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—81no—
157C22×Dic11—81no—
158C22×Dic11C22×C411yescharacteristic
159C22×Dic11C22×C411yescharacteristic
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C411yescharacteristic
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—81no—
168C2×C4×D11—81no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C4×D11C2×D414yes—
172C2×C8×C11—24no—
173C2×C8×C11—82no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C22⋊Dic11—22no—
179C22⋊Dic11—22no—
180C22⋊Dic11—21no—
181C22⋊Dic11—21no—
182C22⋊Dic11C22⋊C412yes—
183C22⋊Dic11C22⋊C412yes—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4C22⋊C414yes—
188Dic11⋊C4—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4—22no—
191Dic11⋊C4C22⋊C414yes—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11—22no—
195C4×Dic11C2×D414yes—
196C2×C11⋊C8—24no—
197C2×C11⋊C8—82no—
198#4313—84no—
199C2×#518—111no—
200#2973—112no—
201#1466—112no—
202#1465—112no—
203#1464—112no—
204#1462—112no—
205#1459—112no—
206C2×#323—111no—
207C2×#323D1111yescharacteristic, complemented
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—81no—
221C23×C11—81no—
222C23×C11—81no—
223C23×C11—81no—
224C23×C11—84no—
225C23×C11—84no—
226C23×C11C2×C22⋊C411yescharacteristic
227C23×C11C2×C22⋊C411yescharacteristic
228C23×C11C2×M1612yes—
229C23×C11C2×M1612yes—
230C23×C11C2×M1612yes—
231C23×C11C2×M1612yes—
232C23×C11C23×C411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—28no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—82no—
243C22×D11—82no—
244C22×D11—84no—
245C22×D11—84no—
246C22×D11C2×C22⋊C412yes—
247C22×D11C2×M1612yes—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—81no—
257C2×C4×C11—81no—
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C22×D412yes—
260C22⋊D11—28no—
261C22⋊D11—28no—
262C22⋊D11—24no—
263C22⋊D11—24no—
264C22⋊D11—24no—
265C22⋊D11—24no—
266C2×Dic11—28no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—82no—
278C2×Dic11—82no—
279C2×Dic11C2×C22⋊C412yes—
280C2×Dic11C2×C22⋊C412yes—
281C2×Dic11C2×C22⋊C412yes—
282C2×Dic11C2×M1612yes—
283C4×D11—44no—
284C4×D11—82no—
285C4×D11—82no—
286C4×D11—82no—
287C8×C11—44no—
288C11⋊C8—44no—
289C23×D4—111no—
290#518—224no—
291#518—224no—
292C2×C4×D4—111no—
293C2×C4×D4—111no—
294C2×C4×D4—111no—
295C2×C4×D4—111no—
296C2×C4×D4—111no—
297C2×C4×D4—111no—
298C2×C4×D4—111no—
299C2×C4×D4—111no—
300C2×#117—111no—
301C2×#117—111no—
302C22×C22⋊C4—111no—
303C22×C22⋊C4—111no—
304C22×C22⋊C4—111no—
305C22×C22⋊C4C2×D1111yescharacteristic
306#435—224no—
307#435—224no—
308#432—114no—
309#407—114no—
310C2×C22⋊C8—112no—
311C2×C22⋊C8C2×D1112yescomplemented
312#324—114no—
313#323—112no—
314#323—112no—
315#323—114no—
316#323C2×D1112yes—
317#323C2×D1112yescomplemented
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—84no—
337C22×C11—84no—
338C22×C11#40712yes—
339C22×C11#40712yes—
340C22×C11C22×C22⋊C411yescharacteristic
341C22×C11C22×M1611yescharacteristic
342C22×C11C22×M1611yescharacteristic
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—42no—
353C2×D11—88no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—41no—
357C4×C11—41no—
358Dic11—22no—
359Dic11—22no—
360Dic11—22no—
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364C25—111no—
365C25C4×D1111yescharacteristic
366C22×D4—111no—
367C22×D4—111no—
368C22×D4—111no—
369C22×D4—111no—
370C22×D4—222no—
371C22×D4—222no—
372C22×D4—224no—
373C22×D4—224no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4C4×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C2×M16—224no—
384C22×C8—22no—
385C22×C8—222no—
386C4×D4—114no—
387C4×D4—114no—
388C4×D4—224no—
389C4×D4—224no—
390C4×D4—224no—
391C4×D4—224no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4—222no—
397C4×D4—222no—
398#117—224no—
399#117—224no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—111no—
413C2×C22⋊C4—111no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—224no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4C4×D1111yescharacteristic
419C2×C22⋊C4C4×D1111yescharacteristic
420C2×C22⋊C4C22×D1111yescharacteristic
421C2×C22⋊C4C22×D1111yescharacteristic
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C4⋊C8—224no—
427C22⋊C8—22no—
428C22⋊C8—114no—
429C22⋊C8—224no—
430C22⋊C8—222no—
431C22⋊C8C22×D1114yes—
432#97—224no—
433C2×C11—21no—
434C2×C11—21no—
435C2×C11—22no—
436C2×C11—22no—
437C2×C11—42no—
438C2×C11—42no—
439C2×C11C2×#40711yescharacteristic
440C2×C11#288311yescharacteristic
441C2×C11#288811yescharacteristic
442D11—42no—
443D11—42no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—81no—
448C24—81no—
449C24—111no—
450C24—111no—
451C24—222no—
452C24—222no—
453C24—222no—
454C24—881no—
455C24—881no—
456C24#431314yescomplemented
457C24C2×C4×D1111yescharacteristic
458C24C2×C4×D1111yescharacteristic
459C24C2×C4×D1111yescharacteristic
460C2×D4—112no—
461C2×D4—112no—
462C2×D4—114no—
463C2×D4—222no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—222no—
467C2×D4—2216no—
468C2×D4—2216no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—222no—
472C2×D4—222no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—222no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—114no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—881no—
496C22×C4—881no—
497C22×C4—881no—
498C22×C4—881no—
499C22×C4—881no—
500C22×C4—881no—
501C22×C4C2×C4×D1111yescharacteristic
502C22×C4C2×C4×D1111yescharacteristic
503C22×C4C2×C4×D1111yescharacteristic
504C22×C4D4×D1112yes—
505C22×C4D4×D1112yes—
506C22×C4C23×D1111yescharacteristic
507M16—884no—
508C2×C8—24no—
509C2×C8—82no—
510C2×C8—224no—
511C2×C8—882no—
512C4⋊C4—114no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—112no—
521C22⋊C4—112no—
522C22⋊C4—114no—
523C22⋊C4—222no—
524C22⋊C4—222no—
525C22⋊C4—222no—
526C22⋊C4—222no—
527C22⋊C4—221no—
528C22⋊C4—221no—
529C22⋊C4—222no—
530C42—114no—
531C42—222no—
532C42—222no—
533C42—222no—
534C11#1736711yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—24no—
540C23—24no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—81no—
548C23—81no—
549C23—81no—
550C23—81no—
551C23—84no—
552C23—84no—
553C23—112no—
554C23—112no—
555C23—228no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—882no—
565C23—882no—
566C23—884no—
567C23—884no—
568C23C22⋊C4×D1111yescharacteristic
569C23C22⋊C4×D1111yescharacteristic
570C23C2×#431312yes—
571C23C2×#431312yes—
572C23C2×#431312yes—
573C23M16×D1112yes—
574C23C22×C4×D1111yescharacteristic
575D4—228no—
576D4—228no—
577D4—224no—
578D4—224no—
579D4—224no—
580D4—224no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—228no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—444no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—882no—
608C2×C4—882no—
609C2×C4—882no—
610C2×C4—882no—
611C2×C4—882no—
612C2×C4C22⋊C4×D1112yes—
613C2×C4C2×D4×D1112yes—
614C8—44no—
615C8—444no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—22no—
623C22—22no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—84no—
635C22—84no—
636C22—222no—
637C22—222no—
638C22—222no—
639C22—222no—
640C22—442no—
641C22—442no—
642C22—442no—
643C22—442no—
644C22—441no—
645C22—441no—
646C22—888no—
647C22#1062233912yes—
648C22#1062233912yes—
649C22C2×C22⋊C4×D1111yescharacteristic
650C22C22×#431311yescharacteristic
651C22C2×M16×D1111yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—222no—
657C4—222no—
658C4—222no—
659C4—222no—
660C4—441no—
661C4—441no—
662C2—21no—
663C2—21no—
664C2—22no—
665C2—22no—
666C2—42no—
667C2—42no—
668C2—442no—
669C2—442no—
670C2C2×#1062233911yescharacteristic
671C2#1307707411yescharacteristic
672C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC22×C11C22×C22⋊C4
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenterC2×#323D11
hypocenterC11#17367
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #13077642C2semidirect
3. #13066955C2semidirect
4. #13066951C2semidirect
5. #13066947C2semidirect
6. #13066941C2semidirect
7. #13066932C2semidirect
8. C2×#10622163C2semidirect
9. C2×C11×#323C2semidirect
27. C2×C11×C22⋊C8C22semidirect
28. C2×C22⋊(C11⋊C8)C22semidirect
31. #10622339C22semidirect
32. #10622332C22semidirect
34. C11×#323C22semidirect
36. #10622163C22semidirect
37. #10622107C22semidirect
38. #10622106C22semidirect
114. C24×C11M16semidirect
150. C2×C22⋊D11M16semidirect
207. C2×#323D11semidirect
311. C2×C22⋊C8C2×D11semidirect
317. #323C2×D11semidirect
456. C24#4313semidirect
534. C11#17367semidirect

Maximal subgroups

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

subgroupindex
C2×#106230172
#130776422
#130669552
#130669512
#130669472
#130669412
#130669322
C2×#106221632
C2×C11×#3232
#1736711