Finite Group Databasebeta

← #25081999

Subgroups — #25081999

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#19145533C211yesmaximal, characteristic, complemented
2#19144377C211yesmaximal, characteristic, complemented
3#19144076C211yesmaximal, characteristic
4#19143704C211yesmaximal, characteristic, complemented
5#19134014C212yesmaximal, complemented
6#19134007C212yesmaximal, complemented
7#19133946C212yesmaximal, complemented
8#19133939C212yesmaximal, complemented
9#19133367C211yesmaximal, characteristic, complemented
10C2×#14582642C211yesmaximal, characteristic, complemented
11C43×#1550C211yesmaximal, characteristic, complemented
12C2×#13063353—21no—
13C2×#13063322C2211yescharacteristic
14C4×#10621898C2211yescharacteristic
15#14583273C2212yes—
16#14583247C2212yes—
17#14583203—21no—
18#14583196—21no—
19#14583191C2211yescharacteristic, complemented
20#14583186C2211yescharacteristic, complemented
21#14583181C2211yescharacteristic, complemented
22#14583176C2211yescharacteristic, complemented
23#14583100—21no—
24#14583100C2212yes—
25#14583099—21no—
26#14583099—21no—
27#14583095—21no—
28#14583095C2212yes—
29#14583049—22no—
30#14583023C2212yescomplemented
31#14582964C2212yescomplemented
32C8×C22⋊D43—22no—
33#14582952C2211yescharacteristic
34#14582951—21no—
35#14582935—21no—
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊C8×D43—21no—
38#14582905—21no—
39#14582893—21no—
40#14582649C2212yescomplemented
41#14582649C2212yescomplemented
42#14582642C2212yes—
43#14582642C2212yes—
44C43×#533C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#333C2212yescomplemented
48C43×#332C2212yescomplemented
49C2×#10621898D411yescharacteristic
50C22×D172—21no—
51C22×D172—21no—
52C22×D172—21no—
53#13063353—44no—
54C2×#10621873—22no—
55C2×#10621884—22no—
56C2×#10621884—22no—
57C2×D344—22no—
58C22×C43⋊C8—21no—
59C2×C8×D43—22no—
60#13063322—21no—
61#13063322—21no—
62#13063322—21no—
63#13063322C2312yes—
64C4×Dic86D411yescharacteristic
65C4×Dic86C2311yescharacteristic
66C4×D172D411yescharacteristic
67C4×D172C2311yescharacteristic
68C4×C22⋊D43—21no—
69C4×C22⋊D43—21no—
70#13063284D411yescharacteristic
71#13063282—21no—
72C42×D43—21no—
73#13063258—21no—
74#13063258—21no—
75#13063256—21no—
76#13063256—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)D411yescharacteristic
79C4⋊(C43⋊C8)D411yescharacteristic
80C4⋊(C43⋊C8)C2311yescharacteristic
81C4⋊(C43⋊C8)C2311yescharacteristic
82Dic43⋊C8—22no—
83#13063248—21no—
84#13063248—21no—
85#13063247—22no—
86#13063247—22no—
87#13063245—21no—
88#13063245—21no—
89#13063245—22no—
90#13063245—22no—
91C22⋊(C43⋊C8)D412yes—
92(C2×D43)⋊C8—22no—
93C4×C43⋊C8C2312yes—
94C8×Dic43—22no—
95C2×M16×C43—21no—
96C22×C8×C43—21no—
97C4⋊Q8×C43C2311yescharacteristic
98C4⋊Q8×C43C2311yescharacteristic
99#125×C43—21no—
100C22⋊Q8×C43—21no—
101C22⋊Q8×C43—21no—
102C4×Q8×C43—21no—
103C4×Q8×C43—21no—
104#117×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109C4⋊C8×C43C2312yes—
110C23×D43—41no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C2×C22⋊D43—21no—
117#10621898—22no—
118#10621898SD1614yescomplemented
119C2×D172—22no—
120C2×D172—22no—
121C2×D172—22no—
122C2×D172—41no—
123C2×D172—41no—
124C2×D172—41no—
125C2×D172—42no—
126C2×D172—42no—
127C2×D172—81no—
128C2×D172—81no—
129C2×D172—82no—
130C2×D172C2×D411yescharacteristic
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×Dic86C2×D411yescharacteristic
135M16×C43—42no—
136C2×C8×C43—22no—
137C2×C8×C43—22no—
138C2×C8×C43—81no—
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#10621884—82no—
153#10621884—82no—
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—
163C2×C43⋊C8—21no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8—42no—
166C2×C43⋊C8C2×D412yes—
167C2×C43⋊C8C2×D412yes—
168D344—44no—
169#10621873—44no—
170C8×D43—82no—
171C23×C43#12111yescharacteristic
172C22×D43—21no—
173C22×D43—42no—
174C22×D43—82no—
175C22×D43—82no—
176C22×D43—82no—
177Q8×C43—41no—
178Q8×C43—41no—
179Q8×C43—81no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43C2×SD1612yes—
189C2×C4×C43#13512yes—
190C2×C4×C43C22×D411yescharacteristic
191C2×C4×C43C22×D411yescharacteristic
192C2×C4×C43C2×#4111yescharacteristic
193C22⋊D43—24no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—21no—
197D172—21no—
198D172—42no—
199D172—42no—
200D172—42no—
201D172—42no—
202D172—82no—
203D172—82no—
204D172—82no—
205D172—82no—
206D172C2×SD1612yes—
207C4×D43—24no—
208C4×D43—41no—
209C4×D43—41no—
210C4×D43—81no—
211Dic86—21no—
212Dic86C2×SD1612yes—
213C8×C43—42no—
214C8×C43—42no—
215C43⋊C8—22no—
216C43⋊C8—22no—
217C43⋊C8—41no—
218C43⋊C8—41no—
219#19409—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43#46512yes—
223C22×C43C2×#12111yescharacteristic
224C2×D43—22no—
225C2×D43—41no—
226C2×D43—41no—
227C2×D43—82no—
228C2×D43—82no—
229C2×D43—82no—
230C2×D43—164no—
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#3208—431no—
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#1550D4311yescharacteristic, complemented
254C2×#331—431no—
255C2×C43—22no—
256C2×C43#304511yescharacteristic
257C2×C43C2×#46511yescharacteristic
258C2×C43#306811yescharacteristic
259D43—42no—
260D43—162no—
261C2×AGL(1,ℤ/8)—861no—
262#533C2×D4311yescharacteristic
263C2×#127—431no—
264C4×#41—431no—
265#492—432no—
266#486—432no—
267#479—861no—
268#478—861no—
269#477—431no—
270#476—431no—
271#475—431no—
272#474—431no—
273#460—432no—
274#460—861no—
275#460—861no—
276#460—861no—
277#459—432no—
278#459—861no—
279#450—862no—
280C8×Q8—432no—
281C8×D4—432no—
282C8×D4—862no—
283#431—431no—
284#431—861no—
285#427—861no—
286#423C2×D4311yescharacteristic
287C2×C4⋊C8—431no—
288C2×C4⋊C8—861no—
289C2×C4⋊C8C2×D4311yescharacteristic
290#418—861no—
291#416—861no—
292#334—432no—
293#334—432no—
294#333C2×D4312yescomplemented
295#332C2×D4312yescomplemented
296#331—432no—
297#331—432no—
298C43#1940911yescharacteristic, complemented, Sylow
299C2×#41—431no—
300C22×D4—861no—
301C22×D4—861no—
302C22×D4—861no—
303AGL(1,ℤ/8)—1724no—
304C2×SD16—862no—
305C2×SD16—862no—
306C2×SD16—862no—
307C2×D8—862no—
308C2×M16—21no—
309C22×C8—21no—
310C22×C8—862no—
311C22×C8—861no—
312C4⋊Q8C22×D4311yescharacteristic
313C4⋊Q8C22×D4311yescharacteristic
314#127—432no—
315#127—861no—
316#127—861no—
317#127—861no—
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—21no—
339C4⋊C8—21no—
340C4⋊C8—431no—
341C4⋊C8—431no—
342C4⋊C8—431no—
343C4⋊C8—431no—
344C4⋊C8—862no—
345C4⋊C8—861no—
346C4⋊C8C22×D4312yes—
347C4⋊C8C22×D4312yes—
348#103—861no—
349#103—861no—
350#102—862no—
351#102—862no—
352#102—861no—
353#102—861no—
354#102—862no—
355#102—862no—
356C22⋊C8—432no—
357C22⋊C8—862no—
358C4×C8—432no—
359C4×C8—862no—
360C24—1721no—
361#41—434no—
362#41—862no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—431no—
366C2×D4—431no—
367C2×D4—861no—
368C2×D4—862no—
369C2×D4—862no—
370C2×D4—862no—
371C2×D4—3441no—
372C2×D4—3441no—
373C2×D4—3442no—
374C2×D4—1721no—
375C2×D4—1721no—
376C2×D4—1721no—
377C2×D4—1722no—
378C2×D4—1722no—
379C22×C4—861no—
380C22×C4—861no—
381C22×C4—861no—
382C22×C4#1062189811yescharacteristic
383C22×C4D4×D4311yescharacteristic
384C22×C4D4×D4311yescharacteristic
385SD16—3442no—
386SD16—3442no—
387SD16—1724no—
388D8—1724no—
389M16—42no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—81no—
393C2×C8—432no—
394C2×C8—432no—
395C2×C8—861no—
396C2×C8—861no—
397C2×C8—3442no—
398C2×C8—1722no—
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—
417C42#1062189811yescharacteristic
418C42D4×D4311yescharacteristic
419C42D4×D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—861no—
422C23—3442no—
423C23—3442no—
424C23—3442no—
425C23—1722no—
426C23#1306329811yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—81no—
430Q8—432no—
431Q8—861no—
432D4—432no—
433D4—864no—
434D4—861no—
435D4—3442no—
436D4—3442no—
437D4—3442no—
438D4—3442no—
439D4—1722no—
440D4—1722no—
441D4—1722no—
442D4—1722no—
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#1306329811yescharacteristic
456C2×C4#1306329811yescharacteristic
457C2×C4#1306329811yescharacteristic
458C2×C4SD16×D4312yes—
459C2×C4#1306334812yes—
460C2×C4C2×D4×D4311yescharacteristic
461C2×C4C2×D4×D4311yescharacteristic
462C2×C4C2×#1062189811yescharacteristic
463C8—42no—
464C8—42no—
465C8—862no—
466C8—862no—
467C8—1721no—
468C8—1721no—
469C22—21no—
470C22—21no—
471C22—862no—
472C22—3442no—
473C22—3442no—
474C22—3442no—
475C22—1721no—
476C22—1721no—
477C22—6884no—
478C22#1458313112yes—
479C22C2×#1306329811yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—81no—
484C4—81no—
485C4—862no—
486C4—1721no—
487C4—1721no—
488C4#1458313112yes—
489C4C2×SD16×D4311yescharacteristic
490C4C2×#1306334811yescharacteristic
491C4#1458370311yescharacteristic
492C4#1458370811yescharacteristic
493C2—22no—
494C2—1722no—
495C2—6882no—
496C2#1914413311yescharacteristic
497C2C2×#1458313111yescharacteristic
498C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1550C2
socleC22×C43C2×#121
prime radical#19144076C2
hypercenter#1550D43
hypocenterC43#19409
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
1. #19145533C2semidirect
2. #19144377C2semidirect
4. #19143704C2semidirect
5. #19134014C2semidirect
6. #19134007C2semidirect
7. #19133946C2semidirect
8. #19133939C2semidirect
9. #19133367C2semidirect
10. C2×#14582642C2semidirect
11. C43×#1550C2semidirect
19. #14583191C22semidirect
20. #14583186C22semidirect
21. #14583181C22semidirect
22. #14583176C22semidirect
30. #14583023C22semidirect
31. #14582964C22semidirect
40. #14582649C22semidirect
41. #14582649C22semidirect
47. C43×#333C22semidirect
48. C43×#332C22semidirect
118. #10621898SD16semidirect
253. #1550D43semidirect
294. #333C2×D43semidirect
295. #332C2×D43semidirect
298. C43#19409semidirect

Maximal subgroups

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

subgroupindex
#191455332
#191443772
#191440762
#191437042
#191340142
#191340072
#191339462
#191339392
#191333672
C2×#145826422
C43×#15502
#1940943