Finite Group Databasebeta

← #14788089

Subgroups — #14788089

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic, complemented
4C4×#66948C211yesmaximal, characteristic
5#13069811C212yesmaximal, complemented
6#13069618C212yesmaximal
7#13069564C211yesmaximal, characteristic, complemented
8#13068969C212yesmaximal, complemented
9#13068886C212yesmaximal, complemented
10#13068593C211yesmaximal, characteristic, complemented
11C11×#1981C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999C2212yes—
14C2×Q8×Dic11C2212yes—
15C22×#4325C2212yes—
16#10623259—24no—
17#10623259—24no—
18C2×#66950—21no—
19C2×#66948C2211yescharacteristic
20C2×#66945—21no—
21C2×#66943—21no—
22C2×#66940—21no—
23C2×C4×D44—21no—
24C2×C4×D44C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C2×C11×#103C2212yes—
29C2×C11×#103C2212yes—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2212yes—
32C2×#66885C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×#66881C2212yes—
35#10622696—24no—
36#10622601C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622598C2211yescharacteristic
39C4×(C2×D11)⋊C4—21no—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41#10622455—24no—
42#10622283—21no—
43#10622278—21no—
44#10622188C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11C2312yes—
48C22×D44—21no—
49C22×D44C2311yescharacteristic
50C22×C4×D11—21no—
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C22×Dic22—21no—
55C22×C8×C11C2312yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8D414yescomplemented
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64#66999—24no—
65#66999—24no—
66Q8×Dic11—24no—
67Q8×Dic11—24no—
68C2×#4325—24no—
69C2×#4325—24no—
70C2×#4325—42no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2312yes—
82C2×Dic11⋊C4—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88#66950—28no—
89#66948—22no—
90#66948—22no—
91#66945—28no—
92#66943—28no—
93#66940—28no—
94C4×D44—22no—
95C4×D44—22no—
96C4×D44—44no—
97C42×D11—22no—
98C42×D11—22no—
99#66922—22no—
100#66922D414yescomplemented
101C11×C4⋊C8—22no—
102C11×#103—24no—
103C11×#103—42no—
104C11×#95—21no—
105#66899—24no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108#66885—24no—
109(C2×D11)⋊C8—42no—
110#66881—24no—
111C4⋊(C11⋊C8)—22no—
112#24151—111nomaximal, Sylow
113C23×D11—21no—
114C23×D11C2×D411yescharacteristic
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11C2×D414yes—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—22no—
128C22×Dic11—21no—
129C22×Dic11C2×D411yescharacteristic
130C22×Dic11C2×D411yescharacteristic
131C22×Dic11C2×D411yescharacteristic
132C2×D44—24no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—42no—
139C2×D44—42no—
140C2×D44#4112yes—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11SD1614yescomplemented
156C2×Dic22—24no—
157C2×Dic22—42no—
158C2×Dic22—42no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4#4112yes—
168C42×C11—42no—
169C42×C11C2×D412yes—
170C42×C11C2×D412yes—
171#4325—48no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178C4⋊Dic11—28no—
179C4⋊Dic11—24no—
180C4⋊Dic11—22no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—42no—
184C4⋊Dic11C2×D414yes—
185Dic11⋊C4—28no—
186C4×Dic11—28no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×#533—111no—
195C2×#476—111no—
196C2×#461—111no—
197C4×#121—111no—
198#2035—112no—
199#2000—112no—
200#1987—111no—
201#1981D1111yescharacteristic, complemented
202#1880—112no—
203#1865—112no—
204#1797—111no—
205C23×C11C22×D411yescharacteristic
206C22×D11—21no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11C2×SD1612yes—
220Q8×C11—24no—
221Q8×C11—24no—
222Q8×C11—42no—
223Q8×C11—42no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11#12012yes—
236C2×C4×C11#12012yes—
237C2×C4×C11C2×SD1612yes—
238C2×C4×C11#13712yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—24no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11C2×SD1612yes—
260D44—22no—
261D44—22no—
262D44—48no—
263D44—41no—
264D44—41no—
265C4×D11—28no—
266C4×D11—44no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—84no—
272Dic22—48no—
273C8×C11—42no—
274C11⋊C8—42no—
275C22×SD16—112no—
276#533—224no—
277#533—224no—
278C2×C4⋊Q8—111no—
279C2×C4⋊Q8C2×D1111yescharacteristic
280C2×#125—221no—
281C2×C22⋊Q8—112no—
282C2×C22⋊Q8—221no—
283C2×#121—111no—
284C2×C4×Q8—112no—
285C2×C4×Q8—221no—
286C2×C4×D4—111no—
287C2×C4×D4—221no—
288C2×#117—221no—
289C22×C42—111no—
290#476—224no—
291#461—224no—
292C2×#106—112no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8C2×D1111yescharacteristic
295C2×#103—112no—
296C2×#103C2×D1112yes—
297C2×#103C2×D1112yes—
298C2×#102—112no—
299C2×C22⋊C8—112no—
300#390—111no—
301#389—111no—
302#388—221no—
303#386—221no—
304#380—111no—
305C4×C4⋊C4C2×D1111yescharacteristic
306C4×C22⋊C4—221no—
307#340—112no—
308#340—112no—
309#336—112no—
310C22×C11C2×#12011yescharacteristic
311C22×C11#52511yescharacteristic
312C22×C11#53711yescharacteristic
313C22×C11C22×SD1611yescharacteristic
314C22×C11C2×#13711yescharacteristic
315C22×C11#57511yescharacteristic
316C22×C11#57511yescharacteristic
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—41no—
321C2×D11—41no—
322C2×D11—41no—
323C2×D11—41no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C4×C11—22no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11—81no—
335C4×C11#44814yes—
336C4×C11#54611yescharacteristic
337C4×C11#54711yescharacteristic
338C4×C11#54811yescharacteristic
339C4×C11#55011yescharacteristic
340Dic11—22no—
341Dic11—41no—
342Dic11—44no—
343Dic11—41no—
344Dic11—81no—
345C22×Q8—221no—
346C22×Q8C22×D1112yes—
347C22×D4—111no—
348C22×D4—221no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—221no—
353C2×SD16—224no—
354C2×SD16—224no—
355C2×SD16—442no—
356C22×C8—112no—
357C22×C8C22×D1112yes—
358C4⋊Q8—22no—
359C4⋊Q8—114no—
360C4⋊Q8—222no—
361C4⋊Q8D4414yescomplemented
362#125—228no—
363C22⋊Q8—228no—
364C22⋊Q8—224no—
365C22⋊Q8—224no—
366#121—222no—
367#121—222no—
368C4×Q8—228no—
369C4×Q8—224no—
370C4×Q8—224no—
371C4×D4—222no—
372C4×D4—222no—
373C4×D4—444no—
374#117—228no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—221no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—21no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—222no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42C22×D1111yescharacteristic
399#106—224no—
400C4⋊C8—22no—
401C4⋊C8—222no—
402#103—24no—
403#103—42no—
404#103—224no—
405#102—224no—
406C22⋊C8—442no—
407#95—21no—
408#95—221no—
409#95—221no—
410C2×C11#240711yescharacteristic
411C2×C11C2×#44811yescharacteristic
412C2×C11#300511yescharacteristic
413C2×C11#310111yescharacteristic
414C2×C11#311611yescharacteristic
415C2×C11#324611yescharacteristic
416C2×C11#325211yescharacteristic
417D11—42no—
418D11—82no—
419C24—111no—
420C24—221no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—224no—
427C2×Q8—442no—
428C2×Q8—442no—
429C2×Q8C2×D4414yes—
430C2×D4—112no—
431C2×D4—224no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—442no—
438C2×D4—442no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—111no—
443C22×C4—114no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4D4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465SD16—448no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—222no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—114no—
478C4⋊C4—228no—
479C4⋊C4—228no—
480C4⋊C4—224no—
481C4⋊C4—222no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4#434112yes—
486C22⋊C4—228no—
487C22⋊C4—224no—
488C22⋊C4—442no—
489C22⋊C4—442no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C42—42no—
493C42—228no—
494C42—222no—
495C42—222no—
496C42—221no—
497C42—221no—
498C42C2×D4412yes—
499C42D4×D1112yes—
500C11#2415111yescharacteristic, complemented, Sylow
501C23—112no—
502C23—221no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23—221no—
507C23—221no—
508C23—222no—
509C23—441no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23—441no—
514C23—441no—
515C23C2×D4×D1111yescharacteristic
516Q8—24no—
517Q8—24no—
518Q8—42no—
519Q8—42no—
520Q8—448no—
521D4—222no—
522D4—222no—
523D4—448no—
524D4—441no—
525D4—441no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—112no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—228no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—224no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—444no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—884no—
559C2×C4#6693512yes—
560C2×C4#6693512yes—
561C2×C4SD16×D1112yes—
562C2×C4#6697112yes—
563C2×C4C22×D4411yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C2×C4#6703711yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C2×C4#6704311yescharacteristic
569C8—42no—
570C8—442no—
571C22—222no—
572C22—222no—
573C22—222no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22—441no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22C2×#6693511yescharacteristic
586C22#1062313711yescharacteristic
587C22#1062313911yescharacteristic
588C22C2×SD16×D1111yescharacteristic
589C22C2×#6697111yescharacteristic
590C22#1062330811yescharacteristic
591C22#1062330811yescharacteristic
592C4—22no—
593C4—44no—
594C4—42no—
595C4—81no—
596C4—222no—
597C4—441no—
598C4—441no—
599C4—444no—
600C4—881no—
601C4#1062241914yes—
602C4#1062308511yescharacteristic
603C4#1062308611yescharacteristic
604C4#1062320811yescharacteristic
605C4#1062324911yescharacteristic
606C2—442no—
607C2—882no—
608C2#1307195911yescharacteristic
609C2C2×#1062241911yescharacteristic
610C2#1307786211yescharacteristic
611C2#1307862311yescharacteristic
612C2#1307877711yescharacteristic
613C2#1307992911yescharacteristic
614C2#1307998711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1981D11
hypocenterC11#24151
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
2. C2×#10622455C2semidirect
3. C2×#10622696C2semidirect
5. #13069811C2semidirect
7. #13069564C2semidirect
8. #13068969C2semidirect
9. #13068886C2semidirect
10. #13068593C2semidirect
11. C11×#1981C2semidirect
57. C11×C4⋊Q8D4semidirect
100. #66922D4semidirect
155. C2×C4×D11SD16semidirect
201. #1981D11semidirect
361. C4⋊Q8D44semidirect
500. C11#24151semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106224552
C2×#106226962
C4×#669482
#130698112
#130696182
#130695642
#130689692
#130688862
#130685932
C11×#19812
#2415111