Finite Group Databasebeta

← #14916927

Subgroups — #14916927

Order 2816.

2090 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2#13071763C214yesmaximal, complemented
3#13071656C212yesmaximal
4#13071648C212yesmaximal, complemented
5#13071587C211yesmaximal, characteristic, complemented
6#13071537C211yesmaximal, characteristic, complemented
7#13071524C211yesmaximal, characteristic, complemented
8#13071504C212yesmaximal, complemented
9#13071477C212yesmaximal, complemented
10#13071394C214yesmaximal, complemented
11#13071353C212yesmaximal, complemented
12#13071330C212yesmaximal, complemented
13#13071260C212yesmaximal, complemented
14#13071247C212yesmaximal, complemented
15#13071022C211yesmaximal, characteristic, complemented
16#13071012C211yesmaximal, characteristic, complemented
17C11×#2356C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×Q8×Dic11C2212yes—
22#10623111C4116yescomplemented
23C2×#66951C2212yes—
24C2×#66948C2211yescharacteristic
25C2×#66947C2212yes—
26C2×#66946C2212yes—
27C2×#66945C2212yes—
28C2×#66943C2211yescharacteristic
29C2×C4×D44C2211yescharacteristic
30C2×C4×D44C2212yes—
31C2×#66925C2212yes—
32C2×C42×D11C2211yescharacteristic
33C11×#391C2212yes—
34C11×#387C2214yes—
35C11×#383C2212yes—
36C11×#382C2211yescharacteristic
37C4×C11×C4⋊C4C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#376C2212yes—
40#10622603C2214yes—
41#10622600C2212yes—
42#10622598C2214yes—
43#10622598C2212yes—
44#10622590C2212yes—
45#10622589C2212yes—
46#10622586C2212yes—
47#10622552C2214yes—
48#10622552C2212yes—
49C4×(C2×D11)⋊C4C2212yes—
50C4×(C2×D11)⋊C4C2214yes—
51#10622549C2212yes—
52#10622549C2211yescharacteristic
53C4×C4⋊Dic11C2212yes—
54C4×C4⋊Dic11C2212yes—
55C4×C4⋊Dic11C2211yescharacteristic
56#10622546C2214yes—
57#10622545C2212yes—
58#10622541C2214yes—
59#10622283C2214yes—
60#10622283C2214yes—
61#10622282C2214yes—
62#10622282C2214yes—
63#10622282C2214yes—
64#10622281C2214yes—
65#10622281C2214yes—
66#10622281C2214yes—
67#10622280C2212yes—
68#10622280C2212yes—
69#10622280C2212yes—
70#10622279C2212yes—
71#10622278C2214yes—
72#10622277C2212yes—
73#10622277C2211yescharacteristic
74#10622277C2211yescharacteristic
75D11×#95C2212yes—
76#10622268C2214yes—
77#10622267C2214yes—
78#10622264C2211yescharacteristic
79#10622264C2211yescharacteristic
80#10622262C2214yes—
81#10622262C2212yes—
82#10622262C2212yes—
83#10622260C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×D44C2312yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2314yes—
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2312yes—
92C4×Q8×C11C2×C418yescomplemented
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2314yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2312yes—
101#67000C2×C418yes—
102#66999C2×C418yescomplemented
103Q8×Dic11—44no—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×(C2×D11)⋊C4C2312yes—
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2314yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133#66951C2×C4116yescomplemented
134#66948C2×C418yes—
135#66947C2×C4116yescomplemented
136#66946—44no—
137#66945—44no—
138#66943C2×C418yescomplemented
139C4×D44C2×C418yes—
140C4×D44C2×C4116yescomplemented
141#66925C2×C4116yescomplemented
142C42×D11C2×C418yescomplemented
143C11×#95C2314yes—
144C11×#95C2312yes—
145C11×#95C2312yes—
146C11×#95C2314yes—
147C11×#95C2311yescharacteristic
148C11×#95C2311yescharacteristic
149C11×#95C2314yes—
150C11⋊#95C2312yes—
151C11⋊#95C2312yes—
152C11⋊#95C2312yes—
153C11⋊#95C2312yes—
154C11⋊#95C2312yes—
155C11⋊#95C2311yescharacteristic
156C11⋊#95C2311yescharacteristic
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163#34392—111nomaximal, Sylow
164C23×D11C2411yescharacteristic
165C23×D11C2412yes—
166C2×Q8×C11—22no—
167C2×Q8×C11—22no—
168C2×Q8×C11C22×C414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2412yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2411yescharacteristic
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2411yescharacteristic
182C22×Dic11C2412yes—
183C22×Dic11C2411yescharacteristic
184C2×D44—22no—
185C2×D44—22no—
186C2×D44—44no—
187C2×D44C22×C414yes—
188C2×D44C22×C418yes—
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—44no—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11C22×C414yes—
198C2×C4×D11C22×C414yes—
199C2×C4×D11C22×C414yes—
200C2×C4×D11C22×C418yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—42no—
203C11×C4⋊C4C22×C414yes—
204C11×C4⋊C4C22×C418yes—
205C42×C11—24no—
206C42×C11—44no—
207C42×C11C22×C414yes—
208C42×C11C22×C418yes—
209(C2×D11)⋊C4—44no—
210(C2×D11)⋊C4—44no—
211(C2×D11)⋊C4—42no—
212(C2×D11)⋊C4—42no—
213(C2×D11)⋊C4—44no—
214(C2×D11)⋊C4—44no—
215(C2×D11)⋊C4C22×C418yes—
216(C2×D11)⋊C4C22×C418yes—
217(C2×D11)⋊C4C22×C418yes—
218(C2×D11)⋊C4C22×C418yes—
219(C2×D11)⋊C4C22×C418yes—
220C4⋊Dic11—24no—
221C4⋊Dic11—44no—
222C4⋊Dic11—42no—
223C4⋊Dic11—44no—
224C4⋊Dic11C22×C414yes—
225C4⋊Dic11C22×C418yes—
226Dic11⋊C4—44no—
227Dic11⋊C4—44no—
228Dic11⋊C4—44no—
229Dic11⋊C4C22×C418yes—
230Dic11⋊C4C22×C418yes—
231C4×Dic11—24no—
232C4×Dic11—44no—
233C4×Dic11—44no—
234C4×Dic11—44no—
235C4×Dic11C22×C414yes—
236C4×Dic11C22×C414yes—
237C4×Dic11C22×C414yes—
238C2×#529—111no—
239#2376—114no—
240#2363—112no—
241#2362—112no—
242#2357—111no—
243#2356D1111yescharacteristic, complemented
244#2351—111no—
245#2349—111no—
246#2347—112no—
247#2343—112no—
248#2334—114no—
249#2330—112no—
250#2326—112no—
251#2319—112no—
252#2318—112no—
253#2285—111no—
254#2283—111no—
255C23×C11C2511yescharacteristic
256C22×D11—21no—
257C22×D11—22no—
258C22×D11—21no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—24no—
262C22×D11—24no—
263C22×D11—22no—
264C22×D11C23×C414yes—
265C22×D11C23×C412yes—
266Q8×C11—28no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11C23×C412yes—
282C2×C4×C11C23×C412yes—
283C2×C4×C11C23×C414yes—
284C2×C4×C11C23×C414yes—
285C2×C4×C11C23×C412yes—
286C2×C4×C11H(5,𝔽2)12yes—
287C2×C4×C112−1+412yes—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—24no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—22no—
300C2×Dic11—22no—
301C2×Dic11—22no—
302C2×Dic11C23×C412yes—
303C2×Dic11C23×C412yes—
304C2×Dic11C23×C412yes—
305C2×Dic11C23×C414yes—
306D44—28no—
307D44—48no—
308C4×D11—28no—
309C4×D11—44no—
310C4×D11—44no—
311C4×D11—48no—
312C4×D11—88no—
313#529—1116no—
314C2×#126—112no—
315C2×#125—111no—
316C2×#124—111no—
317C2×#123—112no—
318C2×C22⋊Q8—111no—
319C2×#121—111no—
320C2×C4×Q8—112no—
321C2×C4×Q8C2×D1111yescharacteristic
322C2×C4×D4—112no—
323C2×C4×D4—112no—
324C2×C4×D4—111no—
325C2×#117—112no—
326C2×#117—112no—
327C22×C42—111no—
328#391C2×D1112yes—
329#390—114no—
330#390—112no—
331#389—112no—
332#389—112no—
333#389—114no—
334#389—114no—
335#389—114no—
336#388—114no—
337#388—114no—
338#388—114no—
339#388—114no—
340#388—114no—
341#388—114no—
342#387—114no—
343#387—114no—
344#387—114no—
345#387C2×D1114yes—
346#386—114no—
347#385—114no—
348#385—114no—
349#385—114no—
350#384—112no—
351#383—111no—
352#383—111no—
353#383C2×D1112yes—
354#382—112no—
355#382—112no—
356#382—111no—
357#382C2×D1111yescharacteristic
358#381—111no—
359#381—111no—
360#381—112no—
361#380—112no—
362#380—112no—
363#380—112no—
364#380—112no—
365C4×C4⋊C4—112no—
366C4×C4⋊C4—112no—
367C4×C4⋊C4—111no—
368C4×C4⋊C4—112no—
369C4×C4⋊C4—114no—
370C4×C4⋊C4—112no—
371C4×C4⋊C4C2×D1112yes—
372C4×C4⋊C4C2×D1111yescharacteristic
373C4×C22⋊C4—114no—
374C4×C22⋊C4—112no—
375C4×C22⋊C4—112no—
376#376—112no—
377#376C2×D1112yes—
378C2×#95—112no—
379C22×C11C24×C411yescharacteristic
380C22×C11C2×H(5,𝔽2)11yescharacteristic
381C22×C11C2×2−1+411yescharacteristic
382C22×C11#58512yes—
383C22×C11#58512yes—
384C2×D11—22no—
385C2×D11—24no—
386C2×D11—22no—
387C2×D11—24no—
388C2×D11—22no—
389C2×D11—24no—
390C2×D11—42no—
391C2×D11—44no—
392C2×D11—42no—
393C2×D11—44no—
394C4×C11—24no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—24no—
398C4×C11—44no—
399C4×C11—42no—
400C4×C11—42no—
401C4×C11#52014yes—
402Dic11—22no—
403Dic11—22no—
404Dic11—24no—
405Dic11—22no—
406Dic11—42no—
407Dic11—42no—
408Dic11—44no—
409C22×Q8C22×D1111yescharacteristic
410C22×D4—111no—
411C22×D4—112no—
412C23×C4—111no—
413C23×C4—112no—
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—114no—
417#126—1116no—
418#125—118no—
419#124—118no—
420#123—1116no—
421C22⋊Q8—118no—
422#121—118no—
423C4×Q8—444no—
424C4×Q8C4×D1118yescomplemented
425C4×D4—118no—
426C4×D4—1116no—
427C4×D4—444no—
428#117—1116no—
429#117—444no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—114no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4C22×D1112yes—
442C2×C4⋊C4C22×D1112yes—
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C4⋊C4C22×D1112yes—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—112no—
447C2×C22⋊C4—112no—
448C2×C22⋊C4—112no—
449C2×C22⋊C4—112no—
450C2×C22⋊C4—114no—
451C2×C22⋊C4—114no—
452C2×C22⋊C4—112no—
453C2×C22⋊C4—112no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—114no—
456C2×C42—111no—
457C2×C42—111no—
458C2×C42—111no—
459C2×C42—118no—
460C2×C42—112no—
461C2×C42—114no—
462C2×C42—114no—
463C2×C42—114no—
464C2×C42C22×D1112yes—
465C2×C42C22×D1114yes—
466C2×C42C22×D1112yes—
467C2×C42C22×D1111yescharacteristic
468#95—111no—
469#95—114no—
470#95—112no—
471#95—112no—
472#95—112no—
473#95—112no—
474#95—112no—
475#95—112no—
476#95—112no—
477#95—114no—
478#95—111no—
479#95—112no—
480#95—114no—
481#95C22×D1112yes—
482#95C22×D1111yescharacteristic
483#95C22×D1114yes—
484#95C22×D1111yescharacteristic
485#95C22×D1112yes—
486#95C22×D1114yes—
487#95C22×D1114yes—
488C2×C11C2×#52011yescharacteristic
489C2×C11#342811yescharacteristic
490C2×C11#342811yescharacteristic
491C2×C11#356212yes—
492C2×C11#356512yes—
493D11—42no—
494D11—44no—
495C24—112no—
496C24—111no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8C2×C4×D1114yes—
500C2×D4—114no—
501C2×D4—118no—
502C2×D4—222no—
503C2×D4—222no—
504C2×D4—444no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—112no—
509C22×C4—114no—
510C22×C4—114no—
511C22×C4—114no—
512C22×C4—118no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—114no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—442no—
519C22×C4—444no—
520C22×C4—442no—
521C22×C4—444no—
522C22×C4—444no—
523C22×C4—444no—
524C22×C4C23×D1112yes—
525C22×C4C23×D1112yes—
526C22×C4C23×D1114yes—
527C22×C4C23×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529C22×C4C23×D1112yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1111yescharacteristic
532C4⋊C4—24no—
533C4⋊C4—42no—
534C4⋊C4—118no—
535C4⋊C4—118no—
536C4⋊C4—114no—
537C4⋊C4—118no—
538C4⋊C4—224no—
539C4⋊C4—444no—
540C4⋊C4—444no—
541C4⋊C4—444no—
542C4⋊C4—444no—
543C4⋊C4—444no—
544C4⋊C4—442no—
545C4⋊C4C2×C4×D1114yes—
546C4⋊C4C2×C4×D1118yes—
547C22⋊C4—118no—
548C22⋊C4—118no—
549C22⋊C4—118no—
550C22⋊C4—118no—
551C22⋊C4—118no—
552C22⋊C4—444no—
553C22⋊C4—444no—
554C22⋊C4—444no—
555C22⋊C4—442no—
556C22⋊C4—444no—
557C22⋊C4—442no—
558C42—24no—
559C42—44no—
560C42—114no—
561C42—114no—
562C42—114no—
563C42—224no—
564C42—444no—
565C42—444no—
566C42—444no—
567C42C2×C4×D1114yes—
568C42C2×C4×D1118yes—
569C11#3439211yescharacteristic, complemented, Sylow
570C23—114no—
571C23—112no—
572C23—221no—
573C23—222no—
574C23—221no—
575C23—222no—
576C23—224no—
577C23—222no—
578C23—222no—
579C23—224no—
580C23C24×D1111yescharacteristic
581Q8—28no—
582D4—228no—
583D4—448no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—114no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—222no—
607C2×C4—228no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—224no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—444no—
618C2×C4—444no—
619C2×C4—448no—
620C2×C4—888no—
621C2×C4C22×C4×D1112yes—
622C2×C4C22×C4×D1112yes—
623C2×C4C22×C4×D1114yes—
624C2×C4C22×C4×D1114yes—
625C2×C4C22×C4×D1112yes—
626C2×C4#6704212yes—
627C2×C4#6704312yes—
628C22—222no—
629C22—224no—
630C22—222no—
631C22—224no—
632C22—224no—
633C22—222no—
634C22—444no—
635C22—442no—
636C22—442no—
637C22—444no—
638C22C23×C4×D1111yescharacteristic
639C22C2×#6704211yescharacteristic
640C22C2×#6704311yescharacteristic
641C22#1062345312yes—
642C22#1062345712yes—
643C4—24no—
644C4—22no—
645C4—24no—
646C4—22no—
647C4—44no—
648C4—42no—
649C4—42no—
650C4—222no—
651C4—222no—
652C4—222no—
653C4—224no—
654C4—442no—
655C4—442no—
656C4—444no—
657C4#1062305414yes—
658C2—442no—
659C2—444no—
660C2C2×#1062305411yescharacteristic
661C2#1308181511yescharacteristic
662C2#1308181811yescharacteristic
663C2#1308321112yes—
664C2#1308326412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2356C2
socle, cosocleC23×C11C25
prime radicalC2×#66948C22
hypercenter#2356D11
hypocenterC11#34392
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2356

Complements

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

NH ≅ G/Ntype
2. #13071763C2semidirect
4. #13071648C2semidirect
5. #13071587C2semidirect
6. #13071537C2semidirect
7. #13071524C2semidirect
8. #13071504C2semidirect
9. #13071477C2semidirect
10. #13071394C2semidirect
11. #13071353C2semidirect
12. #13071330C2semidirect
13. #13071260C2semidirect
14. #13071247C2semidirect
15. #13071022C2semidirect
16. #13071012C2semidirect
17. C11×#2356C2semidirect
22. #10623111C4semidirect
92. C4×Q8×C11C2×C4semidirect
102. #66999C2×C4semidirect
133. #66951C2×C4semidirect
135. #66947C2×C4semidirect
138. #66943C2×C4semidirect
140. C4×D44C2×C4semidirect
141. #66925C2×C4semidirect
142. C42×D11C2×C4semidirect
243. #2356D11semidirect
424. C4×Q8C4×D11semidirect
569. C11#34392semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
#130717632
#130716562
#130716482
#130715872
#130715372
#130715242
#130715042
#130714772
#130713942
#130713532
#130713302
#130712602
#130712472
#130710222
#130710122
C11×#23562
#3439211