Finite Group Databasebeta

← #25079423

Subgroups — #25079423

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144977C211yesmaximal, characteristic, complemented
2#19144599C211yesmaximal, characteristic
3C2×#14583180C211yesmaximal, characteristic
4#19143330C211yesmaximal, characteristic
5#19134173C212yesmaximal, complemented
6#19134145C212yesmaximal, complemented
7#19134049C212yesmaximal, complemented
8#19134021C212yesmaximal, complemented
9#19133345C211yesmaximal, characteristic, complemented
10#19133268C211yesmaximal, characteristic, complemented
11C43×#1550C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13C2×#13063325C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583269—22no—
16#14583251C2212yescomplemented
17#14583251C2212yescomplemented
18#14583227—21no—
19#14583186C2211yescharacteristic
20#14583186C2211yescharacteristic
21#14583180—21no—
22#14583180—21no—
23#14583180C2212yes—
24#14583180C2212yes—
25#14583101C2211yescharacteristic
26#14583101C2211yescharacteristic
27#14583049—21no—
28C4×#10621884—21no—
29C4×#10621884—21no—
30#14582976C2212yes—
31#14582969—22no—
32#14582964C2212yes—
33#14582952C2211yescharacteristic
34C2×#13063259—21no—
35#14582907—21no—
36#14582907—21no—
37C2×#13063247—21no—
38#14582862—21no—
39C4×#10621877C2211yescharacteristic
40#14582651C2212yescomplemented
41#14582649C2212yescomplemented
42#14582646C2212yescomplemented
43#14582646C2212yescomplemented
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#13063259—22no—
74#13063259—22no—
75#13063256—21no—
76#13063256—21no—
77C4⋊(C43⋊C8)C2311yescharacteristic
78C4⋊(C43⋊C8)C2311yescharacteristic
79#13063249—21no—
80#13063249—21no—
81#13063248—22no—
82#13063248—22no—
83#13063248—22no—
84#13063248—22no—
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—42no—
131C2×Dic86—42no—
132C2×Dic86—41no—
133M16×C43—42no—
134C2×C8×C43—22no—
135C2×C8×C43—22no—
136C2×C8×C43—42no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—41no—
142C4⋊C4×C43—41no—
143C22⋊C4×C43—41no—
144C42×C43—41no—
145C42×C43C2×D411yescharacteristic
146C42×C43C2×D411yescharacteristic
147C42×C43#4111yescharacteristic
148C42×C43C2411yescharacteristic
149#10621884—42no—
150#10621884—42no—
151(C2×D43)⋊C4—21no—
152(C2×D43)⋊C4—21no—
153(C2×D43)⋊C4—21no—
154(C2×D43)⋊C4—21no—
155C4⋊Dic43—21no—
156C4⋊Dic43—22no—
157C4⋊Dic43—22no—
158C4⋊Dic43—41no—
159C4⋊Dic43—41no—
160C4⋊Dic43C2×D411yescharacteristic
161C4⋊Dic43C2×D411yescharacteristic
162#10621877—22no—
163#10621877—22no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8C2×D412yes—
167C2×C43⋊C8C2×D412yes—
168#10621872—44no—
169C8×D43—44no—
170C23×C43#12111yescharacteristic
171C22×D43—21no—
172C22×D43—21no—
173C22×D43—42no—
174C22×D43—42no—
175C22×D43—81no—
176Q8×C43—41no—
177Q8×C43—41no—
178Q8×C43—81no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43#12111yescharacteristic
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#13512yes—
188C2×C4×C43AGL(1,ℤ/8)12yes—
189C2×C4×C43C22×D411yescharacteristic
190C2×C4×C43C22×D411yescharacteristic
191C2×C4×C43C2×#4111yescharacteristic
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—42no—
195C2×Dic43—42no—
196C2×Dic43—82no—
197D172—21no—
198D172—21no—
199D172—21no—
200D172—42no—
201D172#13712yes—
202C4×D43—41no—
203C4×D43—41no—
204C4×D43—41no—
205C4×D43—41no—
206C4×D43—42no—
207C4×D43—42no—
208Dic86—42no—
209Dic86—42no—
210Dic86—82no—
211C8×C43—42no—
212C8×C43—42no—
213C43⋊C8—22no—
214C43⋊C8—22no—
215C43⋊C8—41no—
216C43⋊C8—41no—
217#19167—431nomaximal, Sylow
218C22×C43—21no—
219C22×C43—21no—
220C22×C43#46312yes—
221C22×C43C2×#12111yescharacteristic
222C2×D43—22no—
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—41no—
227C2×D43—41no—
228C2×D43—84no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—81no—
233C4×C43—81no—
234C4×C43#46312yes—
235C4×C43C2×#13511yescharacteristic
236C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
237C4×C43C2×#13711yescharacteristic
238C4×C43#57511yescharacteristic
239Dic43—41no—
240Dic43—41no—
241Dic43—82no—
242#3139—431no—
243#3101—431no—
244C2×#474—431no—
245D4×M16—431no—
246#1703—432no—
247#1699—432no—
248#1683—432no—
249#1679—432no—
250#1565—431no—
251#1550D4311yescharacteristic, complemented
252#1546—431no—
253C2×C43—22no—
254C2×C43C2×#46311yescharacteristic
255C2×C43#305611yescharacteristic
256C2×C43#306911yescharacteristic
257D43—42no—
258D43—81no—
259C22×M16—861no—
260#533C2×D4311yescharacteristic
261C2×C4⋊Q8—431no—
262C2×C4×D4—431no—
263#491—862no—
264#487—432no—
265#487—432no—
266#483—861no—
267#476—431no—
268#476—431no—
269#474—432no—
270#474—432no—
271#474—861no—
272#474—861no—
273#461—431no—
274#461—431no—
275#450—861no—
276C4×SD16—861no—
277C4×SD16—861no—
278#436—432no—
279#435—862no—
280C8×D4—432no—
281#431—431no—
282C2×#107—861no—
283#423C2×D4311yescharacteristic
284C2×C4⋊C8C2×D4311yescharacteristic
285#419—861no—
286#419—861no—
287C2×#102—861no—
288#407—861no—
289C4×M16—431no—
290#335—432no—
291#334—432no—
292#333C2×D4312yescomplemented
293#332—432no—
294#332—432no—
295#332C2×D4312yescomplemented
296C43#1916711yescharacteristic, complemented, Sylow
297C22×Q8—861no—
298C22×D4—431no—
299C23×C4—861no—
300C2×SD16—861no—
301C2×SD16—861no—
302C2×M16—21no—
303C2×M16—431no—
304C2×M16—431no—
305C2×M16—862no—
306C2×M16—1724no—
307C22×C8—21no—
308C22×C8—862no—
309C4⋊Q8—432no—
310C4⋊Q8—861no—
311C4⋊Q8—861no—
312C4⋊Q8—861no—
313C4⋊Q8C22×D4311yescharacteristic
314C4⋊Q8C22×D4311yescharacteristic
315#125—21no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×D4—431no—
321C4×D4—431no—
322C4×D4—431no—
323C4×D4—431no—
324C4×D4—861no—
325C4×D4—861no—
326#117—21no—
327C2×C4⋊C4—431no—
328C2×C4⋊C4—861no—
329C2×C4⋊C4—861no—
330C2×C22⋊C4—861no—
331C2×C42C22×D4311yescharacteristic
332#107—862no—
333#107—862no—
334#106—861no—
335#106—861no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8—431no—
339C4⋊C8—431no—
340C4⋊C8C22×D4312yes—
341C4⋊C8C22×D4312yes—
342#103—862no—
343#103—862no—
344#103—862no—
345#103—862no—
346#103—861no—
347#103—861no—
348#102—861no—
349#102—861no—
350#102—862no—
351#102—862no—
352C22⋊C8—862no—
353C22⋊C8—862no—
354C22⋊C8—861no—
355#97—432no—
356C4×C8—432no—
357C4×C8—861no—
358C24—861no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—862no—
362C2×Q8—1722no—
363C2×Q8—1722no—
364C2×Q8—1721no—
365C2×D4—431no—
366C2×D4—431no—
367C2×D4—862no—
368C2×D4—861no—
369C2×D4—1721no—
370C22×C4—861no—
371C22×C4—861no—
372C22×C4—861no—
373C22×C4—861no—
374C22×C4—861no—
375C22×C4—1721no—
376C22×C4—1722no—
377C22×C4—1722no—
378C22×C4#1062189811yescharacteristic
379C22×C4D4×D4311yescharacteristic
380C22×C4D4×D4311yescharacteristic
381SD16—1722no—
382SD16—1722no—
383M16—42no—
384M16—862no—
385M16—862no—
386M16—1724no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—42no—
390C2×C8—432no—
391C2×C8—432no—
392C2×C8—861no—
393C2×C8—861no—
394C2×C8—1724no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—431no—
402C4⋊C4—431no—
403C4⋊C4—861no—
404C4⋊C4—862no—
405C4⋊C4—862no—
406C4⋊C4—1721no—
407C4⋊C4—1721no—
408C22⋊C4—41no—
409C22⋊C4—861no—
410C22⋊C4—861no—
411C22⋊C4—861no—
412C22⋊C4—861no—
413C42—41no—
414C42#1062189811yescharacteristic
415C42D4×D4311yescharacteristic
416C42D4×D4311yescharacteristic
417C42C23×D4311yescharacteristic
418C23—861no—
419C23—861no—
420C23—3441no—
421C23—1722no—
422C23—1722no—
423C23#1306329811yescharacteristic
424Q8—41no—
425Q8—41no—
426Q8—81no—
427Q8—3442no—
428Q8—1722no—
429Q8—1722no—
430D4—432no—
431D4—861no—
432D4—861no—
433D4—861no—
434D4—1722no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—861no—
441C2×C4—861no—
442C2×C4—3442no—
443C2×C4—1722no—
444C2×C4—1722no—
445C2×C4—1722no—
446C2×C4—1722no—
447C2×C4—1721no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4#1306329811yescharacteristic
452C2×C4#1306329811yescharacteristic
453C2×C4#1306329811yescharacteristic
454C2×C4#1306334812yes—
455C2×C4#1306335212yes—
456C2×C4C2×D4×D4311yescharacteristic
457C2×C4C2×D4×D4311yescharacteristic
458C2×C4C2×#1062189811yescharacteristic
459C8—42no—
460C8—42no—
461C8—862no—
462C8—862no—
463C8—1721no—
464C8—1721no—
465C22—21no—
466C22—21no—
467C22—862no—
468C22—3444no—
469C22—1721no—
470C22—1721no—
471C22—1721no—
472C22—1721no—
473C22—1721no—
474C22#1458311712yes—
475C22C2×#1306329811yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—81no—
480C4—81no—
481C4—3442no—
482C4—1721no—
483C4—1721no—
484C4#1458311712yes—
485C4C2×#1306334811yescharacteristic
486C4C2×#1306335211yescharacteristic
487C4#137×D4311yescharacteristic
488C4#1458369511yescharacteristic
489C2—22no—
490C2—3441no—
491C2—1722no—
492C2C2×#1458311711yescharacteristic
493C2#1914422811yescharacteristic
494C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1550C2
socleC22×C43C2×#121
prime radicalC22×D172D4
hypercenter#1550D43
hypocenterC43#19167
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. #19144977C2semidirect
5. #19134173C2semidirect
6. #19134145C2semidirect
7. #19134049C2semidirect
8. #19134021C2semidirect
9. #19133345C2semidirect
10. #19133268C2semidirect
11. C43×#1550C2semidirect
16. #14583251C22semidirect
17. #14583251C22semidirect
40. #14582651C22semidirect
41. #14582649C22semidirect
42. #14582646C22semidirect
43. #14582646C22semidirect
47. C43×#333C22semidirect
48. C43×#332C22semidirect
251. #1550D43semidirect
292. #333C2×D43semidirect
295. #332C2×D43semidirect
296. C43#19167semidirect

Maximal subgroups

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

subgroupindex
#191449772
#191445992
C2×#145831802
#191433302
#191341732
#191341452
#191340492
#191340212
#191333452
#191332682
C43×#15502
#1916743