Finite Group Databasebeta

← #14753899

Subgroups — #14753899

Order 2816.

1336 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4339C211yesmaximal, characteristic
2#13071014C211yesmaximal, characteristic, complemented
3#13068713C212yesmaximal, complemented
4#13068633C214yesmaximal, complemented
5#13068559C212yesmaximal
6#13068429C214yesmaximal, complemented
7C11×#2920C211yesmaximal, characteristic, complemented
8C22×#4339C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C2×C4×C22⋊D11—21no—
11C2×C4×C22⋊D11—21no—
12C2×#66979C2211yescharacteristic
13C4×#4339—21no—
14C4×#4339—21no—
15C4×#4339—21no—
16C4×#4339—21no—
17C4×#4339C412yescomplemented
18C4×#4339C412yescomplemented
19C4×#4339C2212yes—
20C4×#4339C2212yes—
21C2×C4×D44C411yescharacteristic, complemented
22C2×C4×D44C411yescharacteristic, complemented
23C2×#66925—21no—
24C2×C42×D11—21no—
25C2×C4×Dic22C411yescharacteristic, complemented
26C2×C4×Dic22C411yescharacteristic, complemented
27C11×#432—21no—
28C11×#432—21no—
29C11×#431—21no—
30C11×#431—21no—
31C11×#423C2212yescomplemented
32C11×#407C2212yes—
33C4×C11×M16C2212yescomplemented
34#10622825—21no—
35#10622824—21no—
36C4×C22⋊Dic11C2212yes—
37C2×#66889C2218yes—
38#10622550—21no—
39#10622549—21no—
40C4×C4⋊Dic11C2212yescomplemented
41#10622545C2212yescomplemented
42#10622193C2218yescomplemented
43C23×C4×C11D411yescharacteristic
44C23×C4×C11D411yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C22×C22⋊D11—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C2×#4339—28no—
50C2×#4339C2×C412yes—
51C2×#4339C2312yes—
52C22×D44C2×C411yescharacteristic
53C22×C4×D11—21no—
54C22×C4×D11—21no—
55C22×C4×D11—21no—
56C22×Dic22C2×C411yescharacteristic
57C2×C11×M16C2314yes—
58C2×C42×C11C2×C411yescharacteristic
59C2×C42×C11C2×C411yescharacteristic
60C2×C42×C11C2×C411yescharacteristic
61C2×C42×C11C2×C411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C42×C11D411yescharacteristic
66C2×C42×C11D411yescharacteristic
67C2×C42×C11D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—22no—
72C4×C22⋊D11—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—
79C4×C22⋊D11—22no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82#66979—21no—
83#66979—21no—
84#66979C2×C412yes—
85#66979C2312yes—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2314yes—
95C4×D44—21no—
96C4×D44—21no—
97C4×D44—21no—
98C4×D44—21no—
99C4×D44C2×C412yes—
100C4×D44C2×C412yes—
101C4×D44C2×C412yes—
102C4×D44C2×C412yes—
103#66925—22no—
104#66925—22no—
105#66925—22no—
106#66925—22no—
107C42×D11—22no—
108C42×D11—22no—
109C42×D11—22no—
110C42×D11—22no—
111C4×Dic22—21no—
112C4×Dic22—21no—
113C4×Dic22—21no—
114C4×Dic22—21no—
115C4×Dic22C2×C412yes—
116C4×Dic22C2×C412yes—
117C4×Dic22C2×C412yes—
118C4×Dic22C2×C412yes—
119C11×C4⋊C8—22no—
120C11×C4⋊C8—22no—
121C11×C22⋊C8—22no—
122C11×C22⋊C8—22no—
123C11×#97—22no—
124C4×C8×C11—22no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129#66889—216no—
130#20748—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C23×D11—21no—
133C22×C4×C11—24no—
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—28no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—24no—
161#4339—28no—
162#4339—28no—
163#4339—24no—
164#4339—24no—
165#4339—24no—
166#4339#4118yes—
167C2×D44—24no—
168C2×D44—21no—
169C2×D44C22×C412yes—
170C2×C4×D11—28no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—44no—
178C2×C4×D11—44no—
179C2×Dic22—24no—
180C2×Dic22—21no—
181C2×Dic22C22×C412yes—
182C11×M16—28no—
183C2×C8×C11—24no—
184C42×C11C22⋊C411yescharacteristic
185C42×C11C22⋊C411yescharacteristic
186C42×C11C22⋊C411yescharacteristic
187C42×C11C22⋊C411yescharacteristic
188C42×C11C22⋊C411yescharacteristic
189C42×C11C22⋊C411yescharacteristic
190C42×C11C22⋊C411yescharacteristic
191C42×C11C22⋊C411yescharacteristic
192C42×C11C22×C411yescharacteristic
193C42×C11C22×C411yescharacteristic
194C42×C11C22×C411yescharacteristic
195C42×C11C22×C411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D411yescharacteristic
199C42×C11C2×D411yescharacteristic
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C22⋊Dic11—44no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—44no—
210C4⋊Dic11C22×C412yes—
211C4⋊Dic11C22×C412yes—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—22no—
221C4×Dic11—22no—
222C4×Dic11—28no—
223C2×C4×#41—111no—
224#2920D1111yescharacteristic, complemented
225#2283—111no—
226#1826—112no—
227#1806—114no—
228#1789—112no—
229#1759—114no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11C2×C22⋊C411yescharacteristic
234C23×C11C2×C22⋊C411yescharacteristic
235C23×C11C22×D411yescharacteristic
236C22×D11—24no—
237C22×D11—22no—
238C22×D11—42no—
239C22×D11—42no—
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—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
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×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4114yes—
270C22⋊D11—28no—
271C22⋊D11—28no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—44no—
279C2×Dic11—44no—
280C2×Dic11—44no—
281D44—24no—
282D44—22no—
283D44#11714yes—
284C4×D11—28no—
285C4×D11—28no—
286C4×D11—44no—
287C4×D11—44no—
288C4×D11—44no—
289C4×D11—44no—
290Dic22—24no—
291Dic22—22no—
292Dic22#11714yes—
293C8×C11—44no—
294C22×#41—111no—
295C4×#41—112no—
296C4×#41—112no—
297C4×#41—112no—
298C4×#41—112no—
299C4×#41—221no—
300C4×#41—221no—
301C4×#41—221no—
302C4×#41—221no—
303C2×C4×Q8—111no—
304C2×C4×Q8—111no—
305C2×C4×D4—111no—
306C2×C4×D4—111no—
307C2×C4×D4—221no—
308C2×C4×D4—221no—
309C2×#117—111no—
310C2×#117—221no—
311C22×C42—221no—
312C22×C42C2×D1111yescharacteristic
313#432—21no—
314#432—21no—
315#431—21no—
316#431—21no—
317#423C2×D1112yescomplemented
318C2×#104—118no—
319#407C2×D1112yes—
320C4×M16C2×D1112yescomplemented
321#383—221no—
322#382—221no—
323#381—221no—
324#380—221no—
325C4×C4⋊C4—112no—
326C4×C22⋊C4—112no—
327#376—112no—
328#339—118no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—44no—
337C22×C11#42112yes—
338C22×C11C22×C22⋊C411yescharacteristic
339C22×C11#52512yes—
340C2×D11—24no—
341C2×D11—48no—
342C2×D11—42no—
343C2×D11—42no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11#42112yes—
354C4×C11C2×#11712yes—
355C4×C11#52512yes—
356Dic11—24no—
357Dic11—42no—
358Dic11—42no—
359Dic11—84no—
360C2×#41—112no—
361C2×#41—112no—
362C2×#41—228no—
363C2×#41—221no—
364C2×#41—221no—
365C22×Q8—111no—
366C22×D4—111no—
367C22×D4—221no—
368C23×C4—221no—
369C23×C4—221no—
370C23×C4—221no—
371C23×C4D4411yescharacteristic
372C23×C4D4411yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C2×M16C22×D1114yes—
375C4×Q8—112no—
376C4×Q8—112no—
377C4×Q8—112no—
378C4×Q8—112no—
379C4×Q8—221no—
380C4×Q8—221no—
381C4×Q8—221no—
382C4×Q8—221no—
383C4×D4—112no—
384C4×D4—112no—
385C4×D4—112no—
386C4×D4—112no—
387C4×D4—222no—
388C4×D4—222no—
389C4×D4—222no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—222no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—221no—
396C4×D4—221no—
397C4×D4—221no—
398C4×D4—221no—
399#117—112no—
400#117—112no—
401#117—221no—
402#117—221no—
403#117—222no—
404#117—222no—
405#117—222no—
406#117—222no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—222no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—222no—
416C2×C42—114no—
417C2×C42—221no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42—222no—
421C2×C42—222no—
422C2×C42—222no—
423C2×C42—222no—
424C2×C42C4×D1111yescharacteristic
425C2×C42C4×D1111yescharacteristic
426C2×C42C4×D1111yescharacteristic
427C2×C42C4×D1111yescharacteristic
428C2×C42D4411yescharacteristic
429C2×C42D4411yescharacteristic
430C2×C42C22⋊D1111yescharacteristic
431C2×C42C22⋊D1111yescharacteristic
432C2×C42C22⋊D1111yescharacteristic
433C2×C42C22⋊D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436C4⋊C8—22no—
437C4⋊C8—22no—
438#104—2216no—
439C22⋊C8—22no—
440C22⋊C8—22no—
441#97—22no—
442C4×C8—22no—
443#95—222no—
444#95—222no—
445#95—222no—
446#95—222no—
447C2×C11—22no—
448C2×C11—22no—
449C2×C11—41no—
450C2×C11#228011yescharacteristic
451C2×C11C2×#42111yescharacteristic
452C2×C11C2×#42111yescharacteristic
453D11—44no—
454C24—221no—
455C24C2×D4411yescharacteristic
456#41—118no—
457#41—224no—
458#41—224no—
459#41—228no—
460#41—228no—
461#41—224no—
462C2×Q8—112no—
463C2×Q8—224no—
464C2×Q8—221no—
465C2×D4—112no—
466C2×D4—224no—
467C2×D4—228no—
468C2×D4—222no—
469C2×D4—222no—
470C2×D4—221no—
471C22×C4—24no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—228no—
475C22×C4—221no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—444no—
486C22×C4—444no—
487C22×C4(C2×D11)⋊C411yescharacteristic
488C22×C4(C2×D11)⋊C411yescharacteristic
489C22×C4(C2×D11)⋊C411yescharacteristic
490C22×C4(C2×D11)⋊C411yescharacteristic
491C22×C4(C2×D11)⋊C411yescharacteristic
492C22×C4(C2×D11)⋊C411yescharacteristic
493C22×C4(C2×D11)⋊C411yescharacteristic
494C22×C4(C2×D11)⋊C411yescharacteristic
495C22×C4C2×C4×D1111yescharacteristic
496C22×C4C2×C4×D1111yescharacteristic
497C22×C4C2×D4411yescharacteristic
498C22×C4C2×D4411yescharacteristic
499C22×C4C2×D4411yescharacteristic
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×D4411yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C23×D1111yescharacteristic
505M16—28no—
506C2×C8—24no—
507C4⋊C4—112no—
508C4⋊C4—112no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—444no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—444no—
523C42—222no—
524C42—222no—
525C42—222no—
526C42—222no—
527C42—222no—
528C42—222no—
529C42—228no—
530C42(C2×D11)⋊C411yescharacteristic
531C42(C2×D11)⋊C411yescharacteristic
532C42(C2×D11)⋊C411yescharacteristic
533C42(C2×D11)⋊C411yescharacteristic
534C42(C2×D11)⋊C411yescharacteristic
535C42(C2×D11)⋊C411yescharacteristic
536C42(C2×D11)⋊C411yescharacteristic
537C42(C2×D11)⋊C411yescharacteristic
538C42C2×C4×D1111yescharacteristic
539C42C2×C4×D1111yescharacteristic
540C42C2×C4×D1111yescharacteristic
541C42C2×C4×D1111yescharacteristic
542C42C2×C22⋊D1111yescharacteristic
543C42C2×C22⋊D1111yescharacteristic
544C42C2×C22⋊D1111yescharacteristic
545C42C2×C22⋊D1111yescharacteristic
546C11#2074811yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23—41no—
550C23—224no—
551C23—222no—
552C23—442no—
553C23—442no—
554C23C2×(C2×D11)⋊C411yescharacteristic
555C23C2×(C2×D11)⋊C411yescharacteristic
556C23C22×D4411yescharacteristic
557Q8—114no—
558Q8—224no—
559Q8—222no—
560D4—114no—
561D4—224no—
562D4—228no—
563D4—228no—
564D4—222no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—228no—
583C2×C4—224no—
584C2×C4—222no—
585C2×C4—228no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—444no—
589C2×C4—444no—
590C2×C4—444no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—444no—
594C2×C4—444no—
595C2×C4—444no—
596C2×C4—444no—
597C2×C4C2×(C2×D11)⋊C411yescharacteristic
598C2×C4C2×(C2×D11)⋊C411yescharacteristic
599C2×C4C2×(C2×D11)⋊C411yescharacteristic
600C2×C4C2×(C2×D11)⋊C411yescharacteristic
601C2×C4C2×(C2×D11)⋊C411yescharacteristic
602C2×C4C2×(C2×D11)⋊C411yescharacteristic
603C2×C4C2×(C2×D11)⋊C411yescharacteristic
604C2×C4C2×(C2×D11)⋊C411yescharacteristic
605C2×C4C2×(C2×D11)⋊C411yescharacteristic
606C2×C4C2×(C2×D11)⋊C411yescharacteristic
607C2×C4C22×C4×D1111yescharacteristic
608C2×C4#41×D1114yes—
609C2×C4C22×C22⋊D1111yescharacteristic
610C8—44no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—44no—
619C22—224no—
620C22—448no—
621C22—442no—
622C22—442no—
623C22#1062275212yes—
624C22#1062305512yes—
625C22C22×(C2×D11)⋊C411yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—224no—
636C4—442no—
637C4—442no—
638C4—884no—
639C4#1062275212yes—
640C4D11×#11712yes—
641C4#1062335912yes—
642C2—22no—
643C2—22no—
644C2—41no—
645C2—444no—
646C2#1307099511yescharacteristic
647C2C2×#1062275211yescharacteristic
648C2C2×#1062275211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2920C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#2920D11
hypocenterC11#20748
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. #13071014C2semidirect
3. #13068713C2semidirect
4. #13068633C2semidirect
6. #13068429C2semidirect
7. C11×#2920C2semidirect
17. C4×#4339C4semidirect
18. C4×#4339C4semidirect
21. C2×C4×D44C4semidirect
22. C2×C4×D44C4semidirect
25. C2×C4×Dic22C4semidirect
26. C2×C4×Dic22C4semidirect
31. C11×#423C22semidirect
33. C4×C11×M16C22semidirect
40. C4×C4⋊Dic11C22semidirect
41. #10622545C22semidirect
42. #10622193C22semidirect
224. #2920D11semidirect
317. #423C2×D11semidirect
320. C4×M16C2×D11semidirect
546. C11#20748semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43392
#130710142
#130687132
#130686332
#130685592
#130684292
C11×#29202
#2074811