Finite Group Databasebeta

← #25064558

Subgroups — #25064558

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#19147892C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3C4×M16×D43C211yesmaximal, characteristic, complemented
4#19133214C214yesmaximal, complemented
5#19133201C214yesmaximal, complemented
6#19133190C211yesmaximal, characteristic, complemented
7#19133186C211yesmaximal, characteristic, complemented
8#19133186C211yesmaximal, characteristic, complemented
9C43×#1526C211yesmaximal, characteristic, complemented
10C2×M16×D43—21no—
11#14583454C411yescharacteristic
12#14583454C411yescharacteristic
13#14583450C411yescharacteristic
14#14583450C411yescharacteristic
15#14583449C2211yescharacteristic
16#14583436—21no—
17#14583436—21no—
18#14583435—21no—
19#14583435—21no—
20#14583434C2212yes—
21#14583434C2212yes—
22#14583412—21no—
23#14583412—21no—
24#14583411C412yes—
25C4×#10621902—21no—
26C4×#10621902—21no—
27#14583367C412yes—
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#14582641C2214yescomplemented
43#14582638C2214yescomplemented
44#14582638C2214yescomplemented
45C43×#533C2211yescharacteristic
46C4×M16×C43C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×#330C2214yescomplemented
49C2×#10621902—21no—
50C2×#10621902—21no—
51C2×#10621898C2×C412yes—
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621872—22no—
58M16×D43—28no—
59C2×C8×D43—22no—
60#13063325C2×C411yescharacteristic
61#13063322C2×C411yescharacteristic
62#13063320—22no—
63#13063320—22no—
64#13063316—21no—
65#13063316—21no—
66#13063314—21no—
67#13063314—21no—
68#13063313C2312yes—
69#13063310—22no—
70#13063310—22no—
71#13063309—22no—
72#13063305C2×C412yes—
73#13063305C2×C412yes—
74#13063301—21no—
75#13063301—21no—
76#13063300—21no—
77#13063300—21no—
78#13063300C2×C412yes—
79#13063300C2×C412yes—
80#13063299—21no—
81#13063299—21no—
82#13063295—22no—
83Q8×Dic43—21no—
84Q8×Dic43—21no—
85#13063290C2×C412yes—
86#13063290C2×C412yes—
87C4×D172—22no—
88C4×D172—22no—
89C4×D172—21no—
90C4×D172—21no—
91#13063287—22no—
92#13063287—22no—
93#13063287—21no—
94#13063287—21no—
95#13063287C2×C412yes—
96#13063287C2×C412yes—
97(C22⋊D43)⋊C4—22no—
98(C22⋊D43)⋊C4—22no—
99#13063283—21no—
100#13063283—21no—
101#13063283—22no—
102#13063283—22no—
103#13063282—22no—
104C2×C4×Dic43C2×C411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C42×D43—22no—
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×M16×C43—21no—
127C2×M16×C43—21no—
128C4⋊Q8×C43C2×C411yescharacteristic
129C4⋊Q8×C43C2×C411yescharacteristic
130#125×C43C2312yes—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C4×Q8×C43—21no—
134C4×Q8×C43—21no—
135#117×C43C2×C412yes—
136C2×C42×C43C2311yescharacteristic
137#97×C43C2312yes—
138#97×C43C2312yes—
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C23×D43C22⋊C411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C2×C22⋊D43—22no—
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150C22×Dic43C22⋊C411yescharacteristic
151#10621902—44no—
152#10621902—44no—
153#10621898—44no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172C22×C412yes—
159C2×C4×D43—24no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
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×D43C22×C411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×Dic86C22×C412yes—
178M16×C43—24no—
179M16×C43—42no—
180C2×C8×C43—22no—
181C2×C8×C43—22no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43—22no—
186C4⋊C4×C43C22×C412yes—
187C4⋊C4×C43C22×C412yes—
188C22⋊C4×C43—22no—
189C42×C43—22no—
190C42×C43C22×C411yescharacteristic
191C42×C43C2×D411yescharacteristic
192C42×C43C2×D411yescharacteristic
193C42×C43C2411yescharacteristic
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4—22no—
201(C2×D43)⋊C4—22no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43—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—
223#10621877—42no—
224C2×C43⋊C8—22no—
225C2×C43⋊C8—22no—
226#10621872—28no—
227C8×D43—28no—
228C23×C43C2×C22⋊C411yescharacteristic
229C22×D43—22no—
230C22×D43—22no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43C2×C22⋊C411yescharacteristic
234C22×D43C2×C22⋊C411yescharacteristic
235Q8×C43—42no—
236Q8×C43—42no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C22⋊D43—44no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258C2×Dic43C2×C22⋊C411yescharacteristic
259D172—42no—
260D172—44no—
261D172—44no—
262D172—42no—
263D172—42no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—44no—
276C4×D43—44no—
277C4×D43—44no—
278C4×D43#10414yes—
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×C43C22×C22⋊C411yescharacteristic
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—44no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43C2×#10412yes—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—42no—
303C4×C43—42no—
304C4×C43#41312yes—
305C4×C43C2×#10412yes—
306C4×C43#42112yes—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—42no—
313Dic43C2×#10412yes—
314#3444—431no—
315#2920—431no—
316C2×C4×M16—431no—
317#1532—434no—
318#1529—434no—
319#1526—431no—
320#1526D4311yescharacteristic, complemented
321#1525—431no—
322#1525—431no—
323C2×C43—41no—
324C2×C43C2×#41311yescharacteristic
325C2×C43C22×#10411yescharacteristic
326C2×C43C2×#42111yescharacteristic
327D43—22no—
328D43—41no—
329D43—82no—
330C22×M16—861no—
331#533—431no—
332#533—431no—
333#533C2×D4311yescharacteristic
334#532—431no—
335#532—431no—
336#532—431no—
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#330C2×D4314yescomplemented
367#329—434no—
368#329—434no—
369C43#1764911yescharacteristic, complemented, Sylow
370C2×#41—432no—
371C2×#41—861no—
372C2×#41—861no—
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⋊Q8C4×D4311yescharacteristic
385C4⋊Q8C4×D4311yescharacteristic
386#127—431no—
387#126—862no—
388#126—862no—
389#125—861no—
390#125—861no—
391#125C22×D4312yes—
392#124—432no—
393#124—861no—
394#124—861no—
395#123—862no—
396#123—862no—
397#123—862no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—432no—
401C22⋊Q8—432no—
402C22⋊Q8—861no—
403C22⋊Q8—861no—
404#121—432no—
405#121—432no—
406#121—861no—
407#121—861no—
408#121—861no—
409#121—861no—
410#120—862no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—432no—
414C4×Q8—432no—
415C4×Q8—861no—
416C4×Q8—861no—
417C4×D4—432no—
418C4×D4—432no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—861no—
428C4×D4—861no—
429#117—862no—
430#117—862no—
431#117—862no—
432#117—861no—
433#117—861no—
434#117C4×D4312yes—
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—1724no—
464#41—1724no—
465#41—1724no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—432no—
469C2×D4—432no—
470C2×D4—862no—
471C2×D4—862no—
472C2×D4—862no—
473C2×D4—861no—
474C2×D4—861no—
475C22×C4—431no—
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—864no—
491C22×C4—862no—
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—22no—
512C4⋊C4—22no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4C2×C4×D4312yes—
520C4⋊C4C2×C4×D4312yes—
521C22⋊C4—22no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C42—22no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—431no—
543C42—862no—
544C42—862no—
545C42C2×C4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42D4×D4311yescharacteristic
548C42C23×D4311yescharacteristic
549C23—431no—
550C23—431no—
551C23—862no—
552C23—862no—
553C23—1721no—
554C23—1721no—
555C23C22⋊C4×D4311yescharacteristic
556Q8—42no—
557Q8—42no—
558Q8—1722no—
559D4—1722no—
560D4—1724no—
561D4—1724no—
562D4—1724no—
563D4—1722no—
564D4—1722no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
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—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1724no—
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—432no—
609C22—861no—
610C22—861no—
611C22—861no—
612C22—861no—
613C22—861no—
614C22—1724no—
615C22—1722no—
616C22—1722no—
617C22—1722no—
618C22C2×C22⋊C4×D4311yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—432no—
625C4—861no—
626C4—861no—
627C4—861no—
628C4—861no—
629C4—861no—
630C4—1722no—
631C4#1458288212yes—
632C4#104×D4312yes—
633C4#1458291412yes—
634C2—41no—
635C2—862no—
636C2—3442no—
637C2—1721no—
638C2C2×#1458288211yescharacteristic
639C2C2×#104×D4311yescharacteristic
640C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1526C2
socleC22×C43C22×C22⋊C4
prime radical#19147892C2
cosocleC42×C43C24
hypercenter#1526D43
hypocenterC43#17649
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. C4×M16×D43C2semidirect
4. #19133214C2semidirect
5. #19133201C2semidirect
6. #19133190C2semidirect
7. #19133186C2semidirect
8. #19133186C2semidirect
9. C43×#1526C2semidirect
42. #14582641C22semidirect
43. #14582638C22semidirect
44. #14582638C22semidirect
48. C43×#330C22semidirect
320. #1526D43semidirect
366. #330C2×D43semidirect
369. C43#17649semidirect

Maximal subgroups

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

subgroupindex
#191478922
#191432262
C4×M16×D432
#191332142
#191332012
#191331902
#191331862
C43×#15262
#1764943