Finite Group Databasebeta

← #25079108

Subgroups — #25079108

Order 11008.

770 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145021C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic, complemented
3C2×#14582977C211yesmaximal, characteristic, complemented
4#19134082C212yesmaximal, complemented
5#19134072C212yesmaximal, complemented
6#19134062C212yesmaximal, complemented
7#19134058C212yesmaximal, complemented
8#19133341C211yesmaximal, characteristic, complemented
9#19133244C211yesmaximal, characteristic, complemented
10#19133242C211yesmaximal, characteristic, complemented
11C43×#3100C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13C2×#13063345—21no—
14C22×#10621877—21no—
15#14583449C2211yescharacteristic
16#14583281—21no—
17#14583281—21no—
18#14583278C2211yescharacteristic, complemented
19#14583275C2211yescharacteristic, complemented
20#14583273C2211yescharacteristic, complemented
21#14583271C2211yescharacteristic, complemented
22#14583212—21no—
23#14583179C2212yes—
24#14583094C2212yes—
25#14583033—21no—
26C4×#10621882—22no—
27#14582977—21no—
28#14582977—21no—
29#14582977C2212yes—
30#14582977C2212yes—
31#14582952C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)—21no—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582651C2212yescomplemented
36#14582649C2212yescomplemented
37#14582645C2212yescomplemented
38#14582644C2212yescomplemented
39#14582643C2212yescomplemented
40#14582642C2212yescomplemented
41C43×#532C2211yescharacteristic
42C2×C4×D4×C43C2211yescharacteristic
43C43×#480—21no—
44C43×#474C2212yes—
45C43×#459C2212yes—
46C43×#447—21no—
47C4×D8×C43—22no—
48C43×#431C2211yescharacteristic
49C2×#10621898—21no—
50#13063345—44no—
51#13063345—44no—
52C2×#10621885—21no—
53C2×#10621885—21no—
54C2×#10621883—21no—
55C2×#10621883—21no—
56C2×#10621884—21no—
57C2×#10621884—21no—
58C2×#10621882—22no—
59C2×#10621882—21no—
60C2×#10621882—21no—
61C2×#10621877—22no—
62C2×#10621877—22no—
63C2×#10621877—44no—
64C22×C43⋊C8—21no—
65C22×C43⋊C8D411yescharacteristic
66C22×C43⋊C8D411yescharacteristic
67#13063325C2311yescharacteristic
68#13063322C2311yescharacteristic
69#13063313—21no—
70#13063299—21no—
71#13063299—21no—
72C4×D172—21no—
73C4×D172—21no—
74#13063258—22no—
75C4⋊(C43⋊C8)—21no—
76C4⋊(C43⋊C8)C2312yes—
77C4⋊(C43⋊C8)C2312yes—
78#13063246—22no—
79#13063245—22no—
80C22⋊(C43⋊C8)—21no—
81C22⋊(C43⋊C8)—22no—
82C22⋊(C43⋊C8)—22no—
83C4×C43⋊C8—21no—
84C4×C43⋊C8D411yescharacteristic
85C4×C43⋊C8D411yescharacteristic
86C4×C43⋊C8C2311yescharacteristic
87C4×C43⋊C8C2311yescharacteristic
88C2×#41×C43—21no—
89C22×D4×C43D411yescharacteristic
90C23×C4×C43—21no—
91C2×D8×C43—22no—
92C4⋊Q8×C43C2311yescharacteristic
93#127×C43C2311yescharacteristic
94#124×C43—21no—
95#121×C43—21no—
96#121×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43D412yes—
102C4×D4×C43C2312yes—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#107×C43—22no—
107C4⋊C8×C43C2312yes—
108#102×C43—22no—
109#102×C43—22no—
110C22⋊C8×C43—21no—
111C4×C8×C43—21no—
112C24×C43—21no—
113#41×C43—42no—
114#41×C43—42no—
115C2×Q8×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—42no—
121C2×D4×C43—41no—
122C2×D4×C43C2×D412yes—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—21no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—41no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C2×C22⋊D43—41no—
133#10621898—42no—
134#10621898—42no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×C4×D43—41no—
139C2×Dic86—21no—
140D8×C43—44no—
141C2×C8×C43—22no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43C2×D412yes—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43#4111yescharacteristic
153C42×C43C2411yescharacteristic
154#10621885—42no—
155#10621885—42no—
156#10621884—42no—
157#10621884—42no—
158#10621883—42no—
159#10621883—42no—
160#10621882—42no—
161#10621882—44no—
162#10621882—42no—
163(C2×D43)⋊C4—41no—
164(C2×D43)⋊C4—41no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167#10621877—44no—
168#10621877—44no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—42no—
173C2×C43⋊C8D814yescomplemented
174C2×C43⋊C8C2×D411yescharacteristic
175C2×C43⋊C8C2×D411yescharacteristic
176C2×C43⋊C8C2×D411yescharacteristic
177C2×C43⋊C8C2×D411yescharacteristic
178C23×C43—22no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—41no—
183C23×C43#12111yescharacteristic
184C22×D43—41no—
185Q8×C43—41no—
186Q8×C43—41no—
187D4×C43—22no—
188D4×C43—22no—
189D4×C43—42no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—42no—
193D4×C43—81no—
194D4×C43—82no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—41no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—44no—
202C2×C4×C43—41no—
203C2×C4×C43—82no—
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43#12111yescharacteristic
207C2×C4×C43C2×D812yes—
208C2×C4×C43AGL(1,ℤ/8)12yes—
209C2×C4×C43C22×D411yescharacteristic
210C2×C4×C43C22×D411yescharacteristic
211C2×C4×C43C2×#4111yescharacteristic
212C22⋊D43—82no—
213C2×Dic43—41no—
214D172—41no—
215D172—41no—
216D172—42no—
217D172—81no—
218C4×D43—82no—
219Dic86—41no—
220Dic86—41no—
221C8×C43—42no—
222C43⋊C8—21no—
223C43⋊C8—21no—
224C43⋊C8—42no—
225C43⋊C8—42no—
226C43⋊C8C2×D812yes—
227C43⋊C8C2×D812yes—
228#19133—431nomaximal, Sylow
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—42no—
232C22×C43—42no—
233C22×C43—42no—
234C22×C43—84no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43#45912yes—
239C22×C43C2×#12111yescharacteristic
240C2×D43—81no—
241C2×D43—81no—
242C2×D43—81no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—42no—
247C4×C43—81no—
248C4×C43#45912yes—
249C4×C43C22×D811yescharacteristic
250C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
251C4×C43#57512yes—
252Dic43—81no—
253#3147—431no—
254#3100—431no—
255#3100D4311yescharacteristic, complemented
256C2×#436—431no—
257#1689—432no—
258#1687—432no—
259#1685—432no—
260#1685—432no—
261#1564—431no—
262#1540—431no—
263#1540—431no—
264C2×C43—22no—
265C2×C43—82no—
266C2×C43—161no—
267C2×C43C2×#45911yescharacteristic
268C2×C43#305411yescharacteristic
269C2×C43#306711yescharacteristic
270D43—161no—
271C2×#135—861no—
272C2×#135—861no—
273C22×M16—861no—
274#532—431no—
275#532C2×D4311yescharacteristic
276C2×C4×D4C2×D4311yescharacteristic
277#495—861no—
278#495—861no—
279#494—431no—
280#493—431no—
281#492—431no—
282#492—431no—
283#480—21no—
284#480—861no—
285#474—432no—
286#474C2×D4312yes—
287#459—432no—
288#459C2×D4312yes—
289#447—21no—
290#447—861no—
291C4×D8—22no—
292C4×D8—862no—
293#436—432no—
294#436—432no—
295#436—861no—
296#436—861no—
297#431—431no—
298#431C2×D4311yescharacteristic
299C2×C4⋊C8—431no—
300C2×C22⋊C8—861no—
301C2×C4×C8—431no—
302#335—432no—
303#334—432no—
304#332—432no—
305#332—432no—
306#331—432no—
307#331—432no—
308C43#1913311yescharacteristic, complemented, Sylow
309C2×#41—21no—
310C2×#41—861no—
311C22×D4C22⋊D4311yescharacteristic
312C23×C4—21no—
313#135—1724no—
314#135—1724no—
315C2×Q16—861no—
316C2×Q16—861no—
317C2×SD16—861no—
318C2×SD16—861no—
319C2×SD16—861no—
320C2×SD16—861no—
321C2×D8—22no—
322C2×D8—861no—
323C2×D8—861no—
324C2×D8—862no—
325C2×M16—862no—
326C2×M16—862no—
327C2×M16—1724no—
328C22×C8—431no—
329C22×C8—431no—
330C22×C8—861no—
331C4⋊Q8—431no—
332C4⋊Q8C22×D4311yescharacteristic
333#127—431no—
334#127C22×D4311yescharacteristic
335#124—21no—
336#124—861no—
337#121—21no—
338#121—21no—
339#121—861no—
340#121—861no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—21no—
345C4×D4—861no—
346C4×D4—861no—
347C4×D4C22⋊D4312yes—
348C4×D4C22×D4312yes—
349C2×C4⋊C4C22⋊D4311yescharacteristic
350C2×C22⋊C4—21no—
351C2×C42C22×D4311yescharacteristic
352#107—22no—
353#107—862no—
354C4⋊C8—432no—
355C4⋊C8—432no—
356C4⋊C8—861no—
357C4⋊C8C22×D4312yes—
358#102—22no—
359#102—22no—
360#102—862no—
361#102—862no—
362C22⋊C8—21no—
363C22⋊C8—862no—
364C22⋊C8—862no—
365C22⋊C8—861no—
366C4×C8—21no—
367C4×C8—431no—
368C4×C8—431no—
369C4×C8—431no—
370C4×C8—431no—
371C4×C8—861no—
372C24—21no—
373#41—42no—
374#41—42no—
375#41—1722no—
376#41—1722no—
377C2×Q8—21no—
378C2×Q8—861no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—42no—
384C2×D4—41no—
385C2×D4—861no—
386C2×D4—861no—
387C2×D4—861no—
388C2×D4—1721no—
389C2×D4C2×C22⋊D4312yes—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—42no—
394C22×C4—42no—
395C22×C4—41no—
396C22×C4—1721no—
397C22×C4D4×D4311yescharacteristic
398C22×C4#1062190011yescharacteristic
399C22×C4C2×C22⋊D4311yescharacteristic
400Q16—1722no—
401Q16—1722no—
402SD16—1722no—
403SD16—1722no—
404SD16—1722no—
405SD16—1722no—
406D8—44no—
407D8—1722no—
408D8—1722no—
409D8—1724no—
410M16—1724no—
411M16—1724no—
412C2×C8—22no—
413C2×C8—434no—
414C2×C8—431no—
415C2×C8—431no—
416C2×C8—431no—
417C2×C8—431no—
418C2×C8—862no—
419C2×C8—862no—
420C2×C8—862no—
421C2×C8—1722no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4C2×C22⋊D4312yes—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—1721no—
433C22⋊C4—1721no—
434C42D4×D4311yescharacteristic
435C42#1062190011yescharacteristic
436C42C2×C22⋊D4311yescharacteristic
437C42C23×D4311yescharacteristic
438C23—22no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—41no—
443C23—1721no—
444C23#1306329711yescharacteristic
445Q8—41no—
446Q8—41no—
447Q8—1721no—
448Q8—1721no—
449D4—22no—
450D4—22no—
451D4—42no—
452D4—41no—
453D4—41no—
454D4—42no—
455D4—81no—
456D4—82no—
457D4—3441no—
458D4—3442no—
459D4—1721no—
460D4—1721no—
461D4—1722no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—3442no—
472C2×C4—1721no—
473C2×C4#1306329711yescharacteristic
474C2×C4#1306329711yescharacteristic
475C2×C4#1306329711yescharacteristic
476C2×C4D8×D4312yes—
477C2×C4#1306334912yes—
478C2×C4C2×D4×D4311yescharacteristic
479C2×C4C22×C22⋊D4311yescharacteristic
480C2×C4C2×#1062190011yescharacteristic
481C8—42no—
482C8—432no—
483C8—432no—
484C8—861no—
485C8—861no—
486C8—1722no—
487C8—1722no—
488C22—21no—
489C22—21no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—84no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—3441no—
498C22—3441no—
499C22—3441no—
500C22#1458309212yes—
501C22C2×#1306329711yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—42no—
506C4—81no—
507C4—3441no—
508C4#1458309212yes—
509C4C2×D8×D4311yescharacteristic
510C4C2×#1306334911yescharacteristic
511C4#1458369712yes—
512C2—22no—
513C2—82no—
514C2—161no—
515C2—6881no—
516C2C2×#1458309211yescharacteristic
517C2#1914420111yescharacteristic
518C2#1914431211yescharacteristic
subgroupG/H
centerC2×C4#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3100C2
socleC22×C43C2×#121
hypercenter#3100D43
hypocenterC43#19133
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #19145021C2semidirect
2. #19144595C2semidirect
3. C2×#14582977C2semidirect
4. #19134082C2semidirect
5. #19134072C2semidirect
6. #19134062C2semidirect
7. #19134058C2semidirect
8. #19133341C2semidirect
9. #19133244C2semidirect
10. #19133242C2semidirect
11. C43×#3100C2semidirect
18. #14583278C22semidirect
19. #14583275C22semidirect
20. #14583273C22semidirect
21. #14583271C22semidirect
35. #14582651C22semidirect
36. #14582649C22semidirect
37. #14582645C22semidirect
38. #14582644C22semidirect
39. #14582643C22semidirect
40. #14582642C22semidirect
173. C2×C43⋊C8D8semidirect
255. #3100D43semidirect
308. C43#19133semidirect

Maximal subgroups

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

subgroupindex
#191450212
#191445952
C2×#145829772
#191340822
#191340722
#191340622
#191340582
#191333412
#191332442
#191332422
C43×#31002
#1913343