Finite Group Databasebeta

← #14926299

Subgroups — #14926299

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic
3#13074315C214yesmaximal, complemented
4#13073831C211yesmaximal, characteristic, complemented
5#13073605C211yesmaximal, characteristic, complemented
6#13073569C211yesmaximal, characteristic, complemented
7#13073068C212yesmaximal, complemented
8#13072247C212yesmaximal
9#13072047C214yesmaximal, complemented
10#13071878C214yesmaximal, complemented
11#13071185C212yesmaximal, complemented
12#124×Dic11C212yesmaximal, complemented
13#13071144C214yesmaximal, complemented
14C4×#66945C211yesmaximal, characteristic, complemented
15C11×#2547C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#124C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66999C2212yes—
21C2×Q8×Dic11C2212yes—
22C2×#66997C2212yes—
23C2×D4×Dic11C2211yescharacteristic
24C2×C4×C22⋊D11C2212yes—
25C2×#66977C2214yes—
26C22×C4×Dic11C2212yes—
27#10623259—28no—
28C4×#4341—28no—
29C2×#66950C2212yes—
30C2×#66945C2212yes—
31C2×#66945C2212yes—
32C2×#66945C2211yescharacteristic
33C2×#66943C2212yes—
34C2×#66940C2212yes—
35C2×#66940C2211yescharacteristic
36C2×(C22⋊D11)⋊C4C2212yes—
37C2×#66930C2212yes—
38C2×C42×D11C2211yescharacteristic
39C2×#66922C2211yescharacteristic
40C2×C4×Dic22C2211yescharacteristic
41C11×#397C2214yes—
42C11×#391C2212yes—
43C11×#380C2214yes—
44C4×C11×C4⋊C4C2211yescharacteristic
45#10622843C2212yes—
46#10622834C2212yes—
47#10622593C2214yes—
48#10622589C2212yes—
49C4⋊C4×Dic11C2212yes—
50#10622587C2214yes—
51#10622586C2214yes—
52#10622572C2218yes—
53#10622564C2218yes—
54#10622562C2214yes—
55#10622559C2218yes—
56C22⋊C4×Dic11C2218yes—
57C4×(C2×D11)⋊C4C2212yes—
58#10622549C2212yes—
59C4×C4⋊Dic11C2211yescharacteristic
60C42×Dic11C2212yes—
61#10622542C2212yes—
62#10622288C2218yes—
63#10622279C2212yes—
64#10622272C2214yes—
65#10622265C2218yes—
66#10622262C2218yes—
67#10622261C2212yes—
68#10622260C2218yes—
69C22×Q8×C11C2312yes—
70C22×D4×C11C2311yescharacteristic
71C23×C4×C11C2312yes—
72C22×C22⋊D11C2312yes—
73C23×Dic11C2312yes—
74C23×Dic11C2312yes—
75C2×#4341—24no—
76C2×#4341—24no—
77C2×#4341—24no—
78C22×C4×D11C2311yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×Dic22C2312yes—
82C22×Dic22C2311yescharacteristic
83C11×C4⋊Q8—24no—
84C11×#124—28no—
85C4×D4×C11—24no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C11×C22⋊C4C2318yes—
92C2×C42×C11C2312yes—
93C2×C42×C11C2311yescharacteristic
94C2×C22⋊Dic11C2312yes—
95C2×C22⋊Dic11C2318yes—
96#66999—28no—
97Q8×Dic11—28no—
98#66997—28no—
99D4×Dic11—24no—
100C4×C22⋊D11—28no—
101C2×(C2×D11)⋊C4C2312yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2312yes—
109#66977—216no—
110C2×Dic11⋊C4C2312yes—
111C2×Dic11⋊C4C2312yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2318yes—
114C2×Dic11⋊C4C2318yes—
115C2×C4×Dic11—28no—
116C2×C4×Dic11C2312yes—
117C2×C4×Dic11C2312yes—
118C2×C4×Dic11C2312yes—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2311yescharacteristic
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2311yescharacteristic
126#66950—28no—
127#66945—28no—
128#66945—24no—
129#66945—28no—
130#66943—28no—
131#66940—28no—
132#66940—24no—
133(C22⋊D11)⋊C4—28no—
134#66930—28no—
135C42×D11D418yes—
136#66922—24no—
137C4×Dic22—24no—
138C11×#95C2318yes—
139C11×#95C2312yes—
140C11⋊#95C2318yes—
141C11⋊#95C2314yes—
142C11⋊#95C2312yes—
143C11⋊#95C2318yes—
144C11⋊#95C2318yes—
145#34979—111nomaximal, Sylow
146C24×C11C2412yes—
147C23×D11C2411yescharacteristic
148C2×Q8×C11—24no—
149C2×Q8×C11—24no—
150C2×Q8×C11—24no—
151C2×D4×C11—22no—
152C2×D4×C11—22no—
153C2×D4×C11#4114yes—
154C22×C4×C11—24no—
155C22×C4×C11—28no—
156C22×C4×C11C2414yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C2×C22⋊D11—24no—
163C2×C22⋊D11—24no—
164C2×C22⋊D11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—28no—
169C22×Dic11—24no—
170C22×Dic11C2412yes—
171C22×Dic11C2414yes—
172C22×Dic11C2411yescharacteristic
173C22×Dic11C2411yescharacteristic
174C22×Dic11C2414yes—
175C22×Dic11C2412yes—
176C22×Dic11C2411yescharacteristic
177#4341—232no—
178C2×C4×D11—24no—
179C2×C4×D11—24no—
180C2×C4×D11—22no—
181C2×C4×D11—22no—
182C2×C4×D11C2×D414yes—
183C2×C4×D11C2×D414yes—
184C2×C4×D11C2×D414yes—
185C2×Dic22—22no—
186C2×Dic22—24no—
187C2×Dic22—22no—
188C2×Dic22—28no—
189C2×Dic22#4114yes—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C22⋊C4—216no—
195C11×C22⋊C4—24no—
196C42×C11—24no—
197C42×C11C2×D414yes—
198C22⋊Dic11—24no—
199C22⋊Dic11—216no—
200(C2×D11)⋊C4—28no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—28no—
203C4⋊Dic11—28no—
204C4⋊Dic11—22no—
205C4⋊Dic11—24no—
206C4⋊Dic11—24no—
207C4⋊Dic11#4118yescomplemented
208Dic11⋊C4—24no—
209Dic11⋊C4—28no—
210Dic11⋊C4—216no—
211Dic11⋊C4—216no—
212Dic11⋊C4—24no—
213C4×Dic11—24no—
214C4×Dic11—24no—
215C4×Dic11—28no—
216C4×Dic11—28no—
217C4×Dic11—28no—
218C4×Dic11—24no—
219C4×Dic11—24no—
220C4×Dic11C2×D414yes—
221C4×Dic11C2×D414yes—
222C4×Dic11C2×D414yes—
223C2×#533—111no—
224C2×C4×#41—111no—
225#2611—114no—
226#2568—111no—
227#2547D1111yescharacteristic, complemented
228#2546—111no—
229#2542—111no—
230#2499—112no—
231#2432—112no—
232#2415—114no—
233#2395—114no—
234C4×C4⋊Q8—112no—
235C4×#124—112no—
236C4×C22⋊Q8—114no—
237C4×#117—111no—
238C23×C11—22no—
239C23×C11—24no—
240C23×C11—22no—
241C23×C11—24no—
242C23×C11C2×#4114yes—
243C23×C11C2511yescharacteristic
244C22×D11—22no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—22no—
248C22×D11C22×D412yes—
249Q8×C11—48no—
250D4×C11—28no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—48no—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C2×#4112yes—
265C2×C4×C11C2×#4112yes—
266C2×C4×C11C2×#4114yes—
267C22⋊D11—216no—
268C2×Dic11—216no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—28no—
279C2×Dic11—24no—
280C2×Dic11—48no—
281C2×Dic11C22×D412yes—
282C2×Dic11C22×D412yes—
283C2×Dic11C22×D412yes—
284C2×Dic11C2×#4118yes—
285C2×Dic11C2×#4114yes—
286C2×Dic112−1+414yes—
287C4×D11—28no—
288C4×D11—28no—
289C4×D11—28no—
290Dic22—28no—
291Dic22—48no—
292C22×#41—111no—
293#533—228no—
294C2×C4⋊Q8—112no—
295C2×C4⋊Q8—111no—
296C2×C4⋊Q8C2×D1111yescharacteristic
297C2×#125—112no—
298C2×#124C2×D1112yes—
299C2×C22⋊Q8—112no—
300C2×C22⋊Q8—114no—
301C2×C22⋊Q8—112no—
302C4×#41—228no—
303C2×C4×Q8—112no—
304C2×C4×Q8—111no—
305C2×C4×Q8—112no—
306C2×C4×Q8—111no—
307C2×C4×D4—111no—
308C2×C4×D4—112no—
309C2×C4×D4—112no—
310C2×C4×D4C2×D1111yescharacteristic
311C2×#117—112no—
312C2×#117—111no—
313C2×#117—112no—
314C2×#117—112no—
315C22×C42—111no—
316C22×C42—112no—
317#400—114no—
318#399—114no—
319#398—114no—
320#397—118no—
321#397C2×D1114yes—
322#394—118no—
323#391—112no—
324#391—114no—
325#391—112no—
326#391C2×D1112yes—
327#390—112no—
328#389—114no—
329#389—118no—
330#388—118no—
331#387—118no—
332#385—118no—
333#384—112no—
334#382—112no—
335#380C2×D1114yes—
336C4×C4⋊C4—112no—
337C4×C4⋊C4—111no—
338C4×C4⋊C4—118no—
339C4×C4⋊C4C2×D1111yescharacteristic
340C4×C22⋊C4—118no—
341C4×C22⋊C4—112no—
342C4×C22⋊C4—112no—
343#376—112no—
344C43—112no—
345C22×C11—24no—
346C22×C11—28no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—44no—
350C22×C11C23×D411yescharacteristic
351C22×C11C22×#4111yescharacteristic
352C22×C11C22×#4111yescharacteristic
353C22×C11C22×#4112yes—
354C22×C11C2×2−1+412yes—
355C2×D11—22no—
356C2×D11—22no—
357C2×D11—22no—
358C2×D11—42no—
359C2×D11—42no—
360C4×C11—22no—
361C4×C11—44no—
362C4×C11—42no—
363C4×C11—44no—
364C4×C11#52514yes—
365C4×C11#53214yes—
366Dic11—24no—
367Dic11—22no—
368Dic11—22no—
369Dic11—28no—
370Dic11—44no—
371Dic11—42no—
372Dic11#53614yes—
373C2×#41—224no—
374C2×#41—224no—
375C2×#41—224no—
376C22×Q8—111no—
377C22×Q8—112no—
378C22×Q8C22×D1112yes—
379C22×D4—112no—
380C22×D4C22×D1111yescharacteristic
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—112no—
385C23×C4—112no—
386C23×C4C22×D1112yes—
387C4⋊Q8—24no—
388C4⋊Q8—228no—
389C4⋊Q8—224no—
390#125—228no—
391#124—28no—
392C22⋊Q8—228no—
393C22⋊Q8—2216no—
394C22⋊Q8—228no—
395C4×Q8—224no—
396C4×Q8—228no—
397C4×Q8—228no—
398C4×Q8—224no—
399C4×D4—24no—
400C4×D4—224no—
401C4×D4—228no—
402C4×D4—228no—
403#117—228no—
404#117—228no—
405#117—224no—
406#117—228no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—112no—
410C2×C4⋊C4—112no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—114no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—118no—
416C2×C4⋊C4—118no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1112yes—
419C2×C4⋊C4C22×D1112yes—
420C2×C4⋊C4C22×D1112yes—
421C2×C22⋊C4—112no—
422C2×C22⋊C4—118no—
423C2×C22⋊C4—112no—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4C22×D1112yes—
427C2×C22⋊C4C22×D1118yes—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—118no—
432C2×C42—112no—
433C2×C42—114no—
434C2×C42—114no—
435C2×C42—112no—
436C2×C42—112no—
437C2×C42—112no—
438C2×C42—114no—
439C2×C42—228no—
440C2×C42C22×D1112yes—
441C2×C42C22×D1111yescharacteristic
442#95—114no—
443#95—112no—
444#95—118no—
445#95—118no—
446#95—118no—
447#95C22×D1112yes—
448#95C22×D1118yes—
449C2×C11—44no—
450C2×C11C2×#52511yescharacteristic
451C2×C11C2×#53211yescharacteristic
452C2×C11C2×#53611yescharacteristic
453C2×C11#348212yes—
454C2×C11#348212yes—
455D11—42no—
456C24—111no—
457C24C23×D1112yes—
458#41—2232no—
459C2×Q8—24no—
460C2×Q8—24no—
461C2×Q8—24no—
462C2×Q8—114no—
463C2×Q8—222no—
464C2×Q8—224no—
465C2×Q8—222no—
466C2×Q8—228no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—224no—
470C2×D4—224no—
471C2×D4—224no—
472C2×D4#434114yes—
473C22×C4—24no—
474C22×C4—28no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—114no—
478C22×C4—112no—
479C22×C4—111no—
480C22×C4—114no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—112no—
484C22×C4—114no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4—228no—
490C22×C4—224no—
491C22×C4—222no—
492C22×C4—224no—
493C22×C4—222no—
494C22×C4C23×D1114yes—
495C22×C4C23×D1114yes—
496C22×C4C23×D1112yes—
497C22×C4C23×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499C22×C4C23×D1111yescharacteristic
500C4⋊C4—22no—
501C4⋊C4—24no—
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—118no—
505C4⋊C4—224no—
506C4⋊C4—228no—
507C4⋊C4—228no—
508C4⋊C4—2216no—
509C4⋊C4—2216no—
510C4⋊C4—224no—
511C4⋊C4—222no—
512C4⋊C4—224no—
513C4⋊C4—224no—
514C22⋊C4—216no—
515C22⋊C4—24no—
516C22⋊C4—228no—
517C22⋊C4—224no—
518C22⋊C4—228no—
519C22⋊C4—224no—
520C22⋊C4—2216no—
521C42—24no—
522C42—114no—
523C42—114no—
524C42—114no—
525C42—224no—
526C42—224no—
527C42—228no—
528C42—228no—
529C42—228no—
530C42—224no—
531C42—224no—
532C42D4×D1114yes—
533C11#3497911yescharacteristic, complemented, Sylow
534C23—22no—
535C23—24no—
536C23—22no—
537C23—24no—
538C23—112no—
539C23—221no—
540C23—222no—
541C23—221no—
542C23—222no—
543C23C2×#434114yes—
544C23C24×D1111yescharacteristic
545Q8—48no—
546Q8—228no—
547Q8—448no—
548D4—28no—
549D4—2216no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—48no—
560C2×C4—112no—
561C2×C4—114no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—118no—
565C2×C4—114no—
566C2×C4—228no—
567C2×C4—2216no—
568C2×C4—222no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—221no—
574C2×C4—224no—
575C2×C4—228no—
576C2×C4—228no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—228no—
580C2×C4—224no—
581C2×C4—448no—
582C2×C4C2×D4×D1112yes—
583C2×C4C2×D4×D1112yes—
584C2×C4C2×D4×D1112yes—
585C2×C4C2×#434112yes—
586C2×C4#41×D1112yes—
587C2×C4#41×D1114yes—
588C22—24no—
589C22—28no—
590C22—42no—
591C22—42no—
592C22—44no—
593C22—222no—
594C22—222no—
595C22—222no—
596C22—442no—
597C22—442no—
598C22C22×D4×D1111yescharacteristic
599C22C22×#434111yescharacteristic
600C22C2×#41×D1111yescharacteristic
601C22C2×#41×D1112yes—
602C22D11×2−1+412yes—
603C4—22no—
604C4—44no—
605C4—42no—
606C4—44no—
607C4—114no—
608C4—222no—
609C4—224no—
610C4—222no—
611C4—228no—
612C4—444no—
613C4—442no—
614C4#1062313714yes—
615C4#1062319914yes—
616C2—44no—
617C2—442no—
618C2C2×#1062313711yescharacteristic
619C2C2×#1062319911yescharacteristic
620C2D11×#53611yescharacteristic
621C2#1308222812yes—
622C2#1308223512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2547C2
prime radicalC22×#4341C22
hypercenter#2547D11
hypocenterC11#34979
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13074315C2semidirect
4. #13073831C2semidirect
5. #13073605C2semidirect
6. #13073569C2semidirect
7. #13073068C2semidirect
9. #13072047C2semidirect
10. #13071878C2semidirect
11. #13071185C2semidirect
12. #124×Dic11C2semidirect
13. #13071144C2semidirect
14. C4×#66945C2semidirect
15. C11×#2547C2semidirect
207. C4⋊Dic11#41semidirect
227. #2547D11semidirect
533. C11#34979semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×C4×#43412
#130743152
#130738312
#130736052
#130735692
#130730682
#130722472
#130720472
#130718782
#130711852
#124×Dic112
#130711442
C4×#669452
C11×#25472
#3497911