Finite Group Databasebeta

← #25079438

Subgroups — #25079438

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144988C211yesmaximal, characteristic, complemented
2C2×#14583104C211yesmaximal, characteristic, complemented
3D4×#10621877C211yesmaximal, characteristic, complemented
4#19134154C212yesmaximal, complemented
5#19134140C212yesmaximal, complemented
6#19134030C212yesmaximal, complemented
7#19134016C212yesmaximal, complemented
8#19133348C211yesmaximal, characteristic, complemented
9#19133279C211yesmaximal, characteristic, complemented
10#19133272C211yesmaximal, characteristic, complemented
11C43×#3100C211yesmaximal, characteristic
12C22×#10621883—21no—
13C22×#10621877—21no—
14C2×#13063325C2211yescharacteristic
15#14583258—22no—
16#14583249C2212yescomplemented
17#14583245C2212yescomplemented
18#14583104—21no—
19#14583104—21no—
20#14583104C2212yes—
21#14583104C2212yes—
22#14582977C2212yes—
23#14582971—22no—
24D4×C43⋊C8C2212yes—
25#14582923C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27#14582900—21no—
28#14582900—21no—
29C2×#13063248—21no—
30#14582863—21no—
31C4×#10621877C2211yescharacteristic
32#14582651C2212yescomplemented
33#14582649C2212yescomplemented
34#14582646C2212yescomplemented
35#14582646C2212yescomplemented
36#14582645C2212yescomplemented
37#14582643C2212yescomplemented
38C43×#532C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C43×#480—21no—
41C43×#474C2211yescharacteristic
42C43×#474C2211yescharacteristic
43C43×#459C2211yescharacteristic
44C43×#459C2211yescharacteristic
45C43×#447—21no—
46C4×D8×C43—21no—
47C4×D8×C43—21no—
48C43×#431C2211yescharacteristic
49C22×Dic86—21no—
50C2×#10621883—22no—
51C2×#10621883—22no—
52C2×#10621883—44no—
53C2×#10621877—21no—
54C2×#10621877—22no—
55C2×#10621877—44no—
56C2×#10621877D411yescharacteristic
57C2×#10621877D411yescharacteristic
58C22×C43⋊C8—21no—
59C22×C43⋊C8—22no—
60#13063325—21no—
61#13063325—21no—
62#13063325—21no—
63#13063325C2312yes—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C4⋊(C43⋊C8)—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)C2312yes—
69C4⋊(C43⋊C8)C2312yes—
70#13063249—22no—
71#13063249—22no—
72#13063248—22no—
73#13063248—22no—
74#13063246—22no—
75#13063246—22no—
76C22⋊(C43⋊C8)—22no—
77C22⋊(C43⋊C8)—22no—
78#13063236D412yes—
79C4×C43⋊C8C2312yes—
80C2×#41×C43—21no—
81C22×D4×C43D411yescharacteristic
82C23×C4×C43—21no—
83C2×D8×C43—21no—
84C2×D8×C43—21no—
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43C2311yescharacteristic
87#124×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43D411yescharacteristic
95C4×D4×C43D411yescharacteristic
96C4×D4×C43C2311yescharacteristic
97C4×D4×C43C2311yescharacteristic
98C2×C4⋊C4×C43D411yescharacteristic
99C2×C22⋊C4×C43—21no—
100C2×C42×C43C2311yescharacteristic
101#107×C43—21no—
102#107×C43—21no—
103C4⋊C8×C43C2311yescharacteristic
104C4⋊C8×C43C2311yescharacteristic
105#102×C43—21no—
106#102×C43—21no—
107#102×C43—21no—
108#102×C43—21no—
109C22⋊C8×C43—21no—
110C4×C8×C43—21no—
111C24×C43—21no—
112#41×C43—42no—
113#41×C43—42no—
114C2×Q8×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—22no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C2×D4×C43—41no—
122C2×D4×C43C2×D411yescharacteristic
123C2×D4×C43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—41no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43#4111yescharacteristic
135C22×Dic43—41no—
136C2×Dic86—22no—
137C2×Dic86—42no—
138C2×Dic86—42no—
139C2×Dic86—41no—
140D8×C43—42no—
141D8×C43—42no—
142C2×C8×C43—21no—
143C2×C8×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43C2×D411yescharacteristic
148C4⋊C4×C43C2×D411yescharacteristic
149C22⋊C4×C43—21no—
150C22⋊C4×C43—21no—
151C22⋊C4×C43—21no—
152C22⋊C4×C43—21no—
153C22⋊C4×C43—41no—
154C22⋊C4×C43—41no—
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43#4111yescharacteristic
158C42×C43C2411yescharacteristic
159#10621883—44no—
160#10621883—44no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43—41no—
164C4⋊Dic43—41no—
165#10621877—22no—
166#10621877—22no—
167#10621877—44no—
168#10621877—42no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—44no—
172C2×C43⋊C8—42no—
173C2×C43⋊C8C2×D412yes—
174C2×C43⋊C8C2×D412yes—
175C23×C43—21no—
176C23×C43—21no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43—41no—
180C23×C43—81no—
181C23×C43#12111yescharacteristic
182Q8×C43—41no—
183Q8×C43—41no—
184D4×C43—21no—
185D4×C43—21no—
186D4×C43—21no—
187D4×C43—42no—
188D4×C43—41no—
189D4×C43—41no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—81no—
193D4×C43—82no—
194D4×C43AGL(1,ℤ/8)12yes—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—41no—
200C2×C4×C43—42no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—41no—
208C2×C4×C43—82no—
209C2×C4×C43#12111yescharacteristic
210C2×C4×C43#12111yescharacteristic
211C2×C4×C43#12111yescharacteristic
212C2×C4×C43#13512yes—
213C2×C4×C43AGL(1,ℤ/8)12yes—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C2×#4111yescharacteristic
217C2×Dic43—42no—
218C2×Dic43—82no—
219Dic86—42no—
220Dic86—42no—
221Dic86—82no—
222C8×C43—41no—
223C8×C43—41no—
224C43⋊C8—22no—
225C43⋊C8—22no—
226C43⋊C8—42no—
227C43⋊C8—42no—
228#19169—431nomaximal, Sylow
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—22no—
232C22×C43—41no—
233C22×C43—41no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43—84no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43#46312yes—
242C22×C43C2×#12111yescharacteristic
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—21no—
246C4×C43—41no—
247C4×C43—41no—
248C4×C43—81no—
249C4×C43#46312yes—
250C4×C43C2×#13511yescharacteristic
251C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
253C4×C43#57511yescharacteristic
254Dic43—82no—
255#3141—431no—
256#3100D4311yescharacteristic
257C2×#461—431no—
258D4×M16—431no—
259#1701—432no—
260#1699—432no—
261#1681—432no—
262#1679—432no—
263#1565—431no—
264#1549—431no—
265#1547—431no—
266C2×C43—22no—
267C2×C43—42no—
268C2×C43—81no—
269C2×C43—161no—
270C2×C43C2×#46311yescharacteristic
271C2×C43#305511yescharacteristic
272C2×C43#306911yescharacteristic
273C22×SD16—861no—
274C22×M16—861no—
275#532C2×D4311yescharacteristic
276C2×C4⋊Q8—431no—
277C2×C4×D4C2×D4311yescharacteristic
278#489—862no—
279#487—432no—
280#486—432no—
281#480—21no—
282#474C2×D4311yescharacteristic
283#474C2×D4311yescharacteristic
284#461—432no—
285#461—432no—
286#461—861no—
287#461—861no—
288#459C2×D4311yescharacteristic
289#459C2×D4311yescharacteristic
290#447—21no—
291C4×D8—21no—
292C4×D8—21no—
293#436—432no—
294#435—862no—
295C8×D4—432no—
296#431C2×D4311yescharacteristic
297#423—431no—
298C2×C4⋊C8—431no—
299#417—861no—
300#417—861no—
301C2×#103—861no—
302#407—861no—
303C4×M16—431no—
304#335—432no—
305#334—432no—
306#332—432no—
307#332—432no—
308#332—432no—
309#331—432no—
310C43#1916911yescharacteristic, complemented, Sylow
311C2×#41—21no—
312C22×Q8—861no—
313C22×D4C22⋊D4311yescharacteristic
314C23×C4—21no—
315C2×SD16—862no—
316C2×SD16—862no—
317C2×SD16—1724no—
318C2×D8—21no—
319C2×D8—21no—
320C2×M16—431no—
321C2×M16—431no—
322C2×M16—862no—
323C2×M16—861no—
324C2×M16—1724no—
325C22×C8—862no—
326C22×C8—861no—
327C4⋊Q8—432no—
328C4⋊Q8—861no—
329C4⋊Q8—861no—
330C4⋊Q8—861no—
331C4⋊Q8C22×D4311yescharacteristic
332#127C22×D4311yescharacteristic
333#124—21no—
334#121—21no—
335#121—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—21no—
340C4×D4C22⋊D4311yescharacteristic
341C4×D4C22⋊D4311yescharacteristic
342C4×D4C22×D4311yescharacteristic
343C4×D4C22×D4311yescharacteristic
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4C22⋊D4311yescharacteristic
347C2×C22⋊C4—21no—
348C2×C42C22×D4311yescharacteristic
349#107—21no—
350#107—21no—
351C4⋊C8—432no—
352C4⋊C8—432no—
353C4⋊C8—861no—
354C4⋊C8—861no—
355C4⋊C8C22×D4311yescharacteristic
356C4⋊C8C22×D4311yescharacteristic
357#103—862no—
358#103—862no—
359#103—862no—
360#103—862no—
361#102—21no—
362#102—21no—
363#102—21no—
364#102—21no—
365#102—862no—
366#102—862no—
367C22⋊C8—21no—
368C22⋊C8—862no—
369C22⋊C8—862no—
370#97—432no—
371C4×C8—21no—
372C4×C8—432no—
373C24—21no—
374#41—42no—
375#41—42no—
376C2×Q8—21no—
377C2×Q8—862no—
378C2×Q8—1722no—
379C2×Q8—1722no—
380C2×Q8—1721no—
381C2×D4—22no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4C2×C22⋊D4311yescharacteristic
389C2×D4C2×C22⋊D4311yescharacteristic
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—42no—
396C22×C4—42no—
397C22×C4—41no—
398C22×C4—1721no—
399C22×C4D4×D4311yescharacteristic
400C22×C4#1062190011yescharacteristic
401C22×C4C2×C22⋊D4311yescharacteristic
402SD16—1724no—
403SD16—1724no—
404D8—42no—
405D8—42no—
406M16—862no—
407M16—862no—
408M16—1724no—
409M16—1722no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—432no—
413C2×C8—432no—
414C2×C8—862no—
415C2×C8—862no—
416C2×C8—1724no—
417C2×C8—1722no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—862no—
422C4⋊C4—862no—
423C4⋊C4—1721no—
424C4⋊C4—1721no—
425C4⋊C4C2×C22⋊D4311yescharacteristic
426C4⋊C4C2×C22⋊D4311yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C42D4×D4311yescharacteristic
434C42#1062190011yescharacteristic
435C42C2×C22⋊D4311yescharacteristic
436C42C23×D4311yescharacteristic
437C23—21no—
438C23—21no—
439C23—42no—
440C23—42no—
441C23—41no—
442C23—81no—
443C23#1306329711yescharacteristic
444Q8—41no—
445Q8—41no—
446Q8—3442no—
447Q8—1722no—
448Q8—1722no—
449D4—21no—
450D4—21no—
451D4—21no—
452D4—42no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—81no—
458D4—82no—
459D4#1306335012yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4—3442no—
475C2×C4—1722no—
476C2×C4#1306329711yescharacteristic
477C2×C4#1306329711yescharacteristic
478C2×C4#1306329711yescharacteristic
479C2×C4#1306334412yes—
480C2×C4#1306334912yes—
481C2×C4C2×D4×D4311yescharacteristic
482C2×C4C22×C22⋊D4311yescharacteristic
483C2×C4C2×#1062190011yescharacteristic
484C8—41no—
485C8—41no—
486C8—862no—
487C8—862no—
488C8—1722no—
489C8—1722no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—84no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22#1458311212yes—
503C22C2×#1306329711yescharacteristic
504C4—21no—
505C4—21no—
506C4—21no—
507C4—41no—
508C4—41no—
509C4—81no—
510C4—3442no—
511C4#1458311212yes—
512C4C2×#1306334411yescharacteristic
513C4C2×#1306334911yescharacteristic
514C4C2×#1306335011yescharacteristic
515C4#1458369711yescharacteristic
516C2—22no—
517C2—42no—
518C2—81no—
519C2—161no—
520C2C2×#1458311211yescharacteristic
521C2#1914421611yescharacteristic
522C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3100C2
socleC22×C43C2×#121
hypercenter#3100D43
hypocenterC43#19169
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3100

Complements

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

NH ≅ G/Ntype
1. #19144988C2semidirect
2. C2×#14583104C2semidirect
3. D4×#10621877C2semidirect
4. #19134154C2semidirect
5. #19134140C2semidirect
6. #19134030C2semidirect
7. #19134016C2semidirect
8. #19133348C2semidirect
9. #19133279C2semidirect
10. #19133272C2semidirect
16. #14583249C22semidirect
17. #14583245C22semidirect
32. #14582651C22semidirect
33. #14582649C22semidirect
34. #14582646C22semidirect
35. #14582646C22semidirect
36. #14582645C22semidirect
37. #14582643C22semidirect
310. C43#19169semidirect

Maximal subgroups

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

subgroupindex
#191449882
C2×#145831042
D4×#106218772
#191341542
#191341402
#191340302
#191340162
#191333482
#191332792
#191332722
C43×#31002
#1916943