Finite Group Databasebeta

← #14914721

Subgroups — #14914721

Order 2816.

3106 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623105C211yesmaximal, characteristic
2C2×#10623105C211yesmaximal, characteristic
3C2×C4×#4343C211yesmaximal, characteristic
4#13071537C211yesmaximal, characteristic, complemented
5#13071534C211yesmaximal, characteristic, complemented
6Q8×Dic11⋊C4C211yesmaximal, characteristic, complemented
7#13071527C213yesmaximal, complemented
8#13071525C213yesmaximal, complemented
9#13071517C213yesmaximal, complemented
10#13071516C213yesmaximal, complemented
11#13071237C213yesmaximal, complemented
12#13071231C213yesmaximal, complemented
13#13071096C213yesmaximal, complemented
14D11×#389C213yesmaximal, complemented
15Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C2×Q8×Dic11C2211yescharacteristic
23#10623105—28no—
24#10623105C4116yescomplemented
25C4×#4343—28no—
26C2×#66946C2213yes—
27C2×#66946C2213yes—
28C2×#66946C2213yes—
29C2×#66945C2213yes—
30C2×C4⋊C4×D11C2213yes—
31C2×C4⋊C4×D11C2216yes—
32C2×C4⋊C4×D11C2213yes—
33C2×C4×D44C2213yes—
34C2×C4×D44C2213yes—
35C2×C4×D44C2213yes—
36C2×#66925C2213yes—
37C2×#66925C2213yes—
38C2×C42×D11C2213yes—
39C11×#389C2213yes—
40C11×#389C2213yes—
41C11×#384C2213yes—
42C4×C11×C4⋊C4C2213yes—
43#10622602C2216yes—
44#10622602C2216yes—
45#10622602C2213yes—
46#10622602C2213yes—
47#10622600C2216yes—
48#10622598C2213yes—
49#10622598C2213yes—
50#10622590C2213yes—
51#10622589C2213yes—
52#10622586C2213yes—
53#10622586C2213yes—
54#10622585C2216yes—
55#10622585C2213yes—
56#10622585C2211yescharacteristic
57#10622549C2213yes—
58C4×C4⋊Dic11C2213yes—
59C4×Dic11⋊C4C2213yes—
60C4×Dic11⋊C4C2213yes—
61#10622541C2213yes—
62#10622541C2213yes—
63#10622281C2213yes—
64#10622281C2213yes—
65#10622280C2216yes—
66D11×#95C2216yes—
67#10622260C2213yes—
68#10622260C2213yes—
69C22×Q8×C11C2311yescharacteristic
70C2×#4343C2×C418yes—
71C2×#4343D418yes—
72C2×#4343Q818yes—
73C22×D44C2313yes—
74C22×C4×D11C2313yes—
75C22×C4×D11C2313yes—
76C22×C4×D11C2316yes—
77C22×C4×D11C2316yes—
78C22×C4×D11C2313yes—
79C4×Q8×C11—24no—
80C4×Q8×C11—24no—
81C4×Q8×C11C2×C418yescomplemented
82C2×C11×C4⋊C4C2313yes—
83C2×C11×C4⋊C4C2313yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2316yes—
86C2×C11×C4⋊C4C2313yes—
87C2×C11×C4⋊C4C2313yes—
88C2×C42×C11C2313yes—
89C2×C42×C11C2313yes—
90C2×C42×C11C2313yes—
91Q8×Dic11—24no—
92Q8×Dic11—24no—
93Q8×Dic11C2×C418yescomplemented
94C2×(C2×D11)⋊C4C2313yes—
95C2×(C2×D11)⋊C4C2313yes—
96C2×(C2×D11)⋊C4C2316yes—
97C2×(C2×D11)⋊C4C2313yes—
98C2×(C2×D11)⋊C4C2313yes—
99C2×C4⋊Dic11C2313yes—
100C2×C4⋊Dic11C2313yes—
101C2×C4⋊Dic11C2313yes—
102C2×C4⋊Dic11C2313yes—
103C2×C4⋊Dic11C2313yes—
104C2×Dic11⋊C4C2311yescharacteristic
105C2×Dic11⋊C4C2313yes—
106C2×Dic11⋊C4C2313yes—
107C2×Dic11⋊C4C2311yescharacteristic
108C2×Dic11⋊C4C2313yes—
109C2×Dic11⋊C4C2316yes—
110C2×Dic11⋊C4C2313yes—
111C2×Dic11⋊C4C2311yescharacteristic
112C2×Dic11⋊C4C2313yes—
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2313yes—
115C2×C4×Dic11C2313yes—
116C2×C4×Dic11C2313yes—
117C2×C4×Dic11C2313yes—
118#66946—212no—
119#66946—212no—
120#66946C2×C4124yescomplemented
121#66945—212no—
122C4⋊C4×D11—212no—
123C4⋊C4×D11—412no—
124C4⋊C4×D11C2×C4124yescomplemented
125C4×D44—212no—
126C4×D44—212no—
127C4×D44C2×C4124yescomplemented
128#66925—212no—
129#66925C2×C4124yescomplemented
130C42×D11—212no—
131C11×#95C2313yes—
132C11×#95C2313yes—
133C11⋊#95C2313yes—
134C11⋊#95C2313yes—
135C11⋊#95C2316yes—
136C11⋊#95C2316yes—
137C11⋊#95C2311yescharacteristic
138C11⋊#95C2313yes—
139C11⋊#95C2311yescharacteristic
140C11⋊#95C2313yes—
141#34250—111nomaximal, Sylow
142C23×D11C2413yes—
143C2×Q8×C11C22×C414yes—
144C2×Q8×C11C2×D414yes—
145C2×Q8×C11C2×Q814yes—
146C22×C4×C11C2413yes—
147C22×C4×C11C2411yescharacteristic
148C22×C4×C11C2413yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2413yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2413yes—
153C22×Dic11C2413yes—
154C22×Dic11C2411yescharacteristic
155C22×Dic11C2413yes—
156C22×Dic11C2411yescharacteristic
157C22×Dic11C2413yes—
158C22×Dic11C2411yescharacteristic
159C22×Dic11C2411yescharacteristic
160#4343C4⋊C4164yescomplemented
161C2×D44C22×C4112yes—
162C2×D44C2×D4112yes—
163C2×D44C2×Q8112yes—
164C2×C4×D11—26no—
165C2×C4×D11—26no—
166C2×C4×D11—26no—
167C2×C4×D11—212no—
168C2×C4×D11—26no—
169C2×C4×D11—46no—
170C2×C4×D11—46no—
171C2×C4×D11—43no—
172C2×C4×D11—43no—
173C2×C4×D11—46no—
174C2×C4×D11—46no—
175C2×C4×D11C22×C4124yes—
176C2×C4×D11C22×C4112yes—
177C2×C4×D11C2×D4112yes—
178C2×C4×D11C2×Q8112yes—
179C11×C4⋊C4—26no—
180C11×C4⋊C4—26no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—46no—
183C11×C4⋊C4—43no—
184C11×C4⋊C4C22×C4112yes—
185C42×C11—26no—
186C42×C11—26no—
187C42×C11C22×C4112yes—
188(C2×D11)⋊C4—26no—
189(C2×D11)⋊C4—26no—
190(C2×D11)⋊C4—212no—
191(C2×D11)⋊C4C22×C4112yes—
192(C2×D11)⋊C4C22×C4112yes—
193C4⋊Dic11—26no—
194C4⋊Dic11—26no—
195C4⋊Dic11—26no—
196C4⋊Dic11—43no—
197C4⋊Dic11C22×C4112yes—
198Dic11⋊C4—22no—
199Dic11⋊C4—26no—
200Dic11⋊C4—26no—
201Dic11⋊C4—22no—
202Dic11⋊C4—46no—
203Dic11⋊C4—43no—
204Dic11⋊C4—43no—
205Dic11⋊C4C22×C414yes—
206Dic11⋊C4C22×C4112yes—
207C4×Dic11—22no—
208C4×Dic11—26no—
209C4×Dic11—26no—
210C4×Dic11—26no—
211C4×Dic11C22×C4112yes—
212C2×#520—111no—
213C2×#520—111no—
214C2×C4×#41—111no—
215#2351—111no—
216#2351—111no—
217Q8×C4⋊C4—111no—
218Q8×C4⋊C4D1111yescharacteristic, complemented
219#2349—113no—
220#2349—113no—
221D4×C4⋊C4—113no—
222D4×C4⋊C4—113no—
223#2317—113no—
224#2316—113no—
225#2296—113no—
226C2×#389—113no—
227C23×C11C2511yescharacteristic
228C22×D11—23no—
229C22×D11—23no—
230C22×D11—23no—
231C22×D11—23no—
232C22×D11C23×C416yes—
233C22×D11C22×D416yes—
234C22×D11C22×Q816yes—
235Q8×C11C2×C4⋊C4116yescomplemented
236C2×C4×C11—21no—
237C2×C4×C11—23no—
238C2×C4×C11—21no—
239C2×C4×C11—23no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—23no—
243C2×C4×C11—21no—
244C2×C4×C11—23no—
245C2×C4×C11—23no—
246C2×C4×C11—23no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—23no—
250C2×C4×C11—23no—
251C2×C4×C11C23×C412yes—
252C2×C4×C11C23×C416yes—
253C2×C4×C11C23×C416yes—
254C2×C4×C11C22×D416yes—
255C2×C4×C11C22×Q816yes—
256C2×C4×C112−1+412yes—
257C2×Dic11—21no—
258C2×Dic11—23no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—23no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—23no—
265C2×Dic11—23no—
266C2×Dic11—23no—
267C2×Dic11—21no—
268C2×Dic11—23no—
269C2×Dic11—23no—
270C2×Dic11—23no—
271C2×Dic11—21no—
272C2×Dic11C23×C412yes—
273C2×Dic11C23×C416yes—
274C2×Dic11C23×C412yes—
275C2×Dic11C22×D412yes—
276C2×Dic11C22×Q812yes—
277C2×Dic11H(5,𝔽2)12yes—
278D44C2×C4⋊C4148yescomplemented
279C4×D11—424no—
280C4×D11—412no—
281C4×D11—412no—
282C4×D11—812no—
283C4×D11C2×C4⋊C4148yescomplemented
284C22×#41—111no—
285#520—1116no—
286#520—228no—
287C4×#41—228no—
288C2×C4×Q8—111no—
289C2×C4×Q8—111no—
290C2×C4×Q8—111no—
291C2×C4×Q8C2×D1111yescharacteristic
292C2×C4×Q8C2×D1111yescharacteristic
293C2×C4×Q8C2×D1111yescharacteristic
294C2×C4×D4—113no—
295C2×C4×D4—113no—
296C2×C4×D4—113no—
297C2×C4×D4—113no—
298C2×C4×D4—113no—
299C2×C4×D4—113no—
300C2×#117—113no—
301C2×#117—113no—
302C2×#117—113no—
303C22×C4⋊C4—113no—
304C22×C4⋊C4—113no—
305C22×C4⋊C4—116no—
306C22×C42—113no—
307#389—116no—
308#389—113no—
309#389—113no—
310#389—113no—
311#389—113no—
312#389—113no—
313#389—111no—
314#389—113no—
315#389—113no—
316#389—113no—
317#389—113no—
318#389C2×D1113yes—
319#389C2×D1113yes—
320#385—116no—
321#385—116no—
322#385—113no—
323#385—113no—
324#385—113no—
325#385—113no—
326#384—113no—
327#384C2×D1113yes—
328#382—113no—
329#382—113no—
330#380—116no—
331#380—116no—
332C4×C4⋊C4—113no—
333C4×C4⋊C4—113no—
334C4×C4⋊C4—113no—
335C4×C4⋊C4C2×D1113yes—
336C2×#95—116no—
337C22×C11C24×C411yescharacteristic
338C22×C11C23×D411yescharacteristic
339C22×C11C23×Q811yescharacteristic
340C22×C11C2×H(5,𝔽2)11yescharacteristic
341C22×C11C2×2−1+411yescharacteristic
342C22×C11#58511yescharacteristic
343C22×C11#58511yescharacteristic
344C2×D11—26no—
345C2×D11—26no—
346C2×D11—26no—
347C2×D11—26no—
348C2×D11—26no—
349C2×D11—26no—
350C2×D11C22×C4⋊C4112yes—
351C4×C11—26no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—43no—
355C4×C11—43no—
356C4×C11—41no—
357C4×C11C22×C4⋊C4112yes—
358Dic11—26no—
359Dic11—22no—
360Dic11—22no—
361Dic11—43no—
362Dic11—43no—
363Dic11—41no—
364Dic11C22×C4⋊C414yes—
365C2×#41—118no—
366C2×#41—118no—
367C2×#41—118no—
368C22×Q8C22×D1111yescharacteristic
369C22×D4—113no—
370C23×C4—113no—
371C23×C4—116no—
372C23×C4—113no—
373C23×C4—113no—
374C23×C4—116no—
375C4×Q8—24no—
376C4×Q8—24no—
377C4×Q8—118no—
378C4×Q8—224no—
379C4×Q8—224no—
380C4×Q8C4×D1118yescomplemented
381C4×D4—1124no—
382C4×D4—1124no—
383C4×D4—2212no—
384C4×D4—2212no—
385C4×D4—2212no—
386C4×D4—2212no—
387#117—1124no—
388#117—2212no—
389#117—2212no—
390C2×C4⋊C4—113no—
391C2×C4⋊C4—113no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—1124no—
394C2×C4⋊C4—113no—
395C2×C4⋊C4—113no—
396C2×C4⋊C4—113no—
397C2×C4⋊C4—113no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—113no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—116no—
402C2×C4⋊C4—113no—
403C2×C4⋊C4—113no—
404C2×C4⋊C4—113no—
405C2×C4⋊C4—2212no—
406C2×C4⋊C4—4412no—
407C2×C4⋊C4C22×D1113yes—
408C2×C4⋊C4C22×D1113yes—
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1116yes—
411C2×C4⋊C4C22×D1113yes—
412C2×C4⋊C4C22×D1113yes—
413C2×C22⋊C4—113no—
414C2×C22⋊C4—113no—
415C2×C22⋊C4—116no—
416C2×C22⋊C4—113no—
417C2×C22⋊C4—113no—
418C2×C42—113no—
419C2×C42—113no—
420C2×C42—113no—
421C2×C42—113no—
422C2×C42—111no—
423C2×C42—2212no—
424C2×C42C22×D1113yes—
425C2×C42C22×D1113yes—
426C2×C42C22×D1113yes—
427#95—113no—
428#95—116no—
429#95—116no—
430#95—111no—
431#95—111no—
432#95—113no—
433#95—113no—
434#95—113no—
435#95C22×D1113yes—
436#95C22×D1113yes—
437C2×C11C23×C4⋊C411yescharacteristic
438C2×C11C4×H(5,𝔽2)11yescharacteristic
439C2×C11C4×2−1+411yescharacteristic
440C2×C11#348811yescharacteristic
441C2×C11#348911yescharacteristic
442C2×C11#350311yescharacteristic
443C2×C11#350411yescharacteristic
444D11—212no—
445C24—113no—
446#41—1164no—
447C2×Q8C2×C4×D1114yes—
448C2×Q8D4×D1114yes—
449C2×Q8Q8×D1114yes—
450C2×D4—1112no—
451C2×D4—1112no—
452C2×D4—1112no—
453C22×C4—111no—
454C22×C4—1112no—
455C22×C4—1112no—
456C22×C4—1112no—
457C22×C4—111no—
458C22×C4—113no—
459C22×C4—111no—
460C22×C4—1124no—
461C22×C4—113no—
462C22×C4—111no—
463C22×C4—113no—
464C22×C4—226no—
465C22×C4—226no—
466C22×C4—226no—
467C22×C4—2212no—
468C22×C4—226no—
469C22×C4—446no—
470C22×C4—446no—
471C22×C4—443no—
472C22×C4—443no—
473C22×C4—446no—
474C22×C4—446no—
475C22×C4C23×D1113yes—
476C22×C4C23×D1111yescharacteristic
477C22×C4C23×D1113yes—
478C22×C4C23×D1111yescharacteristic
479C22×C4C23×D1113yes—
480C22×C4C23×D1111yescharacteristic
481C22×C4C23×D1113yes—
482C4⋊C4—26no—
483C4⋊C4—26no—
484C4⋊C4—22no—
485C4⋊C4—46no—
486C4⋊C4—43no—
487C4⋊C4—1112no—
488C4⋊C4—1112no—
489C4⋊C4—114no—
490C4⋊C4—226no—
491C4⋊C4—226no—
492C4⋊C4—226no—
493C4⋊C4—222no—
494C4⋊C4—226no—
495C4⋊C4—226no—
496C4⋊C4—222no—
497C4⋊C4—446no—
498C4⋊C4—443no—
499C4⋊C4—443no—
500C4⋊C4—443no—
501C4⋊C4C2×C4×D11112yes—
502C22⋊C4—1112no—
503C22⋊C4—1112no—
504C22⋊C4—226no—
505C22⋊C4—2212no—
506C22⋊C4—226no—
507C42—26no—
508C42—26no—
509C42—1112no—
510C42—222no—
511C42—226no—
512C42—226no—
513C42—226no—
514C42C2×C4×D11112yes—
515C11#3425011yescharacteristic, complemented, Sylow
516C23—116no—
517C23—116no—
518C23—116no—
519C23—223no—
520C23—223no—
521C23—223no—
522C23—223no—
523C23C24×D1111yescharacteristic
524Q8C4⋊C4×D11116yescomplemented
525D4—1148no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—23no—
530C2×C4—23no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—23no—
534C2×C4—23no—
535C2×C4—21no—
536C2×C4—23no—
537C2×C4—23no—
538C2×C4—23no—
539C2×C4—23no—
540C2×C4—21no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—1148no—
545C2×C4—112no—
546C2×C4—116no—
547C2×C4—112no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—223no—
553C2×C4—223no—
554C2×C4—221no—
555C2×C4—223no—
556C2×C4—223no—
557C2×C4—221no—
558C2×C4—223no—
559C2×C4—223no—
560C2×C4—223no—
561C2×C4—221no—
562C2×C4—223no—
563C2×C4—4424no—
564C2×C4—4412no—
565C2×C4—4412no—
566C2×C4—8812no—
567C2×C4C22×C4×D1112yes—
568C2×C4C22×C4×D1116yes—
569C2×C4C22×C4×D1116yes—
570C2×C4C2×D4×D1116yes—
571C2×C4C2×Q8×D1116yes—
572C2×C4#6704012yes—
573C22—1112no—
574C22—226no—
575C22—226no—
576C22—226no—
577C22—226no—
578C22—226no—
579C22—226no—
580C22C23×C4×D1111yescharacteristic
581C22C22×D4×D1111yescharacteristic
582C22C22×Q8×D1111yescharacteristic
583C22C2×#6704011yescharacteristic
584C22#1062345311yescharacteristic
585C22D11×H(5,𝔽2)11yescharacteristic
586C22#1062345711yescharacteristic
587C4—22no—
588C4—26no—
589C4—22no—
590C4—43no—
591C4—43no—
592C4—41no—
593C4—114no—
594C4—222no—
595C4—226no—
596C4—222no—
597C4—443no—
598C4—443no—
599C4—441no—
600C4C2×C4⋊C4×D11112yes—
601C2—2212no—
602C2C22×C4⋊C4×D1111yescharacteristic
603C2#1308182211yescharacteristic
604C2C4×#6704011yescharacteristic
605C2#1308228411yescharacteristic
606C2#1308229311yescharacteristic
607C2#1308243411yescharacteristic
608C2#1308244111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingQ8×C11×C4⋊C4C2
socle, cosocleC23×C11C25
prime radicalC22×#4343C22
hypercenterQ8×C4⋊C4D11
hypocenterC11#34250
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #13071537C2semidirect
5. #13071534C2semidirect
6. Q8×Dic11⋊C4C2semidirect
7. #13071527C2semidirect
8. #13071525C2semidirect
9. #13071517C2semidirect
10. #13071516C2semidirect
11. #13071237C2semidirect
12. #13071231C2semidirect
13. #13071096C2semidirect
14. D11×#389C2semidirect
15. Q8×C11×C4⋊C4C2semidirect
24. #10623105C4semidirect
81. C4×Q8×C11C2×C4semidirect
93. Q8×Dic11C2×C4semidirect
120. #66946C2×C4semidirect
124. C4⋊C4×D11C2×C4semidirect
127. C4×D44C2×C4semidirect
129. #66925C2×C4semidirect
160. #4343C4⋊C4semidirect
218. Q8×C4⋊C4D11semidirect
235. Q8×C11C2×C4⋊C4semidirect
278. D44C2×C4⋊C4semidirect
283. C4×D11C2×C4⋊C4semidirect
380. C4×Q8C4×D11semidirect
515. C11#34250semidirect
524. Q8C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106231052
C2×C4×#43432
#130715372
#130715342
Q8×Dic11⋊C42
#130715272
#130715252
#130715172
#130715162
#130712372
#130712312
#130710962
D11×#3892
Q8×C11×C4⋊C42
#3425011