Finite Group Databasebeta

← #25074384

Subgroups — #25074384

Order 11008.

946 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#19145911C211yesmaximal, characteristic, complemented
2#19145177C211yesmaximal, characteristic, complemented
3#19144392C211yesmaximal, characteristic, complemented
4#19133830C212yesmaximal, complemented
5#19133823C212yesmaximal, complemented
6#19133746C212yesmaximal, complemented
7#19133740C212yesmaximal, complemented
8#19133285C211yesmaximal, characteristic, complemented
9#19133046C211yesmaximal, characteristic, complemented
10C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
11C43×#3506C211yesmaximal, characteristic
12#14583456C2211yescharacteristic
13#14583302C2211yescharacteristic, complemented
14#14583278C2211yescharacteristic, complemented
15#14583251C2211yescharacteristic, complemented
16#14583249C2211yescharacteristic, complemented
17#14583199—22no—
18#14583189C2212yes—
19#14583189C2212yescomplemented
20#14583181—21no—
21#14583179C2212yes—
22#14583138—22no—
23#14583126—22no—
24#14583104C2212yescomplemented
25#14583096—21no—
26C4×#10621885—22no—
27#14582939—21no—
28#14582923C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30#14582904—21no—
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582648C2212yescomplemented
33#14582645C2212yescomplemented
34D4⋊(C43⋊C8)C2212yes—
35D4⋊(C43⋊C8)C2212yes—
36D4⋊(C43⋊C8)C2212yescomplemented
37D4⋊(C43⋊C8)C2212yescomplemented
38C43×#559—22no—
39C43×#556—21no—
40C43×#555C2212yes—
41C43×#553—22no—
42C43×#550—21no—
43C43×#547C2212yes—
44C43×#538—22no—
45C43×#535—21no—
46C43×#533C2211yescharacteristic
47C43×#532C2211yescharacteristic
48C43×#525—22no—
49C43×#520—21no—
50C2×C4×D4×C43C2211yescharacteristic
51C2×#10621885—22no—
52C2×#10621883—22no—
53C2×#10621877—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56#13063325C2311yescharacteristic
57#13063325C2311yescharacteristic
58#13063317—21no—
59#13063304—21no—
60#13063304—21no—
61C4×Dic86—21no—
62C4×Dic86—21no—
63#13063284—21no—
64#13063258—22no—
65#13063258—22no—
66#13063256—22no—
67#13063256—22no—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)C2312yes—
71C4⋊(C43⋊C8)C2312yes—
72#13063249—22no—
73#13063248—22no—
74#13063248—22no—
75#13063246—22no—
76#13063246—22no—
77#13063246—22no—
78C4×C43⋊C8—21no—
79C4×C43⋊C8C2311yescharacteristic
80C4×C43⋊C8C2311yescharacteristic
81C2×#41×C43—22no—
82C2×#41×C43—21no—
83C22×D4×C43D411yescharacteristic
84C23×C4×C43—21no—
85C4⋊Q8×C43D411yescharacteristic
86C4⋊Q8×C43C2311yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43—22no—
89#127×C43D411yescharacteristic
90#126×C43—24no—
91#125×C43—21no—
92#124×C43—22no—
93#124×C43—24no—
94#124×C43—21no—
95#123×C43—24no—
96#123×C43—24no—
97C22⋊Q8×C43—21no—
98C22⋊Q8×C43—22no—
99C22⋊Q8×C43D412yes—
100#121×C43—24no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—22no—
104#121×C43—21no—
105#121×C43D412yes—
106#120×C43—24no—
107C4×Q8×C43—22no—
108C4×Q8×C43—21no—
109C4×Q8×C43D412yes—
110C4×D4×C43—24no—
111C4×D4×C43—22no—
112C4×D4×C43—24no—
113C4×D4×C43—21no—
114C4×D4×C43—21no—
115C4×D4×C43—21no—
116C4×D4×C43D412yes—
117C4×D4×C43C2312yes—
118C4×D4×C43C2312yes—
119#117×C43—21no—
120#117×C43—22no—
121#117×C43—22no—
122C2×C4⋊C4×C43—22no—
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C22⋊C4×C43—21no—
125C2×C42×C43C2311yescharacteristic
126C24×C43—21no—
127#41×C43—42no—
128#41×C43—42no—
129#41×C43—82no—
130#41×C43—82no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43C2×D412yes—
134C2×D4×C43—24no—
135C2×D4×C43—24no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43C2×D412yes—
143C2×D4×C43C2×D412yes—
144C22×C4×C43—24no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—81no—
150C22×C4×C43—81no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C2×Dic86—21no—
155C2×Dic86—21no—
156C4⋊C4×C43—24no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43C2×D412yes—
165C4⋊C4×C43C2×D412yes—
166C4⋊C4×C43C2×D412yes—
167C22⋊C4×C43—24no—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—24no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—22no—
174C22⋊C4×C43—22no—
175C42×C43—24no—
176C42×C43—22no—
177C42×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—41no—
182#10621885—44no—
183#10621883—82no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190C4×Dic43—41no—
191#10621877—42no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—42no—
197C2×C43⋊C8—81no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—42no—
201C23×C43—81no—
202C23×C43—81no—
203C23×C43#12011yescharacteristic
204Q8×C43—42no—
205Q8×C43—41no—
206Q8×C43—41no—
207Q8×C43—42no—
208D4×C43—22no—
209D4×C43—22no—
210D4×C43—22no—
211D4×C43—22no—
212D4×C43—44no—
213D4×C43—42no—
214D4×C43—42no—
215D4×C43—81no—
216D4×C43—84no—
217D4×C43—84no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—82no—
230C2×C4×C43—81no—
231C2×C4×C43—84no—
232C2×C4×C43#12011yescharacteristic
233C2×C4×C43#12011yescharacteristic
234C2×C4×C43#12011yescharacteristic
235C2×C4×C43#13512yes—
236C2×C4×C43#13712yes—
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×Dic43—41no—
241C2×Dic43—41no—
242Dic86—42no—
243Dic86—41no—
244Dic86—41no—
245C43⋊C8—22no—
246C43⋊C8—41no—
247C43⋊C8—42no—
248C43⋊C8—42no—
249#18681—431nomaximal, Sylow
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—84no—
259C22×C43#45212yes—
260C22×C43C2×#12011yescharacteristic
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—42no—
265C4×C43—42no—
266C4×C43—42no—
267C4×C43—42no—
268C4×C43#45212yes—
269C4×C43C2×#13511yescharacteristic
270C4×C43C2×#13711yescharacteristic
271C4×C43#57611yescharacteristic
272C4×C43#57711yescharacteristic
273Dic43—81no—
274Dic43—81no—
275#3506D4311yescharacteristic
276#3246—431no—
277#3170—431no—
278#3077—431no—
279#1647—432no—
280#1646—432no—
281#1635—432no—
282#1634—432no—
283#1550—431no—
284#1492—431no—
285C2×D4⋊C8—431no—
286C2×C43—22no—
287C2×C43—82no—
288C2×C43—82no—
289C2×C43C2×#45211yescharacteristic
290C2×C43#301211yescharacteristic
291C2×C43#301811yescharacteristic
292#559—22no—
293#556—21no—
294#555C2×D4312yes—
295#553—22no—
296#550—21no—
297#547C2×D4312yes—
298#538—22no—
299#535—21no—
300#533—431no—
301#533C2×D4311yescharacteristic
302#532C2×D4311yescharacteristic
303#525—22no—
304#520—21no—
305C2×C4×D4C2×D4311yescharacteristic
306#500—431no—
307#494—431no—
308#487—431no—
309#487—431no—
310#478—862no—
311#476—432no—
312#476—432no—
313#475—861no—
314#474—432no—
315#467—862no—
316#465—862no—
317#461—432no—
318#460—861no—
319C4×Q16—862no—
320#428—861no—
321#423—431no—
322C2×C4⋊C8—431no—
323#418—861no—
324C2×C4×C8—431no—
325#333—432no—
326#332—432no—
327D4⋊C8—432no—
328D4⋊C8—432no—
329D4⋊C8—432no—
330D4⋊C8—432no—
331C43#1868111yescharacteristic, complemented, Sylow
332C2×#41—22no—
333C2×#41—21no—
334C22×D4C22⋊D4311yescharacteristic
335C23×C4—21no—
336C2×Q16—862no—
337C2×SD16—862no—
338C2×M16—861no—
339C22×C8—861no—
340C22×C8—861no—
341C4⋊Q8—431no—
342C4⋊Q8—431no—
343C4⋊Q8C22⋊D4311yescharacteristic
344C4⋊Q8C22×D4311yescharacteristic
345C4⋊Q8C22×D4311yescharacteristic
346#127—22no—
347#127C22⋊D4311yescharacteristic
348#126—24no—
349#125—21no—
350#125—861no—
351#124—22no—
352#124—24no—
353#124—21no—
354#123—24no—
355#123—24no—
356C22⋊Q8—21no—
357C22⋊Q8—22no—
358C22⋊Q8—861no—
359C22⋊Q8—861no—
360C22⋊Q8C22⋊D4312yes—
361#121—24no—
362#121—22no—
363#121—22no—
364#121—22no—
365#121—21no—
366#121C22⋊D4312yes—
367#120—24no—
368C4×Q8—22no—
369C4×Q8—21no—
370C4×Q8—861no—
371C4×Q8—861no—
372C4×Q8C22⋊D4312yes—
373C4×D4—24no—
374C4×D4—22no—
375C4×D4—24no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C22⋊D4312yes—
380C4×D4C22×D4312yes—
381C4×D4C22×D4312yes—
382#117—21no—
383#117—22no—
384#117—22no—
385#117—861no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4C22⋊D4311yescharacteristic
388C2×C22⋊C4—21no—
389C2×C42C22×D4311yescharacteristic
390#107—862no—
391#107—862no—
392#106—862no—
393#106—862no—
394C4⋊C8—432no—
395C4⋊C8—432no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398#103—862no—
399#103—862no—
400#103—862no—
401#102—862no—
402#102—862no—
403#102—862no—
404C4×C8—431no—
405C4×C8—431no—
406C4×C8—861no—
407C24—21no—
408#41—42no—
409#41—42no—
410#41—82no—
411#41—82no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8C2×C22⋊D4312yes—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4C2×C22⋊D4312yes—
426C2×D4C2×C22⋊D4312yes—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437Q16—1724no—
438SD16—3442no—
439M16—1722no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—862no—
443C2×C8—862no—
444C2×C8—3441no—
445C2×C8—1722no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4C2×C22⋊D4312yes—
461C4⋊C4C2×C22⋊D4312yes—
462C4⋊C4C2×C22⋊D4312yes—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—1721no—
472C42—24no—
473C42—22no—
474C42—1721no—
475C42C2×C22⋊D4311yescharacteristic
476C42C2×C22⋊D4311yescharacteristic
477C42C2×C22⋊D4311yescharacteristic
478C42C23×D4311yescharacteristic
479C23—22no—
480C23—22no—
481C23—42no—
482C23—81no—
483C23—81no—
484C23#1306329411yescharacteristic
485Q8—42no—
486Q8—42no—
487Q8—41no—
488Q8—41no—
489Q8—1722no—
490Q8—1721no—
491Q8—1721no—
492D4—22no—
493D4—22no—
494D4—22no—
495D4—22no—
496D4—44no—
497D4—42no—
498D4—42no—
499D4—81no—
500D4—84no—
501D4—84no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—82no—
514C2×C4—81no—
515C2×C4—84no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4#1306329411yescharacteristic
519C2×C4#1306329411yescharacteristic
520C2×C4#1306329411yescharacteristic
521C2×C4#1306334512yes—
522C2×C4#1306335512yes—
523C2×C4C22×C22⋊D4311yescharacteristic
524C2×C4C22×C22⋊D4311yescharacteristic
525C2×C4C22×C22⋊D4311yescharacteristic
526C8—862no—
527C8—1721no—
528C8—1722no—
529C8—1722no—
530C22—21no—
531C22—21no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—84no—
539C22#1458306112yes—
540C22C2×#1306329411yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—42no—
548C4—3441no—
549C4—3441no—
550C4#1458306112yes—
551C4C2×#1306334511yescharacteristic
552C4C2×#1306335511yescharacteristic
553C4#1458370211yescharacteristic
554C4#1458371011yescharacteristic
555C2—22no—
556C2—82no—
557C2—82no—
558C2C2×#1458306111yescharacteristic
559C2#1914389911yescharacteristic
560C2#1914394411yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3506C2
socleC22×C43C2×#120
hypercenter#3506D43
hypocenterC43#18681
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #19145911C2semidirect
2. #19145177C2semidirect
3. #19144392C2semidirect
4. #19133830C2semidirect
5. #19133823C2semidirect
6. #19133746C2semidirect
7. #19133740C2semidirect
8. #19133285C2semidirect
9. #19133046C2semidirect
10. C2×D4⋊(C43⋊C8)C2semidirect
13. #14583302C22semidirect
14. #14583278C22semidirect
15. #14583251C22semidirect
16. #14583249C22semidirect
19. #14583189C22semidirect
24. #14583104C22semidirect
32. #14582648C22semidirect
33. #14582645C22semidirect
36. D4⋊(C43⋊C8)C22semidirect
37. D4⋊(C43⋊C8)C22semidirect
331. C43#18681semidirect

Maximal subgroups

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

subgroupindex
#191459112
#191451772
#191443922
#191338302
#191338232
#191337462
#191337402
#191332852
#191330462
C2×D4⋊(C43⋊C8)2
C43×#35062
#1868143