Finite Group Databasebeta

← #14923743

Subgroups — #14923743

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#13073049C212yesmaximal, complemented
2#13073038C212yesmaximal, complemented
3#13073027C212yesmaximal, complemented
4#13073016C212yesmaximal, complemented
5#13073001C214yesmaximal, complemented
6#13072856C214yesmaximal
7#13071916C214yesmaximal, complemented
8C4×#66932C214yesmaximal, complemented
9#13071099C211yesmaximal, characteristic, complemented
10#13071099C211yesmaximal, characteristic, complemented
11#13071023C211yesmaximal, characteristic, complemented
12#13070999C211yesmaximal, characteristic
13#13070999C211yesmaximal, characteristic
14C4×#66979C211yesmaximal, characteristic, complemented
15C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
16C24×C4×C11C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C2×#66932C2214yes—
25C4×C11×C22⋊C4C2212yes—
26C4×C11×C22⋊C4C2212yes—
27C4×C11×C22⋊C4C2212yes—
28C4×C11×C22⋊C4C2212yes—
29C2×C11×#95C2212yes—
30#10622860C2212yes—
31#10622860C2212yes—
32#10622825C2214yes—
33#10622825C2212yes—
34#10622825C2212yes—
35#10622825C2212yes—
36#10622825C2212yes—
37#10622824C2212yes—
38#10622824C2212yes—
39#10622823C2214yes—
40#10622823C2214yes—
41C4×C22⋊Dic11C2214yes—
42C4×C22⋊Dic11C2214yes—
43C4×C22⋊Dic11C2214yes—
44#10622566C2214yes—
45#10622565C2214yes—
46#10622565C2214yes—
47#10622564C2214yes—
48#10622561C2214yes—
49#10622558C2214yes—
50#10622557C2214yes—
51#10622549C2211yescharacteristic, complemented
52#10622549C2211yescharacteristic, complemented
53#10622548C2211yescharacteristic, complemented
54#10622548C2211yescharacteristic, complemented
55C4×C4⋊Dic11C2214yescomplemented
56C4×C4⋊Dic11C2212yescomplemented
57C4×C4⋊Dic11C2212yescomplemented
58#10622545C2212yescomplemented
59C4×Dic11⋊C4C2212yescomplemented
60C4×Dic11⋊C4C2214yescomplemented
61C4×Dic11⋊C4C2212yescomplemented
62C42×Dic11C2212yescomplemented
63#10622541C2212yescomplemented
64#10622541C2212yescomplemented
65#10622541C2212yescomplemented
66#10622541C2212yescomplemented
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×C11C2312yes—
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2312yes—
82C23×C4×C11C2312yes—
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C2×C11×C22⋊C4—28no—
86C2×C11×C22⋊C4C2312yes—
87C2×C11×C22⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C42×C11—24no—
91C2×C42×C11—24no—
92C2×C42×C11C2312yes—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2312yes—
98C2×C22⋊Dic11C2314yes—
99C2×C22⋊Dic11C2314yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2312yes—
102C2×C22⋊Dic11C2312yes—
103C2×C22⋊Dic11C2312yes—
104C2×C22⋊Dic11C2314yes—
105C2×C22⋊Dic11C2314yes—
106#66979—24no—
107#66979—24no—
108#66979—24no—
109#66979—24no—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2314yes—
128#66932—216no—
129C11×#95C2312yes—
130C11×#95C2312yes—
131C11×#95C2312yes—
132C11×#95C2312yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
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—24no—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—24no—
159C22×C4×C11—24no—
160C22×C4×C11—24no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—24no—
164C22×C4×C11—24no—
165C22×C4×C11—24no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—416no—
169C22×C4×C11#4114yes—
170C22×C4×C11#4114yes—
171C22×C4×C11#4114yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2411yescharacteristic
178C22×C4×C11C2411yescharacteristic
179C22×Dic11C2414yes—
180C22×Dic11C2412yes—
181C22×Dic11C2412yes—
182C22×Dic11C2414yes—
183C22×Dic11C2412yes—
184C22×Dic11C2412yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4—24no—
188C11×C22⋊C4#4118yes—
189C42×C11—22no—
190C42×C11—22no—
191C42×C11—24no—
192C42×C11—24no—
193C42×C11—22no—
194C42×C11—22no—
195C22⋊Dic11—28no—
196C22⋊Dic11—28no—
197C22⋊Dic11—24no—
198C22⋊Dic11—24no—
199C22⋊Dic11—24no—
200C22⋊Dic11—24no—
201C22⋊Dic11—44no—
202C22⋊Dic11—44no—
203C4⋊Dic11—28no—
204C4⋊Dic11—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207C4⋊Dic11—22no—
208C4⋊Dic11—24no—
209C4⋊Dic11—24no—
210C4⋊Dic11—44no—
211Dic11⋊C4—28no—
212Dic11⋊C4—28no—
213Dic11⋊C4—44no—
214Dic11⋊C4—44no—
215C4×Dic11—28no—
216C4×Dic11—24no—
217C4×Dic11—24no—
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#2280—111no—
234C4×#117—111no—
235C2×C4×C22⋊C4D1111yescharacteristic
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×#4114yes—
250C23×C11C2×#4112yes—
251C23×C11C2×#4112yes—
252C23×C11C2×#4112yes—
253C23×C11C2511yescharacteristic
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—48no—
268C2×C4×C11—48no—
269C2×C4×C11—44no—
270C2×C4×C11—48no—
271C2×C4×C11—48no—
272C2×C4×C11#126116yescomplemented
273C2×C4×C11C2×#4114yes—
274C2×C4×C11C2×#4114yes—
275C2×C4×C11C2×#4112yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11C2×#4112yes—
278C2×C4×C11C2×#4112yes—
279C2×C4×C11C2×#4112yes—
280C2×C4×C11C2×#4112yes—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C24×C4C2×D1111yescharacteristic
296C2×#126—114no—
297C2×#117—111no—
298C2×#117—111no—
299C2×#117—111no—
300C2×#117—111no—
301C22×C22⋊C4C2×D1112yes—
302C22×C42C2×D1111yescharacteristic
303C22×C42C2×D1111yescharacteristic
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#381—112no—
331#380—114no—
332#380—112no—
333#380—112no—
334#380—112no—
335#380—112no—
336#379—112no—
337#379—112no—
338C4×C4⋊C4—112no—
339C4×C4⋊C4—114no—
340C4×C4⋊C4—114no—
341C4×C4⋊C4—112no—
342C4×C4⋊C4—112no—
343C4×C4⋊C4—112no—
344C4×C22⋊C4—114no—
345C4×C22⋊C4—114no—
346C4×C22⋊C4—114no—
347C4×C22⋊C4C2×D1112yes—
348C4×C22⋊C4C2×D1112yes—
349C4×C22⋊C4C2×D1112yes—
350C4×C22⋊C4C2×D1112yes—
351#376—112no—
352C2×#95C2×D1112yes—
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×#4112yes—
369C22×C11C22×#4111yescharacteristic
370C22×C11C22×#4111yescharacteristic
371C22×C11#58512yes—
372C4×C11—24no—
373C4×C11—24no—
374C4×C11—42no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11C2×#12614yes—
378C4×C11C2×#12614yes—
379Dic11—42no—
380Dic11—42no—
381Dic11—42no—
382Dic11—42no—
383Dic11—44no—
384Dic11—44no—
385C25C22×D1111yescharacteristic
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4C22×D1111yescharacteristic
390C23×C4C22×D1112yes—
391C23×C4C22×D1112yes—
392C23×C4C22×D1112yes—
393C23×C4C22×D1112yes—
394C23×C4C22×D1111yescharacteristic
395#126—2216no—
396#117—224no—
397#117—224no—
398#117—224no—
399#117—224no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—112no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—112no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—114no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4—114no—
412C2×C22⋊C4—28no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—112no—
415C2×C22⋊C4—112no—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—114no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—114no—
421C2×C22⋊C4C22×D1112yes—
422C2×C22⋊C4C22×D1112yes—
423C2×C22⋊C4C22×D1112yes—
424C2×C22⋊C4C22×D1112yes—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—114no—
428C2×C42—112no—
429C2×C42—112no—
430C2×C42—112no—
431C2×C42—112no—
432C2×C42—114no—
433C2×C42C22×D1112yes—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C2×C42C22×D1111yescharacteristic
437C2×C42C22×D1111yescharacteristic
438C2×C42C22×D1112yes—
439#95—114no—
440#95—114no—
441#95—114no—
442#95—114no—
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#95C22×D1112yes—
452#95C22×D1112yes—
453#95C22×D1112yes—
454#95C22×D1112yes—
455C2×C11—24no—
456C2×C11—44no—
457C2×C11C22×#12611yescharacteristic
458C2×C11#344411yescharacteristic
459C2×C11#345511yescharacteristic
460C2×C11#347512yes—
461C2×C11#347512yes—
462C24—24no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—42no—
467C24C23×D1112yes—
468C24C23×D1111yescharacteristic
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—416no—
485C22×C4—112no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—114no—
491C22×C4#433914yes—
492C22×C4#434114yes—
493C22×C4#434114yes—
494C22×C4C23×D1112yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1112yes—
497C22×C4C23×D1112yes—
498C22×C4C23×D1112yes—
499C22×C4C23×D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—222no—
504C4⋊C4—222no—
505C4⋊C4—228no—
506C4⋊C4—228no—
507C4⋊C4—228no—
508C4⋊C4—224no—
509C4⋊C4—224no—
510C4⋊C4—444no—
511C4⋊C4—444no—
512C4⋊C4—444no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—224no—
517C22⋊C4—224no—
518C22⋊C4—228no—
519C22⋊C4—228no—
520C22⋊C4—224no—
521C22⋊C4—224no—
522C22⋊C4—444no—
523C22⋊C4—444no—
524C22⋊C4#433918yes—
525C42—22no—
526C42—22no—
527C42—24no—
528C42—24no—
529C42—22no—
530C42—22no—
531C42—224no—
532C42—224no—
533C42—228no—
534C42—224no—
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×#433914yes—
552C23C2×#433912yes—
553C23C2×#434112yes—
554C23C2×#434112yes—
555C23C24×D1111yescharacteristic
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—48no—
571C2×C4—44no—
572C2×C4—48no—
573C2×C4—48no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4#66932116yescomplemented
589C2×C4C2×#433914yes—
590C2×C4C2×#433914yes—
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×#433912yes—
612C22C22×#434111yescharacteristic
613C22C22×#434111yescharacteristic
614C22#1062345312yes—
615C4—24no—
616C4—24no—
617C4—42no—
618C4—42no—
619C4—42no—
620C4—442no—
621C4—442no—
622C4—444no—
623C4—444no—
624C4—442no—
625C4—442no—
626C4C2×#6693214yes—
627C4C2×#6693214yes—
628C2—24no—
629C2—44no—
630C2C22×#6693211yescharacteristic
631C2#1308191211yescharacteristic
632C2#1308200611yescharacteristic
633C2#1308217412yes—
634C2#1308217412yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#34814
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #13073049C2semidirect
2. #13073038C2semidirect
3. #13073027C2semidirect
4. #13073016C2semidirect
5. #13073001C2semidirect
7. #13071916C2semidirect
8. C4×#66932C2semidirect
9. #13071099C2semidirect
10. #13071099C2semidirect
11. #13071023C2semidirect
14. C4×#66979C2semidirect
51. #10622549C22semidirect
52. #10622549C22semidirect
53. #10622548C22semidirect
54. #10622548C22semidirect
55. C4×C4⋊Dic11C22semidirect
56. C4×C4⋊Dic11C22semidirect
57. C4×C4⋊Dic11C22semidirect
58. #10622545C22semidirect
59. C4×Dic11⋊C4C22semidirect
60. C4×Dic11⋊C4C22semidirect
61. C4×Dic11⋊C4C22semidirect
62. C42×Dic11C22semidirect
63. #10622541C22semidirect
64. #10622541C22semidirect
65. #10622541C22semidirect
66. #10622541C22semidirect
67. C11⋊#401C22semidirect
68. #10622273C22semidirect
69. #10622272C22semidirect
70. #10622271C22semidirect
71. #10622268C22semidirect
72. #10622266C22semidirect
73. #10622265C22semidirect
74. #10622264C22semidirect
272. C2×C4×C11#126semidirect
537. C11#34814semidirect
588. C2×C4#66932semidirect

Maximal subgroups

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

subgroupindex
#130730492
#130730382
#130730272
#130730162
#130730012
#130728562
#130719162
C4×#669322
#130710992
#130710232
#130709992
C4×#669792
C2×C4×C11×C22⋊C42
#3481411