Finite Group Databasebeta

← #14803652

Subgroups — #14803652

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C211yesmaximal, characteristic
2#13073790C211yesmaximal, characteristic, complemented
3#13071681C211yesmaximal, characteristic, complemented
4#13070032C212yesmaximal, complemented
5#13069925C212yesmaximal, complemented
6#13069565C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13068962C212yesmaximal, complemented
9#13068624C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C11×#486C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×D4×Dic11—21no—
15C2×D4×Dic11C2212yes—
16C22×#4323C2212yes—
17C2×C4×D44C2211yescharacteristic
18C11×#486—24no—
19C2×C11×#102C2212yes—
20C2×C11×#102C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622844—22no—
23#10622834—21no—
24#10622834C2212yes—
25#10622833—22no—
26C2×#66896C2212yes—
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×Dic11⋊C8C2212yes—
30#10622685—24no—
31#10622601C2212yes—
32#10622600—21no—
33#10622600—21no—
34#10622590C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622189C2211yescharacteristic
39#10622189C2211yescharacteristic
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11C2312yes—
47C23×Dic11—22no—
48C22×D44C2311yescharacteristic
49C22×C4×D11—21no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×#127—22no—
55C11×#127D414yes—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62D4×Dic11—24no—
63D4×Dic11—42no—
64D4×Dic11—44no—
65C2×#4323—24no—
66C2×#4323—24no—
67C2×#4323—42no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4×Dic11—21no—
77C2×C4×Dic11C2312yes—
78C22×C11⋊C8C2312yes—
79C4×D44—22no—
80C4×D44—22no—
81C11×#102—24no—
82C11×#102—24no—
83C4×C8×C11—22no—
84#66896—24no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95D412yes—
89#66885—22no—
90#66885—22no—
91Dic11⋊C8—42no—
92C4⋊(C11⋊C8)—22no—
93#25321—111nomaximal, Sylow
94C24×C11—22no—
95C23×D11—21no—
96C2×Q8×C11—42no—
97C2×Q8×C11—81no—
98C2×Q8×C11—81no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—81no—
109C2×D4×C11—81no—
110C2×D4×C11C2×D414yes—
111C22×C4×C11—22no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—44no—
119C22×Dic11—44no—
120C22×Dic11—82no—
121C22×Dic11C2×D412yes—
122C22×Dic11C2×D412yes—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44#4112yes—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—42no—
141C42×C11C2×D412yes—
142C42×C11#4112yes—
143C22⋊Dic11—44no—
144C22⋊Dic11—44no—
145C22⋊Dic11—82no—
146#4323—48no—
147(C2×D11)⋊C4—42no—
148(C2×D11)⋊C4—82no—
149(C2×D11)⋊C4—82no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11#4112yes—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C4×Dic11—42no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×#486D1111yescharacteristic, complemented
165C2×#459—111no—
166#2563—111no—
167#2366—111no—
168#2073—112no—
169#2054—112no—
170#1987—111no—
171#1939—111no—
172#1879—112no—
173#1804—112no—
174C4×#102—111no—
175C23×C11—24no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11C22×D411yescharacteristic
183C22×D11—22no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190Q8×C11—84no—
191D4×C11—24no—
192D4×C11—24no—
193D4×C11—42no—
194D4×C11—42no—
195D4×C11—48no—
196D4×C11—84no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11#13512yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C112−1+411yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—88no—
228D44—22no—
229D44—22no—
230D44—41no—
231D44—41no—
232C4×D11—84no—
233C8×C11—41no—
234C8×C11—41no—
235C11⋊C8—42no—
236C22×D8—112no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×#127C2×D1111yescharacteristic
239C2×C4×D4—112no—
240C2×C4×D4—111no—
241C2×C4×D4—221no—
242#486—24no—
243#459—224no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8—112no—
246C2×#102—112no—
247C2×#102—111no—
248C2×#102—111no—
249C2×#102C2×D1112yes—
250C2×#102C2×D1112yes—
251C2×C4×C8C2×D1111yescharacteristic
252#393—222no—
253#390—112no—
254#390—112no—
255#390—221no—
256#386—222no—
257#382—112no—
258#380—221no—
259#380—221no—
260C4×C4⋊C4—111no—
261C4×C4⋊C4—111no—
262#340—111no—
263#340—111no—
264#340—112no—
265#340—112no—
266#336—112no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—44no—
270C22×C11—82no—
271C22×C11—82no—
272C22×C11—82no—
273C22×C11—82no—
274C22×C11C2×#12111yescharacteristic
275C22×C11#54611yescharacteristic
276C22×C11#54811yescharacteristic
277C22×C11C2×#13511yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C22×C11#57611yescharacteristic
280C22×C11#57611yescharacteristic
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—81no—
285C2×D11—81no—
286C2×D11—81no—
287C2×D11—81no—
288C4×C11—22no—
289C4×C11—82no—
290C4×C11#46314yes—
291C4×C11#52911yescharacteristic
292C4×C11#54211yescharacteristic
293C4×C11#54611yescharacteristic
294C4×C11#54711yescharacteristic
295Dic11—42no—
296Dic11—42no—
297Dic11—42no—
298Dic11—81no—
299Dic11—81no—
300C22×Q8—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—111no—
304C22×D4C22×D1112yes—
305C23×C4—222no—
306C23×C4—221no—
307C2×D8—224no—
308C2×D8—224no—
309C2×D8—442no—
310C22×C8—112no—
311C22×C8C22×D1111yescharacteristic
312C22×C8C22×D1111yescharacteristic
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315#127—22no—
316#127C22⋊D1114yes—
317C4×D4—224no—
318C4×D4—222no—
319C4×D4—222no—
320C4×D4—442no—
321C4×D4—444no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4C22×D1112yes—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—221no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C42—112no—
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—222no—
339C4⋊C8—442no—
340#102—24no—
341#102—24no—
342#102—222no—
343#102—222no—
344#102—224no—
345C4×C8—22no—
346#95—112no—
347#95—222no—
348#95—222no—
349#95—221no—
350C2×C11—84no—
351C2×C11#242711yescharacteristic
352C2×C11C2×#46311yescharacteristic
353C2×C11#304111yescharacteristic
354C2×C11#330511yescharacteristic
355C2×C11#332511yescharacteristic
356C2×C11#336111yescharacteristic
357C2×C11#336611yescharacteristic
358D11—82no—
359C24—22no—
360C24—221no—
361C2×Q8—42no—
362C2×Q8—81no—
363C2×Q8—81no—
364C2×D4—24no—
365C2×D4—24no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—42no—
372C2×D4—42no—
373C2×D4—81no—
374C2×D4—81no—
375C2×D4—112no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—221no—
381C2×D4C2×C22⋊D1114yes—
382C22×C4—22no—
383C22×C4—112no—
384C22×C4—112no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—882no—
394C22×C4D4×D1111yescharacteristic
395C22×C4D4×D1111yescharacteristic
396C22×C4C23×D1111yescharacteristic
397D8—448no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—222no—
405C2×C8—222no—
406C2×C8—222no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—42no—
410C4⋊C4—112no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C22⋊C4—444no—
419C22⋊C4—444no—
420C22⋊C4—442no—
421C22⋊C4—882no—
422C22⋊C4—882no—
423C22⋊C4—882no—
424C42—222no—
425C42—222no—
426C42—442no—
427C42#434112yes—
428C42C2×C22⋊D1112yes—
429C11#2532111yescharacteristic, complemented, Sylow
430C23—24no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—222no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23—441no—
444C23C2×D4×D1111yescharacteristic
445Q8—84no—
446D4—24no—
447D4—24no—
448D4—48no—
449D4—42no—
450D4—42no—
451D4—84no—
452D4—222no—
453D4—222no—
454D4—441no—
455D4—441no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4—222no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—888no—
477C2×C4—884no—
478C2×C4#6696712yes—
479C2×C4#6696912yes—
480C2×C4#6699212yes—
481C2×C4#6699212yes—
482C2×C4C2×#434111yescharacteristic
483C2×C4#41×D1111yescharacteristic
484C2×C4#41×D1111yescharacteristic
485C2×C4#6704211yescharacteristic
486C2×C4#6704311yescharacteristic
487C2×C4C22×C22⋊D1111yescharacteristic
488C8—41no—
489C8—41no—
490C8—442no—
491C22—44no—
492C22—44no—
493C22—44no—
494C22—82no—
495C22—82no—
496C22—82no—
497C22—82no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22—881no—
505C22#1062320711yescharacteristic
506C22#1062320811yescharacteristic
507C22#1062328811yescharacteristic
508C22#1062328811yescharacteristic
509C22C2×#6696711yescharacteristic
510C22C2×#6696911yescharacteristic
511C22C2×#6699211yescharacteristic
512C4—22no—
513C4—82no—
514C4—442no—
515C4—442no—
516C4—442no—
517C4—881no—
518C4—881no—
519C4#1062277814yes—
520C4#1062321111yescharacteristic
521C4#1062321311yescharacteristic
522C4#1062335511yescharacteristic
523C4#1062336011yescharacteristic
524C2—84no—
525C2—882no—
526C2#1307219611yescharacteristic
527C2C2×#1062277811yescharacteristic
528C2#1307811611yescharacteristic
529C2#1308056511yescharacteristic
530C2#1308085711yescharacteristic
531C2#1308128111yescharacteristic
532C2#1308132811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#486C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenterC2×#486D11
hypocenterC11#25321
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
2. #13073790C2semidirect
3. #13071681C2semidirect
4. #13070032C2semidirect
5. #13069925C2semidirect
6. #13069565C2semidirect
7. #13069334C2semidirect
8. #13068962C2semidirect
9. #13068624C2semidirect
10. C4×#66885C2semidirect
11. C2×C11×#486C2semidirect
164. C2×#486D11semidirect
429. C11#25321semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
#130737902
#130716812
#130700322
#130699252
#130695652
#130693342
#130689622
#130686242
C4×#668852
C2×C11×#4862
#2532111