Finite Group Databasebeta

← #14676500

Subgroups — #14676500

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic
3C2×#10622545C211yesmaximal, characteristic
4#13066886C212yesmaximal
5#13066882C212yesmaximal
6#13066851C211yesmaximal, characteristic
7#13066849C211yesmaximal, characteristic
8#13066848C211yesmaximal, characteristic
9#13066842C212yesmaximal
10#13066841C212yesmaximal
11C11×#1436C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×Dic11⋊C4C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17C22×C4×Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C2×#66940—24no—
22C2×#66940—24no—
23C2×#66940C418yescomplemented
24C2×C11×#95C2212yes—
25C2×C11×#95C2212yes—
26C2×C11×#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38#10622545—24no—
39#10622264—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×Dic22—24no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—24no—
55C22×Dic22C2×C414yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4C2×C414yes—
59C2×C42×C11—22no—
60C2×C42×C11—24no—
61C2×Dic11⋊C4—22no—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4C2×C414yes—
66C2×Dic11⋊C4C2×C414yes—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11C2×C414yes—
74C2×C4×Dic11C2×C414yes—
75C2×C4×Dic11C2×C414yes—
76C2×C4×Dic11D414yes—
77C2×C4×Dic11D414yes—
78#66940—232no—
79C11×#95—22no—
80C11×#95—24no—
81C11×#95—24no—
82C11⋊#95—22no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93#13961—111nomaximal, Sylow
94C24×C11C2411yescharacteristic
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
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—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11#4114yes—
123C22×C4×C11#4114yes—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—22no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11C22×C412yes—
149C22×Dic11C22×C412yes—
150C22×Dic11C22×C412yes—
151C22×Dic11C22×C412yes—
152C22×Dic11C2×D412yes—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155C22×Dic11C2×D412yes—
156C22×Dic11#4114yes—
157C22×Dic11#4114yes—
158C2×Dic22—216no—
159C2×Dic22—216no—
160C2×Dic22—28no—
161C2×Dic22—28no—
162C2×Dic22—28no—
163C11×C4⋊C4—28no—
164C42×C11—28no—
165Dic11⋊C4—28no—
166Dic11⋊C4—28no—
167C4×Dic11—28no—
168C4×Dic11—28no—
169C4×Dic11—28no—
170C4×Dic11C22⋊C4116yes—
171C22×C4×Q8—111no—
172C2×#383—111no—
173C2×#376—111no—
174#1446—112no—
175#1445—112no—
176#1436—111no—
177#1436—111no—
178#1436—111no—
179#1436D1111yescharacteristic
180#1434—112no—
181#1434—112no—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D411yescharacteristic
185C23×C11C2×#4112yes—
186C23×C11C2×#4112yes—
187C23×C11C2×#4112yes—
188C23×C11C2×#4112yes—
189C23×C112−1+412yes—
190C23×C112−1+412yes—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—42no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
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×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11C2×C22⋊C414yes—
219C2×C4×C11#11714yes—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—42no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11C2×C22⋊C414yes—
252C2×Dic11C2×C22⋊C414yes—
253C2×Dic11#11714yes—
254Dic22—232no—
255C23×Q8—111no—
256C2×C4×Q8—118no—
257C2×C4×Q8—224no—
258C2×C4×Q8—224no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4C2×D1111yescharacteristic
262C22×C42—111no—
263C22×C42—111no—
264C22×C42—111no—
265C22×C42—111no—
266C22×C42C2×D1111yescharacteristic
267#383—224no—
268#376—224no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—112no—
277C2×#95—111no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95C2×D1112yes—
281C2×#95C2×D1112yes—
282C2×#95C2×D1111yescharacteristic
283C22×C11C22×C22⋊C411yescharacteristic
284C22×C11C2×#11711yescharacteristic
285C22×C11C2×#11711yescharacteristic
286C22×C11C4×#4112yes—
287C22×C11#51912yes—
288C22×C11#52512yes—
289C22×C11#52512yes—
290C22×C11#52511yescharacteristic
291C22×C11#52511yescharacteristic
292C22×C11#53212yes—
293C22×C11#53611yescharacteristic
294C22×C11#53612yes—
295C22×C11#53611yescharacteristic
296C22×C11#55212yes—
297C22×C11#55212yes—
298C22×C11#55212yes—
299C22×C11#55212yes—
300C22×C11#55612yes—
301C22×C11#55612yes—
302C22×C11#55612yes—
303C22×C11#55612yes—
304C4×C11—24no—
305C4×C11—24no—
306C4×C11—44no—
307C4×C11—42no—
308C4×C11—82no—
309Dic11—24no—
310Dic11—24no—
311Dic11—24no—
312Dic11—44no—
313Dic11—42no—
314Dic11—82no—
315C22×Q8—114no—
316C22×Q8—222no—
317C22×Q8—222no—
318C22×Q8—224no—
319C22×Q8—224no—
320C23×C4—111no—
321C23×C4—111no—
322C23×C4—111no—
323C23×C4—111no—
324C23×C4—112no—
325C23×C4—112no—
326C23×C4C22×D1112yes—
327C23×C4C22×D1111yescharacteristic
328C23×C4C22×D1112yes—
329C23×C4C22×D1111yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C4×Q8—2232no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—114no—
335C2×C4⋊C4—114no—
336C2×C4⋊C4—222no—
337C2×C4⋊C4—222no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4C4×D1114yes—
341C2×C42—22no—
342C2×C42—24no—
343C2×C42—114no—
344C2×C42—114no—
345C2×C42—114no—
346C2×C42—114no—
347C2×C42—114no—
348C2×C42—222no—
349C2×C42—222no—
350C2×C42—222no—
351C2×C42—222no—
352C2×C42—224no—
353C2×C42—222no—
354#95—24no—
355#95—22no—
356#95—24no—
357#95—224no—
358#95—224no—
359#95—224no—
360#95—224no—
361#95—224no—
362#95—224no—
363#95—224no—
364#95—224no—
365#95—224no—
366#95—222no—
367#95—224no—
368C2×C11#228011yescharacteristic
369C2×C11#229711yescharacteristic
370C2×C11#231011yescharacteristic
371C2×C11#235612yes—
372C2×C11#235612yes—
373C2×C11#259912yes—
374C2×C11#259912yes—
375C2×C11#260412yes—
376C2×C11#260412yes—
377C24C23×D1111yescharacteristic
378C2×Q8—228no—
379C2×Q8—228no—
380C2×Q8—2216no—
381C2×Q8—2216no—
382C2×Q8—228no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—114no—
413C22×C4—112no—
414C22×C4—114no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—221no—
418C22×C4—221no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4C2×C4×D1112yes—
440C22×C4C2×C4×D1112yes—
441C22×C4C2×C4×D1112yes—
442C22×C4#433914yes—
443C22×C4D4×D1112yes—
444C22×C4D4×D1112yes—
445C22×C4#434114yes—
446C4⋊C4—28no—
447C4⋊C4—228no—
448C4⋊C4—228no—
449C42—28no—
450C42—1116no—
451C42—228no—
452C42—228no—
453C42—228no—
454C11#1396111yescharacteristic, complemented, Sylow
455C23C22×C4×D1111yescharacteristic
456C23C2×#433912yes—
457C23C2×D4×D1111yescharacteristic
458C23C2×D4×D1111yescharacteristic
459C23C2×#434112yes—
460C23#6704012yes—
461C23#41×D1112yes—
462C23#41×D1112yes—
463C23#6704312yes—
464Q8—2232no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—114no—
493C2×C4—114no—
494C2×C4—114no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—441no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—441no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4#6692514yes—
527C2×C4C22⋊C4×D1114yes—
528C22C2×#6692511yescharacteristic
529C22C2×C22⋊C4×D1111yescharacteristic
530C22#1062304412yes—
531C22D11×#11711yescharacteristic
532C22#1062306012yes—
533C22C4×#434112yes—
534C22#1062307312yes—
535C22#1062307812yes—
536C22#1062307812yes—
537C22#1062309912yes—
538C22#1062310312yes—
539C22#1062311711yescharacteristic
540C22#1062312712yes—
541C22#1062315912yes—
542C22#1062317212yes—
543C22#1062318112yes—
544C22#1062318711yescharacteristic
545C22#1062320611yescharacteristic
546C22#1062322412yes—
547C22#1062323312yes—
548C22#1062325511yescharacteristic
549C4—24no—
550C4—24no—
551C4—44no—
552C4—42no—
553C4—82no—
554C4—224no—
555C4—224no—
556C4—224no—
557C4—444no—
558C4—442no—
559C4—882no—
560C2#1307099711yescharacteristic
561C2#1307110111yescharacteristic
562C2#1307119911yescharacteristic
563C2#1307157712yes—
564C2#1307157812yes—
565C2#1307418912yes—
566C2#1307419112yes—
567C2#1307425012yes—
568C2#1307425212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1436D11
hypocenterC11#13961
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
23. C2×#66940C4semidirect
454. C11#13961semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106222642
C2×#106225452
#130668862
#130668822
#130668512
#130668492
#130668482
#130668422
#130668412
C11×#14362
#1396111