Finite Group Databasebeta

← #14914696

Subgroups — #14914696

Order 2816.

2230 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C211yesmaximal, characteristic
2#13071742C214yesmaximal, complemented
3#13071729C214yesmaximal, complemented
4#13071495C212yesmaximal, complemented
5#13071480C212yesmaximal, complemented
6#13071462C212yesmaximal
7#13071458C212yesmaximal
8#13071397C214yesmaximal, complemented
9#13071211C211yesmaximal, characteristic
10#13071166C214yesmaximal, complemented
11#13071010C211yesmaximal, characteristic, complemented
12#13070973C211yesmaximal, characteristic, complemented
13#13070968C211yesmaximal, characteristic
14C4×#66930C211yesmaximal, characteristic, complemented
15C11×#2313C211yesmaximal, characteristic, complemented
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C2×#66979C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×#66951C4116yescomplemented
25C2×#66951C2212yes—
26C2×#66951C2212yes—
27C2×#66951C2212yes—
28C2×#66951C2212yes—
29C2×C22⋊C4×D11C2212yes—
30C2×#66930C2212yes—
31C11×#387C2214yescomplemented
32C11×#387C2214yescomplemented
33C11×#381C2212yes—
34C11×#380C2212yes—
35C4×C11×C22⋊C4C2211yescharacteristic
36C4×C11×C22⋊C4C2211yescharacteristic
37C4×C22⋊Dic11C2212yes—
38C4×C22⋊Dic11C2211yescharacteristic
39C4×C22⋊Dic11C2211yescharacteristic
40#10622603C2214yes—
41#10622602C2214yes—
42C4⋊C4×Dic11C2214yescomplemented
43C4⋊C4×Dic11C2214yescomplemented
44C4⋊C4×Dic11C2214yescomplemented
45#10622586C2214yescomplemented
46#10622568C2212yes—
47#10622556C2212yes—
48#10622555C2212yes—
49#10622555C2212yes—
50C22⋊C4×Dic11C2212yes—
51C22⋊C4×Dic11C2212yes—
52#10622553C2214yes—
53C4×(C2×D11)⋊C4C2214yes—
54#10622545C2212yescomplemented
55C4×Dic11⋊C4C2212yescomplemented
56C4×Dic11⋊C4C2212yescomplemented
57C42×Dic11C2212yescomplemented
58#10622283C2214yes—
59#10622282C2214yes—
60#10622282C2214yes—
61#10622282C2214yes—
62#10622281C2214yes—
63#10622279C2214yes—
64#10622279C2214yes—
65#10622279C2214yes—
66#10622268C2214yescomplemented
67#10622266C2214yescomplemented
68#10622266C2214yescomplemented
69#10622265C2214yescomplemented
70#10622264C2212yescomplemented
71#10622263C2212yescomplemented
72#10622262C2214yescomplemented
73#10622262C2212yescomplemented
74#10622261C2212yescomplemented
75#10622260C2214yescomplemented
76C24×D11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C22×C4×D11C2314yes—
84C2×C11×C4⋊C4C2×C418yescomplemented
85C2×C11×C4⋊C4C2314yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C42×C11C2312yes—
91C2×C42×C11C2312yes—
92C2×C22⋊Dic11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C2×(C2×D11)⋊C4C2×C418yes—
95C2×(C2×D11)⋊C4C2×C418yes—
96C2×(C2×D11)⋊C4C2×C418yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2312yes—
101C2×(C2×D11)⋊C4C2312yes—
102C2×(C2×D11)⋊C4C2312yes—
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2312yes—
106#66979—28no—
107C2×C4⋊Dic11C2×C418yescomplemented
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2312yes—
111C2×Dic11⋊C4C2×C418yescomplemented
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2312yes—
116C2×Dic11⋊C4C2312yes—
117C2×C4×Dic11C2×C418yescomplemented
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2314yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2314yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2311yescharacteristic
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2311yescharacteristic
129#66951C2×C4116yescomplemented
130#66951C2×C4116yescomplemented
131#66951C2×C4116yescomplemented
132#66951C2×C4116yescomplemented
133C22⋊C4×D11—28no—
134#66930—28no—
135C11×#95C2314yes—
136C11×#95C2312yes—
137C11×#95C2314yes—
138C11×#95C2312yes—
139C11×#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2312yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2312yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149#34247—111nomaximal, Sylow
150C24×C11C2411yescharacteristic
151C23×D11—24no—
152C23×D11—42no—
153C23×D11—42no—
154C23×D11C22×C414yes—
155C23×D11C2412yes—
156C22×C4×C11—24no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C22×C414yes—
160C22×C4×C11C22×C414yes—
161C22×C4×C11C22×C414yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C22×Dic11—24no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C22×Dic11C22×C414yes—
172C22×Dic11C22×C414yes—
173C22×Dic11C22×C414yes—
174C22×Dic11C2414yes—
175C22×Dic11C2411yescharacteristic
176C22×Dic11C2411yescharacteristic
177C22×Dic11C2411yescharacteristic
178C22×Dic11C2412yes—
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2414yes—
181C2×C4×D11—28no—
182C2×C4×D11—44no—
183C2×C4×D11—44no—
184C11×C4⋊C4—44no—
185C11×C4⋊C4C22×C418yes—
186C11×C4⋊C4C22×C418yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—24no—
189C42×C11—42no—
190C42×C11—42no—
191C22⋊Dic11—24no—
192C22⋊Dic11#4118yes—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—44no—
195(C2×D11)⋊C4—44no—
196(C2×D11)⋊C4C22×C418yes—
197(C2×D11)⋊C4C22×C418yes—
198(C2×D11)⋊C4C22×C418yes—
199(C2×D11)⋊C4C22×C418yes—
200(C2×D11)⋊C4C22×C418yes—
201(C2×D11)⋊C4C22×C418yes—
202C4⋊Dic11—28no—
203C4⋊Dic11C22×C418yes—
204C4⋊Dic11C22×C418yes—
205Dic11⋊C4—28no—
206Dic11⋊C4—44no—
207Dic11⋊C4—44no—
208Dic11⋊C4C22×C418yes—
209Dic11⋊C4C22×C418yes—
210C4×Dic11—28no—
211C4×Dic11—28no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C4×Dic11—44no—
215C4×Dic11—44no—
216C4×Dic11—44no—
217C4×Dic11C22×C414yes—
218C4×Dic11C22×C414yes—
219C4×Dic11C22×C414yes—
220C4×Dic11C22×C414yes—
221C22×#126—111no—
222#2373—114no—
223#2373—114no—
224#2345—112no—
225#2344—112no—
226#2342—112no—
227#2342—112no—
228#2334—114no—
229#2313D1111yescharacteristic, complemented
230#2312—111no—
231C4×#126—114no—
232#2283—111no—
233#2274—111no—
234#2273—111no—
235C4×#117—111no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11C23×C412yes—
239C23×C11C2×#4114yes—
240C23×C11C2511yescharacteristic
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—28no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—88no—
249C22×D11C23×C414yes—
250C2×C4×C11—28no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—44no—
263C2×C4×C11—44no—
264C2×C4×C11C23×C412yes—
265C2×C4×C11C23×C412yes—
266C2×C4×C11C23×C414yes—
267C2×C4×C11C23×C414yes—
268C2×Dic11—28no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—44no—
280C2×Dic11—44no—
281C2×Dic11C23×C412yes—
282C2×Dic11C23×C412yes—
283C2×Dic11C23×C412yes—
284C2×Dic11C23×C412yes—
285C2×Dic11C23×C414yes—
286C2×Dic11C2×#4118yes—
287C4×D11—88no—
288C2×#126—112no—
289C2×#126—112no—
290C2×#126—112no—
291C2×#126—112no—
292C2×#126—1116no—
293C2×#117—112no—
294C2×#117—112no—
295C22×C4⋊C4—111no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4C2×D1111yescharacteristic
298C22×C22⋊C4—111no—
299C22×C22⋊C4—111no—
300C22×C22⋊C4—111no—
301C22×C22⋊C4—112no—
302C22×C42—111no—
303#389—114no—
304#389—114no—
305#388—114no—
306#388—114no—
307#388—114no—
308#388—114no—
309#388—114no—
310#388—114no—
311#387—114no—
312#387—114no—
313#387—114no—
314#387—114no—
315#387C2×D1114yescomplemented
316#387C2×D1114yescomplemented
317#385—114no—
318#385—114no—
319#383—112no—
320#382—112no—
321#381—112no—
322#381C2×D1112yes—
323#380—112no—
324#380—112no—
325#380C2×D1112yes—
326#379—112no—
327C4×C4⋊C4—114no—
328C4×C4⋊C4—114no—
329C4×C4⋊C4—114no—
330C4×C4⋊C4—112no—
331C4×C4⋊C4—112no—
332C4×C4⋊C4—114no—
333C4×C4⋊C4—112no—
334C4×C22⋊C4—111no—
335C4×C22⋊C4—112no—
336C4×C22⋊C4—111no—
337C4×C22⋊C4—112no—
338C4×C22⋊C4—112no—
339C4×C22⋊C4—114no—
340C4×C22⋊C4—114no—
341C4×C22⋊C4—114no—
342C4×C22⋊C4—114no—
343C4×C22⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4C2×D1111yescharacteristic
345#376—112no—
346#376—112no—
347C43—112no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—28no—
351C22×C11C4×#4114yes—
352C22×C11C24×C411yescharacteristic
353C22×C11C22×#4112yes—
354C22×C11#58512yes—
355C22×C11#58512yes—
356C2×D11—24no—
357C2×D11—24no—
358C2×D11—24no—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—88no—
362C4×C11—24no—
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—24no—
366C4×C11—44no—
367C4×C11—44no—
368Dic11—22no—
369Dic11—22no—
370Dic11—22no—
371Dic11—24no—
372Dic11—22no—
373Dic11—28no—
374Dic11—44no—
375C25—111no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—114no—
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383#126—1116no—
384#126—1116no—
385#126—1116no—
386#126—1116no—
387#117—228no—
388#117—228no—
389C2×C4⋊C4—118no—
390C2×C4⋊C4—118no—
391C2×C4⋊C4—112no—
392C2×C4⋊C4—112no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—112no—
395C2×C4⋊C4—114no—
396C2×C4⋊C4—114no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—114no—
399C2×C4⋊C4C4×D1118yescomplemented
400C2×C4⋊C4C22×D1114yes—
401C2×C4⋊C4C22×D1112yes—
402C2×C4⋊C4C22×D1112yes—
403C2×C22⋊C4—112no—
404C2×C22⋊C4—118no—
405C2×C22⋊C4—118no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—112no—
408C2×C22⋊C4—112no—
409C2×C22⋊C4—112no—
410C2×C22⋊C4—112no—
411C2×C22⋊C4—112no—
412C2×C22⋊C4—112no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—114no—
415C2×C22⋊C4—114no—
416C2×C22⋊C4—114no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4C22×D1112yes—
419C2×C22⋊C4C22×D1112yes—
420C2×C42—118no—
421C2×C42—111no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—114no—
426C2×C42—114no—
427C2×C42—112no—
428C2×C42—114no—
429C2×C42—112no—
430C2×C42—114no—
431C2×C42—114no—
432C2×C42C22×D1112yes—
433C2×C42C22×D1112yes—
434#95—112no—
435#95—114no—
436#95—114no—
437#95—114no—
438#95—114no—
439#95—114no—
440#95—112no—
441#95—114no—
442#95—114no—
443#95C22×D1112yes—
444#95C22×D1112yes—
445#95C22×D1114yes—
446#95C22×D1114yes—
447#95C22×D1114yes—
448C2×C11—24no—
449C2×C11C2×C4×#4111yescharacteristic
450C2×C11#342811yescharacteristic
451C2×C11#342811yescharacteristic
452C2×C11#352114yes—
453D11—44no—
454C24—112no—
455C24—114no—
456C24—224no—
457C24—442no—
458C24—442no—
459C24C23×D1111yescharacteristic
460C22×C4—24no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—114no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—114no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—228no—
474C22×C4—224no—
475C22×C4—444no—
476C22×C4—444no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4C2×C4×D1114yes—
480C22×C4C2×C4×D1114yes—
481C22×C4C2×C4×D1114yes—
482C22×C4C23×D1114yes—
483C22×C4C23×D1114yes—
484C22×C4C23×D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C4⋊C4—44no—
489C4⋊C4—118no—
490C4⋊C4—118no—
491C4⋊C4—118no—
492C4⋊C4—118no—
493C4⋊C4—228no—
494C4⋊C4—228no—
495C4⋊C4—444no—
496C4⋊C4—444no—
497C4⋊C4C2×C4×D1118yes—
498C4⋊C4C2×C4×D1118yes—
499C22⋊C4—24no—
500C22⋊C4—24no—
501C22⋊C4—118no—
502C22⋊C4—118no—
503C22⋊C4—118no—
504C22⋊C4—118no—
505C22⋊C4—118no—
506C22⋊C4—118no—
507C22⋊C4—118no—
508C22⋊C4—228no—
509C22⋊C4—224no—
510C22⋊C4—444no—
511C22⋊C4—444no—
512C42—42no—
513C42—42no—
514C42—114no—
515C42—114no—
516C42—114no—
517C42—114no—
518C42—228no—
519C42—228no—
520C42—442no—
521C42—442no—
522C42—444no—
523C42—444no—
524C42—444no—
525C11#3424711yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—114no—
529C23—222no—
530C23—222no—
531C23—224no—
532C23—224no—
533C23—228no—
534C23—444no—
535C23—444no—
536C23—888no—
537C23C22×C4×D1112yes—
538C23#41×D1114yes—
539C23C24×D1111yescharacteristic
540C2×C4—28no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—112no—
557C2×C4—112no—
558C2×C4—114no—
559C2×C4—118no—
560C2×C4—228no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—222no—
566C2×C4—224no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—444no—
572C2×C4—444no—
573C2×C4—888no—
574C2×C4C22×C4×D1112yes—
575C2×C4C22×C4×D1112yes—
576C2×C4C22×C4×D1114yes—
577C2×C4C22×C4×D1114yes—
578C22—28no—
579C22—22no—
580C22—22no—
581C22—224no—
582C22—224no—
583C22—224no—
584C22—444no—
585C22—444no—
586C22—888no—
587C22#1062305314yes—
588C22C23×C4×D1111yescharacteristic
589C22C2×#41×D1112yes—
590C22#1062345512yes—
591C22#1062345712yes—
592C4—24no—
593C4—22no—
594C4—22no—
595C4—24no—
596C4—44no—
597C4—44no—
598C4—228no—
599C4—222no—
600C4—222no—
601C4—222no—
602C4—222no—
603C4—224no—
604C4—444no—
605C2—24no—
606C2—444no—
607C2C2×#1062305311yescharacteristic
608C2#1308181411yescharacteristic
609C2#1308181811yescharacteristic
610C2#1308267414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2313C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2313D11
hypocenterC11#34247
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2313

Complements

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

NH ≅ G/Ntype
2. #13071742C2semidirect
3. #13071729C2semidirect
4. #13071495C2semidirect
5. #13071480C2semidirect
8. #13071397C2semidirect
10. #13071166C2semidirect
11. #13071010C2semidirect
12. #13070973C2semidirect
14. C4×#66930C2semidirect
15. C11×#2313C2semidirect
24. C2×#66951C4semidirect
31. C11×#387C22semidirect
32. C11×#387C22semidirect
42. C4⋊C4×Dic11C22semidirect
43. C4⋊C4×Dic11C22semidirect
44. C4⋊C4×Dic11C22semidirect
45. #10622586C22semidirect
54. #10622545C22semidirect
55. C4×Dic11⋊C4C22semidirect
56. C4×Dic11⋊C4C22semidirect
57. C42×Dic11C22semidirect
66. #10622268C22semidirect
67. #10622266C22semidirect
68. #10622266C22semidirect
69. #10622265C22semidirect
70. #10622264C22semidirect
71. #10622263C22semidirect
72. #10622262C22semidirect
73. #10622262C22semidirect
74. #10622261C22semidirect
75. #10622260C22semidirect
84. C2×C11×C4⋊C4C2×C4semidirect
107. C2×C4⋊Dic11C2×C4semidirect
111. C2×Dic11⋊C4C2×C4semidirect
117. C2×C4×Dic11C2×C4semidirect
129. #66951C2×C4semidirect
130. #66951C2×C4semidirect
131. #66951C2×C4semidirect
132. #66951C2×C4semidirect
229. #2313D11semidirect
315. #387C2×D11semidirect
316. #387C2×D11semidirect
399. C2×C4⋊C4C4×D11semidirect
525. C11#34247semidirect

Maximal subgroups

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

subgroupindex
C22×#669512
#130717422
#130717292
#130714952
#130714802
#130714622
#130714582
#130713972
#130712112
#130711662
#130710102
#130709732
#130709682
C4×#669302
C11×#23132
#3424711