Finite Group Databasebeta

← #14914520

Subgroups — #14914520

Order 2816.

2238 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#13071673C212yesmaximal, complemented
3#13071669C212yesmaximal, complemented
4#13071626C212yesmaximal
5#13071620C212yesmaximal
6#13071576C212yesmaximal, complemented
7#13071533C212yesmaximal, complemented
8#13071473C212yesmaximal
9#13071469C212yesmaximal
10#13071418C214yesmaximal, complemented
11#13071262C211yesmaximal, characteristic, complemented
12#13071150C214yesmaximal
13#13071008C211yesmaximal, characteristic
14#13070981C211yesmaximal, characteristic, complemented
15#13070979C211yesmaximal, characteristic, complemented
16C4×C4⋊C4×D11C211yesmaximal, characteristic
17C11×#2320C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×Q8×Dic11C2212yes—
21C2×#66997C2211yescharacteristic
22#10623109C4116yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×C4⋊C4×D11C2212yes—
26C2×#66942C2212yes—
27C2×#66941C2211yescharacteristic
28C2×#66940C2214yes—
29C2×#66925C2212yes—
30C2×C42×D11C2212yes—
31C2×C42×D11C2211yescharacteristic
32C2×C4×Dic22C2212yes—
33C2×C4×Dic22C2211yescharacteristic
34C2×C4×Dic22C2212yes—
35C11×#391C2212yes—
36C11×#389C2212yes—
37C11×#387C2214yes—
38C11×#383C2212yes—
39C11×#382C2212yes—
40C4×C11×C4⋊C4C2211yescharacteristic
41C11×#376C2211yescharacteristic
42#10622602C2214yes—
43#10622591C2214yes—
44C4⋊C4×Dic11C2212yes—
45C4⋊C4×Dic11C2214yes—
46C4⋊C4×Dic11C2212yes—
47#10622587C2212yes—
48#10622586C2214yes—
49#10622586C2212yes—
50C4×(C2×D11)⋊C4C2212yes—
51C4×C4⋊Dic11C2212yes—
52C4×C4⋊Dic11C2211yescharacteristic
53C4×C4⋊Dic11C2212yes—
54#10622546C2214yes—
55#10622545C2212yes—
56#10622545C2211yescharacteristic
57C4×Dic11⋊C4C2212yes—
58C4×Dic11⋊C4C2212yes—
59#10622281C2214yes—
60#10622280C2212yes—
61#10622279C2214yes—
62#10622279C2214yes—
63#10622277C2211yescharacteristic
64#10622277C2211yescharacteristic
65D11×#95C2212yes—
66#10622268C2214yes—
67#10622267C2214yes—
68#10622265C2214yes—
69#10622265C2214yes—
70#10622265C2214yes—
71#10622264C2212yes—
72#10622264C2212yes—
73#10622263C2212yes—
74#10622263C2211yescharacteristic
75#10622263C2211yescharacteristic
76#10622262C2214yes—
77#10622262C2214yes—
78#10622262C2212yes—
79#10622262C2212yes—
80#10622261C2212yes—
81#10622260C2214yes—
82#10622260C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2314yes—
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×Dic22C2311yescharacteristic
90C22×Dic22C2312yes—
91C4×Q8×C11C2×C418yescomplemented
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2312yes—
96C2×C42×C11C2312yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2312yes—
100#66999C2×C418yes—
101Q8×Dic11—28no—
102#66997C2×C418yescomplemented
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2312yes—
113C2×Dic11⋊C4C2312yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132#66950C2×C418yes—
133#66949C2×C4116yes—
134C4⋊C4×D11—28no—
135#66942C2×C4116yescomplemented
136#66941C2×C418yescomplemented
137#66940—48no—
138#66925C2×C4116yes—
139C42×D11—44no—
140C42×D11C2×C418yes—
141C4×Dic22—28no—
142C4×Dic22C2×C4116yescomplemented
143C4×Dic22C2×C418yescomplemented
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11×#95C2311yescharacteristic
147C11×#95C2311yescharacteristic
148C11×#95C2312yes—
149C11×#95C2312yes—
150C11×#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2312yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2311yescharacteristic
159C11⋊#95C2311yescharacteristic
160C11⋊#95C2312yes—
161C11⋊#95C2312yes—
162C11⋊#95C2312yes—
163C11⋊#95C2312yes—
164C11⋊#95C2314yes—
165#34235—111nomaximal, Sylow
166C23×D11C2411yescharacteristic
167C2×Q8×C11—24no—
168C2×Q8×C11C22×C414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2411yescharacteristic
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2412yes—
181C22×Dic11C2412yes—
182C22×Dic11C2411yescharacteristic
183C22×Dic11C2414yes—
184C22×Dic11C2411yescharacteristic
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—28no—
188C2×C4×D11—24no—
189C2×C4×D11—28no—
190C2×C4×D11—24no—
191C2×C4×D11—44no—
192C2×C4×D11C22×C414yes—
193C2×C4×D11C22×C414yes—
194C2×C4×D11C22×C414yes—
195C2×Dic22—24no—
196C2×Dic22—24no—
197C2×Dic22—24no—
198C2×Dic22C22×C418yes—
199C2×Dic22C22×C414yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—44no—
202C11×C4⋊C4C22×C414yes—
203C11×C4⋊C4C22×C418yes—
204C42×C11—24no—
205C42×C11—42no—
206C42×C11C22×C414yes—
207C42×C11C22×C418yes—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4C22×C418yes—
211(C2×D11)⋊C4C22×C418yes—
212C4⋊Dic11—28no—
213C4⋊Dic11C22×C414yes—
214C4⋊Dic11C22×C418yes—
215C4⋊Dic11#4118yes—
216Dic11⋊C4—28no—
217Dic11⋊C4—28no—
218Dic11⋊C4—24no—
219Dic11⋊C4—24no—
220Dic11⋊C4—44no—
221Dic11⋊C4C22×C418yes—
222Dic11⋊C4C22×C418yes—
223Dic11⋊C4C22×C418yes—
224Dic11⋊C4C22×C418yes—
225Dic11⋊C4C22×C418yes—
226C4×Dic11—28no—
227C4×Dic11—28no—
228C4×Dic11—28no—
229C4×Dic11—24no—
230C4×Dic11—42no—
231C4×Dic11—44no—
232C4×Dic11—44no—
233C4×Dic11C22×C414yes—
234C4×Dic11C22×C418yes—
235C4×Dic11C22×C414yes—
236C4×Dic11C22×C414yes—
237C2×#533—111no—
238#2365—112no—
239#2365—112no—
240#2360—112no—
241#2360—112no—
242#2356—112no—
243#2351—112no—
244#2343—112no—
245#2343—112no—
246#2336—114no—
247#2320—111no—
248#2320D1111yescharacteristic, complemented
249C4×C22⋊Q8—114no—
250#2283—111no—
251#2276—111no—
252#2276—111no—
253C2×C4×C4⋊C4—111no—
254C23×C11C2511yescharacteristic
255C22×D11—22no—
256C22×D11—21no—
257C22×D11—21no—
258C22×D11C23×C412yes—
259C22×D112−1+414yes—
260Q8×C11—28no—
261C2×C4×C11—24no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11C23×C412yes—
277C2×C4×C11C23×C412yes—
278C2×C4×C11C23×C414yes—
279C2×C4×C11C23×C414yes—
280C2×C4×C11C23×C412yes—
281C2×C4×C11C2×#4114yes—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—24no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11C23×C412yes—
296C2×Dic11C23×C412yes—
297C2×Dic11C23×C414yes—
298C2×Dic11C23×C414yes—
299C2×Dic11C23×C412yes—
300C2×Dic11C2×#4118yes—
301C2×Dic11H(5,𝔽2)12yes—
302C2×Dic112−1+412yes—
303C4×D11—28no—
304C4×D11—28no—
305C4×D11—28no—
306C4×D11—416no—
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—111no—
315C2×C22⋊Q8—112no—
316C2×C4×Q8—112no—
317C2×C4×Q8—114no—
318C2×C4×Q8—111no—
319C2×C4×Q8—112no—
320C2×C4×Q8—112no—
321C2×C4×Q8C2×D1111yescharacteristic
322C2×#117—112no—
323C22×C4⋊C4—112no—
324C22×C42—111no—
325C22×C42—112no—
326#391—112no—
327#391—114no—
328#391C2×D1112yes—
329#389—112no—
330#389—114no—
331#389—114no—
332#389—114no—
333#389C2×D1112yes—
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#385—114no—
343#385—114no—
344#383—112no—
345#383—112no—
346#383C2×D1112yes—
347#382—112no—
348#382—111no—
349#382—111no—
350#382C2×D1112yes—
351#381—111no—
352#381—111no—
353#380—112no—
354C4×C4⋊C4—114no—
355C4×C4⋊C4—112no—
356C4×C4⋊C4—112no—
357C4×C4⋊C4—112no—
358C4×C4⋊C4—112no—
359C4×C4⋊C4—112no—
360C4×C4⋊C4—112no—
361C4×C4⋊C4—111no—
362C4×C4⋊C4—114no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—112no—
365C4×C4⋊C4—114no—
366C4×C4⋊C4C2×D1111yescharacteristic
367C4×C22⋊C4—112no—
368C4×C22⋊C4—114no—
369C4×C22⋊C4—114no—
370#376—111no—
371#376—112no—
372#376—112no—
373#376C2×D1111yescharacteristic
374C2×#95—112no—
375C22×C11C24×C411yescharacteristic
376C22×C11C22×#4112yes—
377C22×C11C2×H(5,𝔽2)11yescharacteristic
378C22×C11C2×2−1+412yes—
379C22×C11C2×2−1+411yescharacteristic
380C2×D11—22no—
381C2×D11—22no—
382C2×D11—24no—
383C2×D11—24no—
384C2×D11#51914yes—
385C4×C11—24no—
386C4×C11—22no—
387C4×C11—24no—
388C4×C11—22no—
389C4×C11—42no—
390C4×C11—44no—
391C4×C11—42no—
392C4×C11C4×#4114yes—
393Dic11—24no—
394Dic11—22no—
395Dic11—22no—
396Dic11—24no—
397Dic11—28no—
398Dic11—42no—
399Dic11—42no—
400Dic11#52014yes—
401C22×Q8—112no—
402C22×Q8—111no—
403C22×Q8C22×D1111yescharacteristic
404C23×C4—111no—
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—114no—
408C4⋊Q8—118no—
409C4⋊Q8—118no—
410#125—1116no—
411C22⋊Q8—118no—
412C22⋊Q8—1116no—
413C22⋊Q8—118no—
414C4×Q8—1116no—
415C4×Q8—118no—
416C4×Q8—228no—
417C4×Q8—228no—
418C4×Q8—448no—
419C4×Q8C4×D1118yescomplemented
420#117—1116no—
421C2×C4⋊C4—112no—
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—111no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—114no—
435C2×C4⋊C4—228no—
436C2×C4⋊C4C22×D1112yes—
437C2×C4⋊C4C22×D1114yes—
438C2×C4⋊C4C22×D1112yes—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C22⋊C4—112no—
441C2×C22⋊C4—112no—
442C2×C22⋊C4—112no—
443C2×C22⋊C4—112no—
444C2×C42—112no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—118no—
449C2×C42—114no—
450C2×C42—114no—
451C2×C42—112no—
452C2×C42—114no—
453C2×C42—114no—
454C2×C42—114no—
455C2×C42—112no—
456C2×C42—444no—
457C2×C42C22×D1112yes—
458C2×C42C22×D1112yes—
459C2×C42C22×D1112yes—
460C2×C42C22×D1111yescharacteristic
461#95—112no—
462#95—114no—
463#95—111no—
464#95—112no—
465#95—111no—
466#95—114no—
467#95—114no—
468#95—112no—
469#95—112no—
470#95—114no—
471#95—114no—
472#95—112no—
473#95—112no—
474#95—114no—
475#95C22×D1112yes—
476#95C22×D1111yescharacteristic
477#95C22×D1112yes—
478#95C22×D1111yescharacteristic
479#95C22×D1114yes—
480#95C22×D1114yes—
481#95C22×D1114yes—
482C2×C11C2×C4×#4111yescharacteristic
483C2×C11C2×#51911yescharacteristic
484C2×C11C2×#52011yescharacteristic
485C2×C11#352012yes—
486C2×C11#352312yes—
487D11—24no—
488C24—111no—
489C2×Q8—24no—
490C2×Q8—118no—
491C2×Q8—114no—
492C2×Q8—224no—
493C2×Q8—224no—
494C2×Q8—224no—
495C2×Q8C2×C4×D1114yes—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—114no—
499C22×C4—112no—
500C22×C4—112no—
501C22×C4—111no—
502C22×C4—114no—
503C22×C4—114no—
504C22×C4—114no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—228no—
510C22×C4—224no—
511C22×C4—228no—
512C22×C4—224no—
513C22×C4—444no—
514C22×C4C23×D1112yes—
515C22×C4C23×D1114yes—
516C22×C4C23×D1112yes—
517C22×C4C23×D1111yescharacteristic
518C22×C4C23×D1111yescharacteristic
519C22×C4C23×D1112yes—
520C22×C4C23×D1112yes—
521C22×C4C23×D1111yescharacteristic
522C4⋊C4—24no—
523C4⋊C4—44no—
524C4⋊C4—118no—
525C4⋊C4—118no—
526C4⋊C4—118no—
527C4⋊C4—118no—
528C4⋊C4—118no—
529C4⋊C4—118no—
530C4⋊C4—114no—
531C4⋊C4—118no—
532C4⋊C4—228no—
533C4⋊C4—228no—
534C4⋊C4—228no—
535C4⋊C4—224no—
536C4⋊C4—224no—
537C4⋊C4—444no—
538C4⋊C4C2×C4×D1118yes—
539C4⋊C4C2×C4×D1114yes—
540C22⋊C4—118no—
541C22⋊C4—118no—
542C22⋊C4—224no—
543C22⋊C4—224no—
544C42—24no—
545C42—42no—
546C42—114no—
547C42—114no—
548C42—114no—
549C42—118no—
550C42—228no—
551C42—228no—
552C42—228no—
553C42—224no—
554C42—442no—
555C42—444no—
556C42—444no—
557C42C2×C4×D1114yes—
558C42C2×C4×D1118yes—
559C11#3423511yescharacteristic, complemented, Sylow
560C23—112no—
561C23—114no—
562C23—222no—
563C23—221no—
564C23—221no—
565C23C24×D1111yescharacteristic
566Q8—28no—
567Q8—2216no—
568Q8—228no—
569C2×C4—24no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—112no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—112no—
589C2×C4—114no—
590C2×C4—114no—
591C2×C4—118no—
592C2×C4—228no—
593C2×C4—228no—
594C2×C4—224no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—222no—
598C2×C4—224no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—228no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—4416no—
609C2×C4C22×C4×D1112yes—
610C2×C4C22×C4×D1112yes—
611C2×C4C22×C4×D1114yes—
612C2×C4C22×C4×D1114yes—
613C2×C4C22×C4×D1112yes—
614C2×C4#41×D1114yes—
615C22—114no—
616C22—224no—
617C22—224no—
618C22—222no—
619C22—222no—
620C22C23×C4×D1111yescharacteristic
621C22C2×#41×D1112yes—
622C22D11×H(5,𝔽2)11yescharacteristic
623C22D11×2−1+412yes—
624C22D11×2−1+411yescharacteristic
625C4—24no—
626C4—22no—
627C4—22no—
628C4—24no—
629C4—44no—
630C4—42no—
631C4—42no—
632C4—114no—
633C4—228no—
634C4—222no—
635C4—224no—
636C4—222no—
637C4—224no—
638C4—442no—
639C4—442no—
640C4#1062305314yes—
641C2—224no—
642C2C2×#1062305311yescharacteristic
643C2D11×#51911yescharacteristic
644C2D11×#52011yescharacteristic
645C2#1308266312yes—
646C2#1308270812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2320C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2320D11
hypocenterC11#34235
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #13071673C2semidirect
3. #13071669C2semidirect
6. #13071576C2semidirect
7. #13071533C2semidirect
10. #13071418C2semidirect
11. #13071262C2semidirect
14. #13070981C2semidirect
15. #13070979C2semidirect
17. C11×#2320C2semidirect
22. #10623109C4semidirect
91. C4×Q8×C11C2×C4semidirect
102. #66997C2×C4semidirect
135. #66942C2×C4semidirect
136. #66941C2×C4semidirect
142. C4×Dic22C2×C4semidirect
143. C4×Dic22C2×C4semidirect
248. #2320D11semidirect
419. C4×Q8C4×D11semidirect
559. C11#34235semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130716732
#130716692
#130716262
#130716202
#130715762
#130715332
#130714732
#130714692
#130714182
#130712622
#130711502
#130710082
#130709812
#130709792
C4×C4⋊C4×D112
C11×#23202
#3423511