Finite Group Databasebeta

← #25077892

Subgroups — #25077892

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145785C211yesmaximal, characteristic, complemented
2#19145582C211yesmaximal, characteristic
3#19144998C211yesmaximal, characteristic, complemented
4#19133929C214yesmaximal, complemented
5#19133893C214yesmaximal, complemented
6#19133222C211yesmaximal, characteristic, complemented
7#19133197C211yesmaximal, characteristic, complemented
8#19133193C211yesmaximal, characteristic, complemented
9C2×C43×#563C211yesmaximal, characteristic, complemented
10#14583449C2211yescharacteristic
11#14583309C2212yescomplemented
12#14583289C2212yes—
13#14583269C2212yescomplemented
14#14583265C2212yescomplemented
15#14583265C2212yescomplemented
16#14583258C2212yes—
17#14583256—22no—
18#14583217—21no—
19#14583212—21no—
20#14583196—22no—
21#14583111—22no—
22#14583038—21no—
23#14583033—21no—
24#14582956C2211yescharacteristic
25#14582956C2211yescharacteristic
26#14582898—21no—
27#14582898—21no—
28C4×#10621877C2211yescharacteristic
29#14582641C2214yescomplemented
30#14582641C2214yescomplemented
31#14582639C2214yes—
32C43×#563—22no—
33C43×#563—22no—
34C43×#563—22no—
35C43×#563C2214yes—
36C2×C4⋊Q8×C43—21no—
37C2×#126×C43—21no—
38C2×#126×C43—21no—
39C2×#125×C43C2211yescharacteristic
40C2×#125×C43C2211yescharacteristic
41C2×#124×C43C2211yescharacteristic
42C2×#123×C43—21no—
43C2×C22⋊Q8×C43—21no—
44C2×C22⋊Q8×C43—21no—
45C2×#10621898—21no—
46C2×#10621884—22no—
47C2×#10621882—22no—
48C2×#10621877—21no—
49#13063325C2311yescharacteristic
50#13063322C2311yescharacteristic
51#13063313—21no—
52#13063299—21no—
53#13063299—21no—
54C4×D172—21no—
55C4×D172—21no—
56#13063258—22no—
57#13063256—22no—
58C4⋊(C43⋊C8)—21no—
59C4⋊(C43⋊C8)—21no—
60#13063249—22no—
61#13063248—22no—
62#13063248—22no—
63#13063246—22no—
64#13063245—22no—
65#13063245—22no—
66#13063245—22no—
67#13063245—22no—
68C22⋊(C43⋊C8)—21no—
69C22⋊(C43⋊C8)—21no—
70#13063236C2312yes—
71#13063236C2312yes—
72#13063236C2312yes—
73C4×C43⋊C8—21no—
74C22×Q8×C43—21no—
75C22×Q8×C43D411yescharacteristic
76C22×D4×C43D411yescharacteristic
77C23×C4×C43—21no—
78C4⋊Q8×C43—24no—
79C4⋊Q8×C43—24no—
80#126×C43—24no—
81#126×C43—24no—
82#126×C43—24no—
83#126×C43—24no—
84#125×C43—21no—
85#125×C43—21no—
86#125×C43—21no—
87#125×C43—21no—
88#125×C43D412yes—
89#125×C43D412yes—
90#125×C43C2312yes—
91#125×C43C2312yes—
92#124×C43—21no—
93#124×C43—21no—
94#124×C43D412yes—
95#124×C43C2312yes—
96#123×C43—24no—
97#123×C43—24no—
98C22⋊Q8×C43—24no—
99C22⋊Q8×C43—24no—
100C22⋊Q8×C43—24no—
101C22⋊Q8×C43—24no—
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×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43C2311yescharacteristic
119C24×C43—21no—
120C2×Q8×C43—24no—
121C2×Q8×C43—21no—
122C2×Q8×C43—81no—
123C2×Q8×C43—82no—
124C2×Q8×C43C2×D412yes—
125C2×D4×C43—21no—
126C2×D4×C43—81no—
127C2×D4×C43C2×D412yes—
128C22×C4×C43—24no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—82no—
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C2×C22⋊D43—41no—
139#10621898—44no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×C4×D43—41no—
144C2×Dic86—21no—
145C4⋊C4×C43—24no—
146C4⋊C4×C43—24no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43C2×D412yes—
160C4⋊C4×C43C2×D412yes—
161C4⋊C4×C43C2×D412yes—
162C4⋊C4×C43C2×D412yes—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C42×C43—24no—
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2411yescharacteristic
175#10621884—82no—
176#10621882—82no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—41no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181#10621877—42no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C23×C43—22no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43#12011yescharacteristic
190C22×D43—41no—
191Q8×C43—42no—
192Q8×C43—81no—
193Q8×C43—84no—
194D4×C43—42no—
195D4×C43—81no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—84no—
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C22⋊D43—82no—
217C2×Dic43—41no—
218D172—42no—
219D172—42no—
220D172—42no—
221C4×D43—82no—
222Dic86—42no—
223C43⋊C8—42no—
224C43⋊C8—42no—
225C43⋊C8—42no—
226#19002—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—42no—
232C22×C43—84no—
233C22×C43#45412yes—
234C22×C43C2×#12011yescharacteristic
235C2×D43—81no—
236C2×D43—81no—
237C2×D43—81no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—42no—
245C4×C43—42no—
246C4×C43—42no—
247C4×C43—42no—
248C4×C43—42no—
249Dic43—81no—
250C2×#563D4311yescharacteristic, complemented
251#3234—431no—
252#3213—431no—
253#3142—431no—
254#1664—434no—
255#1657—434no—
256#1534—431no—
257#1528—431no—
258#1527—431no—
259C2×C43—22no—
260C2×C43—82no—
261C2×C43C2×#45411yescharacteristic
262C2×C43#301911yescharacteristic
263C2×C43#302011yescharacteristic
264D43—161no—
265#563—22no—
266#563—22no—
267#563—22no—
268#563C2×D4314yes—
269#532—431no—
270C2×C4⋊Q8—21no—
271C2×#126—21no—
272C2×#126—21no—
273C2×#125C2×D4311yescharacteristic
274C2×#125C2×D4311yescharacteristic
275C2×#124C2×D4311yescharacteristic
276C2×#123—21no—
277C2×C22⋊Q8—21no—
278C2×C22⋊Q8—21no—
279#501—432no—
280#496—432no—
281#491—432no—
282#490—432no—
283#490—432no—
284#489—432no—
285#488—862no—
286#481—861no—
287#480—861no—
288#478—862no—
289#463—862no—
290#448—861no—
291#447—861no—
292#432—431no—
293#432—431no—
294#417—861no—
295#417—861no—
296C4×M16—431no—
297#330—434no—
298#330—434no—
299#329—434no—
300C43#1900211yescharacteristic, complemented, Sylow
301C2×#41—861no—
302C22×Q8—21no—
303C22×Q8C22⋊D4311yescharacteristic
304C22×D4C22⋊D4311yescharacteristic
305C23×C4—21no—
306C2×SD16—862no—
307C2×D8—862no—
308C2×M16—861no—
309C4⋊Q8—24no—
310C4⋊Q8—24no—
311C4⋊Q8—431no—
312#127—431no—
313#126—24no—
314#126—24no—
315#126—24no—
316#126—24no—
317#125—21no—
318#125—21no—
319#125—21no—
320#125—21no—
321#125C22⋊D4312yes—
322#125C22⋊D4312yes—
323#125C22×D4312yes—
324#125C22×D4312yes—
325#124—21no—
326#124—21no—
327#124—861no—
328#124C22⋊D4312yes—
329#124C22×D4312yes—
330#123—24no—
331#123—24no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—24no—
335C22⋊Q8—24no—
336#121—861no—
337#121—861no—
338C4×D4—861no—
339C4×D4—861no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4C22⋊D4311yescharacteristic
347C2×C4⋊C4C22⋊D4311yescharacteristic
348C2×C4⋊C4C22⋊D4311yescharacteristic
349C2×C4⋊C4C22⋊D4311yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42—21no—
356C2×C42C22×D4311yescharacteristic
357#107—862no—
358#106—862no—
359C4⋊C8—861no—
360C4⋊C8—861no—
361#103—862no—
362#103—862no—
363#103—862no—
364#102—862no—
365#102—862no—
366#102—862no—
367#102—862no—
368#102—862no—
369C22⋊C8—861no—
370C22⋊C8—861no—
371#97—432no—
372#97—432no—
373#97—432no—
374C4×C8—861no—
375C24—21no—
376#41—1724no—
377C2×Q8—24no—
378C2×Q8—21no—
379C2×Q8—81no—
380C2×Q8—82no—
381C2×Q8—861no—
382C2×Q8C2×C22⋊D4312yes—
383C2×D4—21no—
384C2×D4—81no—
385C2×D4—861no—
386C2×D4—861no—
387C2×D4—861no—
388C2×D4—1721no—
389C2×D4C2×C22⋊D4312yes—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—24no—
396C22×C4—82no—
397C22×C4—1721no—
398C22×C4C2×C22⋊D4311yescharacteristic
399C22×C4C2×C22⋊D4311yescharacteristic
400C22×C4C2×C22⋊D4311yescharacteristic
401SD16—3442no—
402D8—3442no—
403M16—1722no—
404C2×C8—862no—
405C2×C8—862no—
406C2×C8—862no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C4⋊C4C2×C22⋊D4312yes—
424C4⋊C4C2×C22⋊D4312yes—
425C4⋊C4C2×C22⋊D4312yes—
426C4⋊C4C2×C22⋊D4312yes—
427C22⋊C4—24no—
428C22⋊C4—24no—
429C22⋊C4—24no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—22no—
434C22⋊C4—1721no—
435C22⋊C4—1721no—
436C42—24no—
437C42C2×C22⋊D4311yescharacteristic
438C42C2×C22⋊D4311yescharacteristic
439C42C2×C22⋊D4311yescharacteristic
440C42C23×D4311yescharacteristic
441C23—22no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—1721no—
446C23#1306329411yescharacteristic
447Q8—42no—
448Q8—81no—
449Q8—84no—
450Q8—1722no—
451D4—42no—
452D4—81no—
453D4—3442no—
454D4—1722no—
455D4—1722no—
456D4—1722no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—84no—
471C2×C4—3442no—
472C2×C4—1721no—
473C2×C4#1306329411yescharacteristic
474C2×C4#1306329411yescharacteristic
475C2×C4#1306329411yescharacteristic
476C2×C4C22×C22⋊D4311yescharacteristic
477C2×C4C22×C22⋊D4311yescharacteristic
478C2×C4C22×C22⋊D4311yescharacteristic
479C8—1722no—
480C8—1722no—
481C8—1722no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—84no—
488C22—3441no—
489C22—3441no—
490C22—3441no—
491C22#1458307212yes—
492C22C2×#1306329411yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—42no—
500C4—42no—
501C4—42no—
502C4—42no—
503C4—42no—
504C4—3441no—
505C2—22no—
506C2—82no—
507C2—6881no—
508C2C2×#1458307211yescharacteristic
509C2#1914395211yescharacteristic
510C2#1914395911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#563C2
socleC22×C43C2×#120
prime radical#19145582C2
hypercenterC2×#563D43
hypocenterC43#19002
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. #19145785C2semidirect
3. #19144998C2semidirect
4. #19133929C2semidirect
5. #19133893C2semidirect
6. #19133222C2semidirect
7. #19133197C2semidirect
8. #19133193C2semidirect
9. C2×C43×#563C2semidirect
11. #14583309C22semidirect
13. #14583269C22semidirect
14. #14583265C22semidirect
15. #14583265C22semidirect
29. #14582641C22semidirect
30. #14582641C22semidirect
250. C2×#563D43semidirect
300. C43#19002semidirect

Maximal subgroups

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

subgroupindex
#191457852
#191455822
#191449982
#191339292
#191338932
#191332222
#191331972
#191331932
C2×C43×#5632
#1900243