Finite Group Databasebeta

← #14804508

Subgroups — #14804508

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622661C212yesmaximal, complemented
2C2×#10622696C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
4#13073529C211yesmaximal, characteristic
5#13069809C212yesmaximal, complemented
6#13069617C212yesmaximal, complemented
7#13069419C211yesmaximal, characteristic, complemented
8#13069379C211yesmaximal, characteristic, complemented
9#13069040C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#2542C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×C22⋊Q8C2212yes—
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4325C2212yes—
17C2×#66991—21no—
18C2×#66983C2212yes—
19C23×C11⋊C8C2212yes—
20C2×C4×D44C2211yescharacteristic
21C11×#399—22no—
22C11×#390—21no—
23C11×#384—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66899C2212yes—
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622696—24no—
31#10622661—28no—
32D4×C11⋊C8—24no—
33#10622600—21no—
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66872C2212yes—
37#10622574—22no—
38#10622548C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—22no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—42no—
55C11×C22⋊Q8—42no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D412yes—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—22no—
71C2×#4325—24no—
72C2×#4325—24no—
73C2×#4325—42no—
74#66991—44no—
75#66983—24no—
76#66983—42no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2312yes—
83C22×C11⋊C8—24no—
84C22×C11⋊C8—24no—
85C22×C11⋊C8—42no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C4×D44—22no—
90C4×D44—22no—
91C11×#95—21no—
92#66899—24no—
93#66899—24no—
94#66899—42no—
95C11⋊#95—22no—
96C22⋊(C11⋊C8)—24no—
97#66873—22no—
98#66873D414yescomplemented
99#66872—24no—
100C4⋊(C11⋊C8)D414yescomplemented
101C4×C11⋊C8—22no—
102#25385—111nomaximal, Sylow
103C24×C11C2×D412yes—
104C23×D11—21no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11SD1614yescomplemented
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—44no—
128C2×C22⋊D11—44no—
129C2×C22⋊D11—82no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44C2×D412yes—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—44no—
145C11×C4⋊C4—44no—
146C11×C4⋊C4—42no—
147C11×C4⋊C4—42no—
148C11×C4⋊C4C2×D412yes—
149C11×C4⋊C4#4112yes—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—44no—
152C11×C22⋊C4—44no—
153C42×C11—42no—
154C42×C11C2×D412yes—
155C42×C11#4112yes—
156C22⋊Dic11—44no—
157#4325—48no—
158(C2×D11)⋊C4—44no—
159(C2×D11)⋊C4—42no—
160C4⋊Dic11—22no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—22no—
164C4⋊Dic11—42no—
165C4⋊Dic11—81no—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—21no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—48no—
174C2×C11⋊C8C2×D414yes—
175C2×C11⋊C8C2×D412yes—
176C2×#465—112no—
177C2×#461—111no—
178C2×C8×D4—111no—
179#2542D1111yescharacteristic, complemented
180#2537—111no—
181#2035—112no—
182#2000—112no—
183#1956—111no—
184#1948—111no—
185#1892—112no—
186C4×#102—111no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11C2×SD1614yes—
194C23×C11C22×D411yescharacteristic
195C22×D11—22no—
196C22×D11—41no—
197C22×D11—41no—
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202Q8×C11—42no—
203Q8×C11—42no—
204Q8×C11—42no—
205Q8×C11—42no—
206D4×C11—28no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11#12112yes—
226C2×C4×C11#12112yes—
227C2×C4×C11C2×SD1612yes—
228C2×C4×C11#13512yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C22⋊D11—88no—
236C2×Dic11—41no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—42no—
242D44—22no—
243D44—22no—
244D44—41no—
245D44—41no—
246C4×D11—84no—
247C11⋊C8—22no—
248C11⋊C8—24no—
249C11⋊C8—41no—
250C22×SD16—112no—
251C23×C8—112no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×C22⋊Q8C2×D1112yes—
254C2×C22⋊Q8C2×D1112yes—
255C2×#121—112no—
256C2×#121—221no—
257C2×C4×D4—111no—
258C2×C4×D4C2×D1111yescharacteristic
259#465—228no—
260#461—224no—
261C8×D4—224no—
262C2×#106—112no—
263C2×C4⋊C8—111no—
264C2×#103—112no—
265C2×#103—112no—
266C2×#103—112no—
267C2×#102—111no—
268C2×#102—111no—
269C2×C22⋊C8—112no—
270C2×C4×C8—111no—
271#399—22no—
272#394—222no—
273#390—21no—
274#384—21no—
275#384—111no—
276#380—112no—
277#380—221no—
278C4×C4⋊C4C2×D1111yescharacteristic
279#340—111no—
280#340—112no—
281#340—111no—
282C22×C11—24no—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11C2×#12111yescharacteristic
290C22×C11D4211yescharacteristic
291C22×C11#54611yescharacteristic
292C22×C11C22×SD1611yescharacteristic
293C22×C11C2×#13511yescharacteristic
294C22×C11#57711yescharacteristic
295C22×C11#57811yescharacteristic
296C2×D11—42no—
297C2×D11—42no—
298C2×D11—42no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C2×D11—81no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—82no—
308C4×C11#46514yescomplemented
309C4×C11#53211yescharacteristic
310C4×C11#54011yescharacteristic
311C4×C11D4211yescharacteristic
312C4×C11#55011yescharacteristic
313Dic11—82no—
314Dic11—81no—
315C22×Q8C22×D1112yes—
316C22×D4—111no—
317C22×D4—222no—
318C22×D4C22⋊D1111yescharacteristic
319C23×C4—221no—
320C23×C4C22×D1112yes—
321C2×SD16—224no—
322C2×SD16—224no—
323C2×SD16—442no—
324C22×C8—111no—
325C22×C8—112no—
326C22×C8—111no—
327C22×C8—224no—
328C22×C8—224no—
329C22×C8—442no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—42no—
335C22⋊Q8—42no—
336#121—224no—
337#121—442no—
338#121—444no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4—222no—
342C4×D4—222no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22⋊D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C4⋊C4C22×D1111yescharacteristic
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—222no—
357C2×C22⋊C4—221no—
358C2×C22⋊C4—222no—
359C2×C22⋊C4C22⋊D1112yes—
360C2×C42—21no—
361C2×C42C22×D1111yescharacteristic
362#106—224no—
363C4⋊C8—114no—
364#103—224no—
365#103—224no—
366#103—442no—
367#102—114no—
368#102—222no—
369C22⋊C8—224no—
370C4×C8—222no—
371#95—21no—
372#95—222no—
373C2×C11—44no—
374C2×C11#242811yescharacteristic
375C2×C11C2×#46511yescharacteristic
376C2×C11#306311yescharacteristic
377C2×C11D4×SD1611yescharacteristic
378C2×C11#328311yescharacteristic
379C2×C11#329811yescharacteristic
380C2×C11#330311yescharacteristic
381D11—82no—
382C24—221no—
383C24C2×C22⋊D1112yes—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—112no—
393C2×D4—221no—
394C2×D4—221no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—444no—
399C2×D4—444no—
400C2×D4—882no—
401C2×D4#432514yescomplemented
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—221no—
412C22×C4—222no—
413C22×C4—442no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4C2×C22⋊D1112yes—
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420SD16—448no—
421C2×C8—114no—
422C2×C8—112no—
423C2×C8—221no—
424C2×C8—222no—
425C2×C8—221no—
426C2×C8—222no—
427C2×C8—221no—
428C2×C8—221no—
429C2×C8—221no—
430C2×C8—448no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—44no—
435C4⋊C4—44no—
436C4⋊C4—42no—
437C4⋊C4—42no—
438C4⋊C4—221no—
439C4⋊C4—222no—
440C4⋊C4—221no—
441C4⋊C4—222no—
442C4⋊C4—442no—
443C4⋊C4—881no—
444C4⋊C4D4×D1112yes—
445C4⋊C4#434112yes—
446C22⋊C4—24no—
447C22⋊C4—44no—
448C22⋊C4—44no—
449C22⋊C4—444no—
450C22⋊C4—444no—
451C22⋊C4—442no—
452C42—42no—
453C42D4×D1112yes—
454C42#434112yes—
455C11#2538511yescharacteristic, complemented, Sylow
456C23—22no—
457C23—22no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—22no—
462C23—222no—
463C23—441no—
464C23—441no—
465C23—441no—
466C23—441no—
467C23—441no—
468C23—441no—
469C23C2×#432514yes—
470C23C22×C22⋊D1111yescharacteristic
471Q8—42no—
472Q8—42no—
473Q8—42no—
474Q8—42no—
475D4—28no—
476D4—222no—
477D4—222no—
478D4—441no—
479D4—441no—
480D4—888no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—442no—
500C2×C4—441no—
501C2×C4—441no—
502C2×C4—442no—
503C2×C4—441no—
504C2×C4—442no—
505C2×C4—884no—
506C2×C4#6699212yes—
507C2×C4#6699212yes—
508C2×C4C2×#432512yes—
509C2×C4#6700312yes—
510C2×C4C2×D4×D1111yescharacteristic
511C2×C4C2×D4×D1111yescharacteristic
512C2×C4C2×#434111yescharacteristic
513C2×C4C2×#434111yescharacteristic
514C2×C4#6703711yescharacteristic
515C2×C4#6703711yescharacteristic
516C8—222no—
517C8—224no—
518C8—441no—
519C22—24no—
520C22—24no—
521C22—24no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—442no—
527C22—442no—
528C22—442no—
529C22—881no—
530C22—881no—
531C22—881no—
532C22—881no—
533C22D4×C22⋊D1111yescharacteristic
534C22C2×#6699211yescharacteristic
535C22#1062333711yescharacteristic
536C22C22×#432511yescharacteristic
537C22C2×#6700311yescharacteristic
538C22#1062336811yescharacteristic
539C22#1062336911yescharacteristic
540C4—22no—
541C4—42no—
542C4—42no—
543C4—42no—
544C4—82no—
545C4—881no—
546C4—882no—
547C4#1062266114yescomplemented
548C4#1062324711yescharacteristic
549C4#1062324811yescharacteristic
550C4#1062324911yescharacteristic
551C4#1062325011yescharacteristic
552C2—44no—
553C2—882no—
554C2#1307220711yescharacteristic
555C2C2×#1062266111yescharacteristic
556C2#1307830311yescharacteristic
557C2D4×#432511yescharacteristic
558C2#1308033411yescharacteristic
559C2#1308048111yescharacteristic
560C2#1308054411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2542C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenter#2542D11
hypocenterC11#25385
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#10622661C2semidirect
2. C2×#10622696C2semidirect
3. C2×D4×C11⋊C8C2semidirect
5. #13069809C2semidirect
6. #13069617C2semidirect
7. #13069419C2semidirect
8. #13069379C2semidirect
9. #13069040C2semidirect
10. C4×#66873C2semidirect
11. C11×#2542C2semidirect
98. #66873D4semidirect
100. C4⋊(C11⋊C8)D4semidirect
113. C2×D4×C11SD16semidirect
179. #2542D11semidirect
308. C4×C11#465semidirect
401. C2×D4#4325semidirect
455. C11#25385semidirect
547. C4#10622661semidirect

Maximal subgroups

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

subgroupindex
C2×#106226612
C2×#106226962
C2×D4×C11⋊C82
#130735292
#130698092
#130696172
#130694192
#130693792
#130690402
C4×#668732
C11×#25422
#2538511