Finite Group Databasebeta

← #25067240

Subgroups — #25067240

Order 11008.

582 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#19145201C211yesmaximal, characteristic
2#19143740C211yesmaximal, characteristic
3#19143692C211yesmaximal, characteristic, complemented
4#19133503C211yesmaximal, characteristic, complemented
5#19133496C211yesmaximal, characteristic, complemented
6#19133491C211yesmaximal, characteristic, complemented
7#19133484C211yesmaximal, characteristic, complemented
8#19133413C211yesmaximal, characteristic, complemented
9#19133406C211yesmaximal, characteristic, complemented
10#19133401C211yesmaximal, characteristic, complemented
11#19133394C211yesmaximal, characteristic, complemented
12#19133053C211yesmaximal, characteristic
13#19133049C211yesmaximal, characteristic, complemented
14M16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#1569C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583308C411yescharacteristic
19#14583293C411yescharacteristic
20#14583268C411yescharacteristic
21#14583259C411yescharacteristic
22#14583157C411yescharacteristic
23#14583157C411yescharacteristic
24#14583145C411yescharacteristic
25#14583145C411yescharacteristic
26#14583027—21no—
27#14583027—21no—
28#14583026C2211yescharacteristic
29#14583026C2211yescharacteristic
30#14583026C2211yescharacteristic
31#14583023C2211yescharacteristic
32#14583023C2211yescharacteristic
33#14583023C2211yescharacteristic
34C4×Dic172C2211yescharacteristic
35C4×Dic172C2211yescharacteristic
36C4×#10621873C2211yescharacteristic
37C4×#10621873C2211yescharacteristic
38#14582976C2211yescharacteristic
39#14582975—21no—
40#14582968—21no—
41#14582964C2211yescharacteristic
42#14582959—21no—
43#14582957—21no—
44#14582957—21no—
45#14582952C2211yescharacteristic
46#14582924—21no—
47C2×C4×C43⋊C8C2211yescharacteristic
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582629C2211yescharacteristic
51#14582629C2211yescharacteristic
52#14582629C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582620C2211yescharacteristic
57#14582620C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×Dic172C2×C411yescharacteristic
68C2×Dic172C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621873C2×C411yescharacteristic
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325C2×C411yescharacteristic
75#13063325C2×C411yescharacteristic
76#13063319—21no—
77#13063317—21no—
78#13063317C2×C411yescharacteristic
79#13063313C2×C411yescharacteristic
80#13063308—21no—
81#13063304—21no—
82#13063304C2×C411yescharacteristic
83#13063304C2×C411yescharacteristic
84#13063304C2×C411yescharacteristic
85#13063299C2×C411yescharacteristic
86C4×Dic86—21no—
87C4×Dic86C2311yescharacteristic
88C4×Dic86C2311yescharacteristic
89C4×Dic86C2311yescharacteristic
90C4×D172C2311yescharacteristic
91C4×C22⋊D43—21no—
92#13063284—21no—
93#13063282—21no—
94#13063259C2×C411yescharacteristic
95#13063259C2×C411yescharacteristic
96#13063257C2×C411yescharacteristic
97#13063257C2×C411yescharacteristic
98C4⋊(C43⋊C8)D411yescharacteristic
99C4⋊(C43⋊C8)D411yescharacteristic
100Dic43⋊C8—21no—
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106#13063250C2×C411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063250C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114C22⋊(C43⋊C8)D411yescharacteristic
115C22⋊(C43⋊C8)D411yescharacteristic
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118#13063235—21no—
119#13063235—21no—
120#13063235—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×M16×C43—21no—
130C2×M16×C43C2×C411yescharacteristic
131C2×M16×C43C2×C411yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×C43C2×C411yescharacteristic
141#97×C43C2×C411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×D172C22×C411yescharacteristic
149C2×C4×D43—21no—
150C2×Dic86—21no—
151C2×Dic86C22×C411yescharacteristic
152C2×Dic86C22×C411yescharacteristic
153C2×Dic86C22×C411yescharacteristic
154M16×C43—22no—
155M16×C43—22no—
156M16×C43—81no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43C22×C411yescharacteristic
162C2×C8×C43C22×C411yescharacteristic
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C42×C43C22×C411yescharacteristic
166C42×C43C2×D411yescharacteristic
167C42×C43#4111yescharacteristic
168C42×C43C2411yescharacteristic
169C22⋊Dic43—21no—
170C22⋊Dic43—21no—
171C22⋊Dic43—21no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43C22×C411yescharacteristic
180C4⋊Dic43C22×C411yescharacteristic
181C4⋊Dic43C22×C411yescharacteristic
182C4⋊Dic43C22×C411yescharacteristic
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—42no—
197C2×C43⋊C8C2×D411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201Dic172—22no—
202Dic172—22no—
203#10621873—22no—
204#10621873—22no—
205#10621872—81no—
206C8×D43—81no—
207C23×C43C4×D411yescharacteristic
208C22×D43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—41no—
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43C4×D411yescharacteristic
216C2×C4×C43C4×D411yescharacteristic
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C22⋊D43—81no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228D172—21no—
229D172—21no—
230C4×D43—41no—
231C4×D43—41no—
232Dic86—21no—
233Dic86—21no—
234Dic86—21no—
235Dic86—21no—
236Dic86—21no—
237Dic86—21no—
238Dic86—81no—
239C8×C43—21no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43#13112yes—
246C8×C43#13112yes—
247C43⋊C8—22no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253#17969—431nomaximal, Sylow
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43C2×C4×D411yescharacteristic
258C2×D43—41no—
259C2×D43—41no—
260C2×D43—41no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43C2×#13111yescharacteristic
266C4×C43C2×#13111yescharacteristic
267C4×C43#57711yescharacteristic
268C4×C43#57811yescharacteristic
269Dic43—41no—
270Dic43—41no—
271Dic43—41no—
272Dic43—41no—
273Dic43—41no—
274Dic43—41no—
275Dic43—41no—
276#3172—431no—
277#2993—431no—
278#2985—431no—
279#1593—431no—
280#1592—431no—
281#1591—431no—
282#1590—431no—
283#1579—431no—
284SD16⋊C8—431no—
285C8×Q16—431no—
286C8×SD16—431no—
287#1569D4311yescharacteristic, complemented
288#1494—431no—
289#1493—431no—
290C8×M16—431no—
291C2×C43—41no—
292C2×C43#293111yescharacteristic
293C2×C43#294711yescharacteristic
294C2×C43#295611yescharacteristic
295D43—81no—
296#533—431no—
297#529—431no—
298#501—431no—
299#497—431no—
300#491—431no—
301#489—431no—
302#470—431no—
303#470—431no—
304#468—431no—
305#468—431no—
306#446—431no—
307#446—431no—
308#446—431no—
309#446—861no—
310#446—861no—
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—431no—
314C4×Q16—431no—
315C4×Q16—431no—
316C4×SD16—431no—
317C4×SD16—431no—
318#436—431no—
319#436—861no—
320#435—861no—
321C8×D4—431no—
322#433—861no—
323#433—861no—
324#433—861no—
325#432C2×D4311yescharacteristic
326#431—431no—
327#424—861no—
328#423C2×D4311yescharacteristic
329C4×M16C2×D4311yescharacteristic
330C2×C4×C8—431no—
331#335C2×D4311yescharacteristic
332#335C2×D4311yescharacteristic
333#334C2×D4311yescharacteristic
334#334C2×D4311yescharacteristic
335Q8⋊C8—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341D4⋊C8—431no—
342D4⋊C8—431no—
343#322—431no—
344#322—431no—
345C82—431no—
346C82—431no—
347C43#1796911yescharacteristic, complemented, Sylow
348C2×Q16—431no—
349C2×Q16—431no—
350C2×SD16—431no—
351C2×SD16—431no—
352C2×M16—21no—
353C2×M16—861no—
354C2×M16C4×D4311yescharacteristic
355C2×M16C4×D4311yescharacteristic
356C22×C8—861no—
357C22×C8—861no—
358C4⋊Q8—431no—
359C4⋊Q8—431no—
360#126—861no—
361#125—431no—
362#125—861no—
363#124—431no—
364#123—861no—
365C22⋊Q8—431no—
366C22⋊Q8—431no—
367C22⋊Q8—431no—
368C22⋊Q8—861no—
369#121—431no—
370C4×Q8—431no—
371C4×Q8—431no—
372C4×Q8—431no—
373C4×Q8—861no—
374C4×D4—431no—
375C4×D4—861no—
376#117—861no—
377#117—861no—
378C2×C42C22×D4311yescharacteristic
379#107—431no—
380#107—431no—
381#106—431no—
382#106—431no—
383C4⋊C8—21no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8C22×D4311yescharacteristic
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—431no—
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#102—431no—
403#102—431no—
404C22⋊C8—21no—
405C22⋊C8—431no—
406C22⋊C8—431no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409#97—21no—
410#97—861no—
411#97—861no—
412#97—861no—
413#97C4×D4311yescharacteristic
414#97C4×D4311yescharacteristic
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C2×Q8—431no—
426C2×Q8—431no—
427C2×Q8—431no—
428C2×Q8—861no—
429C2×D4—431no—
430C2×D4—861no—
431C22×C4—861no—
432C22×C4C2×C4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4#1062190211yescharacteristic
435Q16—862no—
436Q16—862no—
437SD16—862no—
438SD16—862no—
439M16—22no—
440M16—22no—
441M16—81no—
442M16—3441no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—3441no—
454C2×C8—1722no—
455C2×C8C2×C4×D4311yescharacteristic
456C2×C8C2×C4×D4311yescharacteristic
457C2×C8C2×C4×D4311yescharacteristic
458C2×C8C2×C4×D4311yescharacteristic
459C4⋊C4—431no—
460C4⋊C4—431no—
461C4⋊C4—431no—
462C4⋊C4—431no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C42—861no—
482C42—861no—
483C42—861no—
484C42C2×C4×D4311yescharacteristic
485C42D4×D4311yescharacteristic
486C42#1062190211yescharacteristic
487C42C23×D4311yescharacteristic
488C23—861no—
489C23#1306328711yescharacteristic
490Q8—861no—
491Q8—861no—
492Q8—861no—
493Q8—861no—
494Q8—861no—
495Q8—861no—
496Q8—3441no—
497D4—861no—
498D4—861no—
499D4—3441no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4#1306328711yescharacteristic
515C2×C4#1306328711yescharacteristic
516C2×C4#1306328711yescharacteristic
517C2×C4C22×C4×D4311yescharacteristic
518C2×C4C2×D4×D4311yescharacteristic
519C2×C4C2×#1062190211yescharacteristic
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—862no—
527C8—861no—
528C8—861no—
529C8—861no—
530C8—861no—
531C8—1721no—
532C8#1306333312yes—
533C8#1306333312yes—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—1721no—
538C22—1721no—
539C22—1721no—
540C22C2×#1306328711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—1721no—
546C4—1721no—
547C4—1721no—
548C4—1721no—
549C4—1721no—
550C4—1721no—
551C4—1721no—
552C4C2×#1306333311yescharacteristic
553C4C2×#1306333311yescharacteristic
554C4#1458370911yescharacteristic
555C4#1458371511yescharacteristic
556C2—41no—
557C2—3441no—
558C2#1914330611yescharacteristic
559C2#1914343611yescharacteristic
560C2#1914350411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1569C2
socleC22×C43C2×C4×D4
prime radical#13063299C2×C4
cosocleC42×C43C24
hypercenter#1569D43
hypocenterC43#17969
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
3. #19143692C2semidirect
4. #19133503C2semidirect
5. #19133496C2semidirect
6. #19133491C2semidirect
7. #19133484C2semidirect
8. #19133413C2semidirect
9. #19133406C2semidirect
10. #19133401C2semidirect
11. #19133394C2semidirect
13. #19133049C2semidirect
14. M16×C43⋊C8C2semidirect
15. C43×#1569C2semidirect
287. #1569D43semidirect
347. C43#17969semidirect

Maximal subgroups

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

subgroupindex
#191452012
#191437402
#191436922
#191335032
#191334962
#191334912
#191334842
#191334132
#191334062
#191334012
#191333942
#191330532
#191330492
M16×C43⋊C82
C43×#15692
#1796943