Finite Group Databasebeta

← #14923737

Subgroups — #14923737

Order 2816.

1994 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073045C212yesmaximal, complemented
2#13073034C212yesmaximal, complemented
3#13073023C212yesmaximal, complemented
4#13073012C212yesmaximal, complemented
5#13072997C214yesmaximal, complemented
6#13072861C214yesmaximal
7#13071916C214yesmaximal, complemented
8C4×#66932C214yesmaximal, complemented
9#13071100C211yesmaximal, characteristic, complemented
10#13071098C211yesmaximal, characteristic, complemented
11#13071019C211yesmaximal, characteristic, complemented
12#13070999C211yesmaximal, characteristic
13#117×Dic11C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic11C211yesmaximal, characteristic
15C11×#2280C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×#66932C2214yes—
25C11×#381C2212yes—
26C11×#380C2212yes—
27C11×#380C2212yes—
28C11×#379C2212yes—
29C4×C11×C22⋊C4C2214yes—
30#10622860C2212yes—
31#10622825C2212yes—
32#10622825C2212yes—
33#10622824C2212yes—
34C4×C22⋊Dic11C2212yes—
35C4×C22⋊Dic11C2214yes—
36C4×C22⋊Dic11C2212yes—
37C4×C22⋊Dic11C2212yes—
38C4×C22⋊Dic11C2212yes—
39C2×C11⋊#95C2212yes—
40#10622598C2212yescomplemented
41#10622598C2212yescomplemented
42#10622590C2211yescharacteristic, complemented
43#10622590C2211yescharacteristic, complemented
44#10622589C2211yescharacteristic, complemented
45#10622589C2211yescharacteristic, complemented
46C4⋊C4×Dic11C2212yescomplemented
47C4⋊C4×Dic11C2212yescomplemented
48#10622586C2212yescomplemented
49#10622586C2212yescomplemented
50#10622566C2214yes—
51#10622565C2214yes—
52#10622565C2214yes—
53#10622564C2214yes—
54#10622563C2214yes—
55#10622561C2214yes—
56#10622559C2214yes—
57#10622558C2214yes—
58#10622557C2214yes—
59#10622555C2214yes—
60C22⋊C4×Dic11C2214yes—
61C4×C4⋊Dic11C2212yescomplemented
62C4×C4⋊Dic11C2212yescomplemented
63#10622545C2212yescomplemented
64C4×Dic11⋊C4C2214yescomplemented
65C4×Dic11⋊C4C2214yescomplemented
66C42×Dic11C2212yescomplemented
67C11⋊#401C2214yescomplemented
68#10622273C2214yescomplemented
69#10622272C2214yescomplemented
70#10622271C2214yescomplemented
71#10622268C2214yescomplemented
72#10622266C2214yescomplemented
73#10622265C2214yescomplemented
74#10622264C2214yescomplemented
75C25×C11C2311yescharacteristic
76C23×C4×C11—24no—
77C23×C4×C11—24no—
78C23×C4×C11—24no—
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2312yes—
81C23×C4×C11C2312yes—
82C23×C4×C11C2311yescharacteristic
83C23×Dic11C2312yes—
84C23×Dic11C2312yes—
85C11×#117—24no—
86C11×#117—24no—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4C2314yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C11×C22⋊C4C2314yes—
94C2×C42×C11C2312yes—
95C2×C42×C11C2312yes—
96C2×C22⋊Dic11—28no—
97C2×C22⋊Dic11C2314yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2312yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2312yes—
102C2×C22⋊Dic11C2312yes—
103C2×C22⋊Dic11C2314yes—
104C2×C22⋊Dic11C2312yes—
105#66979—24no—
106#66979—24no—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×C4×Dic11—24no—
117C2×C4×Dic11—24no—
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2311yescharacteristic
120C2×C4×Dic11C2312yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2311yescharacteristic
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2314yes—
128#66932—216no—
129C11×#95C2314yes—
130C11×#95C2314yes—
131C11⋊#95C2312yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2312yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2312yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2312yes—
145#34814—111nomaximal, Sylow
146C24×C11—24no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—42no—
151C24×C11C2412yes—
152C24×C11C2411yescharacteristic
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—416no—
163C22×C4×C11#4114yes—
164C22×C4×C11#4114yes—
165C22×C4×C11#4114yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2414yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—42no—
177C22×Dic11—42no—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C22×Dic11C2412yes—
181C22×Dic11C2412yes—
182C22×Dic11C2414yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4—24no—
190C11×C22⋊C4—24no—
191C11×C22⋊C4—44no—
192C42×C11—24no—
193C42×C11—24no—
194C22⋊Dic11—24no—
195C22⋊Dic11—24no—
196C22⋊Dic11—28no—
197C22⋊Dic11—24no—
198C22⋊Dic11—24no—
199C22⋊Dic11—24no—
200C22⋊Dic11—44no—
201C22⋊Dic11#4118yes—
202C4⋊Dic11—28no—
203C4⋊Dic11—24no—
204C4⋊Dic11—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—44no—
207Dic11⋊C4—28no—
208Dic11⋊C4—28no—
209Dic11⋊C4—44no—
210Dic11⋊C4—44no—
211C4×Dic11—28no—
212C4×Dic11—22no—
213C4×Dic11—22no—
214C4×Dic11—24no—
215C4×Dic11—24no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—24no—
219C4×Dic11—24no—
220C4×Dic11—44no—
221#2497—112no—
222#2496—112no—
223#2495—112no—
224#2494—112no—
225#2493—114no—
226#2480—114no—
227#2401—114no—
228C4×#126—114no—
229#2296—111no—
230#2296—111no—
231#2285—111no—
232#2280—111no—
233#2280D1111yescharacteristic
234C4×#117—111no—
235C2×C4×C22⋊C4—111no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—28no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—48no—
246C23×C11—48no—
247C23×C11—44no—
248C23×C11—44no—
249C23×C11C2×#4112yes—
250C23×C11C2×#4112yes—
251C23×C11C2×#4112yes—
252C23×C11C2×#4114yes—
253C23×C11C2511yescharacteristic
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—44no—
265C2×C4×C11—48no—
266C2×C4×C11—48no—
267C2×C4×C11#126116yescomplemented
268C2×C4×C11C2×#4112yes—
269C2×C4×C11C2×#4112yes—
270C2×C4×C11C2×#4112yes—
271C2×C4×C11C2×#4112yes—
272C2×C4×C11C2×#4112yes—
273C2×C4×C11C2×#4112yes—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—22no—
291C2×Dic11—48no—
292C2×Dic11—48no—
293C2×Dic11C2×#4114yes—
294C2×Dic11C2×#4114yes—
295C24×C4C2×D1111yescharacteristic
296C2×#126—114no—
297C2×#117—111no—
298C2×#117—111no—
299C2×#117C2×D1111yescharacteristic
300C2×#117C2×D1111yescharacteristic
301C22×C22⋊C4—112no—
302C22×C42—111no—
303C22×C42—111no—
304#401—114no—
305#400—114no—
306#400—114no—
307#400—114no—
308#397—114no—
309#397—114no—
310#397—114no—
311#396—114no—
312#389—112no—
313#389—112no—
314#389—112no—
315#389—112no—
316#388—114no—
317#388—114no—
318#388—114no—
319#387—114no—
320#387—114no—
321#387—114no—
322#385—114no—
323#385—114no—
324#384—111no—
325#384—111no—
326#383—114no—
327#382—111no—
328#382—111no—
329#381—112no—
330#381C2×D1112yes—
331#380—112no—
332#380—112no—
333#380—114no—
334#380C2×D1112yes—
335#380C2×D1112yes—
336#379—112no—
337#379C2×D1112yes—
338C4×C4⋊C4—112no—
339C4×C4⋊C4—112no—
340C4×C4⋊C4—112no—
341C4×C4⋊C4—114no—
342C4×C4⋊C4—114no—
343C4×C4⋊C4—112no—
344C4×C22⋊C4—112no—
345C4×C22⋊C4—114no—
346C4×C22⋊C4—112no—
347C4×C22⋊C4—112no—
348C4×C22⋊C4—112no—
349C4×C22⋊C4—114no—
350C4×C22⋊C4C2×D1114yes—
351#376—112no—
352C2×#95—112no—
353C43—112no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—24no—
357C22×C11—24no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—24no—
361C22×C11—416no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11C2×#12614yes—
367C22×C11C22×#4111yescharacteristic
368C22×C11C22×#4111yescharacteristic
369C22×C11C22×#4111yescharacteristic
370C22×C11C22×#4112yes—
371C22×C11#58512yes—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11—42no—
375C4×C11—44no—
376C4×C11C2×#12614yes—
377C4×C11C2×#12614yes—
378Dic11—24no—
379Dic11—24no—
380Dic11—42no—
381Dic11—42no—
382Dic11—44no—
383Dic11—42no—
384Dic11—42no—
385C25C22×D1111yescharacteristic
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—112no—
390C23×C4—112no—
391C23×C4C22×D1111yescharacteristic
392C23×C4C22×D1112yes—
393C23×C4C22×D1112yes—
394C23×C4C22×D1111yescharacteristic
395#126—2216no—
396#117—24no—
397#117—24no—
398#117—224no—
399#117—224no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4C22×D1112yes—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C22⋊C4—112no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—112no—
415C2×C22⋊C4—112no—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—112no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4C22×D1112yes—
422C2×C22⋊C4C22×D1112yes—
423C2×C22⋊C4C22×D1114yes—
424C2×C22⋊C4C22×D1114yes—
425C2×C42—114no—
426C2×C42—112no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—112no—
430C2×C42—112no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—112no—
434C2×C42—114no—
435C2×C42—224no—
436C2×C42—224no—
437C2×C42C22×D1112yes—
438C2×C42C22×D1112yes—
439#95—112no—
440#95—112no—
441#95—112no—
442#95—112no—
443#95—114no—
444#95—114no—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—114no—
449#95—114no—
450#95—114no—
451#95—114no—
452#95—114no—
453#95C22×D1114yes—
454#95C22×D1114yes—
455C2×C11—24no—
456C2×C11—44no—
457C2×C11C22×#12611yescharacteristic
458C2×C11#344411yescharacteristic
459C2×C11#345511yescharacteristic
460C2×C11#347512yes—
461C2×C11#347512yes—
462C24—22no—
463C24—24no—
464C24—22no—
465C24—22no—
466C24—42no—
467C24C23×D1112yes—
468C24C23×D1111yescharacteristic
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—416no—
479C22×C4—112no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—112no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4#433914yes—
493C22×C4#434114yes—
494C22×C4#434114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1114yes—
497C22×C4C23×D1112yes—
498C22×C4C23×D1112yes—
499C22×C4C23×D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501C4⋊C4—24no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—228no—
505C4⋊C4—228no—
506C4⋊C4—228no—
507C4⋊C4—224no—
508C4⋊C4—222no—
509C4⋊C4—222no—
510C4⋊C4—444no—
511C4⋊C4—444no—
512C4⋊C4—444no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—28no—
516C22⋊C4—44no—
517C22⋊C4—118no—
518C22⋊C4—224no—
519C22⋊C4—224no—
520C22⋊C4—224no—
521C22⋊C4—224no—
522C22⋊C4—224no—
523C22⋊C4—228no—
524C22⋊C4—444no—
525C42—24no—
526C42—24no—
527C42—228no—
528C42—222no—
529C42—224no—
530C42—222no—
531C42—224no—
532C42—222no—
533C42—224no—
534C42—222no—
535C42—224no—
536C42—444no—
537C11#3481411yescharacteristic, complemented, Sylow
538C23—22no—
539C23—22no—
540C23—28no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—48no—
548C23—48no—
549C23—44no—
550C23—44no—
551C23C2×#433912yes—
552C23C2×#434112yes—
553C23C2×#434112yes—
554C23#41×D1114yes—
555C23C24×D1111yescharacteristic
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—44no—
567C2×C4—48no—
568C2×C4—48no—
569C2×C4—114no—
570C2×C4—114no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—224no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—448no—
589C2×C4—448no—
590C2×C4#66932116yescomplemented
591C2×C4C2×#433912yes—
592C2×C4C2×#433912yes—
593C2×C4C2×#434112yes—
594C2×C4C2×#434112yes—
595C2×C4C2×#434112yes—
596C2×C4C2×#434112yes—
597C22—22no—
598C22—24no—
599C22—24no—
600C22—22no—
601C22—24no—
602C22—24no—
603C22—24no—
604C22—416no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22C2×#6693214yes—
610C22C22×#433911yescharacteristic
611C22C22×#434111yescharacteristic
612C22C22×#434111yescharacteristic
613C22C2×#41×D1112yes—
614C22#1062345312yes—
615C4—42no—
616C4—42no—
617C4—44no—
618C4—42no—
619C4—224no—
620C4—224no—
621C4—442no—
622C4—442no—
623C4—444no—
624C4—442no—
625C4—442no—
626C4C2×#6693214yes—
627C4C2×#6693214yes—
628C2—24no—
629C2—44no—
630C2C22×#6693211yescharacteristic
631C2#1308190811yescharacteristic
632C2#1308200411yescharacteristic
633C2#1308217012yes—
634C2#1308217612yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2280C2
prime radicalC25×C11C23
hypercenter#2280D11
hypocenterC11#34814
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
1. #13073045C2semidirect
2. #13073034C2semidirect
3. #13073023C2semidirect
4. #13073012C2semidirect
5. #13072997C2semidirect
7. #13071916C2semidirect
8. C4×#66932C2semidirect
9. #13071100C2semidirect
10. #13071098C2semidirect
11. #13071019C2semidirect
13. #117×Dic11C2semidirect
40. #10622598C22semidirect
41. #10622598C22semidirect
42. #10622590C22semidirect
43. #10622590C22semidirect
44. #10622589C22semidirect
45. #10622589C22semidirect
46. C4⋊C4×Dic11C22semidirect
47. C4⋊C4×Dic11C22semidirect
48. #10622586C22semidirect
49. #10622586C22semidirect
61. C4×C4⋊Dic11C22semidirect
62. C4×C4⋊Dic11C22semidirect
63. #10622545C22semidirect
64. C4×Dic11⋊C4C22semidirect
65. C4×Dic11⋊C4C22semidirect
66. C42×Dic11C22semidirect
67. C11⋊#401C22semidirect
68. #10622273C22semidirect
69. #10622272C22semidirect
70. #10622271C22semidirect
71. #10622268C22semidirect
72. #10622266C22semidirect
73. #10622265C22semidirect
74. #10622264C22semidirect
267. C2×C4×C11#126semidirect
537. C11#34814semidirect
590. C2×C4#66932semidirect

Maximal subgroups

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

subgroupindex
#130730452
#130730342
#130730232
#130730122
#130729972
#130728612
#130719162
C4×#669322
#130711002
#130710982
#130710192
#130709992
#117×Dic112
C2×C4×C22⋊Dic112
C11×#22802
#3481411