Finite Group Databasebeta

← #14795057

Subgroups — #14795057

Order 2816.

784 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×#10622676C211yesmaximal, characteristic, complemented
2C2×#10622448C211yesmaximal, characteristic
3#13076921C211yesmaximal, characteristic
4C4×#66950C211yesmaximal, characteristic
5#13070054C211yesmaximal, characteristic
6#13070048C211yesmaximal, characteristic
7#13069822C211yesmaximal, characteristic
8#13069815C211yesmaximal, characteristic
9#13069384C211yesmaximal, characteristic, complemented
10#13069358C211yesmaximal, characteristic, complemented
11#13069353C211yesmaximal, characteristic, complemented
12#13069304C211yesmaximal, characteristic, complemented
13#13069304C211yesmaximal, characteristic, complemented
14#13068632C211yesmaximal, characteristic, complemented
15C11×#1989C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×#66950C2211yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×(C2×D11)⋊C8C2211yescharacteristic
24C2×#66880C2211yescharacteristic
25C2×#66880C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28#10622676—24no—
29#10622602—21no—
30#10622602—21no—
31#10622600C2211yescharacteristic
32#10622600C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622591—21no—
36#10622591—21no—
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622586C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C4×(C2×D11)⋊C4—21no—
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11—21no—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622448—24no—
51#10622281—21no—
52#10622266—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#125—22no—
68C11×#125—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66950—22no—
96#66950—22no—
97C42×D11—22no—
98C42×D11—22no—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C11×C4⋊C8—22no—
102C11×#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—22no—
115#66880—22no—
116#66880—22no—
117#66879—22no—
118#66879—22no—
119#66874—22no—
120#66874—22no—
121#66872—22no—
122#66872—22no—
123#66871—22no—
124#66871—22no—
125C4⋊(C11⋊C8)D414yes—
126#24707—111nomaximal, Sylow
127C23×D11C2×D411yescharacteristic
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—41no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22#4112yes—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4#4112yes—
176C42×C11—42no—
177C42×C11C2×D412yes—
178C42×C11#4112yes—
179(C2×D11)⋊C4—24no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183C4⋊Dic11—24no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—42no—
191Dic11⋊C4—42no—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194C4×Dic11—22no—
195C4×Dic11—22no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—42no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C2×D412yes—
204C2×C11⋊C8C2×D412yes—
205C2×#479—111no—
206C2×#432—111no—
207#2851—111no—
208C4×C22⋊Q8—111no—
209#2077—111no—
210#2076—111no—
211#2036—111no—
212#2035—111no—
213#1989D1111yescharacteristic, complemented
214#1949—111no—
215#1944—111no—
216#1943—111no—
217#1935—111no—
218#1935—111no—
219#1805—111no—
220C23×C11C22×D411yescharacteristic
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—21no—
226C22×D11—21no—
227C22×D11#13712yes—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—22no—
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—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11#12112yes—
245C2×C4×C11#12112yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C4×D11—44no—
274C4×D11—44no—
275C4×D11—41no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—41no—
279Dic22—22no—
280Dic22—22no—
281Dic22—41no—
282Dic22—41no—
283C8×C11—41no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—22no—
287C2×#125C2×D1111yescharacteristic
288C2×C22⋊Q8—111no—
289C2×C4×Q8—111no—
290C22×C42—111no—
291#479—224no—
292#432—224no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106—111no—
296C2×#106—111no—
297C2×C4⋊C8—111no—
298C2×C4⋊C8C2×D1111yescharacteristic
299C2×#103—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×C22⋊C8—111no—
304C2×C22⋊C8—111no—
305C2×#97—111no—
306C2×#97—111no—
307#391—111no—
308#389—111no—
309#389—111no—
310#389—111no—
311#387—221no—
312#387—221no—
313#387—221no—
314#385—221no—
315#385—221no—
316#385—221no—
317#382—111no—
318#380—111no—
319#380—111no—
320#380—111no—
321C4×C4⋊C4—221no—
322C4×C4⋊C4C2×D1111yescharacteristic
323C4×C22⋊C4—221no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340C2×D1111yescharacteristic
329#340C2×D1111yescharacteristic
330#340C2×D1111yescharacteristic
331#340C2×D1111yescharacteristic
332C22×C11C2×#12111yescharacteristic
333C22×C11#52511yescharacteristic
334C22×C11#53611yescharacteristic
335C22×C11C2×#13711yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57511yescharacteristic
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C4×C11—22no—
347C4×C11—22no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11#54711yescharacteristic
353C4×C11#54811yescharacteristic
354C4×C11#55211yescharacteristic
355C4×C11#55611yescharacteristic
356Dic11—42no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371#125—22no—
372#125—22no—
373C22⋊Q8—222no—
374C22⋊Q8—222no—
375C4×Q8—222no—
376C4×Q8—222no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C42—21no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—222no—
400C2×C42—222no—
401C2×C42—221no—
402C2×C42C22×D1111yescharacteristic
403#107—222no—
404#107—222no—
405#106—222no—
406#106—222no—
407C4⋊C8—22no—
408C4⋊C8—114no—
409#103—222no—
410#103—222no—
411#103—222no—
412#103—222no—
413C22⋊C8—222no—
414C22⋊C8—222no—
415#97—222no—
416#97—222no—
417#95—21no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428C2×C11#241511yescharacteristic
429C2×C11#305411yescharacteristic
430C2×C11#305611yescharacteristic
431C2×C11#311111yescharacteristic
432C2×C11#311711yescharacteristic
433C2×C11#323611yescharacteristic
434C2×C11#324011yescharacteristic
435D11—42no—
436C24—111no—
437C2×Q8—112no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×Q8—221no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—222no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4D4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—112no—
476C2×C8—112no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—224no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4—442no—
500C4⋊C4—442no—
501C4⋊C4#434312yes—
502C22⋊C4—224no—
503C22⋊C4—442no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C42—42no—
507C42—222no—
508C42—222no—
509C42—221no—
510C42—221no—
511C42—442no—
512C42#433912yes—
513C42D4×D1112yes—
514C11#2470711yescharacteristic, complemented, Sylow
515C23—112no—
516C23—221no—
517C23—221no—
518C23—221no—
519C23—221no—
520C23—221no—
521C23—221no—
522C23C2×D4×D1111yescharacteristic
523Q8—222no—
524Q8—222no—
525Q8—441no—
526Q8—441no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—222no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—444no—
554C2×C4—444no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
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×C4#6693712yes—
571C2×C4#6693712yes—
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C2×C4C2×#434311yescharacteristic
575C2×C4#6704011yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#6704311yescharacteristic
578C8—41no—
579C8—41no—
580C8—222no—
581C8—222no—
582C22—222no—
583C22—222no—
584C22—222no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22—441no—
589C22C2×#6693711yescharacteristic
590C22#1062315811yescharacteristic
591C22#1062315911yescharacteristic
592C22#1062329911yescharacteristic
593C22#1062329911yescharacteristic
594C22#1062330411yescharacteristic
595C22D11×#13711yescharacteristic
596C4—22no—
597C4—22no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—81no—
602C4—441no—
603C4—442no—
604C4—441no—
605C4—441no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4#1062311211yescharacteristic
610C4#1062311511yescharacteristic
611C4#1062320811yescharacteristic
612C4#1062325711yescharacteristic
613C2—442no—
614C2#1307204811yescharacteristic
615C2#1307822411yescharacteristic
616C2#1307824911yescharacteristic
617C2#1307873011yescharacteristic
618C2#1307879211yescharacteristic
619C2#1307982011yescharacteristic
620C2#1307985511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1989C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1989D11
hypocenterC11#24707
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
9. #13069384C2semidirect
10. #13069358C2semidirect
11. #13069353C2semidirect
12. #13069304C2semidirect
13. #13069304C2semidirect
14. #13068632C2semidirect
15. C11×#1989C2semidirect
213. #1989D11semidirect
514. C11#24707semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C2×#106224482
#130769212
C4×#669502
#130700542
#130700482
#130698222
#130698152
#130693842
#130693582
#130693532
#130693042
#130686322
C11×#19892
#2470711