Finite Group Databasebeta

← #25064555

Subgroups — #25064555

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C4×M16×D43C211yesmaximal, characteristic, complemented
4#19133212C214yesmaximal, complemented
5#19133199C214yesmaximal, complemented
6#19133189C211yesmaximal, characteristic, complemented
7#19133189C211yesmaximal, characteristic, complemented
8#19133187C211yesmaximal, characteristic, complemented
9C43×#1525C211yesmaximal, characteristic, complemented
10C2×M16×D43—21no—
11#14583456C2211yescharacteristic
12#14583454C411yescharacteristic
13#14583454C411yescharacteristic
14#14583447C411yescharacteristic
15#14583447C411yescharacteristic
16#14583431—21no—
17#14583431—21no—
18#14583430—21no—
19#14583430—21no—
20#14583428C2212yes—
21#14583428C2212yes—
22#14583409—21no—
23#14583409—21no—
24#14583406C412yes—
25#41×Dic43C412yes—
26C4×#10621900—21no—
27C4×#10621900—21no—
28C2×C42×D43C2211yescharacteristic
29#14582954C2212yes—
30#14582954C2212yes—
31#14582950—21no—
32#14582950—21no—
33#14582922—21no—
34#14582862—21no—
35C4×#10621877C2211yescharacteristic
36C4×#10621877C2211yescharacteristic
37#14582851C2212yes—
38M16×Dic43—21no—
39C4×#10621872—21no—
40#97×D43C2212yes—
41C4×C8×D43—21no—
42#14582640C2214yescomplemented
43#14582640C2214yescomplemented
44#14582639C2214yescomplemented
45C43×#532C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×#329C2214yescomplemented
49C2×#10621900—21no—
50C2×#10621900—21no—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621872—22no—
57M16×D43—28no—
58C2×C8×D43—22no—
59#13063325C2×C411yescharacteristic
60#13063325C2×C411yescharacteristic
61#13063318—22no—
62#13063318—22no—
63#13063317C2312yes—
64#13063316—21no—
65#13063316—21no—
66#13063312—21no—
67#13063312—21no—
68#13063307—22no—
69#13063307—22no—
70#13063306—22no—
71#13063305—21no—
72#13063305—21no—
73#13063304—21no—
74#13063304—21no—
75#13063301C2×C412yes—
76#13063301C2×C412yes—
77#13063296—21no—
78#13063296—21no—
79#13063296C2×C412yes—
80#13063296C2×C412yes—
81#13063293—22no—
82Q8×Dic43C2×C412yes—
83Q8×Dic43C2×C412yes—
84C4×Dic86—21no—
85C4×Dic86—21no—
86#13063290—21no—
87#13063290—21no—
88D4×Dic43—22no—
89D4×Dic43—22no—
90D4×Dic43—21no—
91D4×Dic43—21no—
92D4×Dic43C2×C412yes—
93D4×Dic43C2×C412yes—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—22no—
96(C22⋊D43)⋊C4—22no—
97(C22⋊D43)⋊C4—22no—
98#13063284—22no—
99#13063284C2×C412yes—
100#13063283—21no—
101#13063283—21no—
102#13063281—22no—
103#13063281—22no—
104C2×C4×Dic43—22no—
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
116Dic43⋊C8—22no—
117Dic43⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120#13063236C2312yes—
121#13063236C2312yes—
122#13063235—22no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8—21no—
125C8×Dic43—22no—
126C2×#41×C43C2×C412yes—
127C2×M16×C43—21no—
128C2×M16×C43—21no—
129C4⋊Q8×C43C2×C411yescharacteristic
130#127×C43C2×C411yescharacteristic
131#124×C43C2312yes—
132#121×C43—21no—
133#121×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137#97×C43C2312yes—
138#97×C43C2312yes—
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C23×D43C22⋊C411yescharacteristic
142#41×C43—44no—
143C2×Q8×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—22no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43C22⋊C411yescharacteristic
157C22×Dic43C22⋊C411yescharacteristic
158C22×Dic43C22⋊C411yescharacteristic
159#10621900—44no—
160#10621900—44no—
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—21no—
178M16×C43—24no—
179M16×C43—42no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
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—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—22no—
200C4⋊Dic43—22no—
201C4⋊Dic43C22×C412yes—
202C4⋊Dic43C22×C412yes—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207C4×Dic43—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—
223#10621877—42no—
224C2×C43⋊C8—22no—
225C2×C43⋊C8—22no—
226#10621872—28no—
227C8×D43—28no—
228C23×C43—22no—
229C23×C43C2×C22⋊C411yescharacteristic
230C22×D43—22no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43C2×C22⋊C411yescharacteristic
234C22×D43C2×C22⋊C411yescharacteristic
235Q8×C43—42no—
236D4×C43—42no—
237D4×C43—44no—
238D4×C43—42no—
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×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C22⋊D43—44no—
252C22⋊D43—44no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—44no—
259C2×Dic43—44no—
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43#10414yes—
278Dic86—42no—
279Dic86—42no—
280C8×C43—24no—
281C8×C43—42no—
282C43⋊C8—24no—
283C43⋊C8—42no—
284#17649—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43—21no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43C22×C22⋊C411yescharacteristic
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—44no—
298C2×D43C2×#10412yes—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—42no—
303C4×C43#41312yes—
304C4×C43C2×#10412yes—
305C4×C43#42112yes—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—42no—
312Dic43—42no—
313Dic43C2×#10412yes—
314#3444—431no—
315#2920—431no—
316C2×C4×M16—431no—
317#1532—434no—
318#1529—434no—
319#1526—431no—
320#1526—431no—
321#1525—431no—
322#1525D4311yescharacteristic, complemented
323C2×C43—41no—
324C2×C43—82no—
325C2×C43C2×#41311yescharacteristic
326C2×C43C22×#10411yescharacteristic
327C2×C43C2×#42111yescharacteristic
328D43—22no—
329D43—41no—
330C22×M16—861no—
331#533—431no—
332#533—431no—
333#533—431no—
334#532—431no—
335#532—431no—
336#532C2×D4311yescharacteristic
337#529—432no—
338#529—432no—
339#529—861no—
340#529—861no—
341#529—861no—
342#529—861no—
343#525—432no—
344#525—861no—
345#525—861no—
346C4×#41—432no—
347C4×#41—861no—
348C4×#41—861no—
349C22×C42—431no—
350#432—432no—
351#432—432no—
352#431—861no—
353#431—861no—
354#423—861no—
355#407—861no—
356C4×M16—431no—
357C4×M16—431no—
358C4×M16—432no—
359C4×M16—861no—
360C4×M16—861no—
361C4×M16C2×D4311yescharacteristic
362C4×M16C2×D4311yescharacteristic
363C2×#97—432no—
364C2×C4×C8—861no—
365#330—434no—
366#330—434no—
367#329—434no—
368#329C2×D4314yescomplemented
369C43#1764911yescharacteristic, complemented, Sylow
370C2×#41—861no—
371C2×#41—861no—
372C2×#41C4×D4312yes—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—862no—
379C2×M16—868no—
380C2×M16—861no—
381C2×M16—861no—
382C22×C8—862no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385C4⋊Q8C4×D4311yescharacteristic
386#127C4×D4311yescharacteristic
387#126—862no—
388#126—862no—
389#125—432no—
390#125—861no—
391#125—861no—
392#124—861no—
393#124—861no—
394#124C22×D4312yes—
395#123—862no—
396#123—862no—
397#123—862no—
398C22⋊Q8—432no—
399C22⋊Q8—432no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8—861no—
404#121—21no—
405#121—21no—
406#121—432no—
407#121—432no—
408#121—861no—
409#121—861no—
410#120—862no—
411C4×Q8—432no—
412C4×Q8—432no—
413C4×Q8—861no—
414C4×Q8—861no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—432no—
420C4×D4—432no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429#117—432no—
430#117—862no—
431#117—862no—
432#117—862no—
433#117—861no—
434#117—861no—
435C2×C42—431no—
436C2×C42—431no—
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—862no—
447C2×C42C22×D4311yescharacteristic
448C4⋊C8—862no—
449C4⋊C8—862no—
450C22⋊C8—862no—
451C22⋊C8—862no—
452#97—432no—
453#97—432no—
454#97—862no—
455#97C22×D4312yes—
456#97C22×D4312yes—
457C4×C8—21no—
458C4×C8—21no—
459C4×C8—862no—
460C4×C8—861no—
461C4×C8—861no—
462C24—431no—
463#41—44no—
464#41—1724no—
465#41—1724no—
466C2×Q8—861no—
467C2×Q8—861no—
468C2×Q8C2×C4×D4312yes—
469C2×D4—22no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—862no—
473C2×D4—862no—
474C2×D4C2×C4×D4312yes—
475C22×C4—22no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
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—864no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4C2×C4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499M16—24no—
500M16—42no—
501M16—868no—
502M16—864no—
503M16—1722no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—868no—
507C2×C8—862no—
508C2×C8—862no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—432no—
512C4⋊C4—432no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—862no—
543C42—862no—
544C42—862no—
545C42C2×C4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42D4×D4311yescharacteristic
548C42C23×D4311yescharacteristic
549C23—22no—
550C23—431no—
551C23—431no—
552C23—862no—
553C23—1721no—
554C23—1721no—
555C23C22⋊C4×D4311yescharacteristic
556Q8—42no—
557Q8—1722no—
558Q8—1722no—
559D4—42no—
560D4—44no—
561D4—42no—
562D4—42no—
563D4—1724no—
564D4—1724no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—44no—
570C2×C4—431no—
571C2×C4—434no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—431no—
576C2×C4—431no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1724no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1724no—
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22⋊C4×D4311yescharacteristic
598C2×C4C22×C4×D4311yescharacteristic
599C2×C4C2×D4×D4311yescharacteristic
600C2×C4C2×D4×D4311yescharacteristic
601C8—24no—
602C8—42no—
603C8—864no—
604C8—1722no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—432no—
612C22—861no—
613C22—861no—
614C22—861no—
615C22—861no—
616C22—861no—
617C22—1724no—
618C22C2×C22⋊C4×D4311yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—42no—
623C4—432no—
624C4—861no—
625C4—861no—
626C4—861no—
627C4—861no—
628C4—861no—
629C4—1722no—
630C4—1722no—
631C4#1458288012yes—
632C4#104×D4312yes—
633C4#1458291412yes—
634C2—41no—
635C2—82no—
636C2—862no—
637C2—1721no—
638C2C2×#1458288011yescharacteristic
639C2C2×#104×D4311yescharacteristic
640C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1525C2
socleC22×C43C22×C22⋊C4
prime radical#19147890C2
cosocleC42×C43C24
hypercenter#1525D43
hypocenterC43#17649
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1525

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. C4×M16×D43C2semidirect
4. #19133212C2semidirect
5. #19133199C2semidirect
6. #19133189C2semidirect
7. #19133189C2semidirect
8. #19133187C2semidirect
9. C43×#1525C2semidirect
42. #14582640C22semidirect
43. #14582640C22semidirect
44. #14582639C22semidirect
48. C43×#329C22semidirect
322. #1525D43semidirect
368. #329C2×D43semidirect
369. C43#17649semidirect

Maximal subgroups

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

subgroupindex
#191478902
#191432262
C4×M16×D432
#191332122
#191331992
#191331892
#191331872
C43×#15252
#1764943