Finite Group Databasebeta

← #14756924

Subgroups — #14756924

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622401C211yesmaximal, characteristic
2#13071255C211yesmaximal, characteristic
3#13070981C211yesmaximal, characteristic, complemented
4#13069244C211yesmaximal, characteristic
5#13069242C211yesmaximal, characteristic
6#13069204C211yesmaximal, characteristic, complemented
7#13069198C211yesmaximal, characteristic, complemented
8#13068971C211yesmaximal, characteristic
9#13068969C211yesmaximal, characteristic
10#13068886C211yesmaximal, characteristic, complemented
11#106×Dic11C211yesmaximal, characteristic, complemented
12#13068448C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622603—21no—
32#10622601C2211yescharacteristic
33#10622600—21no—
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11—21no—
36C4⋊C4×Dic11—21no—
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42#10622552C2211yescharacteristic
43C4×C4⋊Dic11—21no—
44C4×C4⋊Dic11C2211yescharacteristic
45#10622545—21no—
46#10622545C2211yescharacteristic
47#10622401C418yescomplemented
48#10622283—21no—
49#10622277—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74Q8×Dic11—22no—
75Q8×Dic11—22no—
76Q8×Dic11—22no—
77Q8×Dic11C2×C414yes—
78C2×#4325—22no—
79C2×#4325—22no—
80C2×#4325C2×C414yes—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102#66946—22no—
103#66946C2×C414yes—
104C11×#106—22no—
105C11×#103—22no—
106C11×#103C2×C414yes—
107C11×#95—21no—
108#66899—22no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66885—22no—
119#66885C2×C414yes—
120#66881—22no—
121#66879—22no—
122C8×Dic11C2×C414yes—
123#66873—22no—
124#66872C2×C414yes—
125#21131—111nomaximal, Sylow
126C23×D11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11C22×C412yes—
131C2×Q8×C11#4112yes—
132C2×Q8×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44C22×C412yes—
153C2×C4×D11—24no—
154C2×C4×D11—81no—
155C2×C4×D11—81no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C22×C412yes—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4C22×C412yes—
169C11×C4⋊C4#4112yes—
170C42×C11—24no—
171C42×C11—21no—
172C42×C11—21no—
173#4325—28no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—81no—
176(C2×D11)⋊C4—81no—
177(C2×D11)⋊C4—81no—
178(C2×D11)⋊C4—81no—
179C4⋊Dic11—24no—
180C4⋊Dic11—24no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—81no—
186C4⋊Dic11C22×C412yes—
187C4⋊Dic11#4112yes—
188C4×Dic11—24no—
189C4×Dic11—24no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—81no—
193C4×Dic11—81no—
194C4×Dic11—81no—
195C4×Dic11—81no—
196C4×Dic11C22×C412yes—
197C4×Dic11#4112yes—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8C22×C412yes—
204C2×C4×SD16—111no—
205#2319—111no—
206#2276—111no—
207#1926—111no—
208#1926—111no—
209#1920—111no—
210#1920—111no—
211#1880—111no—
212#1880—111no—
213#1865—111no—
214#1865D1111yescharacteristic, complemented
215C4×#106—111no—
216#1763—111no—
217#1762—111no—
218#1746—111no—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11#11714yes—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11C4×D412yes—
275C2×Dic11C4×D412yes—
276D44—22no—
277D44—22no—
278D44—41no—
279D44—41no—
280C4×D11—84no—
281C8×C11—22no—
282C8×C11—41no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C22×SD16—111no—
286C2×C4×Q8—111no—
287C2×C4×Q8—111no—
288C2×C4×Q8C2×D1111yescharacteristic
289C2×C4×D4—111no—
290C4×SD16—118no—
291C2×#106—111no—
292C2×#106—111no—
293C2×#106C2×D1111yescharacteristic
294C2×#103—111no—
295C2×#103C2×D1111yescharacteristic
296C2×#103C2×D1111yescharacteristic
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#97—111no—
301C2×C4×C8—111no—
302#390—111no—
303#390—111no—
304#389—111no—
305#389C2×D1111yescharacteristic
306#388—221no—
307#388—221no—
308#381—221no—
309#380—221no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—221no—
315C4×C4⋊C4—221no—
316C4×C4⋊C4—221no—
317#376—111no—
318#376—221no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340C2×D1111yescharacteristic
325#336—111no—
326#336—111no—
327#336—111no—
328#336C2×D1111yescharacteristic
329C22×C11C2×C4×D411yescharacteristic
330C22×C11#52511yescharacteristic
331C22×C11#52511yescharacteristic
332C22×C11#57711yescharacteristic
333C22×C11#57711yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57711yescharacteristic
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C4×C11—24no—
344C4×C11—41no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—42no—
348C4×C11—81no—
349C4×C11C2×#11711yescharacteristic
350C4×C11C4×#4111yescharacteristic
351C4×C11#52911yescharacteristic
352C4×C11#52911yescharacteristic
353Dic11—22no—
354Dic11—22no—
355Dic11—41no—
356Dic11—42no—
357Dic11—41no—
358Dic11—42no—
359Dic11—81no—
360C22×Q8C22×D1111yescharacteristic
361C22×D4—111no—
362C23×C4—221no—
363C2×SD16—114no—
364C2×SD16—222no—
365C2×SD16—222no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8C22×D1111yescharacteristic
369C22×C8C22×D1111yescharacteristic
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—114no—
373C4×Q8—222no—
374C4×Q8—222no—
375C4×Q8—222no—
376C4×D4—114no—
377C4×D4—222no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—21no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42C22×D1111yescharacteristic
404#106—22no—
405#106—114no—
406#106—222no—
407#103—22no—
408#103—222no—
409#103C4×D1114yes—
410#102—114no—
411#102—222no—
412#102—222no—
413#97—222no—
414C4×C8—114no—
415#95—21no—
416#95—111no—
417#95—111no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11#229011yescharacteristic
426C2×C11#294911yescharacteristic
427C2×C11#295211yescharacteristic
428C2×C11#312511yescharacteristic
429C2×C11#312511yescharacteristic
430C2×C11#312611yescharacteristic
431C2×C11#312611yescharacteristic
432D11—82no—
433C24—221no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×C4×D1112yes—
438C2×Q8#434112yes—
439C2×Q8#434312yes—
440C2×D4—112no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—224no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—881no—
459C22×C4—881no—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463SD16—228no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—112no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8C2×C4×D1112yes—
476C4⋊C4—24no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—81no—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—881no—
491C4⋊C4C2×C4×D1112yes—
492C4⋊C4#434112yes—
493C22⋊C4—224no—
494C22⋊C4—881no—
495C22⋊C4—881no—
496C22⋊C4—881no—
497C22⋊C4—881no—
498C42—24no—
499C42—21no—
500C42—21no—
501C42—112no—
502C42—112no—
503C42—224no—
504C42—224no—
505C42—221no—
506C42—221no—
507C42—881no—
508C42—881no—
509C42—881no—
510C42—881no—
511C11#2113111yescharacteristic, complemented, Sylow
512C23—222no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23C2×D4×D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8#6694514yes—
524D4—222no—
525D4—222no—
526D4—441no—
527D4—441no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—222no—
557C2×C4—221no—
558C2×C4—222no—
559C2×C4—221no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—884no—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×#434111yescharacteristic
570C2×C4C2×#434111yescharacteristic
571C2×C4C2×#434311yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C8—22no—
575C8—41no—
576C8—222no—
577C8—441no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22C4×D4×D1111yescharacteristic
586C22#1062311711yescharacteristic
587C22#1062315811yescharacteristic
588C22#1062329311yescharacteristic
589C22#1062330111yescharacteristic
590C22#1062330911yescharacteristic
591C22#1062330911yescharacteristic
592C4—24no—
593C4—41no—
594C4—42no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—222no—
599C4—222no—
600C4—441no—
601C4—442no—
602C4—441no—
603C4—442no—
604C4—881no—
605C4C2×#6694511yescharacteristic
606C4C4×#434111yescharacteristic
607C4#1062315511yescharacteristic
608C4#1062318011yescharacteristic
609C2—882no—
610C2#1307105211yescharacteristic
611C2#1307747011yescharacteristic
612C2#1307749611yescharacteristic
613C2#1307888611yescharacteristic
614C2#1307890011yescharacteristic
615C2#1307890111yescharacteristic
616C2#1307890911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1865D11
hypocenterC11#21131
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
3. #13070981C2semidirect
6. #13069204C2semidirect
7. #13069198C2semidirect
10. #13068886C2semidirect
11. #106×Dic11C2semidirect
12. #13068448C2semidirect
14. #13068366C2semidirect
15. C11×#1865C2semidirect
47. #10622401C4semidirect
214. #1865D11semidirect
511. C11#21131semidirect

Maximal subgroups

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

subgroupindex
C2×#106224012
#130712552
#130709812
#130692442
#130692422
#130692042
#130691982
#130689712
#130689692
#130688862
#106×Dic112
#130684482
#130684402
#130683662
C11×#18652
#2113111