Finite Group Databasebeta

← #25063403

Subgroups — #25063403

Order 11008.

1078 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583431C211yesmaximal, characteristic
2#432×D43C211yesmaximal, characteristic, complemented
3C4×M16×D43C211yesmaximal, characteristic, complemented
4#19133052C214yesmaximal, complemented
5#19133043C211yesmaximal, characteristic, complemented
6#19133041C211yesmaximal, characteristic, complemented
7#19133038C211yesmaximal, characteristic, complemented
8#19133005C214yesmaximal, complemented
9C43×#1490C211yesmaximal, characteristic, complemented
10C2×M16×D43—21no—
11#14583431—21no—
12#14583431—21no—
13#14583431—21no—
14#14583431—21no—
15#14583431C412yes—
16#14583431C412yes—
17#14583431C2212yes—
18#14583431C2212yes—
19C2×#13063318—21no—
20C2×#13063316C411yescharacteristic
21C2×#13063312C411yescharacteristic
22C2×#13063307—21no—
23C2×#13063305C411yescharacteristic
24C2×#13063296C411yescharacteristic
25C2×C4×Dic86C2211yescharacteristic
26C2×C4×C22⋊D43—21no—
27C2×#13063284—21no—
28C2×C42×D43C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582955C2212yescomplemented
31#14582954—21no—
32#14582953—21no—
33C4⋊C8×D43C2212yescomplemented
34C22⋊C8×D43—21no—
35C4×#10621877C2211yescharacteristic
36#14582851—21no—
37M16×Dic43—21no—
38C4×#10621872C2212yescomplemented
39#97×D43—21no—
40#97×D43—21no—
41C4×C8×D43C2212yescomplemented
42#14582631C2214yescomplemented
43#14582629C2214yescomplemented
44D4⋊(C43⋊C8)C2214yescomplemented
45C2×C4×D4×C43C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×D4⋊C8C2214yescomplemented
49C22×Dic86C2×C411yescharacteristic
50C22×C22⋊D43—21no—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×#10621872—22no—
56M16×D43—28no—
57C2×C8×D43—22no—
58C2×C8×D43—22no—
59#13063318—22no—
60#13063318—22no—
61#13063318—22no—
62#13063318—22no—
63#13063316—21no—
64#13063316—21no—
65#13063316C2×C412yes—
66#13063316C2×C412yes—
67#13063312—21no—
68#13063312—21no—
69#13063312C2×C412yes—
70#13063312C2×C412yes—
71#13063307—22no—
72#13063307—22no—
73#13063307—22no—
74#13063307—22no—
75#13063305—21no—
76#13063305—21no—
77#13063305C2×C412yes—
78#13063305C2×C412yes—
79#13063296—21no—
80#13063296—21no—
81#13063296C2×C412yes—
82#13063296C2×C412yes—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86C2×C412yes—
86C4×Dic86C2312yes—
87C4×C22⋊D43—22no—
88C4×C22⋊D43—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91#13063284—22no—
92#13063284—22no—
93#13063284—22no—
94#13063284—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2×C411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43D411yescharacteristic
108C42×D43C2×C411yescharacteristic
109C42×D43C2×C411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43C2311yescharacteristic
115C42×D43C2311yescharacteristic
116C4⋊(C43⋊C8)C2312yes—
117Dic43⋊C8—22no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120#13063236—21no—
121#13063236—21no—
122#13063235—22no—
123#13063235—22no—
124C4×C43⋊C8C2312yes—
125C8×Dic43—22no—
126C22×D4×C43C2×C411yescharacteristic
127C23×C4×C43—21no—
128C2×M16×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43C2×C412yes—
132C4×D4×C43C2312yes—
133C2×C4⋊C4×C43C2×C411yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2312yes—
137C22⋊C8×C43—21no—
138#97×C43—21no—
139#97×C43—21no—
140C4×C8×C43C2312yes—
141C24×C43—21no—
142C23×D43C22⋊C411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43—42no—
145C2×D4×C43C22×C412yes—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—44no—
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—44no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43C22⋊C411yescharacteristic
159C22×Dic43C22⋊C411yescharacteristic
160C22×Dic43C22⋊C411yescharacteristic
161C2×C4×D43—24no—
162C2×C4×D43—42no—
163C2×C4×D43—42no—
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22×C411yescharacteristic
171C2×C4×D43C22×C411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×Dic86—21no—
177C2×Dic86—42no—
178C2×Dic86C22×C412yes—
179M16×C43—24no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43—22no—
202C4⋊Dic43—22no—
203C4⋊Dic43C22×C412yes—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C22×C411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222#10621877—24no—
223C2×C43⋊C8—22no—
224C2×C43⋊C8—22no—
225#10621872—28no—
226C8×D43—28no—
227C8×D43—44no—
228C23×C43—22no—
229C23×C43—42no—
230C23×C43—42no—
231C23×C43—42no—
232C23×C43C2×C22⋊C411yescharacteristic
233C22×D43—41no—
234C22×D43—41no—
235C22×D43#10414yes—
236C22×D43C2×C22⋊C411yescharacteristic
237C22×D43C2×C22⋊C411yescharacteristic
238D4×C43—24no—
239D4×C43—42no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—44no—
245C2×C4×C43—42no—
246C2×C4×C43—44no—
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C2×C22⋊C411yescharacteristic
250C2×C4×C43C23×C411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C2×C4×C43C22×D411yescharacteristic
253C22⋊D43—44no—
254C22⋊D43—44no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
267C2×Dic43C2×C22⋊C411yescharacteristic
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280Dic86—24no—
281Dic86—42no—
282C8×C43—24no—
283C8×C43—42no—
284C43⋊C8—24no—
285C43⋊C8—42no—
286#17502—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—84no—
293C22×C43C2×#10412yes—
294C22×C43C22×C22⋊C411yescharacteristic
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—21no—
298C2×D43—21no—
299C2×D43—44no—
300C2×D43C2×#10412yes—
301C2×D43C2×#10412yes—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43—42no—
307C4×C43#56812yes—
308C4×C43#57512yes—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—21no—
313Dic43—21no—
314Dic43—21no—
315Dic43—42no—
316Dic43—42no—
317C2×#529—431no—
318C2×#432—431no—
319C2×C4×M16—431no—
320#1494—434no—
321#1491—431no—
322#1491—431no—
323#1490—431no—
324#1490D4311yescharacteristic, complemented
325#1483—434no—
326C2×C43—22no—
327C2×C43—82no—
328C2×C43#287911yescharacteristic
329C2×C43#289611yescharacteristic
330C2×C43C22×#10411yescharacteristic
331D43—22no—
332D43—22no—
333C22×M16—861no—
334#529—432no—
335#529—432no—
336#529—432no—
337#529—432no—
338#529—861no—
339#529—861no—
340#529—861no—
341#529—861no—
342C2×#126—861no—
343C2×#125—431no—
344C2×#124—431no—
345C2×#123—861no—
346C2×C22⋊Q8—431no—
347C2×#121—431no—
348C2×C4×Q8—431no—
349C2×C4×D4—861no—
350C2×C4×D4C2×D4311yescharacteristic
351C2×#117—861no—
352C22×C42—431no—
353#432—431no—
354#432—432no—
355#432—861no—
356#432—861no—
357#432C2×D4311yescharacteristic
358C2×C4⋊C8—432no—
359C2×C22⋊C8—861no—
360C4×M16—431no—
361C4×M16—432no—
362C4×M16—861no—
363C4×M16—861no—
364C4×M16C2×D4311yescharacteristic
365C2×#97—861no—
366C2×#97—861no—
367C2×C4×C8—432no—
368Q8⋊C8—434no—
369Q8⋊C8—434no—
370D4⋊C8—434no—
371D4⋊C8C2×D4314yescomplemented
372C43#1750211yescharacteristic, complemented, Sylow
373C22×Q8—431no—
374C22×D4—861no—
375C22×D4C4×D4311yescharacteristic
376C23×C4—21no—
377C23×C4—431no—
378C23×C4—431no—
379C23×C4—431no—
380C2×M16—21no—
381C2×M16—862no—
382C2×M16—868no—
383C2×M16—861no—
384C22×C8—862no—
385C22×C8—862no—
386#126—862no—
387#126—862no—
388#126—862no—
389#126—862no—
390#125—432no—
391#125—432no—
392#125—861no—
393#125—861no—
394#124—432no—
395#124—432no—
396#124—861no—
397#124—861no—
398#123—862no—
399#123—862no—
400#123—862no—
401#123—862no—
402C22⋊Q8—432no—
403C22⋊Q8—432no—
404C22⋊Q8—861no—
405C22⋊Q8—861no—
406#121—432no—
407#121—432no—
408#121—861no—
409#121—861no—
410C4×Q8—432no—
411C4×Q8—432no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—862no—
417C4×D4—862no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4C4×D4312yes—
421C4×D4C22×D4312yes—
422#117—862no—
423#117—862no—
424#117—862no—
425#117—862no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4C4×D4311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—431no—
446C2×C42—431no—
447C2×C42—431no—
448C2×C42—861no—
449C2×C42C22×D4311yescharacteristic
450C4⋊C8—432no—
451C4⋊C8—862no—
452C4⋊C8C22×D4312yes—
453C22⋊C8—21no—
454C22⋊C8—862no—
455C22⋊C8—861no—
456#97—21no—
457#97—21no—
458#97—862no—
459#97—862no—
460#97—861no—
461#97—861no—
462C4×C8—432no—
463C4×C8—862no—
464C4×C8C22×D4312yes—
465C24—21no—
466C24—431no—
467C2×Q8—432no—
468C2×Q8—861no—
469C2×Q8—1722no—
470C2×D4—21no—
471C2×D4—42no—
472C2×D4—862no—
473C2×D4—862no—
474C2×D4—1724no—
475C2×D4C2×C4×D4312yes—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—44no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—864no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—1722no—
499C22×C4—1722no—
500C22×C4C2×C4×D4311yescharacteristic
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4311yescharacteristic
503M16—24no—
504M16—868no—
505M16—864no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—868no—
509C2×C8—862no—
510C2×C8—862no—
511C2×C8—1724no—
512C4⋊C4—21no—
513C4⋊C4—432no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—862no—
522C4⋊C4—862no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—431no—
544C42—431no—
545C42—431no—
546C42—862no—
547C42—862no—
548C42C2×C4×D4311yescharacteristic
549C42D4×D4311yescharacteristic
550C42D4×D4311yescharacteristic
551C42C23×D4311yescharacteristic
552C23—22no—
553C23—42no—
554C23—42no—
555C23—42no—
556C23—431no—
557C23—431no—
558C23—434no—
559C23—1721no—
560C23—1721no—
561C23C22⋊C4×D4311yescharacteristic
562Q8—864no—
563Q8—1722no—
564D4—24no—
565D4—42no—
566D4—1724no—
567D4—1724no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—44no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—431no—
578C2×C4—431no—
579C2×C4—431no—
580C2×C4—431no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4C22⋊C4×D4311yescharacteristic
601C2×C4C22⋊C4×D4311yescharacteristic
602C2×C4C22⋊C4×D4311yescharacteristic
603C2×C4C22×C4×D4311yescharacteristic
604C2×C4C2×D4×D4311yescharacteristic
605C2×C4C2×D4×D4311yescharacteristic
606C8—24no—
607C8—42no—
608C8—864no—
609C8—1722no—
610C22—21no—
611C22—21no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—84no—
616C22—432no—
617C22—432no—
618C22—861no—
619C22—861no—
620C22—861no—
621C22—861no—
622C22—1724no—
623C22#104×D4312yes—
624C22C2×C22⋊C4×D4311yescharacteristic
625C4—21no—
626C4—21no—
627C4—21no—
628C4—21no—
629C4—42no—
630C4—861no—
631C4—861no—
632C4—861no—
633C4—861no—
634C4—861no—
635C4—861no—
636C4—1722no—
637C4—1722no—
638C4#1458366512yes—
639C4#1458369512yes—
640C2—22no—
641C2—82no—
642C2—862no—
643C2—862no—
644C2#1914303811yescharacteristic
645C2#1914310911yescharacteristic
646C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1490C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063296C4
cosocleC42×C43C24
hypercenter#1490D43
hypocenterC43#17502
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #432×D43C2semidirect
3. C4×M16×D43C2semidirect
4. #19133052C2semidirect
5. #19133043C2semidirect
6. #19133041C2semidirect
7. #19133038C2semidirect
8. #19133005C2semidirect
9. C43×#1490C2semidirect
30. #14582955C22semidirect
33. C4⋊C8×D43C22semidirect
38. C4×#10621872C22semidirect
41. C4×C8×D43C22semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
324. #1490D43semidirect
371. D4⋊C8C2×D43semidirect
372. C43#17502semidirect

Maximal subgroups

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

subgroupindex
C2×#145834312
#432×D432
C4×M16×D432
#191330522
#191330432
#191330412
#191330382
#191330052
C43×#14902
#1750243