Finite Group Databasebeta

← #14803619

Subgroups — #14803619

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C211yesmaximal, characteristic
2#13073570C211yesmaximal, characteristic, complemented
3#13071681C211yesmaximal, characteristic, complemented
4#13070022C212yesmaximal, complemented
5#13069925C212yesmaximal, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069334C211yesmaximal, characteristic, complemented
8#13068962C212yesmaximal, complemented
9#13068614C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C11×#486C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#127C2211yescharacteristic
14C2×#66999—21no—
15C2×#66999—21no—
16C2×D4×Dic11—21no—
17C2×D4×Dic11C2212yes—
18C22×#4323C2212yes—
19C2×C4×D44C2211yescharacteristic
20C11×#486—24no—
21C2×C11×#102C2212yes—
22C2×C11×#102C2212yes—
23C2×C4×C8×C11C2211yescharacteristic
24#10622834—21no—
25#10622834C2212yes—
26#10622833—22no—
27C2×#66896C2212yes—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×Dic11⋊C8C2212yes—
31#10622685—24no—
32#10622605—22no—
33#10622601C2212yes—
34#10622589C2212yes—
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—
62#66999—44no—
63#66999—44no—
64D4×Dic11—24no—
65D4×Dic11—42no—
66D4×Dic11—44no—
67C2×#4323—24no—
68C2×#4323—24no—
69C2×#4323—42no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11D411yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11C2312yes—
82C22×C11⋊C8C2312yes—
83C4×D44—22no—
84C4×D44—22no—
85C11×#102—24no—
86C11×#102—24no—
87C4×C8×C11—22no—
88#66896—24no—
89C11⋊#95—21no—
90C11⋊#95D412yes—
91#66885—22no—
92#66885—22no—
93Dic11⋊C8—42no—
94C4⋊(C11⋊C8)—22no—
95#25318—111nomaximal, Sylow
96C24×C11—22no—
97C23×D11—21no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×D4×C11—24no—
102C2×D4×C11—24no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—42no—
109C2×D4×C11—42no—
110C2×D4×C11—81no—
111C2×D4×C11—81no—
112C2×D4×C11C2×D414yes—
113C22×C4×C11—22no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—44no—
121C22×Dic11—44no—
122C22×Dic11—82no—
123C22×Dic11C2×D412yes—
124C22×Dic11C2×D412yes—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×D44—21no—
129C2×D44—21no—
130C2×D44#4112yes—
131C2×C4×D11—42no—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C42×C11C2×D412yes—
144C42×C11#4112yes—
145C22⋊Dic11—44no—
146C22⋊Dic11—44no—
147C22⋊Dic11—82no—
148#4323—48no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—44no—
151(C2×D11)⋊C4—42no—
152C4⋊Dic11—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11D814yescomplemented
159C4⋊Dic11#4112yes—
160Dic11⋊C4—44no—
161Dic11⋊C4—44no—
162C4×Dic11—22no—
163C4×Dic11—22no—
164C4×Dic11—42no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×#486D1111yescharacteristic, complemented
169C2×#459—111no—
170#2542—111no—
171#2366—111no—
172#2071—112no—
173#2054—112no—
174#1988—111no—
175#1939—111no—
176#1879—112no—
177#1802—112no—
178C4×#102—111no—
179C23×C11—24no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—42no—
185C23×C11—42no—
186C23×C11C22×D411yescharacteristic
187C22×D11—22no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192C22×D11—41no—
193C22×D11—41no—
194Q8×C11—84no—
195D4×C11—24no—
196D4×C11—24no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—48no—
200D4×C11—84no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11#12112yes—
207C2×C4×C11#12112yes—
208C2×C4×C11C2×D812yes—
209C2×C4×C11AGL(1,ℤ/8)12yes—
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11C2×#4111yescharacteristic
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11H(5,𝔽2)11yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—88no—
231C2×Dic11C2×D814yes—
232D44—22no—
233D44—22no—
234D44—41no—
235D44—41no—
236C4×D11—84no—
237C8×C11—41no—
238C8×C11—41no—
239C11⋊C8—42no—
240C22×D8—112no—
241C2×C4⋊Q8C2×D1111yescharacteristic
242C2×#127C2×D1111yescharacteristic
243C2×C22⋊Q8—221no—
244C2×C22⋊Q8—221no—
245C2×C4×D4—112no—
246C2×C4×D4—111no—
247C2×C4×D4—221no—
248#486—24no—
249#459—224no—
250C2×C4⋊C8—111no—
251C2×C4⋊C8—112no—
252C2×#102—112no—
253C2×#102—111no—
254C2×#102—111no—
255C2×#102C2×D1112yes—
256C2×#102C2×D1112yes—
257C2×C4×C8C2×D1111yescharacteristic
258#399—222no—
259#390—112no—
260#390—112no—
261#390—221no—
262#386—222no—
263#384—112no—
264C4×C4⋊C4—111no—
265C4×C4⋊C4—111no—
266#340—111no—
267#340—111no—
268#340—112no—
269#340—112no—
270#336—112no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—44no—
274C22×C11—82no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—82no—
278C22×C11C2×#12111yescharacteristic
279C22×C11#54611yescharacteristic
280C22×C11#54811yescharacteristic
281C22×C11C22×D811yescharacteristic
282C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C11#57711yescharacteristic
284C22×C11#57711yescharacteristic
285C2×D11—42no—
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—81no—
289C2×D11—81no—
290C2×D11—81no—
291C2×D11—81no—
292C4×C11—22no—
293C4×C11—82no—
294C4×C11#45914yes—
295C4×C11#52911yescharacteristic
296C4×C11#54211yescharacteristic
297C4×C11#54611yescharacteristic
298C4×C11#54711yescharacteristic
299Dic11—24no—
300Dic11—42no—
301Dic11—42no—
302Dic11—81no—
303Dic11—81no—
304C22×Q8—21no—
305C22×D4—21no—
306C22×D4—21no—
307C22×D4—111no—
308C22×D4C22×D1112yes—
309C23×C4—222no—
310C23×C4—221no—
311C2×D8—224no—
312C2×D8—224no—
313C2×D8—442no—
314C22×C8—112no—
315C22×C8C22×D1111yescharacteristic
316C22×C8C22×D1111yescharacteristic
317C4⋊Q8—22no—
318C4⋊Q8—22no—
319#127—22no—
320#127C22⋊D1114yes—
321C22⋊Q8—444no—
322C22⋊Q8—444no—
323C4×D4—224no—
324C4×D4—222no—
325C4×D4—222no—
326C4×D4—442no—
327C4×D4—444no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—111no—
332C2×C4⋊C4—111no—
333C2×C4⋊C4—111no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—222no—
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—222no—
343C2×C42—112no—
344C2×C42—221no—
345C2×C42C22×D1111yescharacteristic
346C4⋊C8—222no—
347C4⋊C8—442no—
348#102—24no—
349#102—24no—
350#102—222no—
351#102—222no—
352#102—224no—
353C4×C8—22no—
354#95—112no—
355#95—221no—
356C2×C11—84no—
357C2×C11#242711yescharacteristic
358C2×C11C2×#45911yescharacteristic
359C2×C11#304211yescharacteristic
360C2×C11#329411yescharacteristic
361C2×C11#333211yescharacteristic
362C2×C11#335811yescharacteristic
363C2×C11#337311yescharacteristic
364D11—82no—
365C24—22no—
366C24—221no—
367C2×Q8—42no—
368C2×Q8—42no—
369C2×Q8—42no—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—81no—
380C2×D4—81no—
381C2×D4—112no—
382C2×D4—221no—
383C2×D4—221no—
384C2×D4—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4C2×C22⋊D1114yes—
388C22×C4—22no—
389C22×C4—112no—
390C22×C4—112no—
391C22×C4—221no—
392C22×C4—221no—
393C22×C4—221no—
394C22×C4—444no—
395C22×C4—444no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4—882no—
400C22×C4D4×D1111yescharacteristic
401C22×C4D4×D1111yescharacteristic
402C22×C4C23×D1111yescharacteristic
403D8—448no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—222no—
411C2×C8—222no—
412C2×C8—222no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—42no—
416C4⋊C4—114no—
417C4⋊C4—112no—
418C4⋊C4—222no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—444no—
425C4⋊C4—444no—
426C22⋊C4—444no—
427C22⋊C4—444no—
428C22⋊C4—444no—
429C22⋊C4—444no—
430C22⋊C4—442no—
431C22⋊C4—882no—
432C42—222no—
433C42—222no—
434C42—442no—
435C42#434112yes—
436C42C2×C22⋊D1112yes—
437C11#2531811yescharacteristic, complemented, Sylow
438C23—24no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—222no—
446C23—441no—
447C23—441no—
448C23—441no—
449C23—441no—
450C23—441no—
451C23—441no—
452C23C2×D4×D1111yescharacteristic
453Q8—84no—
454D4—24no—
455D4—24no—
456D4—48no—
457D4—42no—
458D4—42no—
459D4—84no—
460D4—222no—
461D4—222no—
462D4—441no—
463D4—441no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—114no—
470C2×C4—222no—
471C2×C4—222no—
472C2×C4—222no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—888no—
485C2×C4—884no—
486C2×C4D8×D1112yes—
487C2×C4#6696412yes—
488C2×C4#6699212yes—
489C2×C4#6699212yes—
490C2×C4C2×#434111yescharacteristic
491C2×C4#41×D1111yescharacteristic
492C2×C4#41×D1111yescharacteristic
493C2×C4#6704211yescharacteristic
494C2×C4#6704311yescharacteristic
495C2×C4C22×C22⋊D1111yescharacteristic
496C8—41no—
497C8—41no—
498C8—442no—
499C22—44no—
500C22—44no—
501C22—44no—
502C22—82no—
503C22—82no—
504C22—82no—
505C22—82no—
506C22—442no—
507C22—442no—
508C22—442no—
509C22—881no—
510C22—881no—
511C22—881no—
512C22—881no—
513C22#1062320711yescharacteristic
514C22#1062320811yescharacteristic
515C22C2×D8×D1111yescharacteristic
516C22C2×#6696411yescharacteristic
517C22#1062329311yescharacteristic
518C22#1062329311yescharacteristic
519C22C2×#6699211yescharacteristic
520C4—22no—
521C4—82no—
522C4—224no—
523C4—442no—
524C4—442no—
525C4—881no—
526C4—881no—
527C4#1062276314yes—
528C4#1062321111yescharacteristic
529C4#1062321311yescharacteristic
530C4#1062335511yescharacteristic
531C4#1062336011yescharacteristic
532C2—84no—
533C2—882no—
534C2#1307219611yescharacteristic
535C2C2×#1062276311yescharacteristic
536C2#1307812511yescharacteristic
537C2#1308042811yescharacteristic
538C2#1308094211yescharacteristic
539C2#1308124811yescharacteristic
540C2#1308141311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#486C2
socleC23×C11C22×D4
prime radicalC2×#10622685C2
hypercenterC2×#486D11
hypocenterC11#25318
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. #13073570C2semidirect
3. #13071681C2semidirect
4. #13070022C2semidirect
5. #13069925C2semidirect
6. #13069569C2semidirect
7. #13069334C2semidirect
8. #13068962C2semidirect
9. #13068614C2semidirect
10. C4×#66885C2semidirect
11. C2×C11×#486C2semidirect
158. C4⋊Dic11D8semidirect
168. C2×#486D11semidirect
437. C11#25318semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
#130735702
#130716812
#130700222
#130699252
#130695692
#130693342
#130689622
#130686142
C4×#668852
C2×C11×#4862
#2531811