Finite Group Databasebeta

← #25070732

Subgroups — #25070732

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145397C211yesmaximal, characteristic, complemented
2#19145392C211yesmaximal, characteristic
3#19140075C211yesmaximal, characteristic, complemented
4#19133626C214yesmaximal, complemented
5#19133524C214yesmaximal, complemented
6#19133115C211yesmaximal, characteristic, complemented
7#19133111C211yesmaximal, characteristic, complemented
8#19132925C211yesmaximal, characteristic, complemented
9C2×C43×#539C211yesmaximal, characteristic, complemented
10C2×#13063299C2211yescharacteristic
11#14583232C2212yescomplemented
12#14583217—21no—
13#14583215C2212yes—
14#14583212—21no—
15#14583150—22no—
16#14583147—22no—
17#14583049C2212yescomplemented
18#14583038—21no—
19#14583033—21no—
20#14583032C2212yes—
21#14582863C2211yescharacteristic
22#14582863C2211yescharacteristic
23#14582838C2212yescomplemented
24#14582816C2212yescomplemented
25#14582789—22no—
26#14582778—21no—
27#14582778—21no—
28C4×C22⋊Dic43C2211yescharacteristic
29#14582636C2214yescomplemented
30#14582633C2214yes—
31#14582625C2214yescomplemented
32C43×#539—22no—
33C43×#539—22no—
34C43×#539—22no—
35C43×#539C2214yes—
36C2×#126×C43—21no—
37C2×#125×C43—21no—
38C2×#123×C43—21no—
39C2×#123×C43—21no—
40C2×C22⋊Q8×C43—21no—
41C2×C22⋊Q8×C43C2211yescharacteristic
42C2×#121×C43C2211yescharacteristic
43C2×C4×D4×C43—21no—
44C22×C4⋊C4×C43C2211yescharacteristic
45C22×D172C2311yescharacteristic
46C22×C22⋊D43—21no—
47C2×#10621884—22no—
48C2×#10621882—22no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51#13063299—21no—
52#13063299—21no—
53#13063299—21no—
54#13063299—21no—
55C2×C4⋊Dic43C2311yescharacteristic
56C2×C22⋊Dic43—21no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—22no—
60C2×C4×Dic43—21no—
61#13063258—22no—
62#13063256—22no—
63#13063249—22no—
64#13063246—22no—
65#13063245—22no—
66#13063245—22no—
67C22⋊(C43⋊C8)—21no—
68C22⋊(C43⋊C8)—21no—
69C22⋊(C43⋊C8)C2312yes—
70C22⋊(C43⋊C8)C2312yes—
71C43⋊#95—22no—
72C43⋊#95—22no—
73C43⋊#95C2312yes—
74C22×Q8×C43D411yescharacteristic
75C22×D4×C43—21no—
76C22×D4×C43D411yescharacteristic
77C23×C4×C43—21no—
78C23×C4×C43D411yescharacteristic
79C23×C4×C43D411yescharacteristic
80C23×C4×C43C2311yescharacteristic
81#126×C43—24no—
82#126×C43—24no—
83#125×C43—24no—
84#125×C43—24no—
85#123×C43—24no—
86#123×C43—24no—
87#123×C43—24no—
88#123×C43—24no—
89C22⋊Q8×C43—24no—
90C22⋊Q8×C43—24no—
91C22⋊Q8×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43D412yes—
94C22⋊Q8×C43C2312yes—
95#121×C43—21no—
96#121×C43—21no—
97#121×C43D412yes—
98#121×C43C2312yes—
99C4×D4×C43—24no—
100C4×D4×C43—24no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43D412yes—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43C2312yes—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C42×C43—21no—
119C24×C43—21no—
120C24×C43C2×D411yescharacteristic
121C23×D43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—81no—
124C2×Q8×C43C2×D412yes—
125C2×D4×C43—21no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—44no—
129C2×D4×C43—81no—
130C2×D4×C43C2×D412yes—
131C22×C4×C43—24no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—42no—
140C22×C4×C43—81no—
141C22×C4×C43—81no—
142C22×C4×C43—82no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—44no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154C22×Dic43—21no—
155C22×Dic43—22no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—81no—
159C4⋊C4×C43—24no—
160C4⋊C4×C43—24no—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43C2×D412yes—
171C4⋊C4×C43C2×D412yes—
172C22⋊C4×C43—24no—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—24no—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C42×C43—24no—
180C22⋊Dic43—42no—
181#10621884—82no—
182#10621882—82no—
183(C2×D43)⋊C4—44no—
184(C2×D43)⋊C4—41no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4—82no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4×Dic43—81no—
190#10621877—81no—
191#10621877—81no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—41no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43#12011yescharacteristic
202C23×C43#12011yescharacteristic
203C23×C43C22×D411yescharacteristic
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—41no—
207C22×D43—42no—
208Q8×C43—42no—
209Q8×C43—81no—
210D4×C43—42no—
211D4×C43—44no—
212D4×C43—44no—
213D4×C43—81no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—81no—
235C2×C4×C43—84no—
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12011yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C22⋊D43—82no—
241C22⋊D43—82no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—41no—
246C2×Dic43—42no—
247D172—42no—
248D172—42no—
249C43⋊C8—42no—
250C43⋊C8—42no—
251#18320—431nomaximal, Sylow
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—44no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—84no—
264C22×C43#45412yes—
265C22×C43C2×#12011yescharacteristic
266C22×C43#57512yes—
267C2×D43—84no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—42no—
276C4×C43—42no—
277C4×C43—42no—
278C4×C43—42no—
279C4×C43—42no—
280Dic43—82no—
281Dic43—81no—
282C2×#539D4311yescharacteristic, complemented
283#3193—431no—
284#3192—431no—
285#2591—431no—
286#1615—434no—
287#1597—434no—
288#1508—431no—
289#1507—431no—
290#1463—431no—
291C2×C43—22no—
292C2×C43—22no—
293C2×C43—41no—
294C2×C43—82no—
295C2×C43#300511yescharacteristic
296C2×C43C2×#45411yescharacteristic
297C2×C43#302611yescharacteristic
298D43—161no—
299#539—22no—
300#539—22no—
301#539—22no—
302#539C2×D4314yes—
303C2×#126—21no—
304C2×#125—21no—
305C2×#123—21no—
306C2×#123—21no—
307C2×C22⋊Q8—21no—
308C2×C22⋊Q8C2×D4311yescharacteristic
309C2×#121—431no—
310C2×#121C2×D4311yescharacteristic
311C2×C4×D4—21no—
312C22×C4⋊C4C2×D4311yescharacteristic
313#484—432no—
314#481—432no—
315#481—861no—
316#480—861no—
317#469—862no—
318#468—862no—
319#450—432no—
320#448—861no—
321#447—432no—
322#447—861no—
323#407—431no—
324#407—431no—
325#400—432no—
326#394—432no—
327#388—862no—
328#386—861no—
329#386—861no—
330C4×C22⋊C4—431no—
331#328—434no—
332#327—434no—
333#324—434no—
334C43#1832011yescharacteristic, complemented, Sylow
335C22×Q8C22⋊D4311yescharacteristic
336C22×D4—21no—
337C22×D4—431no—
338C22×D4—861no—
339C22×D4C22⋊D4311yescharacteristic
340C23×C4—21no—
341C23×C4C22⋊D4311yescharacteristic
342C23×C4C22⋊D4311yescharacteristic
343C23×C4C22×D4311yescharacteristic
344C2×SD16—862no—
345C2×D8—862no—
346C2×M16—861no—
347C2×M16—861no—
348#126—24no—
349#126—24no—
350#125—24no—
351#125—24no—
352#123—24no—
353#123—24no—
354#123—24no—
355#123—24no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8C22⋊D4312yes—
361C22⋊Q8C22×D4312yes—
362#121—21no—
363#121—21no—
364#121—861no—
365#121—861no—
366#121—861no—
367#121—861no—
368#121C22⋊D4312yes—
369#121C22×D4312yes—
370C4×D4—24no—
371C4×D4—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4C22⋊D4312yes—
382C2×C4⋊C4C22⋊D4311yescharacteristic
383C2×C4⋊C4C22⋊D4311yescharacteristic
384C2×C4⋊C4C22×D4312yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—862no—
391C2×C22⋊C4—861no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—862no—
394C2×C42—21no—
395C2×C42—861no—
396#107—862no—
397#106—862no—
398#103—862no—
399#102—862no—
400#102—862no—
401#102—862no—
402C22⋊C8—432no—
403C22⋊C8—432no—
404C22⋊C8—861no—
405C22⋊C8—861no—
406#95—432no—
407#95—862no—
408#95—862no—
409C24—21no—
410C24—861no—
411C24C2×C22⋊D4311yescharacteristic
412C2×Q8—21no—
413C2×Q8—81no—
414C2×Q8C2×C22⋊D4312yes—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—44no—
419C2×D4—81no—
420C2×D4—861no—
421C2×D4—861no—
422C2×D4—3441no—
423C2×D4—1724no—
424C2×D4—1721no—
425C2×D4—1721no—
426C2×D4C2×C22⋊D4312yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—42no—
436C22×C4—81no—
437C22×C4—81no—
438C22×C4—82no—
439C22×C4—862no—
440C22×C4—861no—
441C22×C4C2×C22⋊D4312yes—
442C22×C4C2×C22⋊D4312yes—
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446C22×C4C2×C22⋊D4311yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448C22×C4C23×D4311yescharacteristic
449SD16—3442no—
450D8—3442no—
451M16—3441no—
452M16—3441no—
453C2×C8—862no—
454C2×C8—862no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4C2×C22⋊D4312yes—
469C4⋊C4C2×C22⋊D4312yes—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—3442no—
478C22⋊C4—1724no—
479C22⋊C4—1722no—
480C22⋊C4—1721no—
481C22⋊C4—1721no—
482C42—24no—
483C42—3441no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—41no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—1722no—
492C23—1722no—
493C23—1721no—
494C23—1722no—
495C23#1306329411yescharacteristic
496C23#1306329411yescharacteristic
497C23C22×C22⋊D4311yescharacteristic
498Q8—42no—
499Q8—81no—
500D4—42no—
501D4—44no—
502D4—44no—
503D4—81no—
504D4—3442no—
505D4—3442no—
506D4—1722no—
507D4—1722no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—81no—
529C2×C4—84no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1721no—
534C2×C4—1722no—
535C2×C4#1306329411yescharacteristic
536C2×C4#1306329411yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4C22×C22⋊D4311yescharacteristic
539C8—1722no—
540C8—1722no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—44no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—84no—
553C22—3444no—
554C22—3441no—
555C22—3441no—
556C22—3441no—
557C22#1458307212yes—
558C22C2×#1306329411yescharacteristic
559C22#1458369712yes—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—42no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—3442no—
570C4—3441no—
571C2—22no—
572C2—22no—
573C2—41no—
574C2—82no—
575C2—6881no—
576C2#1914383711yescharacteristic
577C2C2×#1458307211yescharacteristic
578C2#1914399211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#539C2
socleC22×C43C2×#120
prime radical#19145392C2
hypercenterC2×#539D43
hypocenterC43#18320
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. #19145397C2semidirect
3. #19140075C2semidirect
4. #19133626C2semidirect
5. #19133524C2semidirect
6. #19133115C2semidirect
7. #19133111C2semidirect
8. #19132925C2semidirect
9. C2×C43×#539C2semidirect
11. #14583232C22semidirect
17. #14583049C22semidirect
23. #14582838C22semidirect
24. #14582816C22semidirect
29. #14582636C22semidirect
31. #14582625C22semidirect
282. C2×#539D43semidirect
334. C43#18320semidirect

Maximal subgroups

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

subgroupindex
#191453972
#191453922
#191400752
#191336262
#191335242
#191331152
#191331112
#191329252
C2×C43×#5392
#1832043