Finite Group Databasebeta

← #14914310

Subgroups — #14914310

Order 2816.

2138 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13071718C214yesmaximal, complemented
3#13071693C214yesmaximal
4#13071583C212yesmaximal, complemented
5#13071576C212yesmaximal, complemented
6#13071473C212yesmaximal
7#13071469C212yesmaximal
8#13071363C212yesmaximal, complemented
9#13071334C212yesmaximal, complemented
10#13071268C211yesmaximal, characteristic, complemented
11#13071154C212yesmaximal
12#13071146C212yesmaximal
13#13071012C211yesmaximal, characteristic
14#13070981C211yesmaximal, characteristic, complemented
15#13070980C211yesmaximal, characteristic, complemented
16D11×#376C211yesmaximal, characteristic
17C11×#2320C211yesmaximal, 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×C42×D11C2212yes—
30C2×C42×D11C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2212yes—
33C11×#391C2212yes—
34C11×#389C2212yes—
35C11×#387C2214yes—
36C11×#383C2212yes—
37C11×#382C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#376C2211yescharacteristic
40#10622602C2214yes—
41#10622600C2212yes—
42#10622591C2214yes—
43#10622590C2212yes—
44C4⋊C4×Dic11C2212yes—
45C4⋊C4×Dic11C2212yes—
46C4⋊C4×Dic11C2214yes—
47C4⋊C4×Dic11C2214yes—
48#10622587C2214yes—
49C4×(C2×D11)⋊C4C2212yes—
50C4×C4⋊Dic11C2212yes—
51C4×C4⋊Dic11C2211yescharacteristic
52#10622545C2212yes—
53#10622545C2211yescharacteristic
54#10622545C2212yes—
55#10622545C2212yes—
56C4×Dic11⋊C4C2214yes—
57#10622542C2212yes—
58#10622541C2212yes—
59#10622281C2214yes—
60#10622279C2214yes—
61#10622279C2214yes—
62#10622277C2212yes—
63D11×#95C2212yes—
64D11×#95C2211yescharacteristic
65D11×#95C2211yescharacteristic
66#10622268C2214yes—
67#10622268C2214yes—
68#10622268C2214yes—
69#10622267C2214yes—
70#10622265C2214yes—
71#10622265C2214yes—
72#10622265C2214yes—
73#10622265C2214yes—
74#10622264C2212yes—
75#10622264C2212yes—
76#10622263C2212yes—
77#10622262C2214yes—
78#10622262C2212yes—
79#10622261C2212yes—
80#10622261C2211yescharacteristic
81#10622261C2211yescharacteristic
82#10622261C2212yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2312yes—
86C22×C4×D11C2312yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×Dic22C2311yescharacteristic
91C22×Dic22C2312yes—
92C4×Q8×C11C2×C418yescomplemented
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2312yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2312yes—
101#66999C2×C418yes—
102Q8×Dic11—28no—
103#66997C2×C418yescomplemented
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×C4⋊Dic11C2314yes—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2312yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2312yes—
114C2×Dic11⋊C4C2312yes—
115C2×Dic11⋊C4C2312yes—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2312yes—
118C2×C4×Dic11C2312yes—
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2312yes—
130#66950C2×C418yes—
131#66949C2×C4116yes—
132#66942C2×C4116yescomplemented
133#66941C2×C418yescomplemented
134#66940—28no—
135#66925C2×C4116yes—
136C42×D11—28no—
137C42×D11C2×C418yes—
138C4×Dic22C2×C4116yescomplemented
139C4×Dic22C2×C418yescomplemented
140C11×#95C2314yes—
141C11×#95C2312yes—
142C11×#95C2311yescharacteristic
143C11×#95C2311yescharacteristic
144C11×#95C2312yes—
145C11×#95C2314yes—
146C11×#95C2314yes—
147C11⋊#95C2312yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2311yescharacteristic
151C11⋊#95C2311yescharacteristic
152C11⋊#95C2312yes—
153C11⋊#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2312yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163#34221—111nomaximal, Sylow
164C23×D11C2411yescharacteristic
165C2×Q8×C11—24no—
166C2×Q8×C11C22×C414yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2414yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C22×C4×C11C2412yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2411yescharacteristic
175C22×Dic11C2414yes—
176C22×Dic11C2411yescharacteristic
177C22×Dic11C2411yescharacteristic
178C22×Dic11C2411yescharacteristic
179C22×Dic11C2412yes—
180C22×Dic11C2412yes—
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—24no—
189C2×C4×D11—41no—
190C2×C4×D11—41no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11C22×C414yes—
194C2×C4×D11C22×C414yes—
195C2×C4×D11C22×C414yes—
196C2×Dic22—24no—
197C2×Dic22—42no—
198C2×Dic22—42no—
199C2×Dic22C22×C414yes—
200C2×Dic22C22×C418yes—
201C11×C4⋊C4—24no—
202C11×C4⋊C4—44no—
203C11×C4⋊C4C22×C414yes—
204C11×C4⋊C4C22×C418yes—
205C42×C11—24no—
206C42×C11—42no—
207C42×C11C22×C414yes—
208C42×C11C22×C418yes—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4C22×C418yes—
211(C2×D11)⋊C4C22×C418yes—
212C4⋊Dic11—28no—
213C4⋊Dic11—24no—
214C4⋊Dic11C22×C414yes—
215C4⋊Dic11C22×C418yes—
216Dic11⋊C4—28no—
217Dic11⋊C4—44no—
218Dic11⋊C4C22×C418yes—
219Dic11⋊C4C22×C418yes—
220Dic11⋊C4C22×C418yes—
221Dic11⋊C4C22×C418yes—
222Dic11⋊C4C22×C418yes—
223C4×Dic11—24no—
224C4×Dic11—24no—
225C4×Dic11—28no—
226C4×Dic11—28no—
227C4×Dic11—44no—
228C4×Dic11—42no—
229C4×Dic11—44no—
230C4×Dic11C22×C414yes—
231C4×Dic11C22×C418yes—
232C4×Dic11C22×C414yes—
233C4×Dic11C22×C414yes—
234C4×Dic11#4118yes—
235C2×#533—111no—
236#2371—114no—
237#2368—114no—
238#2356—112no—
239#2356—112no—
240#2343—112no—
241#2343—112no—
242#2331—112no—
243#2327—112no—
244#2320—111no—
245#2320D1111yescharacteristic, complemented
246C4×C22⋊Q8—112no—
247C4×C22⋊Q8—112no—
248#2283—111no—
249#2276—111no—
250#2276—111no—
251C2×#376—111no—
252C23×C11C2511yescharacteristic
253C22×D11—22no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11C23×C412yes—
257C22×D112−1+414yes—
258Q8×C11—28no—
259C2×C4×C11—24no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11C23×C412yes—
275C2×C4×C11C23×C412yes—
276C2×C4×C11C23×C414yes—
277C2×C4×C11C23×C414yes—
278C2×C4×C11C23×C412yes—
279C2×C4×C11C2×#4114yes—
280C2×Dic11—22no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11C23×C412yes—
295C2×Dic11C23×C412yes—
296C2×Dic11C23×C412yes—
297C2×Dic11C23×C414yes—
298C2×Dic11C23×C414yes—
299C2×Dic11C2×#4114yes—
300C2×Dic11C2×#4114yes—
301C4×D11—28no—
302C4×D11—28no—
303C4×D11—44no—
304C4×D11—48no—
305C4×D11—48no—
306Dic22—28no—
307Dic22—48no—
308#533—1116no—
309C2×C4⋊Q8—111no—
310C2×C4⋊Q8—111no—
311C2×#125—112no—
312C2×C22⋊Q8—111no—
313C2×C22⋊Q8—112no—
314C2×C22⋊Q8—111no—
315C2×C4×Q8—112no—
316C2×C4×Q8—112no—
317C2×C4×Q8—111no—
318C2×C4×Q8—112no—
319C2×C4×Q8C2×D1111yescharacteristic
320C2×#117—112no—
321C22×C42—111no—
322C22×C42—112no—
323#391—114no—
324#391—112no—
325#391—114no—
326#391C2×D1112yes—
327#389—112no—
328#389C2×D1112yes—
329#387—114no—
330#387—114no—
331#387—114no—
332#387—114no—
333#387—114no—
334#387—114no—
335#387—114no—
336#387—114no—
337#387—114no—
338#387C2×D1114yes—
339#385—114no—
340#385—114no—
341#383—112no—
342#383—112no—
343#383C2×D1112yes—
344#382—112no—
345#382—112no—
346#382C2×D1112yes—
347#381—112no—
348#380—112no—
349C4×C4⋊C4—112no—
350C4×C4⋊C4—112no—
351C4×C4⋊C4—114no—
352C4×C4⋊C4—114no—
353C4×C4⋊C4—111no—
354C4×C4⋊C4—112no—
355C4×C4⋊C4—114no—
356C4×C4⋊C4—112no—
357C4×C4⋊C4—114no—
358C4×C4⋊C4C2×D1111yescharacteristic
359C4×C22⋊C4—112no—
360C4×C22⋊C4—114no—
361C4×C22⋊C4—114no—
362#376—112no—
363#376—112no—
364#376—112no—
365#376—111no—
366#376—112no—
367#376—111no—
368#376—111no—
369#376—112no—
370#376C2×D1111yescharacteristic
371C2×#95—111no—
372C2×#95—111no—
373C2×#95—112no—
374C22×C11C24×C411yescharacteristic
375C22×C11C22×#4112yes—
376C22×C11C2×2−1+412yes—
377C22×C11#58511yescharacteristic
378C22×C11#58511yescharacteristic
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—24no—
382C2×D11—24no—
383C2×D11#51914yes—
384C4×C11—24no—
385C4×C11—22no—
386C4×C11—24no—
387C4×C11—22no—
388C4×C11—44no—
389C4×C11—42no—
390C4×C11—42no—
391C4×C11C4×#4114yes—
392Dic11—24no—
393Dic11—22no—
394Dic11—22no—
395Dic11—22no—
396Dic11—24no—
397Dic11—24no—
398Dic11—24no—
399Dic11—44no—
400C22×Q8—111no—
401C22×Q8—112no—
402C22×Q8C22×D1111yescharacteristic
403C23×C4—111no—
404C23×C4—111no—
405C23×C4—111no—
406C23×C4—112no—
407C23×C4—112no—
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×Q8C4×D1118yescomplemented
419#117—1116no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4C22×D1112yes—
432C2×C4⋊C4C22×D1114yes—
433C2×C4⋊C4C22×D1112yes—
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C22⋊C4—112no—
436C2×C22⋊C4—112no—
437C2×C22⋊C4—114no—
438C2×C42—112no—
439C2×C42—112no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—118no—
444C2×C42—114no—
445C2×C42—114no—
446C2×C42—112no—
447C2×C42—112no—
448C2×C42—112no—
449C2×C42—114no—
450C2×C42—114no—
451C2×C42—228no—
452C2×C42C22×D1112yes—
453C2×C42C22×D1112yes—
454C2×C42C22×D1112yes—
455C2×C42C22×D1111yescharacteristic
456#95—111no—
457#95—111no—
458#95—112no—
459#95—112no—
460#95—112no—
461#95—112no—
462#95—112no—
463#95—114no—
464#95—112no—
465#95—114no—
466#95—114no—
467#95—114no—
468#95—114no—
469#95—114no—
470#95—114no—
471#95—114no—
472#95C22×D1111yescharacteristic
473#95C22×D1111yescharacteristic
474#95C22×D1112yes—
475#95C22×D1112yes—
476#95C22×D1114yes—
477#95C22×D1114yes—
478#95C22×D1114yes—
479C2×C11C2×C4×#4111yescharacteristic
480C2×C11C2×#51911yescharacteristic
481C2×C11#342811yescharacteristic
482C2×C11#349512yes—
483C2×C11#349512yes—
484D11—24no—
485C24—111no—
486C2×Q8—24no—
487C2×Q8—114no—
488C2×Q8—118no—
489C2×Q8—224no—
490C2×Q8—442no—
491C2×Q8—442no—
492C2×Q8C2×C4×D1114yes—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—112no—
496C22×C4—112no—
497C22×C4—111no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—114no—
501C22×C4—114no—
502C22×C4—114no—
503C22×C4—114no—
504C22×C4—224no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—224no—
509C22×C4—224no—
510C22×C4—441no—
511C22×C4—441no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4C23×D1112yes—
515C22×C4C23×D1112yes—
516C22×C4C23×D1114yes—
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—228no—
532C4⋊C4—228no—
533C4⋊C4—224no—
534C4⋊C4—444no—
535C4⋊C4C2×C4×D1118yes—
536C4⋊C4C2×C4×D1114yes—
537C22⋊C4—118no—
538C22⋊C4—118no—
539C22⋊C4—228no—
540C42—24no—
541C42—42no—
542C42—114no—
543C42—114no—
544C42—114no—
545C42—118no—
546C42—118no—
547C42—224no—
548C42—224no—
549C42—228no—
550C42—228no—
551C42—442no—
552C42—444no—
553C42—444no—
554C42C2×C4×D1114yes—
555C42C2×C4×D1118yes—
556C11#3422111yescharacteristic, complemented, Sylow
557C23—112no—
558C23—114no—
559C23—222no—
560C23—221no—
561C23—221no—
562C23C24×D1111yescharacteristic
563Q8—28no—
564Q8—228no—
565Q8—448no—
566C2×C4—24no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—112no—
582C2×C4—112no—
583C2×C4—112no—
584C2×C4—114no—
585C2×C4—114no—
586C2×C4—114no—
587C2×C4—114no—
588C2×C4—228no—
589C2×C4—222no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—221no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—221no—
600C2×C4—228no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—444no—
605C2×C4—448no—
606C2×C4—448no—
607C2×C4C22×C4×D1112yes—
608C2×C4C22×C4×D1112yes—
609C2×C4C22×C4×D1114yes—
610C2×C4C22×C4×D1114yes—
611C2×C4C22×C4×D1112yes—
612C2×C4#41×D1114yes—
613C22—114no—
614C22—222no—
615C22—222no—
616C22—224no—
617C22—224no—
618C22C23×C4×D1111yescharacteristic
619C22C2×#41×D1112yes—
620C22#1062345511yescharacteristic
621C22D11×2−1+412yes—
622C22#1062345711yescharacteristic
623C4—24no—
624C4—22no—
625C4—22no—
626C4—24no—
627C4—42no—
628C4—42no—
629C4—44no—
630C4—222no—
631C4—224no—
632C4—222no—
633C4—222no—
634C4—224no—
635C4—224no—
636C4—224no—
637C4—444no—
638C4#1062305314yes—
639C2—224no—
640C2C2×#1062305311yescharacteristic
641C2D11×#51911yescharacteristic
642C2#1308181611yescharacteristic
643C2#1308236012yes—
644C2#1308236612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2320C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2320D11
hypocenterC11#34221
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #13071718C2semidirect
4. #13071583C2semidirect
5. #13071576C2semidirect
8. #13071363C2semidirect
9. #13071334C2semidirect
10. #13071268C2semidirect
14. #13070981C2semidirect
15. #13070980C2semidirect
17. C11×#2320C2semidirect
22. #10623109C4semidirect
92. C4×Q8×C11C2×C4semidirect
103. #66997C2×C4semidirect
132. #66942C2×C4semidirect
133. #66941C2×C4semidirect
138. C4×Dic22C2×C4semidirect
139. C4×Dic22C2×C4semidirect
245. #2320D11semidirect
418. C4×Q8C4×D11semidirect
556. C11#34221semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130717182
#130716932
#130715832
#130715762
#130714732
#130714692
#130713632
#130713342
#130712682
#130711542
#130711462
#130710122
#130709812
#130709802
D11×#3762
C11×#23202
#3422111