Finite Group Databasebeta

← #25086345

Subgroups — #25086345

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147242C211yesmaximal, characteristic
2#19146878C211yesmaximal, characteristic, complemented
3#19146471C211yesmaximal, characteristic, complemented
4#19134240C211yesmaximal, characteristic, complemented
5#19134168C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134016C211yesmaximal, characteristic, complemented
8#19133986C211yesmaximal, characteristic, complemented
9#19133864C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133808C211yesmaximal, characteristic, complemented
12#19133760C211yesmaximal, characteristic, complemented
13#19133425C211yesmaximal, characteristic
14#19133412C211yesmaximal, characteristic, complemented
15Q8×D8×C43C211yesmaximal, characteristic
16#14583619C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583252—21no—
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583249C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583237—21no—
25#14583232—21no—
26#14583205—21no—
27#14583194C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583155—21no—
31#14583138—21no—
32#14583112—21no—
33#14583106C2211yescharacteristic
34#14583106C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583055—21no—
37#14583055—21no—
38C8×Dic86C2211yescharacteristic
39C4×#10621885C2211yescharacteristic
40#14582990—21no—
41#14582977C2211yescharacteristic
42D4×C43⋊C8C2211yescharacteristic
43#14582908—21no—
44C2×#13063249—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56D4×Q8×C43C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#500—21no—
59C43×#500C2211yescharacteristic
60C43×#474—21no—
61C43×#474—21no—
62C43×#474C2211yescharacteristic
63C43×#474C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×D8×C43—21no—
66C4×D8×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885D411yescharacteristic
70C2×#10621883—21no—
71C2×#10621877—21no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063318—41no—
76#13063316—21no—
77#13063312—21no—
78#13063304—21no—
79#13063304—21no—
80#13063302—41no—
81C4×Dic86C2311yescharacteristic
82#13063290—21no—
83D4×Dic43—21no—
84#13063284—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258D411yescharacteristic
88#13063256—21no—
89#13063256—21no—
90#13063256—41no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249D411yescharacteristic
106#13063248—21no—
107#13063248—41no—
108#13063248D411yescharacteristic
109#13063246—21no—
110C22⋊(C43⋊C8)—21no—
111C22⋊(C43⋊C8)—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×Q8×C43—21no—
116C22×Q8×C43—21no—
117C2×D8×C43D411yescharacteristic
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C22⋊Q8×C43—41no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#107×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43D411yescharacteristic
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—42no—
150C2×Q8×C43—81no—
151C2×Q8×C43—81no—
152C2×Q8×C43C2×D411yescharacteristic
153C2×D4×C43C2×D411yescharacteristic
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C22×Dic43—41no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86C2×D411yescharacteristic
163D8×C43—22no—
164C2×C8×C43—21no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184C22⋊Dic43—41no—
185C22⋊Dic43—41no—
186#10621885—22no—
187#10621885—81no—
188#10621885—81no—
189#10621883—42no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—41no—
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C4×Dic43—41no—
201#10621877—81no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—82no—
217Q8×C43—82no—
218Q8×C43#13512yes—
219D4×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222D4×C43#13712yes—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—82no—
234C2×C4×C43—82no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—161no—
243Dic86—21no—
244Dic86—21no—
245Dic86—41no—
246Dic86—41no—
247Dic86—81no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19782—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43D4211yescharacteristic
265C4×C43—22no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×#13711yescharacteristic
274C4×C43#57611yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—41no—
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280Q8×D8D4311yescharacteristic
281#3360—431no—
282#3328—431no—
283#3299—431no—
284#1718—431no—
285#1703—431no—
286#1684—431no—
287#1679—431no—
288#1674—431no—
289#1652—431no—
290#1651—431no—
291#1644—431no—
292#1637—431no—
293#1581—431no—
294#1579—431no—
295C2×C43—42no—
296C2×C43—81no—
297C2×C43#327011yescharacteristic
298C2×C43#328011yescharacteristic
299C2×C43#328911yescharacteristic
300#556—431no—
301#554—431no—
302D4×Q8C2×D4311yescharacteristic
303D4×Q8C2×D4311yescharacteristic
304#500—21no—
305#500C2×D4311yescharacteristic
306#498—431no—
307#488—861no—
308#487—431no—
309#487—431no—
310#487—431no—
311#487—431no—
312#485—861no—
313#484—861no—
314#479—861no—
315#477—431no—
316#476—431no—
317#475—431no—
318#474—21no—
319#474—21no—
320#474C2×D4311yescharacteristic
321#474C2×D4311yescharacteristic
322#470—861no—
323#467—861no—
324#463—861no—
325#462—431no—
326#462—431no—
327#461—431no—
328#451—861no—
329#451—861no—
330C8×Q8—431no—
331C8×Q8C2×D4311yescharacteristic
332C4×Q16—431no—
333C4×SD16—861no—
334C4×D8—21no—
335C4×D8C2×D4311yescharacteristic
336#436—431no—
337C8×D4—431no—
338#419—861no—
339C2×#103—861no—
340#335—431no—
341#334—431no—
342#333—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350#322—431no—
351C43#1978211yescharacteristic, complemented, Sylow
352C22×Q8—21no—
353C22×Q8—21no—
354C2×Q16—431no—
355C2×Q16—861no—
356C2×Q16—861no—
357C2×SD16—861no—
358C2×D8C22⋊D4311yescharacteristic
359C2×M16—861no—
360C22×C8—861no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—431no—
364C4⋊Q8—431no—
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
367#126—1721no—
368#125—861no—
369#124—861no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—41no—
373C22⋊Q8—41no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376C22⋊Q8—1721no—
377C4×Q8—431no—
378C4×Q8—861no—
379C4×Q8C22×D4311yescharacteristic
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384C4×D4C22×D4311yescharacteristic
385#117—861no—
386C2×C4⋊C4—861no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#107—431no—
392#107—861no—
393#107C22⋊D4311yescharacteristic
394#106—861no—
395#106—861no—
396#106—1721no—
397C4⋊C8—21no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403#103—431no—
404#103—431no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—1721no—
417#102—21no—
418#102—21no—
419#102—861no—
420#102C22⋊D4311yescharacteristic
421#102C22⋊D4311yescharacteristic
422C22⋊C8—861no—
423C22⋊C8—861no—
424C4×C8—21no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—42no—
434C2×Q8—42no—
435C2×Q8—81no—
436C2×Q8—81no—
437C2×Q8—431no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8D4×D4311yescharacteristic
441C2×D4C2×C22⋊D4311yescharacteristic
442C2×D4C2×C22⋊D4311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—1721no—
448Q16—862no—
449Q16—3441no—
450Q16—3441no—
451SD16—1722no—
452D8—22no—
453M16—3441no—
454C2×C8—21no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—3441no—
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C4⋊C4C2×C22⋊D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—1721no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C42—21no—
491C42—861no—
492C42—1721no—
493C42C23×D4311yescharacteristic
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—82no—
502Q8—82no—
503Q8—861no—
504Q8—861no—
505Q8—3441no—
506Q8—1721no—
507Q8—1721no—
508Q8#1306334412yes—
509D4—21no—
510D4—21no—
511D4—21no—
512D4#1306335612yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—6881no—
530C2×C4C2×D4×D4311yescharacteristic
531C2×C4C22×C22⋊D4311yescharacteristic
532C2×C4#1306337011yescharacteristic
533C8—21no—
534C8—21no—
535C8—41no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D4×C22⋊D4311yescharacteristic
549C4—22no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—3441no—
557C4—3441no—
558C4—1721no—
559C4—1721no—
560C4C2×#1306334411yescharacteristic
561C4C2×#1306335611yescharacteristic
562C4#1458370011yescharacteristic
563C4#1458371411yescharacteristic
564C2—42no—
565C2—81no—
566C2#1914616611yescharacteristic
567C2#1914628011yescharacteristic
568C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×D8×C43C2
socleC22×C43D42
prime radicalC2×D8×C43D4
hypercenterQ8×D8D43
hypocenterC43#19782
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×D8

Complements

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

NH ≅ G/Ntype
2. #19146878C2semidirect
3. #19146471C2semidirect
4. #19134240C2semidirect
5. #19134168C2semidirect
6. #19134053C2semidirect
7. #19134016C2semidirect
8. #19133986C2semidirect
9. #19133864C2semidirect
10. #19133858C2semidirect
11. #19133808C2semidirect
12. #19133760C2semidirect
14. #19133412C2semidirect
351. C43#19782semidirect

Maximal subgroups

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

subgroupindex
#191472422
#191468782
#191464712
#191342402
#191341682
#191340532
#191340162
#191339862
#191338642
#191338582
#191338082
#191337602
#191334252
#191334122
Q8×D8×C432
#1978243