Finite Group Databasebeta

← #25062637

Subgroups — #25062637

Order 11008.

976 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583519C211yesmaximal, characteristic
2#19143634C211yesmaximal, characteristic, complemented
3#19143617C211yesmaximal, characteristic, complemented
4#19132959C211yesmaximal, characteristic, complemented
5#19132957C212yesmaximal, complemented
6#19132944C211yesmaximal, characteristic, complemented
7#19132942C212yesmaximal, complemented
8#19132941C211yesmaximal, characteristic, complemented
9#19132917C212yesmaximal, complemented
10#19132908C212yesmaximal, complemented
11C43×#1472C211yesmaximal, characteristic, complemented
12#14583519—22no—
13#14583519—22no—
14#14583519—22no—
15#14583519—22no—
16C2×#13063323C411yescharacteristic
17C2×#13063320C411yescharacteristic
18C2×#13063318C411yescharacteristic
19C2×#13063314C411yescharacteristic
20C2×#13063311C411yescharacteristic
21C2×#13063311C411yescharacteristic
22C2×#13063310C2211yescharacteristic
23C2×#13063308C2211yescharacteristic
24C2×#13063303C411yescharacteristic
25C2×#13063303C2211yescharacteristic
26C2×#13063298C411yescharacteristic
27C2×#13063290C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30#14582975—22no—
31#14582974—22no—
32C8×C22⋊D43—22no—
33(C22⋊D43)⋊C8—22no—
34#14582949C2212yes—
35#14582949C2212yes—
36#14582863C2211yescharacteristic
37#14582861C2212yes—
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C22⋊C8×D43C2212yes—
40#14582625C2212yes—
41#14582625C2212yes—
42#14582624C2212yes—
43#14582624C2212yes—
44#14582622C2212yes—
45#14582622C2212yes—
46C2×C22⋊Q8×C43C2211yescharacteristic
47C43×#407C2211yescharacteristic
48C2×C22⋊C8×C43C2211yescharacteristic
49C43×#324C2212yes—
50C43×#324C2212yes—
51C22×Dic86C2×C411yescharacteristic
52C22×Dic86C2×C411yescharacteristic
53C22×D172C2×C411yescharacteristic
54C22×C22⋊D43C2×C411yescharacteristic
55C22×C22⋊D43C2×C411yescharacteristic
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2311yescharacteristic
58C2×#10621877—21no—
59C2×#10621872—22no—
60C22×C43⋊C8—21no—
61C2×C8×D43—22no—
62#13063323—22no—
63#13063323—22no—
64#13063320—22no—
65#13063320—22no—
66#13063318—22no—
67#13063318—22no—
68#13063314—22no—
69#13063314—22no—
70#13063311—22no—
71#13063311—22no—
72#13063311—22no—
73#13063311—22no—
74#13063310—22no—
75#13063310—22no—
76#13063308—21no—
77#13063308—21no—
78#13063308—21no—
79#13063308—21no—
80#13063303—22no—
81#13063303—22no—
82#13063303—22no—
83#13063303—22no—
84#13063298—22no—
85#13063298—22no—
86#13063290—22no—
87#13063290—22no—
88C4×C22⋊D43D412yes—
89C4×C22⋊D43D412yes—
90C4×C22⋊D43D412yes—
91C4×C22⋊D43D412yes—
92#13063283—22no—
93#13063283—22no—
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4C2×C411yescharacteristic
96C2×Dic43⋊C4C2×C411yescharacteristic
97C2×Dic43⋊C4C2×C411yescharacteristic
98C2×Dic43⋊C4C2×C411yescharacteristic
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2311yescharacteristic
101C2×C22⋊Dic43C2×C411yescharacteristic
102C2×C22⋊Dic43C2×C411yescharacteristic
103C2×(C2×D43)⋊C4C2×C411yescharacteristic
104C2×(C2×D43)⋊C4C2×C411yescharacteristic
105C2×(C2×D43)⋊C4C2×C411yescharacteristic
106C2×(C2×D43)⋊C4C2×C411yescharacteristic
107C2×(C2×D43)⋊C4C2×C411yescharacteristic
108C2×(C2×D43)⋊C4C2×C411yescharacteristic
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2311yescharacteristic
111C2×C4×Dic43C2×C411yescharacteristic
112C2×C4×Dic43C2×C411yescharacteristic
113C2×C4×Dic43C2×C411yescharacteristic
114C2×C4×Dic43C2311yescharacteristic
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119C22⋊(C43⋊C8)C2312yes—
120C22⋊(C43⋊C8)C2312yes—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123C8×Dic43—22no—
124C8×Dic43—22no—
125C22×Q8×C43C2×C411yescharacteristic
126C23×C4×C43C2311yescharacteristic
127C2×M16×C43—21no—
128C22×C8×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43C2×C411yescharacteristic
137C2×C22⋊C4×C43C2×C411yescharacteristic
138C22⋊C8×C43—21no—
139C22⋊C8×C43—21no—
140C22⋊C8×C43C2312yes—
141C22⋊C8×C43C2312yes—
142C24×C43C22×C411yescharacteristic
143C23×D43C22×C411yescharacteristic
144C23×D43C22×C411yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—81no—
148C22×C4×C43—81no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—21no—
161C2×C22⋊D43—21no—
162C2×C22⋊D43—81no—
163C2×C22⋊D43C22⋊C412yes—
164C2×C22⋊D43C22⋊C412yes—
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C22×Dic43C22×C411yescharacteristic
168C22×Dic43C22×C411yescharacteristic
169C22×Dic43C22×C411yescharacteristic
170C22×Dic43C22×C411yescharacteristic
171C2×D172—22no—
172C2×D172—81no—
173C2×C4×D43—22no—
174C2×C4×D43—24no—
175C2×C4×D43—81no—
176C2×C4×D43C2×D412yes—
177C2×C4×D43C2×D412yes—
178C2×Dic86—22no—
179C2×Dic86—24no—
180C2×Dic86—22no—
181C2×Dic86—81no—
182M16×C43—81no—
183C2×C8×C43—22no—
184C2×C8×C43—22no—
185C2×C8×C43—81no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C22⋊C4×C43—21no—
193C22⋊C4×C43—21no—
194C22⋊C4×C43—21no—
195C22⋊C4×C43—21no—
196C22⋊Dic43—21no—
197C22⋊Dic43—21no—
198C22⋊Dic43C22⋊C412yes—
199C22⋊Dic43C22⋊C412yes—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—21no—
202(C2×D43)⋊C4—21no—
203(C2×D43)⋊C4—21no—
204(C2×D43)⋊C4—22no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—22no—
208(C2×D43)⋊C4—22no—
209(C2×D43)⋊C4C22⋊C412yes—
210(C2×D43)⋊C4C22⋊C412yes—
211C4⋊Dic43—22no—
212Dic43⋊C4—21no—
213Dic43⋊C4—21no—
214Dic43⋊C4—21no—
215Dic43⋊C4—21no—
216Dic43⋊C4—22no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219Dic43⋊C4C22⋊C412yes—
220Dic43⋊C4C22⋊C412yes—
221C4×Dic43—22no—
222C4×Dic43—22no—
223C4×Dic43—22no—
224C4×Dic43C2×D412yes—
225C4×Dic43C2×D412yes—
226#10621877—81no—
227C2×C43⋊C8—22no—
228C2×C43⋊C8—22no—
229C2×C43⋊C8—81no—
230#10621872—82no—
231C8×D43—82no—
232C23×C43—22no—
233C23×C43—41no—
234C23×C43—41no—
235C23×C43C2×C22⋊C411yescharacteristic
236C23×C43C2×C22⋊C411yescharacteristic
237C23×C43C23×C411yescharacteristic
238C22×D43—22no—
239C22×D43—21no—
240C22×D43—22no—
241C22×D43—41no—
242C22×D43—41no—
243C22×D43—41no—
244C22×D43—41no—
245C22×D43C2×C22⋊C412yes—
246Q8×C43—81no—
247Q8×C43—81no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43C2×C22⋊C411yescharacteristic
263C2×C4×C43C2×C22⋊C411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C22⋊D43—24no—
267C22⋊D43—24no—
268C22⋊D43—81no—
269C22⋊D43—81no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—22no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43C2×C22⋊C412yes—
279C2×Dic43C2×C22⋊C412yes—
280C2×Dic43C2×C22⋊C412yes—
281C2×Dic43#13114yes—
282D172—82no—
283C4×D43—42no—
284C4×D43—42no—
285C4×D43—44no—
286Dic86—44no—
287Dic86—82no—
288C8×C43—42no—
289C8×C43—42no—
290C43⋊C8—42no—
291C43⋊C8—42no—
292#17388—431nomaximal, Sylow
293C22×C43—21no—
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—21no—
297C22×C43—21no—
298C22×C43—21no—
299C22×C43—21no—
300C22×C43—21no—
301C22×C43—82no—
302C22×C43C22×C22⋊C411yescharacteristic
303C22×C43C2×#13112yes—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—41no—
308C2×D43—41no—
309C2×D43—41no—
310C2×D43—82no—
311C2×D43—82no—
312C4×C43—21no—
313C4×C43—21no—
314C4×C43—21no—
315C4×C43—21no—
316C4×C43—41no—
317C4×C43—41no—
318C4×C43—41no—
319C4×C43—41no—
320Dic43—22no—
321Dic43—22no—
322Dic43—41no—
323Dic43—41no—
324Dic43—41no—
325Dic43#40814yes—
326C2×#542—431no—
327#2975—431no—
328#2972—431no—
329#1472—432no—
330#1472—431no—
331#1472D4311yescharacteristic, complemented
332#1468—431no—
333#1468—431no—
334#1468—432no—
335#1461—432no—
336#1458—432no—
337C2×C43—22no—
338C2×C43—41no—
339C2×C43—41no—
340C2×C43C2×#40811yescharacteristic
341C2×C43#288311yescharacteristic
342C2×C43#288911yescharacteristic
343D43—42no—
344D43—81no—
345#542—862no—
346#542—862no—
347#542—862no—
348#542—862no—
349C2×C4⋊Q8—431no—
350C2×#126—431no—
351C2×#126—431no—
352C2×#124—431no—
353C2×#124—431no—
354C2×#124—431no—
355C2×#123—431no—
356C2×#123—431no—
357C2×C22⋊Q8—431no—
358C2×C22⋊Q8—431no—
359C2×C22⋊Q8C2×D4311yescharacteristic
360C2×#121—431no—
361C2×C4×Q8—431no—
362C2×C4×D4—431no—
363C2×#117—431no—
364#436—862no—
365#436—862no—
366C8×D4—862no—
367C8×D4—862no—
368#431—432no—
369#431—432no—
370#407—431no—
371#407—432no—
372#407C2×D4311yescharacteristic
373C2×C22⋊C8—431no—
374C2×C22⋊C8—432no—
375C2×C22⋊C8C2×D4311yescharacteristic
376#324—432no—
377#324—432no—
378#324—432no—
379#324—432no—
380#324C2×D4312yes—
381#324C2×D4312yes—
382#323—432no—
383#323—432no—
384C43#1738811yescharacteristic, complemented, Sylow
385C22×Q8—431no—
386C22×Q8—431no—
387C22×Q8C4×D4311yescharacteristic
388C22×D4—431no—
389C22×D4—431no—
390C22×D4—431no—
391C23×C4—431no—
392C23×C4—431no—
393C23×C4C22×D4311yescharacteristic
394C2×M16—21no—
395C2×M16—862no—
396C2×M16—861no—
397C22×C8—21no—
398C22×C8—862no—
399C22×C8—861no—
400C4⋊Q8—862no—
401C4⋊Q8—862no—
402#126—862no—
403#126—862no—
404#126—862no—
405#126—862no—
406#124—862no—
407#124—862no—
408#124—862no—
409#124—862no—
410#124—862no—
411#124—862no—
412#123—862no—
413#123—862no—
414#123—861no—
415#123—861no—
416#123—861no—
417#123—861no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8—862no—
423C22⋊Q8—862no—
424C22⋊Q8—862no—
425C22⋊Q8—862no—
426#121—862no—
427#121—862no—
428C4×Q8—862no—
429C4×Q8—862no—
430C4×D4—432no—
431C4×D4—432no—
432C4×D4—432no—
433C4×D4—432no—
434#117—862no—
435#117—862no—
436C2×C4⋊C4—431no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4C4×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—431no—
447C2×C22⋊C4—431no—
448C2×C22⋊C4—431no—
449C2×C22⋊C4—431no—
450C2×C22⋊C4—431no—
451C2×C22⋊C4—431no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—431no—
454C2×C22⋊C4—431no—
455C2×C22⋊C4—431no—
456C2×C22⋊C4C4×D4311yescharacteristic
457C2×C22⋊C4C4×D4311yescharacteristic
458C2×C42—431no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—431no—
462C4⋊C8—862no—
463C4⋊C8—862no—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8—432no—
467C22⋊C8—432no—
468C22⋊C8—862no—
469C22⋊C8—862no—
470C22⋊C8—861no—
471C22⋊C8—861no—
472C22⋊C8C22×D4312yes—
473C22⋊C8C22×D4312yes—
474C4×C8—862no—
475C4×C8—862no—
476C24—431no—
477C24—431no—
478C24C2×C4×D4311yescharacteristic
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—81no—
482C2×Q8—862no—
483C2×Q8—862no—
484C2×Q8—864no—
485C2×Q8—3441no—
486C2×D4—432no—
487C2×D4—432no—
488C2×D4—862no—
489C2×D4—864no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—3441no—
493C2×D4—3441no—
494C22×C4—81no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—432no—
499C22×C4—432no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—862no—
504C22×C4—864no—
505C22×C4—3441no—
506C22×C4C2×C4×D4311yescharacteristic
507C22×C4C2×C4×D4311yescharacteristic
508C22×C4C2×C4×D4311yescharacteristic
509C22×C4C2×C4×D4311yescharacteristic
510C22×C4C2×C4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512C22×C4D4×D4311yescharacteristic
513C22×C4D4×D4311yescharacteristic
514C22×C4D4×D4311yescharacteristic
515C22×C4C23×D4311yescharacteristic
516M16—81no—
517M16—3442no—
518M16—3441no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—81no—
522C2×C8—862no—
523C2×C8—862no—
524C2×C8—3442no—
525C2×C8—3441no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—432no—
533C4⋊C4—432no—
534C4⋊C4—862no—
535C4⋊C4—862no—
536C4⋊C4—862no—
537C4⋊C4—862no—
538C4⋊C4—861no—
539C4⋊C4—861no—
540C4⋊C4—861no—
541C4⋊C4—861no—
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—432no—
547C22⋊C4—432no—
548C22⋊C4—432no—
549C22⋊C4—432no—
550C22⋊C4—862no—
551C22⋊C4—862no—
552C22⋊C4—862no—
553C22⋊C4—862no—
554C22⋊C4—862no—
555C22⋊C4—861no—
556C22⋊C4—861no—
557C22⋊C4—861no—
558C22⋊C4—861no—
559C22⋊C4—861no—
560C22⋊C4—861no—
561C42—432no—
562C42—432no—
563C42—862no—
564C42—862no—
565C42—862no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—432no—
570C23—862no—
571C23—862no—
572C23—861no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23C22⋊C4×D4311yescharacteristic
578C23C22⋊C4×D4311yescharacteristic
579C23C22×C4×D4311yescharacteristic
580Q8—81no—
581Q8—81no—
582Q8—3442no—
583Q8—1724no—
584D4—864no—
585D4—864no—
586D4—3442no—
587D4—3441no—
588D4—3441no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—432no—
604C2×C4—434no—
605C2×C4—432no—
606C2×C4—432no—
607C2×C4—861no—
608C2×C4—861no—
609C2×C4—861no—
610C2×C4—862no—
611C2×C4—1722no—
612C2×C4—1722no—
613C2×C4—1724no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4—1721no—
618C2×C4C22⋊C4×D4311yescharacteristic
619C2×C4C22⋊C4×D4311yescharacteristic
620C2×C4C2×D4×D4311yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C8—42no—
623C8—42no—
624C8—1722no—
625C8—1722no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—82no—
635C22—862no—
636C22—862no—
637C22—862no—
638C22—3442no—
639C22—3442no—
640C22—1721no—
641C22—1721no—
642C22—1721no—
643C22C2×C22⋊C4×D4311yescharacteristic
644C22#131×D4312yes—
645C4—21no—
646C4—21no—
647C4—21no—
648C4—21no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—434no—
654C4—862no—
655C4—862no—
656C4—1721no—
657C4—1721no—
658C4—1721no—
659C2—22no—
660C2—41no—
661C2—41no—
662C2—3441no—
663C2—1722no—
664C2#408×D4311yescharacteristic
665C2#1914305311yescharacteristic
666C2#1914307511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1472C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063298C4
cosocleC22×C4×C43C24
hypercenter#1472D43
hypocenterC43#17388
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
2. #19143634C2semidirect
3. #19143617C2semidirect
4. #19132959C2semidirect
5. #19132957C2semidirect
6. #19132944C2semidirect
7. #19132942C2semidirect
8. #19132941C2semidirect
9. #19132917C2semidirect
10. #19132908C2semidirect
11. C43×#1472C2semidirect
331. #1472D43semidirect
384. C43#17388semidirect

Maximal subgroups

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

subgroupindex
C2×#145835192
#191436342
#191436172
#191329592
#191329572
#191329442
#191329422
#191329412
#191329172
#191329082
C43×#14722
#1738843