Finite Group Databasebeta

← #25064596

Subgroups — #25064596

Order 11008.

964 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148568C211yesmaximal, characteristic
2#19143610C211yesmaximal, characteristic, complemented
3#19143024C211yesmaximal, characteristic, complemented
4#19133214C212yesmaximal, complemented
5#19133210C211yesmaximal, characteristic, complemented
6#19133200C211yesmaximal, characteristic, complemented
7#19133195C212yesmaximal, complemented
8#19133184C211yesmaximal, characteristic, complemented
9#19133182C212yesmaximal, complemented
10#330×D43C212yesmaximal, complemented
11C43×#1526C211yesmaximal, characteristic, complemented
12C2×#13063333—21no—
13#14583624C411yescharacteristic
14#14583610C411yescharacteristic
15#14583610C411yescharacteristic
16#14583593C412yes—
17#14583590—22no—
18#14583588C412yes—
19#14583583—21no—
20#14583552C411yescharacteristic
21#14583551—21no—
22#14583507—21no—
23#14583495—22no—
24#14583434C2212yes—
25#14583433C2211yescharacteristic
26#125×D43C2212yes—
27#14583381—21no—
28C4×#10621898C2211yescharacteristic
29#14583029—21no—
30#14582968—22no—
31C8×D172—21no—
32#14582956C2211yescharacteristic
33#14582954C2212yes—
34#14582857—21no—
35#14582853—22no—
36#14582851C2212yes—
37C2×#13063236C2211yescharacteristic
38#97×D43C2212yes—
39#97×D43C2212yes—
40#14582641C2212yes—
41#14582641C2212yes—
42#14582640C2211yescharacteristic
43#14582640C2211yescharacteristic
44#14582640C2212yes—
45#14582638C2211yescharacteristic
46#14582638C2211yescharacteristic
47#14582638C2212yes—
48C43×#533C2211yescharacteristic
49C4×M16×C43C2211yescharacteristic
50C4×M16×C43C2211yescharacteristic
51C43×#330C2212yes—
52C43×#330C2212yes—
53C2×#10621902—21no—
54C2×#10621898D411yescharacteristic
55#13063333—28no—
56C2×#10621872—22no—
57C22×C43⋊C8—21no—
58C2×C8×D43—22no—
59C2×C8×D43—22no—
60#13063323—21no—
61#13063320—22no—
62#13063319—21no—
63#13063319—22no—
64#13063318—22no—
65#13063317—22no—
66#13063317C2311yescharacteristic
67#13063316—21no—
68#13063316C2×C412yes—
69#13063316C2×C412yes—
70#13063315—22no—
71#13063315—22no—
72#13063315—22no—
73#13063313C2311yescharacteristic
74#13063310—22no—
75#13063310—22no—
76#13063308—21no—
77#13063307—22no—
78#13063307—22no—
79#13063305—21no—
80#13063305C2×C412yes—
81#13063304C2×C411yescharacteristic
82#13063301—22no—
83#13063301—21no—
84#13063301—22no—
85#13063300C2×C412yes—
86#13063299C2×C411yescharacteristic
87#13063298—22no—
88Q8×Dic43—21no—
89C4×Dic86C2×C411yescharacteristic
90C4×Dic86C2×C411yescharacteristic
91C4×Dic86D411yescharacteristic
92#13063290C2×C412yes—
93C4×D172—22no—
94C4×D172C2×C411yescharacteristic
95C4×D172C2×C411yescharacteristic
96C4×D172D411yescharacteristic
97#13063287—21no—
98#13063287—22no—
99#13063287C2×C412yes—
100C4×C22⋊D43—21no—
101C4×C22⋊D43C2×C412yes—
102C4×C22⋊D43D412yes—
103#13063284D411yescharacteristic
104#13063283—22no—
105#13063282—21no—
106#13063282—22no—
107#13063282D412yes—
108C4⋊C4×D43—22no—
109C4⋊C4×D43—22no—
110C4⋊C4×D43—21no—
111C4⋊C4×D43C2×C412yes—
112C4⋊C4×D43C2×C412yes—
113C42×D43C2312yes—
114C4⋊(C43⋊C8)—21no—
115Dic43⋊C8—22no—
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—22no—
118#13063236—21no—
119#13063236C2311yescharacteristic
120#13063236C2312yes—
121#13063236C2311yescharacteristic
122#13063235—22no—
123#13063235—22no—
124C8×Dic43—22no—
125C2×M16×C43—21no—
126C2×M16×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128C4⋊Q8×C43C2×C411yescharacteristic
129#125×C43C2312yes—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134#117×C43C2×C412yes—
135C2×C42×C43C2311yescharacteristic
136#97×C43C2311yescharacteristic
137#97×C43C2312yes—
138#97×C43C2311yescharacteristic
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C2×C22⋊D43—21no—
147C2×C22⋊D43C22⋊C412yes—
148#10621902—44no—
149#10621898—24no—
150C2×D172—22no—
151C2×D172C22⋊C411yescharacteristic
152C2×D172C22×C411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43C22×C412yes—
158C2×C4×D43C2×D412yes—
159C2×C4×D43C2×D412yes—
160C2×Dic86C22⋊C411yescharacteristic
161C2×Dic86C22×C411yescharacteristic
162M16×C43—24no—
163M16×C43—42no—
164C2×C8×C43—22no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43C22×C412yes—
172C4⋊C4×C43C22×C412yes—
173C22⋊C4×C43—22no—
174C42×C43—22no—
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180C22⋊Dic43C22⋊C412yes—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4C22⋊C412yes—
189(C2×D43)⋊C4C22⋊C412yes—
190C4⋊Dic43—22no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43C22⋊C411yescharacteristic
194C4⋊Dic43C22⋊C411yescharacteristic
195C4⋊Dic43C22×C411yescharacteristic
196C4⋊Dic43C22×C411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4C22⋊C412yes—
207Dic43⋊C4C22⋊C412yes—
208C4×Dic43—21no—
209C4×Dic43—22no—
210C4×Dic43C22×C412yes—
211C4×Dic43C2×D412yes—
212C4×Dic43C2×D412yes—
213C2×C43⋊C8—24no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—22no—
217#10621872—28no—
218C8×D43—28no—
219C8×D43—44no—
220C23×C43C2×C22⋊C411yescharacteristic
221C22×D43—21no—
222C22×D43C2×C22⋊C412yes—
223Q8×C43—42no—
224Q8×C43—81no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C2×C22⋊C411yescharacteristic
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43C2×C22⋊C411yescharacteristic
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C22×D411yescharacteristic
236C22⋊D43—24no—
237C22⋊D43—81no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43C2×C22⋊C412yes—
242C2×Dic43C2×C22⋊C412yes—
243C2×Dic43C2×C22⋊C412yes—
244D172—41no—
245D172—44no—
246D172#10414yes—
247C4×D43—24no—
248C4×D43—42no—
249C4×D43—42no—
250C4×D43—44no—
251C4×D43—42no—
252C4×D43—82no—
253C4×D43—82no—
254Dic86—22no—
255Dic86—41no—
256C8×C43—24no—
257C8×C43—22no—
258C8×C43—41no—
259C43⋊C8—22no—
260C43⋊C8—22no—
261C43⋊C8—42no—
262#17653—431nomaximal, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43C22×C22⋊C411yescharacteristic
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43C2×#10414yes—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43C2×#10412yes—
281Dic43—22no—
282Dic43—22no—
283Dic43—22no—
284Dic43—41no—
285Dic43—41no—
286Dic43—41no—
287#3515—431no—
288#2970—431no—
289#2875—431no—
290#1532—432no—
291#1531—431no—
292#1529—431no—
293#1528—432no—
294#1526D4311yescharacteristic, complemented
295#1524—431no—
296#1524—432no—
297C2×#330—432no—
298C2×C43—41no—
299C2×C43#288911yescharacteristic
300C2×C43C22×#10411yescharacteristic
301C2×C43#290111yescharacteristic
302D43—24no—
303D43—81no—
304C2×#131—861no—
305#557—431no—
306#554—431no—
307#554—431no—
308#553—432no—
309#552—432no—
310#552—862no—
311#552—861no—
312#547—431no—
313#547—861no—
314#541—861no—
315#539—862no—
316#533C2×D4311yescharacteristic
317#529—432no—
318#529—431no—
319C2×#125—432no—
320#520—861no—
321C4×#41—431no—
322#446—861no—
323#435—862no—
324C8×D4—861no—
325#432—431no—
326#432—432no—
327#405—862no—
328#405—861no—
329C4×M16—432no—
330C4×M16C2×D4311yescharacteristic
331C4×M16C2×D4311yescharacteristic
332C2×#97—431no—
333C2×#97—432no—
334C2×#97—432no—
335#330—432no—
336#330—432no—
337#330—431no—
338#330—432no—
339#330—431no—
340#330C2×D4312yes—
341#330C2×D4312yes—
342#329—431no—
343#329—432no—
344#329—431no—
345C43#1765311yescharacteristic, complemented, Sylow
346C2×#41—431no—
347C2×#41—861no—
348#131—868no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—862no—
352C22×C8—862no—
353C22×C8—862no—
354C22×C8—861no—
355C4⋊Q8—861no—
356C4⋊Q8C4×D4311yescharacteristic
357C4⋊Q8C4×D4311yescharacteristic
358#126—862no—
359#126—862no—
360#126—862no—
361#126—861no—
362#125—432no—
363#125—432no—
364#125—431no—
365#125—862no—
366#125—862no—
367#125—862no—
368#125—862no—
369#125—861no—
370#125C22×D4312yes—
371#124—431no—
372#123—862no—
373#123—862no—
374#123—862no—
375#123—862no—
376#123—861no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—431no—
380C22⋊Q8—432no—
381C22⋊Q8—862no—
382C22⋊Q8—861no—
383C22⋊Q8—862no—
384C22⋊Q8—861no—
385#121—431no—
386#121—432no—
387#121—862no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—431no—
391C4×Q8—431no—
392C4×Q8—432no—
393C4×Q8—431no—
394C4×Q8—861no—
395C4×D4—432no—
396C4×D4—432no—
397C4×D4—432no—
398C4×D4—431no—
399C4×D4—431no—
400C4×D4—431no—
401C4×D4—862no—
402C4×D4—862no—
403C4×D4—861no—
404C4×D4—861no—
405#117—431no—
406#117—432no—
407#117—862no—
408#117—862no—
409#117—861no—
410#117C4×D4312yes—
411C2×C4⋊C4—432no—
412C2×C4⋊C4—432no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—862no—
415C2×C4⋊C4—862no—
416C2×C42—432no—
417C2×C42C22×D4311yescharacteristic
418C4⋊C8—862no—
419C4⋊C8—861no—
420C22⋊C8—862no—
421C22⋊C8—861no—
422#97—431no—
423#97—431no—
424#97—432no—
425#97—862no—
426#97—862no—
427#97—861no—
428#97C22×D4311yescharacteristic
429#97C22×D4312yes—
430#97C22×D4311yescharacteristic
431C4×C8—21no—
432C4×C8—21no—
433C4×C8—862no—
434#41—864no—
435#41—1724no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—431no—
439C2×Q8—431no—
440C2×D4—432no—
441C2×D4—431no—
442C2×D4—431no—
443C2×D4—862no—
444C2×D4—861no—
445C22×C4—432no—
446C22×C4—432no—
447C22×C4—432no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4C2×C4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4D4×D4311yescharacteristic
455M16—24no—
456M16—42no—
457M16—868no—
458C2×C8—22no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—868no—
462C2×C8—864no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—862no—
466C2×C8—1724no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—431no—
472C4⋊C4—432no—
473C4⋊C4—431no—
474C4⋊C4—432no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4C2×C4×D4312yes—
490C4⋊C4C2×C4×D4312yes—
491C22⋊C4—22no—
492C22⋊C4—432no—
493C22⋊C4—432no—
494C22⋊C4—432no—
495C22⋊C4—862no—
496C22⋊C4—862no—
497C22⋊C4—862no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C22⋊C4—861no—
503C42—22no—
504C42—432no—
505C42—432no—
506C42—432no—
507C42—862no—
508C42—861no—
509C42C2×C4×D4311yescharacteristic
510C42D4×D4311yescharacteristic
511C42D4×D4311yescharacteristic
512C42C23×D4311yescharacteristic
513C23—432no—
514C23—861no—
515C23C22⋊C4×D4311yescharacteristic
516Q8—42no—
517Q8—81no—
518Q8—862no—
519Q8—1721no—
520D4—434no—
521D4—864no—
522D4—3441no—
523D4—1721no—
524D4—1724no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—432no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—864no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—3442no—
538C2×C4—3442no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4—1724no—
542C2×C4—1722no—
543C2×C4C22⋊C4×D4311yescharacteristic
544C2×C4C22⋊C4×D4311yescharacteristic
545C2×C4C22⋊C4×D4311yescharacteristic
546C2×C4C22×C4×D4311yescharacteristic
547C2×C4C2×D4×D4311yescharacteristic
548C2×C4C2×D4×D4311yescharacteristic
549C8—24no—
550C8—22no—
551C8—41no—
552C8—862no—
553C8—862no—
554C8—1722no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—434no—
559C22—862no—
560C22—862no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22C2×C22⋊C4×D4311yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—42no—
571C4—42no—
572C4—862no—
573C4—862no—
574C4—862no—
575C4—1721no—
576C4—1721no—
577C4—1721no—
578C4#104×D4312yes—
579C2—41no—
580C2—864no—
581C2—3441no—
582C2#1914307511yescharacteristic
583C2C2×#104×D4311yescharacteristic
584C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1526C2
socleC22×C43C22×C22⋊C4
prime radical#19148568C2
cosocleC42×C43C24
hypercenter#1526D43
hypocenterC43#17653
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
2. #19143610C2semidirect
3. #19143024C2semidirect
4. #19133214C2semidirect
5. #19133210C2semidirect
6. #19133200C2semidirect
7. #19133195C2semidirect
8. #19133184C2semidirect
9. #19133182C2semidirect
10. #330×D43C2semidirect
11. C43×#1526C2semidirect
294. #1526D43semidirect
345. C43#17653semidirect

Maximal subgroups

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

subgroupindex
#191485682
#191436102
#191430242
#191332142
#191332102
#191332002
#191331952
#191331842
#191331822
#330×D432
C43×#15262
#1765343