Finite Group Databasebeta

← #14804530

Subgroups — #14804530

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×#10622654C212yesmaximal, complemented
2C2×#10622688C211yesmaximal, characteristic, complemented
3C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
4#13073538C211yesmaximal, characteristic, complemented
5#13069802C212yesmaximal, complemented
6#13069619C212yesmaximal, complemented
7#13069423C211yesmaximal, characteristic, complemented
8#13069379C211yesmaximal, characteristic, complemented
9#13069045C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#2541C211yesmaximal, characteristic
12C2×C11×#127—21no—
13C2×C11×#127C2211yescharacteristic
14C2×C11×#121C2212yes—
15C2×C11×#121C2212yes—
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4324C2212yes—
18C2×#66977C2212yes—
19C23×C11⋊C8C2212yes—
20C2×C4×Dic22C2211yescharacteristic
21C11×#392—22no—
22C11×#390—21no—
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622834—21no—
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622688—24no—
31#10622654—28no—
32D4×C11⋊C8—24no—
33#10622586—21no—
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66872C2212yes—
37#10622561—22no—
38#10622548C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11D411yescharacteristic
49C22×D4×C11C2312yes—
50C23×C4×C11C2312yes—
51C22×Dic22C2311yescharacteristic
52C11×#127—22no—
53C11×#127—22no—
54C11×#127—44no—
55C11×#121—24no—
56C11×#121—24no—
57C11×#121—42no—
58C11×#121—42no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4D412yes—
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×#4324—24no—
72C2×#4324—24no—
73C2×#4324—42no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2312yes—
78#66977—24no—
79#66977—42no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—22no—
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—
89C4×Dic22—22no—
90C4×Dic22—22no—
91C11×#95—21no—
92#66896—24no—
93#66896—24no—
94#66896—42no—
95C11⋊#95—22no—
96C22⋊(C11⋊C8)—24no—
97#66874—22no—
98#66874D414yescomplemented
99#66872—24no—
100C4⋊(C11⋊C8)D414yescomplemented
101C4×C11⋊C8—22no—
102#25387—111nomaximal, Sylow
103C24×C11—22no—
104C24×C11C2×D412yes—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—44no—
114C2×D4×C11—44no—
115C2×D4×C11—44no—
116C2×D4×C11—44no—
117C2×D4×C11—42no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—81no—
122C2×D4×C11—81no—
123C2×D4×C11—82no—
124C2×D4×C11—82no—
125C2×D4×C11SD1614yescomplemented
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—22no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22C2×D412yes—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4#4112yes—
152C11×C22⋊C4—24no—
153C11×C22⋊C4—44no—
154C11×C22⋊C4—44no—
155C42×C11—42no—
156C42×C11C2×D412yes—
157C42×C11#4112yes—
158C22⋊Dic11—44no—
159C22⋊Dic11—82no—
160#4324—48no—
161C4⋊Dic11—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—22no—
165C4⋊Dic11—42no—
166C4⋊Dic11—81no—
167Dic11⋊C4—44no—
168Dic11⋊C4—42no—
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#2541D1111yescharacteristic
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×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11C2×SD1614yes—
205C23×C11C22×D411yescharacteristic
206D4×C11—28no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—42no—
211D4×C11—84no—
212D4×C11—88no—
213D4×C11—88no—
214D4×C11—84no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11#12112yes—
231C2×C4×C11#12112yes—
232C2×C4×C11C2×SD1612yes—
233C2×C4×C11#13512yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249Dic22—22no—
250Dic22—22no—
251Dic22—41no—
252Dic22—41no—
253C11⋊C8—22no—
254C11⋊C8—24no—
255C11⋊C8—41no—
256C22×SD16—112no—
257C23×C8—112no—
258C2×#127—21no—
259C2×#127C2×D1111yescharacteristic
260C2×C22⋊Q8—112no—
261C2×#121C2×D1112yes—
262C2×#121C2×D1112yes—
263C2×C4×Q8—111no—
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—222no—
278#392—22no—
279#390—21no—
280#390—221no—
281#389—221no—
282#384—111no—
283#380—112no—
284C4×C4⋊C4C2×D1111yescharacteristic
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×C11—82no—
296C22×C11—82no—
297C22×C11—82no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11C2×#12111yescharacteristic
303C22×C11D4211yescharacteristic
304C22×C11#54611yescharacteristic
305C22×C11C22×SD1611yescharacteristic
306C22×C11C2×#13511yescharacteristic
307C22×C11#57611yescharacteristic
308C22×C11#57711yescharacteristic
309C4×C11—22no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11—42no—
313C4×C11#46514yescomplemented
314C4×C11#53211yescharacteristic
315C4×C11#54011yescharacteristic
316C4×C11D4211yescharacteristic
317C4×C11#55011yescharacteristic
318Dic11—42no—
319Dic11—82no—
320Dic11—81no—
321C22×Q8—111no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C22⋊D1111yescharacteristic
327C22×D4C22×D1112yes—
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—22no—
339#127—22no—
340#127—44no—
341C22⋊Q8—224no—
342C22⋊Q8—442no—
343#121—24no—
344#121—24no—
345#121—42no—
346#121—42no—
347C4×Q8—222no—
348C4×Q8—222no—
349C4×D4—22no—
350C4×D4—22no—
351C2×C4⋊C4—111no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1111yescharacteristic
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—21no—
378#95—222no—
379C2×C11—44no—
380C2×C11—162no—
381C2×C11#242811yescharacteristic
382C2×C11C2×#46511yescharacteristic
383C2×C11#306211yescharacteristic
384C2×C11D4×SD1611yescharacteristic
385C2×C11#328711yescharacteristic
386C2×C11#329511yescharacteristic
387C2×C11#330411yescharacteristic
388C24—22no—
389C24C2×C22⋊D1112yes—
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—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—81no—
413C2×D4—81no—
414C2×D4—82no—
415C2×D4—82no—
416C2×D4#432414yescomplemented
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—222no—
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—21no—
446C4⋊C4—221no—
447C4⋊C4—222no—
448C4⋊C4—221no—
449C4⋊C4—222no—
450C4⋊C4—444no—
451C4⋊C4—442no—
452C4⋊C4—442no—
453C4⋊C4—881no—
454C4⋊C4D4×D1112yes—
455C4⋊C4#434112yes—
456C22⋊C4—24no—
457C22⋊C4—44no—
458C22⋊C4—44no—
459C22⋊C4—444no—
460C22⋊C4—882no—
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—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23C2×#432414yes—
480C23C22×C22⋊D1111yescharacteristic
481Q8—222no—
482Q8—222no—
483Q8—441no—
484Q8—441no—
485D4—28no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—84no—
491D4—88no—
492D4—88no—
493D4—84no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—222no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—442no—
513C2×C4—441no—
514C2×C4—442no—
515C2×C4—441no—
516C2×C4—442no—
517C2×C4—441no—
518C2×C4C2×#432412yes—
519C2×C4#6699212yes—
520C2×C4#6699212yes—
521C2×C4#6700312yes—
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C2×#434111yescharacteristic
526C2×C4#6703711yescharacteristic
527C2×C4#6703711yescharacteristic
528C8—222no—
529C8—224no—
530C8—441no—
531C22—24no—
532C22—24no—
533C22—24no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—82no—
539C22—82no—
540C22—82no—
541C22—82no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22C22×#432411yescharacteristic
546C22D4×C22⋊D1111yescharacteristic
547C22C2×#6699211yescharacteristic
548C22#1062333711yescharacteristic
549C22C2×#6700311yescharacteristic
550C22#1062336611yescharacteristic
551C22#1062336711yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—442no—
557C4—881no—
558C4—882no—
559C4#1062265414yescomplemented
560C4#1062324711yescharacteristic
561C4#1062324811yescharacteristic
562C4#1062324911yescharacteristic
563C4#1062325011yescharacteristic
564C2—44no—
565C2—162no—
566C2#1307220711yescharacteristic
567C2C2×#1062265411yescharacteristic
568C2#1307829211yescharacteristic
569C2D4×#432411yescharacteristic
570C2#1308037211yescharacteristic
571C2#1308044011yescharacteristic
572C2#1308055511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#2541C2
socleC23×C11C22×D4
hypercenter#2541D11
hypocenterC11#25387
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. C2×#10622654C2semidirect
2. C2×#10622688C2semidirect
3. C2×D4×C11⋊C8C2semidirect
4. #13073538C2semidirect
5. #13069802C2semidirect
6. #13069619C2semidirect
7. #13069423C2semidirect
8. #13069379C2semidirect
9. #13069045C2semidirect
10. C4×#66874C2semidirect
98. #66874D4semidirect
100. C4⋊(C11⋊C8)D4semidirect
125. C2×D4×C11SD16semidirect
313. C4×C11#465semidirect
416. C2×D4#4324semidirect
465. C11#25387semidirect
559. C4#10622654semidirect

Maximal subgroups

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

subgroupindex
C2×#106226542
C2×#106226882
C2×D4×C11⋊C82
#130735382
#130698022
#130696192
#130694232
#130693792
#130690452
C4×#668742
C11×#25412
#2538711