Finite Group Databasebeta

← #14763781

Subgroups — #14763781

Order 2816.

1106 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic
2#13071023C211yesmaximal, characteristic, complemented
3#13069560C212yesmaximal, complemented
4#13069535C212yesmaximal, complemented
5#13069062C214yesmaximal, complemented
6#13068633C214yesmaximal, complemented
7C11×#2920C211yesmaximal, characteristic, complemented
8C22×C42×C11C2211yescharacteristic
9#10623322—21no—
10#10623322—21no—
11#10623322C2212yes—
12C2×#66979C2212yes—
13#10623010—21no—
14#10623010—21no—
15#10623010—21no—
16#10623010—21no—
17#10623010C412yescomplemented
18#10623010C412yescomplemented
19#10623008C411yescharacteristic, complemented
20#10623008C411yescharacteristic, complemented
21#10623008C2211yescharacteristic
22C4×#4339—21no—
23C4×#4339—21no—
24C4×#4339C2212yes—
25#10623001C411yescharacteristic, complemented
26#10623001C411yescharacteristic, complemented
27#10623001C2211yescharacteristic
28C11×#432—21no—
29C11×#432—21no—
30C11×#431—21no—
31C11×#431—21no—
32C11×#423C2212yes—
33C11×#407C2212yes—
34C4×C11×M16C2212yes—
35#10622825—21no—
36#10622825—21no—
37C2×#66889C2218yes—
38#10622549—21no—
39#10622548—21no—
40C4×C4⋊Dic11C2212yes—
41C4×C4⋊Dic11C2212yes—
42#10622193C2218yes—
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339C2312yes—
49C2×C11×M16C2314yes—
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11C2×C411yescharacteristic
53C2×C42×C11C2×C411yescharacteristic
54C2×C42×C11D411yescharacteristic
55C2×C42×C11D411yescharacteristic
56C2×C42×C11D411yescharacteristic
57C2×C42×C11D411yescharacteristic
58C2×C42×C11D411yescharacteristic
59C2×C42×C11D411yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62#67006—22no—
63C2×C22⋊Dic11—22no—
64#66983—21no—
65#66983—21no—
66#66983—21no—
67#66983—21no—
68#66983C2×C412yes—
69#66983C2×C412yes—
70#66982—22no—
71#66982—22no—
72#66982—22no—
73C4×C22⋊D11—22no—
74C4×C22⋊D11—22no—
75C4×C22⋊D11—22no—
76C4×C22⋊D11—22no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79#66979—21no—
80#66979—21no—
81#66979—44no—
82#66979C2312yes—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86#66977—21no—
87#66977—21no—
88#66977—21no—
89#66977—21no—
90#66977C2×C412yes—
91#66977C2×C412yes—
92C2×C4×Dic11C2314yes—
93#66929—22no—
94#66929—22no—
95#66928—21no—
96#66928—21no—
97#66928C2×C412yes—
98#66927C2×C411yescharacteristic
99C4×D44—21no—
100C4×D44—21no—
101C4×D44—21no—
102C4×D44—21no—
103C4×D44C2×C412yes—
104C4×D44C2×C412yes—
105#66925—22no—
106#66925—22no—
107#66925—22no—
108C42×D11—22no—
109#66923—21no—
110#66923—21no—
111#66923C2×C412yes—
112#66922C2×C411yescharacteristic
113#66922C2×C411yescharacteristic
114#66922C2×C411yescharacteristic
115C4×Dic22—21no—
116C4×Dic22—21no—
117C4×Dic22—21no—
118C4×Dic22—21no—
119C4×Dic22C2×C412yes—
120C4×Dic22C2×C412yes—
121C11×C4⋊C8—22no—
122C11×C4⋊C8—22no—
123C11×C22⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×#97—22no—
126C4×C8×C11—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129#66889—48no—
130#21900—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11C22⋊C411yescharacteristic
137C22×C4×C11C22⋊C411yescharacteristic
138C22×C4×C11C22⋊C411yescharacteristic
139C22×C4×C11C22⋊C411yescharacteristic
140C22×C4×C11C22⋊C411yescharacteristic
141C22×C4×C11C22⋊C411yescharacteristic
142C22×C4×C11C22⋊C411yescharacteristic
143C22×C4×C11C22⋊C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C22×Dic11—24no—
158#4339—24no—
159#4339—24no—
160#4339—44no—
161#4339—44no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C22×C412yes—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22C22×C412yes—
171C11×M16—24no—
172C11×M16—24no—
173C2×C8×C11—24no—
174C42×C11C22⋊C411yescharacteristic
175C42×C11C22⋊C411yescharacteristic
176C42×C11C22⋊C411yescharacteristic
177C42×C11C22⋊C411yescharacteristic
178C42×C11C22⋊C411yescharacteristic
179C42×C11C22⋊C411yescharacteristic
180C42×C11C22⋊C411yescharacteristic
181C42×C11C22⋊C411yescharacteristic
182C42×C11C22×C411yescharacteristic
183C42×C11C22×C411yescharacteristic
184C42×C11C22×C411yescharacteristic
185C42×C11C22×C411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C22⋊Dic11—22no—
191C22⋊Dic11—22no—
192C22⋊Dic11—22no—
193C22⋊Dic11—44no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—44no—
205C4⋊Dic11—44no—
206C4⋊Dic11—44no—
207C4⋊Dic11C22×C412yes—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—28no—
219#3444—111no—
220#2920D1111yescharacteristic, complemented
221#2285—111no—
222#1986—112no—
223#1980—112no—
224#1897—114no—
225#1806—114no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11C2×C22⋊C411yescharacteristic
231C23×C11C2×C22⋊C411yescharacteristic
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11C2×C22⋊C411yescharacteristic
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11H(5,𝔽2)12yes—
265C2×C4×C112−1+412yes—
266C22⋊D11—44no—
267C22⋊D11—44no—
268C22⋊D11—42no—
269C22⋊D11—42no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—44no—
276D44—24no—
277D44—42no—
278D44—42no—
279C4×D11—44no—
280C4×D11—44no—
281C4×D11—44no—
282Dic22—24no—
283Dic22—42no—
284Dic22—42no—
285C8×C11—44no—
286#533—111no—
287#533—111no—
288#533—111no—
289#532—111no—
290#532—111no—
291#532—111no—
292#529—112no—
293#529—112no—
294#529—221no—
295#529—221no—
296#529—221no—
297#529—221no—
298#525—112no—
299#525—221no—
300#525—221no—
301C4×#41—112no—
302C4×#41—221no—
303C4×#41—221no—
304C2×#117—112no—
305C22×C42C2×D1111yescharacteristic
306#432—21no—
307#432—21no—
308#431—21no—
309#431—21no—
310#423C2×D1112yes—
311C2×#104—118no—
312#407C2×D1112yes—
313C4×M16C2×D1112yes—
314#384—221no—
315#382—221no—
316#380—221no—
317#380—221no—
318C4×C4⋊C4—112no—
319C4×C4⋊C4—112no—
320#339—118no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—21no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11C22×C22⋊C411yescharacteristic
332C22×C11#53511yescharacteristic
333C22×C11#53611yescharacteristic
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C4×C11—21no—
338C4×C11—21no—
339C4×C11—21no—
340C4×C11—21no—
341C4×C11—21no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11#42112yes—
346C4×C11#42112yes—
347C4×C11#52012yes—
348C4×C11#53712yes—
349Dic11—42no—
350Dic11—42no—
351Dic11—42no—
352Dic11—84no—
353C2×#41—112no—
354C2×#41—221no—
355C2×#41—221no—
356C23×C4D4411yescharacteristic
357C23×C4D4411yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C2×M16C22×D1114yes—
360C4⋊Q8—111no—
361C4⋊Q8—111no—
362C4⋊Q8—111no—
363#127—111no—
364#126—222no—
365#126—222no—
366#125—112no—
367#125—221no—
368#125—221no—
369#124—112no—
370#124—221no—
371#124—221no—
372#123—222no—
373#123—222no—
374#123—222no—
375C22⋊Q8—112no—
376C22⋊Q8—112no—
377C22⋊Q8—221no—
378C22⋊Q8—221no—
379C22⋊Q8—221no—
380C22⋊Q8—221no—
381#121—112no—
382#121—112no—
383#121—221no—
384#121—221no—
385#121—221no—
386#121—221no—
387#120—222no—
388C4×Q8—112no—
389C4×Q8—112no—
390C4×Q8—221no—
391C4×Q8—221no—
392C4×Q8—221no—
393C4×Q8—221no—
394C4×D4—112no—
395C4×D4—112no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—221no—
403C4×D4—221no—
404C4×D4—221no—
405C4×D4—221no—
406#117—112no—
407#117—221no—
408#117—221no—
409#117—222no—
410#117—222no—
411#117—222no—
412#117—444no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
416C2×C22⋊C4—222no—
417C2×C42—114no—
418C2×C42—222no—
419C2×C42C4×D1111yescharacteristic
420C2×C42C4×D1111yescharacteristic
421C2×C42C4×D1111yescharacteristic
422C2×C42C4×D1111yescharacteristic
423C2×C42D4411yescharacteristic
424C2×C42D4411yescharacteristic
425C2×C42C22⋊D1111yescharacteristic
426C2×C42C22⋊D1111yescharacteristic
427C2×C42C22⋊D1111yescharacteristic
428C2×C42C22⋊D1111yescharacteristic
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431C4⋊C8—22no—
432C4⋊C8—22no—
433#104—448no—
434C22⋊C8—22no—
435C22⋊C8—22no—
436#97—22no—
437C4×C8—22no—
438#95—222no—
439#95—222no—
440C2×C11—21no—
441C2×C11—21no—
442C2×C11—41no—
443C2×C11—41no—
444C2×C11#231111yescharacteristic
445C2×C11C2×#42111yescharacteristic
446C2×C11C2×#42111yescharacteristic
447D11—82no—
448C24C2×D4411yescharacteristic
449#41—224no—
450#41—224no—
451#41—444no—
452#41—444no—
453C2×Q8—112no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×D4—112no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—221no—
461C2×D4—221no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—224no—
470C22×C4(C2×D11)⋊C411yescharacteristic
471C22×C4(C2×D11)⋊C411yescharacteristic
472C22×C4(C2×D11)⋊C411yescharacteristic
473C22×C4(C2×D11)⋊C411yescharacteristic
474C22×C4(C2×D11)⋊C411yescharacteristic
475C22×C4(C2×D11)⋊C411yescharacteristic
476C22×C4(C2×D11)⋊C411yescharacteristic
477C22×C4(C2×D11)⋊C411yescharacteristic
478C22×C4C2×C4×D1111yescharacteristic
479C22×C4C2×C4×D1111yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4411yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488M16—24no—
489M16—24no—
490C2×C8—24no—
491C4⋊C4—112no—
492C4⋊C4—112no—
493C4⋊C4—222no—
494C4⋊C4—222no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—222no—
500C4⋊C4—222no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C4⋊C4—444no—
504C4⋊C4—444no—
505C4⋊C4—444no—
506C22⋊C4—222no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C22⋊C4—222no—
512C22⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—222no—
515C22⋊C4—444no—
516C42—222no—
517C42—222no—
518C42—222no—
519C42—228no—
520C42(C2×D11)⋊C411yescharacteristic
521C42(C2×D11)⋊C411yescharacteristic
522C42(C2×D11)⋊C411yescharacteristic
523C42(C2×D11)⋊C411yescharacteristic
524C42(C2×D11)⋊C411yescharacteristic
525C42(C2×D11)⋊C411yescharacteristic
526C42(C2×D11)⋊C411yescharacteristic
527C42(C2×D11)⋊C411yescharacteristic
528C42C2×C4×D1111yescharacteristic
529C42C2×C4×D1111yescharacteristic
530C42C2×C4×D1111yescharacteristic
531C42C2×C4×D1111yescharacteristic
532C42C2×C22⋊D1111yescharacteristic
533C42C2×C22⋊D1111yescharacteristic
534C42C2×C22⋊D1111yescharacteristic
535C42C2×C22⋊D1111yescharacteristic
536C11#2190011yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—41no—
540C23—41no—
541C23—222no—
542C23C2×(C2×D11)⋊C411yescharacteristic
543C23C2×(C2×D11)⋊C411yescharacteristic
544C23C22×D4411yescharacteristic
545Q8—224no—
546Q8—442no—
547Q8—442no—
548D4—224no—
549D4—442no—
550D4—444no—
551D4—444no—
552D4—442no—
553D4—442no—
554D4—442no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—444no—
577C2×C4—444no—
578C2×C4—444no—
579C2×C4—444no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4C2×(C2×D11)⋊C411yescharacteristic
583C2×C4C2×(C2×D11)⋊C411yescharacteristic
584C2×C4C2×(C2×D11)⋊C411yescharacteristic
585C2×C4C2×(C2×D11)⋊C411yescharacteristic
586C2×C4C2×(C2×D11)⋊C411yescharacteristic
587C2×C4C2×(C2×D11)⋊C411yescharacteristic
588C2×C4C2×(C2×D11)⋊C411yescharacteristic
589C2×C4C2×(C2×D11)⋊C411yescharacteristic
590C2×C4C2×(C2×D11)⋊C411yescharacteristic
591C2×C4C2×(C2×D11)⋊C411yescharacteristic
592C2×C4C22×C4×D1111yescharacteristic
593C2×C4#6704212yes—
594C2×C4#6704312yes—
595C2×C4C22×C22⋊D1111yescharacteristic
596C8—44no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—42no—
606C22—42no—
607C22—442no—
608C22—442no—
609C22—442no—
610C22#1062305611yescharacteristic
611C22#1062305711yescharacteristic
612C22C22×(C2×D11)⋊C411yescharacteristic
613C4—21no—
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—442no—
622C4—442no—
623C4—442no—
624C4—884no—
625C4#1062275212yes—
626C4#1062275212yes—
627C4#1062305412yes—
628C4#1062336412yes—
629C2—21no—
630C2—21no—
631C2—41no—
632C2—41no—
633C2—882no—
634C2#1307120411yescharacteristic
635C2C2×#1062275211yescharacteristic
636C2C2×#1062275211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2920C2
socleC22×C11C22×C22⋊C4
prime radical#13081912C2
cosocleC22×C4×C11C24
hypercenter#2920D11
hypocenterC11#21900
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
2. #13071023C2semidirect
3. #13069560C2semidirect
4. #13069535C2semidirect
5. #13069062C2semidirect
6. #13068633C2semidirect
7. C11×#2920C2semidirect
17. #10623010C4semidirect
18. #10623010C4semidirect
19. #10623008C4semidirect
20. #10623008C4semidirect
25. #10623001C4semidirect
26. #10623001C4semidirect
220. #2920D11semidirect
536. C11#21900semidirect

Maximal subgroups

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

subgroupindex
#130819122
#130710232
#130695602
#130695352
#130690622
#130686332
C11×#29202
#2190011