Finite Group Databasebeta

← #25082000

Subgroups — #25082000

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#19145538C211yesmaximal, characteristic, complemented
2#19144383C211yesmaximal, characteristic, complemented
3#19144075C211yesmaximal, characteristic
4#19134011C212yesmaximal, complemented
5#19134004C212yesmaximal, complemented
6#19133943C212yesmaximal, complemented
7#19133936C212yesmaximal, complemented
8#19133366C211yesmaximal, characteristic, complemented
9#19133283C211yesmaximal, characteristic, complemented
10C2×#14582642C211yesmaximal, characteristic, complemented
11C43×#2988C211yesmaximal, characteristic, complemented
12C2×#13063350—21no—
13#14583456C2211yescharacteristic
14C2×#13063322C2211yescharacteristic
15#14583272C2212yes—
16#14583246C2212yes—
17#14583206—21no—
18#14583199—21no—
19#14583194C2211yescharacteristic, complemented
20#14583189C2211yescharacteristic, complemented
21#14583184C2211yescharacteristic, complemented
22#14583179C2211yescharacteristic, complemented
23#14583100—21no—
24#14583100—21no—
25#14583099—21no—
26#14583099C2212yes—
27#14583094—21no—
28#14583094C2212yes—
29#14583052—22no—
30#14582935—21no—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582903—21no—
34#14582895—21no—
35#14582650C2212yescomplemented
36#14582650C2212yescomplemented
37#14582647C2212yescomplemented
38#14582646C2212yescomplemented
39#14582642C2212yes—
40#14582642C2212yes—
41C4×#41×C43C2211yescharacteristic
42C8×Q8×C43C2212yescomplemented
43C8×D4×C43—22no—
44C8×D4×C43C2212yescomplemented
45C43×#431—21no—
46C43×#431C2211yescharacteristic
47C2×C4⋊C8×C43—21no—
48C2×C4⋊C8×C43C2211yescharacteristic
49C22×D172—21no—
50C22×D172—21no—
51C22×D172—21no—
52#13063350—44no—
53C2×#10621873—22no—
54C2×#10621873—22no—
55C2×#10621884—22no—
56C2×#10621882—22no—
57C2×#10621877—21no—
58C22×C43⋊C8—21no—
59#13063325C2311yescharacteristic
60#13063325C2311yescharacteristic
61#13063322—21no—
62#13063322—21no—
63#13063322—21no—
64#13063322C2312yes—
65#13063317—21no—
66#13063304—21no—
67#13063304—21no—
68C4×Dic86—21no—
69C4×Dic86—21no—
70#13063284—21no—
71#13063258—21no—
72#13063258—21no—
73#13063256—21no—
74#13063256—21no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)—21no—
77C4⋊(C43⋊C8)C2312yes—
78C4⋊(C43⋊C8)C2311yescharacteristic
79C4⋊(C43⋊C8)C2311yescharacteristic
80#13063249—21no—
81#13063249—21no—
82#13063247—22no—
83#13063247—22no—
84#13063246—21no—
85#13063246—21no—
86#13063245—22no—
87#13063245—22no—
88C2×#41×C43D411yescharacteristic
89C22×C8×C43—21no—
90C22×C8×C43—22no—
91C4×Q8×C43D411yescharacteristic
92C4×Q8×C43C2311yescharacteristic
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43D411yescharacteristic
96C4×D4×C43C2311yescharacteristic
97#117×C43—21no—
98#117×C43D411yescharacteristic
99C2×C42×C43—21no—
100C2×C42×C43C2311yescharacteristic
101C4⋊C8×C43—22no—
102C4⋊C8×C43—21no—
103C4⋊C8×C43D411yescharacteristic
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43C2312yes—
106C22⋊C8×C43—22no—
107C22⋊C8×C43D412yes—
108C4×C8×C43—22no—
109C4×C8×C43C2312yes—
110C23×D43—41no—
111#41×C43—22no—
112#41×C43SD1614yescomplemented
113C2×Q8×C43C2×D411yescharacteristic
114C2×D4×C43—21no—
115C2×D4×C43C2×D411yescharacteristic
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C2×D172—22no—
123C2×D172—22no—
124C2×D172—22no—
125C2×D172—41no—
126C2×D172—41no—
127C2×D172—41no—
128C2×D172—42no—
129C2×D172—42no—
130C2×D172—81no—
131C2×D172—81no—
132C2×D172—82no—
133C2×Dic86—21no—
134C2×Dic86—21no—
135C2×C8×C43—22no—
136C2×C8×C43—82no—
137C2×C8×C43—81no—
138C2×C8×C43C2×D412yes—
139C2×C8×C43C2×D412yes—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43C2×D411yescharacteristic
143C4⋊C4×C43C2×D411yescharacteristic
144C22⋊C4×C43—21no—
145C22⋊C4×C43—21no—
146C22⋊C4×C43—21no—
147C42×C43—21no—
148C42×C43—21no—
149C42×C43—21no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154C22⋊Dic43—41no—
155#10621884—44no—
156#10621882—44no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161Dic43⋊C4—41no—
162Dic43⋊C4—41no—
163C4×Dic43—41no—
164#10621877—42no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—21no—
168C2×C43⋊C8—42no—
169#10621873—82no—
170#10621873—82no—
171C23×C43—21no—
172C23×C43#12111yescharacteristic
173C22×D43—42no—
174C22×D43—82no—
175C22×D43—82no—
176C22×D43—82no—
177Q8×C43—21no—
178Q8×C43C2×SD1612yes—
179D4×C43—24no—
180D4×C43—21no—
181D4×C43C2×SD1612yes—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—24no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—81no—
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43C2×SD1612yes—
196C2×C4×C43#13512yes—
197C2×C4×C43C22×D411yescharacteristic
198C2×C4×C43C22×D411yescharacteristic
199C2×C4×C43C2×#4111yescharacteristic
200C2×Dic43—41no—
201C2×Dic43—41no—
202D172—42no—
203D172—42no—
204D172—42no—
205D172—42no—
206D172—82no—
207D172—82no—
208D172—82no—
209D172—82no—
210Dic86—41no—
211Dic86—41no—
212Dic86—81no—
213C8×C43—22no—
214C8×C43—22no—
215C8×C43—42no—
216C43⋊C8—42no—
217C43⋊C8—41no—
218C43⋊C8—41no—
219#19409—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—22no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43#46512yes—
226C22×C43C2×#12111yescharacteristic
227C2×D43—82no—
228C2×D43—82no—
229C2×D43—82no—
230C2×D43—164no—
231C4×C43—21no—
232C4×C43—22no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—41no—
236C4×C43—41no—
237C4×C43#46512yes—
238C4×C43C22×SD1611yescharacteristic
239C4×C43C2×#13511yescharacteristic
240C4×C43#57611yescharacteristic
241C4×C43#57711yescharacteristic
242Dic43—81no—
243Dic43—81no—
244#3208—431no—
245#3076—431no—
246#3038—431no—
247#2988D4311yescharacteristic, complemented
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—42no—
257C2×C43#304511yescharacteristic
258C2×C43C2×#46511yescharacteristic
259C2×C43#306811yescharacteristic
260D43—162no—
261C2×AGL(1,ℤ/8)—861no—
262#533—431no—
263C2×#127—431no—
264C4×#41C2×D4311yescharacteristic
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×Q8C2×D4312yescomplemented
281C8×D4—22no—
282C8×D4C2×D4312yescomplemented
283#431—21no—
284#431C2×D4311yescharacteristic
285#427—861no—
286#423—431no—
287C2×C4⋊C8—21no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8C2×D4311yescharacteristic
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×#41D17211yescharacteristic
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—861no—
309C22×C8—21no—
310C22×C8—22no—
311C22×C8—861no—
312C4⋊Q8—431no—
313C4⋊Q8—431no—
314#127—432no—
315#127—861no—
316#127—861no—
317#127—861no—
318#125—861no—
319C22⋊Q8—861no—
320C22⋊Q8—861no—
321C4×Q8—861no—
322C4×Q8—861no—
323C4×Q8D17211yescharacteristic
324C4×Q8C22×D4311yescharacteristic
325C4×D4—21no—
326C4×D4—21no—
327C4×D4D17211yescharacteristic
328C4×D4C22×D4311yescharacteristic
329#117—21no—
330#117—861no—
331#117D17211yescharacteristic
332C2×C42—21no—
333C2×C42C22×D4311yescharacteristic
334#107—861no—
335#107—861no—
336#106—861no—
337#106—861no—
338C4⋊C8—22no—
339C4⋊C8—21no—
340C4⋊C8—431no—
341C4⋊C8—431no—
342C4⋊C8—432no—
343C4⋊C8—861no—
344C4⋊C8—861no—
345C4⋊C8C22⋊D4311yescharacteristic
346C4⋊C8C22⋊D4311yescharacteristic
347C4⋊C8C22×D4312yes—
348#103—861no—
349#103—861no—
350#102—861no—
351#102—861no—
352#102—862no—
353#102—862no—
354#102—862no—
355#102—862no—
356C22⋊C8—22no—
357C22⋊C8C22⋊D4312yes—
358C4×C8—22no—
359C4×C8C22×D4312yes—
360C24—1721no—
361#41—22no—
362#41#1062187314yescomplemented
363C2×Q8—861no—
364C2×Q8—861no—
365C2×Q8C2×D17211yescharacteristic
366C2×D4—21no—
367C2×D4—862no—
368C2×D4—862no—
369C2×D4—862no—
370C2×D4—3441no—
371C2×D4—3441no—
372C2×D4—3442no—
373C2×D4—1721no—
374C2×D4—1721no—
375C2×D4—1721no—
376C2×D4—1722no—
377C2×D4—1722no—
378C2×D4C2×D17211yescharacteristic
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4C2×D17211yescharacteristic
383C22×C4#1062189811yescharacteristic
384C22×C4C2×C22⋊D4311yescharacteristic
385SD16—3442no—
386SD16—3442no—
387SD16—1724no—
388D8—1724no—
389M16—1722no—
390C2×C8—22no—
391C2×C8—82no—
392C2×C8—81no—
393C2×C8—862no—
394C2×C8—861no—
395C2×C8—861no—
396C2×C8—1722no—
397C2×C8C2×C22⋊D4312yes—
398C2×C8C2×C22⋊D4312yes—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—861no—
402C4⋊C4—861no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C4⋊C4C2×D17211yescharacteristic
408C4⋊C4C2×D17211yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—1721no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—1721no—
417C42C2×D17211yescharacteristic
418C42#1062189811yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—21no—
422C23—3442no—
423C23—3442no—
424C23—3442no—
425C23—1722no—
426C23#1306329911yescharacteristic
427Q8—21no—
428Q8—3441no—
429Q8—1721no—
430Q8—1721no—
431Q8C2×#1062187312yes—
432D4—24no—
433D4—21no—
434D4—3442no—
435D4—3442no—
436D4—3442no—
437D4—3442no—
438D4—1722no—
439D4—1722no—
440D4—1722no—
441D4—1722no—
442D4C2×#1062187312yes—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4#1306329911yescharacteristic
456C2×C4#1306329911yescharacteristic
457C2×C4#1306329911yescharacteristic
458C2×C4C2×#1062187312yes—
459C2×C4#1306334712yes—
460C2×C4C22×C22⋊D4311yescharacteristic
461C2×C4C22×D17211yescharacteristic
462C2×C4C2×#1062189811yescharacteristic
463C8—22no—
464C8—22no—
465C8—42no—
466C8—1722no—
467C8—1721no—
468C8—1721no—
469C22—21no—
470C22—21no—
471C22—22no—
472C22—41no—
473C22—41no—
474C22—3442no—
475C22—3442no—
476C22—3442no—
477C22—6884no—
478C22#1458312812yes—
479C22C2×#1306329911yescharacteristic
480C4—21no—
481C4—21no—
482C4—21no—
483C4—22no—
484C4—41no—
485C4—41no—
486C4—3441no—
487C4—3441no—
488C4#1458312812yes—
489C4C22×#1062187311yescharacteristic
490C4C2×#1306334711yescharacteristic
491C4#1458370211yescharacteristic
492C4#1458370711yescharacteristic
493C2—22no—
494C2—42no—
495C2—6882no—
496C2#1914413411yescharacteristic
497C2C2×#1458312811yescharacteristic
498C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
prime radical#19144075C2
hypercenter#2988D43
hypocenterC43#19409
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #19145538C2semidirect
2. #19144383C2semidirect
4. #19134011C2semidirect
5. #19134004C2semidirect
6. #19133943C2semidirect
7. #19133936C2semidirect
8. #19133366C2semidirect
9. #19133283C2semidirect
10. C2×#14582642C2semidirect
11. C43×#2988C2semidirect
19. #14583194C22semidirect
20. #14583189C22semidirect
21. #14583184C22semidirect
22. #14583179C22semidirect
35. #14582650C22semidirect
36. #14582650C22semidirect
37. #14582647C22semidirect
38. #14582646C22semidirect
42. C8×Q8×C43C22semidirect
44. C8×D4×C43C22semidirect
112. #41×C43SD16semidirect
247. #2988D43semidirect
280. C8×Q8C2×D43semidirect
282. C8×D4C2×D43semidirect
298. C43#19409semidirect
362. #41#10621873semidirect

Maximal subgroups

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

subgroupindex
#191455382
#191443832
#191440752
#191340112
#191340042
#191339432
#191339362
#191333662
#191332832
C2×#145826422
C43×#29882
#1940943