Finite Group Databasebeta

← #25064322

Subgroups — #25064322

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148434C211yesmaximal, characteristic
2#19137535C211yesmaximal, characteristic, complemented
3#19133173C212yesmaximal, complemented
4#19133168C211yesmaximal, characteristic, complemented
5#19133164C211yesmaximal, characteristic, complemented
6#19133152C212yesmaximal, complemented
7#19133087C212yesmaximal, complemented
8#19133082C212yesmaximal, complemented
9C2×#14582637C211yesmaximal, characteristic, complemented
10C2×#14582634C211yesmaximal, characteristic, complemented
11C43×#2972C211yesmaximal, characteristic, complemented
12#14583598—22no—
13#14583595C412yescomplemented
14#14583589C412yescomplemented
15#14583578—22no—
16#14583558C412yescomplemented
17#14583545C412yescomplemented
18#14583496—21no—
19#14583487—21no—
20#14583458—21no—
21#14583433C2212yes—
22#14583410C2212yes—
23C2×#13063304C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25#14583372—21no—
26#14582792—21no—
27#14582785—21no—
28#14582779—21no—
29#14582767C2211yescharacteristic, complemented
30#14582762C2211yescharacteristic, complemented
31#14582759C2211yescharacteristic
32C22⋊C4×Dic43—21no—
33C4×C22⋊Dic43C2211yescharacteristic, complemented
34#14582745C2211yescharacteristic, complemented
35C2×C43⋊#95C2211yescharacteristic
36#14582637C2212yescomplemented
37#14582637C2212yescomplemented
38#14582637C2212yescomplemented
39#14582637C2212yescomplemented
40#14582634C2212yes—
41#14582634C2212yes—
42#14582634C2212yes—
43#14582634C2212yes—
44C2×C4×D4×C43C2211yescharacteristic
45C8×D4×C43—22no—
46C8×D4×C43—22no—
47C43×#431C2212yescomplemented
48C2×C22⋊C8×C43C2211yescharacteristic
49C2×C22⋊C8×C43C2211yescharacteristic
50C2×C22⋊C8×C43C2212yescomplemented
51C2×#10621898C2×C412yescomplemented
52C22×Dic86C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×C22⋊D43—21no—
55C23×Dic43—21no—
56#13063320—22no—
57#13063319—22no—
58#13063318—22no—
59#13063317C2×C412yescomplemented
60#13063315—22no—
61#13063313C2×C412yescomplemented
62#13063311—22no—
63#13063310—22no—
64#13063308—22no—
65#13063308—22no—
66#13063307—22no—
67#13063306—22no—
68#13063304—21no—
69#13063304—21no—
70#13063304C2×C412yes—
71#13063304C2×C412yescomplemented
72#13063304C2312yes—
73#13063303—22no—
74#13063299—21no—
75#13063299—21no—
76#13063299C2×C412yes—
77#13063299C2×C412yescomplemented
78#13063299C2312yes—
79#13063298—22no—
80#13063297—22no—
81#13063297—22no—
82#13063294—22no—
83#13063293—22no—
84C4×Dic86C2×C412yescomplemented
85C4×D172C2×C412yescomplemented
86C4×C22⋊D43—22no—
87C4×C22⋊D43—22no—
88C4×C22⋊D43—22no—
89(C22⋊D43)⋊C4—22no—
90(C22⋊D43)⋊C4—22no—
91#13063284C2×C412yescomplemented
92#13063282—22no—
93#13063281—22no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43C2×C411yescharacteristic
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C22⋊C4×D43—22no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95C2311yescharacteristic
112C43⋊#95C2311yescharacteristic
113C43⋊#95C2311yescharacteristic
114C43⋊#95C2311yescharacteristic
115C22×D4×C43D411yescharacteristic
116C23×C4×C43C2311yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C22×C8×C43—21no—
119C22×C8×C43—21no—
120C22×C8×C43—22no—
121C4×D4×C43C2×C412yes—
122C4×D4×C43C2×C412yes—
123C4×D4×C43D412yes—
124C4×D4×C43D412yes—
125C2×C4⋊C4×C43D411yescharacteristic
126C2×C22⋊C4×C43D411yescharacteristic
127C2×C22⋊C4×C43D411yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—22no—
130C22⋊C8×C43—21no—
131C22⋊C8×C43—21no—
132C22⋊C8×C43—22no—
133C22⋊C8×C43C2312yes—
134C22⋊C8×C43C2312yes—
135C4×C8×C43—22no—
136C24×C43C2×D411yescharacteristic
137C24×C43C2×D411yescharacteristic
138C23×D43—21no—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43C22⋊C412yes—
142C2×D4×C43C22⋊C412yes—
143C22×C4×C43—81no—
144C22×C4×C43—81no—
145C22×C4×C43C22×C411yescharacteristic
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C412yes—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—42no—
161C2×C22⋊D43—42no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—42no—
170C22×Dic43—42no—
171C22×Dic43—81no—
172#10621898—82no—
173C2×D172—21no—
174C2×D172—81no—
175C2×D172C22×C412yes—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×Dic86—21no—
179C2×Dic86—81no—
180C2×Dic86C22×C412yes—
181C2×C8×C43—22no—
182C2×C8×C43—22no—
183C2×C8×C43—81no—
184C2×C8×C43—81no—
185C2×C8×C43—82no—
186C4⋊C4×C43C22⋊C412yes—
187C4⋊C4×C43C22⋊C412yes—
188C22⋊C4×C43C22⋊C412yes—
189C22⋊C4×C43C22⋊C412yes—
190C22⋊C4×C43C22⋊C412yes—
191C22⋊C4×C43C22⋊C412yes—
192C42×C43C22×C412yes—
193C42×C43C2×D412yes—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—42no—
199C22⋊Dic43—42no—
200C22⋊Dic43—81no—
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—
206(C2×D43)⋊C4—22no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43—81no—
210C4⋊Dic43C22×C412yes—
211C4⋊Dic43C22×C412yes—
212Dic43⋊C4—22no—
213Dic43⋊C4—22no—
214Dic43⋊C4—22no—
215Dic43⋊C4—22no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218C4×Dic43—22no—
219C4×Dic43—22no—
220C4×Dic43—42no—
221C4×Dic43—81no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43C2×C22⋊C412yes—
229C23×C43C2×C22⋊C411yescharacteristic
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43#13512yes—
232C23×C43#13512yes—
233C23×C43C22×D411yescharacteristic
234C22×D43—22no—
235C22×D43—42no—
236C22×D43—81no—
237C22×D43—81no—
238D4×C43—24no—
239D4×C43—24no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—42no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—42no—
251C2×C4×C43—41no—
252C2×C4×C43C2×C22⋊C412yes—
253C2×C4×C43C2×C22⋊C412yes—
254C2×C4×C43C2×C22⋊C411yescharacteristic
255C2×C4×C43C2×C22⋊C412yes—
256C2×C4×C43C2×C22⋊C411yescharacteristic
257C2×C4×C43C23×C411yescharacteristic
258C2×C4×C43C22×D411yescharacteristic
259C22⋊D43—42no—
260C22⋊D43—42no—
261C22⋊D43—44no—
262C22⋊D43—82no—
263C22⋊D43—82no—
264C2×Dic43—22no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—42no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—81no—
281C2×Dic43—81no—
282C2×Dic43—84no—
283D172—42no—
284D172—81no—
285C4×D43—82no—
286C4×D43—82no—
287Dic86—42no—
288Dic86—81no—
289C8×C43—42no—
290C8×C43—42no—
291#17615—431nomaximal, Sylow
292C22×C43—21no—
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—22no—
299C22×C43—22no—
300C22×C43—22no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43#41612yes—
306C22×C43#41612yes—
307C22×C43C22×C22⋊C411yescharacteristic
308C22×C43C2×#13511yescharacteristic
309C22×C43C2×#13511yescharacteristic
310C2×D43—42no—
311C2×D43—42no—
312C2×D43—42no—
313C2×D43—162no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—21no—
317C4×C43—22no—
318C4×C43—21no—
319C4×C43—22no—
320C4×C43—22no—
321Dic43—42no—
322Dic43—42no—
323Dic43—42no—
324Dic43—42no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328#3505—431no—
329#2972D4311yescharacteristic, complemented
330#2353—431no—
331#1521—432no—
332#1520—431no—
333#1519—431no—
334#1516—432no—
335#1501—432no—
336#1500—432no—
337C2×#328—431no—
338C2×#327—431no—
339C2×C43—21no—
340C2×C43—21no—
341C2×C43—22no—
342C2×C43—22no—
343C2×C43—42no—
344C2×C43#288311yescharacteristic
345C2×C43C2×#41611yescharacteristic
346C2×C43#290111yescharacteristic
347D43—82no—
348#553—432no—
349#553—862no—
350#552—432no—
351#551—862no—
352#548—432no—
353#546—432no—
354#539—861no—
355#538—861no—
356#534—861no—
357#529—432no—
358#525—432no—
359C2×C22⋊Q8—431no—
360C2×#121—431no—
361#518—861no—
362C2×C4×D4C2×D4311yescharacteristic
363C8×D4—22no—
364C8×D4—22no—
365#431C2×D4312yescomplemented
366C2×C22⋊C8C2×D4311yescharacteristic
367C2×C22⋊C8C2×D4311yescharacteristic
368C2×C22⋊C8C2×D4312yescomplemented
369#388—861no—
370#387—861no—
371#386—861no—
372#383—431no—
373#381—431no—
374#380—431no—
375C4×C22⋊C4—431no—
376C4×C22⋊C4—861no—
377#376—431no—
378C2×#95—431no—
379#328—432no—
380#328—432no—
381#328—432no—
382#328—432no—
383#327—432no—
384#327—432no—
385#327—432no—
386#327—432no—
387C43#1761511yescharacteristic, complemented, Sylow
388C2×#41—432no—
389C22×Q8—431no—
390C22×D4—431no—
391C22×D4—861no—
392C22×D4D17211yescharacteristic
393C23×C4—861no—
394C23×C4C22×D4311yescharacteristic
395C23×C4C22×D4311yescharacteristic
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—22no—
399#126—862no—
400#126—862no—
401#126—862no—
402#125—432no—
403#125—862no—
404#124—432no—
405#124—862no—
406#123—862no—
407#123—862no—
408#123—862no—
409#123—862no—
410#123—862no—
411C22⋊Q8—432no—
412C22⋊Q8—432no—
413C22⋊Q8—432no—
414C22⋊Q8—861no—
415C22⋊Q8—861no—
416C22⋊Q8—862no—
417#121—432no—
418#121—432no—
419#121—432no—
420#121—862no—
421#121—862no—
422#121—861no—
423#121—861no—
424#121—862no—
425#120—862no—
426#120—862no—
427C4×Q8—432no—
428C4×D4—432no—
429C4×D4—862no—
430C4×D4—862no—
431C4×D4—862no—
432C4×D4—862no—
433C4×D4—862no—
434C4×D4C4×D4312yes—
435C4×D4C4×D4312yes—
436C4×D4C22⋊D4312yes—
437C4×D4C22⋊D4312yes—
438#117—432no—
439#117—862no—
440#117—862no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4D17211yescharacteristic
446C2×C22⋊C4—861no—
447C2×C22⋊C4—861no—
448C2×C22⋊C4—862no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4D17211yescharacteristic
453C2×C22⋊C4D17211yescharacteristic
454C2×C42—861no—
455C2×C42—861no—
456C2×C42C22×D4311yescharacteristic
457C4⋊C8—22no—
458C22⋊C8—21no—
459C22⋊C8—21no—
460C22⋊C8—22no—
461C22⋊C8C22×D4312yes—
462C22⋊C8C22×D4312yes—
463C4×C8—22no—
464#95—431no—
465#95—431no—
466#95—431no—
467#95—431no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473C24—861no—
474C24C2×D17211yescharacteristic
475C24C2×D17211yescharacteristic
476#41—3442no—
477C2×Q8—432no—
478C2×Q8—861no—
479C2×Q8—3441no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—432no—
483C2×D4—862no—
484C2×D4—862no—
485C2×D4—862no—
486C2×D4—862no—
487C2×D4—861no—
488C2×D4—3441no—
489C2×D4—1722no—
490C2×D4—1722no—
491C2×D4(C2×D43)⋊C412yes—
492C2×D4(C2×D43)⋊C412yes—
493C22×C4—81no—
494C22×C4—81no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—861no—
504C22×C4—3441no—
505C22×C4—1722no—
506C22×C4—1722no—
507C22×C4C2×C4×D4311yescharacteristic
508C22×C4C2×C4×D4311yescharacteristic
509C22×C4C2×C4×D4312yes—
510C22×C4C2×D17211yescharacteristic
511C22×C4C2×D17211yescharacteristic
512C22×C4C2×D17211yescharacteristic
513C22×C4C2×D17211yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4312yes—
517C22×C4C23×D4311yescharacteristic
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—81no—
521C2×C8—81no—
522C2×C8—82no—
523C4⋊C4—432no—
524C4⋊C4—432no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—862no—
531C4⋊C4—862no—
532C4⋊C4—862no—
533C4⋊C4—3441no—
534C4⋊C4(C2×D43)⋊C412yes—
535C4⋊C4(C2×D43)⋊C412yes—
536C22⋊C4—862no—
537C22⋊C4—862no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C22⋊C4—862no—
546C22⋊C4—3441no—
547C22⋊C4—1722no—
548C22⋊C4—1722no—
549C22⋊C4(C2×D43)⋊C412yes—
550C22⋊C4(C2×D43)⋊C412yes—
551C22⋊C4(C2×D43)⋊C412yes—
552C22⋊C4(C2×D43)⋊C412yes—
553C42—862no—
554C42—862no—
555C42—3441no—
556C42—1722no—
557C42C2×C4×D4312yes—
558C42C2×C22⋊D4312yes—
559C23—21no—
560C23—21no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—862no—
566C23—3441no—
567C23—3441no—
568C23—1722no—
569C23C2×(C2×D43)⋊C412yes—
570C23C2×(C2×D43)⋊C411yescharacteristic
571C23C2×(C2×D43)⋊C411yescharacteristic
572C23#1306334712yes—
573C23#1306334712yes—
574C23C22×D17211yescharacteristic
575Q8—3441no—
576Q8—1722no—
577D4—24no—
578D4—24no—
579D4—3441no—
580D4—3442no—
581D4—3442no—
582D4—1722no—
583D4—1724no—
584D4—1722no—
585D4—1722no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—3442no—
603C2×C4—3442no—
604C2×C4—3444no—
605C2×C4—3441no—
606C2×C4—3441no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1722no—
618C2×C4—1721no—
619C2×C4C2×(C2×D43)⋊C412yes—
620C2×C4C2×(C2×D43)⋊C412yes—
621C2×C4C2×(C2×D43)⋊C412yes—
622C2×C4C2×(C2×D43)⋊C411yescharacteristic
623C2×C4C2×(C2×D43)⋊C411yescharacteristic
624C2×C4C22×C4×D4311yescharacteristic
625C2×C4C22×C22⋊D4311yescharacteristic
626C8—42no—
627C8—42no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—1722no—
642C22—1722no—
643C22—1722no—
644C22—6882no—
645C22#1458289612yes—
646C22#1458289612yes—
647C22C22×(C2×D43)⋊C411yescharacteristic
648C22C2×#1306334711yescharacteristic
649C22C2×#1306334711yescharacteristic
650C4—21no—
651C4—21no—
652C4—22no—
653C4—21no—
654C4—21no—
655C4—22no—
656C4—22no—
657C4—3441no—
658C4—3441no—
659C4—3441no—
660C4—1722no—
661C4—1722no—
662C4—1722no—
663C4—1722no—
664C2—21no—
665C2—21no—
666C2—22no—
667C2—22no—
668C2—42no—
669C2—3442no—
670C2#1914305511yescharacteristic
671C2C2×#1458289611yescharacteristic
672C2#1914314011yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2972C2
socleC22×C43C22×C22⋊C4
prime radical#19148434C2
cosocleC22×C4×C43C24
hypercenter#2972D43
hypocenterC43#17615
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #19137535C2semidirect
3. #19133173C2semidirect
4. #19133168C2semidirect
5. #19133164C2semidirect
6. #19133152C2semidirect
7. #19133087C2semidirect
8. #19133082C2semidirect
9. C2×#14582637C2semidirect
10. C2×#14582634C2semidirect
11. C43×#2972C2semidirect
13. #14583595C4semidirect
14. #14583589C4semidirect
16. #14583558C4semidirect
17. #14583545C4semidirect
29. #14582767C22semidirect
30. #14582762C22semidirect
33. C4×C22⋊Dic43C22semidirect
34. #14582745C22semidirect
36. #14582637C22semidirect
37. #14582637C22semidirect
38. #14582637C22semidirect
39. #14582637C22semidirect
47. C43×#431C22semidirect
50. C2×C22⋊C8×C43C22semidirect
51. C2×#10621898C2×C4semidirect
59. #13063317C2×C4semidirect
61. #13063313C2×C4semidirect
71. #13063304C2×C4semidirect
77. #13063299C2×C4semidirect
84. C4×Dic86C2×C4semidirect
85. C4×D172C2×C4semidirect
91. #13063284C2×C4semidirect
329. #2972D43semidirect
365. #431C2×D43semidirect
368. C2×C22⋊C8C2×D43semidirect
387. C43#17615semidirect

Maximal subgroups

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

subgroupindex
#191484342
#191375352
#191331732
#191331682
#191331642
#191331522
#191330872
#191330822
C2×#145826372
C2×#145826342
C43×#29722
#1761543