Finite Group Databasebeta

← #25087470

Subgroups — #25087470

Order 11008.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147648C211yesmaximal, characteristic, complemented
2#19147468C211yesmaximal, characteristic, complemented
3#19146983C211yesmaximal, characteristic, complemented
4#19134216C211yesmaximal, characteristic, complemented
5#19134121C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19133977C211yesmaximal, characteristic, complemented
8#19133934C211yesmaximal, characteristic
9#19133809C211yesmaximal, characteristic, complemented
10#19133752C211yesmaximal, characteristic, complemented
11#19133716C211yesmaximal, characteristic, complemented
12#19133665C211yesmaximal, characteristic
13#19133432C211yesmaximal, characteristic, complemented
14#19133412C211yesmaximal, characteristic, complemented
15C43×#3361C211yesmaximal, characteristic
16#14583628C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583299—21no—
20#14583297C2211yescharacteristic
21#14583294—21no—
22#14583271C2211yescharacteristic
23#14583271C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583234—21no—
26#14583232—21no—
27#14583204—21no—
28#14583201—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583191C2211yescharacteristic
32#14583179C2211yescharacteristic
33#14583138—21no—
34#14583118—21no—
35#14583109C2211yescharacteristic
36#14583104—21no—
37#14583096C2211yescharacteristic
38#14583030C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14582999—21no—
41C4×#10621885C2211yescharacteristic
42SD16×Dic43—21no—
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063258—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#559C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#488—21no—
59C43×#486C2211yescharacteristic
60C43×#478—21no—
61C43×#477C2211yescharacteristic
62C43×#463—21no—
63C43×#459C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43C2211yescharacteristic
66C4×D8×C43—21no—
67C2×#10621885—21no—
68C2×#10621885D411yescharacteristic
69C2×#10621883—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—41no—
73C22×C43⋊C8—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063316—21no—
78#13063316—21no—
79#13063316—41no—
80#13063304—21no—
81#13063302—41no—
82Q8×Dic43—21no—
83C4×Dic86—21no—
84C4×Dic86C2311yescharacteristic
85D4×Dic43—21no—
86C2×C4⋊Dic43—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063258D411yescharacteristic
94#13063257—21no—
95#13063257—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—41no—
104#13063249D411yescharacteristic
105#13063248—21no—
106#13063248—21no—
107#13063248D411yescharacteristic
108#13063246—21no—
109#13063246—21no—
110C22⋊(C43⋊C8)—21no—
111#13063236—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×SD16×C43D411yescharacteristic
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#125×C43—21no—
120#124×C43—21no—
121#124×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43C2311yescharacteristic
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C22×C4×C43—41no—
154C22×Dic43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86C2×D411yescharacteristic
158SD16×C43—22no—
159D8×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43C2×D411yescharacteristic
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C22⋊C4×C43—21no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—41no—
181#10621885—22no—
182#10621885—81no—
183#10621883—42no—
184#10621883—81no—
185#10621883—81no—
186#10621883—82no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—41no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43—41no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—81no—
214D4×C43—21no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—81no—
220D4×C43#13712yes—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—161no—
230C2×C4×C43—161no—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—161no—
239Dic86—21no—
240Dic86—21no—
241Dic86—41no—
242Dic86—41no—
243Dic86—81no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8#13512yes—
253#19857—431nomaximal, Sylow
254C22×C43—22no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43D4211yescharacteristic
261C4×C43—21no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43C2×#13511yescharacteristic
269C4×C43C2×#13711yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272Dic43—41no—
273Dic43—41no—
274Dic43—81no—
275Dic43—81no—
276#3400—431no—
277#3381—431no—
278#3361D4311yescharacteristic
279#3338—431no—
280#1714—431no—
281#1696—431no—
282#1678—431no—
283#1672—431no—
284#1665—431no—
285#1644—431no—
286#1636—431no—
287#1630—431no—
288#1622—431no—
289#1582—431no—
290#1579—431no—
291C2×C43—42no—
292C2×C43—161no—
293C2×C43#327011yescharacteristic
294C2×C43#328411yescharacteristic
295C2×C43#328811yescharacteristic
296#559C2×D4311yescharacteristic
297#557—431no—
298#554—431no—
299#554C2×D4311yescharacteristic
300#500—431no—
301#499—861no—
302#498—431no—
303#497—861no—
304#492—431no—
305#492—431no—
306#488—21no—
307#487—431no—
308#486C2×D4311yescharacteristic
309#484—861no—
310#484—861no—
311#479—861no—
312#478—21no—
313#478—861no—
314#477—431no—
315#477—431no—
316#477—431no—
317#477C2×D4311yescharacteristic
318#474—431no—
319#467—861no—
320#464—861no—
321#463—21no—
322#462—431no—
323#461—861no—
324#460—431no—
325#459C2×D4311yescharacteristic
326#446—431no—
327C8×Q8—431no—
328C8×Q8C2×D4311yescharacteristic
329#440—861no—
330C4×Q16—431no—
331C4×SD16—861no—
332C4×SD16C2×D4311yescharacteristic
333C4×D8—21no—
334C8×D4—431no—
335C2×#107—861no—
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#331—431no—
342Q8⋊C8—431no—
343Q8⋊C8—431no—
344Q8⋊C8—431no—
345D4⋊C8—431no—
346#322—431no—
347C43#1985711yescharacteristic, complemented, Sylow
348C2×Q16—431no—
349C2×Q16—861no—
350C2×SD16—861no—
351C2×SD16—861no—
352C2×SD16—861no—
353C2×SD16—1721no—
354C2×SD16C22⋊D4311yescharacteristic
355C2×D8—21no—
356C22×C8—861no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359C4⋊Q8—861no—
360C4⋊Q8C22×D4311yescharacteristic
361#127C22×D4311yescharacteristic
362#125—21no—
363#125—861no—
364#125—861no—
365#125—1721no—
366#124—21no—
367#124—21no—
368#123—41no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C22⋊Q8—861no—
372C22⋊Q8—1721no—
373C4×Q8—431no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×Q8C22×D4311yescharacteristic
377C4×Q8C22×D4311yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—861no—
382C4×D4C22×D4311yescharacteristic
383C2×C4⋊C4—21no—
384C2×C4⋊C4—861no—
385#107—21no—
386#107—431no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394#106—861no—
395#106C22⋊D4311yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403#103—21no—
404#103—431no—
405#103—431no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—1721no—
411#103C22⋊D4311yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—861no—
416#102—861no—
417#102C22⋊D4311yescharacteristic
418C22⋊C8—861no—
419#97—861no—
420C4×C8—21no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—861no—
424C4×C8C22×D4311yescharacteristic
425C2×Q8—21no—
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8D4×D4311yescharacteristic
430C2×Q8C2×C22⋊D4311yescharacteristic
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4C2×C22⋊D4311yescharacteristic
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—1721no—
439Q16—862no—
440Q16—3441no—
441SD16—22no—
442SD16—3441no—
443SD16—3441no—
444SD16—3442no—
445SD16—1722no—
446D8—42no—
447C2×C8—21no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—1722no—
455C2×C8C2×C22⋊D4311yescharacteristic
456C2×C8C2×C22⋊D4311yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—431no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—1721no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4D4×D4311yescharacteristic
475C4⋊C4C2×C22⋊D4311yescharacteristic
476C4⋊C4C2×C22⋊D4311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—1721no—
483C42—21no—
484C42—21no—
485C42—861no—
486C42—1721no—
487C42C23×D4311yescharacteristic
488C23—21no—
489C23—41no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—861no—
496Q8—861no—
497Q8—3441no—
498Q8—1721no—
499Q8—1721no—
500D4—21no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—81no—
506D4#1306335512yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—161no—
516C2×C4—161no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—6881no—
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C22×C22⋊D4311yescharacteristic
524C2×C4#1306337011yescharacteristic
525C8—21no—
526C8—21no—
527C8—41no—
528C8—432no—
529C8—861no—
530C8—1721no—
531C8—1721no—
532C8—1721no—
533C8—1721no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22D4×C22⋊D4311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—3441no—
549C4—3441no—
550C4—1721no—
551C4—1721no—
552C4#135×D4311yescharacteristic
553C4C2×#1306335511yescharacteristic
554C4#1458370611yescharacteristic
555C4#1458371411yescharacteristic
556C2—42no—
557C2—161no—
558C2#1914616111yescharacteristic
559C2#1914631911yescharacteristic
560C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3361C2
socleC22×C43D42
prime radicalC43×#459C22
hypercenter#3361D43
hypocenterC43#19857
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3361

Complements

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

NH ≅ G/Ntype
1. #19147648C2semidirect
2. #19147468C2semidirect
3. #19146983C2semidirect
4. #19134216C2semidirect
5. #19134121C2semidirect
6. #19134008C2semidirect
7. #19133977C2semidirect
9. #19133809C2semidirect
10. #19133752C2semidirect
11. #19133716C2semidirect
13. #19133432C2semidirect
14. #19133412C2semidirect
347. C43#19857semidirect

Maximal subgroups

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

subgroupindex
#191476482
#191474682
#191469832
#191342162
#191341212
#191340082
#191339772
#191339342
#191338092
#191337522
#191337162
#191336652
#191334322
#191334122
C43×#33612
#1985743