Finite Group Databasebeta

← #25079425

Subgroups — #25079425

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144591C211yesmaximal, characteristic
2C2×#14583186C211yesmaximal, characteristic, complemented
3M16×D172C211yesmaximal, characteristic, complemented
4#19134167C212yesmaximal, complemented
5#19134125C212yesmaximal, complemented
6#19134043C212yesmaximal, complemented
7#19134001C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133276C211yesmaximal, characteristic, complemented
10#19133272C211yesmaximal, characteristic, complemented
11C43×#3141C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13C2×C4×D172C2211yescharacteristic
14#14583210—21no—
15#14583186—21no—
16#14583186—21no—
17#14583186C2212yes—
18#14583186C2212yes—
19#14583176C2211yescharacteristic
20#14583176C2211yescharacteristic
21#14583091C2211yescharacteristic
22#14583091C2211yescharacteristic
23#14583032—21no—
24C4×#10621882—21no—
25C4×#10621882—21no—
26#14582978C2212yes—
27#14582972—22no—
28C8×D172C2212yes—
29#14582952C2211yescharacteristic
30C2×#13063256—21no—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063245—21no—
34#14582862—21no—
35#14582652C2212yescomplemented
36#14582650C2212yescomplemented
37#14582648C2212yescomplemented
38#14582648C2212yescomplemented
39#14582645C2212yescomplemented
40#14582643C2212yescomplemented
41C43×#532C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#489—22no—
44C43×#487C2212yescomplemented
45C43×#486C2212yescomplemented
46C43×#417—21no—
47C43×#417—21no—
48C4×M16×C43C2211yescharacteristic
49C22×D172D411yescharacteristic
50C22×C4×D43—21no—
51C2×#10621882—21no—
52C2×#10621882—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—21no—
67#13063258—21no—
68#13063256—22no—
69#13063256—22no—
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#13063246—21no—
77#13063246—21no—
78#13063245—22no—
79#13063245—22no—
80#13063245—21no—
81#13063245—21no—
82C22⋊(C43⋊C8)—21no—
83(C2×D43)⋊C8—22no—
84(C2×D43)⋊C8—22no—
85C4×C43⋊C8—21no—
86C2×#41×C43—21no—
87C22×Q8×C43—21no—
88C2×M16×C43D411yescharacteristic
89C2×M16×C43D411yescharacteristic
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43C2312yes—
94C4⋊Q8×C43C2311yescharacteristic
95#127×C43C2311yescharacteristic
96#124×C43—21no—
97#121×C43—21no—
98#121×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#103×C43—22no—
105#103×C43—22no—
106#102×C43—22no—
107#102×C43—22no—
108#97×C43D412yes—
109C4×C8×C43C2312yes—
110C23×D43—21no—
111#41×C43—42no—
112#41×C43—42no—
113C2×Q8×C43—21no—
114C2×Q8×C43—22no—
115C2×Q8×C43—41no—
116C2×Q8×C43—82no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C22×Dic43—21no—
127C2×D172—21no—
128C2×D172—22no—
129C2×D172—41no—
130C2×D172C2×D411yescharacteristic
131C2×D172C2×D411yescharacteristic
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—42no—
137C2×C4×D43—42no—
138M16×C43—22no—
139M16×C43—22no—
140C2×C8×C43C2×D412yes—
141C2×C8×C43C2×D412yes—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—41no—
147C4⋊C4×C43—41no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154#10621882—42no—
155#10621882—42no—
156(C2×D43)⋊C4—21no—
157(C2×D43)⋊C4—21no—
158(C2×D43)⋊C4—21no—
159(C2×D43)⋊C4—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43C2×D411yescharacteristic
162C4⋊Dic43C2×D411yescharacteristic
163#10621877—42no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—42no—
169#10621872—44no—
170C8×D43—44no—
171C23×C43—41no—
172C23×C43#12111yescharacteristic
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—42no—
176C22×D43—42no—
177C22×D43—81no—
178Q8×C43—41no—
179Q8×C43—41no—
180Q8×C43—82no—
181Q8×C43—82no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—41no—
186D4×C43—81no—
187D4×C43—82no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—82no—
194C2×C4×C43—82no—
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#13512yes—
199C2×C4×C43AGL(1,ℤ/8)12yes—
200C2×C4×C43C22×D411yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C2×#4111yescharacteristic
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—42no—
206D172—21no—
207D172—21no—
208D172—21no—
209D172—42no—
210D172#13712yes—
211C4×D43—41no—
212C4×D43—41no—
213C4×D43—41no—
214C4×D43—41no—
215C4×D43—42no—
216C4×D43—42no—
217C8×C43—22no—
218C8×C43—22no—
219C43⋊C8—42no—
220C43⋊C8—41no—
221C43⋊C8—42no—
222C43⋊C8—41no—
223#19168—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43#46312yes—
230C22×C43C2×#12111yescharacteristic
231C2×D43—22no—
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—41no—
235C2×D43—41no—
236C2×D43—41no—
237C2×D43—84no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—81no—
242C4×C43—82no—
243C4×C43#46312yes—
244C4×C43C2×#13511yescharacteristic
245C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C43C2×#13711yescharacteristic
247C4×C43#57511yescharacteristic
248Dic43—41no—
249Dic43—41no—
250#3141D4311yescharacteristic, complemented
251#3100—431no—
252C2×#476—431no—
253D4×M16—431no—
254#1703—432no—
255#1697—432no—
256#1683—432no—
257#1677—432no—
258#1565—431no—
259#1548—431no—
260#1547—431no—
261C2×C43—22no—
262C2×C43—161no—
263C2×C43C2×#46311yescharacteristic
264C2×C43#305611yescharacteristic
265C2×C43#306811yescharacteristic
266D43—42no—
267D43—81no—
268C22×M16—861no—
269#532C2×D4311yescharacteristic
270C2×C4⋊Q8C2×D4311yescharacteristic
271C2×C4×D4—431no—
272#489—22no—
273#487C2×D4312yescomplemented
274#486C2×D4312yescomplemented
275#480—861no—
276#476—432no—
277#476—432no—
278#476—861no—
279#476—861no—
280#474—431no—
281#474—431no—
282#459—431no—
283#459—431no—
284#447—861no—
285C4×D8—861no—
286C4×D8—861no—
287#436—432no—
288#435—862no—
289C8×D4—432no—
290#431—431no—
291C2×#106—861no—
292#423—431no—
293C2×C4⋊C8—431no—
294#417—21no—
295#417—21no—
296C2×#102—861no—
297#407—861no—
298C4×M16C2×D4311yescharacteristic
299#335—432no—
300#334—432no—
301#333—432no—
302#333—432no—
303#332—432no—
304#331—432no—
305C43#1916811yescharacteristic, complemented, Sylow
306C2×#41—21no—
307C22×Q8—21no—
308C22×D4—431no—
309C23×C4—861no—
310C2×D8—861no—
311C2×D8—861no—
312C2×M16—861no—
313C2×M16—862no—
314C2×M16—1724no—
315C2×M16C22⋊D4311yescharacteristic
316C2×M16C22⋊D4311yescharacteristic
317C22×C8—861no—
318C22×C8—862no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8C22×D4312yes—
323C4⋊Q8C22×D4311yescharacteristic
324#127C22×D4311yescharacteristic
325#124—21no—
326#121—21no—
327#121—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—431no—
331C4×D4—431no—
332C4×D4—431no—
333C4×D4—431no—
334C4×D4—861no—
335C4×D4—861no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—431no—
339C2×C22⋊C4—861no—
340C2×C42C22×D4311yescharacteristic
341#107—861no—
342#107—861no—
343#106—862no—
344#106—862no—
345C4⋊C8—432no—
346C4⋊C8—432no—
347C4⋊C8—431no—
348C4⋊C8—431no—
349C4⋊C8—861no—
350C4⋊C8—861no—
351#103—22no—
352#103—22no—
353#102—22no—
354#102—22no—
355#102—862no—
356#102—862no—
357#102—861no—
358#102—861no—
359#102—861no—
360#102—861no—
361C22⋊C8—861no—
362C22⋊C8—862no—
363C22⋊C8—862no—
364#97C22⋊D4312yes—
365C4×C8—861no—
366C4×C8C22×D4312yes—
367C24—861no—
368#41—42no—
369#41—42no—
370C2×Q8—21no—
371C2×Q8—22no—
372C2×Q8—41no—
373C2×Q8—82no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—431no—
379C2×D4—431no—
380C2×D4—862no—
381C2×D4—861no—
382C2×D4—1721no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—861no—
390C22×C4—1722no—
391C22×C4—1722no—
392C22×C4D4×D4311yescharacteristic
393C22×C4#1062190011yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395D8—1722no—
396D8—1722no—
397M16—22no—
398M16—22no—
399M16—1724no—
400M16—1722no—
401C2×C8—861no—
402C2×C8—861no—
403C2×C8—862no—
404C2×C8—862no—
405C2×C8—1724no—
406C2×C8—1722no—
407C2×C8C2×C22⋊D4312yes—
408C2×C8C2×C22⋊D4312yes—
409C4⋊C4—22no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—431no—
416C4⋊C4—431no—
417C4⋊C4—861no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—861no—
421C22⋊C4—861no—
422C22⋊C4—861no—
423C22⋊C4—861no—
424C42D4×D4311yescharacteristic
425C42#1062190011yescharacteristic
426C42C2×C22⋊D4311yescharacteristic
427C42C23×D4311yescharacteristic
428C23—41no—
429C23—861no—
430C23—861no—
431C23—3441no—
432C23—1722no—
433C23—1722no—
434C23#1306329611yescharacteristic
435Q8—41no—
436Q8—41no—
437Q8—82no—
438Q8—82no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—81no—
444D4—82no—
445D4—432no—
446D4—861no—
447D4—861no—
448D4—861no—
449D4—1722no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—82no—
456C2×C4—82no—
457C2×C4—861no—
458C2×C4—861no—
459C2×C4—1722no—
460C2×C4—1722no—
461C2×C4—1722no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4#1306329611yescharacteristic
467C2×C4#1306329611yescharacteristic
468C2×C4#1306329611yescharacteristic
469C2×C4#1306334512yes—
470C2×C4#1306335012yes—
471C2×C4C2×D4×D4311yescharacteristic
472C2×C4C22×C22⋊D4311yescharacteristic
473C2×C4C2×#1062190011yescharacteristic
474C8—22no—
475C8—22no—
476C8—1722no—
477C8—1721no—
478C8—1722no—
479C8—1721no—
480C22—21no—
481C22—21no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—862no—
486C22—3444no—
487C22—1721no—
488C22—1721no—
489C22—1721no—
490C22—1721no—
491C22—1721no—
492C22#1458311112yes—
493C22C2×#1306329611yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—81no—
498C4—82no—
499C4—1721no—
500C4—1721no—
501C4#1458311112yes—
502C4C2×#1306334511yescharacteristic
503C4C2×#1306335011yescharacteristic
504C4#137×D4311yescharacteristic
505C4#1458369811yescharacteristic
506C2—22no—
507C2—161no—
508C2—3441no—
509C2—1722no—
510C2C2×#1458311111yescharacteristic
511C2#1914421911yescharacteristic
512C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3141C2
socleC22×C43C2×#121
prime radical#19144591C2
hypercenter#3141D43
hypocenterC43#19168
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
2. C2×#14583186C2semidirect
3. M16×D172C2semidirect
4. #19134167C2semidirect
5. #19134125C2semidirect
6. #19134043C2semidirect
7. #19134001C2semidirect
8. #19133347C2semidirect
9. #19133276C2semidirect
10. #19133272C2semidirect
11. C43×#3141C2semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582648C22semidirect
38. #14582648C22semidirect
39. #14582645C22semidirect
40. #14582643C22semidirect
44. C43×#487C22semidirect
45. C43×#486C22semidirect
250. #3141D43semidirect
273. #487C2×D43semidirect
274. #486C2×D43semidirect
305. C43#19168semidirect

Maximal subgroups

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

subgroupindex
#191445912
C2×#145831862
M16×D1722
#191341672
#191341252
#191340432
#191340012
#191333472
#191332762
#191332722
C43×#31412
#1916843