Finite Group Databasebeta

← #14804529

Subgroups — #14804529

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622661C212yesmaximal, complemented
2C2×#10622640C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
4#13073562C211yesmaximal, characteristic
5#13069805C212yesmaximal, complemented
6#13069617C212yesmaximal, complemented
7#13069421C211yesmaximal, characteristic, complemented
8#13069377C211yesmaximal, characteristic, complemented
9#13069042C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic, complemented
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4325C2212yes—
16C2×#66993—21no—
17C2×#66983C2212yes—
18C2×#66983C2212yes—
19C23×C11⋊C8C2212yes—
20C2×#66927C2211yescharacteristic
21C11×#396—22no—
22C11×#390—21no—
23C11×#389—21no—
24C11×#384C2211yescharacteristic
25C11×#380C2212yes—
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622661—28no—
30#10622640—24no—
31D4×C11⋊C8—24no—
32#10622601—21no—
33C2×#66873C2212yes—
34C2×#66873C2212yes—
35C2×#66873C2212yes—
36C2×#66872C2212yes—
37#10622573—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2311yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11C2312yes—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44C2312yes—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—42no—
54C4×Q8×C11—22no—
55C4×Q8×C11—22no—
56C4×D4×C11—22no—
57C4×D4×C11—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C4⋊C4C2312yes—
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×#4325—24no—
71C2×#4325—24no—
72C2×#4325—42no—
73#66993—44no—
74#66983—24no—
75#66983—24no—
76#66983—42no—
77#66983—42no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4×Dic11—21no—
83C22×C11⋊C8—24no—
84C22×C11⋊C8—24no—
85C22×C11⋊C8—42no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89#66927—22no—
90#66927—22no—
91C11×#95—22no—
92#66899—22no—
93#66899D414yescomplemented
94C11⋊#95—21no—
95C22⋊(C11⋊C8)—24no—
96#66873—24no—
97#66873—24no—
98#66873—42no—
99#66872—24no—
100C4⋊(C11⋊C8)D414yescomplemented
101C4×C11⋊C8—22no—
102#25387—111nomaximal, Sylow
103C24×C11C2×D412yes—
104C23×D11—22no—
105C2×Q8×C11—21no—
106C2×Q8×C11—21no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11C2×D412yes—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11SD1614yescomplemented
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
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—44no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—82no—
132C2×C22⋊D11—82no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—42no—
142C2×D44—42no—
143C2×D44—42no—
144C2×D44—42no—
145C2×D44—81no—
146C2×D44—81no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—44no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—81no—
156C11×C22⋊C4—24no—
157C11×C22⋊C4—44no—
158C11×C22⋊C4—82no—
159C42×C11—42no—
160C42×C11C2×D412yes—
161C42×C11#4112yes—
162#4325—48no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—44no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11C2×D412yes—
168C4⋊Dic11#4112yes—
169C4×Dic11—42no—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—48no—
178C2×C11⋊C8C2×D414yes—
179C2×C11⋊C8C2×D412yes—
180C2×#465—112no—
181C2×#460—111no—
182C2×C8×D4—111no—
183#2541—111no—
184#2538D1111yescharacteristic, complemented
185#2034—112no—
186#2000—112no—
187#1957—111no—
188#1948—111no—
189#1893—112no—
190C4×#103—111no—
191C23×C11—22no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11C2×SD1614yes—
198C23×C11C22×D411yescharacteristic
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206Q8×C11—22no—
207Q8×C11—22no—
208Q8×C11—41no—
209Q8×C11—41no—
210D4×C11—28no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11#12112yes—
230C2×C4×C11#12112yes—
231C2×C4×C11C2×SD1612yes—
232C2×C4×C11#13512yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11H(5,𝔽2)11yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C22⋊D11—88no—
240C22⋊D11—88no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247D44—42no—
248D44—42no—
249D44—42no—
250D44—42no—
251D44—84no—
252D44—84no—
253C11⋊C8—22no—
254C11⋊C8—24no—
255C11⋊C8—41no—
256C22×SD16—112no—
257C23×C8—112no—
258C2×#127—111no—
259C2×#127—221no—
260C2×C22⋊Q8C2×D1112yes—
261C2×#121—112no—
262C2×#121—112no—
263C2×C4×Q8C2×D1111yescharacteristic
264C2×C4×D4C2×D1111yescharacteristic
265#465—228no—
266#460—224no—
267C8×D4—224no—
268C2×#106—112no—
269C2×C4⋊C8—111no—
270C2×#103—111no—
271C2×#103—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×C22⋊C8—112no—
276C2×C4×C8—111no—
277#396—22no—
278#392—222no—
279#390—21no—
280#390—221no—
281#389—21no—
282#384C2×D1111yescharacteristic
283#380C2×D1112yes—
284C4×C4⋊C4—111no—
285#340—111no—
286#340—112no—
287#340—111no—
288C22×C11—24no—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11C2×#12111yescharacteristic
296C22×C11D4211yescharacteristic
297C22×C11#54611yescharacteristic
298C22×C11C22×SD1611yescharacteristic
299C22×C11C2×#13511yescharacteristic
300C22×C11#57611yescharacteristic
301C22×C11#57711yescharacteristic
302C2×D11—82no—
303C2×D11—82no—
304C2×D11—82no—
305C2×D11—82no—
306C2×D11—82no—
307C2×D11—82no—
308C2×D11—82no—
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—82no—
313C4×C11—81no—
314C4×C11#46514yescomplemented
315C4×C11#53211yescharacteristic
316C4×C11#54011yescharacteristic
317C4×C11D4211yescharacteristic
318C4×C11#55011yescharacteristic
319Dic11—42no—
320Dic11—42no—
321C22×Q8C22×D1111yescharacteristic
322C22×D4—112no—
323C22×D4—222no—
324C22×D4—222no—
325C22×D4—221no—
326C22×D4—221no—
327C22×D4C22⋊D1111yescharacteristic
328C23×C4C22×D1112yes—
329C2×SD16—224no—
330C2×SD16—224no—
331C2×SD16—442no—
332C22×C8—111no—
333C22×C8—112no—
334C22×C8—111no—
335C22×C8—224no—
336C22×C8—224no—
337C22×C8—442no—
338#127—222no—
339#127—222no—
340#127—444no—
341C22⋊Q8—24no—
342C22⋊Q8—42no—
343#121—224no—
344#121—224no—
345#121—442no—
346#121—442no—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×D4—22no—
350C4×D4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1112yes—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4C22⋊D1112yes—
365C2×C42—21no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368#106—224no—
369C4⋊C8—114no—
370#103—114no—
371#103—222no—
372#102—224no—
373#102—224no—
374#102—442no—
375C22⋊C8—224no—
376C4×C8—222no—
377#95—22no—
378#95—221no—
379C2×C11—44no—
380C2×C11#242811yescharacteristic
381C2×C11C2×#46511yescharacteristic
382C2×C11#306211yescharacteristic
383C2×C11D4×SD1611yescharacteristic
384C2×C11#328711yescharacteristic
385C2×C11#329511yescharacteristic
386C2×C11#330411yescharacteristic
387D11—162no—
388C24—222no—
389C24C2×C22⋊D1112yes—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8D4×D1112yes—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—222no—
401C2×D4—222no—
402C2×D4—222no—
403C2×D4—222no—
404C2×D4—444no—
405C2×D4—444no—
406C2×D4—444no—
407C2×D4—444no—
408C2×D4—442no—
409C2×D4—442no—
410C2×D4—442no—
411C2×D4—442no—
412C2×D4—881no—
413C2×D4—881no—
414C2×D4—882no—
415C2×D4—882no—
416C2×D4#432514yescomplemented
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C22⋊D1112yes—
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432SD16—448no—
433C2×C8—114no—
434C2×C8—112no—
435C2×C8—221no—
436C2×C8—222no—
437C2×C8—221no—
438C2×C8—222no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—448no—
443C4⋊C4—22no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—44no—
449C4⋊C4—42no—
450C4⋊C4—42no—
451C4⋊C4—81no—
452C4⋊C4—112no—
453C4⋊C4—112no—
454C4⋊C4—221no—
455C4⋊C4—221no—
456C22⋊C4—24no—
457C22⋊C4—44no—
458C22⋊C4—82no—
459C22⋊C4—444no—
460C22⋊C4—444no—
461C42—42no—
462C42—442no—
463C42D4×D1112yes—
464C42#434112yes—
465C11#2538711yescharacteristic, complemented, Sylow
466C23—22no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—442no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23—442no—
477C23—442no—
478C23—442no—
479C23C2×#432514yes—
480C23C22×C22⋊D1111yescharacteristic
481Q8—22no—
482Q8—22no—
483Q8—41no—
484Q8—41no—
485D4—28no—
486D4—442no—
487D4—442no—
488D4—442no—
489D4—442no—
490D4—884no—
491D4—888no—
492D4—888no—
493D4—884no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4#6699212yes—
519C2×C4#6699212yes—
520C2×C4C2×#432512yes—
521C2×C4#6700312yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#41×D1111yescharacteristic
527C2×C4#6704211yescharacteristic
528C8—222no—
529C8—224no—
530C8—441no—
531C22—24no—
532C22—24no—
533C22—24no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—882no—
539C22—882no—
540C22—882no—
541C22—882no—
542C22—882no—
543C22—882no—
544C22—882no—
545C22D4×C22⋊D1111yescharacteristic
546C22C2×#6699211yescharacteristic
547C22C22×#432511yescharacteristic
548C22C2×#6700311yescharacteristic
549C22#1062336011yescharacteristic
550C22#1062336611yescharacteristic
551C22#1062336811yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—82no—
557C4—442no—
558C4—442no—
559C4#1062266114yescomplemented
560C4#1062312711yescharacteristic
561C4#1062313011yescharacteristic
562C4#1062314011yescharacteristic
563C4#1062315011yescharacteristic
564C2—44no—
565C2—1762no—
566C2#1307220611yescharacteristic
567C2C2×#1062266111yescharacteristic
568C2#1307829811yescharacteristic
569C2D4×#432511yescharacteristic
570C2#1308037211yescharacteristic
571C2#1308043411yescharacteristic
572C2#1308054911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radical#13073562C2
hypercenter#2538D11
hypocenterC11#25387
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#10622661C2semidirect
2. C2×#10622640C2semidirect
3. C2×D4×C11⋊C8C2semidirect
5. #13069805C2semidirect
6. #13069617C2semidirect
7. #13069421C2semidirect
8. #13069377C2semidirect
9. #13069042C2semidirect
10. C4×#66899C2semidirect
11. C11×#2538C2semidirect
93. #66899D4semidirect
100. C4⋊(C11⋊C8)D4semidirect
113. C2×D4×C11SD16semidirect
184. #2538D11semidirect
314. C4×C11#465semidirect
416. C2×D4#4325semidirect
465. C11#25387semidirect
559. 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×#106226402
C2×D4×C11⋊C82
#130735622
#130698052
#130696172
#130694212
#130693772
#130690422
C4×#668992
C11×#25382
#2538711