Finite Group Databasebeta

← #14756849

Subgroups — #14756849

Order 2816.

890 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622631C211yesmaximal, characteristic
2#13071268C211yesmaximal, characteristic, complemented
3#13069257C211yesmaximal, characteristic, complemented
4#13069250C211yesmaximal, characteristic, complemented
5#13069208C211yesmaximal, characteristic, complemented
6#13069187C211yesmaximal, characteristic, complemented
7#13068950C211yesmaximal, characteristic
8#13068950C211yesmaximal, characteristic
9#13068877C211yesmaximal, characteristic
10#13068863C211yesmaximal, characteristic
11#13068514C211yesmaximal, characteristic, complemented
12C4×#66874C211yesmaximal, characteristic, complemented
13C4×#66896C211yesmaximal, characteristic
14#13068368C211yesmaximal, characteristic, complemented
15C11×#2275C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C4×C11×C22⋊C4—21no—
25C4×C11×C22⋊C4—21no—
26C4×C11×C22⋊C4—21no—
27C11×#376C2211yescharacteristic
28C2×C11×#95—21no—
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622631C418yescomplemented
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622542C2211yescharacteristic
41#10622542C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46#10622265—21no—
47#10622265—21no—
48#10622264—21no—
49#10622263—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C22×Dic22C2311yescharacteristic
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11C2×C414yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×#4324—22no—
84C2×#4324—22no—
85C2×#4324C2×C414yes—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C4×Dic22—22no—
99C4×Dic22C2×C414yescomplemented
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107#66896—22no—
108#66896—22no—
109#66896C2×C414yes—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66874—22no—
118#66874—22no—
119#66874C2×C414yescomplemented
120#66872—22no—
121#66871—22no—
122#66871C2×C414yescomplemented
123#66867C2×C414yescomplemented
124C4×C11⋊C8—22no—
125#21125—111nomaximal, Sylow
126C24×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11C22×C412yes—
131C2×D4×C11#4112yes—
132C2×D4×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—81no—
140C22×C4×C11—81no—
141C22×C4×C11—81no—
142C22×C4×C11—81no—
143C22×C4×C11—81no—
144C22×C4×C11—81no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22×C412yes—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22×C412yes—
166C11×C4⋊C4#4112yes—
167C11×C4⋊C4#4112yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—81no—
176C42×C11—81no—
177C42×C11—81no—
178C42×C11C22×C412yes—
179C42×C11#4112yes—
180#4324—28no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190C4×Dic11—24no—
191C4×Dic11—81no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C412yes—
204C2×#440—111no—
205#2320—111no—
206#2275D1111yescharacteristic
207#1928—111no—
208#1927—111no—
209#1921—111no—
210#1918—111no—
211#1877—111no—
212#1877—111no—
213#1864—111no—
214#1862—111no—
215#1776—111no—
216C4×#103—111no—
217C4×#102—111no—
218#1746—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11C22×D411yescharacteristic
227D4×C11—22no—
228D4×C11—22no—
229D4×C11—22no—
230D4×C11#11714yes—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—84no—
257C2×C4×C11—84no—
258C2×C4×C11—84no—
259C2×C4×C11C4×D412yes—
260C2×C4×C11C4×D412yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279Dic22—22no—
280Dic22—22no—
281Dic22—41no—
282Dic22—41no—
283C11⋊C8—22no—
284C11⋊C8—22no—
285C11⋊C8—41no—
286C11⋊C8—41no—
287C22×SD16—111no—
288C2×C4×Q8—111no—
289C2×C4×D4C2×D1111yescharacteristic
290C2×C4×D4C2×D1111yescharacteristic
291C2×C4×D4C2×D1111yescharacteristic
292#440—118no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—111no—
302C2×#97—111no—
303C2×C4×C8—111no—
304#391—111no—
305#391—111no—
306#389—111no—
307#389—111no—
308#387—221no—
309#387—221no—
310#383—221no—
311#382—221no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4C2×D1111yescharacteristic
314C4×C4⋊C4C2×D1111yescharacteristic
315C4×C4⋊C4C2×D1111yescharacteristic
316C4×C22⋊C4—21no—
317C4×C22⋊C4—21no—
318C4×C22⋊C4—21no—
319#376C2×D1111yescharacteristic
320C2×#95—21no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#336—111no—
328#336—111no—
329#336—111no—
330#336—111no—
331C22×C11—24no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11C2×C4×D411yescharacteristic
339C22×C11#52511yescharacteristic
340C22×C11#52511yescharacteristic
341C22×C11#57611yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57711yescharacteristic
344C22×C11#57811yescharacteristic
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—42no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11C2×#11711yescharacteristic
355C4×C11C4×#4111yescharacteristic
356C4×C11#52911yescharacteristic
357C4×C11#52911yescharacteristic
358Dic11—42no—
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8—111no—
363C22×D4C22×D1111yescharacteristic
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—21no—
367C2×SD16—114no—
368C2×SD16—222no—
369C2×SD16—222no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8—111no—
374C4×Q8—114no—
375C4×Q8—222no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—22no—
379C4×D4—22no—
380C4×D4—22no—
381C4×D4C4×D1114yes—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401C2×C42C22×D1111yescharacteristic
402#107—114no—
403#107—222no—
404#106—222no—
405#103—114no—
406#103—222no—
407#103—222no—
408#102—114no—
409#102—222no—
410#102—222no—
411#97—114no—
412C4×C8—222no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95C22⋊D1111yescharacteristic
424#95C22⋊D1111yescharacteristic
425#95C22⋊D1111yescharacteristic
426#95C22⋊D1111yescharacteristic
427C2×C11—44no—
428C2×C11#229011yescharacteristic
429C2×C11#294611yescharacteristic
430C2×C11#294711yescharacteristic
431C2×C11#311811yescharacteristic
432C2×C11#312011yescharacteristic
433C2×C11#312311yescharacteristic
434C2×C11#312411yescharacteristic
435C24—21no—
436C2×Q8—112no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C2×C4×D1112yes—
446C2×D4#433912yes—
447C2×D4#433912yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—81no—
457C22×C4—81no—
458C22×C4—81no—
459C22×C4—81no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4C2×C22⋊D1111yescharacteristic
465C22×C4C2×C22⋊D1111yescharacteristic
466C22×C4C2×C22⋊D1111yescharacteristic
467C22×C4C2×C22⋊D1111yescharacteristic
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471SD16—228no—
472C2×C8—112no—
473C2×C8—112no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—112no—
488C4⋊C4—224no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4C2×C4×D1112yes—
497C4⋊C4#433912yes—
498C4⋊C4#433912yes—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—24no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—81no—
507C42—81no—
508C42—81no—
509C42—224no—
510C42—881no—
511C42C2×C4×D1112yes—
512C42#433912yes—
513C11#2112511yescharacteristic, complemented, Sylow
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×C22⋊D1111yescharacteristic
522Q8—222no—
523Q8—222no—
524Q8—441no—
525Q8—441no—
526D4—22no—
527D4—22no—
528D4—22no—
529D4#6692514yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4—84no—
557C2×C4—84no—
558C2×C4—222no—
559C2×C4—222no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4C4×C22⋊D1112yes—
571C2×C4C4×C22⋊D1112yes—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×#433911yescharacteristic
575C2×C4C2×#433911yescharacteristic
576C2×C4C2×#433911yescharacteristic
577C2×C4C2×#433911yescharacteristic
578C8—222no—
579C8—222no—
580C8—441no—
581C8—441no—
582C22—24no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22C2×C4×C22⋊D1111yescharacteristic
590C22#1062332211yescharacteristic
591C22#1062332211yescharacteristic
592C22#1062336611yescharacteristic
593C22#1062336711yescharacteristic
594C22#1062336711yescharacteristic
595C22#1062336911yescharacteristic
596C4—22no—
597C4—22no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—442no—
606C4—442no—
607C4—881no—
608C4—881no—
609C4C2×#6692511yescharacteristic
610C4C4×#433911yescharacteristic
611C4#1062301011yescharacteristic
612C4#1062301011yescharacteristic
613C2—44no—
614C2#1307105911yescharacteristic
615C2#1307744811yescharacteristic
616C2#1307745511yescharacteristic
617C2#1307880011yescharacteristic
618C2#1307883011yescharacteristic
619C2#1307886811yescharacteristic
620C2#1307887811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2275C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#2275D11
hypocenterC11#21125
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #13071268C2semidirect
3. #13069257C2semidirect
4. #13069250C2semidirect
5. #13069208C2semidirect
6. #13069187C2semidirect
11. #13068514C2semidirect
12. C4×#66874C2semidirect
14. #13068368C2semidirect
32. #10622631C4semidirect
99. C4×Dic22C2×C4semidirect
119. #66874C2×C4semidirect
122. #66871C2×C4semidirect
123. #66867C2×C4semidirect
513. C11#21125semidirect

Maximal subgroups

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

subgroupindex
C2×#106226312
#130712682
#130692572
#130692502
#130692082
#130691872
#130689502
#130688772
#130688632
#130685142
C4×#668742
C4×#668962
#130683682
C11×#22752
#2112511