Finite Group Databasebeta

← #25067790

Subgroups — #25067790

Order 11008.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144675C211yesmaximal, characteristic
2#19143757C211yesmaximal, characteristic
3#19133490C211yesmaximal, characteristic, complemented
4#19133485C211yesmaximal, characteristic, complemented
5#19133473C211yesmaximal, characteristic, complemented
6#19133466C211yesmaximal, characteristic, complemented
7#19133464C211yesmaximal, characteristic, complemented
8#19133450C211yesmaximal, characteristic, complemented
9C8×#10621885C211yesmaximal, characteristic, complemented
10C8×#10621884C211yesmaximal, characteristic, complemented
11#19133381C211yesmaximal, characteristic, complemented
12#19133053C211yesmaximal, characteristic
13C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
14#19132879C211yesmaximal, characteristic, complemented
15C43×#2984C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583229C411yescharacteristic
18#14583212C411yescharacteristic
19#14583206C411yescharacteristic
20#14583206C411yescharacteristic
21#14583121C411yescharacteristic
22#14583121C411yescharacteristic
23#14583055C411yescharacteristic
24#14583038C411yescharacteristic
25#14583029C2211yescharacteristic
26C8×Dic86C2211yescharacteristic
27C4×#10621885C2211yescharacteristic
28C4×#10621885C2211yescharacteristic
29C4×#10621884C2211yescharacteristic
30C4×#10621884C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582967—21no—
33C8×D172C2211yescharacteristic
34(C22⋊D43)⋊C8—21no—
35#14582959—21no—
36#14582952C2211yescharacteristic
37#14582924—21no—
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46Q8⋊(C43⋊C8)C2211yescharacteristic
47Q8⋊(C43⋊C8)C2211yescharacteristic
48#14582629C2211yescharacteristic
49#14582629C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C43×#446—21no—
58C43×#446—21no—
59C43×#446C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C8×Q8×C43C2211yescharacteristic
63C43×#432—21no—
64C43×#432C2211yescharacteristic
65C43×#431—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063319—21no—
76#13063317C2×C411yescharacteristic
77#13063313C2×C411yescharacteristic
78#13063308—21no—
79#13063304C2×C411yescharacteristic
80#13063299C2×C411yescharacteristic
81C4×Dic86C2311yescharacteristic
82C4×D172C2311yescharacteristic
83C4×C22⋊D43—21no—
84#13063282—21no—
85#13063258C2×C411yescharacteristic
86#13063258C2×C411yescharacteristic
87#13063256C2×C411yescharacteristic
88#13063256C2×C411yescharacteristic
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2×C411yescharacteristic
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95Dic43⋊C8—21no—
96#13063249C2×C411yescharacteristic
97#13063249C2×C411yescharacteristic
98#13063249C2×C411yescharacteristic
99#13063249C2×C411yescharacteristic
100#13063248C2×C411yescharacteristic
101#13063248C2×C411yescharacteristic
102#13063245C2×C411yescharacteristic
103#13063245C2×C411yescharacteristic
104C22⋊(C43⋊C8)C2×C411yescharacteristic
105C22⋊(C43⋊C8)C2×C411yescharacteristic
106(C2×D43)⋊C8—21no—
107(C2×D43)⋊C8—21no—
108#13063235—21no—
109C4×C43⋊C8—21no—
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×Q8×C43C2×C411yescharacteristic
116C4×Q8×C43—21no—
117C4×Q8×C43—21no—
118C4×Q8×C43C2×C411yescharacteristic
119C4×Q8×C43C2×C411yescharacteristic
120C4×Q8×C43C2311yescharacteristic
121C4×Q8×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43C2×C411yescharacteristic
124C2×C42×C43—21no—
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—21no—
127C4⋊C8×C43—21no—
128C4⋊C8×C43—21no—
129C4⋊C8×C43—21no—
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43D411yescharacteristic
136C22⋊C8×C43D411yescharacteristic
137#97×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—22no—
146C2×Q8×C43—41no—
147C2×Q8×C43C22×C411yescharacteristic
148C2×Q8×C43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×C22⋊D43—21no—
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×Dic86C22×C411yescharacteristic
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C411yescharacteristic
170C4⋊C4×C43C22×C411yescharacteristic
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180#10621885—22no—
181#10621885—41no—
182#10621884—22no—
183#10621884—41no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C2×C43⋊C8—24no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—81no—
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205#10621872—81no—
206C8×D43—81no—
207C23×C43C4×D411yescharacteristic
208C22×D43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—42no—
213Q8×C43#13112yes—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43C4×D411yescharacteristic
226C2×C4×C43C4×D411yescharacteristic
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C23×C411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C22⋊D43—42no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235D172—21no—
236D172—21no—
237C4×D43—41no—
238C4×D43—41no—
239Dic86—21no—
240Dic86—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—22no—
248C43⋊C8—22no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#18017—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43#44312yes—
259C22×C43C2×C4×D411yescharacteristic
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—41no—
263C4×C43—21no—
264C4×C43—22no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43C2×#13111yescharacteristic
272C4×C43#56811yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—41no—
276Dic43—41no—
277Dic43—41no—
278#3108—431no—
279#2994—431no—
280#2984D4311yescharacteristic, complemented
281#1591—431no—
282#1590—431no—
283#1588—431no—
284#1587—431no—
285#1587—431no—
286#1585—431no—
287C8×Q16—431no—
288C8×SD16—431no—
289#1573—431no—
290#1494—431no—
291C2×Q8⋊C8—431no—
292#1450—431no—
293C2×C43—22no—
294C2×C43#293311yescharacteristic
295C2×C43#294711yescharacteristic
296C2×C43C2×#44311yescharacteristic
297D43—81no—
298#529—431no—
299C2×C4×Q8C2×D4311yescharacteristic
300#483—431no—
301#480—431no—
302#479—431no—
303#479—431no—
304#464—431no—
305#464—431no—
306#451—431no—
307#448—431no—
308#446—21no—
309#446—21no—
310#446—431no—
311#446C2×D4311yescharacteristic
312#446C2×D4311yescharacteristic
313C8×Q8—431no—
314C8×Q8C2×D4311yescharacteristic
315C8×Q8C2×D4311yescharacteristic
316C4×Q16—431no—
317C4×Q16—431no—
318C4×SD16—431no—
319C4×SD16—431no—
320#436—431no—
321#435—861no—
322C8×D4—431no—
323C8×D4—861no—
324#433—861no—
325#432—21no—
326#432C2×D4311yescharacteristic
327#431—21no—
328#431—431no—
329#431C2×D4311yescharacteristic
330#424—861no—
331C2×C4⋊C8—431no—
332C2×C4×C8—431no—
333#335—431no—
334#335—431no—
335#334—431no—
336#334—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339Q8⋊C8—431no—
340Q8⋊C8—431no—
341Q8⋊C8—431no—
342Q8⋊C8—431no—
343D4⋊C8—431no—
344D4⋊C8—431no—
345#322—431no—
346#322—431no—
347C82—431no—
348C82—431no—
349C43#1801711yescharacteristic, complemented, Sylow
350C22×Q8C4×D4311yescharacteristic
351C2×Q16—431no—
352C2×Q16—431no—
353C2×SD16—431no—
354C2×SD16—431no—
355C2×M16—861no—
356C22×C8—861no—
357C22×C8—861no—
358C22×C8—861no—
359#126—861no—
360#125—431no—
361#124—431no—
362#123—861no—
363C22⋊Q8—431no—
364#121—431no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—431no—
368C4×Q8C4×D4311yescharacteristic
369C4×Q8C4×D4311yescharacteristic
370C4×Q8C22×D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×D4—431no—
373C4×D4—861no—
374#117—861no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4C4×D4311yescharacteristic
377C2×C42—21no—
378C2×C42C22×D4311yescharacteristic
379#107—431no—
380#107—431no—
381#106—431no—
382#106—431no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—861no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22⋊D4311yescharacteristic
395C4⋊C8C22⋊D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
398#103—431no—
399#103—431no—
400#103—431no—
401#103—431no—
402#103—431no—
403#103—431no—
404#102—431no—
405#102—431no—
406C22⋊C8—21no—
407C22⋊C8—431no—
408C22⋊C8—431no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411C22⋊C8C22⋊D4311yescharacteristic
412C22⋊C8C22⋊D4311yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416#97—861no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—431no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8C22×D4311yescharacteristic
426C4×C8C22×D4311yescharacteristic
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—431no—
431C2×Q8C2×C4×D4311yescharacteristic
432C2×Q8C2×C4×D4311yescharacteristic
433C2×D4—431no—
434C2×D4—861no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—861no—
438C22×C4C2×C4×D4311yescharacteristic
439C22×C4#1062189811yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441Q16—862no—
442Q16—1721no—
443SD16—862no—
444SD16—1721no—
445M16—3441no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—864no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—3441no—
458C2×C8—3441no—
459C2×C8C2×C22⋊D4311yescharacteristic
460C2×C8C2×C22⋊D4311yescharacteristic
461C2×C8C2×C22⋊D4311yescharacteristic
462C2×C8C2×C22⋊D4311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—431no—
469C4⋊C4—431no—
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—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—861no—
486C42C2×C4×D4311yescharacteristic
487C42#1062189811yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—861no—
491C23C4×C22⋊D4311yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—42no—
496Q8—861no—
497Q8—861no—
498Q8#1306333312yes—
499D4—861no—
500D4—861no—
501D4—1722no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4C4×C22⋊D4311yescharacteristic
519C2×C4C4×C22⋊D4311yescharacteristic
520C2×C4C4×C22⋊D4311yescharacteristic
521C2×C4C22×C4×D4311yescharacteristic
522C2×C4C22×C22⋊D4311yescharacteristic
523C2×C4C2×#1062189811yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—862no—
531C8—862no—
532C8—861no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—1721no—
537C8—1721no—
538C22—21no—
539C22—21no—
540C22—1721no—
541C22—1721no—
542C22—1721no—
543C22#1458301412yes—
544C22C2×C4×C22⋊D4311yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—1721no—
554C4—1721no—
555C4—1721no—
556C4C2×#1306333311yescharacteristic
557C4#1458366511yescharacteristic
558C4#1458370711yescharacteristic
559C4#1458371411yescharacteristic
560C2—22no—
561C2—3441no—
562C2#1914332011yescharacteristic
563C2#1914343811yescharacteristic
564C2C2×#1458301411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2984C2
socleC22×C43C2×C4×D4
prime radical#13063299C2×C4
cosocleC42×C43C24
hypercenter#2984D43
hypocenterC43#18017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2984

Complements

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

NH ≅ G/Ntype
3. #19133490C2semidirect
4. #19133485C2semidirect
5. #19133473C2semidirect
6. #19133466C2semidirect
7. #19133464C2semidirect
8. #19133450C2semidirect
9. C8×#10621885C2semidirect
10. C8×#10621884C2semidirect
11. #19133381C2semidirect
13. C2×Q8⋊(C43⋊C8)C2semidirect
14. #19132879C2semidirect
15. C43×#2984C2semidirect
280. #2984D43semidirect
349. C43#18017semidirect

Maximal subgroups

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

subgroupindex
#191446752
#191437572
#191334902
#191334852
#191334732
#191334662
#191334642
#191334502
C8×#106218852
C8×#106218842
#191333812
#191330532
C2×Q8⋊(C43⋊C8)2
#191328792
C43×#29842
#1801743