Finite Group Databasebeta

← #25079392

Subgroups — #25079392

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144599C211yesmaximal, characteristic
2C2×#14583186C211yesmaximal, characteristic
3M16×D172C211yesmaximal, characteristic
4#19134115C212yesmaximal, complemented
5#19134091C212yesmaximal, complemented
6#19133991C212yesmaximal, complemented
7#19133967C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10#19133276C211yesmaximal, characteristic, complemented
11C43×#3165C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13C2×C4×D172C2211yescharacteristic
14#14583227—21no—
15#14583186—21no—
16#14583186—21no—
17#14583186C2212yes—
18#14583186C2211yescharacteristic
19#14583186C2212yes—
20#14583186C2211yescharacteristic
21#14583101C2211yescharacteristic
22#14583101C2211yescharacteristic
23#14583049—21no—
24C4×#10621884—21no—
25C4×#10621884—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#14582648C2212yescomplemented
40#14582645C2212yescomplemented
41C43×#533C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#501—22no—
44C43×#500C2212yescomplemented
45C43×#498C2212yescomplemented
46C43×#428—21no—
47C43×#428—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#13063256—22no—
67#13063256—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×C43C2311yescharacteristic
93C4⋊Q8×C43C2312yes—
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#107×C43—22no—
105#107×C43—22no—
106#106×C43—22no—
107#106×C43—22no—
108#97×C43D412yes—
109C4×C8×C43C2312yes—
110C23×D43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—22no—
114C2×Q8×C43—41no—
115C2×Q8×C43—82no—
116C22×C4×C43—41no—
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43#4111yescharacteristic
120C22×Dic43—21no—
121C2×D172—21no—
122C2×D172—22no—
123C2×D172—41no—
124C2×D172C2×D411yescharacteristic
125C2×D172C2×D411yescharacteristic
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×C4×D43—21no—
130C2×C4×D43—42no—
131C2×C4×D43—42no—
132M16×C43—22no—
133M16×C43SD1614yescomplemented
134C2×C8×C43C2×D412yes—
135C2×C8×C43C2×D412yes—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—22no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C42×C43—41no—
148C42×C43C2×D411yescharacteristic
149C42×C43C2×D411yescharacteristic
150C42×C43#4111yescharacteristic
151C42×C43C2411yescharacteristic
152#10621884—42no—
153#10621884—42no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156(C2×D43)⋊C4—21no—
157(C2×D43)⋊C4—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43C2×D411yescharacteristic
160C4⋊Dic43C2×D411yescharacteristic
161#10621877—42no—
162C2×C43⋊C8—21no—
163C2×C43⋊C8—21no—
164C2×C43⋊C8—22no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—42no—
167#10621872—44no—
168C8×D43—44no—
169C23×C43#12111yescharacteristic
170C22×D43—21no—
171C22×D43—21no—
172C22×D43—42no—
173C22×D43—42no—
174C22×D43—81no—
175Q8×C43—41no—
176Q8×C43—41no—
177Q8×C43—81no—
178Q8×C43—82no—
179Q8×C43—82no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—42no—
186C2×C4×C43—82no—
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43C2×SD1612yes—
191C2×C4×C43#13712yes—
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C2×#4111yescharacteristic
195C2×Dic43—21no—
196C2×Dic43—21no—
197C2×Dic43—42no—
198D172—21no—
199D172—21no—
200D172—21no—
201D172—42no—
202D172#13712yes—
203C4×D43—41no—
204C4×D43—41no—
205C4×D43—41no—
206C4×D43—41no—
207C4×D43—42no—
208C4×D43—42no—
209C8×C43—22no—
210C8×C43C2×SD1614yes—
211C43⋊C8—42no—
212C43⋊C8—41no—
213C43⋊C8—42no—
214C43⋊C8—41no—
215#19165—431nomaximal, Sylow
216C22×C43—21no—
217C22×C43—21no—
218C22×C43#46112yes—
219C22×C43C2×#12111yescharacteristic
220C2×D43—22no—
221C2×D43—41no—
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—84no—
227C4×C43—21no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—81no—
231C4×C43—82no—
232C4×C43—81no—
233C4×C43#46112yes—
234C4×C43C22×SD1611yescharacteristic
235C4×C43C2×#13711yescharacteristic
236C4×C43C2×#13711yescharacteristic
237C4×C43#57511yescharacteristic
238Dic43—41no—
239Dic43—41no—
240#3165D4311yescharacteristic, complemented
241#3101—431no—
242C2×#476—431no—
243D4×M16—431no—
244#1695—432no—
245#1691—432no—
246#1675—432no—
247#1671—432no—
248#1565—431no—
249#1550—431no—
250#1548—431no—
251C2×C43—22no—
252C2×C43C2×#46111yescharacteristic
253C2×C43#305611yescharacteristic
254C2×C43#306811yescharacteristic
255D43—42no—
256D43—81no—
257C22×M16—861no—
258#533C2×D4311yescharacteristic
259C2×C4⋊Q8C2×D4311yescharacteristic
260C2×C4×D4—431no—
261#501—22no—
262#500C2×D4312yescomplemented
263#498C2×D4312yescomplemented
264#483—861no—
265#476—431no—
266#476—431no—
267#476—432no—
268#476—432no—
269#476—861no—
270#476—861no—
271#461—431no—
272#461—431no—
273#450—861no—
274C4×SD16—861no—
275C4×SD16—861no—
276#436—432no—
277#435—862no—
278C8×D4—432no—
279#431—431no—
280#428—21no—
281#428—21no—
282C2×#106—861no—
283#423—431no—
284C2×C4⋊C8—431no—
285C2×#102—861no—
286#407—861no—
287C4×M16C2×D4311yescharacteristic
288#335—432no—
289#334—432no—
290#333—432no—
291#333—432no—
292#333—432no—
293#332—432no—
294C43#1916511yescharacteristic, complemented, Sylow
295C22×Q8—21no—
296C22×D4—431no—
297C23×C4—861no—
298C2×SD16—861no—
299C2×SD16—861no—
300C2×M16—861no—
301C2×M16—862no—
302C2×M16—1724no—
303C2×M16C22⋊D4311yescharacteristic
304C2×M16C22⋊D4311yescharacteristic
305C22×C8—861no—
306C22×C8—862no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8C22×D4312yes—
311C4⋊Q8C22×D4311yescharacteristic
312C4⋊Q8C22×D4311yescharacteristic
313#125—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×D4—431no—
319C4×D4—431no—
320C4×D4—431no—
321C4×D4—431no—
322C4×D4—861no—
323C4×D4—861no—
324#117—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—431no—
328C2×C22⋊C4—861no—
329C2×C42C22×D4311yescharacteristic
330#107—22no—
331#107—22no—
332#106—22no—
333#106—22no—
334#106—862no—
335#106—862no—
336#106—861no—
337#106—861no—
338C4⋊C8—432no—
339C4⋊C8—432no—
340C4⋊C8—431no—
341C4⋊C8—431no—
342C4⋊C8—861no—
343C4⋊C8—861no—
344#103—861no—
345#103—861no—
346#102—862no—
347#102—862no—
348#102—861no—
349#102—861no—
350C22⋊C8—861no—
351C22⋊C8—862no—
352C22⋊C8—862no—
353#97C22⋊D4312yes—
354C4×C8—861no—
355C4×C8C22×D4312yes—
356C24—861no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—82no—
362C2×D4—431no—
363C2×D4—431no—
364C2×D4—862no—
365C2×D4—861no—
366C2×D4—1721no—
367C22×C4—41no—
368C22×C4—861no—
369C22×C4—861no—
370C22×C4—861no—
371C22×C4—861no—
372C22×C4—861no—
373C22×C4—1722no—
374C22×C4—1722no—
375C22×C4D4×D4311yescharacteristic
376C22×C4#1062190011yescharacteristic
377C22×C4C2×C22⋊D4311yescharacteristic
378SD16—1722no—
379SD16—1722no—
380M16—22no—
381M16—1722no—
382M16—1724no—
383M16#1062188414yescomplemented
384C2×C8—861no—
385C2×C8—861no—
386C2×C8—862no—
387C2×C8—862no—
388C2×C8—1722no—
389C2×C8—1724no—
390C2×C8C2×C22⋊D4312yes—
391C2×C8C2×C22⋊D4312yes—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—431no—
403C4⋊C4—431no—
404C4⋊C4—861no—
405C22⋊C4—41no—
406C22⋊C4—861no—
407C22⋊C4—861no—
408C22⋊C4—861no—
409C22⋊C4—861no—
410C42—41no—
411C42D4×D4311yescharacteristic
412C42#1062190011yescharacteristic
413C42C2×C22⋊D4311yescharacteristic
414C42C23×D4311yescharacteristic
415C23—861no—
416C23—861no—
417C23—3441no—
418C23—1722no—
419C23—1722no—
420C23#1306329611yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—82no—
424Q8—81no—
425Q8—82no—
426D4—432no—
427D4—861no—
428D4—861no—
429D4—861no—
430D4—1722no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—82no—
438C2×C4—861no—
439C2×C4—861no—
440C2×C4—1722no—
441C2×C4—1722no—
442C2×C4—1722no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4#1306329611yescharacteristic
448C2×C4#1306329611yescharacteristic
449C2×C4#1306329611yescharacteristic
450C2×C4C2×#1062188412yes—
451C2×C4#1306335612yes—
452C2×C4C2×D4×D4311yescharacteristic
453C2×C4C22×C22⋊D4311yescharacteristic
454C2×C4C2×#1062190011yescharacteristic
455C8—22no—
456C8—1722no—
457C8—1721no—
458C8—1722no—
459C8—1721no—
460C8C2×#1062188414yes—
461C22—21no—
462C22—21no—
463C22—862no—
464C22—3444no—
465C22—1721no—
466C22—1721no—
467C22—1721no—
468C22—1721no—
469C22—1721no—
470C22#1458310112yes—
471C22C2×#1306329611yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—81no—
476C4—82no—
477C4—81no—
478C4—1721no—
479C4—1721no—
480C4#1458310112yes—
481C4C22×#1062188411yescharacteristic
482C4#137×D4311yescharacteristic
483C4C2×#1306335611yescharacteristic
484C4#1458369811yescharacteristic
485C2—22no—
486C2—3441no—
487C2—1722no—
488C2C2×#1458310111yescharacteristic
489C2#1914421911yescharacteristic
490C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3165C2
socleC22×C43C2×#121
prime radicalC22×D172D4
hypercenter#3165D43
hypocenterC43#19165
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
4. #19134115C2semidirect
5. #19134091C2semidirect
6. #19133991C2semidirect
7. #19133967C2semidirect
8. #19133347C2semidirect
9. #19133285C2semidirect
10. #19133276C2semidirect
11. C43×#3165C2semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582648C22semidirect
38. #14582648C22semidirect
39. #14582648C22semidirect
40. #14582645C22semidirect
44. C43×#500C22semidirect
45. C43×#498C22semidirect
133. M16×C43SD16semidirect
240. #3165D43semidirect
262. #500C2×D43semidirect
263. #498C2×D43semidirect
294. C43#19165semidirect
383. M16#10621884semidirect

Maximal subgroups

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

subgroupindex
#191445992
C2×#145831862
M16×D1722
#191341152
#191340912
#191339912
#191339672
#191333472
#191332852
#191332762
C43×#31652
#1916543