Finite Group Databasebeta

← #25063418

Subgroups — #25063418

Order 11008.

1112 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#423×D43C211yesmaximal, characteristic, complemented
3C2×C4×#10621872C211yesmaximal, characteristic, complemented
4#19133051C211yesmaximal, characteristic, complemented
5#19133049C211yesmaximal, characteristic, complemented
6#19133046C211yesmaximal, characteristic, complemented
7#19133031C214yesmaximal, complemented
8#19133005C214yesmaximal, complemented
9C43×#1492C211yesmaximal, characteristic, complemented
10C22×#10621872—21no—
11C2×M16×D43—21no—
12#14583456C2211yescharacteristic
13#14583454C411yescharacteristic
14#14583454C411yescharacteristic
15#14583447C411yescharacteristic
16#14583447C411yescharacteristic
17#14583431—21no—
18#14583431C2212yes—
19#14583430—21no—
20#14583430C412yes—
21#14583428—21no—
22#14583428—21no—
23#14583409—21no—
24#14583409C412yes—
25#14583406—21no—
26#41×Dic43—21no—
27C4×#10621900—21no—
28C4×#10621900C2212yes—
29C2×C42×D43C2211yescharacteristic
30#14582923C2211yescharacteristic
31#14582922—21no—
32#14582921—21no—
33#14582921C2212yes—
34C4⋊C8×D43—21no—
35C4⋊C8×D43C2212yes—
36C4×#10621872—21no—
37C4×#10621872—21no—
38C4×#10621872C2212yes—
39C4×#10621872C2212yes—
40C2×#13063235—21no—
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582631C2214yescomplemented
43#14582629C2214yescomplemented
44D4⋊(C43⋊C8)C2214yescomplemented
45C43×#532C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C2×C4×C8×C43C2211yescharacteristic
48C43×D4⋊C8C2214yescomplemented
49C2×#10621900—21no—
50C2×#10621900C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×#10621872—28no—
56C2×#10621872—22no—
57C2×#10621872—22no—
58C2×#10621872—22no—
59M16×D43—44no—
60C22×C43⋊C8—21no—
61C2×C8×D43—22no—
62#13063325C2×C411yescharacteristic
63#13063325C2×C411yescharacteristic
64#13063318—22no—
65#13063318—22no—
66#13063317—21no—
67#13063316—21no—
68#13063316C2×C412yes—
69#13063312—21no—
70#13063312C2×C412yes—
71#13063307—22no—
72#13063307—22no—
73#13063306—22no—
74#13063305—21no—
75#13063305C2×C412yes—
76#13063304—21no—
77#13063304C2×C412yes—
78#13063301—21no—
79#13063301—21no—
80#13063296—21no—
81#13063296—21no—
82#13063296—21no—
83#13063296C2×C412yes—
84#13063293—22no—
85Q8×Dic43—21no—
86Q8×Dic43—21no—
87C4×Dic86—21no—
88C4×Dic86C2312yes—
89#13063290—21no—
90#13063290C2×C412yes—
91D4×Dic43—22no—
92D4×Dic43—22no—
93D4×Dic43—21no—
94D4×Dic43—21no—
95D4×Dic43—21no—
96D4×Dic43C2×C412yes—
97C4×C22⋊D43—22no—
98C4×C22⋊D43—22no—
99(C22⋊D43)⋊C4—22no—
100(C22⋊D43)⋊C4—22no—
101#13063284—21no—
102#13063284—22no—
103#13063283—21no—
104#13063283C2×C412yes—
105#13063281—22no—
106#13063281—22no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43C2×C411yescharacteristic
109C2×C4×Dic43D411yescharacteristic
110C2×C4×Dic43D411yescharacteristic
111C42×D43C2×C411yescharacteristic
112C42×D43C2×C411yescharacteristic
113C42×D43D411yescharacteristic
114C42×D43D411yescharacteristic
115C42×D43D411yescharacteristic
116C42×D43D411yescharacteristic
117C42×D43C2311yescharacteristic
118C42×D43C2311yescharacteristic
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)C2312yes—
121Dic43⋊C8—22no—
122Dic43⋊C8—22no—
123#13063235—22no—
124#13063235—22no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8C2312yes—
127C2×#41×C43—21no—
128C2×M16×C43—21no—
129C22×C8×C43—21no—
130C4⋊Q8×C43C2×C411yescharacteristic
131#127×C43C2×C411yescharacteristic
132#124×C43—21no—
133#121×C43—21no—
134#121×C43C2×C412yes—
135C4×D4×C43—21no—
136C4×D4×C43C2312yes—
137C2×C42×C43C2311yescharacteristic
138C4⋊C8×C43—21no—
139C4⋊C8×C43C2312yes—
140C4×C8×C43—21no—
141C4×C8×C43C2312yes—
142C23×D43C22⋊C411yescharacteristic
143#41×C43—42no—
144#41×C43—42no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—22no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—22no—
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C22×Dic43—22no—
157C22×Dic43—22no—
158C22×Dic43C22⋊C411yescharacteristic
159C22×Dic43C22⋊C411yescharacteristic
160C22×Dic43C22⋊C411yescharacteristic
161#10621900—44no—
162#10621900—44no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—24no—
166C2×C4×D43—42no—
167C2×C4×D43C22⋊C411yescharacteristic
168C2×C4×D43C22⋊C411yescharacteristic
169C2×C4×D43C22⋊C411yescharacteristic
170C2×C4×D43C22⋊C411yescharacteristic
171C2×C4×D43C22⋊C411yescharacteristic
172C2×C4×D43C22⋊C411yescharacteristic
173C2×C4×D43C22×C411yescharacteristic
174C2×C4×D43C22×C411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×Dic86—21no—
180C2×Dic86C22×C412yes—
181M16×C43—42no—
182C2×C8×C43—24no—
183C2×C8×C43—22no—
184C2×C8×C43—22no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43C22×C412yes—
187C22⋊C4×C43—22no—
188C22⋊C4×C43—22no—
189C42×C43C22×C411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2411yescharacteristic
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43C22×C412yes—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C22⋊C411yescharacteristic
219C4×Dic43C22×C411yescharacteristic
220C4×Dic43C22×C411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C4×Dic43C2×D411yescharacteristic
223C4×Dic43C2×D411yescharacteristic
224C4×Dic43C2×D411yescharacteristic
225#10621877—42no—
226C2×C43⋊C8—24no—
227C2×C43⋊C8—22no—
228C2×C43⋊C8—22no—
229#10621872—28no—
230#10621872—28no—
231#10621872—44no—
232C8×D43—44no—
233C23×C43—22no—
234C23×C43C2×C22⋊C411yescharacteristic
235C22×D43—22no—
236C22×D43—22no—
237C22×D43—41no—
238C22×D43C2×C22⋊C411yescharacteristic
239C22×D43C2×C22⋊C411yescharacteristic
240Q8×C43—42no—
241D4×C43—24no—
242D4×C43—44no—
243D4×C43—42no—
244D4×C43—42no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—42no—
249C2×C4×C43—42no—
250C2×C4×C43C2×C22⋊C411yescharacteristic
251C2×C4×C43C2×C22⋊C411yescharacteristic
252C2×C4×C43C2×C22⋊C411yescharacteristic
253C2×C4×C43AGL(1,ℤ/8)12yes—
254C2×C4×C43#13712yes—
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×D411yescharacteristic
258C22⋊D43—44no—
259C22⋊D43—44no—
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—41no—
265C2×Dic43—44no—
266C2×Dic43—44no—
267C2×Dic43C2×C22⋊C411yescharacteristic
268C2×Dic43C2×C22⋊C411yescharacteristic
269C2×Dic43C2×C22⋊C411yescharacteristic
270C2×Dic43C2×C22⋊C411yescharacteristic
271C2×Dic43C2×C22⋊C411yescharacteristic
272C2×Dic43C2×C22⋊C411yescharacteristic
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—21no—
277C4×D43—21no—
278C4×D43—21no—
279C4×D43—21no—
280C4×D43—22no—
281C4×D43—22no—
282C4×D43—22no—
283C4×D43—22no—
284C4×D43—41no—
285C4×D43—41no—
286C4×D43#10414yes—
287Dic86—24no—
288Dic86—42no—
289C8×C43—24no—
290C8×C43—42no—
291C43⋊C8—24no—
292C43⋊C8—42no—
293#17504—431nomaximal, Sylow
294C22×C43—21no—
295C22×C43—21no—
296C22×C43—42no—
297C22×C43—42no—
298C22×C43—42no—
299C22×C43#41712yes—
300C22×C43C22×C22⋊C411yescharacteristic
301C2×D43—21no—
302C2×D43—21no—
303C2×D43—21no—
304C2×D43—21no—
305C2×D43—21no—
306C2×D43—44no—
307C2×D43C2×#10412yes—
308C4×C43—21no—
309C4×C43—21no—
310C4×C43—42no—
311C4×C43#41712yes—
312C4×C43C2×#10412yes—
313C4×C43#56812yes—
314C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
315C4×C43C2×#13711yescharacteristic
316Dic43—21no—
317Dic43—21no—
318Dic43—21no—
319Dic43—21no—
320Dic43—21no—
321Dic43—42no—
322Dic43—42no—
323Dic43C2×#10412yes—
324#3444—431no—
325C2×#423—431no—
326C2×C4×M16—431no—
327#1493—431no—
328#1493—431no—
329#1492—431no—
330#1492D4311yescharacteristic, complemented
331#1489—434no—
332#1483—434no—
333C2×C43—22no—
334C2×C43—82no—
335C2×C43#287911yescharacteristic
336C2×C43C2×#41711yescharacteristic
337C2×C43C22×#10411yescharacteristic
338D43—22no—
339D43—41no—
340C22×M16—861no—
341C22×M16—861no—
342#533—431no—
343#533—431no—
344#533—431no—
345#532—431no—
346#532—431no—
347#532C2×D4311yescharacteristic
348#529—432no—
349#529—432no—
350#529—861no—
351#529—861no—
352#529—861no—
353#529—861no—
354#525—432no—
355#525—861no—
356#525—861no—
357C4×#41—432no—
358C4×#41—861no—
359C4×#41—861no—
360C22×C42—431no—
361#423—431no—
362#423—432no—
363#423—861no—
364#423—861no—
365#423C2×D4311yescharacteristic
366C2×C4⋊C8—432no—
367C2×C4⋊C8—861no—
368C4×M16—432no—
369C4×M16—432no—
370C4×M16—861no—
371C4×M16—861no—
372C2×#97—861no—
373C2×C4×C8—431no—
374C2×C4×C8C2×D4311yescharacteristic
375Q8⋊C8—434no—
376Q8⋊C8—434no—
377D4⋊C8—434no—
378D4⋊C8C2×D4314yescomplemented
379C43#1750411yescharacteristic, complemented, Sylow
380C2×#41—21no—
381C2×#41—432no—
382C2×#41—861no—
383C23×C4—431no—
384C23×C4—431no—
385C23×C4—431no—
386C2×M16—21no—
387C2×M16—862no—
388C2×M16—862no—
389C2×M16—868no—
390C2×M16—862no—
391C2×M16—861no—
392C2×M16—1724no—
393C22×C8—21no—
394C22×C8—862no—
395C22×C8—861no—
396C4⋊Q8—431no—
397C4⋊Q8—431no—
398C4⋊Q8C4×D4311yescharacteristic
399#127C4×D4311yescharacteristic
400#126—862no—
401#126—862no—
402#125—432no—
403#125—861no—
404#125—861no—
405#124—21no—
406#124—432no—
407#124—861no—
408#123—862no—
409#123—862no—
410#123—862no—
411C22⋊Q8—432no—
412C22⋊Q8—432no—
413C22⋊Q8—861no—
414C22⋊Q8—861no—
415C22⋊Q8—861no—
416C22⋊Q8—861no—
417#121—21no—
418#121—432no—
419#121—861no—
420#121—861no—
421#121—861no—
422#121C4×D4312yes—
423#120—862no—
424C4×Q8—432no—
425C4×Q8—432no—
426C4×Q8—861no—
427C4×Q8—861no—
428C4×Q8—861no—
429C4×Q8—861no—
430C4×D4—21no—
431C4×D4—432no—
432C4×D4—861no—
433C4×D4—861no—
434C4×D4—861no—
435C4×D4—862no—
436C4×D4—862no—
437C4×D4—862no—
438C4×D4—862no—
439C4×D4—862no—
440C4×D4—862no—
441C4×D4C22×D4312yes—
442#117—432no—
443#117—862no—
444#117—862no—
445#117—862no—
446#117—861no—
447#117—861no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—431no—
451C2×C42—431no—
452C2×C42—431no—
453C2×C42—431no—
454C2×C42—431no—
455C2×C42—431no—
456C2×C42—431no—
457C2×C42—431no—
458C2×C42—431no—
459C2×C42—862no—
460C2×C42C22×D4311yescharacteristic
461C4⋊C8—21no—
462C4⋊C8—432no—
463C4⋊C8—862no—
464C4⋊C8—862no—
465C4⋊C8—861no—
466C4⋊C8C22×D4312yes—
467#97—862no—
468#97—862no—
469C4×C8—21no—
470C4×C8—432no—
471C4×C8—861no—
472C4×C8C22×D4312yes—
473C24—431no—
474#41—42no—
475#41—42no—
476#41—1724no—
477#41—1724no—
478C2×Q8—21no—
479C2×Q8—432no—
480C2×Q8—861no—
481C2×D4—22no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—862no—
485C2×D4—862no—
486C2×D4C2×C4×D4312yes—
487C22×C4—22no—
488C22×C4—431no—
489C22×C4—431no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—431no—
497C22×C4—431no—
498C22×C4—431no—
499C22×C4—431no—
500C22×C4—431no—
501C22×C4—431no—
502C22×C4—431no—
503C22×C4—864no—
504C22×C4—862no—
505C22×C4—862no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4—1722no—
509C22×C4C2×C4×D4311yescharacteristic
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512M16—42no—
513M16—868no—
514M16—868no—
515M16—1724no—
516M16—1722no—
517C2×C8—24no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—864no—
521C2×C8—862no—
522C2×C8—862no—
523C2×C8—1724no—
524C4⋊C4—21no—
525C4⋊C4—432no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—862no—
534C4⋊C4—862no—
535C4⋊C4C2×C4×D4312yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—862no—
539C22⋊C4—862no—
540C22⋊C4—862no—
541C22⋊C4—862no—
542C22⋊C4—862no—
543C22⋊C4—862no—
544C22⋊C4—862no—
545C42—431no—
546C42—431no—
547C42—431no—
548C42—431no—
549C42—431no—
550C42—431no—
551C42—431no—
552C42—431no—
553C42—431no—
554C42—431no—
555C42—431no—
556C42—431no—
557C42—862no—
558C42—862no—
559C42—862no—
560C42C2×C4×D4311yescharacteristic
561C42D4×D4311yescharacteristic
562C42D4×D4311yescharacteristic
563C42C23×D4311yescharacteristic
564C23—22no—
565C23—431no—
566C23—431no—
567C23—862no—
568C23—862no—
569C23—1721no—
570C23C22⋊C4×D4311yescharacteristic
571Q8—42no—
572Q8—864no—
573Q8—1722no—
574D4—24no—
575D4—44no—
576D4—42no—
577D4—42no—
578D4—1724no—
579D4—1724no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—431no—
586C2×C4—434no—
587C2×C4—431no—
588C2×C4—431no—
589C2×C4—431no—
590C2×C4—431no—
591C2×C4—431no—
592C2×C4—862no—
593C2×C4—862no—
594C2×C4—862no—
595C2×C4—862no—
596C2×C4—862no—
597C2×C4—862no—
598C2×C4—862no—
599C2×C4—862no—
600C2×C4—862no—
601C2×C4—861no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—862no—
606C2×C4—862no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1724no—
610C2×C4—1721no—
611C2×C4—1724no—
612C2×C4C22⋊C4×D4311yescharacteristic
613C2×C4C22⋊C4×D4311yescharacteristic
614C2×C4C22⋊C4×D4311yescharacteristic
615C2×C4#1306334912yes—
616C2×C4#1306335412yes—
617C2×C4C22×C4×D4311yescharacteristic
618C2×C4C2×D4×D4311yescharacteristic
619C2×C4C2×D4×D4311yescharacteristic
620C8—24no—
621C8—42no—
622C8—864no—
623C8—1722no—
624C22—21no—
625C22—21no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—432no—
630C22—861no—
631C22—861no—
632C22—861no—
633C22—861no—
634C22—861no—
635C22—1724no—
636C22#1458289712yes—
637C22C2×C22⋊C4×D4311yescharacteristic
638C4—21no—
639C4—21no—
640C4—42no—
641C4—432no—
642C4—861no—
643C4—861no—
644C4—861no—
645C4—861no—
646C4—861no—
647C4—1722no—
648C4—1722no—
649C4#1458289712yes—
650C4#104×D4312yes—
651C4#1458366412yes—
652C4C2×#1306334911yescharacteristic
653C4C2×#1306335411yescharacteristic
654C2—22no—
655C2—82no—
656C2—862no—
657C2—1721no—
658C2#1914303711yescharacteristic
659C2C2×#1458289711yescharacteristic
660C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1492C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC42×C43C24
hypercenter#1492D43
hypocenterC43#17504
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #423×D43C2semidirect
3. C2×C4×#10621872C2semidirect
4. #19133051C2semidirect
5. #19133049C2semidirect
6. #19133046C2semidirect
7. #19133031C2semidirect
8. #19133005C2semidirect
9. C43×#1492C2semidirect
42. #14582631C22semidirect
43. #14582629C22semidirect
44. D4⋊(C43⋊C8)C22semidirect
48. C43×D4⋊C8C22semidirect
330. #1492D43semidirect
378. D4⋊C8C2×D43semidirect
379. C43#17504semidirect

Maximal subgroups

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

subgroupindex
#191478902
#423×D432
C2×C4×#106218722
#191330512
#191330492
#191330462
#191330312
#191330052
C43×#14922
#1750443