Finite Group Databasebeta

← #14725310

Subgroups — #14725310

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#13077629C211yesmaximal, characteristic, complemented
2C4×#66967C211yesmaximal, characteristic
3#13077352C211yesmaximal, characteristic, complemented
4#13067519C211yesmaximal, characteristic, complemented
5#13067483C211yesmaximal, characteristic, complemented
6#13067476C211yesmaximal, characteristic, complemented
7#13067450C211yesmaximal, characteristic, complemented
8#13067443C211yesmaximal, characteristic, complemented
9#13067439C211yesmaximal, characteristic, complemented
10C8×D88C211yesmaximal, characteristic, complemented
11#13067380C211yesmaximal, characteristic, complemented
12#13067057C211yesmaximal, characteristic, complemented
13#13067054C211yesmaximal, characteristic, complemented
14#13066918C211yesmaximal, characteristic, complemented
15C11×#1590C211yesmaximal, characteristic, complemented
16C2×#66967C411yescharacteristic
17C2×M16×D11—21no—
18C4×#4343C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C11×#446C2211yescharacteristic, complemented
21C4×C11×SD16C2211yescharacteristic
22C11×#436C2211yescharacteristic
23#10622777C411yescharacteristic
24#10622740—21no—
25C4×#4325C2211yescharacteristic
26#10622637C2211yescharacteristic, complemented
27C4×#4323C2211yescharacteristic
28#10622625C2211yescharacteristic
29#10622482C411yescharacteristic
30#10622474C411yescharacteristic
31#10622450C2211yescharacteristic
32#10622449—21no—
33#10622448—21no—
34#10622448C2211yescharacteristic
35#10622447C2211yescharacteristic
36#10622447C2211yescharacteristic, complemented
37#10622430C411yescharacteristic
38#10622416C411yescharacteristic
39#10622398C411yescharacteristic
40#10622383C411yescharacteristic
41#10622341—21no—
42#10622339—21no—
43#10622319—21no—
44D11×#97—21no—
45C4×D88C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48C4×#4313C2211yescharacteristic
49C8×D44C2211yescharacteristic
50C8×D44C2211yescharacteristic, complemented
51C11×#334C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic
54C82×C11C2211yescharacteristic, complemented
55Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic, complemented
63#10622096C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622093C2211yescharacteristic, complemented
66#10622093C2211yescharacteristic, complemented
67C2×#4343C2×C411yescharacteristic
68C2×D4×D11C2×C411yescharacteristic
69C22×C4×D11—21no—
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×M16—21no—
72C4×Q8×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74Q8×Dic11C2×C411yescharacteristic
75C2×#4325C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C2×#4318—21no—
80#66967—24no—
81M16×D11—44no—
82C2×D88C2×C411yescharacteristic
83C2×#4313—21no—
84C2×#4313—21no—
85C2×#4313C2×C411yescharacteristic
86C2×#4313C2×C411yescharacteristic
87C2×#4313D411yescharacteristic
88C2×#4313D411yescharacteristic
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91C2×C8×D11—21no—
92C2×C8×D11—21no—
93#66946—21no—
94#66946C2×C411yescharacteristic
95#66946C2×C411yescharacteristic
96#66945—21no—
97#66945C2×C411yescharacteristic
98C4⋊C4×D11C2×C411yescharacteristic
99(C22⋊D11)⋊C4—21no—
100C22⋊C4×D11—21no—
101C4×D44—21no—
102C4×D44C2311yescharacteristic
103C4×D44C2311yescharacteristic
104C42×D11—21no—
105C42×D11C2311yescharacteristic
106C11×#106C2×C411yescharacteristic
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#103C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×C22⋊C8—21no—
113C11×#97—21no—
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66899C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119C22⋊(C11⋊C8)—21no—
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127#66882C2×C411yescharacteristic
128#66879—21no—
129#66879—21no—
130#66879C2×C411yescharacteristic
131#66879C2×C411yescharacteristic
132#66879D411yescharacteristic
133#66879D411yescharacteristic
134Dic11⋊C8—21no—
135#66873C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66871C2×C411yescharacteristic
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#18046—111nomaximal, Sylow
147C23×D11—21no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C22×Dic11—21no—
153#4343—22no—
154#4343—41no—
155D4×D11—22no—
156D4×D11—41no—
157C2×D44—21no—
158C2×D44C22×C411yescharacteristic
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11C22×C411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×C4×D11#4111yescharacteristic
171C11×SD16—22no—
172C11×M16—42no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C22×C411yescharacteristic
177C2×C8×C11C22×C411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C11×C4⋊C4—21no—
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C22⋊C4—21no—
184C42×C11—21no—
185C42×C11C2411yescharacteristic
186C22⋊Dic11—21no—
187#4325—22no—
188#4323—22no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197Dic11⋊C4—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11C22×C411yescharacteristic
201C4×Dic11C2×D411yescharacteristic
202C4×Dic11#4111yescharacteristic
203#4318—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C22×C411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211D88M1614yescomplemented
212#4313—22no—
213#4313—22no—
214#4313—41no—
215#4313—41no—
216#4313—42no—
217#4313—42no—
218C8×D11—42no—
219C8×D11—42no—
220C8×D11—42no—
221C8×D11—42no—
222#2970—111no—
223C4×AGL(1,ℤ/8)—111no—
224D4×M16—111no—
225#1592—111no—
226#1590D1111yescharacteristic, complemented
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—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—42no—
241C22×D11—42no—
242C22×D11—81no—
243C22×D11C4×D411yescharacteristic
244Q8×C11—21no—
245Q8×C11—21no—
246D4×C11—21no—
247D4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C22⋊D11—42no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—42no—
260C2×Dic11C4×D411yescharacteristic
261C2×Dic11C4×D411yescharacteristic
262C2×Dic11C4×D411yescharacteristic
263D44—21no—
264D44—21no—
265D44—42no—
266D44C2×M1612yes—
267D44C2×M1612yescomplemented
268C4×D11—21no—
269C4×D11—21no—
270C4×D11—21no—
271C4×D11—21no—
272C4×D11—41no—
273C4×D11—42no—
274C4×D11—42no—
275C4×D11—42no—
276C4×D11—41no—
277C4×D11—41no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—81no—
281C8×C11—22no—
282C8×C11—21no—
283C8×C11—21no—
284C8×C11—41no—
285C8×C11—41no—
286C8×C11C2×M1612yescomplemented
287C8×C11AGL(1,ℤ/8)12yescomplemented
288C11⋊C8—21no—
289C11⋊C8—21no—
290C11⋊C8—21no—
291C11⋊C8—21no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C2×AGL(1,ℤ/8)—111no—
296C22×M16—221no—
297C4×#41—111no—
298C2×C4×D4—111no—
299#446—111no—
300#446C2×D1111yescharacteristic, complemented
301#442—111no—
302#442—111no—
303#440—111no—
304#440—111no—
305C4×SD16—111no—
306C4×SD16C2×D1111yescharacteristic
307C4×D8—111no—
308C4×D8—111no—
309#436—111no—
310#436C2×D1111yescharacteristic
311#435—221no—
312#435—221no—
313#435—221no—
314#435—221no—
315C8×D4—111no—
316C8×D4—111no—
317C8×D4—111no—
318C8×D4—111no—
319#432—111no—
320#432—221no—
321#428—111no—
322#423—111no—
323#418—111no—
324#417—111no—
325#407—221no—
326C4×M16—111no—
327C4×M16—111no—
328C4×M16—111no—
329C2×#97—221no—
330#335—111no—
331#335—111no—
332#334—111no—
333#334C2×D1111yescharacteristic, complemented
334Q8⋊C8—111no—
335Q8⋊C8C2×D1111yescharacteristic, complemented
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—111no—
339D4⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8C2×D1111yescharacteristic
342#322—111no—
343#322—111no—
344#322—111no—
345C82C2×D1111yescharacteristic, complemented
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11C2×C4×D411yescharacteristic
350C2×D11—22no—
351C2×D11—22no—
352C2×D11—21no—
353C2×D11—21no—
354C2×D11—21no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—84no—
360C4×C11—21no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11C22×M1611yescharacteristic
365C4×C11#56811yescharacteristic
366C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
367C4×C11#57511yescharacteristic
368Dic11—21no—
369Dic11—21no—
370Dic11—21no—
371Dic11—41no—
372Dic11—41no—
373C2×#41—111no—
374C22×D4—111no—
375C23×C4—221no—
376AGL(1,ℤ/8)—224no—
377C2×SD16—111no—
378C2×SD16C4×D1111yescharacteristic
379C2×D8—111no—
380C2×D8—111no—
381C2×M16—21no—
382C2×M16—111no—
383C2×M16—111no—
384C2×M16—111no—
385C2×M16—111no—
386C2×M16—221no—
387C2×M16—221no—
388C2×M16—221no—
389C2×M16—444no—
390C22×C8—221no—
391C22×C8—221no—
392C22×C8—221no—
393C22×C8—221no—
394C4×Q8—111no—
395C4×Q8C22×D1111yescharacteristic
396C4×D4—111no—
397C4×D4—111no—
398C4×D4—111no—
399C4×D4—111no—
400C4×D4—111no—
401C4×D4—221no—
402C4×D4—221no—
403C4×D4—221no—
404C4×D4—221no—
405C4×D4C22×D1111yescharacteristic
406#117—111no—
407#117—221no—
408C2×C4⋊C4—111no—
409C2×C22⋊C4—221no—
410C2×C42—111no—
411C2×C42—221no—
412#107—111no—
413#107—111no—
414#106—111no—
415#106C4×D1111yescharacteristic
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#103C4×D1111yescharacteristic
425#102—111no—
426#102—111no—
427#102—111no—
428#102—111no—
429#102—111no—
430#102C4×D1111yescharacteristic
431C22⋊C8—21no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C22⋊C8—221no—
436C22⋊C8—221no—
437C22⋊C8—221no—
438#97—21no—
439#97—111no—
440#97—111no—
441#97—111no—
442#97—111no—
443#97—221no—
444#97—221no—
445#97—221no—
446C4×C8—111no—
447C4×C8—111no—
448C4×C8—111no—
449C4×C8C22×D1111yescharacteristic
450C4×C8C22×D1111yescharacteristic
451C4×C8C22×D1111yescharacteristic
452C2×C11—81no—
453C2×C11D4×M1611yescharacteristic
454C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
455C2×C11#295611yescharacteristic
456D11—41no—
457D11—42no—
458D11—42no—
459C24—221no—
460#41—222no—
461#41—441no—
462C2×Q8C2×C4×D1111yescharacteristic
463C2×D4—111no—
464C2×D4—111no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—222no—
468C2×D4—441no—
469C2×D4C2×C4×D1111yescharacteristic
470C22×C4—21no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—442no—
482C22×C4—442no—
483SD16—22no—
484SD16—222no—
485D8—114no—
486D8—222no—
487M16—42no—
488M16—222no—
489M16—222no—
490M16—441no—
491M16—441no—
492M16—442no—
493M16—442no—
494M16—442no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—111no—
499C2×C8—111no—
500C2×C8—111no—
501C2×C8—111no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—442no—
506C2×C8—442no—
507C2×C8—442no—
508C2×C8—442no—
509C2×C8C2×C4×D1111yescharacteristic
510C2×C8C2×C4×D1111yescharacteristic
511C2×C8D4×D1111yescharacteristic
512C2×C8D4×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—221no—
522C22⋊C4—221no—
523C22⋊C4—221no—
524C22⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C42—21no—
528C42—111no—
529C42—111no—
530C42—111no—
531C42—221no—
532C42—221no—
533C42C23×D1111yescharacteristic
534C11#1804611yescharacteristic, complemented, Sylow
535C23—21no—
536C23—111no—
537C23—221no—
538C23—221no—
539C23—442no—
540C23—442no—
541C23—881no—
542Q8—21no—
543Q8—21no—
544D4—21no—
545D4—21no—
546D4—112no—
547D4—112no—
548D4—221no—
549D4—221no—
550D4—442no—
551D4—442no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—111no—
558C2×C4—111no—
559C2×C4—111no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—441no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—881no—
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C8—22no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—221no—
585C8—221no—
586C8—221no—
587C8—221no—
588C8—441no—
589C8—441no—
590C8—441no—
591C8M16×D1112yescomplemented
592C8#6696712yescomplemented
593C22—41no—
594C22—41no—
595C22—41no—
596C22—221no—
597C22—221no—
598C22—222no—
599C22—222no—
600C22—221no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22—884no—
606C22C4×D4×D1111yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—221no—
612C4—221no—
613C4—221no—
614C4—441no—
615C4—441no—
616C4C2×M16×D1111yescharacteristic
617C4#1062328111yescharacteristic
618C4C2×#6696711yescharacteristic
619C4#1062329911yescharacteristic
620C2—81no—
621C2—441no—
622C2—442no—
623C2—442no—
624C2#1307735211yescharacteristic
625C2C4×#6696711yescharacteristic
626C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1590C2
socleC22×C11C2×C4×D4
prime radicalC2×#66967C4
cosocleC42×C11C24
hypercenter#1590D11
hypocenterC11#18046
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
1. #13077629C2semidirect
3. #13077352C2semidirect
4. #13067519C2semidirect
5. #13067483C2semidirect
6. #13067476C2semidirect
7. #13067450C2semidirect
8. #13067443C2semidirect
9. #13067439C2semidirect
10. C8×D88C2semidirect
11. #13067380C2semidirect
12. #13067057C2semidirect
13. #13067054C2semidirect
14. #13066918C2semidirect
15. C11×#1590C2semidirect
20. C11×#446C22semidirect
26. #10622637C22semidirect
36. #10622447C22semidirect
50. C8×D44C22semidirect
51. C11×#334C22semidirect
52. C11×Q8⋊C8C22semidirect
54. C82×C11C22semidirect
55. Q8⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622117C22semidirect
62. #10622097C22semidirect
63. #10622096C22semidirect
64. #10622093C22semidirect
65. #10622093C22semidirect
66. #10622093C22semidirect
211. D88M16semidirect
226. #1590D11semidirect
267. D44C2×M16semidirect
286. C8×C11C2×M16semidirect
287. C8×C11AGL(1,ℤ/8)semidirect
300. #446C2×D11semidirect
333. #334C2×D11semidirect
335. Q8⋊C8C2×D11semidirect
345. C82C2×D11semidirect
534. C11#18046semidirect
591. C8M16×D11semidirect
592. C8#66967semidirect

Maximal subgroups

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

subgroupindex
#130776292
C4×#669672
#130773522
#130675192
#130674832
#130674762
#130674502
#130674432
#130674392
C8×D882
#130673802
#130670572
#130670542
#130669182
C11×#15902
#1804611