Finite Group Databasebeta

← #14675626

Subgroups — #14675626

Order 2816.

1398 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622599C211yesmaximal, characteristic
2C2×C4⋊C4×Dic11C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4#13066883C211yesmaximal, characteristic
5#13066876C212yesmaximal
6#13066875C211yesmaximal, characteristic
7#13066872C212yesmaximal
8#95×Dic11C211yesmaximal, characteristic
9#95×Dic11C212yesmaximal
10#95×Dic11C212yesmaximal
11C11×#1441C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4×Dic11C2212yes—
17C22×C4×Dic11C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C2×C11×#95C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35#10622599C418yescomplemented
36C4⋊C4×Dic11—24no—
37C4⋊C4×Dic11—24no—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C414yes—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—22no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11C2×C414yes—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—24no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—24no—
65C2×C4×Dic11—24no—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—24no—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—24no—
71C2×C4×Dic11D414yes—
72C2×C4×Dic11Q814yes—
73C11×#95—24no—
74C11×#95—22no—
75C11×#95—24no—
76C11⋊#95—22no—
77C11⋊#95—24no—
78C11⋊#95—24no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—22no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95C2×C414yes—
85C11⋊#95C2×C418yes—
86C11⋊#95C2×C418yes—
87C4×#400—111nomaximal, Sylow
88C24×C11C2411yescharacteristic
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×Q812yes—
116C22×C4×C11#4114yes—
117C22×C4×C11#4114yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×Dic11—21no—
121C22×Dic11—22no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11C22×C414yes—
145C22×Dic11C22×C414yes—
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D412yes—
148C22×Dic11C2×Q812yes—
149C22×Dic11C2×Q812yes—
150C22×Dic11#4112yes—
151C22×Dic11#4112yes—
152C22×Dic11#4114yes—
153C22×Dic11#4114yes—
154C11×C4⋊C4—28no—
155C11×C4⋊C4—28no—
156C4⋊Dic11—28no—
157C4⋊Dic11—28no—
158C4×Dic11—28no—
159C4×Dic11—28no—
160C4×Dic11—44no—
161C4×Dic11—48no—
162C4×Dic11—48no—
163C2×#400—111no—
164C2×C4×C4⋊C4—111no—
165C2×C4×C4⋊C4—111no—
166#1445—111no—
167#1443—112no—
168#1442—112no—
169#1442—111no—
170#1441D1111yescharacteristic
171C4×#95—111no—
172C4×#95—112no—
173C4×#95—112no—
174C23×C11C23×C411yescharacteristic
175C23×C11C22×D411yescharacteristic
176C23×C11C22×Q811yescharacteristic
177C23×C11C2×#4111yescharacteristic
178C23×C11C2×#4111yescharacteristic
179C23×C11C2×#4112yes—
180C23×C11C2×#4112yes—
181C23×C11C2×#4111yescharacteristic
182C23×C11C2×#4112yes—
183C23×C11C2×#4111yescharacteristic
184C23×C11C2×#4112yes—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11C4×D414yes—
215C2×C4×C11C4×Q814yes—
216C2×Dic11—24no—
217C2×Dic11—24no—
218C2×Dic11—24no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—24no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11C22⋊Q814yes—
246C2×Dic11#12314yes—
247C2×Dic11#12414yes—
248C2×Dic11#12518yes—
249C2×Dic11#12618yes—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4C2×D1111yescharacteristic
253C22×C4⋊C4C2×D1111yescharacteristic
254C22×C42—111no—
255C22×C42—111no—
256C22×C42—112no—
257C22×C42—111no—
258C22×C42—112no—
259#400—118no—
260C4×C4⋊C4—224no—
261C4×C4⋊C4—224no—
262C2×#95—112no—
263C2×#95—111no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—111no—
272C2×#95—111no—
273C2×#95C2×D1112yes—
274C2×#95C2×D1112yes—
275C2×#95C2×D1111yescharacteristic
276C22×C11C2×C4×D411yescharacteristic
277C22×C11C2×C4×Q811yescharacteristic
278C22×C11C4×#4111yescharacteristic
279C22×C11C4×#4112yes—
280C22×C11C4×#4112yes—
281C22×C11C2×C22⋊Q811yescharacteristic
282C22×C11C2×#12311yescharacteristic
283C22×C11#52511yescharacteristic
284C22×C11#52511yescharacteristic
285C22×C11C2×#12411yescharacteristic
286C22×C11C2×#12512yes—
287C22×C11C2×#12612yes—
288C22×C11#52912yes—
289C22×C11#52911yescharacteristic
290C22×C11#52912yes—
291C22×C11#52912yes—
292C22×C11#52912yes—
293C22×C11#52912yes—
294C22×C11#52912yes—
295C22×C11#52912yes—
296C22×C11#53211yescharacteristic
297C22×C11#53312yes—
298C22×C11#53311yescharacteristic
299C4×C11—24no—
300C4×C11—24no—
301C4×C11—44no—
302C4×C11—44no—
303C4×C11—42no—
304Dic11—44no—
305Dic11—42no—
306Dic11—42no—
307Dic11—42no—
308Dic11—44no—
309Dic11#40018yescomplemented
310C23×C4—111no—
311C23×C4—112no—
312C23×C4—111no—
313C23×C4—111no—
314C23×C4—112no—
315C23×C4—111no—
316C23×C4C22×D1111yescharacteristic
317C23×C4C22×D1112yes—
318C23×C4C22×D1112yes—
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1111yescharacteristic
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—222no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4C4×D1114yes—
332C2×C42—114no—
333C2×C42—114no—
334C2×C42—222no—
335C2×C42—222no—
336C2×C42—224no—
337C2×C42—222no—
338C2×C42—224no—
339C2×C42—224no—
340C2×C42—224no—
341C2×C42—224no—
342C2×C42—224no—
343C2×C42—224no—
344C2×C42—224no—
345#95—24no—
346#95—22no—
347#95—24no—
348#95—114no—
349#95—118no—
350#95—118no—
351#95—224no—
352#95—222no—
353#95—224no—
354#95—222no—
355#95—224no—
356#95—224no—
357#95—224no—
358#95—224no—
359C2×C11C4×#12311yescharacteristic
360C2×C11C4×C22⋊Q811yescharacteristic
361C2×C11C4×#12411yescharacteristic
362C2×C11C4×#12612yes—
363C2×C11C4×#12512yes—
364C2×C11C2×#40011yescharacteristic
365C2×C11#239511yescharacteristic
366C2×C11#239611yescharacteristic
367C2×C11#239811yescharacteristic
368C2×C11#240112yes—
369C2×C11#240212yes—
370C24C23×D1111yescharacteristic
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—112no—
394C22×C4—112no—
395C22×C4—112no—
396C22×C4—114no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—114no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—221no—
404C22×C4—222no—
405C22×C4—221no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4C2×C4×D1112yes—
428C22×C4C2×C4×D1112yes—
429C22×C4C2×C4×D1112yes—
430C22×C4D4×D1112yes—
431C22×C4#434114yes—
432C22×C4#434112yes—
433C22×C4#434112yes—
434C22×C4Q8×D1112yes—
435C22×C4#434314yes—
436C4⋊C4—28no—
437C4⋊C4—28no—
438C4⋊C4—228no—
439C4⋊C4—228no—
440C42—228no—
441C42—228no—
442C42—448no—
443C42—444no—
444C42—448no—
445C11C4×#40011yescharacteristic, complemented, Sylow
446C23C22×C4×D1111yescharacteristic
447C23C2×D4×D1111yescharacteristic
448C23C2×#434112yes—
449C23C2×#434111yescharacteristic
450C23C2×#434111yescharacteristic
451C23C2×Q8×D1111yescharacteristic
452C23C2×#434312yes—
453C23#41×D1111yescharacteristic
454C23#41×D1112yes—
455C23#41×D1112yes—
456C23#41×D1111yescharacteristic
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—24no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—118no—
487C2×C4—114no—
488C2×C4—114no—
489C2×C4—114no—
490C2×C4—118no—
491C2×C4—222no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—442no—
505C2×C4—441no—
506C2×C4—441no—
507C2×C4—442no—
508C2×C4—441no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—441no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4(C22⋊D11)⋊C414yes—
521C2×C4#6694014yes—
522C22C2×(C22⋊D11)⋊C411yescharacteristic
523C22C2×#6694011yescharacteristic
524C22#1062305311yescharacteristic
525C22C4×#434112yes—
526C22C4×#434312yes—
527C22#1062311711yescharacteristic
528C22#1062313112yes—
529C22#1062313112yes—
530C22#1062313111yescharacteristic
531C22#1062313711yescharacteristic
532C22#1062315311yescharacteristic
533C22#1062315512yes—
534C22#1062315512yes—
535C22#1062315512yes—
536C22D11×C22⋊Q811yescharacteristic
537C22#1062318012yes—
538C22D11×#12311yescharacteristic
539C22D11×#12411yescharacteristic
540C22D11×#12512yes—
541C22#1062322212yes—
542C22D11×#12612yes—
543C22#1062325611yescharacteristic
544C22#1062325912yes—
545C4—24no—
546C4—24no—
547C4—44no—
548C4—42no—
549C4—44no—
550C4—118no—
551C4—442no—
552C4—442no—
553C4—442no—
554C4—444no—
555C4—444no—
556C2#1307114111yescharacteristic
557C2#1307114411yescharacteristic
558C2#1307115911yescharacteristic
559C2#1307116612yes—
560C2#1307117512yes—
561C2D11×#40011yescharacteristic
562C2#1307188011yescharacteristic
563C2#1307188711yescharacteristic
564C2#1307190411yescharacteristic
565C2#1307191812yes—
566C2#1307192012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1441C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1441D11
hypocenterC11C4×#400
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
35. #10622599C4semidirect
309. Dic11#400semidirect
445. C11C4×#400semidirect

Maximal subgroups

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

subgroupindex
C2×#106225992
C2×C4⋊C4×Dic112
#130668832
#130668762
#130668752
#130668722
#95×Dic112
C11×#14412
C4×#40011