Finite Group Databasebeta

← #25088170

Subgroups — #25088170

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147579C211yesmaximal, characteristic
2Q8×#10621882C211yesmaximal, characteristic
3#19146880C211yesmaximal, characteristic, complemented
4#19134191C211yesmaximal, characteristic, complemented
5#19134142C211yesmaximal, characteristic, complemented
6#19134139C211yesmaximal, characteristic, complemented
7#19133987C211yesmaximal, characteristic, complemented
8#19133963C211yesmaximal, characteristic, complemented
9#19133865C211yesmaximal, characteristic, complemented
10#19133863C211yesmaximal, characteristic, complemented
11#19133858C211yesmaximal, characteristic, complemented
12#19133857C211yesmaximal, characteristic, complemented
13#19133478C211yesmaximal, characteristic
14Q16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3328C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17Q8×D172C2211yescharacteristic
18#14583302—21no—
19#14583302C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583281—21no—
23#14583278C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583242—21no—
26#14583184C2211yescharacteristic
27#14583179—21no—
28#14583179C2211yescharacteristic
29#14583176—21no—
30#14583176C2211yescharacteristic
31#14583156—21no—
32#14583121—21no—
33#14583118—21no—
34#14583109C2211yescharacteristic
35#14583104C2211yescharacteristic
36#14583101C2211yescharacteristic
37#14583053—21no—
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621885—21no—
41C4×#10621882—21no—
42C4×#10621882C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582906—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582646C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#556C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#485—21no—
60C43×#475C2211yescharacteristic
61C43×#470—21no—
62C43×#462C2211yescharacteristic
63C43×#451—21no—
64C4×Q16×C43C2211yescharacteristic
65C43×#436C2211yescharacteristic
66C43×#419—21no—
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621885—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621882D411yescharacteristic
74C2×#10621872—21no—
75#13063325—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063320—41no—
79#13063313—21no—
80#13063305—21no—
81#13063305—41no—
82#13063301—21no—
83C4×Dic86—21no—
84C4×D172—21no—
85C4×D172C2311yescharacteristic
86#13063283—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258D411yescharacteristic
92#13063256—21no—
93#13063256—41no—
94#13063256—41no—
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100#13063250—21no—
101#13063250—21no—
102#13063249—21no—
103#13063249—21no—
104#13063248—21no—
105#13063248—21no—
106#13063246—21no—
107#13063246D411yescharacteristic
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43D411yescharacteristic
118C2×M16×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#126×C43—41no—
123#124×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—42no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154Q8×D43—42no—
155Q8×D43—81no—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162Q16×C43—22no—
163Q16×C43—81no—
164M16×C43—81no—
165C2×C8×C43—21no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—41no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2411yescharacteristic
187#10621885—42no—
188#10621885—81no—
189#10621885—81no—
190#10621884—81no—
191#10621883—81no—
192#10621882—22no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—41no—
195(C2×D43)⋊C4—41no—
196(C2×D43)⋊C4—41no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—41no—
202C4⋊Dic43C2×D411yescharacteristic
203Dic43⋊C4—41no—
204C4×Dic43—41no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C2×D411yescharacteristic
210C2×C43⋊C8C2×D411yescharacteristic
211#10621872—81no—
212C23×C43—21no—
213C22×D43—21no—
214Q8×C43—21no—
215Q8×C43—21no—
216Q8×C43—21no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—82no—
222Q8×C43#13512yes—
223D4×C43—21no—
224D4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—82no—
235C2×C4×C43C22×D411yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241D172—21no—
242D172—21no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—82no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—82no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—41no—
254C43⋊C8—22no—
255C43⋊C8—21no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8#13712yes—
260#19907—431nomaximal, Sylow
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43D4211yescharacteristic
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C4×C43—22no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43C2×#13511yescharacteristic
277C4×C43C2×#13711yescharacteristic
278C4×C43#57611yescharacteristic
279C4×C43#57711yescharacteristic
280Dic43—41no—
281Dic43—81no—
282Dic43—81no—
283#3393—431no—
284Q8×D8—431no—
285#3328—431no—
286#3328D4311yescharacteristic, complemented
287#1707—431no—
288#1699—431no—
289#1699—431no—
290#1674—431no—
291#1670—431no—
292#1652—431no—
293#1652—431no—
294#1651—431no—
295#1651—431no—
296#1589—431no—
297C8×Q16—431no—
298C2×C43—81no—
299C2×C43#327811yescharacteristic
300C2×C43#328011yescharacteristic
301C2×C43#329311yescharacteristic
302D43—81no—
303#556—431no—
304#556C2×D4311yescharacteristic
305D4×Q8—431no—
306D4×Q8C2×D4311yescharacteristic
307#500—431no—
308#500—861no—
309#498—431no—
310#498—431no—
311#495—861no—
312#494—431no—
313#487—431no—
314#487C2×D4311yescharacteristic
315#485—21no—
316#485—861no—
317#475—431no—
318#475C2×D4311yescharacteristic
319#474—431no—
320#474—431no—
321#474—861no—
322#474—861no—
323#470—21no—
324#470—861no—
325#464—861no—
326#464—861no—
327#462—431no—
328#462C2×D4311yescharacteristic
329#461—431no—
330#461—431no—
331#451—21no—
332#451—861no—
333C8×Q8—431no—
334C8×Q8—431no—
335C4×Q16—861no—
336C4×Q16C2×D4311yescharacteristic
337C4×D8—431no—
338C4×D8—861no—
339#436—431no—
340#436C2×D4311yescharacteristic
341#419—21no—
342#419—861no—
343#335—431no—
344#335—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348#332—431no—
349Q8⋊C8—431no—
350Q8⋊C8—431no—
351D4⋊C8—431no—
352D4⋊C8—431no—
353C82—431no—
354C43#1990711yescharacteristic, complemented, Sylow
355C22×Q8—21no—
356C22×Q8—861no—
357C2×Q16—21no—
358C2×Q16—861no—
359C2×Q16—861no—
360C2×Q16—861no—
361C2×Q16C22⋊D4311yescharacteristic
362C2×SD16—861no—
363C2×SD16—861no—
364C2×D8—431no—
365C2×M16—21no—
366C2×M16—861no—
367C4⋊Q8—21no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8—861no—
371C4⋊Q8C22×D4311yescharacteristic
372C4⋊Q8C22×D4311yescharacteristic
373#126—41no—
374#126—1721no—
375#124—21no—
376#124—861no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380C22⋊Q8—861no—
381C22⋊Q8—861no—
382C22⋊Q8—1721no—
383C4×Q8—21no—
384C4×Q8—861no—
385C4×Q8C22×D4311yescharacteristic
386C4×Q8C22×D4311yescharacteristic
387C4×D4—21no—
388C4×D4—431no—
389C4×D4—861no—
390C4×D4C22×D4311yescharacteristic
391#117—21no—
392#117—861no—
393#107—431no—
394#107—861no—
395#107—861no—
396#107—861no—
397#107—861no—
398#107C22⋊D4311yescharacteristic
399#106—21no—
400#106—861no—
401#106—1721no—
402#106—1721no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103C22⋊D4311yescharacteristic
420#103C22⋊D4311yescharacteristic
421#102—431no—
422#102—431no—
423#102—861no—
424#102—861no—
425C22⋊C8—21no—
426C22⋊C8—861no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8C22×D4311yescharacteristic
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—41no—
435C2×Q8—42no—
436C2×Q8—81no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—3441no—
440C2×Q8—1721no—
441C2×Q8—1722no—
442C2×Q8C2×C22⋊D4311yescharacteristic
443C2×Q8C2×C22⋊D4311yescharacteristic
444C2×D4—431no—
445C2×D4D4×D4311yescharacteristic
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—861no—
449C22×C4—1721no—
450Q16—22no—
451Q16—81no—
452Q16—3441no—
453Q16—3441no—
454Q16—1722no—
455SD16—3441no—
456SD16—3441no—
457D8—862no—
458M16—81no—
459M16—3441no—
460C2×C8—21no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—1721no—
483C4⋊C4—1721no—
484C4⋊C4D4×D4311yescharacteristic
485C4⋊C4C2×C22⋊D4311yescharacteristic
486C4⋊C4C2×C22⋊D4311yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—861no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C22⋊C4—1721no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42—1721no—
499C42C23×D4311yescharacteristic
500C23—21no—
501C23—861no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510Q8—3442no—
511Q8—1721no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8#1306334512yes—
516D4—21no—
517D4—21no—
518D4—861no—
519D4—861no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—861no—
531C2×C4—3442no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4#1306337011yescharacteristic
539C8—21no—
540C8—21no—
541C8—41no—
542C8—432no—
543C8—862no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—1721no—
552C22—1721no—
553C22—1721no—
554C22D4×C22⋊D4311yescharacteristic
555C4—22no—
556C4—21no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—3441no—
564C4—3441no—
565C4—1721no—
566C4C2×#1306334511yescharacteristic
567C4#137×D4311yescharacteristic
568C4#1458370211yescharacteristic
569C4#1458370811yescharacteristic
570C2—81no—
571C2—3441no—
572C2#1914625511yescharacteristic
573C2#1914627611yescharacteristic
574C2#1914639711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3328C2
socleC22×C43D42
prime radicalC2×#10621882D4
hypercenter#3328D43
hypocenterC43#19907
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3328

Complements

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

NH ≅ G/Ntype
3. #19146880C2semidirect
4. #19134191C2semidirect
5. #19134142C2semidirect
6. #19134139C2semidirect
7. #19133987C2semidirect
8. #19133963C2semidirect
9. #19133865C2semidirect
10. #19133863C2semidirect
11. #19133858C2semidirect
12. #19133857C2semidirect
14. Q16×C43⋊C8C2semidirect
15. C43×#3328C2semidirect
286. #3328D43semidirect
354. C43#19907semidirect

Maximal subgroups

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

subgroupindex
#191475792
Q8×#106218822
#191468802
#191341912
#191341422
#191341392
#191339872
#191339632
#191338652
#191338632
#191338582
#191338572
#191334782
Q16×C43⋊C82
C43×#33282
#1990743