Finite Group Databasebeta

← #14912765

Subgroups — #14912765

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13071418C214yesmaximal, complemented
3#13071370C214yesmaximal
4#13071363C212yesmaximal, complemented
5#13071334C212yesmaximal, complemented
6#13071301C212yesmaximal
7#13071296C212yesmaximal
8#13071111C212yesmaximal
9#13071109C212yesmaximal
10#13071093C211yesmaximal, characteristic, complemented
11#13071090C212yesmaximal, complemented
12#13071088C212yesmaximal, complemented
13#13071012C211yesmaximal, characteristic
14C4×Q8×Dic11C211yesmaximal, characteristic, complemented
15C4×#66940C211yesmaximal, characteristic, complemented
16C4×#66925C211yesmaximal, characteristic
17C11×#2295C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×Q8×Dic11C2212yes—
21C2×#66997C2211yescharacteristic
22#10623109C4116yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×#66942C2212yes—
26C2×#66941C2211yescharacteristic
27C2×#66940C2212yes—
28C2×#66925C2212yes—
29C2×#66925C2212yes—
30C2×C42×D11C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2212yes—
33C11×#391C2212yes—
34C11×#389C2212yes—
35C11×#387C2214yes—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2211yescharacteristic
38C11×#376C2212yes—
39C43×C11C2211yescharacteristic
40#10622603C2214yes—
41#10622600C2212yes—
42#10622591C2214yes—
43#10622590C2212yes—
44C4⋊C4×Dic11C2212yes—
45C4⋊C4×Dic11C2212yes—
46C4⋊C4×Dic11C2214yes—
47#10622587C2214yes—
48#10622586C2214yes—
49C4×(C2×D11)⋊C4C2211yescharacteristic
50C4×(C2×D11)⋊C4C2212yes—
51C4×(C2×D11)⋊C4C2211yescharacteristic
52C4×(C2×D11)⋊C4C2212yes—
53C4×C4⋊Dic11C2212yes—
54C4×C4⋊Dic11C2211yescharacteristic
55#10622546C2214yes—
56#10622545C2212yes—
57#10622545C2212yes—
58#10622545C2212yes—
59C4×Dic11⋊C4C2212yes—
60C4×Dic11⋊C4C2212yes—
61C4×Dic11⋊C4C2212yes—
62C4×Dic11⋊C4C2211yescharacteristic
63C4×Dic11⋊C4C2211yescharacteristic
64C42×Dic11C2212yes—
65C42×Dic11C2212yes—
66C42×Dic11C2211yescharacteristic
67#10622542C2212yes—
68#10622541C2212yes—
69#10622283C2214yes—
70#10622282C2214yes—
71#10622282C2214yes—
72#10622277C2212yes—
73#10622268C2214yes—
74#10622268C2214yes—
75#10622267C2214yes—
76#10622265C2214yes—
77#10622265C2214yes—
78#10622265C2214yes—
79#10622265C2214yes—
80#10622264C2212yes—
81#10622262C2214yes—
82#10622260C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C22×Dic22C2312yes—
90C4×Q8×C11C2×C418yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2312yes—
95C2×C42×C11C2312yes—
96C2×C42×C11C2312yes—
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2312yes—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2312yes—
102#66999C2×C418yes—
103Q8×Dic11—28no—
104#66997C2×C418yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2312yes—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2312yes—
114C2×Dic11⋊C4C2312yes—
115C2×Dic11⋊C4C2312yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2312yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2311yescharacteristic
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2311yescharacteristic
134C2×C4×Dic11C2311yescharacteristic
135C2×C4×Dic11C2312yes—
136#66950C2×C418yes—
137#66949C2×C4116yes—
138#66942C2×C4116yes—
139#66941C2×C418yes—
140#66940—28no—
141#66925—28no—
142#66925C2×C4116yes—
143C42×D11C2×C418yes—
144C4×Dic22C2×C4116yes—
145C4×Dic22C2×C418yes—
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2312yes—
149C11×#95C2314yes—
150C11⋊#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163#34085—111nomaximal, Sylow
164C23×D11C2411yescharacteristic
165C2×Q8×C11—24no—
166C2×Q8×C11C22×C414yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2412yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×Dic11C2414yes—
176C22×Dic11C2411yescharacteristic
177C22×Dic11C2411yescharacteristic
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—42no—
187C2×C4×D11C22×C414yes—
188C2×C4×D11C22×C414yes—
189C2×C4×D11C22×C414yes—
190C2×Dic22—24no—
191C2×Dic22—44no—
192C2×Dic22C22×C414yes—
193C2×Dic22C22×C418yes—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—44no—
196C11×C4⋊C4C22×C414yes—
197C11×C4⋊C4C22×C418yes—
198C42×C11—24no—
199C42×C11—22no—
200C42×C11—24no—
201C42×C11—22no—
202C42×C11—42no—
203C42×C11C22×C414yes—
204C42×C11C22×C418yes—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—24no—
207(C2×D11)⋊C4—44no—
208(C2×D11)⋊C4C22×C418yes—
209(C2×D11)⋊C4C22×C418yes—
210C4⋊Dic11—28no—
211C4⋊Dic11—24no—
212C4⋊Dic11C22×C414yes—
213C4⋊Dic11C22×C418yes—
214Dic11⋊C4—24no—
215Dic11⋊C4—24no—
216Dic11⋊C4—28no—
217Dic11⋊C4—44no—
218Dic11⋊C4C22×C418yes—
219Dic11⋊C4C22×C418yes—
220Dic11⋊C4C22×C418yes—
221Dic11⋊C4C22×C418yes—
222Dic11⋊C4C22×C418yes—
223C4×Dic11—28no—
224C4×Dic11—28no—
225C4×Dic11—22no—
226C4×Dic11—24no—
227C4×Dic11—22no—
228C4×Dic11—42no—
229C4×Dic11—44no—
230C4×Dic11—44no—
231C4×Dic11C22×C414yes—
232C4×Dic11C22×C418yes—
233C4×Dic11C22×C414yes—
234C4×Dic11C22×C414yes—
235C4×Dic11#4118yes—
236C2×#533—111no—
237#2336—114no—
238#2332—114no—
239#2331—112no—
240#2327—112no—
241#2323—112no—
242#2323—112no—
243#2298—112no—
244#2298—112no—
245#2295—112no—
246#2295—112no—
247#2295—111no—
248#2295D1111yescharacteristic, complemented
249#2283—111no—
250C42×Q8—111no—
251C42×Q8—111no—
252C4×#117—111no—
253C23×C11C2511yescharacteristic
254C22×D11—22no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—22no—
258C22×D11C23×C412yes—
259Q8×C11—28no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11C23×C412yes—
273C2×C4×C11C23×C414yes—
274C2×C4×C11C23×C414yes—
275C2×C4×C11C23×C412yes—
276C2×C4×C11C23×C412yes—
277C2×C4×C11C2×#4114yes—
278C2×C4×C112−1+412yes—
279C2×C4×C112−1+412yes—
280C2×Dic11—24no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—24no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11C23×C412yes—
294C2×Dic11C23×C412yes—
295C2×Dic11C23×C412yes—
296C2×Dic11C23×C414yes—
297C2×Dic11C23×C414yes—
298C2×Dic11C2×#4114yes—
299C2×Dic11C2×#4114yes—
300C4×D11—28no—
301C4×D11—28no—
302C4×D11—44no—
303Dic22—28no—
304Dic22—48no—
305#533—1116no—
306C2×C4⋊Q8—111no—
307C2×C4⋊Q8—111no—
308C2×#125—112no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×C22⋊Q8—112no—
312C2×C4×Q8—112no—
313C2×C4×Q8—112no—
314C2×C4×Q8—111no—
315C2×C4×Q8—112no—
316C2×C4×Q8C2×D1111yescharacteristic
317C2×#117—112no—
318C2×#117—112no—
319C22×C42—111no—
320#391—114no—
321#391—112no—
322#391—114no—
323#391C2×D1112yes—
324#389—114no—
325#389—112no—
326#389—114no—
327#389C2×D1112yes—
328#388—114no—
329#388—114no—
330#388—114no—
331#388—114no—
332#387—114no—
333#387—114no—
334#387—114no—
335#387—114no—
336#387—114no—
337#387—114no—
338#387—114no—
339#387—114no—
340#387—114no—
341#387C2×D1114yes—
342#383—112no—
343#382—112no—
344#381—112no—
345#380—112no—
346C4×C4⋊C4—112no—
347C4×C4⋊C4—112no—
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×D1111yescharacteristic
358C4×C4⋊C4C2×D1112yes—
359C4×C22⋊C4—112no—
360C4×C22⋊C4—111no—
361C4×C22⋊C4—111no—
362C4×C22⋊C4—112no—
363#376—112no—
364#376—112no—
365#376—112no—
366#376C2×D1112yes—
367C43—111no—
368C43—112no—
369C43—112no—
370C43C2×D1111yescharacteristic
371C22×C11C24×C411yescharacteristic
372C22×C11C22×#4112yes—
373C22×C11C2×2−1+411yescharacteristic
374C22×C11C2×2−1+411yescharacteristic
375C22×C11#58512yes—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—42no—
380C2×D11—42no—
381C4×C11—24no—
382C4×C11—24no—
383C4×C11—22no—
384C4×C11—44no—
385C4×C11—42no—
386C4×C11—42no—
387C4×C11C4×#4114yes—
388C4×C11#51914yes—
389Dic11—24no—
390Dic11—22no—
391Dic11—22no—
392Dic11—22no—
393Dic11—24no—
394Dic11—24no—
395Dic11—24no—
396Dic11—44no—
397C22×Q8—111no—
398C22×Q8—112no—
399C22×Q8C22×D1111yescharacteristic
400C23×C4—111no—
401C23×C4—111no—
402C23×C4—111no—
403C4⋊Q8—118no—
404C4⋊Q8—118no—
405#125—1116no—
406C22⋊Q8—118no—
407C22⋊Q8—1116no—
408C22⋊Q8—118no—
409C4×Q8—1116no—
410C4×Q8—118no—
411C4×Q8—228no—
412C4×Q8—228no—
413C4×Q8C4×D1118yes—
414#117—1116no—
415#117—228no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—114no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4C22×D1112yes—
430C2×C4⋊C4C22×D1114yes—
431C2×C4⋊C4C22×D1112yes—
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—112no—
434C2×C22⋊C4—112no—
435C2×C22⋊C4—112no—
436C2×C22⋊C4—112no—
437C2×C22⋊C4—114no—
438C2×C42—112no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—112no—
442C2×C42—111no—
443C2×C42—118no—
444C2×C42—114no—
445C2×C42—114no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—112no—
449C2×C42—112no—
450C2×C42—114no—
451C2×C42—114no—
452C2×C42C22×D1112yes—
453C2×C42C22×D1112yes—
454C2×C42C22×D1111yescharacteristic
455C2×C42C22×D1111yescharacteristic
456C2×C42C22×D1112yes—
457C2×C42C22×D1112yes—
458C2×C42C22×D1111yescharacteristic
459#95—112no—
460#95—112no—
461#95—112no—
462#95—112no—
463#95—114no—
464#95—114no—
465#95—114no—
466#95—114no—
467#95—114no—
468#95—112no—
469#95—114no—
470#95—114no—
471#95—114no—
472#95C22×D1114yes—
473#95C22×D1114yes—
474#95C22×D1112yes—
475#95C22×D1114yes—
476C2×C11C2×C4×#4111yescharacteristic
477C2×C11C2×#51911yescharacteristic
478C2×C11#342811yescharacteristic
479C2×C11#346112yes—
480C2×C11#346112yes—
481D11—42no—
482C24—111no—
483C2×Q8—24no—
484C2×Q8—114no—
485C2×Q8—118no—
486C2×Q8—224no—
487C2×Q8—444no—
488C2×Q8C2×C4×D1114yes—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—112no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—111no—
496C22×C4—114no—
497C22×C4—114no—
498C22×C4—114no—
499C22×C4—114no—
500C22×C4—222no—
501C22×C4—224no—
502C22×C4—222no—
503C22×C4—442no—
504C22×C4C23×D1112yes—
505C22×C4C23×D1114yes—
506C22×C4C23×D1112yes—
507C22×C4C23×D1111yescharacteristic
508C22×C4C23×D1112yes—
509C22×C4C23×D1112yes—
510C22×C4C23×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512C4⋊C4—24no—
513C4⋊C4—44no—
514C4⋊C4—118no—
515C4⋊C4—118no—
516C4⋊C4—118no—
517C4⋊C4—118no—
518C4⋊C4—118no—
519C4⋊C4—118no—
520C4⋊C4—114no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—228no—
524C4⋊C4—228no—
525C4⋊C4—224no—
526C4⋊C4—444no—
527C4⋊C4C2×C4×D1118yes—
528C4⋊C4C2×C4×D1114yes—
529C22⋊C4—118no—
530C22⋊C4—118no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—444no—
534C42—22no—
535C42—24no—
536C42—24no—
537C42—22no—
538C42—42no—
539C42—114no—
540C42—114no—
541C42—114no—
542C42—118no—
543C42—118no—
544C42—228no—
545C42—228no—
546C42—222no—
547C42—224no—
548C42—222no—
549C42—442no—
550C42—444no—
551C42—444no—
552C42C2×C4×D1114yes—
553C42C2×C4×D1118yes—
554C11#3408511yescharacteristic, complemented, Sylow
555C23—112no—
556C23—221no—
557C23—222no—
558C23—221no—
559C23—222no—
560C23C24×D1111yescharacteristic
561Q8—28no—
562Q8—228no—
563Q8—448no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—112no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—114no—
580C2×C4—114no—
581C2×C4—114no—
582C2×C4—114no—
583C2×C4—222no—
584C2×C4—221no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—221no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—224no—
592C2×C4—222no—
593C2×C4—228no—
594C2×C4—228no—
595C2×C4—224no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—444no—
599C2×C4C22×C4×D1112yes—
600C2×C4C22×C4×D1114yes—
601C2×C4C22×C4×D1114yes—
602C2×C4C22×C4×D1112yes—
603C2×C4C22×C4×D1112yes—
604C2×C4#6704012yes—
605C2×C4#41×D1114yes—
606C2×C4#6704312yes—
607C22—222no—
608C22—222no—
609C22—222no—
610C22—442no—
611C22—442no—
612C22C23×C4×D1111yescharacteristic
613C22C2×#6704011yescharacteristic
614C22C2×#41×D1112yes—
615C22C2×#6704311yescharacteristic
616C22#1062345312yes—
617C4—24no—
618C4—22no—
619C4—24no—
620C4—42no—
621C4—44no—
622C4—42no—
623C4—224no—
624C4—224no—
625C4—222no—
626C4—224no—
627C4—222no—
628C4—222no—
629C4—224no—
630C4—444no—
631C4#1062305314yes—
632C4#1062310314yes—
633C2—442no—
634C2C2×#1062305311yescharacteristic
635C2C2×#1062310311yescharacteristic
636C2#1308181511yescharacteristic
637C2#1308204112yes—
638C2#1308204712yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2295C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2295D11
hypocenterC11#34085
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2295

Complements

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

NH ≅ G/Ntype
2. #13071418C2semidirect
4. #13071363C2semidirect
5. #13071334C2semidirect
10. #13071093C2semidirect
11. #13071090C2semidirect
12. #13071088C2semidirect
14. C4×Q8×Dic11C2semidirect
15. C4×#66940C2semidirect
17. C11×#2295C2semidirect
22. #10623109C4semidirect
248. #2295D11semidirect
554. C11#34085semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130714182
#130713702
#130713632
#130713342
#130713012
#130712962
#130711112
#130711092
#130710932
#130710902
#130710882
#130710122
C4×Q8×Dic112
C4×#669402
C4×#669252
C11×#22952
#3408511