Finite Group Databasebeta

← #14913541

Subgroups — #14913541

Order 2816.

2290 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13071719C214yesmaximal, complemented
3#13071675C212yesmaximal, complemented
4#13071670C212yesmaximal, complemented
5#13071645C212yesmaximal
6#13071644C214yesmaximal
7#13071639C212yesmaximal
8#13071113C212yesmaximal
9#13071109C212yesmaximal
10#13071094C211yesmaximal, characteristic, complemented
11#13071093C211yesmaximal, characteristic, complemented
12#13071092C212yesmaximal, complemented
13C42×Dic22C212yesmaximal, complemented
14C4×#66940C211yesmaximal, characteristic, complemented
15C4×#66925C211yesmaximal, characteristic
16C4×#66945C211yesmaximal, characteristic
17C42×Q8×C11C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22#10623109C4116yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×#66945C2212yes—
26C2×#66942C2212yes—
27C2×#66941C2211yescharacteristic
28C2×#66940C2212yes—
29C2×#66925C2212yes—
30C2×#66925C2212yes—
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22C2214yes—
33C2×C4×Dic22C2211yescharacteristic
34C2×C4×Dic22C2212yes—
35C4×C11×C4⋊C4C2212yes—
36C4×C11×C4⋊C4C2214yes—
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C43×C11C2212yes—
40C43×C11C2211yescharacteristic
41#10622843C2212yes—
42#10622603C2214yes—
43#10622598C2212yes—
44#10622594C2214yes—
45#10622591C2214yes—
46#10622591C2214yes—
47C4⋊C4×Dic11C2212yes—
48C4⋊C4×Dic11C2212yes—
49#10622585C2214yes—
50#10622553C2214yes—
51#10622553C2214yes—
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C4×(C2×D11)⋊C4C2212yes—
54C4×(C2×D11)⋊C4C2211yescharacteristic
55C4×(C2×D11)⋊C4C2212yes—
56C4×C4⋊Dic11C2212yes—
57C4×C4⋊Dic11C2214yes—
58C4×C4⋊Dic11C2211yescharacteristic
59#10622546C2214yes—
60#10622546C2214yes—
61#10622546C2214yes—
62#10622545C2212yes—
63#10622545C2212yes—
64#10622545C2212yes—
65C4×Dic11⋊C4C2212yes—
66C4×Dic11⋊C4C2212yes—
67C4×Dic11⋊C4C2214yes—
68C4×Dic11⋊C4C2214yes—
69C4×Dic11⋊C4C2212yes—
70C4×Dic11⋊C4C2211yescharacteristic
71C4×Dic11⋊C4C2211yescharacteristic
72C42×Dic11C2212yes—
73C42×Dic11C2212yes—
74C42×Dic11C2211yescharacteristic
75#10622542C2212yes—
76#10622541C2212yes—
77#10622283C2214yes—
78#10622279C2212yes—
79#10622268C2214yes—
80#10622266C2214yes—
81#10622262C2214yes—
82#10622261C2212yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2312yes—
89C22×Dic22C2311yescharacteristic
90C4×Q8×C11—28no—
91C4×Q8×C11C2×C418yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C42×C11C2314yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2312yes—
99C2×C42×C11C2312yes—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2314yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2312yes—
105#66999C2×C418yes—
106#66997C2×C418yes—
107C2×(C2×D11)⋊C4C2312yes—
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×C4⋊Dic11C2314yes—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2312yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2311yescharacteristic
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138#66950C2×C418yes—
139#66949C2×C4116yes—
140#66945—28no—
141#66942C2×C4116yes—
142#66941C2×C418yes—
143#66940—28no—
144#66925—28no—
145#66925C2×C4116yes—
146C42×D11C2×C418yes—
147C4×Dic22—216no—
148C4×Dic22C2×C4116yes—
149C4×Dic22C2×C418yes—
150C11×#95C2314yes—
151C11×#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165#34154—111nomaximal, Sylow
166C23×D11C2411yescharacteristic
167C2×Q8×C11—24no—
168C2×Q8×C11C22×C414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2411yescharacteristic
172C22×C4×C11C2412yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2414yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×Dic11C2412yes—
178C22×Dic11C2414yes—
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C22×Dic11C2412yes—
184C22×Dic11C2411yescharacteristic
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—22no—
188C2×C4×D11—22no—
189C2×C4×D11C22×C414yes—
190C2×C4×D11C22×C414yes—
191C2×C4×D11C22×C414yes—
192C2×Dic22—28no—
193C2×Dic22—24no—
194C2×Dic22C22×C418yes—
195C2×Dic22C22×C414yes—
196C11×C4⋊C4—28no—
197C11×C4⋊C4C22×C414yes—
198C11×C4⋊C4C22×C418yes—
199C11×C4⋊C4#4118yes—
200C42×C11—28no—
201C42×C11—24no—
202C42×C11—28no—
203C42×C11—24no—
204C42×C11—22no—
205C42×C11—24no—
206C42×C11—22no—
207C42×C11C22×C414yes—
208C42×C11C22×C418yes—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—28no—
212(C2×D11)⋊C4C22×C418yes—
213(C2×D11)⋊C4C22×C418yes—
214C4⋊Dic11—28no—
215C4⋊Dic11—24no—
216C4⋊Dic11C22×C414yes—
217C4⋊Dic11C22×C418yes—
218Dic11⋊C4—24no—
219Dic11⋊C4—28no—
220Dic11⋊C4—28no—
221Dic11⋊C4C22×C418yes—
222Dic11⋊C4C22×C418yes—
223Dic11⋊C4C22×C418yes—
224Dic11⋊C4C22×C418yes—
225Dic11⋊C4C22×C418yes—
226Dic11⋊C4#4118yes—
227C4×Dic11—28no—
228C4×Dic11—28no—
229C4×Dic11—24no—
230C4×Dic11—28no—
231C4×Dic11—24no—
232C4×Dic11—28no—
233C4×Dic11—22no—
234C4×Dic11—24no—
235C4×Dic11—22no—
236C4×Dic11C22×C414yes—
237C4×Dic11C22×C418yes—
238C4×Dic11C22×C414yes—
239C4×Dic11C22×C414yes—
240C2×#533—111no—
241#2371—114no—
242#2365—112no—
243#2365—112no—
244#2362—114no—
245#2362—112no—
246#2362—112no—
247#2298—112no—
248#2298—112no—
249#2295—112no—
250#2295—111no—
251#2295—111no—
252C42×Q8—111no—
253C42×Q8—112no—
254C42×Q8D1111yescharacteristic, complemented
255C4×#117—111no—
256C4×#117—111no—
257C23×C11C2511yescharacteristic
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—21no—
261C22×D11—21no—
262C22×D11C23×C412yes—
263Q8×C11—28no—
264C2×C4×C11—24no—
265C2×C4×C11—22no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11C23×C412yes—
275C2×C4×C11C23×C414yes—
276C2×C4×C11C23×C414yes—
277C2×C4×C11C23×C412yes—
278C2×C4×C11C23×C412yes—
279C2×C4×C11C2×#4118yes—
280C2×C4×C11C2×#4114yes—
281C2×C4×C11C2×#4114yes—
282C2×C4×C112−1+412yes—
283C2×C4×C112−1+412yes—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—22no—
292C2×Dic11—24no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—24no—
296C2×Dic11—22no—
297C2×Dic11C23×C412yes—
298C2×Dic11C23×C412yes—
299C2×Dic11C23×C414yes—
300C2×Dic11C23×C414yes—
301C2×Dic11C23×C412yes—
302C2×Dic11C2×#4114yes—
303C2×Dic11C2×#4114yes—
304C4×D11—28no—
305C4×D11—28no—
306C4×D11—28no—
307Dic22—28no—
308Dic22—216no—
309#533—1116no—
310C2×C4⋊Q8—111no—
311C2×C4⋊Q8—111no—
312C2×#125—112no—
313C2×C22⋊Q8—111no—
314C2×C22⋊Q8—112no—
315C2×C22⋊Q8—111no—
316C2×C4×Q8—112no—
317C2×C4×Q8—111no—
318C2×C4×Q8—112no—
319C2×C4×Q8—114no—
320C2×C4×Q8C2×D1112yes—
321C2×C4×Q8C2×D1111yescharacteristic
322C2×#117—112no—
323C2×#117—112no—
324C2×#117—112no—
325C22×C42—111no—
326#391—112no—
327#391—112no—
328#391—114no—
329#389—114no—
330#389—112no—
331#389—112no—
332#388—114no—
333#388—114no—
334#388—114no—
335#388—114no—
336#387—114no—
337#387—114no—
338#387—114no—
339#387—114no—
340#387—114no—
341#387—114no—
342#387—114no—
343#387—114no—
344C4×C4⋊C4—112no—
345C4×C4⋊C4—112no—
346C4×C4⋊C4—114no—
347C4×C4⋊C4—114no—
348C4×C4⋊C4—114no—
349C4×C4⋊C4—112no—
350C4×C4⋊C4—111no—
351C4×C4⋊C4—111no—
352C4×C4⋊C4—112no—
353C4×C4⋊C4—112no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4—112no—
356C4×C4⋊C4—114no—
357C4×C4⋊C4C2×D1112yes—
358C4×C4⋊C4C2×D1114yes—
359C4×C4⋊C4C2×D1111yescharacteristic
360C4×C4⋊C4C2×D1112yes—
361C4×C22⋊C4—112no—
362C4×C22⋊C4—111no—
363C4×C22⋊C4—112no—
364C4×C22⋊C4—111no—
365C4×C22⋊C4—112no—
366#376—112no—
367#376—112no—
368#376—112no—
369#376—112no—
370C43—112no—
371C43—111no—
372C43—112no—
373C43C2×D1111yescharacteristic
374C43C2×D1112yes—
375C22×C11C24×C411yescharacteristic
376C22×C11C22×#4112yes—
377C22×C11C22×#4112yes—
378C22×C11C2×2−1+411yescharacteristic
379C22×C11C2×2−1+411yescharacteristic
380C2×D11—22no—
381C2×D11—22no—
382C2×D11—22no—
383C2×D11—42no—
384C2×D11—42no—
385C4×C11—24no—
386C4×C11—24no—
387C4×C11—22no—
388C4×C11—28no—
389C4×C11—24no—
390C4×C11—42no—
391C4×C11C4×#4114yes—
392C4×C11#51914yes—
393Dic11—24no—
394Dic11—24no—
395Dic11—22no—
396Dic11—22no—
397Dic11—24no—
398Dic11—42no—
399Dic11—44no—
400Dic11C4×#4114yes—
401C22×Q8—112no—
402C22×Q8—111no—
403C22×Q8C22×D1111yescharacteristic
404C23×C4—111no—
405C23×C4—111no—
406C23×C4—111no—
407C4⋊Q8—118no—
408C4⋊Q8—118no—
409#125—1116no—
410C22⋊Q8—118no—
411C22⋊Q8—1116no—
412C22⋊Q8—118no—
413C4×Q8—28no—
414C4×Q8—1116no—
415C4×Q8—118no—
416C4×Q8—2216no—
417C4×Q8—228no—
418C4×Q8C4×D1118yes—
419#117—1116no—
420#117—228no—
421#117—228no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—114no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4C22×D1114yes—
436C2×C4⋊C4C22×D1112yes—
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1112yes—
439C2×C22⋊C4—112no—
440C2×C22⋊C4—112no—
441C2×C22⋊C4—112no—
442C2×C22⋊C4—114no—
443C2×C22⋊C4—112no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—112no—
447C2×C42—111no—
448C2×C42—118no—
449C2×C42—112no—
450C2×C42—114no—
451C2×C42—114no—
452C2×C42—112no—
453C2×C42—114no—
454C2×C42—114no—
455C2×C42—111no—
456C2×C42—112no—
457C2×C42—111no—
458C2×C42C22×D1112yes—
459C2×C42C22×D1114yes—
460C2×C42C22×D1112yes—
461C2×C42C22×D1114yes—
462C2×C42C22×D1112yes—
463C2×C42C22×D1111yescharacteristic
464C2×C42C22×D1111yescharacteristic
465C2×C42C22×D1112yes—
466C2×C42C22×D1111yescharacteristic
467#95—112no—
468#95—112no—
469#95—114no—
470#95—112no—
471#95—112no—
472#95—112no—
473#95—114no—
474#95—114no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95C22×D1112yes—
481#95C22×D1114yes—
482C2×C11C2×C4×#4111yescharacteristic
483C2×C11C2×C4×#4111yescharacteristic
484C2×C11C2×#51911yescharacteristic
485C2×C11#348212yes—
486C2×C11#348212yes—
487D11—42no—
488C24—111no—
489C2×Q8—24no—
490C2×Q8—118no—
491C2×Q8—114no—
492C2×Q8—228no—
493C2×Q8—224no—
494C2×Q8C2×C4×D1114yes—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—112no—
498C22×C4—111no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—114no—
502C22×C4—114no—
503C22×C4—114no—
504C22×C4—114no—
505C22×C4—112no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4C23×D1112yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1111yescharacteristic
513C22×C4C23×D1112yes—
514C22×C4C23×D1114yes—
515C22×C4C23×D1112yes—
516C22×C4C23×D1111yescharacteristic
517C22×C4C23×D1111yescharacteristic
518C4⋊C4—28no—
519C4⋊C4—118no—
520C4⋊C4—118no—
521C4⋊C4—118no—
522C4⋊C4—118no—
523C4⋊C4—118no—
524C4⋊C4—118no—
525C4⋊C4—114no—
526C4⋊C4—118no—
527C4⋊C4—224no—
528C4⋊C4—228no—
529C4⋊C4—224no—
530C4⋊C4—228no—
531C4⋊C4—228no—
532C4⋊C4C2×C4×D1118yes—
533C4⋊C4C2×C4×D1114yes—
534C4⋊C4#433918yes—
535C22⋊C4—118no—
536C22⋊C4—118no—
537C22⋊C4—224no—
538C22⋊C4—228no—
539C22⋊C4—224no—
540C42—28no—
541C42—24no—
542C42—22no—
543C42—24no—
544C42—28no—
545C42—24no—
546C42—22no—
547C42—114no—
548C42—114no—
549C42—114no—
550C42—118no—
551C42—224no—
552C42—228no—
553C42—228no—
554C42—228no—
555C42—228no—
556C42—224no—
557C42—222no—
558C42—224no—
559C42—222no—
560C42C2×C4×D1114yes—
561C42C2×C4×D1118yes—
562C11#3415411yescharacteristic, complemented, Sylow
563C23—112no—
564C23—222no—
565C23—221no—
566C23—222no—
567C23—221no—
568C23C24×D1111yescharacteristic
569Q8—28no—
570Q8—2216no—
571Q8—228no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—112no—
583C2×C4—114no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—114no—
587C2×C4—114no—
588C2×C4—114no—
589C2×C4—228no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—221no—
595C2×C4—224no—
596C2×C4—221no—
597C2×C4—228no—
598C2×C4—228no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—222no—
605C2×C4C22×C4×D1112yes—
606C2×C4C22×C4×D1114yes—
607C2×C4C22×C4×D1114yes—
608C2×C4C22×C4×D1112yes—
609C2×C4C22×C4×D1112yes—
610C2×C4C2×#433918yes—
611C2×C4C2×#433914yes—
612C2×C4#6704012yes—
613C2×C4#41×D1114yes—
614C2×C4#6704312yes—
615C22—222no—
616C22—222no—
617C22—222no—
618C22—442no—
619C22—442no—
620C22C23×C4×D1111yescharacteristic
621C22C22×#433912yes—
622C22C2×#6704011yescharacteristic
623C22C2×#41×D1112yes—
624C22C2×#6704311yescharacteristic
625C4—28no—
626C4—24no—
627C4—22no—
628C4—24no—
629C4—24no—
630C4—42no—
631C4—114no—
632C4—224no—
633C4—224no—
634C4—222no—
635C4—224no—
636C4—222no—
637C4—442no—
638C4—444no—
639C4C4×#433914yes—
640C4#1062310314yes—
641C2—442no—
642C2C4×#41×D1111yescharacteristic
643C2C2×C4×#433911yescharacteristic
644C2C2×#1062310311yescharacteristic
645C2#1308223112yes—
646C2#1308223312yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC42×Q8×C11C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterC42×Q8D11
hypocenterC11#34154
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
2. #13071719C2semidirect
3. #13071675C2semidirect
4. #13071670C2semidirect
10. #13071094C2semidirect
11. #13071093C2semidirect
12. #13071092C2semidirect
13. C42×Dic22C2semidirect
14. C4×#66940C2semidirect
17. C42×Q8×C11C2semidirect
22. #10623109C4semidirect
254. C42×Q8D11semidirect
562. C11#34154semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130717192
#130716752
#130716702
#130716452
#130716442
#130716392
#130711132
#130711092
#130710942
#130710932
#130710922
C42×Dic222
C4×#669402
C4×#669252
C4×#669452
C42×Q8×C112
#3415411