Finite Group Databasebeta

← #25079401

Subgroups — #25079401

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#19145142C211yesmaximal, characteristic, complemented
2#19144599C211yesmaximal, characteristic
3C2×#14583190C211yesmaximal, characteristic
4#19143330C211yesmaximal, characteristic
5#19134117C212yesmaximal, complemented
6#19134093C212yesmaximal, complemented
7#19133993C212yesmaximal, complemented
8#19133969C212yesmaximal, complemented
9#19133345C211yesmaximal, characteristic, complemented
10#19133277C211yesmaximal, characteristic, complemented
11C43×#1550C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13C2×#13063325C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583309—22no—
16#14583302C2212yescomplemented
17#14583295C2212yescomplemented
18#14583227—21no—
19#14583190—21no—
20#14583190—21no—
21#14583190C2212yes—
22#14583190C2212yes—
23#14583186C2211yescharacteristic
24#14583186C2211yescharacteristic
25#14583101C2211yescharacteristic
26#14583101C2211yescharacteristic
27#14583049—21no—
28C4×#10621884—21no—
29C4×#10621884—21no—
30#14582976C2212yes—
31#14582969—22no—
32#14582964C2212yes—
33#14582952C2211yescharacteristic
34#14582942—21no—
35#14582942—21no—
36C2×#13063257—21no—
37C2×#13063247—21no—
38#14582862—21no—
39C4×#10621877C2211yescharacteristic
40#14582651C2212yescomplemented
41#14582649C2212yescomplemented
42#14582647C2212yescomplemented
43#14582647C2212yescomplemented
44C43×#533C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#333C2212yescomplemented
48C43×#332C2212yescomplemented
49C22×Dic86—21no—
50C22×D172D411yescharacteristic
51C22×C4×D43—21no—
52C2×#10621884—21no—
53C2×#10621884—21no—
54C2×#10621877D411yescharacteristic
55C2×#10621877D411yescharacteristic
56C2×#10621872—22no—
57M16×D43—44no—
58C2×C8×D43—22no—
59#13063325—21no—
60#13063325—21no—
61#13063325—21no—
62#13063325C2312yes—
63C4×D172—21no—
64C4×D172—21no—
65C4×D172D411yescharacteristic
66C4×D172D411yescharacteristic
67C4×D172C2311yescharacteristic
68C4×D172C2311yescharacteristic
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×(C2×D43)⋊C4—21no—
73#13063258—22no—
74#13063258—22no—
75#13063257—22no—
76#13063257—22no—
77#13063256—21no—
78#13063256—21no—
79#13063256—22no—
80#13063256—22no—
81C4⋊(C43⋊C8)C2311yescharacteristic
82C4⋊(C43⋊C8)C2311yescharacteristic
83#13063249—21no—
84#13063249—21no—
85#13063247—22no—
86#13063247—22no—
87#13063245—21no—
88#13063245—21no—
89C22⋊(C43⋊C8)—21no—
90(C2×D43)⋊C8—22no—
91(C2×D43)⋊C8—22no—
92#13063236D412yes—
93C4×C43⋊C8—21no—
94C4×C43⋊C8C2312yes—
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—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43#4111yescharacteristic
116C22×Dic43—21no—
117C22×Dic43—41no—
118C2×D172—21no—
119C2×D172—22no—
120C2×D172—41no—
121C2×D172C2×D411yescharacteristic
122C2×D172C2×D411yescharacteristic
123C2×C4×D43—21no—
124C2×C4×D43—21no—
125C2×C4×D43—21no—
126C2×C4×D43—21no—
127C2×C4×D43—42no—
128C2×C4×D43—42no—
129C2×Dic86—22no—
130C2×Dic86—41no—
131C2×Dic86—82no—
132M16×C43—42no—
133C2×C8×C43—22no—
134C2×C8×C43—22no—
135C2×C8×C43—42no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43—41no—
142C22⋊C4×C43—41no—
143C42×C43—41no—
144C42×C43C2×D411yescharacteristic
145C42×C43C2×D411yescharacteristic
146C42×C43#4111yescharacteristic
147C42×C43C2411yescharacteristic
148#10621884—42no—
149#10621884—42no—
150(C2×D43)⋊C4—21no—
151(C2×D43)⋊C4—21no—
152(C2×D43)⋊C4—21no—
153(C2×D43)⋊C4—21no—
154C4⋊Dic43—21no—
155C4⋊Dic43—22no—
156C4⋊Dic43—22no—
157C4⋊Dic43—41no—
158C4⋊Dic43—41no—
159C4⋊Dic43C2×D411yescharacteristic
160C4⋊Dic43C2×D411yescharacteristic
161#10621877—22no—
162#10621877SD1614yescomplemented
163C2×C43⋊C8—21no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8C2×D412yes—
166C2×C43⋊C8C2×D412yes—
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—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43#12111yescharacteristic
184C2×C4×C43#12111yescharacteristic
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43C2×SD1612yes—
187C2×C4×C43#13712yes—
188C2×C4×C43C22×D411yescharacteristic
189C2×C4×C43C22×D411yescharacteristic
190C2×C4×C43C2×#4111yescharacteristic
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—42no—
194C2×Dic43—42no—
195C2×Dic43—82no—
196D172—21no—
197D172—21no—
198D172—21no—
199D172—42no—
200D172#13712yes—
201C4×D43—41no—
202C4×D43—41no—
203C4×D43—41no—
204C4×D43—41no—
205C4×D43—42no—
206C4×D43—42no—
207Dic86—82no—
208Dic86—82no—
209C8×C43—42no—
210C8×C43—42no—
211C43⋊C8—22no—
212C43⋊C8—41no—
213C43⋊C8—41no—
214C43⋊C8C2×SD1614yes—
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—81no—
232C4×C43#46112yes—
233C4×C43C22×SD1611yescharacteristic
234C4×C43C2×#13711yescharacteristic
235C4×C43C2×#13711yescharacteristic
236C4×C43#57511yescharacteristic
237Dic43—41no—
238Dic43—41no—
239Dic43—82no—
240#3165—431no—
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#1550D4311yescharacteristic, complemented
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⋊Q8—431no—
260C2×C4×D4—431no—
261#501—862no—
262#500—432no—
263#498—432no—
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—861no—
281#428—861no—
282C2×#106—861no—
283#423C2×D4311yescharacteristic
284C2×C4⋊C8C2×D4311yescharacteristic
285C2×#102—861no—
286#407—861no—
287C4×M16—431no—
288#335—432no—
289#334—432no—
290#333—432no—
291#333—432no—
292#333C2×D4312yescomplemented
293#332C2×D4312yescomplemented
294C43#1916511yescharacteristic, complemented, Sylow
295C22×Q8—861no—
296C22×D4—431no—
297C23×C4—861no—
298C2×SD16—861no—
299C2×SD16—861no—
300C2×M16—21no—
301C2×M16—431no—
302C2×M16—431no—
303C2×M16—862no—
304C2×M16—1724no—
305C22×C8—21no—
306C22×C8—862no—
307C4⋊Q8—432no—
308C4⋊Q8—861no—
309C4⋊Q8—861no—
310C4⋊Q8—861no—
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—431no—
326C2×C4⋊C4—861no—
327C2×C4⋊C4—861no—
328C2×C22⋊C4—861no—
329C2×C42C22×D4311yescharacteristic
330#107—862no—
331#107—862no—
332#106—861no—
333#106—861no—
334#106—862no—
335#106—862no—
336#106—862no—
337#106—862no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8—431no—
341C4⋊C8—431no—
342C4⋊C8C22×D4312yes—
343C4⋊C8C22×D4312yes—
344#103—861no—
345#103—861no—
346#102—861no—
347#102—861no—
348#102—862no—
349#102—862no—
350C22⋊C8—862no—
351C22⋊C8—862no—
352C22⋊C8—861no—
353#97—432no—
354C4×C8—432no—
355C4×C8—861no—
356C24—861no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—862no—
360C2×Q8—3442no—
361C2×Q8—1721no—
362C2×D4—431no—
363C2×D4—431no—
364C2×D4—862no—
365C2×D4—861no—
366C2×D4—1721no—
367C22×C4—861no—
368C22×C4—861no—
369C22×C4—861no—
370C22×C4—861no—
371C22×C4—861no—
372C22×C4—1721no—
373C22×C4—1722no—
374C22×C4—1722no—
375C22×C4#1062189811yescharacteristic
376C22×C4D4×D4311yescharacteristic
377C22×C4D4×D4311yescharacteristic
378SD16—1722no—
379SD16—1722no—
380M16—42no—
381M16—434no—
382M16—862no—
383M16—1724no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—42no—
387C2×C8—432no—
388C2×C8—432no—
389C2×C8—861no—
390C2×C8—861no—
391C2×C8—1724no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—431no—
399C4⋊C4—431no—
400C4⋊C4—861no—
401C4⋊C4—862no—
402C4⋊C4—862no—
403C4⋊C4—1721no—
404C4⋊C4—1721no—
405C22⋊C4—41no—
406C22⋊C4—861no—
407C22⋊C4—861no—
408C22⋊C4—861no—
409C22⋊C4—861no—
410C42—41no—
411C42#1062189811yescharacteristic
412C42D4×D4311yescharacteristic
413C42D4×D4311yescharacteristic
414C42C23×D4311yescharacteristic
415C23—861no—
416C23—861no—
417C23—3441no—
418C23—1722no—
419C23—1722no—
420C23#1306329811yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—81no—
424Q8—3442no—
425Q8—3442no—
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—861no—
437C2×C4—861no—
438C2×C4—3442no—
439C2×C4—1722no—
440C2×C4—1722no—
441C2×C4—1722no—
442C2×C4—1722no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1721no—
447C2×C4#1306329811yescharacteristic
448C2×C4#1306329811yescharacteristic
449C2×C4#1306329811yescharacteristic
450C2×C4SD16×D4312yes—
451C2×C4#1306335712yes—
452C2×C4C2×D4×D4311yescharacteristic
453C2×C4C2×D4×D4311yescharacteristic
454C2×C4C2×#1062189811yescharacteristic
455C8—42no—
456C8—42no—
457C8—434no—
458C8—862no—
459C8—1721no—
460C8—1721no—
461C22—21no—
462C22—21no—
463C22—862no—
464C22—3444no—
465C22—1721no—
466C22—1721no—
467C22—1721no—
468C22—1721no—
469C22—1721no—
470C22#1458310312yes—
471C22C2×#1306329811yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—81no—
476C4—81no—
477C4—3442no—
478C4—1721no—
479C4—1721no—
480C4#1458310312yes—
481C4C2×SD16×D4311yescharacteristic
482C4#137×D4311yescharacteristic
483C4C2×#1306335711yescharacteristic
484C4#1458369511yescharacteristic
485C2—22no—
486C2—3441no—
487C2—1722no—
488C2C2×#1458310311yescharacteristic
489C2#1914422811yescharacteristic
490C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1550C2
socleC22×C43C2×#121
prime radicalC22×D172D4
hypercenter#1550D43
hypocenterC43#19165
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. #19145142C2semidirect
5. #19134117C2semidirect
6. #19134093C2semidirect
7. #19133993C2semidirect
8. #19133969C2semidirect
9. #19133345C2semidirect
10. #19133277C2semidirect
11. C43×#1550C2semidirect
16. #14583302C22semidirect
17. #14583295C22semidirect
40. #14582651C22semidirect
41. #14582649C22semidirect
42. #14582647C22semidirect
43. #14582647C22semidirect
47. C43×#333C22semidirect
48. C43×#332C22semidirect
162. #10621877SD16semidirect
249. #1550D43semidirect
292. #333C2×D43semidirect
293. #332C2×D43semidirect
294. C43#19165semidirect

Maximal subgroups

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

subgroupindex
#191451422
#191445992
C2×#145831902
#191433302
#191341172
#191340932
#191339932
#191339692
#191333452
#191332772
C43×#15502
#1916543