Finite Group Databasebeta

← #14725301

Subgroups — #14725301

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
1C4×#67002C211yesmaximal, characteristic
2M16×D44C211yesmaximal, characteristic, complemented
3#13067516C211yesmaximal, characteristic, complemented
4#13067506C211yesmaximal, characteristic, complemented
5#13067480C211yesmaximal, characteristic, complemented
6#13067471C211yesmaximal, characteristic, complemented
7#13067450C211yesmaximal, characteristic, complemented
8#13067445C211yesmaximal, characteristic, complemented
9#13067438C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067384C211yesmaximal, characteristic, complemented
12#13067058C211yesmaximal, characteristic, complemented
13#13067055C211yesmaximal, characteristic, complemented
14#13066919C211yesmaximal, characteristic, complemented
15C11×#2970C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17C2×#67002C411yescharacteristic
18C2×M16×D11—21no—
19C2×C4×D44C2211yescharacteristic
20C11×#446C2211yescharacteristic, complemented
21C11×#446C2211yescharacteristic, complemented
22C11×#435—21no—
23C11×#435—21no—
24C8×D4×C11C2211yescharacteristic, complemented
25C8×D4×C11C2211yescharacteristic, complemented
26C11×#432—21no—
27C11×#432C2211yescharacteristic
28C4×C11×M16C2211yescharacteristic
29C2×C11×#97—21no—
30#10622845C411yescharacteristic
31#10622739—21no—
32#10622639C411yescharacteristic
33#10622639C411yescharacteristic
34C4×#4325C2211yescharacteristic
35C4×#4325C2211yescharacteristic
36#10622627C411yescharacteristic
37#10622627C411yescharacteristic
38C4×#4323C2211yescharacteristic
39C4×#4323C2211yescharacteristic
40#10622614C411yescharacteristic
41#10622608C411yescharacteristic
42#10622537C2211yescharacteristic
43C4×#4318C2211yescharacteristic
44C4×#4318C2211yescharacteristic
45#10622319—21no—
46#10622319—21no—
47#10622301C2211yescharacteristic
48#10622301C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C8×D44C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
52Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
53D4⋊(C11⋊C8)C2211yescharacteristic, complemented
54D4⋊(C11⋊C8)C2211yescharacteristic, complemented
55#10622121C2211yescharacteristic
56#10622121C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
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
67C2×C11×#41C2×C411yescharacteristic
68C22×D44C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C22×C8×C11—21no—
73C22×C8×C11—21no—
74C4×Q8×C11C2×C411yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C4×D4×C11—21no—
77C4×D4×C11—21no—
78C4×D4×C11C2×C411yescharacteristic
79C4×D4×C11C2311yescharacteristic
80C11×#117—21no—
81C11×#117C2×C411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84#67002—24no—
85C2×#4325C2×C411yescharacteristic
86C2×#4325C2×C411yescharacteristic
87C2×#4323C2×C411yescharacteristic
88C2×#4323C2×C411yescharacteristic
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11C2×C411yescharacteristic
91C2×#4318—21no—
92C2×#4318—21no—
93C2×#4318C2×C411yescharacteristic
94C2×#4318C2×C411yescharacteristic
95M16×D11—44no—
96C2×#4313—21no—
97C2×#4313—21no—
98C2×C8×D11—21no—
99C2×C8×D11—21no—
100C4×D44—21no—
101C4×D44—21no—
102C4×D44C2×C411yescharacteristic
103C4×D44C2×C411yescharacteristic
104C4×D44C2311yescharacteristic
105C4×D44C2311yescharacteristic
106C11×C4⋊C8—21no—
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×C22⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×#97—21no—
114C11×#97—21no—
115C11×#97—21no—
116C11×#97D411yescharacteristic
117C11×#97D411yescharacteristic
118C4×C8×C11C2311yescharacteristic
119C4×C8×C11C2311yescharacteristic
120#66899C2×C411yescharacteristic
121#66899C2×C411yescharacteristic
122#66896C2×C411yescharacteristic
123#66896C2×C411yescharacteristic
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128#66873C2×C411yescharacteristic
129#66873C2×C411yescharacteristic
130#66873C2×C411yescharacteristic
131#66873C2×C411yescharacteristic
132#66872C2×C411yescharacteristic
133#66872C2×C411yescharacteristic
134#66871C2×C411yescharacteristic
135#66871C2×C411yescharacteristic
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
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
147C23×D11—21no—
148C11×#41—22no—
149C11×#41—41no—
150C2×Q8×C11C22×C411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11C22×C411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C22×Dic11—21no—
160C2×D44—22no—
161C2×D44—21no—
162C2×D44—41no—
163C2×D44C22×C411yescharacteristic
164C2×D44C22×C411yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C11×M16—22no—
172C11×M16—41no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—42no—
176C2×C8×C11—42no—
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C22×C411yescharacteristic
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11C22×C411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11#4111yescharacteristic
194C42×C11C2411yescharacteristic
195#4325—22no—
196#4325—22no—
197#4323—22no—
198#4323M1614yescomplemented
199(C2×D11)⋊C4—21no—
200(C2×D11)⋊C4—21no—
201(C2×D11)⋊C4—21no—
202(C2×D11)⋊C4—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C22×C411yescharacteristic
205C4⋊Dic11C22×C411yescharacteristic
206#4318—22no—
207#4318—41no—
208#4318—42no—
209#4318—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C22×C411yescharacteristic
215C2×C11⋊C8C22×C411yescharacteristic
216C2×C11⋊C8C22×C411yescharacteristic
217C2×C11⋊C8C22×C411yescharacteristic
218#4313—42no—
219#4313—42no—
220C8×D11—42no—
221C8×D11—42no—
222#2970D1111yescharacteristic, complemented
223C4×AGL(1,ℤ/8)—111no—
224D4×M16—111no—
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×C11C4×D411yescharacteristic
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—42no—
242C22×D11—42no—
243C22×D11—81no—
244Q8×C11—21no—
245Q8×C11—21no—
246D4×C11—21no—
247D4×C11—42no—
248D4×C11C2×M1612yescomplemented
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—21no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—81no—
261C2×C4×C11C4×D411yescharacteristic
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—42no—
270D44—21no—
271D44—21no—
272D44—21no—
273D44—42no—
274D44C2×M1612yes—
275C4×D11—42no—
276C4×D11—42no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—41no—
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—221no—
297C4×#41C2×D1111yescharacteristic
298C2×C4×D4—111no—
299#446C2×D1111yescharacteristic, complemented
300#446C2×D1111yescharacteristic, complemented
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#436—111no—
310#436—111no—
311#435—21no—
312#435—21no—
313#435—221no—
314#435—221no—
315C8×D4—111no—
316C8×D4—111no—
317C8×D4C2×D1111yescharacteristic, complemented
318C8×D4C2×D1111yescharacteristic, complemented
319#432—21no—
320#432C2×D1111yescharacteristic
321#428—111no—
322#423—111no—
323#418—111no—
324#417—111no—
325#407—221no—
326C4×M16—111no—
327C4×M16—111no—
328C4×M16C2×D1111yescharacteristic
329C2×#97—21no—
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×C11C2×C4×D411yescharacteristic
353C2×D11—22no—
354C2×D11—41no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—84no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11C22×M1611yescharacteristic
368C4×C11#56811yescharacteristic
369C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C4×C11#57511yescharacteristic
371Dic11—41no—
372Dic11—41no—
373C2×#41C4×D1111yescharacteristic
374C22×D4—111no—
375C23×C4—221no—
376AGL(1,ℤ/8)—224no—
377C2×SD16—111no—
378C2×SD16—111no—
379C2×D8—111no—
380C2×D8—111no—
381C2×M16—111no—
382C2×M16—111no—
383C2×M16—221no—
384C2×M16—221no—
385C2×M16—221no—
386C2×M16—221no—
387C2×M16—444no—
388C2×M16C22⋊D1111yescharacteristic
389C2×M16C22⋊D1111yescharacteristic
390C22×C8—21no—
391C22×C8—21no—
392C22×C8—221no—
393C22×C8—221no—
394C4×Q8C4×D1111yescharacteristic
395C4×Q8C22×D1111yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—111no—
399C4×D4—111no—
400C4×D4—111no—
401C4×D4—111no—
402C4×D4—221no—
403C4×D4—221no—
404C4×D4C4×D1111yescharacteristic
405C4×D4C22×D1111yescharacteristic
406#117—21no—
407#117C4×D1111yescharacteristic
408C2×C4⋊C4—111no—
409C2×C22⋊C4—221no—
410C2×C42—21no—
411C2×C42C22×D1111yescharacteristic
412#107—111no—
413#107—111no—
414#106—111no—
415#106—111no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—111no—
419C4⋊C8—111no—
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—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438#97—21no—
439#97—21no—
440#97—21no—
441#97—111no—
442#97—111no—
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×C11D4×M1611yescharacteristic
455C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
456C2×C11#295611yescharacteristic
457D11—42no—
458D11—81no—
459C24—221no—
460#41—22no—
461#41—41no—
462C2×Q8C2×C4×D1111yescharacteristic
463C2×D4—21no—
464C2×D4—111no—
465C2×D4—111no—
466C2×D4—222no—
467C2×D4—221no—
468C2×D4—441no—
469C2×D4C2×C4×D1111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4#433911yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483SD16—222no—
484SD16—222no—
485D8—114no—
486D8—222no—
487M16—22no—
488M16—41no—
489M16—222no—
490M16—442no—
491M16—441no—
492M16—442no—
493M16—442no—
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—21no—
515C4⋊C4—111no—
516C4⋊C4—111no—
517C4⋊C4—221no—
518C4⋊C4C2×C4×D1111yescharacteristic
519C4⋊C4C2×C4×D1111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42C2×C4×D1111yescharacteristic
531C42#433911yescharacteristic
532C42C2×C22⋊D1111yescharacteristic
533C42C23×D1111yescharacteristic
534C11#1804611yescharacteristic, complemented, Sylow
535C23—21no—
536C23—221no—
537C23—221no—
538C23—442no—
539C23—442no—
540C23—881no—
541C23C4×C22⋊D1111yescharacteristic
542Q8—21no—
543Q8—21no—
544D4—21no—
545D4—42no—
546D4—112no—
547D4—221no—
548D4—221no—
549D4—221no—
550D4—442no—
551D4M16×D1112yescomplemented
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—81no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
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#6700212yescomplemented
593C22—21no—
594C22—21no—
595C22—22no—
596C22—21no—
597C22—41no—
598C22—41no—
599C22—222no—
600C22—441no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22—884no—
606C22C2×C4×C22⋊D1111yescharacteristic
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—441no—
615C4—441no—
616C4C2×M16×D1111yescharacteristic
617C4#1062327611yescharacteristic
618C4C2×#6700211yescharacteristic
619C4#1062335311yescharacteristic
620C2—41no—
621C2—42no—
622C2—442no—
623C2—881no—
624C2M16×C22⋊D1111yescharacteristic
625C2C4×#6700211yescharacteristic
626C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2970C2
socleC22×C11C2×C4×D4
prime radicalC2×#67002C4
cosocleC42×C11C24
hypercenter#2970D11
hypocenterC11#18046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. M16×D44C2semidirect
3. #13067516C2semidirect
4. #13067506C2semidirect
5. #13067480C2semidirect
6. #13067471C2semidirect
7. #13067450C2semidirect
8. #13067445C2semidirect
9. #13067438C2semidirect
10. C8×#4323C2semidirect
11. #13067384C2semidirect
12. #13067058C2semidirect
13. #13067055C2semidirect
14. #13066919C2semidirect
15. C11×#2970C2semidirect
20. C11×#446C22semidirect
21. C11×#446C22semidirect
24. C8×D4×C11C22semidirect
25. C8×D4×C11C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
52. Q8⋊(C11⋊C8)C22semidirect
53. D4⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
61. #10622117C22semidirect
62. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
198. #4323M16semidirect
222. #2970D11semidirect
248. D4×C11C2×M16semidirect
286. C8×C11AGL(1,ℤ/8)semidirect
294. C11⋊C8C2×M16semidirect
299. #446C2×D11semidirect
300. #446C2×D11semidirect
317. C8×D4C2×D11semidirect
318. C8×D4C2×D11semidirect
534. C11#18046semidirect
551. D4M16×D11semidirect
592. C8#67002semidirect

Maximal subgroups

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

subgroupindex
C4×#670022
M16×D442
#130675162
#130675062
#130674802
#130674712
#130674502
#130674452
#130674382
C8×#43232
#130673842
#130670582
#130670552
#130669192
C11×#29702
#1804611