Finite Group Databasebeta

← #25067663

Subgroups — #25067663

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#19144642C211yesmaximal, characteristic
2#19143599C211yesmaximal, characteristic, complemented
3#19133497C211yesmaximal, characteristic, complemented
4#19133478C211yesmaximal, characteristic, complemented
5#19133457C211yesmaximal, characteristic, complemented
6#19133452C211yesmaximal, characteristic, complemented
7#19133436C211yesmaximal, characteristic, complemented
8#19133424C211yesmaximal, characteristic, complemented
9#19133417C211yesmaximal, characteristic, complemented
10C8×#10621883C211yesmaximal, characteristic, complemented
11#19133386C211yesmaximal, characteristic, complemented
12#19133058C211yesmaximal, characteristic, complemented
13#19132986C211yesmaximal, characteristic, complemented
14#19132892C211yesmaximal, characteristic, complemented
15D4×M16×C43C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583234C411yescharacteristic
18#14583217C411yescharacteristic
19#14583199C411yescharacteristic
20#14583199C411yescharacteristic
21#14583114C411yescharacteristic
22#14583114C411yescharacteristic
23#14583050C411yescharacteristic
24#14583033C411yescharacteristic
25#14583029C2211yescharacteristic, complemented
26C8×Dic86C2211yescharacteristic, complemented
27C4×#10621883C2211yescharacteristic
28C4×#10621883C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic, complemented
32#14582975—21no—
33#14582968—21no—
34C8×D172C2211yescharacteristic, complemented
35#14582961—21no—
36#14582952C2211yescharacteristic
37#14582952C2211yescharacteristic
38#14582952C2211yescharacteristic
39#14582856—21no—
40#14582651C2211yescharacteristic, complemented
41#14582651C2211yescharacteristic, complemented
42#14582649C2211yescharacteristic, complemented
43#14582649C2211yescharacteristic, complemented
44#14582629C2211yescharacteristic, complemented
45#14582629C2211yescharacteristic, complemented
46D4⋊(C43⋊C8)C2211yescharacteristic
47D4⋊(C43⋊C8)C2211yescharacteristic
48D4⋊(C43⋊C8)C2211yescharacteristic
49D4⋊(C43⋊C8)C2211yescharacteristic
50#14582626C2211yescharacteristic, complemented
51#14582626C2211yescharacteristic, complemented
52#14582621C2211yescharacteristic, complemented
53#14582621C2211yescharacteristic, complemented
54#14582620C2211yescharacteristic, complemented
55C8×C43⋊C8C2211yescharacteristic, complemented
56C22×M16×C43—21no—
57C2×C4×D4×C43C2211yescharacteristic
58C43×#436C2211yescharacteristic
59C43×#436C2211yescharacteristic
60C43×#435—21no—
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C8×D4×C43C2211yescharacteristic
64C43×#423C2211yescharacteristic
65C43×#407—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621883C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621882C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×C8×D43—21no—
73#13063319—21no—
74#13063317C2×C411yescharacteristic
75#13063313C2×C411yescharacteristic
76#13063308—21no—
77#13063304C2×C411yescharacteristic
78#13063299C2×C411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×D172C2311yescharacteristic
81C4×C22⋊D43—21no—
82#13063282—21no—
83#13063258C2×C411yescharacteristic
84#13063258C2×C411yescharacteristic
85#13063256C2×C411yescharacteristic
86#13063256C2×C411yescharacteristic
87C4⋊(C43⋊C8)—21no—
88C4⋊(C43⋊C8)C2×C411yescharacteristic
89C4⋊(C43⋊C8)C2×C411yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94#13063248C2×C411yescharacteristic
95#13063248C2×C411yescharacteristic
96#13063246C2×C411yescharacteristic
97#13063246C2×C411yescharacteristic
98#13063246C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063245C2×C411yescharacteristic
101#13063245C2×C411yescharacteristic
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)C2×C411yescharacteristic
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106(C2×D43)⋊C8—21no—
107(C2×D43)⋊C8—21no—
108#13063235—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×D4×C43C2×C411yescharacteristic
116C23×C4×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43—44no—
121C2×M16×C43D411yescharacteristic
122C2×M16×C43D411yescharacteristic
123C22×C8×C43—21no—
124C22×C8×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43C2×C411yescharacteristic
128C4×D4×C43C2×C411yescharacteristic
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C22⋊C8×C43—21no—
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141#97×C43D411yescharacteristic
142#97×C43D411yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C24×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—22no—
148C2×D4×C43—41no—
149C2×D4×C43C22×C411yescharacteristic
150C2×D4×C43C22×C411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C2×C22⋊D43—21no—
162C2×D172C22×C411yescharacteristic
163C2×C4×D43—21no—
164C2×Dic86C22×C411yescharacteristic
165M16×C43—22no—
166M16×C43—41no—
167M16×C43—42no—
168M16×C43—42no—
169M16×C43—42no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—42no—
173C2×C8×C43—42no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C4⋊C4×C43—21no—
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43C22×C411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43#4111yescharacteristic
188C42×C43C2411yescharacteristic
189C22⋊Dic43—21no—
190#10621883—22no—
191#10621883—41no—
192#10621882—22no—
193#10621882—41no—
194(C2×D43)⋊C4—21no—
195(C2×D43)⋊C4—21no—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198C4⋊Dic43C22×C411yescharacteristic
199C4⋊Dic43C22×C411yescharacteristic
200Dic43⋊C4—21no—
201Dic43⋊C4—21no—
202Dic43⋊C4—21no—
203Dic43⋊C4—21no—
204C4×Dic43—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C22×C411yescharacteristic
210C2×C43⋊C8C22×C411yescharacteristic
211C2×C43⋊C8C22×C411yescharacteristic
212C2×C43⋊C8C22×C411yescharacteristic
213#10621872—42no—
214C8×D43—42no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—42no—
218C23×C43—42no—
219C23×C43—81no—
220C23×C43C4×D411yescharacteristic
221C22×D43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225D4×C43—42no—
226D4×C43#13112yes—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—41no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C4×D411yescharacteristic
242C2×C4×C43C4×D411yescharacteristic
243C2×C4×C43C4×D411yescharacteristic
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C22⋊D43—81no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251D172—21no—
252D172—21no—
253C4×D43—41no—
254C4×D43—41no—
255Dic86—21no—
256Dic86—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43AGL(1,ℤ/8)12yes—
263C43⋊C8—21no—
264C43⋊C8—21no—
265C43⋊C8—21no—
266C43⋊C8—21no—
267C43⋊C8—41no—
268C43⋊C8—41no—
269C43⋊C8—41no—
270C43⋊C8—41no—
271#18008—431nomaximal, Sylow
272C22×C43—22no—
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—84no—
282C22×C43C2×C4×D411yescharacteristic
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C4×C43—21no—
287C4×C43—21no—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43C2×#13111yescharacteristic
293C4×C43#56811yescharacteristic
294C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C4×C43#57511yescharacteristic
296Dic43—41no—
297Dic43—41no—
298Dic43—41no—
299#3105—431no—
300#2969—431no—
301D4×M16D4311yescharacteristic, complemented
302#1592—431no—
303#1589—431no—
304#1586—431no—
305#1585—431no—
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—41no—
315C2×C43—42no—
316C2×C43—81no—
317C2×C43#293311yescharacteristic
318C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
319C2×C43#295711yescharacteristic
320D43—81no—
321C22×M16—21no—
322#529—431no—
323C2×C4×D4C2×D4311yescharacteristic
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#446—431no—
333C8×Q8—431no—
334C4×SD16—431no—
335C4×SD16—431no—
336C4×D8—431no—
337C4×D8—431no—
338#436—431no—
339#436—861no—
340#436C2×D4311yescharacteristic
341#436C2×D4311yescharacteristic
342#435—21no—
343#435—21no—
344#435—861no—
345C8×D4—431no—
346C8×D4C2×D4311yescharacteristic
347C8×D4C2×D4311yescharacteristic
348#433—861no—
349#431—431no—
350#431—431no—
351#431—431no—
352#423C2×D4311yescharacteristic
353#407—21no—
354#405—861no—
355C4×M16C2×D4311yescharacteristic
356#335—431no—
357#335—431no—
358#334—431no—
359#334—431no—
360Q8⋊C8—431no—
361Q8⋊C8—431no—
362D4⋊C8—431no—
363D4⋊C8—431no—
364D4⋊C8—431no—
365D4⋊C8—431no—
366D4⋊C8—431no—
367D4⋊C8—431no—
368#322—431no—
369#322—431no—
370#322—431no—
371C82—431no—
372C43#1800811yescharacteristic, complemented, Sylow
373C22×D4C4×D4311yescharacteristic
374C23×C4—21no—
375C2×SD16—431no—
376C2×SD16—431no—
377C2×D8—431no—
378C2×D8—431no—
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—44no—
383C2×M16—861no—
384C2×M16C22⋊D4311yescharacteristic
385C2×M16C22⋊D4311yescharacteristic
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—861no—
389#126—861no—
390#125—431no—
391#124—431no—
392#123—861no—
393C22⋊Q8—431no—
394#121—431no—
395C4×Q8—431no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—431no—
399C4×D4—861no—
400C4×D4C4×D4311yescharacteristic
401C4×D4C4×D4311yescharacteristic
402C4×D4C22×D4311yescharacteristic
403C4×D4C22×D4311yescharacteristic
404#117—861no—
405C2×C4⋊C4C4×D4311yescharacteristic
406C2×C22⋊C4—21no—
407C2×C42C22×D4311yescharacteristic
408#107—431no—
409#107—431no—
410#106—431no—
411#106—431no—
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#103—431no—
424#102—431no—
425#102—431no—
426#102—431no—
427#102—431no—
428#102—431no—
429#102—431no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—21no—
433C22⋊C8—21no—
434C22⋊C8—431no—
435C22⋊C8—431no—
436C22⋊C8—861no—
437C22⋊C8—861no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440#97—861no—
441#97C22⋊D4311yescharacteristic
442#97C22⋊D4311yescharacteristic
443C4×C8—431no—
444C4×C8—431no—
445C4×C8—431no—
446C4×C8—431no—
447C4×C8—861no—
448C4×C8—861no—
449C4×C8C22×D4311yescharacteristic
450C4×C8C22×D4311yescharacteristic
451C24—21no—
452C2×Q8—431no—
453C2×D4—22no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—431no—
457C2×D4—861no—
458C2×D4C2×C4×D4311yescharacteristic
459C2×D4C2×C4×D4311yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—861no—
468C22×C4C2×C4×D4311yescharacteristic
469C22×C4#1062189811yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471SD16—862no—
472SD16—1721no—
473D8—862no—
474D8—1721no—
475M16—22no—
476M16—41no—
477M16—42no—
478M16—42no—
479M16—42no—
480M16—1722no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—42no—
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—861no—
493C2×C8—1722no—
494C2×C8C2×C22⋊D4311yescharacteristic
495C2×C8C2×C22⋊D4311yescharacteristic
496C2×C8C2×C22⋊D4311yescharacteristic
497C2×C8C2×C22⋊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—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—861no—
512C22⋊C4—861no—
513C22⋊C4—861no—
514C22⋊C4—861no—
515C22⋊C4—861no—
516C42—861no—
517C42C2×C4×D4311yescharacteristic
518C42#1062189811yescharacteristic
519C42C2×C22⋊D4311yescharacteristic
520C42C23×D4311yescharacteristic
521C23—21no—
522C23—21no—
523C23—42no—
524C23—42no—
525C23—81no—
526C23—861no—
527C23C4×C22⋊D4311yescharacteristic
528Q8—861no—
529Q8—861no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—42no—
534D4—861no—
535D4—861no—
536D4—3441no—
537D4#1306333312yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4C4×C22⋊D4311yescharacteristic
558C2×C4C4×C22⋊D4311yescharacteristic
559C2×C4C4×C22⋊D4311yescharacteristic
560C2×C4C22×C4×D4311yescharacteristic
561C2×C4C22×C22⋊D4311yescharacteristic
562C2×C4C2×#1062189811yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—861no—
569C8—861no—
570C8—861no—
571C8—861no—
572C8—1721no—
573C8—1721no—
574C8—1721no—
575C8—1721no—
576C8#1306335112yes—
577C22—21no—
578C22—21no—
579C22—22no—
580C22—21no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—84no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22C2×C4×C22⋊D4311yescharacteristic
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—41no—
597C4—1721no—
598C4—1721no—
599C4—1721no—
600C4C2×#1306333311yescharacteristic
601C4#1458366511yescharacteristic
602C4C2×#1306335111yescharacteristic
603C4#1458369711yescharacteristic
604C2—41no—
605C2—42no—
606C2—81no—
607C2—3441no—
608C2#1914332011yescharacteristic
609C2C4×#1306335111yescharacteristic
610C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingD4×M16×C43C2
socleC22×C43C2×C4×D4
prime radical#14583033C4
cosocleC42×C43C24
hypercenterD4×M16D43
hypocenterC43#18008
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #19143599C2semidirect
3. #19133497C2semidirect
4. #19133478C2semidirect
5. #19133457C2semidirect
6. #19133452C2semidirect
7. #19133436C2semidirect
8. #19133424C2semidirect
9. #19133417C2semidirect
10. C8×#10621883C2semidirect
11. #19133386C2semidirect
12. #19133058C2semidirect
13. #19132986C2semidirect
14. #19132892C2semidirect
15. D4×M16×C43C2semidirect
25. #14583029C22semidirect
26. C8×Dic86C22semidirect
31. #14582978C22semidirect
34. C8×D172C22semidirect
40. #14582651C22semidirect
41. #14582651C22semidirect
42. #14582649C22semidirect
43. #14582649C22semidirect
44. #14582629C22semidirect
45. #14582629C22semidirect
50. #14582626C22semidirect
51. #14582626C22semidirect
52. #14582621C22semidirect
53. #14582621C22semidirect
54. #14582620C22semidirect
55. C8×C43⋊C8C22semidirect
301. D4×M16D43semidirect
372. C43#18008semidirect

Maximal subgroups

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

subgroupindex
#191446422
#191435992
#191334972
#191334782
#191334572
#191334522
#191334362
#191334242
#191334172
C8×#106218832
#191333862
#191330582
#191329862
#191328922
D4×M16×C432
#1800843