Finite Group Databasebeta

← #25067666

Subgroups — #25067666

Order 11008.

670 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144646C211yesmaximal, characteristic
2#19143601C211yesmaximal, characteristic, complemented
3D4×#10621872C211yesmaximal, characteristic, complemented
4#19133495C211yesmaximal, characteristic, complemented
5#19133479C211yesmaximal, characteristic, complemented
6#19133461C211yesmaximal, characteristic, complemented
7#19133435C211yesmaximal, characteristic, complemented
8#19133421C211yesmaximal, characteristic, complemented
9#19133417C211yesmaximal, characteristic, complemented
10SD16×C43⋊C8C211yesmaximal, characteristic, complemented
11#19133385C211yesmaximal, characteristic, complemented
12#19133059C211yesmaximal, characteristic, complemented
13#19132984C211yesmaximal, characteristic, complemented
14#19132891C211yesmaximal, characteristic, complemented
15C43×#1585C211yesmaximal, characteristic, complemented
16C22×#10621872—21no—
17#14583436C2211yescharacteristic
18C4×D4×D43C2211yescharacteristic
19#14583233C411yescharacteristic
20#14583219C411yescharacteristic
21#14583198C411yescharacteristic
22#14583197C411yescharacteristic
23#14583117C411yescharacteristic
24#14583116C411yescharacteristic
25#14583048C411yescharacteristic
26#14583034C411yescharacteristic
27Q8×C43⋊C8C2211yescharacteristic, complemented
28C4×#10621884C2211yescharacteristic
29C4×D344C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582976—21no—
33#14582976C2211yescharacteristic
34#14582976C2211yescharacteristic, complemented
35#14582972—21no—
36#14582970—21no—
37#14582967—21no—
38C8×D172C2211yescharacteristic, complemented
39D4×C43⋊C8C2211yescharacteristic
40#14582959—21no—
41#14582951C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582921C2211yescharacteristic
45#14582861—21no—
46#14582856—21no—
47C4×#10621872C2211yescharacteristic
48#14582651C2211yescharacteristic, complemented
49#14582650C2211yescharacteristic, complemented
50#14582649C2211yescharacteristic, complemented
51Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
52#14582628C2211yescharacteristic
53#14582628C2211yescharacteristic, complemented
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic, complemented
57#14582621C2211yescharacteristic, complemented
58#14582621C2211yescharacteristic, complemented
59C8×C43⋊C8C2211yescharacteristic, complemented
60C43×#446C2211yescharacteristic, complemented
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic, complemented
64C43×Q8⋊C8C2211yescharacteristic, complemented
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic, complemented
67C2×D4×D43C2×C411yescharacteristic
68C22×C4×D43—21no—
69C2×#10621884C2×C411yescharacteristic
70C2×D344C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621872—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C2×#10621872—44no—
77C2×#10621872D411yescharacteristic
78C2×#10621872D411yescharacteristic
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81#13063320—21no—
82#13063316C2×C411yescharacteristic
83#13063314C2×C411yescharacteristic
84#13063310—21no—
85#13063301C2×C411yescharacteristic
86#13063300C2×C411yescharacteristic
87C4×D172—21no—
88C4×D172C2311yescharacteristic
89C4×D172C2311yescharacteristic
90D4×Dic43C2×C411yescharacteristic
91#13063287C2×C411yescharacteristic
92C4×C22⋊D43—21no—
93(C22⋊D43)⋊C4—21no—
94#13063282—21no—
95C4⋊C4×D43C2×C411yescharacteristic
96C22⋊C4×D43—21no—
97C42×D43C2311yescharacteristic
98#13063259C2×C411yescharacteristic
99#13063258C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8C2×C411yescharacteristic
107Dic43⋊C8C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063247C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113#13063245C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8C2×C411yescharacteristic
122(C2×D43)⋊C8C2×C411yescharacteristic
123#13063235D411yescharacteristic
124#13063235D411yescharacteristic
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43—21no—
130C2×SD16×C43C2×C411yescharacteristic
131C22×C8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C23×D43—21no—
146C2×Q8×C43C22×C411yescharacteristic
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C2×C22⋊D43—21no—
150C22×Dic43—21no—
151D4×D43—22no—
152D4×D43—41no—
153C2×D172—21no—
154C2×D172C22×C411yescharacteristic
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43C22×C411yescharacteristic
163C2×C4×D43C2×D411yescharacteristic
164C2×C4×D43#4111yescharacteristic
165SD16×C43—22no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—42no—
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181#10621884—41no—
182#10621882—22no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C22×C411yescharacteristic
192C4⋊Dic43C22×C411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—42no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207D344—41no—
208#10621872—22no—
209#10621872—41no—
210#10621872—42no—
211#10621872—42no—
212#10621872—42no—
213#10621872—42no—
214C8×D43—42no—
215C23×C43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—42no—
219C22×D43—42no—
220C22×D43—81no—
221C22×D43C4×D411yescharacteristic
222Q8×C43—21no—
223Q8×C43—21no—
224D4×C43—21no—
225D4×C43#13112yes—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C22⋊D43—42no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—42no—
238C2×Dic43C4×D411yescharacteristic
239C2×Dic43C4×D411yescharacteristic
240C2×Dic43C4×D411yescharacteristic
241D172—21no—
242D172—21no—
243D172—21no—
244D172—21no—
245D172—81no—
246C4×D43—21no—
247C4×D43—21no—
248C4×D43—21no—
249C4×D43—21no—
250C4×D43—41no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—41no—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—41no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—21no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8AGL(1,ℤ/8)12yes—
271#18008—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43C2×C4×D411yescharacteristic
276C2×D43—21no—
277C2×D43—21no—
278C2×D43—21no—
279C2×D43—41no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—84no—
286C4×C43—21no—
287C4×C43—41no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43C2×#13111yescharacteristic
291C4×C43#56811yescharacteristic
292C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C43#57511yescharacteristic
294Dic43—21no—
295Dic43—21no—
296Dic43—21no—
297Dic43—41no—
298Dic43—41no—
299#3105—431no—
300#2969—431no—
301D4×M16—431no—
302#1592—431no—
303#1589—431no—
304#1586—431no—
305#1585D4311yescharacteristic, complemented
306#1583—431no—
307#1581—431no—
308#1580—431no—
309C8×SD16—431no—
310#1574—431no—
311#1495—431no—
312#1478—431no—
313#1453—431no—
314C2×C43—42no—
315C2×C43#293311yescharacteristic
316C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
317C2×C43#295711yescharacteristic
318D43—41no—
319D43—81no—
320D43—81no—
321C22×M16—861no—
322#529—431no—
323C2×C4×D4—431no—
324#484—431no—
325#481—431no—
326#478—431no—
327#478—431no—
328#463—431no—
329#463—431no—
330#450—431no—
331#447—431no—
332#446C2×D4311yescharacteristic, complemented
333C8×Q8—431no—
334C4×SD16—431no—
335C4×SD16C2×D4311yescharacteristic
336C4×D8—431no—
337C4×D8—431no—
338#436—431no—
339#436—431no—
340#436—431no—
341#436—861no—
342#435—861no—
343#435—861no—
344#435—861no—
345C8×D4—431no—
346C8×D4—431no—
347C8×D4C2×D4311yescharacteristic
348#433—861no—
349#431—431no—
350#431—431no—
351#431—431no—
352#423—431no—
353#407—861no—
354#405—861no—
355C4×M16—431no—
356#335—431no—
357#335C2×D4311yescharacteristic, complemented
358#334—431no—
359#334—431no—
360Q8⋊C8—431no—
361Q8⋊C8C2×D4311yescharacteristic, complemented
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8C2×D4311yescharacteristic
368#322—431no—
369#322—431no—
370#322C2×D4311yescharacteristic, complemented
371C82—431no—
372C43#1800811yescharacteristic, complemented, Sylow
373C22×D4—431no—
374C23×C4—861no—
375C2×SD16—431no—
376C2×SD16C4×D4311yescharacteristic
377C2×D8—431no—
378C2×D8—431no—
379C2×M16—431no—
380C2×M16—431no—
381C2×M16—861no—
382C2×M16—861no—
383C2×M16—861no—
384C2×M16—861no—
385C2×M16—1724no—
386C22×C8—21no—
387C22×C8—861no—
388C22×C8—861no—
389#126—861no—
390#125—431no—
391#124—431no—
392#123—861no—
393C22⋊Q8—431no—
394#121—431no—
395C4×Q8C22×D4311yescharacteristic
396C4×D4—431no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—431no—
400C4×D4—861no—
401C4×D4—861no—
402C4×D4—861no—
403C4×D4C22×D4311yescharacteristic
404#117—861no—
405C2×C4⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C42—431no—
408#107—431no—
409#107—431no—
410#106—431no—
411#106C4×D4311yescharacteristic
412C4⋊C8—21no—
413C4⋊C8—431no—
414C4⋊C8—431no—
415C4⋊C8—431no—
416C4⋊C8—431no—
417C4⋊C8—861no—
418C4⋊C8—861no—
419C4⋊C8—861no—
420C4⋊C8C22×D4311yescharacteristic
421C4⋊C8C22×D4311yescharacteristic
422#103—431no—
423#103C4×D4311yescharacteristic
424#102—431no—
425#102—431no—
426#102—431no—
427#102—431no—
428#102—431no—
429#102C4×D4311yescharacteristic
430C22⋊C8—21no—
431C22⋊C8—431no—
432C22⋊C8—431no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435C22⋊C8—861no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440#97—21no—
441#97—431no—
442#97—431no—
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—861no—
447C4×C8—861no—
448C4×C8C22×D4311yescharacteristic
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451C24—861no—
452C2×Q8C2×C4×D4311yescharacteristic
453C2×D4—431no—
454C2×D4—431no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—862no—
458C2×D4—1721no—
459C2×D4C2×C4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—431no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—1722no—
470C22×C4—1722no—
471SD16—22no—
472SD16—1721no—
473D8—862no—
474D8—1721no—
475M16—862no—
476M16—1721no—
477M16—1722no—
478M16—1722no—
479M16—1722no—
480M16—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—431no—
486C2×C8—431no—
487C2×C8—431no—
488C2×C8—431no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8—861no—
492C2×C8—1722no—
493C2×C8—1722no—
494C2×C8C2×C4×D4311yescharacteristic
495C2×C8C2×C4×D4311yescharacteristic
496C2×C8D4×D4311yescharacteristic
497C2×C8D4×D4311yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—431no—
500C4⋊C4—431no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4C2×C4×D4311yescharacteristic
506C4⋊C4C2×C4×D4311yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—861no—
509C22⋊C4—861no—
510C22⋊C4—861no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C42—21no—
517C42—431no—
518C42—431no—
519C42—431no—
520C42C23×D4311yescharacteristic
521C23—21no—
522C23—431no—
523C23—861no—
524C23—861no—
525C23—3441no—
526C23—1722no—
527C23—1722no—
528Q8—21no—
529Q8—21no—
530D4—21no—
531D4—861no—
532D4—861no—
533D4—861no—
534D4—861no—
535D4—3441no—
536D4—1722no—
537D4#1306333312yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—431no—
544C2×C4—431no—
545C2×C4—431no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—1721no—
553C2×C4—1722no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C2×D4×D4311yescharacteristic
562C2×C4#41×D4311yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—432no—
571C8—861no—
572C8—861no—
573C8—861no—
574C8—1721no—
575C8—1721no—
576C8—1721no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—861no—
581C22—861no—
582C22—861no—
583C22—3444no—
584C22—1721no—
585C22—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22C4×D4×D4311yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—861no—
596C4—861no—
597C4—861no—
598C4—1721no—
599C4—1721no—
600C4C2×#1306333311yescharacteristic
601C4#1458366411yescharacteristic
602C4AGL(1,ℤ/8)×D4311yescharacteristic
603C4#1458369811yescharacteristic
604C2—42no—
605C2—3441no—
606C2—3441no—
607C2—1721no—
608C2#1914332111yescharacteristic
609C2#1914340011yescharacteristic
610C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1585C2
socleC22×C43C2×C4×D4
prime radical#14583034C4
cosocleC42×C43C24
hypercenter#1585D43
hypocenterC43#18008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1585

Complements

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

NH ≅ G/Ntype
2. #19143601C2semidirect
3. D4×#10621872C2semidirect
4. #19133495C2semidirect
5. #19133479C2semidirect
6. #19133461C2semidirect
7. #19133435C2semidirect
8. #19133421C2semidirect
9. #19133417C2semidirect
10. SD16×C43⋊C8C2semidirect
11. #19133385C2semidirect
12. #19133059C2semidirect
13. #19132984C2semidirect
14. #19132891C2semidirect
15. C43×#1585C2semidirect
27. Q8×C43⋊C8C22semidirect
34. #14582976C22semidirect
38. C8×D172C22semidirect
48. #14582651C22semidirect
49. #14582650C22semidirect
50. #14582649C22semidirect
51. Q8⋊(C43⋊C8)C22semidirect
53. #14582628C22semidirect
56. #14582626C22semidirect
57. #14582621C22semidirect
58. #14582621C22semidirect
59. C8×C43⋊C8C22semidirect
60. C43×#446C22semidirect
63. C43×#335C22semidirect
64. C43×Q8⋊C8C22semidirect
66. C43×#322C22semidirect
305. #1585D43semidirect
332. #446C2×D43semidirect
357. #335C2×D43semidirect
361. Q8⋊C8C2×D43semidirect
370. #322C2×D43semidirect
372. C43#18008semidirect

Maximal subgroups

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

subgroupindex
#191446462
#191436012
D4×#106218722
#191334952
#191334792
#191334612
#191334352
#191334212
#191334172
SD16×C43⋊C82
#191333852
#191330592
#191329842
#191328912
C43×#15852
#1800843