Finite Group Databasebeta

← #14675583

Subgroups — #14675583

Order 2816.

1942 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
1C22×#66940C211yesmaximal, characteristic
2C2×#10622269C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C212yesmaximal
4C2×#10622262C211yesmaximal, characteristic
5#13066886C211yesmaximal, characteristic
6#13066879C212yesmaximal
7#13066868C212yesmaximal
8#13066866C211yesmaximal, characteristic
9#95×Dic11C211yesmaximal, characteristic
10#95×Dic11C212yesmaximal
11C11×#1444C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C4⋊Dic11C2212yes—
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C2×#66940—24no—
25C2×#66940—28no—
26C2×C11×#95C2212yes—
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C4⋊C4×Dic11—28no—
38#10622269C418yescomplemented
39#10622262—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—24no—
54C22×Dic22—24no—
55C22×Dic22C2×C414yes—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—24no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—24no—
61C2×C4⋊Dic11—24no—
62C2×C4⋊Dic11—24no—
63C2×C4⋊Dic11C2×C418yes—
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4C2×C414yes—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11D414yes—
83C2×C4×Dic11D418yes—
84C2×C4×Dic11Q818yescomplemented
85C2×C4×Dic11Q814yescomplemented
86#66940—232no—
87C11×#95—22no—
88C11×#95—24no—
89C11×#95C2×C414yes—
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95C2×C418yes—
98C4×#395—111nomaximal, Sylow
99C24×C11C2411yescharacteristic
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C414yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×Q812yes—
125C22×C4×C11C2×Q814yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4114yes—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11C22×C412yes—
152C22×Dic11C22×C414yes—
153C22×Dic11C22×C412yes—
154C22×Dic11C2×D412yes—
155C22×Dic11C2×D414yes—
156C22×Dic11C2×D412yes—
157C22×Dic11C2×D414yes—
158C22×Dic11C2×Q814yes—
159C22×Dic11C2×Q812yes—
160C22×Dic11C2×Q814yes—
161C22×Dic11C2×Q812yes—
162C22×Dic11#4114yes—
163C22×Dic11#4112yes—
164C22×Dic11#4112yes—
165C2×Dic22—28no—
166C2×Dic22—28no—
167C2×Dic22—216no—
168C2×Dic22—216no—
169C2×Dic22—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—216no—
172C4⋊Dic11—216no—
173Dic11⋊C4—216no—
174Dic11⋊C4—28no—
175Dic11⋊C4—28no—
176C4×Dic11—28no—
177C4×Dic11—216no—
178C4×Dic11—216no—
179C4×Dic11—28no—
180C4×Dic11—44no—
181C22×C4×Q8—111no—
182C2×#395—111no—
183C2×C4×C4⋊C4—111no—
184C2×C4×C4⋊C4—112no—
185#1446—111no—
186#1444—112no—
187#1444D1111yescharacteristic
188#1441—112no—
189#1441—111no—
190C4×#95—112no—
191C4×#95—111no—
192C23×C11C23×C411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C22×D412yes—
195C23×C11C22×Q812yes—
196C23×C11C22×Q811yescharacteristic
197C23×C11C2×#4112yes—
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11C2×#4112yes—
201C23×C11C2×#4111yescharacteristic
202C23×C11C2×#4111yescharacteristic
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11C4×D414yes—
231C2×C4×C11C4×Q818yescomplemented
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—41no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11C4×D418yes—
262C2×Dic11C4×Q814yescomplemented
263C2×Dic11#12014yes—
264C2×Dic11C22⋊Q814yes—
265C2×Dic11C22⋊Q818yes—
266C2×Dic11C4⋊Q818yes—
267C2×Dic11C4⋊Q814yes—
268Dic22—232no—
269C23×Q8—111no—
270C2×C4×Q8—224no—
271C2×C4×Q8—228no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4—111no—
276C22×C4⋊C4C2×D1111yescharacteristic
277C22×C4⋊C4C2×D1112yes—
278C22×C42—112no—
279C22×C42—111no—
280C22×C42—111no—
281C22×C42—112no—
282C22×C42—111no—
283#395—118no—
284C4×C4⋊C4—224no—
285C4×C4⋊C4—228no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—111no—
291C2×#95—111no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95C2×D1112yes—
295C2×#95C2×D1111yescharacteristic
296C2×#95C2×D1111yescharacteristic
297C22×C11C2×C4×D411yescharacteristic
298C22×C11C2×C4×D412yes—
299C22×C11C2×C4×Q812yes—
300C22×C11C2×C4×Q811yescharacteristic
301C22×C11C4×#4111yescharacteristic
302C22×C11C2×#12011yescharacteristic
303C22×C11C2×C22⋊Q811yescharacteristic
304C22×C11C2×C22⋊Q812yes—
305C22×C11#52512yes—
306C22×C11#52511yescharacteristic
307C22×C11#52512yes—
308C22×C11#52511yescharacteristic
309C22×C11#52912yes—
310C22×C11#52911yescharacteristic
311C22×C11C2×C4⋊Q812yes—
312C22×C11C2×C4⋊Q811yescharacteristic
313C22×C11#53211yescharacteristic
314C22×C11#53212yes—
315C22×C11#53312yes—
316C22×C11#53311yescharacteristic
317C22×C11#53312yes—
318C22×C11#53312yes—
319C22×C11#53312yes—
320C4×C11—24no—
321C4×C11—28no—
322C4×C11—44no—
323C4×C11—42no—
324C4×C11—42no—
325Dic11—28no—
326Dic11—24no—
327Dic11—42no—
328Dic11—44no—
329Dic11—42no—
330Dic11#39518yescomplemented
331C22×Q8—114no—
332C22×Q8—224no—
333C22×Q8—224no—
334C22×Q8—222no—
335C22×Q8—222no—
336C23×C4—111no—
337C23×C4—112no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—112no—
342C23×C4C22×D1112yes—
343C23×C4C22×D1111yescharacteristic
344C23×C4C22×D1111yescharacteristic
345C23×C4C22×D1111yescharacteristic
346C23×C4C22×D1112yes—
347C4×Q8—2232no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—224no—
356C2×C4⋊C4—224no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—224no—
361C2×C4⋊C4—224no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—222no—
365C2×C42—118no—
366C2×C42—114no—
367C2×C42—114no—
368C2×C42—118no—
369C2×C42—224no—
370C2×C42—224no—
371C2×C42—224no—
372C2×C42—224no—
373C2×C42—222no—
374C2×C42—224no—
375C2×C42—222no—
376C2×C42—222no—
377C2×C42—224no—
378#95—22no—
379#95—24no—
380#95—118no—
381#95—224no—
382#95—224no—
383#95—222no—
384#95—224no—
385#95—224no—
386#95—224no—
387#95—222no—
388#95C4×D1114yes—
389C2×C11C4×#12011yescharacteristic
390C2×C11C4×C22⋊Q811yescharacteristic
391C2×C11C4×C22⋊Q812yes—
392C2×C11C4×C4⋊Q811yescharacteristic
393C2×C11C4×C4⋊Q812yes—
394C2×C11C2×#39511yescharacteristic
395C2×C11#238811yescharacteristic
396C2×C11#239611yescharacteristic
397C2×C11#239612yes—
398C2×C11#239912yes—
399C2×C11#239911yescharacteristic
400C24C23×D1111yescharacteristic
401C2×Q8—2216no—
402C2×Q8—228no—
403C2×Q8—2216no—
404C2×Q8—228no—
405C2×Q8—228no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—112no—
427C22×C4—114no—
428C22×C4—114no—
429C22×C4—112no—
430C22×C4—112no—
431C22×C4—112no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—114no—
440C22×C4—221no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—222no—
446C22×C4—221no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—221no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—221no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—221no—
462C22×C4C2×C4×D1114yes—
463C22×C4C2×C4×D1112yes—
464C22×C4D4×D1114yes—
465C22×C4D4×D1112yes—
466C22×C4#434112yes—
467C22×C4#434114yes—
468C22×C4Q8×D1112yes—
469C22×C4Q8×D1114yes—
470C22×C4#434312yes—
471C4⋊C4—28no—
472C4⋊C4—216no—
473C4⋊C4—2216no—
474C4⋊C4—2216no—
475C4⋊C4—228no—
476C4⋊C4—228no—
477C42—228no—
478C42—2216no—
479C42—2216no—
480C42—228no—
481C42—444no—
482C11C4×#39511yescharacteristic, complemented, Sylow
483C23C22×C4×D1111yescharacteristic
484C23C2×D4×D1111yescharacteristic
485C23C2×D4×D1112yes—
486C23C2×#434112yes—
487C23C2×#434111yescharacteristic
488C23C2×Q8×D1112yes—
489C23C2×Q8×D1111yescharacteristic
490C23C2×#434311yescharacteristic
491C23#41×D1111yescharacteristic
492C23#41×D1112yes—
493C23#41×D1111yescharacteristic
494Q8—2232no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—118no—
523C2×C4—114no—
524C2×C4—114no—
525C2×C4—114no—
526C2×C4—118no—
527C2×C4—118no—
528C2×C4—114no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—222no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—442no—
550C2×C4—441no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—441no—
557C2×C4—442no—
558C2×C4#6694018yescomplemented
559C2×C4#6694614yes—
560C22C2×#6694012yes—
561C22C2×#6694611yescharacteristic
562C22C4×#434111yescharacteristic
563C22C4×D4×D1112yes—
564C22C4×Q8×D1111yescharacteristic
565C22#1062311712yes—
566C22D11×#12011yescharacteristic
567C22#1062312712yes—
568C22#1062313711yescharacteristic
569C22#1062315312yes—
570C22#1062315312yes—
571C22D11×C22⋊Q811yescharacteristic
572C22D11×C22⋊Q812yes—
573C22#1062315812yes—
574C22#1062318012yes—
575C22#1062318711yescharacteristic
576C22#1062321912yes—
577C22#1062322211yescharacteristic
578C22#1062324711yescharacteristic
579C22D11×C4⋊Q812yes—
580C22D11×C4⋊Q811yescharacteristic
581C22#1062325912yes—
582C22#1062325911yescharacteristic
583C4—24no—
584C4—28no—
585C4—42no—
586C4—44no—
587C4—42no—
588C4—118no—
589C4—228no—
590C4—224no—
591C4—442no—
592C4—444no—
593C4—442no—
594C2#1307111711yescharacteristic
595C2#1307114611yescharacteristic
596C2#1307114812yes—
597C2#1307118311yescharacteristic
598C2#1307118712yes—
599C2D11×#39511yescharacteristic
600C2#1307182811yescharacteristic
601C2#1307188511yescharacteristic
602C2#1307189312yes—
603C2#1307190612yes—
604C2#1307190811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1444C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1444D11
hypocenterC11C4×#395
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
38. #10622269C4semidirect
84. C2×C4×Dic11Q8semidirect
85. C2×C4×Dic11Q8semidirect
231. C2×C4×C11C4×Q8semidirect
262. C2×Dic11C4×Q8semidirect
330. Dic11#395semidirect
482. C11C4×#395semidirect
558. C2×C4#66940semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106222692
C2×C4⋊C4×Dic112
C2×#106222622
#130668862
#130668792
#130668682
#130668662
#95×Dic112
C11×#14442
C4×#39511