Finite Group Databasebeta

← #14960582

Subgroups — #14960582

Order 2816.

2326 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623154C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic
3#13076901C212yesmaximal
4#13075079C214yesmaximal, complemented
5#13075075C214yesmaximal, complemented
6#13074928C214yesmaximal, complemented
7#13074925C214yesmaximal, complemented
8#13074433C212yesmaximal, complemented
9#13073774C211yesmaximal, characteristic
10#13072900C212yesmaximal, complemented
11#13072887C212yesmaximal
12#13072261C211yesmaximal, characteristic, complemented
13#13072260C211yesmaximal, characteristic, complemented
14#13071216C211yesmaximal, characteristic, complemented
15C11×#2561C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C2×#66997C2212yescomplemented
22C2×#66997C2212yescomplemented
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×Dic11⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27#10623154—28no—
28C2×#66942C2212yescomplemented
29C2×#66942C2212yescomplemented
30C2×#66941C2212yescomplemented
31C2×#66931—28no—
32C2×#66931C2212yes—
33C2×#66931C2214yes—
34C2×#66931C2214yes—
35C2×#66931C2214yes—
36C2×#66930C2212yes—
37C2×#66922C2212yescomplemented
38C11×#397C2212yes—
39C11×#393C2212yes—
40C11×#388C2214yes—
41C11×#381C2212yes—
42C11×#379C2212yes—
43C4×C11×C22⋊C4C2211yescharacteristic
44#10622860C2212yes—
45#10622824C2212yes—
46C4×C22⋊Dic11C2211yescharacteristic
47#10622592C2214yescomplemented
48#10622587C2212yescomplemented
49#10622566C2212yes—
50#10622565C2214yes—
51#10622564C2214yes—
52#10622563C2212yes—
53#10622563C2212yes—
54#10622563C2214yes—
55#10622562C2214yes—
56#10622560C2212yes—
57#10622559C2212yes—
58#10622559C2212yes—
59#10622559C2214yes—
60#10622558C2214yes—
61#10622558C2214yes—
62#10622556C2212yes—
63#10622555C2212yes—
64#10622555C2214yes—
65#10622546C2214yescomplemented
66#10622542C2212yescomplemented
67#10622274C2214yescomplemented
68#10622273C2214yescomplemented
69#10622271C2214yescomplemented
70#10622270C2214yescomplemented
71#10622270C2214yescomplemented
72#10622269C2214yescomplemented
73#10622269C2214yescomplemented
74#10622267C2214yescomplemented
75#10622265C2214yescomplemented
76#10622265C2214yescomplemented
77C25×C11C2311yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×Dic11—24no—
82C23×Dic11—44no—
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2314yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C22×Dic22—24no—
89C22×Dic22—44no—
90C22×Dic22C2312yes—
91C22×Dic22C2312yes—
92C22×Dic22C2311yescharacteristic
93C22×Dic22C2312yes—
94C11×C22⋊Q8—24no—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—24no—
98C2×C11×C22⋊C4C2312yes—
99C2×C11×C22⋊C4C2312yes—
100C2×C11×C22⋊C4C2312yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yes—
104C2×C42×C11C2312yes—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11C2312yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2312yes—
109C2×C22⋊Dic11C2314yes—
110C2×C22⋊Dic11C2314yes—
111#66997—28no—
112#66997—44no—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2314yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2314yes—
119#66977—24no—
120C2×Dic11⋊C4—24no—
121C2×Dic11⋊C4D418yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2314yes—
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×Dic11C2312yes—
136#66942—28no—
137#66942—28no—
138#66941—28no—
139#66931—28no—
140#66931—216no—
141#66931—216no—
142#66931—48no—
143#66930—28no—
144#66922—44no—
145C11×#95C2312yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158#36708—111nomaximal, Sylow
159C24×C11—22no—
160C24×C11—24no—
161C24×C11—24no—
162C24×C11—42no—
163C24×C11C2412yes—
164C24×C11C2411yescharacteristic
165C2×Q8×C11—22no—
166C2×Q8×C11—42no—
167C22×C4×C11—22no—
168C22×C4×C11—24no—
169C22×C4×C11—42no—
170C22×C4×C11C2×D414yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×Dic11—24no—
178C22×Dic11—28no—
179C22×Dic11—28no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—24no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—44no—
186C22×Dic11—416no—
187C22×Dic11C2×D414yes—
188C22×Dic11C2×D414yes—
189C22×Dic11C2414yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193C22×Dic11C2412yes—
194C22×Dic11C2412yes—
195C22×Dic11C2412yes—
196C2×Dic22—24no—
197C2×Dic22—24no—
198C2×Dic22—24no—
199C2×Dic22—24no—
200C2×Dic22—24no—
201C2×Dic22—22no—
202C2×Dic22—42no—
203C2×Dic22—42no—
204C2×Dic22—42no—
205C2×Dic22—44no—
206C2×Dic22—416no—
207C11×C4⋊C4—24no—
208C11×C4⋊C4—22no—
209C11×C22⋊C4—24no—
210C11×C22⋊C4—28no—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—24no—
213C11×C22⋊C4—24no—
214C11×C22⋊C4—44no—
215C42×C11—42no—
216C22⋊Dic11—28no—
217C22⋊Dic11—24no—
218C22⋊Dic11—28no—
219C22⋊Dic11—24no—
220C22⋊Dic11—44no—
221C4⋊Dic11—28no—
222C4⋊Dic11—24no—
223C4⋊Dic11—28no—
224C4⋊Dic11—22no—
225C4⋊Dic11—44no—
226Dic11⋊C4—24no—
227Dic11⋊C4—24no—
228Dic11⋊C4—28no—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231Dic11⋊C4—28no—
232Dic11⋊C4—24no—
233Dic11⋊C4—44no—
234Dic11⋊C4—44no—
235Dic11⋊C4C2×D418yes—
236Dic11⋊C4C2×D418yes—
237C4×Dic11—24no—
238C4×Dic11—24no—
239C4×Dic11—42no—
240C2×#544—111no—
241C22×C22⋊Q8—111no—
242#2848—112no—
243#2690—114no—
244#2690—114no—
245#2677—114no—
246#2677—114no—
247#2627—112no—
248#2561—111no—
249#2561D1111yescharacteristic
250#2484—112no—
251#2482—112no—
252#2434—111no—
253#2434—111no—
254#2313—111no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—28no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—22no—
261C23×C11—24no—
262C23×C11—416no—
263C23×C11—44no—
264C23×C11—44no—
265C23×C11C22×D412yes—
266C23×C112−1+414yes—
267C23×C112−1+414yes—
268C23×C11C2511yescharacteristic
269Q8×C11—82no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—44no—
282C2×C4×C11—44no—
283C2×C4×C11C22×D412yes—
284C2×C4×C11C22×D412yes—
285C2×Dic11—28no—
286C2×Dic11—28no—
287C2×Dic11—22no—
288C2×Dic11—24no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—22no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—44no—
302C2×Dic11—416no—
303C2×Dic11—44no—
304C2×Dic11C22×D414yes—
305C2×Dic11C22×D414yes—
306C2×Dic11H(5,𝔽2)14yes—
307Dic22—48no—
308Dic22—48no—
309Dic22—84no—
310Dic22—82no—
311C23×Q8—111no—
312C24×C4—111no—
313#544—228no—
314C2×C4⋊Q8—112no—
315C2×C4⋊Q8—112no—
316C2×C4⋊Q8—112no—
317C2×C4⋊Q8—112no—
318C2×#125—112no—
319C2×#125—112no—
320C2×C22⋊Q8—111no—
321C2×C22⋊Q8—112no—
322C2×C22⋊Q8—114no—
323C2×C22⋊Q8—114no—
324C2×C22⋊Q8—114no—
325C2×C22⋊Q8—228no—
326C2×C22⋊Q8C2×D1111yescharacteristic
327C2×#117—112no—
328C22×C4⋊C4—111no—
329C22×C4⋊C4—111no—
330C22×C4⋊C4—111no—
331C22×C22⋊C4—111no—
332C22×C22⋊C4C2×D1111yescharacteristic
333#400—114no—
334#400—114no—
335#399—114no—
336#398—114no—
337#398—114no—
338#398—114no—
339#397—112no—
340#397—114no—
341#397C2×D1112yes—
342#395—114no—
343#395—114no—
344#395—114no—
345#393—112no—
346#393C2×D1112yes—
347#391—112no—
348#391—112no—
349#388—114no—
350#388—114no—
351#388—114no—
352#388C2×D1114yes—
353#387—114no—
354#387—114no—
355#387—114no—
356#387—114no—
357#385—114no—
358#385—112no—
359#385—114no—
360#385—112no—
361#385—112no—
362#385—112no—
363#381—112no—
364#381—112no—
365#381C2×D1112yes—
366#380—112no—
367#380—114no—
368#379—112no—
369#379C2×D1112yes—
370C4×C22⋊C4—111no—
371C4×C22⋊C4C2×D1111yescharacteristic
372C22×C11—22no—
373C22×C11—22no—
374C22×C11—28no—
375C22×C11—24no—
376C22×C11—28no—
377C22×C11—416no—
378C22×C11—42no—
379C22×C11—42no—
380C22×C11—44no—
381C22×C11#53614yes—
382C22×C11C23×D411yescharacteristic
383C22×C11C2×H(5,𝔽2)12yes—
384C22×C11C2×2−1+412yes—
385C22×C11C2×2−1+412yes—
386C4×C11—22no—
387C4×C11—22no—
388C4×C11—42no—
389C4×C11—42no—
390C4×C11—42no—
391C4×C11—44no—
392Dic11—24no—
393Dic11—24no—
394Dic11—24no—
395Dic11—42no—
396Dic11—42no—
397Dic11—42no—
398Dic11—44no—
399C25C22×D1111yescharacteristic
400C22×Q8—112no—
401C22×Q8—112no—
402C22×Q8—112no—
403C22×Q8—111no—
404C22×Q8—224no—
405C22×Q8—444no—
406C22×Q8C22×D1111yescharacteristic
407C23×C4—111no—
408C23×C4—111no—
409C23×C4—111no—
410C23×C4—114no—
411C23×C4—111no—
412C23×C4—224no—
413C23×C4—444no—
414C23×C4C22×D1111yescharacteristic
415C23×C4C22×D1111yescharacteristic
416C4⋊Q8—228no—
417C4⋊Q8—228no—
418C4⋊Q8—444no—
419C4⋊Q8—444no—
420#125—228no—
421#125—228no—
422C22⋊Q8—24no—
423C22⋊Q8—2216no—
424C22⋊Q8—2216no—
425C22⋊Q8—228no—
426C22⋊Q8—224no—
427C22⋊Q8—448no—
428#117—228no—
429C2×C4⋊C4—118no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—114no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—112no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4—114no—
444C2×C4⋊C4—114no—
445C2×C4⋊C4—114no—
446C2×C4⋊C4—224no—
447C2×C4⋊C4—224no—
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C4⋊C4C22×D1112yes—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—114no—
452C2×C22⋊C4—112no—
453C2×C22⋊C4—112no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—114no—
456C2×C22⋊C4—224no—
457C2×C22⋊C4C22×D1112yes—
458C2×C22⋊C4C22×D1112yes—
459C2×C22⋊C4C22×D1112yes—
460C2×C22⋊C4C22×D1112yes—
461C2×C22⋊C4C22×D1114yes—
462C2×C22⋊C4C22×D1114yes—
463C2×C42—112no—
464C2×C42—112no—
465C2×C42—112no—
466C2×C42C22×D1112yes—
467#95—112no—
468#95—114no—
469#95—114no—
470#95—114no—
471#95—114no—
472#95—114no—
473#95—114no—
474#95—114no—
475#95—114no—
476#95—114no—
477#95C22×D1112yes—
478#95C22×D1114yes—
479#95C22×D1114yes—
480C2×C11—24no—
481C2×C11—44no—
482C2×C11C2×#53611yescharacteristic
483C2×C11#348411yescharacteristic
484C2×C11#348611yescharacteristic
485C2×C11#353814yes—
486C24—22no—
487C24—24no—
488C24—24no—
489C24—42no—
490C24C23×D1112yes—
491C24C23×D1111yescharacteristic
492C2×Q8—22no—
493C2×Q8—42no—
494C2×Q8—224no—
495C2×Q8—224no—
496C2×Q8—224no—
497C2×Q8—224no—
498C2×Q8—224no—
499C2×Q8—222no—
500C2×Q8—442no—
501C2×Q8—442no—
502C2×Q8—444no—
503C2×Q8—442no—
504C2×Q8—4416no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—42no—
508C22×C4—114no—
509C22×C4—112no—
510C22×C4—112no—
511C22×C4—112no—
512C22×C4—114no—
513C22×C4—114no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—112no—
517C22×C4—224no—
518C22×C4—228no—
519C22×C4—228no—
520C22×C4—222no—
521C22×C4—224no—
522C22×C4—222no—
523C22×C4—442no—
524C22×C4—444no—
525C22×C4—442no—
526C22×C4—4416no—
527C22×C4D4×D1114yes—
528C22×C4C23×D1114yes—
529C22×C4C23×D1112yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1111yescharacteristic
533C22×C4C23×D1111yescharacteristic
534C4⋊C4—22no—
535C4⋊C4—24no—
536C4⋊C4—118no—
537C4⋊C4—118no—
538C4⋊C4—228no—
539C4⋊C4—228no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4—228no—
546C4⋊C4—228no—
547C4⋊C4—222no—
548C4⋊C4—224no—
549C4⋊C4—444no—
550C4⋊C4—444no—
551C4⋊C4—444no—
552C22⋊C4—24no—
553C22⋊C4—28no—
554C22⋊C4—24no—
555C22⋊C4—24no—
556C22⋊C4—24no—
557C22⋊C4—44no—
558C22⋊C4—228no—
559C22⋊C4—224no—
560C22⋊C4—228no—
561C22⋊C4—224no—
562C22⋊C4—444no—
563C42—42no—
564C42—224no—
565C42—224no—
566C42—442no—
567C11#3670811yescharacteristic, complemented, Sylow
568C23—22no—
569C23—22no—
570C23—28no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—24no—
575C23—416no—
576C23—44no—
577C23—44no—
578C23C2×D4×D1112yes—
579C23#6704314yes—
580C23#6704314yes—
581C23C24×D1111yescharacteristic
582Q8—82no—
583Q8—448no—
584Q8—448no—
585Q8—882no—
586Q8—884no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—114no—
601C2×C4—114no—
602C2×C4—114no—
603C2×C4—228no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—228no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—224no—
615C2×C4—224no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—444no—
620C2×C4—4416no—
621C2×C4—444no—
622C2×C4C2×D4×D1112yes—
623C2×C4C2×D4×D1112yes—
624C22—22no—
625C22—22no—
626C22—28no—
627C22—24no—
628C22—28no—
629C22—416no—
630C22—42no—
631C22—42no—
632C22—44no—
633C22#1062320614yes—
634C22C22×D4×D1111yescharacteristic
635C22C2×#6704312yes—
636C22C2×#6704312yes—
637C22D11×H(5,𝔽2)12yes—
638C4—22no—
639C4—22no—
640C4—42no—
641C4—42no—
642C4—42no—
643C4—44no—
644C4—224no—
645C4—224no—
646C4—224no—
647C4—442no—
648C4—442no—
649C4—442no—
650C4—444no—
651C2—24no—
652C2—44no—
653C2C2×#1062320611yescharacteristic
654C2#1308224811yescharacteristic
655C2#1308226311yescharacteristic
656C2#1308285614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2561C2
prime radicalC25×C11C23
hypercenter#2561D11
hypocenterC11#36708
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2561

Complements

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

NH ≅ G/Ntype
1. C2×#10623154C2semidirect
4. #13075079C2semidirect
5. #13075075C2semidirect
6. #13074928C2semidirect
7. #13074925C2semidirect
8. #13074433C2semidirect
10. #13072900C2semidirect
12. #13072261C2semidirect
13. #13072260C2semidirect
14. #13071216C2semidirect
21. C2×#66997C22semidirect
22. C2×#66997C22semidirect
28. C2×#66942C22semidirect
29. C2×#66942C22semidirect
30. C2×#66941C22semidirect
37. C2×#66922C22semidirect
47. #10622592C22semidirect
48. #10622587C22semidirect
65. #10622546C22semidirect
66. #10622542C22semidirect
67. #10622274C22semidirect
68. #10622273C22semidirect
69. #10622271C22semidirect
70. #10622270C22semidirect
71. #10622270C22semidirect
72. #10622269C22semidirect
73. #10622269C22semidirect
74. #10622267C22semidirect
75. #10622265C22semidirect
76. #10622265C22semidirect
567. 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×#669312
#130769012
#130750792
#130750752
#130749282
#130749252
#130744332
#130737742
#130729002
#130728872
#130722612
#130722602
#130712162
C11×#25612
#3670811