Finite Group Databasebeta

← #14719680

Subgroups — #14719680

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077645C212yesmaximal, complemented
2#13066957C212yesmaximal, complemented
3#13066954C212yesmaximal, complemented
4#13066950C212yesmaximal, complemented
5#13066943C212yesmaximal, complemented
6#13066934C212yesmaximal, complemented
7C2×#10622163C212yesmaximal, complemented
8C2×C11×#518C211yesmaximal, characteristic
9C23×D4×C11C411yescharacteristic
10C11×#518—28no—
11C2×C4×D4×C11C411yescharacteristic
12C2×C4×D4×C11C411yescharacteristic
13C2×C4×D4×C11C411yescharacteristic
14C2×C4×D4×C11C411yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C411yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C22×C11×C22⋊C4C411yescharacteristic
22C22×C11×C22⋊C4C411yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25#10622820C2214yescomplemented
26C2×C22⋊(C11⋊C8)C2214yescomplemented
27#10622624—28no—
28#10622539C2214yescomplemented
29#10622166C2214yescomplemented
30#10622163C2214yes—
31#10622163C2214yescomplemented
32#10622163C2214yescomplemented
33C25×C11C2×C411yescharacteristic
34C25×C11C2×C411yescharacteristic
35C22×D4×C11—24no—
36C22×D4×C11—24no—
37C22×D4×C11—24no—
38C22×D4×C11C2×C411yescharacteristic
39C22×D4×C11C2×C411yescharacteristic
40C22×D4×C11C2×C411yescharacteristic
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C411yescharacteristic
43C23×C4×C11C2×C411yescharacteristic
44C23×C4×C11C2×C411yescharacteristic
45C23×C4×C11C2×C411yescharacteristic
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C4×D4×C11—24no—
52C4×D4×C11—24no—
53C4×D4×C11—24no—
54C4×D4×C11—24no—
55C4×D4×C11—24no—
56C4×D4×C11—24no—
57C4×D4×C11—24no—
58C4×D4×C11D418yes—
59C11×#117—24no—
60C11×#117—24no—
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—24no—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C11×C22⋊C4C2×C411yescharacteristic
75C2×C11×C22⋊C4C2×C411yescharacteristic
76C2×C11×C22⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4C2×C411yescharacteristic
78C2×C11×C22⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4C2311yescharacteristic
81C2×C42×C11C2×C411yescharacteristic
82C2×C42×C11C2×C411yescharacteristic
83C2×C42×C11C2×C411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×#4318—24no—
86C22×C11⋊C8—24no—
87C22⋊(C11⋊C8)—24no—
88C22⋊(C11⋊C8)—24no—
89C22⋊(C11⋊C8)C2318yes—
90C4⋊(C11⋊C8)—24no—
91#66867—24no—
92#17367—111nomaximal, Sylow
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—81no—
99C24×C11—81no—
100C24×C11—81no—
101C24×C11—81no—
102C24×C11M1614yescomplemented
103C24×C11C22×C411yescharacteristic
104C24×C11C22×C411yescharacteristic
105C24×C11C22×C411yescharacteristic
106C24×C11C22×C411yescharacteristic
107C24×C11C22×C411yescharacteristic
108C2×D4×C11—232no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11C22⋊C414yes—
120C2×D4×C11M1614yescomplemented
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—81no—
131C22×C4×C11—81no—
132C22×C4×C11—81no—
133C22×C4×C11—81no—
134C22×C4×C11—81no—
135C22×C4×C11—81no—
136C22×C4×C11—81no—
137C22×C4×C11—81no—
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2411yescharacteristic
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C22⋊C414yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C11×C22⋊C4C22⋊C414yes—
165C11×C22⋊C4C22⋊C414yes—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11C2×D414yes—
170#4318—84no—
171C2×C11⋊C8—28no—
172C2×C11⋊C8—84no—
173C2×#518D1111yescharacteristic
174#2973—112no—
175#1466—112no—
176#1465—112no—
177#1464—112no—
178#1462—112no—
179#1459—112no—
180C2×#323—112no—
181C23×C11—28no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—28no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—82no—
202C23×C11—82no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11—84no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11C2×C22⋊C412yes—
210C23×C11C2×C22⋊C412yes—
211C23×C11C2×M1612yes—
212C23×C11C2×M1612yes—
213C23×C11C2×M1612yes—
214C23×C11C2×M1612yes—
215C23×C11C2×M1612yes—
216C23×C11C23×C411yescharacteristic
217D4×C11—28no—
218D4×C11—28no—
219D4×C11—28no—
220D4×C11—28no—
221C2×C4×C11—28no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—44no—
231C2×C4×C11—44no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—82no—
241C2×C4×C11—82no—
242C2×C4×C11—82no—
243C2×C4×C11—82no—
244C2×C4×C11—82no—
245C2×C4×C11—82no—
246C2×C4×C11C2×C22⋊C412yes—
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C2×C22⋊C412yes—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C2×M1612yes—
251C2×C4×C11C22×D412yes—
252C11⋊C8—48no—
253C23×D4Dic1111yescharacteristic
254#518—28no—
255C2×C4×D4Dic1111yescharacteristic
256C2×C4×D4Dic1111yescharacteristic
257C2×C4×D4Dic1111yescharacteristic
258C2×C4×D4Dic1111yescharacteristic
259C2×C4×D4C2×D1111yescharacteristic
260C2×C4×D4C2×D1111yescharacteristic
261C2×C4×D4C2×D1111yescharacteristic
262C2×C4×D4C2×D1111yescharacteristic
263C2×#117Dic1111yescharacteristic
264C2×#117C2×D1111yescharacteristic
265C22×C22⋊C4Dic1111yescharacteristic
266C22×C22⋊C4Dic1111yescharacteristic
267C22×C22⋊C4C2×D1111yescharacteristic
268C22×C22⋊C4C2×D1111yescharacteristic
269#435—228no—
270#432—114no—
271#407—114no—
272C2×C22⋊C8—114no—
273#324—114no—
274#323—114no—
275#323—114no—
276#323—114no—
277C22×C11—21no—
278C22×C11—22no—
279C22×C11—21no—
280C22×C11—22no—
281C22×C11—22no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—22no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—41no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—88no—
304C22×C11—88no—
305C22×C11#40714yes—
306C22×C11C22×C22⋊C411yescharacteristic
307C22×C11C22×M1611yescharacteristic
308C22×C11C22×M1611yescharacteristic
309C4×C11—22no—
310C4×C11—22no—
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—22no—
315C4×C11—41no—
316C4×C11—41no—
317C4×C11—41no—
318C4×C11—41no—
319C25C2×Dic1111yescharacteristic
320C25C2×Dic1111yescharacteristic
321C22×D4—24no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4C2×Dic1111yescharacteristic
325C22×D4C2×Dic1111yescharacteristic
326C22×D4C2×Dic1111yescharacteristic
327C22×D4C2×Dic1111yescharacteristic
328C23×C4C2×Dic1111yescharacteristic
329C23×C4C2×Dic1111yescharacteristic
330C23×C4C2×Dic1111yescharacteristic
331C23×C4C2×Dic1111yescharacteristic
332C23×C4C2×Dic1111yescharacteristic
333C23×C4C2×Dic1111yescharacteristic
334C23×C4C2×Dic1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C2×M16—224no—
338C22×C8—224no—
339C4×D4—24no—
340C4×D4—24no—
341C4×D4—24no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—24no—
345C4×D4—24no—
346C4×D4C22⋊D1118yes—
347#117—24no—
348#117—24no—
349C2×C4⋊C4C2×Dic1111yescharacteristic
350C2×C4⋊C4C2×Dic1111yescharacteristic
351C2×C4⋊C4C2×Dic1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4C2×Dic1111yescharacteristic
358C2×C22⋊C4C2×Dic1111yescharacteristic
359C2×C22⋊C4C2×Dic1111yescharacteristic
360C2×C22⋊C4C2×Dic1111yescharacteristic
361C2×C22⋊C4C2×Dic1111yescharacteristic
362C2×C22⋊C4C2×Dic1111yescharacteristic
363C2×C22⋊C4C2×Dic1111yescharacteristic
364C2×C22⋊C4C2×Dic1111yescharacteristic
365C2×C22⋊C4C2×Dic1111yescharacteristic
366C2×C22⋊C4C22×D1111yescharacteristic
367C2×C22⋊C4C22×D1111yescharacteristic
368C2×C22⋊C4C22×D1111yescharacteristic
369C2×C42C2×Dic1111yescharacteristic
370C2×C42C2×Dic1111yescharacteristic
371C2×C42C2×Dic1111yescharacteristic
372C2×C42C22×D1111yescharacteristic
373C4⋊C8—224no—
374C22⋊C8—118no—
375C22⋊C8—224no—
376C22⋊C8—224no—
377#97—224no—
378C2×C11—21no—
379C2×C11—21no—
380C2×C11—24no—
381C2×C11—42no—
382C2×C11—42no—
383C2×C11—42no—
384C2×C11—42no—
385C2×C11C2×#40711yescharacteristic
386C2×C11#288311yescharacteristic
387C2×C11#288811yescharacteristic
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—81no—
394C24—81no—
395C24—81no—
396C24—81no—
397C24#431814yescomplemented
398C24C22×Dic1111yescharacteristic
399C24C22×Dic1111yescharacteristic
400C24C22×Dic1111yescharacteristic
401C24C22×Dic1111yescharacteristic
402C24C22×Dic1111yescharacteristic
403C2×D4—232no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4#431814yescomplemented
415C2×D4C22⋊Dic1114yes—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—81no—
426C22×C4—81no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4—81no—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4C22×Dic1111yescharacteristic
434C22×C4C22×Dic1111yescharacteristic
435C22×C4C22×Dic1111yescharacteristic
436C22×C4C22×Dic1111yescharacteristic
437C22×C4C22×Dic1111yescharacteristic
438C22×C4C22×Dic1111yescharacteristic
439C22×C4C22×Dic1111yescharacteristic
440C22×C4C22×Dic1111yescharacteristic
441C22×C4C22×Dic1111yescharacteristic
442C22×C4C2×C22⋊D1114yes—
443C22×C4C2×C22⋊D1114yes—
444C22×C4C23×D1111yescharacteristic
445M16—884no—
446C2×C8—228no—
447C2×C8—884no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4C22⋊Dic1114yes—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4C22⋊Dic1114yes—
463C22⋊C4C22⋊Dic1114yes—
464C42—22no—
465C42—22no—
466C42—22no—
467C42C2×C22⋊D1114yes—
468C11#1736711yescharacteristic, complemented, Sylow
469C23—28no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—28no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—82no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23—84no—
494C23—84no—
495C23—84no—
496C23—84no—
497C23C2×#431812yes—
498C23C2×#431812yes—
499C23C2×#431812yes—
500C23C2×#431812yes—
501C23C2×#431812yes—
502C23C2×C22⋊Dic1112yes—
503C23C2×C22⋊Dic1112yes—
504C23C23×Dic1111yescharacteristic
505D4—28no—
506D4—28no—
507D4—28no—
508D4—28no—
509C2×C4—28no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—82no—
529C2×C4—82no—
530C2×C4—82no—
531C2×C4—82no—
532C2×C4—82no—
533C2×C4—82no—
534C2×C4C2×#431812yes—
535C2×C4C2×C22⋊Dic1112yes—
536C2×C4C2×C22⋊Dic1112yes—
537C2×C4C2×C22⋊Dic1112yes—
538C2×C4C2×C22⋊Dic1112yes—
539C2×C4C22×C22⋊D1112yes—
540C8—448no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—88no—
568C22—88no—
569C22#1062282014yes—
570C22C22×#431811yescharacteristic
571C22C22×#431811yescharacteristic
572C22C22×C22⋊Dic1111yescharacteristic
573C4—22no—
574C4—22no—
575C4—22no—
576C4—22no—
577C4—22no—
578C4—22no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C2—21no—
584C2—21no—
585C2—24no—
586C2—42no—
587C2—42no—
588C2—42no—
589C2—42no—
590C2C2×#1062282011yescharacteristic
591C2#1307707711yescharacteristic
592C2#1307709511yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#518C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D4×C11C4
cosocleC22×C4×C11C24
hypercenterC2×#518D11
hypocenterC11#17367
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#518

Complements

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

NH ≅ G/Ntype
1. #13077645C2semidirect
2. #13066957C2semidirect
3. #13066954C2semidirect
4. #13066950C2semidirect
5. #13066943C2semidirect
6. #13066934C2semidirect
7. C2×#10622163C2semidirect
25. #10622820C22semidirect
26. C2×C22⋊(C11⋊C8)C22semidirect
28. #10622539C22semidirect
29. #10622166C22semidirect
31. #10622163C22semidirect
32. #10622163C22semidirect
102. C24×C11M16semidirect
120. C2×D4×C11M16semidirect
397. C24#4318semidirect
414. C2×D4#4318semidirect
468. C11#17367semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130669572
#130669542
#130669502
#130669432
#130669342
C2×#106221632
C2×C11×#5182
#1736711