Finite Group Databasebeta

← #25074362

Subgroups — #25074362

Order 11008.

946 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145937C211yesmaximal, characteristic, complemented
2#19145150C211yesmaximal, characteristic, complemented
3#19144392C211yesmaximal, characteristic, complemented
4#19133865C212yesmaximal, complemented
5#19133788C212yesmaximal, complemented
6#19133767C212yesmaximal, complemented
7#19133722C212yesmaximal, complemented
8#19133272C211yesmaximal, characteristic, complemented
9#19133050C211yesmaximal, characteristic, complemented
10C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
11C43×#3506C211yesmaximal, characteristic
12#14583456C2211yescharacteristic
13#14583295C2211yescharacteristic, complemented
14#14583271C2211yescharacteristic, complemented
15#14583251C2211yescharacteristic, complemented
16#14583245C2211yescharacteristic, complemented
17#14583199—22no—
18#14583194C2212yescomplemented
19#14583191—21no—
20#14583189C2212yes—
21#14583179C2212yes—
22#14583138—22no—
23#14583126—22no—
24#14583109C2212yescomplemented
25#14583106—21no—
26C4×#10621883—22no—
27#14582939—21no—
28#14582923C2211yescharacteristic
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30#14582904—21no—
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582645C2212yescomplemented
33#14582643C2212yescomplemented
34Q8⋊(C43⋊C8)C2212yescomplemented
35Q8⋊(C43⋊C8)C2212yescomplemented
36D4⋊(C43⋊C8)C2212yes—
37D4⋊(C43⋊C8)C2212yes—
38C43×#559—22no—
39C43×#556C2212yes—
40C43×#555—21no—
41C43×#553—22no—
42C43×#550C2212yes—
43C43×#547—21no—
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×C43D411yescharacteristic
87C4⋊Q8×C43C2311yescharacteristic
88#127×C43—22no—
89#127×C43C2311yescharacteristic
90#126×C43—24no—
91#125×C43—21no—
92#124×C43—24no—
93#124×C43—22no—
94#124×C43—21no—
95#123×C43—24no—
96#123×C43—24no—
97C22⋊Q8×C43—22no—
98C22⋊Q8×C43—21no—
99C22⋊Q8×C43D412yes—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—24no—
103#121×C43—21no—
104#121×C43—22no—
105#121×C43D412yes—
106#120×C43—24no—
107C4×Q8×C43—22no—
108C4×Q8×C43—21no—
109C4×Q8×C43C2312yes—
110C4×D4×C43—24no—
111C4×D4×C43—24no—
112C4×D4×C43—22no—
113C4×D4×C43—21no—
114C4×D4×C43—21no—
115C4×D4×C43—21no—
116C4×D4×C43D412yes—
117C4×D4×C43D412yes—
118C4×D4×C43C2312yes—
119#117×C43—22no—
120#117×C43—21no—
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—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—22no—
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—82no—
183#10621883—44no—
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—22no—
205Q8×C43—22no—
206Q8×C43—41no—
207Q8×C43—41no—
208Q8×C43—81no—
209D4×C43—22no—
210D4×C43—22no—
211D4×C43—42no—
212D4×C43—44no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—42no—
218D4×C43—84no—
219D4×C43—84no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—41no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—44no—
230C2×C4×C43—82no—
231C2×C4×C43—81no—
232C2×C4×C43—84no—
233C2×C4×C43#12011yescharacteristic
234C2×C4×C43#12011yescharacteristic
235C2×C4×C43#12011yescharacteristic
236C2×C4×C43#13512yes—
237C2×C4×C43#13712yes—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×Dic43—41no—
242C2×Dic43—41no—
243Dic86—42no—
244Dic86—41no—
245Dic86—41no—
246C43⋊C8—22no—
247C43⋊C8—41no—
248C43⋊C8—42no—
249C43⋊C8—42no—
250#18679—431nomaximal, Sylow
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—42no—
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—84no—
260C22×C43#45212yes—
261C22×C43C2×#12011yescharacteristic
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—42no—
266C4×C43—42no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43#45212yes—
270C4×C43C2×#13511yescharacteristic
271C4×C43C2×#13711yescharacteristic
272C4×C43#57611yescharacteristic
273C4×C43#57711yescharacteristic
274Dic43—81no—
275Dic43—81no—
276#3506D4311yescharacteristic
277#3249—431no—
278#3167—431no—
279#3077—431no—
280#1652—432no—
281#1641—432no—
282#1638—432no—
283#1631—432no—
284#1547—431no—
285#1493—431no—
286C2×D4⋊C8—431no—
287C2×C43—22no—
288C2×C43—82no—
289C2×C43—82no—
290C2×C43C2×#45211yescharacteristic
291C2×C43#301211yescharacteristic
292C2×C43#301811yescharacteristic
293#559—22no—
294#556C2×D4312yes—
295#555—21no—
296#553—22no—
297#550C2×D4312yes—
298#547—21no—
299#538—22no—
300#535—21no—
301#533—431no—
302#533C2×D4311yescharacteristic
303#532C2×D4311yescharacteristic
304#525—22no—
305#520—21no—
306C2×C4×D4C2×D4311yescharacteristic
307#498—431no—
308#492—431no—
309#487—431no—
310#486—431no—
311#478—862no—
312#477—432no—
313#477—861no—
314#476—432no—
315#474—432no—
316#467—862no—
317#465—862no—
318#462—432no—
319#462—861no—
320C4×SD16—862no—
321#428—861no—
322#423—431no—
323C2×C4⋊C8—431no—
324#418—861no—
325C2×C4×C8—431no—
326#332—432no—
327#331—432no—
328Q8⋊C8—432no—
329Q8⋊C8—432no—
330D4⋊C8—432no—
331D4⋊C8—432no—
332C43#1867911yescharacteristic, complemented, Sylow
333C2×#41—22no—
334C2×#41—21no—
335C22×D4C22⋊D4311yescharacteristic
336C23×C4—21no—
337C2×Q16—862no—
338C2×SD16—862no—
339C2×M16—861no—
340C22×C8—861no—
341C22×C8—861no—
342C4⋊Q8—431no—
343C4⋊Q8—431no—
344C4⋊Q8C22⋊D4311yescharacteristic
345C4⋊Q8C22⋊D4311yescharacteristic
346C4⋊Q8C22×D4311yescharacteristic
347#127—22no—
348#127C22×D4311yescharacteristic
349#126—24no—
350#125—21no—
351#125—861no—
352#124—24no—
353#124—22no—
354#124—21no—
355#123—24no—
356#123—24no—
357C22⋊Q8—22no—
358C22⋊Q8—21no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361C22⋊Q8C22⋊D4312yes—
362#121—22no—
363#121—22no—
364#121—24no—
365#121—21no—
366#121—22no—
367#121C22⋊D4312yes—
368#120—24no—
369C4×Q8—22no—
370C4×Q8—21no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8C22×D4312yes—
374C4×D4—24no—
375C4×D4—24no—
376C4×D4—22no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C22⋊D4312yes—
381C4×D4C22⋊D4312yes—
382C4×D4C22×D4312yes—
383#117—22no—
384#117—21no—
385#117—22no—
386#117—861no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4C22⋊D4311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C42C22×D4311yescharacteristic
391#107—862no—
392#107—862no—
393#106—862no—
394#106—862no—
395C4⋊C8—432no—
396C4⋊C8—432no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399#103—862no—
400#103—862no—
401#103—862no—
402#102—862no—
403#102—862no—
404#102—862no—
405C4×C8—431no—
406C4×C8—431no—
407C4×C8—861no—
408C24—21no—
409#41—42no—
410#41—42no—
411#41—82no—
412#41—82no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×Q8C2×C22⋊D4312yes—
418C2×D4—22no—
419C2×D4—24no—
420C2×D4—24no—
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C2×C22⋊D4312yes—
427C2×D4C2×C22⋊D4312yes—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438Q16—3442no—
439SD16—1724no—
440M16—1722no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—862no—
444C2×C8—862no—
445C2×C8—3441no—
446C2×C8—1722no—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4C2×C22⋊D4312yes—
462C4⋊C4C2×C22⋊D4312yes—
463C4⋊C4C2×C22⋊D4312yes—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—1721no—
473C42—24no—
474C42—22no—
475C42—1721no—
476C42C2×C22⋊D4311yescharacteristic
477C42C2×C22⋊D4311yescharacteristic
478C42C2×C22⋊D4311yescharacteristic
479C42C23×D4311yescharacteristic
480C23—22no—
481C23—22no—
482C23—42no—
483C23—81no—
484C23—81no—
485C23#1306329411yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—41no—
489Q8—41no—
490Q8—81no—
491Q8—1722no—
492Q8—1721no—
493Q8—1721no—
494D4—22no—
495D4—22no—
496D4—42no—
497D4—44no—
498D4—42no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—84no—
504D4—84no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—41no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—81no—
517C2×C4—84no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4#1306329411yescharacteristic
521C2×C4#1306329411yescharacteristic
522C2×C4#1306329411yescharacteristic
523C2×C4#1306334512yes—
524C2×C4#1306335512yes—
525C2×C4C22×C22⋊D4311yescharacteristic
526C2×C4C22×C22⋊D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C8—862no—
529C8—1721no—
530C8—1722no—
531C8—1722no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—84no—
541C22#1458306112yes—
542C22C2×#1306329411yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—42no—
550C4—3441no—
551C4—3441no—
552C4#1458306112yes—
553C4C2×#1306334511yescharacteristic
554C4C2×#1306335511yescharacteristic
555C4#1458370211yescharacteristic
556C4#1458371011yescharacteristic
557C2—22no—
558C2—82no—
559C2—82no—
560C2C2×#1458306111yescharacteristic
561C2#1914389911yescharacteristic
562C2#1914394411yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3506C2
socleC22×C43C2×#120
hypercenter#3506D43
hypocenterC43#18679
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. #19145937C2semidirect
2. #19145150C2semidirect
3. #19144392C2semidirect
4. #19133865C2semidirect
5. #19133788C2semidirect
6. #19133767C2semidirect
7. #19133722C2semidirect
8. #19133272C2semidirect
9. #19133050C2semidirect
10. C2×D4⋊(C43⋊C8)C2semidirect
13. #14583295C22semidirect
14. #14583271C22semidirect
15. #14583251C22semidirect
16. #14583245C22semidirect
18. #14583194C22semidirect
24. #14583109C22semidirect
32. #14582645C22semidirect
33. #14582643C22semidirect
34. Q8⋊(C43⋊C8)C22semidirect
35. Q8⋊(C43⋊C8)C22semidirect
332. C43#18679semidirect

Maximal subgroups

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

subgroupindex
#191459372
#191451502
#191443922
#191338652
#191337882
#191337672
#191337222
#191332722
#191330502
C2×D4⋊(C43⋊C8)2
C43×#35062
#1867943