Finite Group Databasebeta

← #14960588

Subgroups — #14960588

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623154C211yesmaximal, characteristic, complemented
2C22×#66949C211yesmaximal, characteristic
3#13076904C211yesmaximal, characteristic
4#13076900C211yesmaximal, characteristic
5#13075088C214yesmaximal, complemented
6#13075084C214yesmaximal, complemented
7#13074933C214yesmaximal, complemented
8#13074930C214yesmaximal, complemented
9#13074429C211yesmaximal, characteristic, complemented
10#13073773C212yesmaximal
11#13072900C212yesmaximal, complemented
12#13072889C212yesmaximal
13#13072258C212yesmaximal, complemented
14#13071218C211yesmaximal, characteristic, complemented
15C11×#2627C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66999C2212yes—
21C2×#66997C2212yescomplemented
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27#10623154—28no—
28C2×#66950C2212yes—
29C2×#66949—28no—
30C2×#66949C2214yes—
31C2×#66949C2214yes—
32C2×#66942C2212yescomplemented
33C2×#66942C2212yescomplemented
34C2×#66941C2212yescomplemented
35C2×#66941C2214yescomplemented
36C2×#66931C2212yes—
37C2×#66930C2212yes—
38C11×#400C2212yescomplemented
39C11×#398C2214yescomplemented
40C11×#395C2212yescomplemented
41C11×#385C2212yes—
42C11×#381C2212yes—
43C11×#380C2211yescharacteristic
44#10622825C2211yescharacteristic
45#10622824C2212yes—
46#10622823C2212yes—
47#10622605C2214yes—
48#10622603C2214yes—
49#10622602C2214yes—
50#10622600C2212yes—
51#10622600C2212yes—
52#10622599C2212yescomplemented
53#10622597C2214yescomplemented
54#10622592C2214yescomplemented
55#10622592C2212yescomplemented
56#10622591C2214yescomplemented
57#10622568C2212yes—
58#10622568C2212yes—
59#10622563C2212yes—
60#10622559C2212yes—
61#10622556C2212yes—
62C22⋊C4×Dic11C2212yes—
63#10622288C2214yes—
64#10622288C2214yes—
65#10622286C2214yes—
66#10622283C2214yes—
67#10622282C2214yes—
68#10622282C2214yes—
69#10622281C2214yes—
70#10622271C2214yescomplemented
71#10622270C2214yescomplemented
72#10622269C2214yescomplemented
73#10622268C2214yescomplemented
74#10622267C2214yescomplemented
75#10622265C2214yescomplemented
76#10622259C2214yescomplemented
77C24×D11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C22×C4×D11—24no—
86C22×C4×D11—44no—
87C22×C4×D11C2312yes—
88C22×C4×D11C2312yes—
89C22×Dic22—24no—
90C22×Dic22—44no—
91C22×Dic22C2314yes—
92C22×Dic22C2312yes—
93C22×Dic22C2311yescharacteristic
94C11×C22⋊Q8—24no—
95C2×C11×C4⋊C4—24no—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2312yes—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C22⋊C4C2312yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C22⋊Dic11C2312yes—
105C2×C22⋊Dic11C2312yes—
106#66999—44no—
107#66997—28no—
108C2×(C2×D11)⋊C4—24no—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2314yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114C2×(C2×D11)⋊C4C2314yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2312yes—
120#66977—24no—
121C2×Dic11⋊C4—24no—
122C2×Dic11⋊C4D418yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2312yes—
129C2×Dic11⋊C4C2314yes—
130C2×Dic11⋊C4C2314yes—
131C2×Dic11⋊C4C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2314yes—
136#66950—44no—
137#66949—216no—
138#66949—216no—
139#66942—28no—
140#66942—28no—
141#66941—28no—
142#66941—48no—
143#66931—28no—
144#66930—28no—
145C11×#95C2314yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2312yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158#36708—111nomaximal, Sylow
159C24×C11C2411yescharacteristic
160C23×D11—22no—
161C23×D11—24no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—42no—
165C23×D11C2412yes—
166C2×Q8×C11—22no—
167C2×Q8×C11—42no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—42no—
173C22×C4×C11—42no—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2414yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2411yescharacteristic
181C22×C4×C11C2411yescharacteristic
182C22×Dic11—24no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—42no—
187C22×Dic11C2×D414yes—
188C22×Dic11C2×D414yes—
189C22×Dic11C2414yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C22×Dic11C2412yes—
194C22×Dic11C2412yes—
195C2×C4×D11—24no—
196C2×C4×D11—24no—
197C2×C4×D11—24no—
198C2×C4×D11—24no—
199C2×C4×D11—42no—
200C2×C4×D11—42no—
201C2×C4×D11—416no—
202C2×Dic22—28no—
203C2×Dic22—28no—
204C2×Dic22—24no—
205C2×Dic22—22no—
206C2×Dic22—44no—
207C2×Dic22—44no—
208C2×Dic22—42no—
209C2×Dic22—416no—
210C11×C4⋊C4—24no—
211C11×C4⋊C4—22no—
212C11×C4⋊C4—24no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—44no—
215C11×C4⋊C4—42no—
216C11×C22⋊C4—24no—
217C11×C22⋊C4—24no—
218C22⋊Dic11—24no—
219C22⋊Dic11—24no—
220(C2×D11)⋊C4—28no—
221(C2×D11)⋊C4—28no—
222(C2×D11)⋊C4—28no—
223(C2×D11)⋊C4—28no—
224(C2×D11)⋊C4—44no—
225(C2×D11)⋊C4—44no—
226C4⋊Dic11—24no—
227C4⋊Dic11—28no—
228C4⋊Dic11—22no—
229C4⋊Dic11—42no—
230Dic11⋊C4—24no—
231Dic11⋊C4—24no—
232Dic11⋊C4—24no—
233Dic11⋊C4—24no—
234Dic11⋊C4—28no—
235Dic11⋊C4—28no—
236Dic11⋊C4—24no—
237Dic11⋊C4—44no—
238Dic11⋊C4C2×D418yes—
239Dic11⋊C4C2×D418yes—
240C4×Dic11—24no—
241C4×Dic11—24no—
242C4×Dic11—44no—
243C2×#544—111no—
244C22×C22⋊Q8—111no—
245#2848—111no—
246#2848—111no—
247#2690—114no—
248#2690—114no—
249#2677—114no—
250#2677—114no—
251#2627—111no—
252#2627D1111yescharacteristic, complemented
253#2561—112no—
254#2484—112no—
255#2482—112no—
256#2434—112no—
257#2313—111no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11C22×D412yes—
261C23×C112−1+412yes—
262C23×C112−1+412yes—
263C23×C11C2511yescharacteristic
264C22×D11—28no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—22no—
270C22×D11—22no—
271C22×D11—48no—
272C22×D11—48no—
273C22×D11—44no—
274C22×D11—44no—
275C22×D112−1+414yes—
276Q8×C11—82no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—24no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—44no—
292C2×C4×C11—44no—
293C2×C4×C11—44no—
294C2×C4×C11C22×D412yes—
295C2×C4×C11C22×D412yes—
296C2×Dic11—28no—
297C2×Dic11—28no—
298C2×Dic11—22no—
299C2×Dic11—24no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—44no—
311C2×Dic11C22×D414yes—
312C2×Dic11C22×D414yes—
313C2×Dic11H(5,𝔽2)14yes—
314C4×D11—48no—
315C4×D11—48no—
316Dic22—416no—
317Dic22—84no—
318Dic22—82no—
319C23×Q8—111no—
320C24×C4—111no—
321#544—228no—
322C2×C4⋊Q8—112no—
323C2×C4⋊Q8—112no—
324C2×C4⋊Q8—114no—
325C2×#125—112no—
326C2×#125—112no—
327C2×C22⋊Q8—111no—
328C2×C22⋊Q8—112no—
329C2×C22⋊Q8—114no—
330C2×C22⋊Q8—114no—
331C2×C22⋊Q8—112no—
332C2×C22⋊Q8—112no—
333C2×C22⋊Q8—228no—
334C2×C22⋊Q8C2×D1111yescharacteristic
335C2×#117—112no—
336C22×C4⋊C4—111no—
337C22×C4⋊C4—111no—
338C22×C4⋊C4C2×D1111yescharacteristic
339C22×C22⋊C4—111no—
340C22×C22⋊C4—111no—
341#400—112no—
342#400—114no—
343#400C2×D1112yescomplemented
344#399—114no—
345#398—114no—
346#398—114no—
347#398C2×D1114yescomplemented
348#397—114no—
349#397—114no—
350#395—112no—
351#395—114no—
352#395—114no—
353#395C2×D1112yescomplemented
354#393—114no—
355#391—114no—
356#388—114no—
357#388—114no—
358#388—114no—
359#388—114no—
360#387—114no—
361#387—114no—
362#387—114no—
363#387—114no—
364#385—112no—
365#385—114no—
366#385—112no—
367#385—112no—
368#385—114no—
369#385C2×D1112yes—
370#381—112no—
371#381—112no—
372#381C2×D1112yes—
373#380—111no—
374#380—112no—
375#380—112no—
376#380C2×D1111yescharacteristic
377#379—112no—
378#379—112no—
379C4×C22⋊C4—112no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—24no—
383C22×C11—24no—
384C22×C11#53614yes—
385C22×C11C23×D411yescharacteristic
386C22×C11C2×H(5,𝔽2)12yes—
387C22×C11C2×2−1+411yescharacteristic
388C22×C11C2×2−1+411yescharacteristic
389C22×C11C2×2−1+412yes—
390C2×D11—24no—
391C2×D11—24no—
392C2×D11—24no—
393C2×D11—416no—
394C2×D11—42no—
395C2×D11—42no—
396C2×D11—42no—
397C2×D11—42no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—42no—
401C4×C11—42no—
402C4×C11—42no—
403C4×C11—42no—
404C4×C11—44no—
405Dic11—24no—
406Dic11—24no—
407Dic11—24no—
408Dic11—42no—
409Dic11—42no—
410Dic11—44no—
411C25—111no—
412C22×Q8—114no—
413C22×Q8—111no—
414C22×Q8—112no—
415C22×Q8—224no—
416C22×Q8—444no—
417C22×Q8C22×D1111yescharacteristic
418C23×C4—111no—
419C23×C4—111no—
420C23×C4—111no—
421C23×C4—112no—
422C23×C4—112no—
423C23×C4—224no—
424C23×C4—444no—
425C23×C4C22×D1111yescharacteristic
426C23×C4C22×D1111yescharacteristic
427C23×C4C22×D1111yescharacteristic
428C4⋊Q8—228no—
429C4⋊Q8—228no—
430C4⋊Q8—448no—
431#125—228no—
432#125—228no—
433C22⋊Q8—24no—
434C22⋊Q8—228no—
435C22⋊Q8—2216no—
436C22⋊Q8—2216no—
437C22⋊Q8—224no—
438C22⋊Q8—444no—
439C22⋊Q8—444no—
440#117—228no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—118no—
443C2×C4⋊C4—112no—
444C2×C4⋊C4—112no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—112no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—111no—
449C2×C4⋊C4—112no—
450C2×C4⋊C4—112no—
451C2×C4⋊C4—112no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4—114no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—114no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4C22×D1112yes—
459C2×C4⋊C4C22×D1112yes—
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1112yes—
462C2×C4⋊C4C22×D1112yes—
463C2×C4⋊C4C22×D1114yes—
464C2×C22⋊C4—112no—
465C2×C22⋊C4—112no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—114no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4C22×D1112yes—
475C2×C22⋊C4C22×D1112yes—
476C2×C42—112no—
477C2×C42—112no—
478C2×C42—114no—
479#95—114no—
480#95—112no—
481#95—114no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95—114no—
486#95—114no—
487#95—114no—
488#95C22×D1112yes—
489#95C22×D1114yes—
490#95C22×D1114yes—
491#95C22×D1114yes—
492C2×C11—24no—
493C2×C11C2×#53611yescharacteristic
494C2×C11#348411yescharacteristic
495C2×C11#348611yescharacteristic
496C2×C11#353812yes—
497C2×C11#353812yes—
498D11—44no—
499C24—112no—
500C24—224no—
501C24—222no—
502C24—222no—
503C24—222no—
504C24—442no—
505C24C23×D1111yescharacteristic
506C2×Q8—22no—
507C2×Q8—42no—
508C2×Q8—228no—
509C2×Q8—228no—
510C2×Q8—224no—
511C2×Q8—222no—
512C2×Q8—444no—
513C2×Q8—442no—
514C2×Q8—444no—
515C2×Q8—4416no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—114no—
523C22×C4—112no—
524C22×C4—112no—
525C22×C4—112no—
526C22×C4—114no—
527C22×C4—114no—
528C22×C4—112no—
529C22×C4—112no—
530C22×C4—224no—
531C22×C4—224no—
532C22×C4—224no—
533C22×C4—222no—
534C22×C4—222no—
535C22×C4—222no—
536C22×C4—224no—
537C22×C4—224no—
538C22×C4—442no—
539C22×C4—442no—
540C22×C4—4416no—
541C22×C4—442no—
542C22×C4D4×D1114yes—
543C22×C4C23×D1114yes—
544C22×C4C23×D1112yes—
545C22×C4C23×D1112yes—
546C22×C4C23×D1112yes—
547C22×C4C23×D1112yes—
548C22×C4C23×D1111yescharacteristic
549C22×C4C23×D1111yescharacteristic
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—22no—
553C4⋊C4—24no—
554C4⋊C4—42no—
555C4⋊C4—44no—
556C4⋊C4—118no—
557C4⋊C4—118no—
558C4⋊C4—228no—
559C4⋊C4—224no—
560C4⋊C4—224no—
561C4⋊C4—224no—
562C4⋊C4—224no—
563C4⋊C4—224no—
564C4⋊C4—228no—
565C4⋊C4—228no—
566C4⋊C4—222no—
567C4⋊C4—224no—
568C4⋊C4—442no—
569C4⋊C4—444no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—228no—
573C22⋊C4—228no—
574C22⋊C4—228no—
575C22⋊C4—228no—
576C22⋊C4—224no—
577C22⋊C4—224no—
578C22⋊C4—444no—
579C22⋊C4—444no—
580C42—224no—
581C42—224no—
582C42—444no—
583C11#3670811yescharacteristic, complemented, Sylow
584C23—22no—
585C23—22no—
586C23—114no—
587C23—228no—
588C23—222no—
589C23—222no—
590C23—222no—
591C23—222no—
592C23—222no—
593C23—222no—
594C23—448no—
595C23—448no—
596C23—444no—
597C23—444no—
598C23C2×D4×D1112yes—
599C23#6704012yes—
600C23#6704312yes—
601C23C24×D1111yescharacteristic
602Q8—82no—
603Q8—4416no—
604Q8—882no—
605Q8—884no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—114no—
624C2×C4—114no—
625C2×C4—114no—
626C2×C4—228no—
627C2×C4—228no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—224no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—222no—
635C2×C4—224no—
636C2×C4—224no—
637C2×C4—224no—
638C2×C4—224no—
639C2×C4—224no—
640C2×C4—448no—
641C2×C4—448no—
642C2×C4—444no—
643C2×C4C2×D4×D1112yes—
644C2×C4C2×D4×D1112yes—
645C22—22no—
646C22—22no—
647C22—24no—
648C22—24no—
649C22—224no—
650C22—224no—
651C22—224no—
652C22—4416no—
653C22—442no—
654C22—442no—
655C22—442no—
656C22—442no—
657C22#1062315914yes—
658C22C22×D4×D1111yescharacteristic
659C22C2×#6704011yescharacteristic
660C22C2×#6704311yescharacteristic
661C22D11×H(5,𝔽2)12yes—
662C22D11×2−1+412yes—
663C4—22no—
664C4—22no—
665C4—42no—
666C4—42no—
667C4—42no—
668C4—42no—
669C4—44no—
670C4—224no—
671C4—224no—
672C4—224no—
673C4—442no—
674C4—442no—
675C4—444no—
676C2—24no—
677C2—444no—
678C2C2×#1062315911yescharacteristic
679C2#1308224811yescharacteristic
680C2#1308226511yescharacteristic
681C2#1308285812yes—
682C2#1308286312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2627C2
prime radicalC24×D11C23
hypercenter#2627D11
hypocenterC11#36708
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2627

Complements

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

NH ≅ G/Ntype
1. C2×#10623154C2semidirect
5. #13075088C2semidirect
6. #13075084C2semidirect
7. #13074933C2semidirect
8. #13074930C2semidirect
9. #13074429C2semidirect
11. #13072900C2semidirect
13. #13072258C2semidirect
14. #13071218C2semidirect
15. C11×#2627C2semidirect
21. C2×#66997C22semidirect
32. C2×#66942C22semidirect
33. C2×#66942C22semidirect
34. C2×#66941C22semidirect
35. C2×#66941C22semidirect
38. C11×#400C22semidirect
39. C11×#398C22semidirect
40. C11×#395C22semidirect
52. #10622599C22semidirect
53. #10622597C22semidirect
54. #10622592C22semidirect
55. #10622592C22semidirect
56. #10622591C22semidirect
70. #10622271C22semidirect
71. #10622270C22semidirect
72. #10622269C22semidirect
73. #10622268C22semidirect
74. #10622267C22semidirect
75. #10622265C22semidirect
76. #10622259C22semidirect
252. #2627D11semidirect
343. #400C2×D11semidirect
347. #398C2×D11semidirect
353. #395C2×D11semidirect
583. C11#36708semidirect

Maximal subgroups

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

subgroupindex
C2×#106231542
C22×#669492
#130769042
#130769002
#130750882
#130750842
#130749332
#130749302
#130744292
#130737732
#130729002
#130728892
#130722582
#130712182
C11×#26272
#3670811