Finite Group Databasebeta

← #14725305

Subgroups — #14725305

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077631C211yesmaximal, characteristic, complemented
2C4×#66985C211yesmaximal, characteristic
3#13067518C211yesmaximal, characteristic, complemented
4#13067504C211yesmaximal, characteristic, complemented
5#13067478C211yesmaximal, characteristic, complemented
6#13067473C211yesmaximal, characteristic, complemented
7#13067452C211yesmaximal, characteristic, complemented
8#13067443C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067381C211yesmaximal, characteristic, complemented
12#13067059C211yesmaximal, characteristic, complemented
13#13067053C211yesmaximal, characteristic, complemented
14#13066919C211yesmaximal, characteristic, complemented
15D4×C11×M16C211yesmaximal, characteristic, complemented
16C22×C11×M16—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66985C411yescharacteristic
19C4×#4339C2211yescharacteristic
20C11×#436C2211yescharacteristic
21C11×#436C2211yescharacteristic
22C11×#435—21no—
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C11×#423C2211yescharacteristic
27C11×#407—21no—
28C4×C11×M16C2211yescharacteristic
29#10622828C411yescharacteristic
30#10622740—21no—
31#10622740—21no—
32#10622631C411yescharacteristic
33#10622631C411yescharacteristic
34C4×#4324C2211yescharacteristic
35C4×#4324C2211yescharacteristic
36#10622627C411yescharacteristic
37#10622627C411yescharacteristic
38C4×#4323C2211yescharacteristic
39C4×#4323C2211yescharacteristic
40#10622579C411yescharacteristic
41#10622577C411yescharacteristic
42#10622539C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622318—21no—
46D11×#97—21no—
47C8×D44C2211yescharacteristic, complemented
48C8×D44C2211yescharacteristic, complemented
49#10622292C2211yescharacteristic, complemented
50#10622292C2211yescharacteristic, complemented
51D4⋊(C11⋊C8)C2211yescharacteristic
52D4⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55#10622122C2211yescharacteristic, complemented
56#10622122C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic, complemented
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622117C2211yescharacteristic, complemented
62#10622117C2211yescharacteristic, complemented
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D4×C11C2×C411yescharacteristic
68C23×C4×C11—21no—
69C2×#4339C2×C411yescharacteristic
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C2×C11×M16—21no—
73C2×C11×M16—44no—
74C2×C11×M16D411yescharacteristic
75C2×C11×M16D411yescharacteristic
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C4×D4×C11—21no—
79C4×D4×C11—21no—
80C4×D4×C11C2×C411yescharacteristic
81C4×D4×C11C2×C411yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C2×C11×C4⋊C4C2×C411yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×#4324C2×C411yescharacteristic
88C2×#4324C2×C411yescharacteristic
89#66985—24no—
90C2×#4323C2×C411yescharacteristic
91C2×#4323C2×C411yescharacteristic
92C4×C22⋊D11—21no—
93C4×C22⋊D11—21no—
94#66979C2×C411yescharacteristic
95C2×#4318—21no—
96C2×#4318C2×C411yescharacteristic
97C2×#4318C2×C411yescharacteristic
98C2×C8×D11—21no—
99C2×C8×D11—21no—
100C4×D44C2×C411yescharacteristic
101C4×D44C2311yescharacteristic
102#66925—21no—
103C42×D11—21no—
104C4×Dic22C2×C411yescharacteristic
105C4×Dic22C2311yescharacteristic
106C11×C4⋊C8—21no—
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×#97D411yescharacteristic
114C11×#97D411yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66896C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119#66896C2×C411yescharacteristic
120#66896C2×C411yescharacteristic
121C22⋊(C11⋊C8)—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124#66879—21no—
125#66879—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128#66874C2×C411yescharacteristic
129#66874C2×C411yescharacteristic
130#66873C2×C411yescharacteristic
131#66873C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139#66867—21no—
140#66867C2×C411yescharacteristic
141#66867C2×C411yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#18046—111nomaximal, Sylow
147C24×C11—21no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11—41no—
151C2×D4×C11C22×C411yescharacteristic
152C2×D4×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4111yescharacteristic
163C2×C22⋊D11—21no—
164#4339—22no—
165#4339—41no—
166C2×D44C22×C411yescharacteristic
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×Dic22C22×C411yescharacteristic
171C11×M16—22no—
172C11×M16—41no—
173C11×M16—42no—
174C11×M16—42no—
175C11×M16—42no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—42no—
179C2×C8×C11—42no—
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2×D411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C11×C4⋊C4—21no—
185C11×C4⋊C4C22×C411yescharacteristic
186C11×C4⋊C4C22×C411yescharacteristic
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C11×C22⋊C4—21no—
190C11×C22⋊C4—21no—
191C42×C11C22×C411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11#4111yescharacteristic
194C42×C11C2411yescharacteristic
195C22⋊Dic11—21no—
196#4324—22no—
197#4324—22no—
198#4323—22no—
199#4323M1614yescomplemented
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—21no—
202C4⋊Dic11C22×C411yescharacteristic
203C4⋊Dic11C22×C411yescharacteristic
204Dic11⋊C4—21no—
205Dic11⋊C4—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209#4318—22no—
210#4318—41no—
211#4318—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C22×C411yescharacteristic
217C2×C11⋊C8C22×C411yescharacteristic
218C2×C11⋊C8C22×C411yescharacteristic
219C2×C11⋊C8C22×C411yescharacteristic
220C8×D11—42no—
221C8×D11—42no—
222#2970—111no—
223C4×AGL(1,ℤ/8)—111no—
224D4×M16D1111yescharacteristic, complemented
225#1592—111no—
226#1590—111no—
227#1586—111no—
228#1585—111no—
229#1582—111no—
230#1581—111no—
231#1580—111no—
232C8×D8—111no—
233#1569—111no—
234#1490—111no—
235#1489—111no—
236#1455—111no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—81no—
242C23×C11C4×D411yescharacteristic
243C22×D11—21no—
244D4×C11—21no—
245D4×C11—21no—
246D4×C11—21no—
247D4×C11—42no—
248D4×C11C2×M1612yes—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C22⋊D11—42no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273D44—21no—
274D44C2×M1612yescomplemented
275C4×D11—42no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—81no—
279Dic22—21no—
280Dic22—21no—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11AGL(1,ℤ/8)12yescomplemented
287C11⋊C8—22no—
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—21no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8C2×M1612yescomplemented
295C2×AGL(1,ℤ/8)—111no—
296C22×M16—21no—
297C4×#41—111no—
298C2×C4×D4C2×D1111yescharacteristic
299#446—111no—
300#446—111no—
301#442—111no—
302#442—111no—
303#440—111no—
304#440—111no—
305C4×SD16—111no—
306C4×SD16—111no—
307C4×D8—111no—
308C4×D8—111no—
309#436C2×D1111yescharacteristic
310#436C2×D1111yescharacteristic
311#435—21no—
312#435—21no—
313#435—221no—
314#435—221no—
315C8×D4—111no—
316C8×D4—111no—
317C8×D4C2×D1111yescharacteristic
318C8×D4C2×D1111yescharacteristic
319#432—111no—
320#432—221no—
321#428—111no—
322#423C2×D1111yescharacteristic
323#418—111no—
324#417—111no—
325#407—21no—
326C4×M16—111no—
327C4×M16—111no—
328C4×M16C2×D1111yescharacteristic
329C2×#97—221no—
330#335—111no—
331#335—111no—
332#334—111no—
333#334—111no—
334Q8⋊C8—111no—
335Q8⋊C8—111no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342#322—111no—
343#322—111no—
344#322—111no—
345C82—111no—
346C22×C11—21no—
347C22×C11—22no—
348C22×C11—21no—
349C22×C11—21no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—84no—
356C22×C11C2×C4×D411yescharacteristic
357C2×D11—22no—
358C2×D11—41no—
359C2×D11—41no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11C22×M1611yescharacteristic
367C4×C11#56811yescharacteristic
368C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C4×C11#57511yescharacteristic
370Dic11—41no—
371Dic11—41no—
372Dic11—41no—
373C2×#41—111no—
374C22×D4C4×D1111yescharacteristic
375C23×C4—21no—
376AGL(1,ℤ/8)—224no—
377C2×SD16—111no—
378C2×SD16—111no—
379C2×D8—111no—
380C2×D8—111no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—44no—
385C2×M16—111no—
386C2×M16—111no—
387C2×M16—221no—
388C2×M16C22⋊D1111yescharacteristic
389C2×M16C22⋊D1111yescharacteristic
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—221no—
393C22×C8—221no—
394C4×Q8—111no—
395C4×Q8—111no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—111no—
399C4×D4—111no—
400C4×D4—221no—
401C4×D4—221no—
402C4×D4C4×D1111yescharacteristic
403C4×D4C4×D1111yescharacteristic
404C4×D4C22×D1111yescharacteristic
405C4×D4C22×D1111yescharacteristic
406#117—111no—
407#117—221no—
408C2×C4⋊C4C4×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C42—221no—
411C2×C42C22×D1111yescharacteristic
412#107—111no—
413#107—111no—
414#106—111no—
415#106—111no—
416C4⋊C8—21no—
417C4⋊C8—111no—
418C4⋊C8—111no—
419C4⋊C8—221no—
420C4⋊C8—221no—
421C4⋊C8C22×D1111yescharacteristic
422C4⋊C8C22×D1111yescharacteristic
423#103—111no—
424#103—111no—
425#102—111no—
426#102—111no—
427#102—111no—
428#102—111no—
429#102—111no—
430#102—111no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438#97—111no—
439#97—111no—
440#97—221no—
441#97—221no—
442#97—221no—
443#97—221no—
444#97C22⋊D1111yescharacteristic
445#97C22⋊D1111yescharacteristic
446C4×C8—111no—
447C4×C8—111no—
448C4×C8—111no—
449C4×C8—111no—
450C4×C8C22×D1111yescharacteristic
451C4×C8C22×D1111yescharacteristic
452C2×C11—41no—
453C2×C11—42no—
454C2×C11—81no—
455C2×C11D4×M1611yescharacteristic
456C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
457C2×C11#295611yescharacteristic
458D11—42no—
459C24—21no—
460#41—222no—
461#41—441no—
462C2×Q8—111no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—111no—
467C2×D4—221no—
468C2×D4C2×C4×D1111yescharacteristic
469C2×D4C2×C4×D1111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4#433911yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483SD16—222no—
484SD16—222no—
485D8—114no—
486D8—222no—
487M16—22no—
488M16—41no—
489M16—42no—
490M16—42no—
491M16—42no—
492M16—222no—
493M16—441no—
494M16—442no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—42no—
498C2×C8—42no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—111no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—442no—
508C2×C8—442no—
509C2×C8C2×C22⋊D1111yescharacteristic
510C2×C8C2×C22⋊D1111yescharacteristic
511C2×C8C2×C22⋊D1111yescharacteristic
512C2×C8C2×C22⋊D1111yescharacteristic
513C4⋊C4—21no—
514C4⋊C4—111no—
515C4⋊C4—111no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4C2×C4×D1111yescharacteristic
519C4⋊C4C2×C4×D1111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42C2×C4×D1111yescharacteristic
531C42#433911yescharacteristic
532C42C2×C22⋊D1111yescharacteristic
533C42C23×D1111yescharacteristic
534C11#1804611yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—42no—
538C23—42no—
539C23—81no—
540C23—221no—
541C23C4×C22⋊D1111yescharacteristic
542Q8—221no—
543Q8—221no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—42no—
548D4—112no—
549D4—221no—
550D4—442no—
551D4M16×D1112yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—442no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—881no—
573C2×C4C4×C22⋊D1111yescharacteristic
574C2×C4C4×C22⋊D1111yescharacteristic
575C2×C4C4×C22⋊D1111yescharacteristic
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C2×#433911yescharacteristic
578C2×C4C22×C22⋊D1111yescharacteristic
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—112no—
585C8—222no—
586C8—221no—
587C8—221no—
588C8—221no—
589C8—441no—
590C8—441no—
591C8—441no—
592C8#6698512yescomplemented
593C22—21no—
594C22—21no—
595C22—22no—
596C22—21no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—84no—
603C22—222no—
604C22—441no—
605C22—441no—
606C22C2×C4×C22⋊D1111yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—41no—
612C4—41no—
613C4—441no—
614C4—441no—
615C4—441no—
616C4C2×M16×D1111yescharacteristic
617C4#1062327611yescharacteristic
618C4C2×#6698511yescharacteristic
619C4#1062335311yescharacteristic
620C2—41no—
621C2—42no—
622C2—81no—
623C2—442no—
624C2M16×C22⋊D1111yescharacteristic
625C2C4×#6698511yescharacteristic
626C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingD4×C11×M16C2
socleC22×C11C2×C4×D4
prime radicalC2×#66985C4
cosocleC42×C11C24
hypercenterD4×M16D11
hypocenterC11#18046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
1. #13077631C2semidirect
3. #13067518C2semidirect
4. #13067504C2semidirect
5. #13067478C2semidirect
6. #13067473C2semidirect
7. #13067452C2semidirect
8. #13067443C2semidirect
9. #13067438C2semidirect
10. C8×#4323C2semidirect
11. #13067381C2semidirect
12. #13067059C2semidirect
13. #13067053C2semidirect
14. #13066919C2semidirect
15. D4×C11×M16C2semidirect
47. C8×D44C22semidirect
48. C8×D44C22semidirect
49. #10622292C22semidirect
50. #10622292C22semidirect
55. #10622122C22semidirect
56. #10622122C22semidirect
57. #10622121C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
199. #4323M16semidirect
224. D4×M16D11semidirect
274. D44C2×M16semidirect
286. C8×C11AGL(1,ℤ/8)semidirect
294. C11⋊C8C2×M16semidirect
534. C11#18046semidirect
592. C8#66985semidirect

Maximal subgroups

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

subgroupindex
#130776312
C4×#669852
#130675182
#130675042
#130674782
#130674732
#130674522
#130674432
#130674382
C8×#43232
#130673812
#130670592
#130670532
#130669192
D4×C11×M162
#1804611