Finite Group Databasebeta

← #25099607

Subgroups — #25099607

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582997C211yesmaximal, characteristic
2C42×D172C211yesmaximal, characteristic
3#19135233C211yesmaximal, characteristic, complemented
4#19135226C211yesmaximal, characteristic, complemented
5#19135184C211yesmaximal, characteristic, complemented
6#19135163C211yesmaximal, characteristic, complemented
7#19134932C211yesmaximal, characteristic
8#19134932C211yesmaximal, characteristic
9#19134855C211yesmaximal, characteristic
10#19134841C211yesmaximal, characteristic
11#19134493C211yesmaximal, characteristic, complemented
12#19134425C211yesmaximal, characteristic, complemented
13#19134423C211yesmaximal, characteristic
14#19134344C211yesmaximal, characteristic, complemented
15C43×#2295C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×C4×D172C2211yescharacteristic
18C2×C4×D172C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×C42×D43—21no—
21#14582997C418yescomplemented
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063236C2211yescharacteristic
32C2×#13063236C2211yescharacteristic
33C4×C4⋊Dic43C2211yescharacteristic
34C4×C4⋊Dic43C2211yescharacteristic
35C4×C4⋊Dic43C2211yescharacteristic
36C4×(C2×D43)⋊C4—21no—
37C4×(C2×D43)⋊C4—21no—
38C4×(C2×D43)⋊C4—21no—
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582654C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582654C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C43×#391C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#389C2211yescharacteristic
54C43×#387—21no—
55C43×#387—21no—
56C4×C4⋊C4×C43—21no—
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#376—21no—
59C43×C43C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×C4×D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C2×#10621884—22no—
65C2×#10621884—22no—
66C2×#10621884C2×C414yes—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C4×D172—22no—
72C4×D172—22no—
73C4×D172—22no—
74C4×D172—22no—
75C4×D172—22no—
76C4×D172C2×C414yes—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C42×D43—44no—
87#13063258—22no—
88#13063258C2×C414yescomplemented
89#13063256—22no—
90#13063249—22no—
91#13063249—22no—
92#13063249C2×C414yescomplemented
93#13063245—22no—
94#13063245—22no—
95#13063245C2×C414yes—
96#13063236—22no—
97#13063236C2×C414yescomplemented
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C22×Q8×C43C2311yescharacteristic
102C4×Q8×C43—22no—
103C4×Q8×C43C2×C414yescomplemented
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112C2×C42×C43D411yescharacteristic
113C2×C42×C43D411yescharacteristic
114C2×C42×C43D411yescharacteristic
115C2×C42×C43D411yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118C2×C42×C43C2311yescharacteristic
119#95×C43—21no—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43C22×C412yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172C22×C412yes—
151C2×D172#4112yes—
152C2×D172#4112yes—
153C2×C4×D43—24no—
154C2×C4×D43—24no—
155C2×C4×D43—24no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—42no—
169C4⋊C4×C43—42no—
170C4⋊C4×C43C22×C412yes—
171C42×C43—24no—
172C42×C43—22no—
173C42×C43—22no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—41no—
179C42×C43—41no—
180C42×C43—42no—
181C42×C43C22×C412yes—
182C42×C43#4112yes—
183#10621884—28no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—24no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C22×C412yes—
191C4⋊Dic43#4112yes—
192C4⋊Dic43#4112yes—
193C4×Dic43—42no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8C22×C412yes—
207C2×C43⋊C8C22×C412yes—
208C23×C43C22×D411yescharacteristic
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—22no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215C22×D43—41no—
216Q8×C43—22no—
217Q8×C43—22no—
218Q8×C43—41no—
219Q8×C43—41no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43C4×D412yes—
247C2×C4×C43C4×D412yes—
248C2×C4×C43AGL(1,ℤ/8)12yes—
249C2×C4×C43#13712yes—
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265D172—22no—
266D172—22no—
267D172—22no—
268D172#11714yes—
269C4×D43—48no—
270C4×D43—48no—
271C4×D43—48no—
272C43⋊C8—22no—
273C43⋊C8—22no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#21121—431nomaximal, Sylow
277C22×C43C2×C4×D411yescharacteristic
278C22×C43#52511yescharacteristic
279C22×C43#52511yescharacteristic
280C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C43C2×#13711yescharacteristic
282C22×C43#57511yescharacteristic
283C22×C43#57511yescharacteristic
284C2×D43—24no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—42no—
291C4×C43—22no—
292C4×C43—22no—
293C4×C43—22no—
294C4×C43—22no—
295C4×C43—41no—
296C4×C43—41no—
297C4×C43—42no—
298C4×C43—42no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43C2×#11711yescharacteristic
302C4×C43C4×#4111yescharacteristic
303C4×C43#52911yescharacteristic
304C4×C43#52911yescharacteristic
305Dic43—42no—
306Dic43—42no—
307Dic43—42no—
308C2×#440—431no—
309#2295D4311yescharacteristic, complemented
310C42×D4—431no—
311#1928—431no—
312#1927—431no—
313#1921—431no—
314#1918—431no—
315#1877—431no—
316#1877—431no—
317#1864—431no—
318#1862—431no—
319#1776—431no—
320#1763—431no—
321#1762—431no—
322#1745—431no—
323C2×C43#229011yescharacteristic
324C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
325C2×C43C4×#13711yescharacteristic
326C2×C43#311011yescharacteristic
327C2×C43#311111yescharacteristic
328C2×C43#311411yescharacteristic
329C2×C43#311611yescharacteristic
330D43—44no—
331C22×SD16—431no—
332C2×C4×Q8C2×D4311yescharacteristic
333C2×C4×D4—431no—
334C2×C4×D4—431no—
335C2×C4×D4—431no—
336C22×C42—861no—
337#440—438no—
338C2×#107—431no—
339C2×#107—431no—
340C2×#106—431no—
341C2×#103—431no—
342C2×#103—431no—
343C2×#103—431no—
344C2×#102—431no—
345C2×#102—431no—
346C2×#102—431no—
347C2×#97—431no—
348C2×#97—431no—
349#391C2×D4311yescharacteristic
350#391C2×D4311yescharacteristic
351#389C2×D4311yescharacteristic
352#389C2×D4311yescharacteristic
353#387—21no—
354#387—21no—
355C4×C4⋊C4—21no—
356C4×C4⋊C4—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—431no—
359C4×C4⋊C4C2×D4311yescharacteristic
360C4×C22⋊C4—861no—
361C4×C22⋊C4—861no—
362C4×C22⋊C4—861no—
363#376—21no—
364C43C2×D4311yescharacteristic
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340—431no—
371#336—431no—
372#336—431no—
373#336—431no—
374#336—431no—
375C43#2112111yescharacteristic, complemented, Sylow
376C22×Q8C22×D4311yescharacteristic
377C22×D4—431no—
378C23×C4—861no—
379C23×C4—861no—
380C23×C4—861no—
381C2×SD16—434no—
382C2×SD16—862no—
383C2×SD16—862no—
384C22×C8—431no—
385C22×C8—431no—
386C22×C8—431no—
387C22×C8—431no—
388C4×Q8—22no—
389C4×Q8C4×D4314yescomplemented
390C4×D4—434no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—862no—
394C4×D4—862no—
395C4×D4—862no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—431no—
401C2×C4⋊C4—431no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42—1724no—
414C2×C42C22⋊D4311yescharacteristic
415C2×C42C22⋊D4311yescharacteristic
416C2×C42C22⋊D4311yescharacteristic
417C2×C42C22⋊D4311yescharacteristic
418C2×C42C22×D4311yescharacteristic
419C2×C42C22×D4311yescharacteristic
420C2×C42C22×D4311yescharacteristic
421#107—434no—
422#107—862no—
423#106—862no—
424#103—434no—
425#103—862no—
426#103—862no—
427#102—434no—
428#102—862no—
429#102—862no—
430#97—434no—
431#97—862no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24—861no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×C4×D4312yes—
449C2×D4—432no—
450C2×D4—432no—
451C2×D4—432no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—864no—
460C22×C4—864no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—864no—
465C22×C4—1722no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4C2×C22⋊D4311yescharacteristic
472C22×C4C2×C22⋊D4311yescharacteristic
473C22×C4C2×C22⋊D4311yescharacteristic
474C22×C4C2×C22⋊D4311yescharacteristic
475C22×C4C2×C22⋊D4311yescharacteristic
476C22×C4C2×C22⋊D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478SD16—868no—
479C2×C8—432no—
480C2×C8—432no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C4⋊C4—24no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—432no—
500C4⋊C4—432no—
501C4⋊C4—432no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C4⋊C4C2×C4×D4312yes—
506C22⋊C4—864no—
507C22⋊C4—864no—
508C22⋊C4—864no—
509C42—24no—
510C42—22no—
511C42—22no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—41no—
517C42—41no—
518C42—42no—
519C42—1722no—
520C42—1722no—
521C42—1722no—
522C42C2×C4×D4312yes—
523C42#1062189812yes—
524C23—862no—
525C23—862no—
526C23—862no—
527C23—1721no—
528C23—1721no—
529C23—1721no—
530C23—1721no—
531C23C22×C22⋊D4311yescharacteristic
532Q8—22no—
533Q8—22no—
534Q8—41no—
535Q8—41no—
536D4—434no—
537D4—862no—
538D4—862no—
539D4—862no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—862no—
567C2×C4—862no—
568C2×C4—862no—
569C2×C4—1728no—
570C2×C4—1728no—
571C2×C4—1728no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4C4×C22⋊D4312yes—
579C2×C4C4×C22⋊D4312yes—
580C2×C4#1306335012yes—
581C2×C4#1306335612yes—
582C2×C4C22×C4×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C2×C4#41×D4311yescharacteristic
586C2×C4#41×D4311yescharacteristic
587C2×C4C2×#1062189811yescharacteristic
588C8—862no—
589C8—862no—
590C8—1721no—
591C8—1721no—
592C22—864no—
593C22—1722no—
594C22—1722no—
595C22—1722no—
596C22—1722no—
597C22—1722no—
598C22—1722no—
599C22C2×C4×C22⋊D4311yescharacteristic
600C22#1458340611yescharacteristic
601C22#1458340611yescharacteristic
602C22C2×#1306335011yescharacteristic
603C22C2×#1306335611yescharacteristic
604C22#1458369711yescharacteristic
605C22#1458369711yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—42no—
611C4—41no—
612C4—42no—
613C4—41no—
614C4—81no—
615C4—81no—
616C4—1722no—
617C4—1722no—
618C4—1722no—
619C4#117×D4311yescharacteristic
620C4#1458336711yescharacteristic
621C4#1458342711yescharacteristic
622C4#1458342711yescharacteristic
623C2—1724no—
624C2#1913703211yescharacteristic
625C2C4×#1306335011yescharacteristic
626C2C4×#1306335611yescharacteristic
627C2#1914469011yescharacteristic
628C2#1914469811yescharacteristic
629C2#1914472911yescharacteristic
630C2#1914475111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2295C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#2295D43
hypocenterC43#21121
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
3. #19135233C2semidirect
4. #19135226C2semidirect
5. #19135184C2semidirect
6. #19135163C2semidirect
11. #19134493C2semidirect
12. #19134425C2semidirect
14. #19134344C2semidirect
15. C43×#2295C2semidirect
21. #14582997C4semidirect
88. #13063258C2×C4semidirect
92. #13063249C2×C4semidirect
97. #13063236C2×C4semidirect
103. C4×Q8×C43C2×C4semidirect
309. #2295D43semidirect
375. C43#21121semidirect
389. C4×Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829972
C42×D1722
#191352332
#191352262
#191351842
#191351632
#191349322
#191348552
#191348412
#191344932
#191344252
#191344232
#191343442
C43×#22952
#2112143