Finite Group Databasebeta

← #25079414

Subgroups — #25079414

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144599C211yesmaximal, characteristic
2C2×#14583176C211yesmaximal, characteristic
3M16×D172C211yesmaximal, characteristic
4#19134167C212yesmaximal, complemented
5#19134139C212yesmaximal, complemented
6#19134043C212yesmaximal, complemented
7#19134015C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10#19133267C211yesmaximal, characteristic, complemented
11C43×#3139C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13C2×C4×D172C2211yescharacteristic
14#14583227—21no—
15#14583186C2211yescharacteristic
16#14583186C2211yescharacteristic
17#14583176—21no—
18#14583176—21no—
19#14583176C2212yes—
20#14583176C2212yes—
21#14583101C2211yescharacteristic
22#14583101C2211yescharacteristic
23#14583049—21no—
24C4×#10621884—21no—
25C4×#10621884—21no—
26#14582978C2212yes—
27#14582972—22no—
28C8×D172C2212yes—
29#14582952C2211yescharacteristic
30C2×#13063258—21no—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063245—21no—
34#14582862—21no—
35#14582652C2212yescomplemented
36#14582650C2212yescomplemented
37#14582648C2212yescomplemented
38#14582645C2212yescomplemented
39#14582645C2212yescomplemented
40#14582645C2212yescomplemented
41C43×#533C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#491—22no—
44C43×#487C2212yescomplemented
45C43×#487C2212yescomplemented
46C43×#419—21no—
47C43×#419—21no—
48C4×M16×C43C2211yescharacteristic
49C22×D172D411yescharacteristic
50C22×C4×D43—21no—
51C2×#10621884—21no—
52C2×#10621884—21no—
53C2×#10621877—21no—
54C2×#10621872—22no—
55M16×D43—44no—
56C22×C43⋊C8—21no—
57C2×C8×D43—22no—
58C4×D172—21no—
59C4×D172—21no—
60C4×D172D411yescharacteristic
61C4×D172D411yescharacteristic
62C4×D172C2311yescharacteristic
63C4×D172C2311yescharacteristic
64C2×C4⋊Dic43D411yescharacteristic
65C2×(C2×D43)⋊C4—21no—
66#13063258—22no—
67#13063258—22no—
68#13063256—21no—
69#13063256—21no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)C2311yescharacteristic
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2312yes—
75C4⋊(C43⋊C8)C2312yes—
76#13063249—21no—
77#13063249—21no—
78#13063245—21no—
79#13063245—21no—
80#13063245—22no—
81#13063245—22no—
82C22⋊(C43⋊C8)—21no—
83(C2×D43)⋊C8—22no—
84(C2×D43)⋊C8—22no—
85C4×C43⋊C8—21no—
86C22×Q8×C43—21no—
87C2×M16×C43D411yescharacteristic
88C2×M16×C43D411yescharacteristic
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43C2312yes—
93C4⋊Q8×C43C2311yescharacteristic
94C4⋊Q8×C43C2311yescharacteristic
95#125×C43—21no—
96C22⋊Q8×C43—21no—
97C22⋊Q8×C43—21no—
98C4×Q8×C43—21no—
99C4×Q8×C43—21no—
100#117×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#103×C43—22no—
105#103×C43—22no—
106#103×C43—22no—
107#103×C43—22no—
108#97×C43D412yes—
109C4×C8×C43C2312yes—
110C23×D43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—41no—
115C2×Q8×C43—42no—
116C2×Q8×C43—42no—
117C22×C4×C43—41no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C22×Dic43—21no—
122C2×D172—21no—
123C2×D172—22no—
124C2×D172—41no—
125C2×D172C2×D411yescharacteristic
126C2×D172C2×D411yescharacteristic
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×C4×D43—21no—
130C2×C4×D43—21no—
131C2×C4×D43—42no—
132C2×C4×D43—42no—
133M16×C43—22no—
134M16×C43—22no—
135C2×C8×C43C2×D412yes—
136C2×C8×C43C2×D412yes—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C42×C43—41no—
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43#4111yescharacteristic
152C42×C43C2411yescharacteristic
153#10621884—42no—
154#10621884—42no—
155(C2×D43)⋊C4—21no—
156(C2×D43)⋊C4—21no—
157(C2×D43)⋊C4—21no—
158(C2×D43)⋊C4—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43C2×D411yescharacteristic
161C4⋊Dic43C2×D411yescharacteristic
162#10621877—42no—
163C2×C43⋊C8—21no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8—42no—
168#10621872—44no—
169C8×D43—44no—
170C23×C43#12111yescharacteristic
171C22×D43—21no—
172C22×D43—21no—
173C22×D43—42no—
174C22×D43—42no—
175C22×D43—81no—
176Q8×C43—42no—
177Q8×C43—42no—
178Q8×C43—41no—
179Q8×C43—41no—
180Q8×C43—81no—
181Q8×C43—82no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—42no—
188C2×C4×C43—82no—
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43#13512yes—
193C2×C4×C43AGL(1,ℤ/8)12yes—
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C22×D411yescharacteristic
196C2×C4×C43C2×#4111yescharacteristic
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—42no—
200D172—21no—
201D172—21no—
202D172—21no—
203D172—42no—
204D172#13712yes—
205C4×D43—41no—
206C4×D43—41no—
207C4×D43—41no—
208C4×D43—41no—
209C4×D43—42no—
210C4×D43—42no—
211C8×C43—22no—
212C8×C43—22no—
213C43⋊C8—42no—
214C43⋊C8—41no—
215C43⋊C8—42no—
216C43⋊C8—41no—
217#19167—431nomaximal, Sylow
218C22×C43—21no—
219C22×C43—21no—
220C22×C43#46312yes—
221C22×C43C2×#12111yescharacteristic
222C2×D43—22no—
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—41no—
227C2×D43—41no—
228C2×D43—84no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—82no—
233C4×C43—81no—
234C4×C43—81no—
235C4×C43#46312yes—
236C4×C43C2×#13511yescharacteristic
237C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C43C2×#13711yescharacteristic
239C4×C43#57511yescharacteristic
240Dic43—41no—
241Dic43—41no—
242#3139D4311yescharacteristic, complemented
243#3101—431no—
244C2×#474—431no—
245D4×M16—431no—
246#1703—432no—
247#1699—432no—
248#1683—432no—
249#1679—432no—
250#1565—431no—
251#1550—431no—
252#1546—431no—
253C2×C43—22no—
254C2×C43C2×#46311yescharacteristic
255C2×C43#305611yescharacteristic
256C2×C43#306911yescharacteristic
257D43—42no—
258D43—81no—
259C22×M16—861no—
260#533C2×D4311yescharacteristic
261C2×C4⋊Q8C2×D4311yescharacteristic
262C2×C4×D4—431no—
263#491—22no—
264#487C2×D4312yescomplemented
265#487C2×D4312yescomplemented
266#483—861no—
267#476—431no—
268#476—431no—
269#474—432no—
270#474—432no—
271#474—861no—
272#474—861no—
273#461—431no—
274#461—431no—
275#450—861no—
276C4×SD16—861no—
277C4×SD16—861no—
278#436—432no—
279#435—862no—
280C8×D4—432no—
281#431—431no—
282C2×#107—861no—
283#423—431no—
284C2×C4⋊C8—431no—
285#419—21no—
286#419—21no—
287C2×#102—861no—
288#407—861no—
289C4×M16C2×D4311yescharacteristic
290#335—432no—
291#334—432no—
292#333—432no—
293#332—432no—
294#332—432no—
295#332—432no—
296C43#1916711yescharacteristic, complemented, Sylow
297C22×Q8—21no—
298C22×D4—431no—
299C23×C4—861no—
300C2×SD16—861no—
301C2×SD16—861no—
302C2×M16—861no—
303C2×M16—862no—
304C2×M16—1724no—
305C2×M16C22⋊D4311yescharacteristic
306C2×M16C22⋊D4311yescharacteristic
307C22×C8—861no—
308C22×C8—862no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8—21no—
312C4⋊Q8C22×D4312yes—
313C4⋊Q8C22×D4311yescharacteristic
314C4⋊Q8C22×D4311yescharacteristic
315#125—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×D4—431no—
321C4×D4—431no—
322C4×D4—431no—
323C4×D4—431no—
324C4×D4—861no—
325C4×D4—861no—
326#117—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—431no—
330C2×C22⋊C4—861no—
331C2×C42C22×D4311yescharacteristic
332#107—862no—
333#107—862no—
334#106—861no—
335#106—861no—
336C4⋊C8—432no—
337C4⋊C8—431no—
338C4⋊C8—431no—
339C4⋊C8—432no—
340C4⋊C8—861no—
341C4⋊C8—861no—
342#103—22no—
343#103—22no—
344#103—22no—
345#103—22no—
346#103—861no—
347#103—861no—
348#102—862no—
349#102—862no—
350#102—861no—
351#102—861no—
352C22⋊C8—861no—
353C22⋊C8—862no—
354C22⋊C8—862no—
355#97C22⋊D4312yes—
356C4×C8—861no—
357C4×C8C22×D4312yes—
358C24—861no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—21no—
362C2×Q8—41no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×D4—431no—
366C2×D4—431no—
367C2×D4—862no—
368C2×D4—861no—
369C2×D4—1721no—
370C22×C4—41no—
371C22×C4—861no—
372C22×C4—861no—
373C22×C4—861no—
374C22×C4—861no—
375C22×C4—861no—
376C22×C4—1722no—
377C22×C4—1722no—
378C22×C4D4×D4311yescharacteristic
379C22×C4#1062190011yescharacteristic
380C22×C4C2×C22⋊D4311yescharacteristic
381SD16—1722no—
382SD16—1722no—
383M16—22no—
384M16—22no—
385M16—1724no—
386M16—1722no—
387C2×C8—861no—
388C2×C8—861no—
389C2×C8—862no—
390C2×C8—862no—
391C2×C8—1724no—
392C2×C8—1722no—
393C2×C8C2×C22⋊D4312yes—
394C2×C8C2×C22⋊D4312yes—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—431no—
406C4⋊C4—431no—
407C4⋊C4—861no—
408C22⋊C4—41no—
409C22⋊C4—861no—
410C22⋊C4—861no—
411C22⋊C4—861no—
412C22⋊C4—861no—
413C42—41no—
414C42D4×D4311yescharacteristic
415C42#1062190011yescharacteristic
416C42C2×C22⋊D4311yescharacteristic
417C42C23×D4311yescharacteristic
418C23—861no—
419C23—861no—
420C23—3441no—
421C23—1722no—
422C23—1722no—
423C23#1306329611yescharacteristic
424Q8—42no—
425Q8—42no—
426Q8—41no—
427Q8—41no—
428Q8—81no—
429Q8—82no—
430D4—432no—
431D4—861no—
432D4—861no—
433D4—861no—
434D4—1722no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—82no—
442C2×C4—861no—
443C2×C4—861no—
444C2×C4—1722no—
445C2×C4—1722no—
446C2×C4—1722no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4#1306329611yescharacteristic
452C2×C4#1306329611yescharacteristic
453C2×C4#1306329611yescharacteristic
454C2×C4#1306334512yes—
455C2×C4#1306335012yes—
456C2×C4C2×D4×D4311yescharacteristic
457C2×C4C22×C22⋊D4311yescharacteristic
458C2×C4C2×#1062190011yescharacteristic
459C8—22no—
460C8—22no—
461C8—1722no—
462C8—1721no—
463C8—1722no—
464C8—1721no—
465C22—21no—
466C22—21no—
467C22—862no—
468C22—3444no—
469C22—1721no—
470C22—1721no—
471C22—1721no—
472C22—1721no—
473C22—1721no—
474C22#1458311112yes—
475C22C2×#1306329611yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—81no—
480C4—82no—
481C4—81no—
482C4—1721no—
483C4—1721no—
484C4#1458311112yes—
485C4C2×#1306334511yescharacteristic
486C4C2×#1306335011yescharacteristic
487C4#137×D4311yescharacteristic
488C4#1458369811yescharacteristic
489C2—22no—
490C2—3441no—
491C2—1722no—
492C2C2×#1458311111yescharacteristic
493C2#1914421911yescharacteristic
494C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3139C2
socleC22×C43C2×#121
prime radicalC22×D172D4
hypercenter#3139D43
hypocenterC43#19167
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
4. #19134167C2semidirect
5. #19134139C2semidirect
6. #19134043C2semidirect
7. #19134015C2semidirect
8. #19133347C2semidirect
9. #19133285C2semidirect
10. #19133267C2semidirect
11. C43×#3139C2semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582648C22semidirect
38. #14582645C22semidirect
39. #14582645C22semidirect
40. #14582645C22semidirect
44. C43×#487C22semidirect
45. C43×#487C22semidirect
242. #3139D43semidirect
264. #487C2×D43semidirect
265. #487C2×D43semidirect
296. C43#19167semidirect

Maximal subgroups

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

subgroupindex
#191445992
C2×#145831762
M16×D1722
#191341672
#191341392
#191340432
#191340152
#191333472
#191332852
#191332672
C43×#31392
#1916743