Finite Group Databasebeta

← #14912539

Subgroups — #14912539

Order 2816.

3134 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623055C211yesmaximal, characteristic
2C2×#10623053C211yesmaximal, characteristic, complemented
3C22×#66925C211yesmaximal, characteristic, complemented
4#13071307C214yesmaximal, complemented
5#13071296C214yesmaximal, complemented
6#13071284C214yesmaximal, complemented
7#13071273C214yesmaximal, complemented
8#13071106C211yesmaximal, characteristic, complemented
9#13071077C214yesmaximal, complemented
10#13071057C214yesmaximal, complemented
11#13070995C211yesmaximal, characteristic, complemented
12#117×Dic11C211yesmaximal, characteristic, complemented
13C11×#2296C211yesmaximal, characteristic, complemented
14C22×#4339C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C2×#66979C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23#10623055C4116yescomplemented
24#10623053—28no—
25C2×#66950C2212yes—
26C2×#66948C2212yes—
27C2×#66946C2212yescomplemented
28C2×#66940C2212yescomplemented
29C2×#66939C2212yes—
30C2×#66935C2212yes—
31C2×(C22⋊D11)⋊C4C2214yes—
32C2×C4×D44C2214yes—
33C2×#66925—28no—
34C2×#66925C2214yes—
35C2×#66925C2212yes—
36C2×#66925C2212yes—
37C2×#66925C2212yescomplemented
38C2×C42×D11C2212yescomplemented
39C11×#389C2214yescomplemented
40C11×#385C2214yes—
41C4×C11×C4⋊C4C2214yescomplemented
42#10622826C2214yes—
43#10622603C2218yes—
44#10622602C2218yescomplemented
45#10622601C2218yes—
46#10622600C2214yes—
47C4⋊C4×Dic11C2214yescomplemented
48#10622586C2218yescomplemented
49#10622568C2212yes—
50#10622556C2212yes—
51C22⋊C4×Dic11C2214yes—
52#10622552C2212yescomplemented
53C4×(C2×D11)⋊C4C2214yes—
54C4×(C2×D11)⋊C4C2214yescomplemented
55#10622545C2212yescomplemented
56C42×Dic11C2212yescomplemented
57#10622542C2212yescomplemented
58#10622282C2218yes—
59#10622282C2218yescomplemented
60#10622278C2218yes—
61#10622267C2218yescomplemented
62C24×D11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C2×#4339—24no—
69C2×#4339—24no—
70C2×#4339C2×C418yes—
71C22×D44C2311yescharacteristic
72C22×D44C2314yes—
73C22×C4×D11—24no—
74C22×C4×D11—24no—
75C22×C4×D11C2×C418yescomplemented
76C22×C4×D11C2312yes—
77C22×C4×D11C2312yes—
78C22×C4×D11C2312yes—
79C22×C4×D11C2314yes—
80C22×Dic22C2311yescharacteristic
81C11×#117—24no—
82C11×#117C2×C418yescomplemented
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C22⋊C4C2312yes—
87C2×C11×C22⋊C4C2312yes—
88C2×C42×C11—24no—
89C2×C42×C11C2312yes—
90C2×C42×C11C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C2×(C2×D11)⋊C4—28no—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2314yes—
102#66979—24no—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2314yes—
105C2×Dic11⋊C4—28no—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×C4×Dic11D418yescomplemented
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2318yes—
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2312yes—
116#66950C2×C4116yescomplemented
117#66948C2×C4116yescomplemented
118#66946—28no—
119#66940—28no—
120#66939C2×C4116yescomplemented
121#66935C2×C4116yescomplemented
122(C22⋊D11)⋊C4—216no—
123C4×D44C2×C4132yescomplemented
124#66925—28no—
125#66925—28no—
126#66925—216no—
127#66925—28no—
128C42×D11—28no—
129C11×#95C2318yes—
130C11⋊#95C2318yes—
131C11⋊#95C2318yes—
132C11⋊#95C2318yes—
133#34065—111nomaximal, Sylow
134C24×C11C2411yescharacteristic
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—44no—
138C23×D11C22×C414yes—
139C23×D11C2412yes—
140C23×D11C2412yes—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11C22×C414yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11#4114yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—24no—
153C2×C22⋊D11C22×C418yes—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—44no—
157C22×Dic11C22×C414yes—
158C22×Dic11C2×D418yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164#4339—232no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—48no—
168C2×D44C22×C414yes—
169C2×D44C22×C4116yes—
170C2×C4×D11—28no—
171C2×C4×D11—232no—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—24no—
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—24no—
178C2×C4×D11—48no—
179C2×C4×D11C22×C418yes—
180C2×C4×D11C22×C418yes—
181C2×C4×D11C22×C418yes—
182C2×Dic22—22no—
183C2×Dic22—22no—
184C2×Dic22C22×C414yes—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—48no—
187C11×C4⋊C4C22×C418yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4C22×C418yes—
190C42×C11—24no—
191C42×C11—24no—
192C42×C11—24no—
193C42×C11C22×C418yes—
194C22⋊Dic11—24no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—28no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—48no—
199(C2×D11)⋊C4—48no—
200(C2×D11)⋊C4C22×C4116yes—
201(C2×D11)⋊C4C22×C4116yes—
202C4⋊Dic11—24no—
203C4⋊Dic11C22×C4116yes—
204Dic11⋊C4—28no—
205Dic11⋊C4—28no—
206Dic11⋊C4—28no—
207C4×Dic11—28no—
208C4×Dic11—24no—
209C4×Dic11—48no—
210C4×Dic11C2×D414yes—
211C4×Dic11C2×D414yes—
212C4×Dic11C2×D418yes—
213C2×#525—111no—
214C2×C4×#41—111no—
215C22×#117—111no—
216#2324—114no—
217#2323—114no—
218#2322—114no—
219#2321—114no—
220#2297—111no—
221#2296D1111yescharacteristic, complemented
222#2293—114no—
223#2290—114no—
224#2280—111no—
225C4×#117—111no—
226C23×C11—24no—
227C23×C11C23×C412yes—
228C23×C11C22×D412yes—
229C23×C11C2×#4112yes—
230C23×C11C2511yescharacteristic
231C22×D11—28no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—24no—
237C22×D11—28no—
238C22×D11—24no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11C23×C414yes—
243C22×D11C23×C414yes—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—28no—
249C2×C4×C11—24no—
250C2×C4×C11—48no—
251C2×C4×C11C4×D4116yes—
252C2×C4×C11C23×C418yes—
253C2×C4×C11C23×C412yes—
254C2×C4×C11C23×C412yes—
255C2×C4×C11C22×D412yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C2×#4112yes—
258C2×C4×C11C2×#4112yes—
259C22⋊D11—216no—
260C2×Dic11—28no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—28no—
269C2×Dic11—48no—
270C2×Dic11C23×C414yes—
271C2×Dic11C23×C414yes—
272C2×Dic11C22×D414yes—
273C2×Dic11C22×D414yes—
274D44—28no—
275D44—416no—
276C4×D11—216no—
277C4×D11—216no—
278C4×D11—216no—
279C4×D11—416no—
280Dic22—28no—
281C22×#41—111no—
282C24×C4—111no—
283#525—1116no—
284C2×#123—112no—
285C2×C22⋊Q8—112no—
286C2×#121—112no—
287C2×#120—112no—
288C4×#41—228no—
289C2×C4×Q8—112no—
290C2×C4×D4—112no—
291C2×C4×D4—114no—
292C2×C4×D4—114no—
293C2×#117—111no—
294C2×#117—114no—
295C2×#117—112no—
296C2×#117—112no—
297C2×#117—112no—
298C2×#117—228no—
299C2×#117C2×D1111yescharacteristic
300C2×#117C2×D1111yescharacteristic
301C22×C4⋊C4—112no—
302C22×C22⋊C4—112no—
303C22×C42—111no—
304C22×C42—112no—
305C22×C42C2×D1111yescharacteristic
306#391—112no—
307#390—118no—
308#390—112no—
309#389—118no—
310#389C2×D1114yescomplemented
311#388—118no—
312#388—118no—
313#388—118no—
314#387—118no—
315#386—114no—
316#386—118no—
317#385—118no—
318#385C2×D1114yes—
319#381—112no—
320#380—114no—
321#379—112no—
322C4×C4⋊C4—114no—
323C4×C4⋊C4C2×D1114yescomplemented
324C4×C22⋊C4—114no—
325C4×C22⋊C4—114no—
326C4×C22⋊C4—114no—
327#376—112no—
328C43—112no—
329C22×C11—24no—
330C22×C11—24no—
331C22×C11—24no—
332C22×C11C2×C4×D414yes—
333C22×C11C24×C411yescharacteristic
334C22×C11C23×D411yescharacteristic
335C22×C11C22×#4111yescharacteristic
336C22×C11#58514yes—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—28no—
342C2×D11—416no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C4×C11—28no—
348C4×C11—44no—
349C4×C11—44no—
350C4×C11C2×C4×D414yes—
351C4×C11C2×C4×D414yes—
352Dic11—24no—
353Dic11—24no—
354Dic11—24no—
355Dic11—24no—
356Dic11—44no—
357C25—111no—
358C2×#41—118no—
359C2×#41—224no—
360C2×#41—224no—
361C22×Q8—111no—
362C22×D4—112no—
363C22×D4—111no—
364C22×D4—114no—
365C23×C4—111no—
366C23×C4—112no—
367C23×C4—118no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4—114no—
372C23×C4—224no—
373C23×C4—224no—
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376#123—1116no—
377C22⋊Q8—1116no—
378#121—1116no—
379#120—1116no—
380C4×Q8—228no—
381C4×D4—1132no—
382C4×D4—228no—
383C4×D4—2216no—
384#117—24no—
385#117—228no—
386#117—228no—
387#117—2216no—
388#117—228no—
389#117—224no—
390#117C4×D1118yescomplemented
391C2×C4⋊C4—114no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—114no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—112no—
396C2×C4⋊C4—228no—
397C2×C4⋊C4C22×D1112yes—
398C2×C4⋊C4C22×D1118yes—
399C2×C4⋊C4C22×D1112yes—
400C2×C22⋊C4—114no—
401C2×C22⋊C4—114no—
402C2×C22⋊C4—112no—
403C2×C22⋊C4—114no—
404C2×C22⋊C4—114no—
405C2×C22⋊C4—114no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—118no—
408C2×C22⋊C4—228no—
409C2×C22⋊C4C22×D1112yes—
410C2×C22⋊C4C22×D1112yes—
411C2×C42—24no—
412C2×C42—118no—
413C2×C42—112no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—114no—
417C2×C42—112no—
418C2×C42—118no—
419C2×C42—228no—
420C2×C42C22×D1112yes—
421C2×C42C22×D1112yes—
422C2×C42C22×D1112yes—
423C2×C42C22×D1112yes—
424#95—118no—
425#95—118no—
426#95—118no—
427#95C22×D1118yes—
428C2×C11—24no—
429C2×C11C22×C4×D411yescharacteristic
430C2×C11#342812yes—
431C2×C11#344912yes—
432C2×C11#345512yes—
433D11—44no—
434D11—44no—
435C24—112no—
436C24—112no—
437C24—114no—
438C24—222no—
439C24—222no—
440C24—444no—
441C24C23×D1111yescharacteristic
442#41—2232no—
443C2×Q8—114no—
444C2×Q8—222no—
445C2×Q8—222no—
446C2×D4—118no—
447C2×D4—114no—
448C2×D4—1116no—
449C2×D4—224no—
450C2×D4—224no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—448no—
454C22×C4—24no—
455C22×C4—44no—
456C22×C4—114no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—118no—
462C22×C4—118no—
463C22×C4—118no—
464C22×C4—118no—
465C22×C4—114no—
466C22×C4—228no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—2232no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—448no—
477C22×C4—444no—
478C22×C4C2×C4×D1114yes—
479C22×C4D4×D1114yes—
480C22×C4#434314yes—
481C22×C4C23×D1114yes—
482C22×C4C23×D1114yes—
483C22×C4C23×D1114yes—
484C22×C4C23×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486C4⋊C4—24no—
487C4⋊C4—48no—
488C4⋊C4—1116no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—228no—
492C4⋊C4—224no—
493C4⋊C4C2×C4×D1118yes—
494C22⋊C4—24no—
495C22⋊C4—1116no—
496C22⋊C4—1116no—
497C22⋊C4—228no—
498C22⋊C4—228no—
499C22⋊C4—228no—
500C22⋊C4—224no—
501C22⋊C4—448no—
502C22⋊C4—448no—
503C22⋊C4C2×C4×D1118yes—
504C42—24no—
505C42—24no—
506C42—24no—
507C42—114no—
508C42—114no—
509C42—118no—
510C42—228no—
511C42—224no—
512C42—448no—
513C42C2×C4×D1118yes—
514C11#3406511yescharacteristic, complemented, Sylow
515C23—24no—
516C23—114no—
517C23—114no—
518C23—228no—
519C23—222no—
520C23—222no—
521C23—222no—
522C23—222no—
523C23—224no—
524C23—228no—
525C23—224no—
526C23—448no—
527C23—448no—
528C23—448no—
529C23C22×C4×D1112yes—
530C23C2×D4×D1112yes—
531C23C2×#434312yes—
532C23C24×D1111yescharacteristic
533Q8—228no—
534D4—2216no—
535D4—228no—
536D4—4416no—
537C2×C4—28no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—28no—
542C2×C4—24no—
543C2×C4—48no—
544C2×C4—114no—
545C2×C4—114no—
546C2×C4—114no—
547C2×C4—114no—
548C2×C4—228no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—222no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—2216no—
556C2×C4—2216no—
557C2×C4—2216no—
558C2×C4—224no—
559C2×C4—228no—
560C2×C4—4416no—
561C2×C4—448no—
562C2×C4#66946116yes—
563C2×C4C22×C4×D1118yes—
564C2×C4C22×C4×D1112yes—
565C2×C4C22×C4×D1112yes—
566C2×C4C2×D4×D1112yes—
567C2×C4C2×D4×D1112yes—
568C2×C4C2×#434312yes—
569C2×C4C2×#434312yes—
570C22—24no—
571C22—24no—
572C22—24no—
573C22—224no—
574C22—224no—
575C22—224no—
576C22—228no—
577C22—224no—
578C22—4416no—
579C22—444no—
580C22—444no—
581C22—444no—
582C22—444no—
583C22C2×#6694614yes—
584C22C23×C4×D1111yescharacteristic
585C22C22×D4×D1111yescharacteristic
586C22C22×#434311yescharacteristic
587C22#1062345314yes—
588C4—28no—
589C4—44no—
590C4—44no—
591C4—224no—
592C4—224no—
593C4—224no—
594C4—224no—
595C4—444no—
596C4C2×#6694614yes—
597C4C2×#6694614yes—
598C2—24no—
599C2—444no—
600C2—444no—
601C2C22×#6694611yescharacteristic
602C2#1308181512yes—
603C2#1308194612yes—
604C2#1308200812yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2296C2
socle, cosocleC23×C11C25
prime radicalC2×#10623055C2
hypercenter#2296D11
hypocenterC11#34065
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2296

Complements

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

NH ≅ G/Ntype
2. C2×#10623053C2semidirect
3. C22×#66925C2semidirect
4. #13071307C2semidirect
5. #13071296C2semidirect
6. #13071284C2semidirect
7. #13071273C2semidirect
8. #13071106C2semidirect
9. #13071077C2semidirect
10. #13071057C2semidirect
11. #13070995C2semidirect
12. #117×Dic11C2semidirect
13. C11×#2296C2semidirect
23. #10623055C4semidirect
27. C2×#66946C22semidirect
28. C2×#66940C22semidirect
37. C2×#66925C22semidirect
38. C2×C42×D11C22semidirect
39. C11×#389C22semidirect
41. C4×C11×C4⋊C4C22semidirect
44. #10622602C22semidirect
47. C4⋊C4×Dic11C22semidirect
48. #10622586C22semidirect
52. #10622552C22semidirect
54. C4×(C2×D11)⋊C4C22semidirect
55. #10622545C22semidirect
56. C42×Dic11C22semidirect
57. #10622542C22semidirect
59. #10622282C22semidirect
61. #10622267C22semidirect
75. C22×C4×D11C2×C4semidirect
82. C11×#117C2×C4semidirect
109. C2×C4×Dic11D4semidirect
116. #66950C2×C4semidirect
117. #66948C2×C4semidirect
120. #66939C2×C4semidirect
121. #66935C2×C4semidirect
123. C4×D44C2×C4semidirect
221. #2296D11semidirect
310. #389C2×D11semidirect
323. C4×C4⋊C4C2×D11semidirect
390. #117C4×D11semidirect
514. C11#34065semidirect

Maximal subgroups

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

subgroupindex
C2×#106230552
C2×#106230532
C22×#669252
#130713072
#130712962
#130712842
#130712732
#130711062
#130710772
#130710572
#130709952
#117×Dic112
C11×#22962
#3406511