Finite Group Databasebeta

← #14804521

Subgroups — #14804521

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×#10622727C212yesmaximal, complemented
2C2×#10622461C211yesmaximal, characteristic, complemented
3#13073562C211yesmaximal, characteristic
4#13073538C211yesmaximal, characteristic, complemented
5#13069806C212yesmaximal, complemented
6#13069621C212yesmaximal, complemented
7#13069422C211yesmaximal, characteristic, complemented
8#13069380C211yesmaximal, characteristic, complemented
9#13069044C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C2×C8×D4×C11C211yesmaximal, characteristic, complemented
12C23×C8×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66993—21no—
15C2×#66983C2212yes—
16C2×#66983C2212yes—
17C2×#66977C2212yes—
18C22×#4314C2212yes—
19C2×#66927C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C8×D4×C11—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25#10622834—21no—
26#10622825C2212yes—
27#10622727—28no—
28C2×#66885C2212yes—
29C2×#66885C2212yes—
30C2×#66885C2212yes—
31C2×#66881C2212yes—
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34#10622601—21no—
35#10622586—21no—
36#10622573—22no—
37#10622561—22no—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622461—24no—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×C22⋊D11—22no—
47C22×C22⋊D11—22no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44C2312yes—
51C22×Dic22C2311yescharacteristic
52C22×C8×C11—24no—
53C22×C8×C11—24no—
54C22×C8×C11—42no—
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2312yes—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C22⋊C4D412yes—
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65#66993—44no—
66#66983—24no—
67#66983—24no—
68#66983—42no—
69#66983—42no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78#66977—24no—
79#66977—42no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—22no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—21no—
84C2×#4314—24no—
85C2×#4314—24no—
86C2×#4314—42no—
87#66927—22no—
88#66927—22no—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C11×C4⋊C8D414yescomplemented
92C11×C22⋊C8—24no—
93C4×C8×C11—22no—
94C11⋊#95—21no—
95C11⋊#95—22no—
96#66885—24no—
97#66885—24no—
98#66885—42no—
99#66881—24no—
100#66880—22no—
101#66880D414yescomplemented
102#25387—111nomaximal, Sylow
103C24×C11C2×D412yes—
104C23×D11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11SD1614yescomplemented
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—44no—
119C2×C22⋊D11—44no—
120C2×C22⋊D11—44no—
121C2×C22⋊D11—44no—
122C2×C22⋊D11—82no—
123C2×C22⋊D11—82no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—42no—
136C2×D44—42no—
137C2×D44—42no—
138C2×D44—42no—
139C2×D44—81no—
140C2×D44—81no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22C2×D412yes—
147C2×C8×C11—22no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—22no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—48no—
155C2×C8×C11C2×D412yes—
156C2×C8×C11C2×D414yes—
157C11×C4⋊C4—22no—
158C11×C22⋊C4—24no—
159C42×C11C2×D412yes—
160C42×C11#4112yes—
161C22⋊Dic11—44no—
162C22⋊Dic11—82no—
163(C2×D11)⋊C4—44no—
164(C2×D11)⋊C4—44no—
165C4⋊Dic11—22no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—22no—
171C4⋊Dic11—42no—
172C4⋊Dic11—81no—
173C4⋊Dic11C2×D412yes—
174C4⋊Dic11#4112yes—
175Dic11⋊C4—44no—
176Dic11⋊C4—42no—
177C4×Dic11—42no—
178C4×Dic11—42no—
179#4314—48no—
180C2×#465—112no—
181C2×#460—111no—
182C2×C8×D4D1111yescharacteristic, complemented
183#2541—111no—
184#2538—111no—
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—
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—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11#12112yes—
217C2×C4×C11#12112yes—
218C2×C4×C11C2×SD1612yes—
219C2×C4×C11#13512yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C11H(5,𝔽2)11yescharacteristic
226C22⋊D11—88no—
227C22⋊D11—88no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243D44—42no—
244D44—42no—
245D44—42no—
246D44—42no—
247D44—84no—
248D44—84no—
249Dic22—22no—
250Dic22—22no—
251Dic22—41no—
252Dic22—41no—
253C8×C11—24no—
254C8×C11—22no—
255C8×C11—41no—
256C22×SD16—112no—
257C23×C8C2×D1112yes—
258C2×#127—111no—
259C2×#127—221no—
260C2×C22⋊Q8—112no—
261C2×#121—112no—
262C2×#121—112no—
263C2×C4×Q8—111no—
264C2×C4×D4C2×D1111yescharacteristic
265#465—228no—
266#460—224no—
267C8×D4—24no—
268C2×#106—112no—
269C2×C4⋊C8C2×D1111yescharacteristic
270C2×#103—111no—
271C2×#103—111no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#102—112no—
275C2×C22⋊C8C2×D1112yes—
276C2×C4×C8C2×D1111yescharacteristic
277#396—222no—
278#392—222no—
279#390—221no—
280#390—221no—
281#389—221no—
282#384—111no—
283#380—112no—
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#46514yescomplemented
312C4×C11#53211yescharacteristic
313C4×C11#54011yescharacteristic
314C4×C11D4211yescharacteristic
315C4×C11#55011yescharacteristic
316Dic11—42no—
317Dic11—42no—
318Dic11—42no—
319Dic11—82no—
320Dic11—81no—
321C22×Q8—111no—
322C22×D4—112no—
323C22×D4—222no—
324C22×D4—222no—
325C22×D4—221no—
326C22×D4—221no—
327C22×D4D4411yescharacteristic
328C23×C4C22×D1112yes—
329C2×SD16—224no—
330C2×SD16—224no—
331C2×SD16—442no—
332C22×C8—24no—
333C22×C8—24no—
334C22×C8—42no—
335C22×C8C22×D1111yescharacteristic
336C22×C8C22×D1111yescharacteristic
337C22×C8C22×D1112yes—
338#127—222no—
339#127—222no—
340#127—444no—
341C22⋊Q8—224no—
342C22⋊Q8—442no—
343#121—224no—
344#121—224no—
345#121—442no—
346#121—442no—
347C4×Q8—222no—
348C4×Q8—222no—
349C4×D4—22no—
350C4×D4—22no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—112no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4D4411yescharacteristic
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C22⋊C4D4412yes—
365C2×C42—221no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368#106—224no—
369C4⋊C8C22⋊D1114yescomplemented
370#103—114no—
371#103—222no—
372#102—224no—
373#102—224no—
374#102—442no—
375C22⋊C8—24no—
376C4×C8—22no—
377#95—221no—
378#95—222no—
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×D4412yes—
390C2×Q8—112no—
391C2×Q8—221no—
392C2×Q8—221no—
393C2×Q8—221no—
394C2×Q8—221no—
395C2×Q8—221no—
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#431414yescomplemented
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—222no—
428C22×C4C2×D4412yes—
429C22×C4C2×D4411yescharacteristic
430C22×C4C2×D4411yescharacteristic
431C22×C4C23×D1111yescharacteristic
432SD16—448no—
433C2×C8—22no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—48no—
441C2×C8D4×D1112yes—
442C2×C8C2×C22⋊D1114yes—
443C4⋊C4—22no—
444C4⋊C4—112no—
445C4⋊C4—112no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C4⋊C4—221no—
449C4⋊C4—222no—
450C4⋊C4—222no—
451C4⋊C4—221no—
452C4⋊C4—444no—
453C4⋊C4—442no—
454C4⋊C4—442no—
455C4⋊C4—881no—
456C22⋊C4—24no—
457C22⋊C4—444no—
458C22⋊C4—444no—
459C22⋊C4—444no—
460C22⋊C4—882no—
461C42—442no—
462C42—442no—
463C42#433912yes—
464C42C2×C22⋊D1112yes—
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×#431414yes—
480C23C22×D4411yescharacteristic
481Q8—222no—
482Q8—222no—
483Q8—441no—
484Q8—441no—
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—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—441no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—441no—
517C2×C4—442no—
518C2×C4C2×#431412yes—
519C2×C4#6695712yes—
520C2×C4#6698312yes—
521C2×C4#6698312yes—
522C2×C4C2×#433911yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4#6703711yescharacteristic
525C2×C4#41×D1111yescharacteristic
526C2×C4#6704211yescharacteristic
527C2×C4C22×C22⋊D1111yescharacteristic
528C8—22no—
529C8—24no—
530C8—41no—
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×D4411yescharacteristic
546C22#1062308511yescharacteristic
547C22C22×#431411yescharacteristic
548C22C2×#6695711yescharacteristic
549C22#1062328211yescharacteristic
550C22#1062328311yescharacteristic
551C22C2×#6698311yescharacteristic
552C4—22no—
553C4—42no—
554C4—442no—
555C4—442no—
556C4—442no—
557C4—881no—
558C4—882no—
559C4#1062272714yescomplemented
560C4#1062307911yescharacteristic
561C4#1062309311yescharacteristic
562C4D4×C22⋊D1111yescharacteristic
563C4#1062336511yescharacteristic
564C2—44no—
565C2—1762no—
566C2#1307219811yescharacteristic
567C2C2×#1062272711yescharacteristic
568C2#1307829611yescharacteristic
569C2D4×#431411yescharacteristic
570C2#1308037611yescharacteristic
571C2#1308044111yescharacteristic
572C2#1308055611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11C22×D4
prime radical#13073562C2
hypercenterC2×C8×D4D11
hypocenterC11#25387
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622727C2semidirect
2. C2×#10622461C2semidirect
4. #13073538C2semidirect
5. #13069806C2semidirect
6. #13069621C2semidirect
7. #13069422C2semidirect
8. #13069380C2semidirect
9. #13069044C2semidirect
10. C4×#66880C2semidirect
11. C2×C8×D4×C11C2semidirect
91. C11×C4⋊C8D4semidirect
101. #66880D4semidirect
107. C2×D4×C11SD16semidirect
182. C2×C8×D4D11semidirect
311. C4×C11#465semidirect
369. C4⋊C8C22⋊D11semidirect
416. C2×D4#4314semidirect
465. C11#25387semidirect
559. C4#10622727semidirect

Maximal subgroups

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

subgroupindex
C2×#106227272
C2×#106224612
#130735622
#130735382
#130698062
#130696212
#130694222
#130693802
#130690442
C4×#668802
C2×C8×D4×C112
#2538711