Finite Group Databasebeta

← #14756913

Subgroups — #14756913

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×#10622371C211yesmaximal, characteristic
2#13071263C211yesmaximal, characteristic, complemented
3#13070977C211yesmaximal, characteristic
4#13069258C211yesmaximal, characteristic, complemented
5#13069256C211yesmaximal, characteristic, complemented
6#13069204C211yesmaximal, characteristic, complemented
7#13069198C211yesmaximal, characteristic, complemented
8#13068950C211yesmaximal, characteristic
9#13068948C211yesmaximal, characteristic
10#13068865C211yesmaximal, characteristic
11#107×Dic11C211yesmaximal, characteristic, complemented
12#13068445C211yesmaximal, characteristic, complemented
13#13068443C211yesmaximal, characteristic
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C4×C22⋊Dic11—21no—
27C2×C11⋊#95—21no—
28C2×#66882C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622591—21no—
35#10622590—21no—
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622587C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C22⋊C4×Dic11—21no—
43C22⋊C4×Dic11—21no—
44C4×C4⋊Dic11C2211yescharacteristic
45#10622545C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622371C418yescomplemented
48#10622268—21no—
49#10622264—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77D4×Dic11—22no—
78D4×Dic11—22no—
79D4×Dic11—22no—
80D4×Dic11C2×C414yes—
81C2×#4324—22no—
82C2×#4324—22no—
83C2×#4324C2×C414yes—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66940—22no—
99#66940C2×C414yescomplemented
100C11×#107—22no—
101C11×#102—22no—
102C11×#102C2×C414yes—
103C11×#95—21no—
104#66896—22no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117C11⋊#95D411yescharacteristic
118#66882—22no—
119#66880—22no—
120#66880C2×C414yescomplemented
121#66879—22no—
122C8×Dic11C2×C414yescomplemented
123#66874—22no—
124#66872C2×C414yescomplemented
125#21130—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—24no—
136C22×C4×C11—21no—
137C22×C4×C11—81no—
138C22×C4×C11—81no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—81no—
149C22×Dic11—81no—
150C22×Dic11—81no—
151C22×Dic11—81no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22×C412yes—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C22×C412yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4C22×C412yes—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—24no—
176C42×C11—21no—
177C42×C11—21no—
178C22⋊Dic11—24no—
179C22⋊Dic11—24no—
180#4324—28no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—81no—
186C4⋊Dic11C22×C412yes—
187C4⋊Dic11#4112yes—
188Dic11⋊C4—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#2320—111no—
206#2275—111no—
207#1928—111no—
208#1928—111no—
209#1920—111no—
210#1920—111no—
211#1877—111no—
212#1877—111no—
213#1862—111no—
214#1862D1111yescharacteristic
215C4×#107—111no—
216#1763—111no—
217#1762—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—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—84no—
247C2×C4×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—84no—
276C2×Dic11—84no—
277C2×Dic11C4×D412yes—
278C2×Dic11C4×D412yes—
279Dic22—22no—
280Dic22—22no—
281Dic22—41no—
282Dic22—41no—
283C8×C11—22no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C22×SD16—111no—
288C2×C4×Q8—111no—
289C2×C4×D4—111no—
290C2×C4×D4—111no—
291C2×C4×D4C2×D1111yescharacteristic
292C4×SD16—118no—
293C2×#107—111no—
294C2×#107C2×D1111yescharacteristic
295C2×#106—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#102—111no—
300C2×#102C2×D1111yescharacteristic
301C2×#102C2×D1111yescharacteristic
302C2×#97—111no—
303C2×C4×C8—111no—
304#391—111no—
305#391—111no—
306#389—111no—
307#389C2×D1111yescharacteristic
308#387—221no—
309#387—221no—
310#383—221no—
311#382—221no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C22⋊C4—221no—
317C4×C22⋊C4—221no—
318C4×C22⋊C4—221no—
319#376—111no—
320C2×#95—221no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340C2×D1111yescharacteristic
327#336—111no—
328#336—111no—
329#336—111no—
330#336C2×D1111yescharacteristic
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—41no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—81no—
350C4×C11C2×#11711yescharacteristic
351C4×C11C4×#4111yescharacteristic
352C4×C11#52911yescharacteristic
353C4×C11#52911yescharacteristic
354Dic11—22no—
355Dic11—22no—
356Dic11—41no—
357Dic11—42no—
358Dic11—41no—
359Dic11—42no—
360Dic11—42no—
361Dic11—81no—
362C22×Q8—111no—
363C22×D4C22×D1111yescharacteristic
364C23×C4—21no—
365C23×C4—221no—
366C23×C4—221no—
367C2×SD16—114no—
368C2×SD16—222no—
369C2×SD16—222no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C4×Q8—114no—
375C4×Q8—222no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—114no—
379C4×D4—222no—
380C4×D4—222no—
381C4×D4—222no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
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—221no—
393C2×C22⋊C4—221no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—22no—
403#107—222no—
404#106—114no—
405#103—114no—
406#103—222no—
407#103—222no—
408#102—22no—
409#102—222no—
410#102C4×D1114yes—
411#97—222no—
412C4×C8—114no—
413#95—21no—
414#95—111no—
415#95—111no—
416#95—111no—
417#95—111no—
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—
427C2×C11—44no—
428C2×C11#229011yescharacteristic
429C2×C11#294911yescharacteristic
430C2×C11#295111yescharacteristic
431C2×C11#311811yescharacteristic
432C2×C11#311811yescharacteristic
433C2×C11#312011yescharacteristic
434C2×C11#312011yescharacteristic
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#434112yes—
447C2×D4#434312yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—224no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—224no—
463C22×C4—221no—
464C22×C4—881no—
465C22×C4—881no—
466C22×C4—881no—
467C22×C4—881no—
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471SD16—228no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—112no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8C2×C4×D1112yes—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—81no—
489C4⋊C4—112no—
490C4⋊C4—112no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—881no—
497C4⋊C4C2×C4×D1112yes—
498C4⋊C4#434112yes—
499C22⋊C4—24no—
500C22⋊C4—224no—
501C22⋊C4—224no—
502C42—21no—
503C42—21no—
504C42—112no—
505C42—112no—
506C42—224no—
507C42—221no—
508C42—221no—
509C42—881no—
510C42—881no—
511C42—881no—
512C42—881no—
513C11#2113011yescharacteristic, complemented, Sylow
514C23—22no—
515C23—22no—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C2×D4×D1111yescharacteristic
522Q8—222no—
523Q8—222no—
524Q8—441no—
525Q8—441no—
526D4—22no—
527D4—22no—
528D4—22no—
529D4#6694514yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
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—222no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—222no—
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—884no—
571C2×C4—884no—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×#434111yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4C2×#434311yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C8—22no—
579C8—41no—
580C8—222no—
581C8—441no—
582C22—24no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—42no—
589C22C4×D4×D1111yescharacteristic
590C22#1062311711yescharacteristic
591C22#1062315811yescharacteristic
592C22#1062328811yescharacteristic
593C22#1062330211yescharacteristic
594C22#1062330611yescharacteristic
595C22#1062330911yescharacteristic
596C4—41no—
597C4—42no—
598C4—41no—
599C4—42no—
600C4—81no—
601C4—222no—
602C4—222no—
603C4—441no—
604C4—442no—
605C4—441no—
606C4—442no—
607C4—442no—
608C4—881no—
609C4C2×#6694511yescharacteristic
610C4C4×#434111yescharacteristic
611C4#1062315511yescharacteristic
612C4#1062318011yescharacteristic
613C2—44no—
614C2#1307105211yescharacteristic
615C2#1307747211yescharacteristic
616C2#1307748611yescharacteristic
617C2#1307879311yescharacteristic
618C2#1307880711yescharacteristic
619C2#1307883111yescharacteristic
620C2#1307883511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1862D11
hypocenterC11#21130
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #13071263C2semidirect
4. #13069258C2semidirect
5. #13069256C2semidirect
6. #13069204C2semidirect
7. #13069198C2semidirect
11. #107×Dic11C2semidirect
12. #13068445C2semidirect
14. #13068366C2semidirect
47. #10622371C4semidirect
99. #66940C2×C4semidirect
120. #66880C2×C4semidirect
122. C8×Dic11C2×C4semidirect
124. #66872C2×C4semidirect
513. C11#21130semidirect

Maximal subgroups

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

subgroupindex
C2×#106223712
#130712632
#130709772
#130692582
#130692562
#130692042
#130691982
#130689502
#130689482
#130688652
#107×Dic112
#130684452
#130684432
#130683662
C11×#18622
#2113011