Finite Group Databasebeta

← #25079428

Subgroups — #25079428

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144988C211yesmaximal, characteristic, complemented
2#19144591C211yesmaximal, characteristic
3C2×#14583190C211yesmaximal, characteristic, complemented
4#19143330C211yesmaximal, characteristic, complemented
5#19134169C212yesmaximal, complemented
6#19134127C212yesmaximal, complemented
7#19134045C212yesmaximal, complemented
8#19134003C212yesmaximal, complemented
9#19133345C211yesmaximal, characteristic, complemented
10#19133277C211yesmaximal, characteristic, complemented
11C43×#1547C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13C2×#13063325C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583258—22no—
16#14583249C2212yescomplemented
17#14583245C2212yescomplemented
18#14583210—21no—
19#14583190—21no—
20#14583190—21no—
21#14583190C2212yes—
22#14583190C2212yes—
23#14583176C2211yescharacteristic
24#14583176C2211yescharacteristic
25#14583091C2211yescharacteristic
26#14583091C2211yescharacteristic
27#14583032—21no—
28C4×#10621882—21no—
29C4×#10621882—21no—
30#14582976C2212yes—
31#14582969—22no—
32#14582964C2212yes—
33#14582952C2211yescharacteristic
34C2×#13063257—21no—
35#14582900—21no—
36#14582900—21no—
37C2×#13063247—21no—
38#14582862—21no—
39C4×#10621877C2211yescharacteristic
40#14582651C2212yescomplemented
41#14582649C2212yescomplemented
42#14582647C2212yescomplemented
43#14582647C2212yescomplemented
44C43×#532C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#332C2212yescomplemented
48C43×#331C2212yescomplemented
49C22×Dic86—21no—
50C22×D172D411yescharacteristic
51C22×C4×D43—21no—
52C2×#10621882—21no—
53C2×#10621882—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—21no—
74#13063258—21no—
75#13063257—22no—
76#13063257—22no—
77C4⋊(C43⋊C8)C2311yescharacteristic
78C4⋊(C43⋊C8)C2311yescharacteristic
79#13063249—22no—
80#13063249—22no—
81#13063247—22no—
82#13063247—22no—
83#13063246—21no—
84#13063246—21no—
85#13063246—22no—
86#13063246—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×#41×C43—21no—
96C2×M16×C43—21no—
97C22×C8×C43—21no—
98C4⋊Q8×C43C2311yescharacteristic
99#127×C43C2311yescharacteristic
100#124×C43—21no—
101#121×C43—21no—
102#121×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109C4⋊C8×C43C2312yes—
110C23×D43—21no—
111#41×C43—42no—
112#41×C43—42no—
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C22×Dic43—21no—
123C22×Dic43—41no—
124C2×D172—21no—
125C2×D172—22no—
126C2×D172—41no—
127C2×D172C2×D411yescharacteristic
128C2×D172C2×D411yescharacteristic
129C2×C4×D43—21no—
130C2×C4×D43—21no—
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—42no—
134C2×C4×D43—42no—
135C2×Dic86—22no—
136C2×Dic86—41no—
137C2×Dic86—82no—
138M16×C43—42no—
139C2×C8×C43—22no—
140C2×C8×C43—22no—
141C2×C8×C43—42no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43#4111yescharacteristic
149C42×C43C2411yescharacteristic
150#10621882—42no—
151#10621882—42no—
152(C2×D43)⋊C4—21no—
153(C2×D43)⋊C4—21no—
154(C2×D43)⋊C4—21no—
155(C2×D43)⋊C4—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—22no—
158C4⋊Dic43—22no—
159C4⋊Dic43—41no—
160C4⋊Dic43—41no—
161C4⋊Dic43C2×D411yescharacteristic
162C4⋊Dic43C2×D411yescharacteristic
163#10621877—22no—
164#10621877—22no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8C2×D412yes—
168C2×C43⋊C8C2×D412yes—
169#10621872—44no—
170C8×D43—44no—
171C23×C43—41no—
172C23×C43#12111yescharacteristic
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—42no—
176C22×D43—42no—
177C22×D43—81no—
178Q8×C43—41no—
179Q8×C43—41no—
180D4×C43—41no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—81no—
185D4×C43—82no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—82no—
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43#13512yes—
195C2×C4×C43AGL(1,ℤ/8)12yes—
196C2×C4×C43C22×D411yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C2×C4×C43C2×#4111yescharacteristic
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—42no—
202C2×Dic43—42no—
203C2×Dic43—82no—
204D172—21no—
205D172—21no—
206D172—21no—
207D172—42no—
208D172#13712yes—
209C4×D43—41no—
210C4×D43—41no—
211C4×D43—41no—
212C4×D43—41no—
213C4×D43—42no—
214C4×D43—42no—
215Dic86—82no—
216Dic86—82no—
217C8×C43—42no—
218C8×C43—42no—
219C43⋊C8—22no—
220C43⋊C8—22no—
221C43⋊C8—41no—
222C43⋊C8—41no—
223#19168—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43—81no—
229C22×C43#46312yes—
230C22×C43C2×#12111yescharacteristic
231C2×D43—22no—
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—41no—
235C2×D43—41no—
236C2×D43—41no—
237C2×D43—84no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—81no—
242C4×C43#46312yes—
243C4×C43C2×#13511yescharacteristic
244C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C43C2×#13711yescharacteristic
246C4×C43#57511yescharacteristic
247Dic43—41no—
248Dic43—41no—
249Dic43—82no—
250#3141—431no—
251#3100—431no—
252C2×#476—431no—
253D4×M16—431no—
254#1703—432no—
255#1697—432no—
256#1683—432no—
257#1677—432no—
258#1565—431no—
259#1548—431no—
260#1547D4311yescharacteristic, complemented
261C2×C43—22no—
262C2×C43—161no—
263C2×C43C2×#46311yescharacteristic
264C2×C43#305611yescharacteristic
265C2×C43#306811yescharacteristic
266D43—42no—
267D43—81no—
268C22×M16—861no—
269#532C2×D4311yescharacteristic
270C2×C4⋊Q8—431no—
271C2×C4×D4—431no—
272#489—862no—
273#487—432no—
274#486—432no—
275#480—861no—
276#476—432no—
277#476—432no—
278#476—861no—
279#476—861no—
280#474—431no—
281#474—431no—
282#459—431no—
283#459—431no—
284#447—861no—
285C4×D8—861no—
286C4×D8—861no—
287#436—432no—
288#435—862no—
289C8×D4—432no—
290#431—431no—
291C2×#106—861no—
292#423C2×D4311yescharacteristic
293C2×C4⋊C8C2×D4311yescharacteristic
294#417—861no—
295#417—861no—
296C2×#102—861no—
297#407—861no—
298C4×M16—431no—
299#335—432no—
300#334—432no—
301#333—432no—
302#333—432no—
303#332C2×D4312yescomplemented
304#331C2×D4312yescomplemented
305C43#1916811yescharacteristic, complemented, Sylow
306C2×#41—21no—
307C22×Q8—861no—
308C22×D4—431no—
309C23×C4—861no—
310C2×D8—861no—
311C2×D8—861no—
312C2×M16—21no—
313C2×M16—431no—
314C2×M16—431no—
315C2×M16—862no—
316C2×M16—1724no—
317C22×C8—21no—
318C22×C8—862no—
319C4⋊Q8—432no—
320C4⋊Q8—861no—
321C4⋊Q8—861no—
322C4⋊Q8—861no—
323C4⋊Q8C22×D4311yescharacteristic
324#127C22×D4311yescharacteristic
325#124—21no—
326#121—21no—
327#121—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—431no—
331C4×D4—431no—
332C4×D4—431no—
333C4×D4—431no—
334C4×D4—861no—
335C4×D4—861no—
336C2×C4⋊C4—431no—
337C2×C4⋊C4—861no—
338C2×C4⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C42C22×D4311yescharacteristic
341#107—861no—
342#107—861no—
343#106—862no—
344#106—862no—
345C4⋊C8—21no—
346C4⋊C8—21no—
347C4⋊C8—431no—
348C4⋊C8—431no—
349C4⋊C8C22×D4312yes—
350C4⋊C8C22×D4312yes—
351#103—862no—
352#103—862no—
353#102—861no—
354#102—861no—
355#102—861no—
356#102—861no—
357#102—862no—
358#102—862no—
359#102—862no—
360#102—862no—
361C22⋊C8—862no—
362C22⋊C8—862no—
363C22⋊C8—861no—
364#97—432no—
365C4×C8—432no—
366C4×C8—861no—
367C24—861no—
368#41—42no—
369#41—42no—
370C2×Q8—21no—
371C2×Q8—862no—
372C2×Q8—3442no—
373C2×Q8—1721no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—431no—
379C2×D4—431no—
380C2×D4—862no—
381C2×D4—861no—
382C2×D4—1721no—
383C22×C4—41no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—861no—
388C22×C4—861no—
389C22×C4—1721no—
390C22×C4—1722no—
391C22×C4—1722no—
392C22×C4#1062189811yescharacteristic
393C22×C4D4×D4311yescharacteristic
394C22×C4D4×D4311yescharacteristic
395D8—1722no—
396D8—1722no—
397M16—42no—
398M16—862no—
399M16—862no—
400M16—1724no—
401C2×C8—22no—
402C2×C8—22no—
403C2×C8—42no—
404C2×C8—432no—
405C2×C8—432no—
406C2×C8—861no—
407C2×C8—861no—
408C2×C8—1724no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—431no—
412C4⋊C4—431no—
413C4⋊C4—861no—
414C4⋊C4—862no—
415C4⋊C4—862no—
416C4⋊C4—1721no—
417C4⋊C4—1721no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—861no—
421C22⋊C4—861no—
422C22⋊C4—861no—
423C22⋊C4—861no—
424C42#1062189811yescharacteristic
425C42D4×D4311yescharacteristic
426C42D4×D4311yescharacteristic
427C42C23×D4311yescharacteristic
428C23—41no—
429C23—861no—
430C23—861no—
431C23—3441no—
432C23—1722no—
433C23—1722no—
434C23#1306329811yescharacteristic
435Q8—41no—
436Q8—41no—
437Q8—3442no—
438Q8—3442no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—81no—
444D4—82no—
445D4—432no—
446D4—861no—
447D4—861no—
448D4—861no—
449D4—1722no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—82no—
455C2×C4—861no—
456C2×C4—861no—
457C2×C4—3442no—
458C2×C4—1722no—
459C2×C4—1722no—
460C2×C4—1722no—
461C2×C4—1722no—
462C2×C4—1721no—
463C2×C4—1721no—
464C2×C4—1721no—
465C2×C4—1721no—
466C2×C4#1306329811yescharacteristic
467C2×C4#1306329811yescharacteristic
468C2×C4#1306329811yescharacteristic
469C2×C4#1306334612yes—
470C2×C4#1306334912yes—
471C2×C4C2×D4×D4311yescharacteristic
472C2×C4C2×D4×D4311yescharacteristic
473C2×C4C2×#1062189811yescharacteristic
474C8—42no—
475C8—42no—
476C8—862no—
477C8—862no—
478C8—1721no—
479C8—1721no—
480C22—21no—
481C22—21no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—862no—
486C22—3444no—
487C22—1721no—
488C22—1721no—
489C22—1721no—
490C22—1721no—
491C22—1721no—
492C22#1458311312yes—
493C22C2×#1306329811yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—81no—
498C4—3442no—
499C4—1721no—
500C4—1721no—
501C4#1458311312yes—
502C4C2×#1306334611yescharacteristic
503C4C2×#1306334911yescharacteristic
504C4#137×D4311yescharacteristic
505C4#1458369511yescharacteristic
506C2—22no—
507C2—161no—
508C2—3441no—
509C2—1722no—
510C2C2×#1458311311yescharacteristic
511C2#1914422811yescharacteristic
512C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1547C2
socleC22×C43C2×#121
prime radical#19144591C2
hypercenter#1547D43
hypocenterC43#19168
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
1. #19144988C2semidirect
3. C2×#14583190C2semidirect
4. #19143330C2semidirect
5. #19134169C2semidirect
6. #19134127C2semidirect
7. #19134045C2semidirect
8. #19134003C2semidirect
9. #19133345C2semidirect
10. #19133277C2semidirect
11. C43×#1547C2semidirect
16. #14583249C22semidirect
17. #14583245C22semidirect
40. #14582651C22semidirect
41. #14582649C22semidirect
42. #14582647C22semidirect
43. #14582647C22semidirect
47. C43×#332C22semidirect
48. C43×#331C22semidirect
260. #1547D43semidirect
303. #332C2×D43semidirect
304. #331C2×D43semidirect
305. C43#19168semidirect

Maximal subgroups

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

subgroupindex
#191449882
#191445912
C2×#145831902
#191433302
#191341692
#191341272
#191340452
#191340032
#191333452
#191332772
C43×#15472
#1916843