Finite Group Databasebeta

← #25067189

Subgroups — #25067189

Order 11008.

594 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#19145199C211yesmaximal, characteristic
2#19143569C211yesmaximal, characteristic
3#19143526C211yesmaximal, characteristic, complemented
4#19133502C211yesmaximal, characteristic, complemented
5#19133499C211yesmaximal, characteristic, complemented
6#19133495C211yesmaximal, characteristic, complemented
7Q16×C43⋊C8C211yesmaximal, characteristic, complemented
8#19133399C211yesmaximal, characteristic, complemented
9#19133394C211yesmaximal, characteristic, complemented
10#19133392C211yesmaximal, characteristic, complemented
11#19133359C211yesmaximal, characteristic, complemented
12#19133066C211yesmaximal, characteristic, complemented
13#19133059C211yesmaximal, characteristic
14#19132874C211yesmaximal, characteristic, complemented
15C43×#1593C211yesmaximal, characteristic, complemented
16#14583453C2211yescharacteristic
17#14583436C2211yescharacteristic
18#14583307C411yescharacteristic
19#14583292C411yescharacteristic
20#14583266C411yescharacteristic
21#14583260C411yescharacteristic
22#14583156C411yescharacteristic
23#14583154C411yescharacteristic
24#14583148C411yescharacteristic
25#14583146C411yescharacteristic
26#14583029C2211yescharacteristic
27#14583027—21no—
28Q8×C43⋊C8C2211yescharacteristic
29Q8×C43⋊C8C2211yescharacteristic
30#14583023—21no—
31#14583023C2211yescharacteristic
32C4×#10621885C2211yescharacteristic
33C4×#10621873C2211yescharacteristic
34C4×#10621884C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582972—21no—
37#14582964—21no—
38#14582964C2211yescharacteristic
39#14582959—21no—
40#14582955C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582924—21no—
43#14582921C2211yescharacteristic
44#14582856—21no—
45#14582856—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C43×#446C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621873C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621872—21no—
71C2×#10621872—21no—
72C2×#10621872C2×C411yescharacteristic
73C2×#10621872C2×C411yescharacteristic
74C2×C8×D43—21no—
75C2×C8×D43D411yescharacteristic
76C2×C8×D43D411yescharacteristic
77#13063324C2×C411yescharacteristic
78#13063323C2×C411yescharacteristic
79#13063320—21no—
80#13063316C2×C411yescharacteristic
81#13063315—21no—
82#13063314C2×C411yescharacteristic
83#13063310—21no—
84#13063305C2×C411yescharacteristic
85#13063303—21no—
86#13063301C2×C411yescharacteristic
87#13063301C2×C411yescharacteristic
88#13063300C2×C411yescharacteristic
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91C4×D172—21no—
92C4×D172C2311yescharacteristic
93#13063282—21no—
94#13063282—21no—
95C42×D43C2311yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063257C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99C4⋊(C43⋊C8)—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250C2×C411yescharacteristic
108#13063249C2×C411yescharacteristic
109#13063249C2×C411yescharacteristic
110#13063248C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117#13063235—21no—
118#13063235—21no—
119#13063235C2×C411yescharacteristic
120#13063235C2×C411yescharacteristic
121C4×C43⋊C8—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×Q16×C43C2×C411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43C2×C411yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#103×C43C2×C411yescharacteristic
139#97×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×D172—21no—
147C2×D172C22×C411yescharacteristic
148C2×C4×D43—21no—
149C2×C4×D43C22×C411yescharacteristic
150C2×C4×D43C2×D411yescharacteristic
151C2×C4×D43#4111yescharacteristic
152C2×Dic86—21no—
153C2×Dic86C22×C411yescharacteristic
154Q16×C43—22no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43C22×C411yescharacteristic
159C2×C8×C43C22×C411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43C22×C411yescharacteristic
165C4⋊C4×C43C22×C411yescharacteristic
166C42×C43—21no—
167C42×C43—21no—
168C42×C43C2411yescharacteristic
169#10621885—22no—
170#10621884—22no—
171(C2×D43)⋊C4—21no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176(C2×D43)⋊C4—21no—
177(C2×D43)⋊C4—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43C22×C411yescharacteristic
181C4⋊Dic43C22×C411yescharacteristic
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189C4×Dic43—21no—
190C4×Dic43C22×C411yescharacteristic
191C4×Dic43C2×D411yescharacteristic
192C4×Dic43#4111yescharacteristic
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8C22×C411yescharacteristic
197C2×C43⋊C8C22×C411yescharacteristic
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200#10621873—22no—
201#10621872—22no—
202#10621872—22no—
203#10621872—42no—
204#10621872—42no—
205C8×D43—22no—
206C8×D43—41no—
207C8×D43—42no—
208C22×D43—21no—
209C22×D43C4×D411yescharacteristic
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43C23×C411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43C4×D411yescharacteristic
225C2×Dic43C4×D411yescharacteristic
226C2×Dic43C4×D411yescharacteristic
227D172—21no—
228D172—21no—
229D172—42no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—41no—
235C4×D43—41no—
236C4×D43—41no—
237Dic86—21no—
238Dic86—21no—
239Dic86—42no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43#13112yes—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8#13112yes—
253C43⋊C8#13712yes—
254#17965—431nomaximal, Sylow
255C22×C43C2×C4×D411yescharacteristic
256C2×D43—21no—
257C2×D43—21no—
258C2×D43—21no—
259C2×D43—41no—
260C2×D43—41no—
261C2×D43—41no—
262C4×C43—21no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43C2×#13111yescharacteristic
268C4×C43C2×#13111yescharacteristic
269C4×C43C2×#13711yescharacteristic
270C4×C43#57511yescharacteristic
271Dic43—21no—
272Dic43—21no—
273Dic43—21no—
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277#3172—431no—
278#2966—431no—
279#2960—431no—
280#1593—431no—
281#1593D4311yescharacteristic, complemented
282#1592—431no—
283#1592—431no—
284C8×Q16—431no—
285C8×Q16—431no—
286C8×SD16—431no—
287C8×SD16—431no—
288#1569—431no—
289#1497—431no—
290#1495—431no—
291C8×M16—431no—
292C2×C43#293111yescharacteristic
293C2×C43C4×#13711yescharacteristic
294C2×C43#295511yescharacteristic
295D43—41no—
296D43—81no—
297#533—431no—
298#529—431no—
299#501—431no—
300#497—431no—
301#491—431no—
302#489—431no—
303#470—431no—
304#470—431no—
305#468—431no—
306#468—431no—
307#446—431no—
308#446—861no—
309#446C2×D4311yescharacteristic
310#446C2×D4311yescharacteristic
311C8×Q8—431no—
312C8×Q8—431no—
313C8×Q8—431no—
314C8×Q8—861no—
315C4×Q16—431no—
316C4×Q16C2×D4311yescharacteristic
317C4×SD16—431no—
318C4×SD16—431no—
319#436—431no—
320#435—861no—
321C8×D4—431no—
322C8×D4—861no—
323#433—861no—
324#432—431no—
325#431—431no—
326#424—861no—
327#423—431no—
328#405—861no—
329#405—861no—
330C4×M16—431no—
331C2×C4×C8—431no—
332#335—431no—
333#335—431no—
334#334—431no—
335#334C2×D4311yescharacteristic
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8C2×D4311yescharacteristic
341Q8⋊C8C2×D4311yescharacteristic
342D4⋊C8—431no—
343D4⋊C8—431no—
344#322—431no—
345#322C2×D4311yescharacteristic
346C82—431no—
347C82—431no—
348C43#1796511yescharacteristic, complemented, Sylow
349C2×Q16—431no—
350C2×Q16C4×D4311yescharacteristic
351C2×SD16—431no—
352C2×SD16—431no—
353C2×M16—431no—
354C2×M16—431no—
355C2×M16—861no—
356C2×M16—861no—
357C22×C8—431no—
358C22×C8—431no—
359C22×C8—861no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362#126—861no—
363#125—431no—
364#125—861no—
365#124—431no—
366#123—861no—
367C22⋊Q8—431no—
368C22⋊Q8—431no—
369C22⋊Q8—431no—
370C22⋊Q8—861no—
371#121—431no—
372C4×Q8—431no—
373C4×Q8—861no—
374C4×Q8C22×D4311yescharacteristic
375C4×Q8C22×D4311yescharacteristic
376C4×D4—431no—
377C4×D4—861no—
378#117—861no—
379#117—861no—
380C2×C42—431no—
381#107—431no—
382#107C4×D4311yescharacteristic
383#106—431no—
384#106—431no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397#103—431no—
398#103—431no—
399#103—431no—
400#103—431no—
401#103C4×D4311yescharacteristic
402#103C4×D4311yescharacteristic
403#102—431no—
404#102—431no—
405C22⋊C8—861no—
406C22⋊C8—861no—
407C22⋊C8—861no—
408C22⋊C8—861no—
409#97—21no—
410#97—21no—
411#97—431no—
412#97—431no—
413#97—861no—
414#97—861no—
415C4×C8—431no—
416C4×C8—431no—
417C4×C8—431no—
418C4×C8—431no—
419C4×C8—431no—
420C4×C8—861no—
421C4×C8—861no—
422C4×C8—861no—
423C4×C8C22×D4311yescharacteristic
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8C2×C4×D4311yescharacteristic
429C2×Q8C2×C4×D4311yescharacteristic
430C2×D4—431no—
431C2×D4—861no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—861no—
436Q16—22no—
437Q16—862no—
438SD16—862no—
439SD16—862no—
440M16—862no—
441M16—862no—
442M16—1722no—
443M16—1722no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—862no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—1721no—
456C2×C8—1722no—
457C2×C8C2×C4×D4311yescharacteristic
458C2×C8C2×C4×D4311yescharacteristic
459C2×C8D4×D4311yescharacteristic
460C2×C8D4×D4311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—431no—
464C4⋊C4—431no—
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—
474C4⋊C4C2×C4×D4311yescharacteristic
475C4⋊C4C2×C4×D4311yescharacteristic
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C42—21no—
484C42—21no—
485C42—431no—
486C42—431no—
487C42—431no—
488C42—861no—
489C42C23×D4311yescharacteristic
490C23—431no—
491C23—861no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—861no—
497Q8—861no—
498Q8—1722no—
499D4—861no—
500D4—861no—
501D4—1722no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—431no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4C22×C4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4#41×D4311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—432no—
529C8—432no—
530C8—861no—
531C8—861no—
532C8—1721no—
533C8—1721no—
534C8—1721no—
535C8#1306333312yes—
536C22—861no—
537C22—861no—
538C22—861no—
539C22—1721no—
540C22—1721no—
541C22—1721no—
542C22C4×D4×D4311yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—861no—
549C4—861no—
550C4—861no—
551C4—1721no—
552C4—1721no—
553C4—1721no—
554C4#131×D4311yescharacteristic
555C4C2×#1306333311yescharacteristic
556C4#137×D4311yescharacteristic
557C4#1458369811yescharacteristic
558C2—3441no—
559C2—1721no—
560C2#1914330411yescharacteristic
561C2#1914341111yescharacteristic
562C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1593C2
socleC22×C43C2×C4×D4
prime radical#13063300C2×C4
cosocleC42×C43C24
hypercenter#1593D43
hypocenterC43#17965
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1593

Complements

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

NH ≅ G/Ntype
3. #19143526C2semidirect
4. #19133502C2semidirect
5. #19133499C2semidirect
6. #19133495C2semidirect
7. Q16×C43⋊C8C2semidirect
8. #19133399C2semidirect
9. #19133394C2semidirect
10. #19133392C2semidirect
11. #19133359C2semidirect
12. #19133066C2semidirect
14. #19132874C2semidirect
15. C43×#1593C2semidirect
281. #1593D43semidirect
348. C43#17965semidirect

Maximal subgroups

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

subgroupindex
#191451992
#191435692
#191435262
#191335022
#191334992
#191334952
Q16×C43⋊C82
#191333992
#191333942
#191333922
#191333592
#191330662
#191330592
#191328742
C43×#15932
#1796543