Finite Group Databasebeta

← #25062926

Subgroups — #25062926

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×#14583632C211yesmaximal, characteristic
2#19143630C211yesmaximal, characteristic, complemented
3#19132948C211yesmaximal, characteristic, complemented
4#19132946C211yesmaximal, characteristic, complemented
5#19132944C212yesmaximal, complemented
6#19132941C212yesmaximal, complemented
7#19132938C211yesmaximal, characteristic, complemented
8#19132931C212yesmaximal, complemented
9#19132918C211yesmaximal, characteristic, complemented
10#19132911C212yesmaximal, complemented
11C43×#2974C211yesmaximal, characteristic, complemented
12#14583632—21no—
13#14583632—22no—
14#14583632—21no—
15#14583632—21no—
16#14583632—22no—
17#14583632—21no—
18C2×#13063321C411yescharacteristic
19C2×#13063313C2211yescharacteristic
20C2×#13063312C411yescharacteristic
21C2×#13063311C412yes—
22C2×#13063308C2212yes—
23C2×#13063307C412yes—
24C2×C4×Dic86C2211yescharacteristic
25C2×#13063290C411yescharacteristic
26C2×#13063287C411yescharacteristic
27C2×C4×C22⋊D43C2212yes—
28#14582977—21no—
29#14582971—22no—
30D4×C43⋊C8—21no—
31#14582956C2211yescharacteristic
32#14582952C2211yescharacteristic
33#14582863C2212yes—
34C2×C22⋊(C43⋊C8)C2212yes—
35#14582624C2211yescharacteristic
36#14582624C2212yes—
37#14582624C2212yes—
38#14582624C2211yescharacteristic
39#14582624C2211yescharacteristic
40#14582624C2211yescharacteristic
41#14582622C2212yes—
42#14582622C2212yes—
43#14582622C2212yes—
44#14582622C2212yes—
45C2×C4×D4×C43C2211yescharacteristic
46C43×#436—21no—
47C43×#435—22no—
48C8×D4×C43—21no—
49C43×#432C2211yescharacteristic
50C43×#431C2211yescharacteristic
51C43×#407C2212yes—
52C2×C22⋊C8×C43C2212yes—
53C22×Dic86C2×C411yescharacteristic
54C22×Dic86C2×C411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C22×C22⋊D43C2×C412yes—
57C22×C22⋊D43C2×C412yes—
58C22×C4×D43C2×C412yes—
59C2×#10621877—22no—
60C22×C43⋊C8—22no—
61#13063321—21no—
62#13063321—21no—
63#13063321—22no—
64#13063313—21no—
65#13063313—21no—
66#13063313—21no—
67#13063313—21no—
68#13063312—21no—
69#13063312—21no—
70#13063312—22no—
71#13063311—22no—
72#13063311—22no—
73#13063311—22no—
74#13063311—22no—
75#13063308—22no—
76#13063308—22no—
77#13063308—22no—
78#13063308—22no—
79#13063307—22no—
80#13063307—22no—
81#13063307—22no—
82#13063307—22no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87#13063290—22no—
88#13063290—21no—
89#13063290—21no—
90#13063287—22no—
91#13063287—21no—
92#13063287—21no—
93C4×C22⋊D43—22no—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—22no—
96C4×C22⋊D43—22no—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C412yes—
99C2×Dic43⋊C4C2311yescharacteristic
100C2×Dic43⋊C4C2311yescharacteristic
101C2×C22⋊Dic43C2×C412yes—
102C2×C22⋊Dic43C2×C412yes—
103C2×(C2×D43)⋊C4C2×C412yes—
104C2×(C2×D43)⋊C4C2×C412yes—
105C2×(C2×D43)⋊C4C2312yes—
106C2×C4×Dic43C2×C412yes—
107C2×C4×Dic43C2×C411yescharacteristic
108C2×C4×Dic43C2×C411yescharacteristic
109C4⋊(C43⋊C8)—21no—
110C4⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)C2311yescharacteristic
114C22⋊(C43⋊C8)C2312yes—
115C22⋊(C43⋊C8)C2311yescharacteristic
116#13063236—21no—
117C4×C43⋊C8—21no—
118C22×D4×C43C2×C411yescharacteristic
119C23×C4×C43C2312yes—
120C2×M16×C43—22no—
121C22×C8×C43—22no—
122C4×D4×C43D411yescharacteristic
123C4×D4×C43D412yes—
124C4×D4×C43D411yescharacteristic
125C4×D4×C43D411yescharacteristic
126C4×D4×C43D412yes—
127C4×D4×C43D411yescharacteristic
128C2×C4⋊C4×C43C2×C411yescharacteristic
129C2×C22⋊C4×C43C2×C412yes—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43—21no—
133C22⋊C8×C43—22no—
134C22⋊C8×C43—22no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2311yescharacteristic
138#97×C43—21no—
139C4×C8×C43—21no—
140C24×C43C22×C412yes—
141C23×D43C22×C412yes—
142C2×D4×C43—42no—
143C2×D4×C43C22⋊C411yescharacteristic
144C2×D4×C43C22⋊C411yescharacteristic
145C2×D4×C43C22⋊C412yes—
146C22×C4×C43—82no—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C412yes—
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—24no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—42no—
161C2×C22⋊D43—82no—
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C412yes—
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—42no—
170C2×C4×D43—22no—
171C2×C4×D43—22no—
172C2×C4×D43—82no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—22no—
178C2×Dic86—41no—
179C2×Dic86—42no—
180M16×C43—82no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—22no—
184C2×C8×C43—82no—
185C4⋊C4×C43C22⋊C412yes—
186C4⋊C4×C43C22⋊C411yescharacteristic
187C4⋊C4×C43C22⋊C411yescharacteristic
188C22⋊C4×C43C22⋊C412yes—
189C22⋊C4×C43C22⋊C412yes—
190C22⋊C4×C43C22⋊C412yes—
191C22⋊C4×C43C22⋊C412yes—
192C42×C43C2×D411yescharacteristic
193C42×C43C2×D411yescharacteristic
194C42×C43C2×D411yescharacteristic
195C42×C43C2×D411yescharacteristic
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202(C2×D43)⋊C4—22no—
203(C2×D43)⋊C4—22no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—21no—
211Dic43⋊C4—21no—
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214C4×Dic43—22no—
215C4×Dic43—22no—
216C4×Dic43—21no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220#10621877—82no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—22no—
224C2×C43⋊C8—82no—
225C23×C43—22no—
226C23×C43—22no—
227C23×C43—42no—
228C23×C43—42no—
229C23×C43C2×C22⋊C412yes—
230C23×C43C2×C22⋊C412yes—
231C23×C43C23×C411yescharacteristic
232C22×D43—22no—
233C22×D43—22no—
234C22×D43—22no—
235C22×D43—42no—
236C22×D43—42no—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—42no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43—41no—
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C2×C22⋊C412yes—
251C2×C4×C43C2×C22⋊C412yes—
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43C2×C22⋊C411yescharacteristic
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C22⋊D43—44no—
258C22⋊D43—44no—
259C22⋊D43—82no—
260C22⋊D43—82no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—42no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43#13112yes—
273D172—42no—
274D172—42no—
275C4×D43—82no—
276C4×D43—82no—
277Dic86—42no—
278Dic86—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—22no—
291C22×C43—22no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—82no—
297C22×C43—82no—
298C22×C43C22×C22⋊C411yescharacteristic
299C22×C43C2×#13111yescharacteristic
300C22×C43#56811yescharacteristic
301C2×D43—42no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—82no—
305C2×D43—82no—
306C4×C43—21no—
307C4×C43—21no—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—21no—
313C4×C43#41312yes—
314Dic43—22no—
315Dic43—41no—
316Dic43—41no—
317Dic43—41no—
318Dic43—42no—
319C2×#559—431no—
320#2974—431no—
321#2974D4311yescharacteristic, complemented
322#1469—431no—
323#1469—431no—
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—42no—
333C2×C43—42no—
334C2×C43#288011yescharacteristic
335C2×C43#288311yescharacteristic
336C2×C43C2×#41311yescharacteristic
337D43—82no—
338#559—861no—
339#559—862no—
340#559—861no—
341#559—861no—
342#559—862no—
343#559—861no—
344C2×#127—431no—
345C2×#124—431no—
346C2×#124—432no—
347C2×#124—431no—
348C2×#123—432no—
349C2×#123—432no—
350C2×C4×Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×D4—432no—
353C2×C4×D4—431no—
354C2×C4×D4C2×D4311yescharacteristic
355#436—21no—
356#436—861no—
357#435—22no—
358#435—862no—
359C8×D4—21no—
360C8×D4—861no—
361#432—431no—
362#432C2×D4311yescharacteristic
363#431—431no—
364#431C2×D4311yescharacteristic
365#407—432no—
366#407C2×D4312yes—
367C2×C22⋊C8—432no—
368C2×C22⋊C8C2×D4312yes—
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#323—432no—
378#323—432no—
379C43#1742911yescharacteristic, complemented, Sylow
380C22×Q8—431no—
381C22×Q8—431no—
382C22×D4—432no—
383C22×D4—432no—
384C22×D4—431no—
385C22×D4C4×D4311yescharacteristic
386C23×C4—432no—
387C23×C4C22×D4312yes—
388C2×M16—22no—
389C2×M16—862no—
390C22×C8—22no—
391C22×C8—862no—
392#127—861no—
393#127—861no—
394#127—862no—
395#124—861no—
396#124—861no—
397#124—862no—
398#124—862no—
399#124—862no—
400#124—862no—
401#124—862no—
402#124—861no—
403#124—861no—
404#124—861no—
405#124—861no—
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—862no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—861no—
427C4×D4—861no—
428C4×D4D17211yescharacteristic
429C4×D4D17212yes—
430C4×D4D17211yescharacteristic
431C4×D4C22⋊D4311yescharacteristic
432C4×D4C22⋊D4312yes—
433C4×D4C22⋊D4311yescharacteristic
434C2×C4⋊C4—432no—
435C2×C4⋊C4—431no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4C4×D4311yescharacteristic
439C2×C22⋊C4—432no—
440C2×C22⋊C4—432no—
441C2×C22⋊C4—432no—
442C2×C22⋊C4—432no—
443C2×C22⋊C4—432no—
444C2×C22⋊C4C4×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—22no—
454C22⋊C8—22no—
455C22⋊C8—431no—
456C22⋊C8—432no—
457C22⋊C8—431no—
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—862no—
470C2×Q8—861no—
471C2×Q8—861no—
472C2×Q8—861no—
473C2×Q8—861no—
474C2×Q8—1721no—
475C2×Q8—1722no—
476C2×D4—42no—
477C2×D4—864no—
478C2×D4—862no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—862no—
482C2×D4—861no—
483C2×D4—861no—
484C2×D4—3442no—
485C2×D4—1722no—
486C2×D4—1722no—
487C2×D4(C2×D43)⋊C411yescharacteristic
488C2×D4(C2×D43)⋊C411yescharacteristic
489C2×D4(C2×D43)⋊C412yes—
490C22×C4—82no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—432no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—3442no—
499C22×C4C2×C4×D4311yescharacteristic
500C22×C4C2×C4×D4311yescharacteristic
501C22×C4C2×C4×D4312yes—
502C22×C4C2×D17212yes—
503C22×C4C2×D17212yes—
504C22×C4C2×C22⋊D4312yes—
505C22×C4C2×C22⋊D4312yes—
506C22×C4C23×D4311yescharacteristic
507M16—82no—
508M16—3442no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—22no—
512C2×C8—82no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—862no—
516C2×C8—3442no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4(C2×D43)⋊C412yes—
526C4⋊C4(C2×D43)⋊C411yescharacteristic
527C4⋊C4(C2×D43)⋊C411yescharacteristic
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—862no—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4(C2×D43)⋊C412yes—
539C22⋊C4(C2×D43)⋊C412yes—
540C22⋊C4(C2×D43)⋊C412yes—
541C22⋊C4(C2×D43)⋊C412yes—
542C42—862no—
543C42—862no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42C2×D17211yescharacteristic
549C42C2×D17211yescharacteristic
550C42C2×C22⋊D4311yescharacteristic
551C42C2×C22⋊D4311yescharacteristic
552C23—22no—
553C23—22no—
554C23—42no—
555C23—42no—
556C23—862no—
557C23—862no—
558C23—862no—
559C23—1722no—
560C23—1722no—
561C23C2×(C2×D43)⋊C412yes—
562C23C2×(C2×D43)⋊C412yes—
563C23C22×C4×D4311yescharacteristic
564Q8—1722no—
565Q8—1722no—
566Q8—1722no—
567Q8—1722no—
568D4—22no—
569D4—22no—
570D4—42no—
571D4—3442no—
572D4—3442no—
573D4—1722no—
574D4—1724no—
575D4—1724no—
576D4—1722no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—432no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—862no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—3442no—
596C2×C4—3442no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1722no—
600C2×C4C2×(C2×D43)⋊C411yescharacteristic
601C2×C4C2×(C2×D43)⋊C412yes—
602C2×C4C2×(C2×D43)⋊C412yes—
603C2×C4C2×(C2×D43)⋊C411yescharacteristic
604C2×C4C2×(C2×D43)⋊C411yescharacteristic
605C2×C4C2×(C2×D43)⋊C411yescharacteristic
606C2×C4C22×C22⋊D4311yescharacteristic
607C2×C4C22×D17211yescharacteristic
608C8—41no—
609C8—42no—
610C8—41no—
611C8—1721no—
612C8—1722no—
613C8—1721no—
614C22—21no—
615C22—21no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—82no—
623C22—82no—
624C22—3442no—
625C22—3442no—
626C22—1722no—
627C22—1722no—
628C22—1722no—
629C22C22×(C2×D43)⋊C411yescharacteristic
630C22#131×D4311yescharacteristic
631C22#1458366411yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—22no—
637C4—22no—
638C4—21no—
639C4—862no—
640C4—1721no—
641C4—1721no—
642C4—1721no—
643C4—1722no—
644C4#1458288112yes—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—42no—
649C2—3442no—
650C2#1914304211yescharacteristic
651C2#1914305511yescharacteristic
652C2C2×#1458288111yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2974C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063321C4
cosocleC22×C4×C43C24
hypercenter#2974D43
hypocenterC43#17429
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #19143630C2semidirect
3. #19132948C2semidirect
4. #19132946C2semidirect
5. #19132944C2semidirect
6. #19132941C2semidirect
7. #19132938C2semidirect
8. #19132931C2semidirect
9. #19132918C2semidirect
10. #19132911C2semidirect
11. C43×#2974C2semidirect
321. #2974D43semidirect
379. C43#17429semidirect

Maximal subgroups

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

subgroupindex
C2×#145836322
#191436302
#191329482
#191329462
#191329442
#191329412
#191329382
#191329312
#191329182
#191329112
C43×#29742
#1742943