Finite Group Databasebeta

← #25062886

Subgroups — #25062886

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583599C211yesmaximal, characteristic
2#19143630C211yesmaximal, characteristic, complemented
3#19132952C211yesmaximal, characteristic, complemented
4#19132950C211yesmaximal, characteristic, complemented
5#19132944C212yesmaximal, complemented
6#19132941C212yesmaximal, complemented
7#19132935C211yesmaximal, characteristic, complemented
8#19132931C212yesmaximal, complemented
9#19132915C211yesmaximal, characteristic, complemented
10#19132911C212yesmaximal, complemented
11C43×#2974C211yesmaximal, characteristic, complemented
12#14583599—21no—
13#14583599—22no—
14#14583599—21no—
15#14583599—21no—
16#14583599—22no—
17#14583599—21no—
18C2×#13063318C412yes—
19C2×#13063317C2211yescharacteristic
20C2×#13063308C2212yes—
21C2×#13063298C412yes—
22C2×#13063296C411yescharacteristic
23C2×#13063296C411yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×C4×C22⋊D43C2212yes—
26C2×#13063283C411yescharacteristic
27C2×C4⋊C4×D43C411yescharacteristic
28#14582977—21no—
29#14582971—22no—
30D4×C43⋊C8—21no—
31#14582956C2211yescharacteristic
32#14582952C2211yescharacteristic
33#14582863C2212yes—
34C2×C22⋊(C43⋊C8)C2212yes—
35#14582624C2212yes—
36#14582624C2212yes—
37#14582624C2212yes—
38#14582624C2212yes—
39#14582622C2211yescharacteristic
40#14582622C2212yes—
41#14582622C2212yes—
42#14582622C2211yescharacteristic
43#14582622C2211yescharacteristic
44#14582622C2211yescharacteristic
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×D172C2×C411yescharacteristic
54C22×C22⋊D43C2×C412yes—
55C22×C22⋊D43C2×C412yes—
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2×C411yescharacteristic
58C22×C4×D43C2×C412yes—
59C2×#10621877—22no—
60C22×C43⋊C8—22no—
61#13063318—22no—
62#13063318—22no—
63#13063318—22no—
64#13063318—22no—
65#13063317—21no—
66#13063317—21no—
67#13063317—21no—
68#13063317—21no—
69#13063308—22no—
70#13063308—22no—
71#13063308—22no—
72#13063308—22no—
73#13063298—22no—
74#13063298—22no—
75#13063298—22no—
76#13063298—22no—
77#13063296—21no—
78#13063296—21no—
79#13063296—22no—
80#13063296—21no—
81#13063296—21no—
82#13063296—22no—
83C4×D172—21no—
84C4×D172—21no—
85C4×D172—21no—
86C4×D172—21no—
87C4×C22⋊D43—22no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063283—22no—
92#13063283—21no—
93#13063283—21no—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×C4⋊Dic43C2×C411yescharacteristic
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C412yes—
98C2×Dic43⋊C4C2×C412yes—
99C2×Dic43⋊C4C2312yes—
100C4⋊C4×D43—22no—
101C4⋊C4×D43—21no—
102C4⋊C4×D43—21no—
103C2×C22⋊Dic43C2×C412yes—
104C2×C22⋊Dic43C2×C412yes—
105C2×(C2×D43)⋊C4C2×C412yes—
106C2×(C2×D43)⋊C4C2311yescharacteristic
107C2×(C2×D43)⋊C4C2311yescharacteristic
108C2×C4×Dic43C2×C412yes—
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×C411yescharacteristic
142C23×D43C22×C411yescharacteristic
143C2×D4×C43—42no—
144C2×D4×C43C22⋊C411yescharacteristic
145C2×D4×C43C22⋊C411yescharacteristic
146C2×D4×C43C22⋊C412yes—
147C22×C4×C43—82no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—82no—
163C22×Dic43C22×C412yes—
164C22×Dic43C22×C411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C412yes—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—22no—
170C2×D172—41no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—82no—
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—21no—
203(C2×D43)⋊C4—21no—
204(C2×D43)⋊C4—21no—
205(C2×D43)⋊C4—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43—21no—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
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—21no—
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—21no—
236C22×D43—21no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43#13112yes—
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—42no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43—42no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—41no—
254C2×C4×C43C2×C22⋊C412yes—
255C2×C4×C43C2×C22⋊C412yes—
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C2×C22⋊C411yescharacteristic
258C2×C4×C43C2×C22⋊C411yescharacteristic
259C2×C4×C43C2×C22⋊C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C22⋊D43—44no—
263C22⋊D43—44no—
264C22⋊D43—82no—
265C22⋊D43—82no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—21no—
270C2×Dic43—22no—
271C2×Dic43—22no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—42no—
275D172—42no—
276D172—42no—
277C4×D43—42no—
278C4×D43—42no—
279C4×D43—42no—
280C4×D43—42no—
281C4×D43—82no—
282C4×D43—82no—
283C8×C43—41no—
284C8×C43—42no—
285C8×C43—41no—
286C43⋊C8—41no—
287C43⋊C8—42no—
288C43⋊C8—41no—
289#17424—431nomaximal, Sylow
290C22×C43—21no—
291C22×C43—21no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—22no—
296C22×C43—22no—
297C22×C43—22no—
298C22×C43—82no—
299C22×C43—82no—
300C22×C43C22×C22⋊C411yescharacteristic
301C22×C43C2×#13111yescharacteristic
302C22×C43#56811yescharacteristic
303C2×D43—22no—
304C2×D43—42no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—42no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—41no—
311C2×D43—81no—
312C2×D43—81no—
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—22no—
318C4×C43—22no—
319C4×C43—21no—
320C4×C43#41312yes—
321Dic43—42no—
322Dic43—42no—
323Dic43—41no—
324Dic43—41no—
325C2×#553—431no—
326#2974—431no—
327#2974D4311yescharacteristic, complemented
328#1470—431no—
329#1470—431no—
330#1468—432no—
331#1468—432no—
332#1466—431no—
333#1465—432no—
334#1460—431no—
335#1459—432no—
336C2×C43—21no—
337C2×C43—21no—
338C2×C43—42no—
339C2×C43—42no—
340C2×C43#288011yescharacteristic
341C2×C43#288311yescharacteristic
342C2×C43C2×#41311yescharacteristic
343D43—42no—
344D43—81no—
345#553—861no—
346#553—862no—
347#553—861no—
348#553—861no—
349#553—862no—
350#553—861no—
351C2×#126—432no—
352C2×#125—431no—
353C2×#123—432no—
354C2×#121—431no—
355C2×#121—431no—
356C2×#121—432no—
357C2×C4×D4—432no—
358C2×C4×D4—431no—
359C2×C4×D4C2×D4311yescharacteristic
360C2×#117—431no—
361C22×C4⋊C4—431no—
362#436—21no—
363#436—861no—
364#435—22no—
365#435—862no—
366C8×D4—21no—
367C8×D4—861no—
368#432—431no—
369#432C2×D4311yescharacteristic
370#431—431no—
371#431C2×D4311yescharacteristic
372#407—432no—
373#407C2×D4312yes—
374C2×C22⋊C8—432no—
375C2×C22⋊C8C2×D4312yes—
376#324—432no—
377#324—432no—
378#324—432no—
379#324—432no—
380#323—431no—
381#323—432no—
382#323—431no—
383#323—431no—
384#323—431no—
385#323—432no—
386C43#1742411yescharacteristic, complemented, Sylow
387C22×D4—432no—
388C22×D4—432no—
389C22×D4—431no—
390C22×D4C4×D4311yescharacteristic
391C23×C4—432no—
392C23×C4—431no—
393C23×C4—431no—
394C23×C4C22×D4312yes—
395C2×M16—22no—
396C2×M16—862no—
397C22×C8—22no—
398C22×C8—862no—
399#126—862no—
400#126—862no—
401#126—862no—
402#126—862no—
403#125—861no—
404#125—861no—
405#125—861no—
406#125—861no—
407#123—862no—
408#123—862no—
409#123—862no—
410#123—862no—
411#121—861no—
412#121—861no—
413#121—862no—
414#121—861no—
415#121—861no—
416#121—862no—
417#121—862no—
418#121—862no—
419#121—862no—
420#121—862no—
421C4×D4—862no—
422C4×D4—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—861no—
426C4×D4—861no—
427C4×D4—861no—
428C4×D4—861no—
429C4×D4D17211yescharacteristic
430C4×D4D17212yes—
431C4×D4D17211yescharacteristic
432C4×D4C22⋊D4311yescharacteristic
433C4×D4C22⋊D4312yes—
434C4×D4C22⋊D4311yescharacteristic
435#117—862no—
436#117—861no—
437#117—861no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—432no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—432no—
443C2×C4⋊C4—432no—
444C2×C4⋊C4—862no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4—861no—
447C2×C4⋊C4C4×D4311yescharacteristic
448C2×C22⋊C4—432no—
449C2×C22⋊C4—432no—
450C2×C22⋊C4—432no—
451C2×C22⋊C4—431no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4C4×D4312yes—
454C2×C42—432no—
455C2×C42C22×D4311yescharacteristic
456C4⋊C8—21no—
457C4⋊C8—21no—
458C4⋊C8—861no—
459C4⋊C8—861no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8—431no—
463C22⋊C8—432no—
464C22⋊C8—431no—
465C22⋊C8—862no—
466C22⋊C8—862no—
467C22⋊C8C22×D4311yescharacteristic
468C22⋊C8C22×D4312yes—
469C22⋊C8C22×D4311yescharacteristic
470#97—21no—
471#97—861no—
472C4×C8—21no—
473C4×C8—861no—
474C24—431no—
475C24—431no—
476C24C2×C4×D4312yes—
477C2×D4—42no—
478C2×D4—862no—
479C2×D4—862no—
480C2×D4—862no—
481C2×D4—864no—
482C2×D4—862no—
483C2×D4—862no—
484C2×D4—861no—
485C2×D4—861no—
486C2×D4—3442no—
487C2×D4—1721no—
488C2×D4—1722no—
489C2×D4(C2×D43)⋊C411yescharacteristic
490C2×D4(C2×D43)⋊C411yescharacteristic
491C2×D4(C2×D43)⋊C412yes—
492C22×C4—82no—
493C22×C4—432no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—432no—
497C22×C4—862no—
498C22×C4—862no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—3442no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4C2×C4×D4311yescharacteristic
507C22×C4C2×C4×D4311yescharacteristic
508C22×C4C2×C4×D4312yes—
509C22×C4C2×D17212yes—
510C22×C4C2×D17212yes—
511C22×C4C2×C22⋊D4312yes—
512C22×C4C2×C22⋊D4312yes—
513C22×C4C23×D4311yescharacteristic
514M16—82no—
515M16—3442no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—22no—
519C2×C8—82no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8—862no—
523C2×C8—3442no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—862no—
533C4⋊C4—862no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4(C2×D43)⋊C412yes—
537C4⋊C4(C2×D43)⋊C411yescharacteristic
538C4⋊C4(C2×D43)⋊C411yescharacteristic
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—861no—
546C22⋊C4—861no—
547C22⋊C4—861no—
548C22⋊C4—861no—
549C22⋊C4(C2×D43)⋊C412yes—
550C22⋊C4(C2×D43)⋊C412yes—
551C22⋊C4(C2×D43)⋊C412yes—
552C22⋊C4(C2×D43)⋊C412yes—
553C42—862no—
554C42—862no—
555C42C2×D17211yescharacteristic
556C42C2×D17211yescharacteristic
557C42C2×C22⋊D4311yescharacteristic
558C42C2×C22⋊D4311yescharacteristic
559C23—22no—
560C23—22no—
561C23—42no—
562C23—42no—
563C23—432no—
564C23—861no—
565C23—861no—
566C23—861no—
567C23—861no—
568C23—861no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23—1721no—
573C23C2×(C2×D43)⋊C412yes—
574C23C2×(C2×D43)⋊C412yes—
575C23C22×C4×D4311yescharacteristic
576D4—22no—
577D4—22no—
578D4—42no—
579D4—3442no—
580D4—3442no—
581D4—1722no—
582D4—1722no—
583D4—1724no—
584D4—1724no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—861no—
595C2×C4—862no—
596C2×C4—861no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—3442no—
601C2×C4—3442no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4C2×(C2×D43)⋊C412yes—
610C2×C4C2×(C2×D43)⋊C412yes—
611C2×C4C2×(C2×D43)⋊C411yescharacteristic
612C2×C4C2×(C2×D43)⋊C411yescharacteristic
613C2×C4C2×(C2×D43)⋊C411yescharacteristic
614C2×C4C2×(C2×D43)⋊C411yescharacteristic
615C2×C4C22×C22⋊D4311yescharacteristic
616C2×C4C22×D17211yescharacteristic
617C8—41no—
618C8—42no—
619C8—41no—
620C8—1721no—
621C8—1722no—
622C8—1721no—
623C22—21no—
624C22—21no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—82no—
632C22—82no—
633C22—862no—
634C22—3441no—
635C22—3441no—
636C22—1722no—
637C22—1722no—
638C22—1721no—
639C22—1721no—
640C22—1721no—
641C22—1721no—
642C22—1721no—
643C22C22×(C2×D43)⋊C411yescharacteristic
644C22#131×D4311yescharacteristic
645C22#1458366411yescharacteristic
646C4—21no—
647C4—21no—
648C4—21no—
649C4—21no—
650C4—22no—
651C4—22no—
652C4—21no—
653C4—1722no—
654C4—1722no—
655C4—1721no—
656C4—1721no—
657C4#1458288112yes—
658C2—21no—
659C2—21no—
660C2—42no—
661C2—42no—
662C2—3441no—
663C2—1722no—
664C2#1914304211yescharacteristic
665C2#1914305511yescharacteristic
666C2C2×#1458288111yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2974C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583599C2
cosocleC22×C4×C43C24
hypercenter#2974D43
hypocenterC43#17424
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. #19132952C2semidirect
4. #19132950C2semidirect
5. #19132944C2semidirect
6. #19132941C2semidirect
7. #19132935C2semidirect
8. #19132931C2semidirect
9. #19132915C2semidirect
10. #19132911C2semidirect
11. C43×#2974C2semidirect
327. #2974D43semidirect
386. C43#17424semidirect

Maximal subgroups

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

subgroupindex
C2×#145835992
#191436302
#191329522
#191329502
#191329442
#191329412
#191329352
#191329312
#191329152
#191329112
C43×#29742
#1742443