Finite Group Databasebeta

← #14719918

Subgroups — #14719918

Order 2816.

1048 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077657C211yesmaximal, characteristic, complemented
2#13077645C211yesmaximal, characteristic, complemented
3#13066985C212yesmaximal, complemented
4#13066976C212yesmaximal, complemented
5#13066968C212yesmaximal, complemented
6#13066964C212yesmaximal, complemented
7#13066954C212yesmaximal, complemented
8#13066943C212yesmaximal, complemented
9C2×C11×#538C211yesmaximal, characteristic
10C11×#538—24no—
11C11×#538—24no—
12C2×C11×#126C411yescharacteristic
13C2×C11×#126C2211yescharacteristic
14C2×C11×#124C411yescharacteristic
15C2×C11×#124C2211yescharacteristic
16C2×C11×#123C411yescharacteristic
17C2×C11×#123C2211yescharacteristic
18C2×C11×C22⋊Q8C411yescharacteristic
19C2×C11×#121C411yescharacteristic
20C2×C11×#121C411yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C11×#120C411yescharacteristic
23C2×C11×#120C411yescharacteristic
24C2×C4×D4×C11C2211yescharacteristic
25C2×C4×D4×C11C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27#10622820C2212yes—
28#10622820C2212yes—
29#10622820C2212yescomplemented
30C2×C22⋊(C11⋊C8)C2212yescomplemented
31#10622625—24no—
32#10622624—24no—
33#10622539C2212yescomplemented
34#10622538C2212yescomplemented
35#10622166C2214yescomplemented
36#10622163C2214yes—
37#10622163C2214yes—
38#10622163C2214yescomplemented
39C25×C11C2×C411yescharacteristic
40C22×Q8×C11C2×C411yescharacteristic
41C22×D4×C11C2×C411yescharacteristic
42C22×D4×C11C2×C411yescharacteristic
43C22×D4×C11C2×C411yescharacteristic
44C22×D4×C11C2×C411yescharacteristic
45C22×D4×C11C2×C411yescharacteristic
46C22×D4×C11C2×C411yescharacteristic
47C22×D4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2×C411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C11×#126—24no—
53C11×#126—22no—
54C11×#126—22no—
55C11×#124—24no—
56C11×#124—22no—
57C11×#124—22no—
58C11×#123—22no—
59C11×#123—22no—
60C11×#123—24no—
61C11×C22⋊Q8—24no—
62C11×#121—24no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121—24no—
66C11×#120—24no—
67C11×#120—24no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11D414yes—
71C4×D4×C11D414yes—
72C2×C11×C4⋊C4C2×C411yescharacteristic
73C2×C11×C4⋊C4C2×C411yescharacteristic
74C2×C11×C4⋊C4C2×C411yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4C2×C411yescharacteristic
81C2×C11×C22⋊C4C2×C411yescharacteristic
82C2×C11×C22⋊C4C2×C411yescharacteristic
83C2×C11×C22⋊C4C2×C411yescharacteristic
84C2×C11×C22⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4C2×C411yescharacteristic
86C2×C11×C22⋊C4C2×C411yescharacteristic
87C2×C11×C22⋊C4C2×C411yescharacteristic
88C2×C11×C22⋊C4C2×C411yescharacteristic
89C2×C11×C22⋊C4C2×C411yescharacteristic
90C2×C11×C22⋊C4C2×C411yescharacteristic
91C2×C11×C22⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4C2311yescharacteristic
94C2×C42×C11C2×C411yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—22no—
99C22×C11⋊C8—22no—
100C22⋊(C11⋊C8)—22no—
101C22⋊(C11⋊C8)—22no—
102C22⋊(C11⋊C8)—22no—
103C22⋊(C11⋊C8)—22no—
104C22⋊(C11⋊C8)C2314yes—
105C22⋊(C11⋊C8)C2314yes—
106C4⋊(C11⋊C8)—22no—
107C4⋊(C11⋊C8)—22no—
108#66867—22no—
109C4×C11⋊C8—22no—
110#17405—111nomaximal, Sylow
111C24×C11—22no—
112C24×C11—42no—
113C24×C11—81no—
114C24×C11—81no—
115C24×C11C22×C411yescharacteristic
116C24×C11C22×C411yescharacteristic
117C24×C11C22×C411yescharacteristic
118C24×C11C22×C411yescharacteristic
119C24×C11C22×C411yescharacteristic
120C2×Q8×C11—22no—
121C2×Q8×C11—81no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—81no—
131C2×D4×C11—81no—
132C2×D4×C11—81no—
133C2×D4×C11—81no—
134C2×D4×C11—81no—
135C2×D4×C11C22⋊C414yes—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—81no—
139C22×C4×C11—81no—
140C22×C4×C11—81no—
141C22×C4×C11—81no—
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2411yescharacteristic
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C22⋊C414yes—
163C11×C22⋊C4—22no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4C22⋊C414yes—
179C11×C22⋊C4C22⋊C414yes—
180C42×C11—22no—
181C42×C11C2×D412yes—
182C42×C11C2×D412yes—
183#4318—82no—
184#4318—82no—
185#4318—82no—
186C2×C11⋊C8—24no—
187C2×C11⋊C8—24no—
188C2×C11⋊C8—82no—
189C2×#538D1111yescharacteristic
190#2975—111no—
191#2973—111no—
192#1473—112no—
193#1471—112no—
194#1469—112no—
195#1468—112no—
196#1465—112no—
197#1462—112no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—21no—
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—44no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—88no—
220C23×C11C2×C22⋊C412yes—
221C23×C11C2×C22⋊C412yes—
222C23×C11C23×C411yescharacteristic
223Q8×C11—82no—
224D4×C11—44no—
225D4×C11—44no—
226D4×C11—82no—
227D4×C11—82no—
228D4×C11—82no—
229D4×C11—82no—
230D4×C11—82no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—82no—
251C2×C4×C11—82no—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C11⋊C8—44no—
259C11⋊C8—44no—
260#538—24no—
261#538—24no—
262C2×#126Dic1111yescharacteristic
263C2×#126C2×D1111yescharacteristic
264C2×#124Dic1111yescharacteristic
265C2×#124C2×D1111yescharacteristic
266C2×#123Dic1111yescharacteristic
267C2×#123C2×D1111yescharacteristic
268C2×C22⋊Q8Dic1111yescharacteristic
269C2×#121Dic1111yescharacteristic
270C2×#121Dic1111yescharacteristic
271C2×#121C2×D1111yescharacteristic
272C2×#120Dic1111yescharacteristic
273C2×#120Dic1111yescharacteristic
274C2×C4×D4C2×D1111yescharacteristic
275C2×C4×D4C2×D1111yescharacteristic
276C22×C22⋊C4C2×D1111yescharacteristic
277#436—224no—
278#435—224no—
279#432—112no—
280#431—112no—
281#407—112no—
282#407—112no—
283#407—112no—
284C2×C22⋊C8—112no—
285#324—114no—
286#323—114no—
287#323—114no—
288#323—114no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—44no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—41no—
305C22×C11—41no—
306C22×C11—41no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11—88no—
312C22×C11C22×C22⋊C411yescharacteristic
313C22×C11#56812yes—
314C4×C11—22no—
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—22no—
320C4×C11—41no—
321C4×C11—41no—
322C4×C11—41no—
323C4×C11—41no—
324C4×C11—41no—
325C25C2×Dic1111yescharacteristic
326C22×Q8C2×Dic1111yescharacteristic
327C22×D4C2×Dic1111yescharacteristic
328C22×D4C2×Dic1111yescharacteristic
329C22×D4C2×Dic1111yescharacteristic
330C22×D4C2×Dic1111yescharacteristic
331C22×D4C2×Dic1111yescharacteristic
332C22×D4C2×Dic1111yescharacteristic
333C22×D4C2×Dic1111yescharacteristic
334C23×C4C2×Dic1111yescharacteristic
335C23×C4C2×Dic1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1111yescharacteristic
338C2×M16—222no—
339C2×M16—222no—
340C2×M16—222no—
341C22×C8—222no—
342#126—24no—
343#126—22no—
344#126—22no—
345#124—24no—
346#124—22no—
347#124—22no—
348#123—22no—
349#123—22no—
350#123—24no—
351C22⋊Q8—24no—
352#121—24no—
353#121—22no—
354#121—22no—
355#121—24no—
356#120—24no—
357#120—24no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4C22⋊D1114yes—
361C4×D4C22⋊D1114yes—
362C2×C4⋊C4C2×Dic1111yescharacteristic
363C2×C4⋊C4C2×Dic1111yescharacteristic
364C2×C4⋊C4C2×Dic1111yescharacteristic
365C2×C4⋊C4C2×Dic1111yescharacteristic
366C2×C4⋊C4C2×Dic1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4C2×Dic1111yescharacteristic
371C2×C22⋊C4C2×Dic1111yescharacteristic
372C2×C22⋊C4C2×Dic1111yescharacteristic
373C2×C22⋊C4C2×Dic1111yescharacteristic
374C2×C22⋊C4C2×Dic1111yescharacteristic
375C2×C22⋊C4C2×Dic1111yescharacteristic
376C2×C22⋊C4C2×Dic1111yescharacteristic
377C2×C22⋊C4C2×Dic1111yescharacteristic
378C2×C22⋊C4C2×Dic1111yescharacteristic
379C2×C22⋊C4C2×Dic1111yescharacteristic
380C2×C22⋊C4C2×Dic1111yescharacteristic
381C2×C22⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4C22×D1111yescharacteristic
384C2×C42C2×Dic1111yescharacteristic
385C2×C42C22×D1111yescharacteristic
386C4⋊C8—222no—
387C4⋊C8—222no—
388C22⋊C8—114no—
389C22⋊C8—114no—
390C22⋊C8—222no—
391C22⋊C8—222no—
392C22⋊C8—222no—
393C22⋊C8—222no—
394#97—222no—
395C4×C8—222no—
396C2×C11—22no—
397C2×C11—42no—
398C2×C11—42no—
399C2×C11—81no—
400C2×C11—81no—
401C2×C11—81no—
402C2×C11#287911yescharacteristic
403C2×C11#288311yescharacteristic
404C2×C11#288811yescharacteristic
405C24—22no—
406C24—42no—
407C24—81no—
408C24—81no—
409C24C22×Dic1111yescharacteristic
410C24C22×Dic1111yescharacteristic
411C24C22×Dic1111yescharacteristic
412C24C22×Dic1111yescharacteristic
413C24C22×Dic1111yescharacteristic
414C2×Q8—22no—
415C2×Q8—81no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—81no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C2×D4C22⋊Dic1114yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4C22×Dic1111yescharacteristic
437C22×C4C22×Dic1111yescharacteristic
438C22×C4C22×Dic1111yescharacteristic
439C22×C4C22×Dic1111yescharacteristic
440C22×C4C22×Dic1111yescharacteristic
441C22×C4C22×Dic1111yescharacteristic
442C22×C4C22×Dic1111yescharacteristic
443C22×C4C22×Dic1111yescharacteristic
444C22×C4C22×Dic1111yescharacteristic
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1112yes—
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1112yes—
449C22×C4C23×D1111yescharacteristic
450M16—882no—
451M16—882no—
452M16—882no—
453C2×C8—224no—
454C2×C8—224no—
455C2×C8—882no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4C22⋊Dic1114yes—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4C22⋊Dic1114yes—
479C22⋊C4C22⋊Dic1114yes—
480C42—22no—
481C42C2×C22⋊D1112yes—
482C42C2×C22⋊D1112yes—
483C11#1740511yescharacteristic, complemented, Sylow
484C23—22no—
485C23—22no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—44no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—82no—
504C23—82no—
505C23—88no—
506C23C2×C22⋊Dic1112yes—
507C23C2×C22⋊Dic1112yes—
508C23C23×Dic1111yescharacteristic
509Q8—82no—
510D4—44no—
511D4—44no—
512D4—82no—
513D4—82no—
514D4—82no—
515D4—82no—
516D4—82no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4C2×C22⋊Dic1112yes—
539C2×C4C2×C22⋊Dic1112yes—
540C2×C4C2×C22⋊Dic1112yes—
541C2×C4C2×C22⋊Dic1112yes—
542C2×C4C22×C22⋊D1111yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C8—444no—
545C8—444no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—44no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22—88no—
569C22#1062335012yes—
570C22C22×C22⋊Dic1111yescharacteristic
571C4—22no—
572C4—21no—
573C4—21no—
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C2—22no—
583C2—42no—
584C2—42no—
585C2—81no—
586C2—81no—
587C2—81no—
588C2#1307706111yescharacteristic
589C2#1307707711yescharacteristic
590C2#1307709511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#538C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenterC2×#538D11
hypocenterC11#17405
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #13077657C2semidirect
2. #13077645C2semidirect
3. #13066985C2semidirect
4. #13066976C2semidirect
5. #13066968C2semidirect
6. #13066964C2semidirect
7. #13066954C2semidirect
8. #13066943C2semidirect
29. #10622820C22semidirect
30. C2×C22⋊(C11⋊C8)C22semidirect
33. #10622539C22semidirect
34. #10622538C22semidirect
35. #10622166C22semidirect
38. #10622163C22semidirect
483. C11#17405semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130776452
#130669852
#130669762
#130669682
#130669642
#130669542
#130669432
C2×C11×#5382
#1740511