Finite Group Databasebeta

← #25081996

Subgroups — #25081996

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144377C211yesmaximal, characteristic, complemented
2#19144071C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic, complemented
4#19134008C212yesmaximal, complemented
5#19134001C212yesmaximal, complemented
6#19133940C212yesmaximal, complemented
7#19133933C212yesmaximal, complemented
8#19133366C211yesmaximal, characteristic, complemented
9#19133285C211yesmaximal, characteristic, complemented
10C2×#14582643C211yesmaximal, characteristic, complemented
11C43×#3208C211yesmaximal, characteristic, complemented
12C2×#13063351—21no—
13C4×#10621898C2211yescharacteristic
14#14583203—21no—
15#14583196—21no—
16#14583191C2211yescharacteristic, complemented
17#14583186C2211yescharacteristic, complemented
18#14583181C2211yescharacteristic, complemented
19#14583176C2211yescharacteristic, complemented
20#14583096—21no—
21#14583096C2212yes—
22#14583091—21no—
23#14583091C2212yes—
24C8×Dic86C2212yescomplemented
25C8×D172C2212yescomplemented
26(C22⋊D43)⋊C8—22no—
27#14582951—21no—
28#14582935—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C4⋊C8×D43—21no—
33#14582904—21no—
34#14582893—21no—
35#14582650C2212yescomplemented
36#14582650C2212yescomplemented
37#14582648C2212yescomplemented
38#14582645C2212yescomplemented
39#14582643C2212yes—
40#14582643C2212yes—
41C43×#533C2211yescharacteristic
42C2×#127×C43C2211yescharacteristic
43C43×#492C2212yes—
44C43×#486C2212yes—
45C43×#460—21no—
46C43×#460—21no—
47C43×#450—22no—
48C43×#431C2211yescharacteristic
49C2×#10621898D411yescharacteristic
50#13063351—44no—
51C2×#10621883—22no—
52C2×#10621882—22no—
53C2×#10621877—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C2×C8×D43—22no—
57C4×Dic86D411yescharacteristic
58C4×Dic86C2311yescharacteristic
59C4×D172D411yescharacteristic
60C4×D172C2311yescharacteristic
61C4×C22⋊D43—21no—
62C4×C22⋊D43—21no—
63#13063284D411yescharacteristic
64#13063282—21no—
65C42×D43—21no—
66#13063258—21no—
67#13063258—21no—
68#13063256—21no—
69#13063256—21no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)C2312yes—
74C4⋊(C43⋊C8)C2312yes—
75C4⋊(C43⋊C8)C2311yescharacteristic
76C4⋊(C43⋊C8)C2311yescharacteristic
77Dic43⋊C8—22no—
78#13063248—21no—
79#13063248—21no—
80#13063246—22no—
81#13063246—22no—
82#13063245—21no—
83#13063245—21no—
84(C2×D43)⋊C8—22no—
85C8×Dic43—22no—
86C22×D4×C43—21no—
87C22×D4×C43—21no—
88C22×D4×C43—21no—
89C2×SD16×C43—22no—
90C2×SD16×C43—22no—
91C4⋊Q8×C43C2311yescharacteristic
92C4⋊Q8×C43C2311yescharacteristic
93#127×C43—21no—
94#127×C43—21no—
95#127×C43—21no—
96#127×C43C2312yes—
97#125×C43—21no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43—21no—
100C4×Q8×C43—21no—
101C4×Q8×C43—21no—
102#117×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106#102×C43—22no—
107#102×C43—22no—
108C22⋊C8×C43D412yes—
109C4×C8×C43C2312yes—
110C24×C43—41no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—41no—
117C2×D4×C43—41no—
118C2×D4×C43—41no—
119C2×D4×C43—42no—
120C2×D4×C43—42no—
121C2×D4×C43—81no—
122C2×D4×C43—81no—
123C2×D4×C43—82no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4111yescharacteristic
127C2×C22⋊D43—21no—
128#10621898—22no—
129#10621898SD1614yescomplemented
130C2×D172C2×D411yescharacteristic
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×Dic86C2×D411yescharacteristic
135SD16×C43—82no—
136SD16×C43—82no—
137C2×C8×C43C2×D412yes—
138C2×C8×C43C2×D412yes—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C42×C43—41no—
147C42×C43C2×D411yescharacteristic
148C42×C43C2×D411yescharacteristic
149C42×C43#4111yescharacteristic
150C42×C43C2411yescharacteristic
151C22⋊Dic43—21no—
152#10621883—44no—
153#10621882—44no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156C4⋊Dic43C2×D411yescharacteristic
157C4⋊Dic43C2×D411yescharacteristic
158Dic43⋊C4—21no—
159Dic43⋊C4—21no—
160C4×Dic43—21no—
161C4×Dic43—21no—
162C4×Dic43—21no—
163#10621877—42no—
164C2×C43⋊C8—22no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—42no—
169C2×C43⋊C8—81no—
170C8×D43—82no—
171C23×C43—42no—
172C23×C43—82no—
173C23×C43—82no—
174C23×C43—82no—
175C23×C43#12111yescharacteristic
176C22×D43—21no—
177Q8×C43—41no—
178Q8×C43—41no—
179Q8×C43—81no—
180D4×C43—42no—
181D4×C43—42no—
182D4×C43—42no—
183D4×C43—42no—
184D4×C43—82no—
185D4×C43—82no—
186D4×C43—82no—
187D4×C43—82no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43C2×SD1612yes—
197C2×C4×C43#13512yes—
198C2×C4×C43C22×D411yescharacteristic
199C2×C4×C43C22×D411yescharacteristic
200C2×C4×C43C2×#4111yescharacteristic
201C22⋊D43—24no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205D172—21no—
206D172C2×SD1612yes—
207C4×D43—24no—
208C4×D43—41no—
209C4×D43—41no—
210C4×D43—81no—
211Dic86—21no—
212Dic86C2×SD1612yes—
213C8×C43—22no—
214C8×C43—22no—
215C43⋊C8—42no—
216C43⋊C8—41no—
217C43⋊C8—41no—
218C43⋊C8—42no—
219#19409—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—82no—
223C22×C43—82no—
224C22×C43—82no—
225C22×C43—164no—
226C22×C43#46512yes—
227C22×C43C2×#12111yescharacteristic
228C2×D43—22no—
229C2×D43—41no—
230C2×D43—41no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—81no—
235C4×C43—81no—
236C4×C43#46512yes—
237C4×C43C22×SD1611yescharacteristic
238C4×C43C2×#13511yescharacteristic
239C4×C43#57611yescharacteristic
240C4×C43#57711yescharacteristic
241Dic43—22no—
242Dic43—41no—
243Dic43—41no—
244#3208D4311yescharacteristic, complemented
245#3076—431no—
246#3038—431no—
247#2988—431no—
248#1678—432no—
249#1677—432no—
250#1666—432no—
251#1665—432no—
252#1570—431no—
253#1550—431no—
254C2×#331—431no—
255C2×C43—22no—
256C2×C43—162no—
257C2×C43#304511yescharacteristic
258C2×C43C2×#46511yescharacteristic
259C2×C43#306811yescharacteristic
260D43—42no—
261C2×AGL(1,ℤ/8)—861no—
262#533C2×D4311yescharacteristic
263C2×#127C2×D4311yescharacteristic
264C4×#41—431no—
265#492C2×D4312yes—
266#486C2×D4312yes—
267#479—861no—
268#478—861no—
269#477—431no—
270#476—431no—
271#475—431no—
272#474—431no—
273#460—21no—
274#460—21no—
275#460—432no—
276#460—861no—
277#459—432no—
278#459—861no—
279#450—22no—
280C8×Q8—432no—
281C8×D4—432no—
282C8×D4—862no—
283#431—861no—
284#431C2×D4311yescharacteristic
285#427—861no—
286#423—431no—
287C2×C4⋊C8—431no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8—861no—
290#418—861no—
291#416—861no—
292#334—432no—
293#334—432no—
294#333—432no—
295#332—432no—
296#331—432no—
297#331—432no—
298C43#1940911yescharacteristic, complemented, Sylow
299C2×#41—431no—
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303AGL(1,ℤ/8)—1724no—
304C2×SD16—22no—
305C2×SD16—22no—
306C2×SD16—862no—
307C2×D8—862no—
308C2×M16—861no—
309C22×C8—861no—
310C22×C8—861no—
311C22×C8—862no—
312C4⋊Q8C22×D4311yescharacteristic
313C4⋊Q8C22×D4311yescharacteristic
314#127—21no—
315#127—21no—
316#127—21no—
317#127C22×D4312yes—
318#125—21no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—431no—
324C4×Q8—431no—
325C4×D4—431no—
326C4×D4—431no—
327C4×D4—861no—
328C4×D4—861no—
329#117—21no—
330#117—431no—
331#117—861no—
332C2×C42—861no—
333C2×C42C22×D4311yescharacteristic
334#107—861no—
335#107—861no—
336#106—861no—
337#106—861no—
338C4⋊C8—432no—
339C4⋊C8—431no—
340C4⋊C8—431no—
341C4⋊C8—432no—
342C4⋊C8—862no—
343C4⋊C8—861no—
344C4⋊C8—861no—
345C4⋊C8—861no—
346C4⋊C8C22⋊D4311yescharacteristic
347C4⋊C8C22⋊D4311yescharacteristic
348#103—861no—
349#103—861no—
350#102—22no—
351#102—22no—
352#102—861no—
353#102—861no—
354#102—862no—
355#102—862no—
356C22⋊C8—862no—
357C22⋊C8C22⋊D4312yes—
358C4×C8—862no—
359C4×C8C22×D4312yes—
360C24—41no—
361#41—434no—
362#41—862no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—431no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—81no—
375C2×D4—81no—
376C2×D4—82no—
377C2×D4—431no—
378C2×D4—861no—
379C22×C4—861no—
380C22×C4—861no—
381C22×C4—861no—
382C22×C4D4×D4311yescharacteristic
383C22×C4#1062190011yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385SD16—82no—
386SD16—82no—
387SD16—1724no—
388D8—1724no—
389M16—1722no—
390C2×C8—862no—
391C2×C8—861no—
392C2×C8—861no—
393C2×C8—862no—
394C2×C8—3442no—
395C2×C8—3441no—
396C2×C8—1722no—
397C2×C8C2×C22⋊D4312yes—
398C2×C8C2×C22⋊D4312yes—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—431no—
406C4⋊C4—431no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C22⋊C4—41no—
410C22⋊C4—861no—
411C22⋊C4—861no—
412C22⋊C4—861no—
413C42—41no—
414C42—861no—
415C42—861no—
416C42—861no—
417C42D4×D4311yescharacteristic
418C42#1062190011yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—42no—
422C23—82no—
423C23—82no—
424C23—82no—
425C23—861no—
426C23#1306329611yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—81no—
430Q8—432no—
431Q8—861no—
432D4—42no—
433D4—42no—
434D4—42no—
435D4—42no—
436D4—82no—
437D4—82no—
438D4—82no—
439D4—82no—
440D4—432no—
441D4—864no—
442D4—861no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—861no—
449C2×C4—864no—
450C2×C4—861no—
451C2×C4—861no—
452C2×C4—3441no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4#1306329611yescharacteristic
456C2×C4#1306329611yescharacteristic
457C2×C4#1306329611yescharacteristic
458C2×C4SD16×D4312yes—
459C2×C4#1306334612yes—
460C2×C4C2×D4×D4311yescharacteristic
461C2×C4C22×C22⋊D4311yescharacteristic
462C2×C4C2×#1062190011yescharacteristic
463C8—22no—
464C8—22no—
465C8—1722no—
466C8—1721no—
467C8—1721no—
468C8—1722no—
469C22—21no—
470C22—21no—
471C22—82no—
472C22—82no—
473C22—82no—
474C22—164no—
475C22—862no—
476C22—1721no—
477C22—1721no—
478C22#1458312512yes—
479C22C2×#1306329611yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—81no—
485C4—862no—
486C4—1721no—
487C4—1721no—
488C4#1458312512yes—
489C4C2×SD16×D4311yescharacteristic
490C4C2×#1306334611yescharacteristic
491C4#1458370211yescharacteristic
492C4#1458371011yescharacteristic
493C2—22no—
494C2—162no—
495C2—1722no—
496C2#1914413011yescharacteristic
497C2C2×#1458312511yescharacteristic
498C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3208C2
socleC22×C43C2×#121
prime radical#19144071C2
hypercenter#3208D43
hypocenterC43#19409
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3208

Complements

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

NH ≅ G/Ntype
1. #19144377C2semidirect
3. #19143703C2semidirect
4. #19134008C2semidirect
5. #19134001C2semidirect
6. #19133940C2semidirect
7. #19133933C2semidirect
8. #19133366C2semidirect
9. #19133285C2semidirect
10. C2×#14582643C2semidirect
11. C43×#3208C2semidirect
16. #14583191C22semidirect
17. #14583186C22semidirect
18. #14583181C22semidirect
19. #14583176C22semidirect
24. C8×Dic86C22semidirect
25. C8×D172C22semidirect
35. #14582650C22semidirect
36. #14582650C22semidirect
37. #14582648C22semidirect
38. #14582645C22semidirect
129. #10621898SD16semidirect
244. #3208D43semidirect
298. C43#19409semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191440712
#191437032
#191340082
#191340012
#191339402
#191339332
#191333662
#191332852
C2×#145826432
C43×#32082
#1940943