Finite Group Databasebeta

← #25079455

Subgroups — #25079455

Order 11008.

766 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#19145048C211yesmaximal, characteristic
2C2×#14583099C211yesmaximal, characteristic, complemented
3Q8×#10621877C211yesmaximal, characteristic, complemented
4#19134077C212yesmaximal, complemented
5#19134069C212yesmaximal, complemented
6#19133953C212yesmaximal, complemented
7#19133945C212yesmaximal, complemented
8#19133348C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10#19133262C211yesmaximal, characteristic, complemented
11C43×#3103C211yesmaximal, characteristic, complemented
12C2×#13063350—21no—
13C2×#13063350—21no—
14C22×#10621884—21no—
15C2×#13063322C2211yescharacteristic
16#14583289—22no—
17#14583275C2212yes—
18#14583273C2212yes—
19#14583099—21no—
20#14583099—21no—
21#14583099C2212yes—
22#14583099C2212yes—
23#14583030—22no—
24#14583030C2212yescomplemented
25Q8×C43⋊C8C2212yescomplemented
26#14582923—21no—
27#14582923C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063245—21no—
30C4×#10621877—21no—
31C4×#10621877C2211yescharacteristic
32#14582651C2212yescomplemented
33#14582649C2212yescomplemented
34#14582645C2212yescomplemented
35#14582643C2212yescomplemented
36#14582642C2212yes—
37#14582642C2212yes—
38C43×#532C2211yescharacteristic
39C2×C4×Q8×C43C2211yescharacteristic
40C43×#481—21no—
41C43×#475C2211yescharacteristic, complemented
42C43×#475C2211yescharacteristic, complemented
43C43×#460C2211yescharacteristic, complemented
44C43×#460C2211yescharacteristic, complemented
45C43×#448—21no—
46C4×SD16×C43—21no—
47C4×SD16×C43—21no—
48C43×#431C2211yescharacteristic
49C22×D172—21no—
50C22×D172—21no—
51C22×D172—21no—
52#13063350—44no—
53#13063350—44no—
54C2×#10621884—22no—
55C2×#10621884—22no—
56C2×#10621884—22no—
57C2×#10621884—22no—
58C2×#10621884—44no—
59C2×#10621882—22no—
60C2×#10621882—22no—
61C2×#10621877—21no—
62C2×#10621877D411yescharacteristic
63C2×#10621877D411yescharacteristic
64C22×C43⋊C8—21no—
65#13063322—21no—
66#13063322—21no—
67#13063322—21no—
68#13063322C2312yes—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—22no—
72C4⋊(C43⋊C8)—22no—
73C4⋊(C43⋊C8)C2312yes—
74C4⋊(C43⋊C8)C2312yes—
75#13063245—22no—
76#13063245—22no—
77#13063236—22no—
78#13063236D412yes—
79C4×C43⋊C8—22no—
80C4×C43⋊C8C2312yes—
81C2×#41×C43—21no—
82C22×Q8×C43D411yescharacteristic
83C2×SD16×C43—21no—
84C2×SD16×C43—21no—
85C4⋊Q8×C43C2311yescharacteristic
86#127×C43C2311yescharacteristic
87#124×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43D411yescharacteristic
93C4×Q8×C43D411yescharacteristic
94C4×Q8×C43C2311yescharacteristic
95C4×Q8×C43C2311yescharacteristic
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43D411yescharacteristic
100C2×C42×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#106×C43—21no—
103#106×C43—21no—
104C4⋊C8×C43C2311yescharacteristic
105C4⋊C8×C43C2311yescharacteristic
106#103×C43—21no—
107#103×C43—21no—
108#102×C43—21no—
109#102×C43—21no—
110C22⋊C8×C43—21no—
111C4×C8×C43—21no—
112C23×D43—41no—
113#41×C43—42no—
114#41×C43—42no—
115C2×Q8×C43—21no—
116C2×Q8×C43—22no—
117C2×Q8×C43—21no—
118C2×Q8×C43—41no—
119C2×Q8×C43C2×D411yescharacteristic
120C2×Q8×C43C2×D411yescharacteristic
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—41no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—41no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C2×D172—22no—
132C2×D172—22no—
133C2×D172—22no—
134C2×D172—41no—
135C2×D172—41no—
136C2×D172—41no—
137C2×D172—42no—
138C2×D172—42no—
139C2×D172—42no—
140C2×D172—42no—
141C2×D172—82no—
142SD16×C43—42no—
143SD16×C43—42no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43C2×D411yescharacteristic
154C4⋊C4×C43C2×D411yescharacteristic
155C22⋊C4×C43—41no—
156C22⋊C4×C43—41no—
157C42×C43—21no—
158C42×C43—21no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43C2×D411yescharacteristic
162C42×C43C2×D411yescharacteristic
163C42×C43#4111yescharacteristic
164C42×C43C2411yescharacteristic
165#10621884—44no—
166#10621884—44no—
167#10621884—44no—
168#10621884—44no—
169#10621882—44no—
170#10621882—44no—
171#10621877—22no—
172#10621877—42no—
173#10621877SD1614yescomplemented
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—42no—
177C2×C43⋊C8C2×D412yes—
178C2×C43⋊C8C2×D412yes—
179C23×C43—41no—
180C23×C43#12111yescharacteristic
181C22×D43—42no—
182C22×D43—82no—
183C22×D43—82no—
184C22×D43—82no—
185Q8×C43—21no—
186Q8×C43—21no—
187Q8×C43—21no—
188Q8×C43—42no—
189Q8×C43—41no—
190Q8×C43—41no—
191Q8×C43AGL(1,ℤ/8)12yescomplemented
192D4×C43—41no—
193D4×C43—41no—
194D4×C43—41no—
195D4×C43—41no—
196D4×C43—81no—
197D4×C43—82no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—81no—
208C2×C4×C43—82no—
209C2×C4×C43#12111yescharacteristic
210C2×C4×C43#12111yescharacteristic
211C2×C4×C43#12111yescharacteristic
212C2×C4×C43C2×SD1612yes—
213C2×C4×C43AGL(1,ℤ/8)12yes—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C2×#4111yescharacteristic
217D172—42no—
218D172—42no—
219D172—42no—
220D172—42no—
221D172—82no—
222D172—82no—
223D172—82no—
224D172—82no—
225C8×C43—41no—
226C8×C43—41no—
227C43⋊C8—22no—
228C43⋊C8—42no—
229C43⋊C8—42no—
230C43⋊C8C2×SD1614yescomplemented
231#19170—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43#46012yes—
238C22×C43C2×#12111yescharacteristic
239C2×D43—82no—
240C2×D43—82no—
241C2×D43—82no—
242C2×D43—164no—
243C4×C43—21no—
244C4×C43—22no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—41no—
248C4×C43—41no—
249C4×C43—41no—
250C4×C43—81no—
251C4×C43#46012yes—
252C4×C43C22×SD1611yescharacteristic
253C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
254C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
255C4×C43#57511yescharacteristic
256#3151—431no—
257#3103D4311yescharacteristic, complemented
258C2×#460—431no—
259Q8×M16—431no—
260#1688—432no—
261#1686—432no—
262#1668—432no—
263#1666—432no—
264#1565—431no—
265#1547—431no—
266#1545—431no—
267C2×C43—22no—
268C2×C43—161no—
269C2×C43C2×#46011yescharacteristic
270C2×C43#305511yescharacteristic
271C2×C43#306811yescharacteristic
272D43—162no—
273C2×AGL(1,ℤ/8)—861no—
274C2×AGL(1,ℤ/8)—861no—
275C22×SD16—861no—
276#532C2×D4311yescharacteristic
277C2×#127—431no—
278C2×C4×Q8C2×D4311yescharacteristic
279#496—862no—
280#493—432no—
281#492—432no—
282#481—21no—
283#475C2×D4311yescharacteristic, complemented
284#475C2×D4311yescharacteristic, complemented
285#460—432no—
286#460—432no—
287#460—861no—
288#460—861no—
289#460C2×D4311yescharacteristic, complemented
290#460C2×D4311yescharacteristic, complemented
291#448—21no—
292#446—432no—
293#446—862no—
294C8×Q8—432no—
295C4×SD16—21no—
296C4×SD16—21no—
297#431C2×D4311yescharacteristic
298#423—431no—
299#423—861no—
300C2×C4⋊C8—431no—
301C2×#102—861no—
302C4×M16—431no—
303C4×M16—861no—
304#335—432no—
305#334—432no—
306#332—432no—
307#331—432no—
308#331—432no—
309#331—432no—
310C43#1917011yescharacteristic, complemented, Sylow
311C2×#41—21no—
312C22×Q8C22⋊D4311yescharacteristic
313C22×D4—861no—
314C22×D4—861no—
315C22×D4—861no—
316AGL(1,ℤ/8)—1724no—
317AGL(1,ℤ/8)—1724no—
318C2×SD16—21no—
319C2×SD16—21no—
320C2×SD16—862no—
321C2×SD16—862no—
322C2×SD16—862no—
323C2×SD16—862no—
324C2×SD16—1724no—
325C2×D8—862no—
326C2×D8—862no—
327C2×M16—431no—
328C2×M16—431no—
329C2×M16—861no—
330C22×C8—861no—
331C4⋊Q8C22×D4311yescharacteristic
332#127—432no—
333#127—861no—
334#127—861no—
335#127—861no—
336#127C22×D4311yescharacteristic
337#124—21no—
338#121—21no—
339#121—21no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×Q8C22⋊D4311yescharacteristic
343C4×Q8C22⋊D4311yescharacteristic
344C4×Q8C22×D4311yescharacteristic
345C4×Q8C22×D4311yescharacteristic
346C4×D4—21no—
347C4×D4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4C22⋊D4311yescharacteristic
350C2×C42—21no—
351C2×C42C22×D4311yescharacteristic
352#106—21no—
353#106—21no—
354C4⋊C8—432no—
355C4⋊C8—432no—
356C4⋊C8—862no—
357C4⋊C8—862no—
358C4⋊C8—861no—
359C4⋊C8—861no—
360C4⋊C8C22×D4311yescharacteristic
361C4⋊C8C22×D4311yescharacteristic
362#103—21no—
363#103—21no—
364#102—21no—
365#102—21no—
366#102—862no—
367#102—862no—
368C22⋊C8—21no—
369#97—432no—
370#97—862no—
371C4×C8—21no—
372C4×C8—432no—
373C4×C8—862no—
374C24—1721no—
375#41—42no—
376#41—42no—
377C2×Q8—21no—
378C2×Q8—22no—
379C2×Q8—21no—
380C2×Q8—41no—
381C2×Q8C2×C22⋊D4311yescharacteristic
382C2×Q8C2×C22⋊D4311yescharacteristic
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—41no—
387C2×D4—862no—
388C2×D4—862no—
389C2×D4—862no—
390C2×D4—3442no—
391C2×D4—1722no—
392C2×D4—1722no—
393C2×D4—1721no—
394C2×D4—1721no—
395C2×D4—1721no—
396C2×D4—1722no—
397C2×D4—1722no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—41no—
401C22×C4D4×D4311yescharacteristic
402C22×C4#1062190011yescharacteristic
403C22×C4C2×C22⋊D4311yescharacteristic
404SD16—42no—
405SD16—42no—
406SD16—1724no—
407SD16—1724no—
408SD16—1724no—
409SD16—1724no—
410D8—1724no—
411D8—1724no—
412M16—434no—
413M16—862no—
414M16—1722no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—432no—
418C2×C8—432no—
419C2×C8—862no—
420C2×C8—862no—
421C2×C8—1722no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4C2×C22⋊D4311yescharacteristic
430C4⋊C4C2×C22⋊D4311yescharacteristic
431C22⋊C4—41no—
432C22⋊C4—41no—
433C42—21no—
434C42—21no—
435C42—21no—
436C42—21no—
437C42D4×D4311yescharacteristic
438C42#1062190011yescharacteristic
439C42C2×C22⋊D4311yescharacteristic
440C42C23×D4311yescharacteristic
441C23—41no—
442C23—3442no—
443C23—3442no—
444C23—3442no—
445C23—1722no—
446C23#1306329711yescharacteristic
447Q8—21no—
448Q8—21no—
449Q8—21no—
450Q8—42no—
451Q8—41no—
452Q8—41no—
453Q8#1306335012yescomplemented
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—81no—
459D4—82no—
460D4—3442no—
461D4—3442no—
462D4—3442no—
463D4—3442no—
464D4—1722no—
465D4—1722no—
466D4—1722no—
467D4—1722no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—81no—
478C2×C4—82no—
479C2×C4#1306329711yescharacteristic
480C2×C4#1306329711yescharacteristic
481C2×C4#1306329711yescharacteristic
482C2×C4SD16×D4312yes—
483C2×C4#1306335212yes—
484C2×C4C2×D4×D4311yescharacteristic
485C2×C4C22×C22⋊D4311yescharacteristic
486C2×C4C2×#1062190011yescharacteristic
487C8—41no—
488C8—41no—
489C8—434no—
490C8—862no—
491C8—1722no—
492C8—1722no—
493C22—21no—
494C22—21no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—3442no—
499C22—3442no—
500C22—3442no—
501C22—6884no—
502C22#1458309712yes—
503C22C2×#1306329711yescharacteristic
504C4—21no—
505C4—22no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—41no—
511C4—81no—
512C4#1458309712yes—
513C4C2×SD16×D4311yescharacteristic
514C4C2×#1306335011yescharacteristic
515C4C2×#1306335211yescharacteristic
516C4#1458369711yescharacteristic
517C2—22no—
518C2—161no—
519C2—6882no—
520C2C2×#1458309711yescharacteristic
521C2#1914421611yescharacteristic
522C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3103C2
socleC22×C43C2×#121
prime radical#19145048C2
hypercenter#3103D43
hypocenterC43#19170
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
2. C2×#14583099C2semidirect
3. Q8×#10621877C2semidirect
4. #19134077C2semidirect
5. #19134069C2semidirect
6. #19133953C2semidirect
7. #19133945C2semidirect
8. #19133348C2semidirect
9. #19133272C2semidirect
10. #19133262C2semidirect
11. C43×#3103C2semidirect
24. #14583030C22semidirect
25. Q8×C43⋊C8C22semidirect
32. #14582651C22semidirect
33. #14582649C22semidirect
34. #14582645C22semidirect
35. #14582643C22semidirect
41. C43×#475C22semidirect
42. C43×#475C22semidirect
43. C43×#460C22semidirect
44. C43×#460C22semidirect
173. #10621877SD16semidirect
191. Q8×C43AGL(1,ℤ/8)semidirect
230. C43⋊C8C2×SD16semidirect
257. #3103D43semidirect
283. #475C2×D43semidirect
284. #475C2×D43semidirect
289. #460C2×D43semidirect
290. #460C2×D43semidirect
310. C43#19170semidirect
453. Q8#13063350semidirect

Maximal subgroups

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

subgroupindex
#191450482
C2×#145830992
Q8×#106218772
#191340772
#191340692
#191339532
#191339452
#191333482
#191332722
#191332622
C43×#31032
#1917043