Finite Group Databasebeta

← #25062928

Subgroups — #25062928

Order 11008.

1016 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583631C211yesmaximal, characteristic
2#19143632C211yesmaximal, characteristic, complemented
3#19143629C211yesmaximal, characteristic, complemented
4#19132947C211yesmaximal, characteristic, complemented
5#19132940C212yesmaximal, complemented
6#19132940C212yesmaximal, complemented
7#19132938C211yesmaximal, characteristic, complemented
8#19132930C212yesmaximal, complemented
9#19132918C211yesmaximal, characteristic, complemented
10#19132910C212yesmaximal, complemented
11C43×#1469C211yesmaximal, characteristic, complemented
12#14583631—21no—
13#14583631—21no—
14#14583631—22no—
15#14583631—22no—
16#14583631—21no—
17#14583631—21no—
18C2×#13063321C411yescharacteristic
19C2×#13063314C411yescharacteristic
20C2×#13063311C412yes—
21C2×#13063309C412yes—
22C2×#13063307C2212yes—
23C2×Q8×Dic43C411yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26C2×D4×Dic43C411yescharacteristic
27C2×(C22⋊D43)⋊C4C2212yes—
28#14582978—21no—
29#14582976—21no—
30#14582972—22no—
31#14582969—22no—
32C8×D172—21no—
33#14582964—21no—
34#14582956C2211yescharacteristic
35#14582952C2211yescharacteristic
36#14582861C2212yes—
37#14582861C2212yes—
38C22⋊C8×D43C2212yes—
39C22⋊C8×D43C2212yes—
40#14582624C2211yescharacteristic
41#14582624C2212yes—
42#14582624C2212yes—
43#14582624C2211yescharacteristic
44#14582624C2211yescharacteristic
45#14582624C2211yescharacteristic
46#14582623C2212yes—
47#14582623C2212yes—
48C2×#124×C43C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#431C2211yescharacteristic
51C43×#323C2212yes—
52C43×#323C2212yes—
53C22×Dic86C2×C411yescharacteristic
54C22×D172C2×C411yescharacteristic
55C22×C22⋊D43C2×C412yes—
56C22×C22⋊D43C2×C412yes—
57C23×Dic43C2×C412yes—
58C22×C4×D43C2312yes—
59C2×#10621872—22no—
60C2×#10621872—22no—
61C2×C8×D43—22no—
62C2×C8×D43—22no—
63#13063321—21no—
64#13063321—21no—
65#13063321—22no—
66#13063314—21no—
67#13063314—21no—
68#13063314—22no—
69#13063311—22no—
70#13063311—22no—
71#13063311—22no—
72#13063311—22no—
73#13063309—22no—
74#13063309—22no—
75#13063309—22no—
76#13063309—22no—
77#13063307—22no—
78#13063307—22no—
79#13063307—22no—
80#13063307—22no—
81Q8×Dic43—22no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88C4×D172D411yescharacteristic
89C4×D172D411yescharacteristic
90C4×D172D412yes—
91C4×D172D412yes—
92C4×D172D411yescharacteristic
93C4×D172D411yescharacteristic
94D4×Dic43—22no—
95D4×Dic43—21no—
96D4×Dic43—21no—
97(C22⋊D43)⋊C4—22no—
98(C22⋊D43)⋊C4—22no—
99(C22⋊D43)⋊C4—22no—
100(C22⋊D43)⋊C4—22no—
101C2×C4⋊Dic43C2×C411yescharacteristic
102C2×C4⋊Dic43C2×C412yes—
103C2×C4⋊Dic43C2×C411yescharacteristic
104C2×Dic43⋊C4C2311yescharacteristic
105C2×Dic43⋊C4C2311yescharacteristic
106C2×C22⋊Dic43C2×C412yes—
107C2×(C2×D43)⋊C4C2×C412yes—
108C2×(C2×D43)⋊C4C2×C412yes—
109C2×(C2×D43)⋊C4C2×C412yes—
110C2×C4×Dic43C2×C412yes—
111C2×C4×Dic43C2×C411yescharacteristic
112C2×C4×Dic43C2×C411yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115C22⋊(C43⋊C8)C2311yescharacteristic
116C22⋊(C43⋊C8)C2312yes—
117C22⋊(C43⋊C8)C2311yescharacteristic
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—22no—
122#13063236—21no—
123C4×C43⋊C8—21no—
124C22×Q8×C43C2×C411yescharacteristic
125C22×D4×C43C2×C411yescharacteristic
126#124×C43—21no—
127#124×C43—21no—
128#124×C43—21no—
129#124×C43—21no—
130C2×C22⋊C4×C43C2×C412yes—
131C2×C22⋊C4×C43C2312yes—
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2311yescharacteristic
138#97×C43—21no—
139C4×C8×C43—21no—
140C24×C43C22×C412yes—
141C23×D43C22×C412yes—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—42no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—42no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C412yes—
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—24no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—42no—
158C2×C22⋊D43—82no—
159C22×Dic43—22no—
160C22×Dic43—22no—
161C22×Dic43—82no—
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C412yes—
167C2×D172—42no—
168C2×D172C22⋊C411yescharacteristic
169C2×D172C22⋊C411yescharacteristic
170C2×D172C22⋊C412yes—
171C2×C4×D43—82no—
172C2×C4×D43C2×D412yes—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D412yes—
175C2×C4×D43C2×D412yes—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—22no—
179C2×Dic86—41no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—22no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C22⋊C4×C43—22no—
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4C22⋊C412yes—
198(C2×D43)⋊C4C22⋊C412yes—
199(C2×D43)⋊C4C22⋊C412yes—
200(C2×D43)⋊C4C22⋊C412yes—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43C22⋊C412yes—
206C4⋊Dic43C22⋊C411yescharacteristic
207C4⋊Dic43C22⋊C411yescharacteristic
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210Dic43⋊C4—21no—
211Dic43⋊C4—21no—
212C4×Dic43—21no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—22no—
217C4×Dic43—22no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—22no—
221#10621872—82no—
222#10621872—82no—
223C8×D43—82no—
224C8×D43—82no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43—22no—
228C23×C43—42no—
229C23×C43—42no—
230C23×C43C23×C411yescharacteristic
231C22×D43—22no—
232C22×D43—22no—
233C22×D43—42no—
234C22×D43—42no—
235C22×D43C2×C22⋊C412yes—
236C22×D43C2×C22⋊C412yes—
237Q8×C43—42no—
238Q8×C43—42no—
239D4×C43—42no—
240D4×C43—42no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—41no—
246C2×C4×C43—42no—
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C22⋊D43—44no—
254C22⋊D43—44no—
255C22⋊D43—82no—
256C22⋊D43—82no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—42no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—82no—
268C2×Dic43—82no—
269C2×Dic43C2×C22⋊C412yes—
270C2×Dic43C2×C22⋊C412yes—
271C2×Dic43#13112yes—
272D172—22no—
273D172—22no—
274D172—42no—
275C4×D43—42no—
276C4×D43—42no—
277C4×D43—42no—
278C4×D43—42no—
279Dic86—42no—
280Dic86—42no—
281C8×C43—41no—
282C8×C43—42no—
283C8×C43—41no—
284C43⋊C8—41no—
285C43⋊C8—42no—
286C43⋊C8—41no—
287#17429—431nomaximal, Sylow
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—82no—
294C22×C43—82no—
295C22×C43C22×C22⋊C411yescharacteristic
296C22×C43C2×#13111yescharacteristic
297C22×C43#56811yescharacteristic
298C2×D43—22no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—82no—
305C2×D43—82no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—21no—
311C4×C43—42no—
312C4×C43#41312yes—
313Dic43—22no—
314Dic43—22no—
315Dic43—22no—
316Dic43—41no—
317Dic43—41no—
318Dic43—41no—
319C2×#559—431no—
320#2974—431no—
321#2974—431no—
322#1469—431no—
323#1469D4311yescharacteristic, complemented
324#1468—432no—
325#1468—432no—
326#1467—431no—
327#1465—432no—
328#1461—431no—
329#1459—432no—
330C2×C43—21no—
331C2×C43—21no—
332C2×C43—82no—
333C2×C43#288011yescharacteristic
334C2×C43#288311yescharacteristic
335C2×C43C2×#41311yescharacteristic
336D43—42no—
337D43—42no—
338#559—861no—
339#559—861no—
340#559—862no—
341#559—862no—
342#559—861no—
343#559—861no—
344C2×#127—431no—
345C2×#124—431no—
346C2×#124—432no—
347C2×#124C2×D4311yescharacteristic
348C2×#123—432no—
349C2×#123—432no—
350C2×C4×Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×D4—431no—
353C2×C4×D4—432no—
354C2×C4×D4—431no—
355#436—861no—
356#436—861no—
357#435—862no—
358#435—862no—
359C8×D4—861no—
360C8×D4—861no—
361#432—431no—
362#432C2×D4311yescharacteristic
363#431—431no—
364#431C2×D4311yescharacteristic
365#407—432no—
366#407—432no—
367C2×C22⋊C8—432no—
368C2×C22⋊C8—432no—
369#324—431no—
370#324—432no—
371#324—431no—
372#324—431no—
373#324—431no—
374#324—432no—
375#323—432no—
376#323—432no—
377#323C2×D4312yes—
378#323C2×D4312yes—
379C43#1742911yescharacteristic, complemented, Sylow
380C22×Q8—431no—
381C22×Q8C4×D4311yescharacteristic
382C22×D4—432no—
383C22×D4—432no—
384C22×D4—431no—
385C22×D4C4×D4311yescharacteristic
386C23×C4—432no—
387C23×C4—432no—
388C2×M16—862no—
389C2×M16—862no—
390C22×C8—862no—
391C22×C8—862no—
392#127—861no—
393#127—861no—
394#127—862no—
395#124—21no—
396#124—21no—
397#124—21no—
398#124—21no—
399#124—862no—
400#124—862no—
401#124—862no—
402#124—862no—
403#124—861no—
404#124—861no—
405#124—862no—
406#123—862no—
407#123—862no—
408#123—862no—
409#123—862no—
410#123—862no—
411#123—862no—
412#123—862no—
413#123—862no—
414C4×Q8—862no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×Q8—861no—
418C4×Q8—861no—
419C4×Q8—861no—
420C4×Q8—861no—
421C4×D4—431no—
422C4×D4—431no—
423C4×D4—432no—
424C4×D4—432no—
425C4×D4—431no—
426C4×D4—431no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—861no—
433C4×D4—861no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—432no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C22⋊C4—432no—
440C2×C22⋊C4—432no—
441C2×C22⋊C4—432no—
442C2×C22⋊C4—432no—
443C2×C22⋊C4C4×D4312yes—
444C2×C22⋊C4C22×D4312yes—
445C2×C42—432no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42C22×D4311yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—861no—
452C4⋊C8—861no—
453C22⋊C8—431no—
454C22⋊C8—432no—
455C22⋊C8—431no—
456C22⋊C8—862no—
457C22⋊C8—862no—
458C22⋊C8—862no—
459C22⋊C8—862no—
460C22⋊C8C22×D4311yescharacteristic
461C22⋊C8C22×D4312yes—
462C22⋊C8C22×D4311yescharacteristic
463#97—21no—
464#97—861no—
465C4×C8—21no—
466C4×C8—861no—
467C24—432no—
468C24C2×C4×D4312yes—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—42no—
472C2×Q8—862no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—1721no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—42no—
479C2×D4—431no—
480C2×D4—431no—
481C2×D4—432no—
482C2×D4—864no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—862no—
486C2×D4—862no—
487C2×D4—3442no—
488C2×D4—1722no—
489C2×D4—1722no—
490C22×C4—431no—
491C22×C4—432no—
492C22×C4—432no—
493C22×C4—432no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—3442no—
502C22×C4—3442no—
503C22×C4C2×C4×D4311yescharacteristic
504C22×C4C2×C4×D4311yescharacteristic
505C22×C4C2×C4×D4312yes—
506C22×C4C23×D4311yescharacteristic
507M16—3442no—
508M16—3442no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—22no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—862no—
515C2×C8—3442no—
516C2×C8—3442no—
517C4⋊C4—432no—
518C4⋊C4—431no—
519C4⋊C4—431no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—432no—
533C22⋊C4—432no—
534C22⋊C4—432no—
535C22⋊C4—432no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C42—862no—
543C42—862no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42D4×D4311yescharacteristic
549C42D4×D4311yescharacteristic
550C42D4×D4311yescharacteristic
551C42D4×D4311yescharacteristic
552C23—22no—
553C23—22no—
554C23—22no—
555C23—42no—
556C23—42no—
557C23—432no—
558C23—432no—
559C23—862no—
560C23—862no—
561C23—1722no—
562C23—1722no—
563C23C22×C4×D4311yescharacteristic
564Q8—42no—
565Q8—42no—
566Q8—1722no—
567Q8—1722no—
568D4—42no—
569D4—42no—
570D4—862no—
571D4—862no—
572D4—3442no—
573D4—3442no—
574D4—1722no—
575D4—1724no—
576D4—1724no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—432no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—3442no—
594C2×C4—3442no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4C22⋊C4×D4311yescharacteristic
604C2×C4C22⋊C4×D4311yescharacteristic
605C2×C4C22⋊C4×D4311yescharacteristic
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4C2×D4×D4311yescharacteristic
608C8—41no—
609C8—42no—
610C8—41no—
611C8—1721no—
612C8—1722no—
613C8—1721no—
614C22—21no—
615C22—21no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—82no—
620C22—82no—
621C22—862no—
622C22—862no—
623C22—862no—
624C22—862no—
625C22—862no—
626C22—862no—
627C22—3442no—
628C22—3442no—
629C22C2×C22⋊C4×D4311yescharacteristic
630C22#131×D4311yescharacteristic
631C22#1458366411yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—42no—
638C4—862no—
639C4—862no—
640C4—862no—
641C4—1721no—
642C4—1721no—
643C4—1721no—
644C4#1458288012yes—
645C2—21no—
646C2—21no—
647C2—82no—
648C2—1722no—
649C2—1722no—
650C2#1914304311yescharacteristic
651C2#1914305411yescharacteristic
652C2C2×#1458288011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1469C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063321C4
cosocleC22×C4×C43C24
hypercenter#1469D43
hypocenterC43#17429
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1469

Complements

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

NH ≅ G/Ntype
2. #19143632C2semidirect
3. #19143629C2semidirect
4. #19132947C2semidirect
5. #19132940C2semidirect
6. #19132940C2semidirect
7. #19132938C2semidirect
8. #19132930C2semidirect
9. #19132918C2semidirect
10. #19132910C2semidirect
11. C43×#1469C2semidirect
323. #1469D43semidirect
379. C43#17429semidirect

Maximal subgroups

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

subgroupindex
C2×#145836312
#191436322
#191436292
#191329472
#191329402
#191329382
#191329302
#191329182
#191329102
C43×#14692
#1742943