Finite Group Databasebeta

← #25064671

Subgroups — #25064671

Order 11008.

984 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
1C2×#14583428C211yesmaximal, characteristic
2#19143226C211yesmaximal, characteristic, complemented
3#432×D43C211yesmaximal, characteristic, complemented
4#19133223C214yesmaximal, complemented
5#19133212C214yesmaximal, complemented
6#19133198C211yesmaximal, characteristic, complemented
7#19133196C211yesmaximal, characteristic, complemented
8#19133193C211yesmaximal, characteristic, complemented
9C43×#1527C211yesmaximal, characteristic, complemented
10#14583428—21no—
11#14583428—21no—
12#14583428—21no—
13#14583428—21no—
14#14583428C412yes—
15#14583428C412yes—
16#14583428C2212yes—
17#14583428C2212yes—
18C2×#13063318—21no—
19C2×#13063317C2211yescharacteristic
20C2×#13063307—21no—
21C2×#13063301C411yescharacteristic
22C2×#13063296C411yescharacteristic
23C2×Q8×Dic43C411yescharacteristic
24C2×D4×Dic43C411yescharacteristic
25C2×(C22⋊D43)⋊C4—21no—
26C2×#13063281—21no—
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582955—21no—
30#14582954C2212yescomplemented
31#14582954C2212yescomplemented
32#14582954C2212yescomplemented
33#14582953—21no—
34#14582950—21no—
35#14582950—21no—
36#14582922—21no—
37C4⋊C8×D43—21no—
38#14582862—21no—
39C22⋊C8×D43—21no—
40C4×#10621877C2211yescharacteristic
41#97×D43C2212yescomplemented
42#14582640C2214yescomplemented
43#14582640C2214yescomplemented
44#14582639C2214yescomplemented
45C2×#124×C43C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C4×M16×C43C2211yescharacteristic
48C43×#329C2214yescomplemented
49C22×C22⋊D43—21no—
50C23×Dic43—21no—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C2×#10621877—21no—
55C2×C8×D43—22no—
56#13063318—22no—
57#13063318—22no—
58#13063318—22no—
59#13063318—22no—
60#13063317—21no—
61#13063317—21no—
62#13063317C2×C412yes—
63#13063317C2312yes—
64#13063307—22no—
65#13063307—22no—
66#13063307—22no—
67#13063307—22no—
68#13063301—21no—
69#13063301—21no—
70#13063301C2×C412yes—
71#13063301C2×C412yes—
72#13063296—21no—
73#13063296—21no—
74#13063296C2×C412yes—
75#13063296C2×C412yes—
76Q8×Dic43—21no—
77Q8×Dic43—21no—
78Q8×Dic43C2×C412yes—
79Q8×Dic43C2×C412yes—
80D4×Dic43—21no—
81D4×Dic43—21no—
82D4×Dic43C2×C412yes—
83D4×Dic43C2×C412yes—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86(C22⋊D43)⋊C4—22no—
87(C22⋊D43)⋊C4—22no—
88#13063281—22no—
89#13063281—22no—
90#13063281—22no—
91#13063281—22no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×C4⋊Dic43C2×C411yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C42×D43C2×C411yescharacteristic
106C42×D43C2×C411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43C2311yescharacteristic
112C42×D43C2311yescharacteristic
113C4⋊(C43⋊C8)—21no—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063236C2312yes—
122#13063236C2312yes—
123#13063235—22no—
124C4×C43⋊C8—21no—
125C22×Q8×C43C2×C411yescharacteristic
126C22×D4×C43C2×C411yescharacteristic
127C2×M16×C43—21no—
128#124×C43—21no—
129#124×C43—21no—
130#124×C43C2×C412yes—
131#124×C43C2312yes—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43C2312yes—
138#97×C43C2312yes—
139C4×C8×C43—21no—
140C24×C43—21no—
141C23×D43C22⋊C411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—42no—
144C2×Q8×C43C22×C412yes—
145C2×D4×C43—21no—
146C2×D4×C43—42no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43—44no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—44no—
160C22×Dic43C22⋊C411yescharacteristic
161C22×Dic43C22⋊C411yescharacteristic
162C22×Dic43C22⋊C411yescharacteristic
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
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×D43C22×C411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×C4×D43C2×D411yescharacteristic
176C2×C4×D43C2×D411yescharacteristic
177C2×C4×D43C2×D411yescharacteristic
178M16×C43—42no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C42×C43C22×C411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2411yescharacteristic
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43C22×C412yes—
200C4⋊Dic43C22×C412yes—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C22×C411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221#10621877—42no—
222C2×C43⋊C8—22no—
223C2×C43⋊C8—22no—
224C8×D43—44no—
225C23×C43—22no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43—42no—
229C23×C43C2×C22⋊C411yescharacteristic
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—41no—
233C22×D43C2×C22⋊C411yescharacteristic
234C22×D43C2×C22⋊C411yescharacteristic
235Q8×C43—42no—
236Q8×C43—42no—
237D4×C43—42no—
238D4×C43—42no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—41no—
243C2×C4×C43—42no—
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C22⋊D43—44no—
251C22⋊D43—44no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—44no—
258C2×Dic43—44no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C2×Dic43C2×C22⋊C411yescharacteristic
266C2×Dic43C2×C22⋊C411yescharacteristic
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—41no—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C8×C43—42no—
280C8×C43—42no—
281C43⋊C8—42no—
282C43⋊C8—42no—
283#17668—431nomaximal, Sylow
284C22×C43—21no—
285C22×C43—21no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—84no—
290C22×C43#42112yes—
291C22×C43C22×C22⋊C411yescharacteristic
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—21no—
297C2×D43—44no—
298C2×D43#42112yes—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43#41312yes—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—21no—
312Dic43—42no—
313Dic43—42no—
314C2×#529—431no—
315#2920—431no—
316C2×#432—431no—
317#1535—434no—
318#1532—434no—
319#1528—431no—
320#1528—431no—
321#1527—431no—
322#1527D4311yescharacteristic, complemented
323C2×C43—22no—
324C2×C43—82no—
325C2×C43C2×#41311yescharacteristic
326C2×C43C2×#42111yescharacteristic
327C2×C43C2×#42111yescharacteristic
328D43—22no—
329D43—41no—
330#529—432no—
331#529—432no—
332#529—432no—
333#529—432no—
334#529—861no—
335#529—861no—
336#529—861no—
337#529—861no—
338C2×#126—861no—
339C2×#125—431no—
340C2×#124C2×D4311yescharacteristic
341C2×#123—861no—
342C2×C22⋊Q8—431no—
343C2×#121—431no—
344C2×C4×Q8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—861no—
347C2×#117—861no—
348C22×C42—431no—
349#432—431no—
350#432—432no—
351#432—432no—
352#432—432no—
353#432—861no—
354#432—861no—
355#432C2×D4311yescharacteristic
356#431—861no—
357#431—861no—
358#423—861no—
359C2×C4⋊C8—861no—
360#407—861no—
361C2×C22⋊C8—861no—
362C4×M16—431no—
363C4×M16C2×D4311yescharacteristic
364C2×#97—432no—
365#330—434no—
366#330—434no—
367#329—434no—
368#329C2×D4314yescomplemented
369C43#1766811yescharacteristic, complemented, Sylow
370C22×Q8C4×D4311yescharacteristic
371C22×D4—861no—
372C22×D4C4×D4311yescharacteristic
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—861no—
377C2×M16—21no—
378C2×M16—861no—
379C22×C8—862no—
380#126—862no—
381#126—862no—
382#126—862no—
383#126—862no—
384#125—432no—
385#125—432no—
386#125—861no—
387#125—861no—
388#124—21no—
389#124—21no—
390#124C4×D4312yes—
391#124C22×D4312yes—
392#123—862no—
393#123—862no—
394#123—862no—
395#123—862no—
396C22⋊Q8—432no—
397C22⋊Q8—432no—
398C22⋊Q8—861no—
399C22⋊Q8—861no—
400#121—432no—
401#121—432no—
402#121—861no—
403#121—861no—
404C4×Q8—432no—
405C4×Q8—432no—
406C4×Q8—861no—
407C4×Q8—861no—
408C4×D4—432no—
409C4×D4—432no—
410C4×D4—861no—
411C4×D4—861no—
412C4×D4—862no—
413C4×D4—862no—
414C4×D4—862no—
415C4×D4—862no—
416#117—862no—
417#117—862no—
418#117—862no—
419#117—862no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—431no—
442C2×C42—861no—
443C2×C42C22×D4311yescharacteristic
444C4⋊C8—21no—
445C4⋊C8—862no—
446C4⋊C8—862no—
447C4⋊C8—862no—
448C4⋊C8—861no—
449C22⋊C8—21no—
450C22⋊C8—862no—
451C22⋊C8—862no—
452C22⋊C8—862no—
453C22⋊C8—861no—
454#97—432no—
455#97—432no—
456#97—862no—
457#97C22×D4312yes—
458#97C22×D4312yes—
459C4×C8—21no—
460C4×C8—861no—
461C24—21no—
462C24—431no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8C2×C4×D4312yes—
466C2×D4—21no—
467C2×D4—42no—
468C2×D4—862no—
469C2×D4—862no—
470C2×D4—1724no—
471C2×D4C2×C4×D4312yes—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
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—862no—
489C22×C4—862no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4—1722no—
495C22×C4—1724no—
496C22×C4C2×C4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499M16—42no—
500M16—1722no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—862no—
504C2×C8—862no—
505C2×C8—1724no—
506C4⋊C4—432no—
507C4⋊C4—432no—
508C4⋊C4—862no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—862no—
541C42—862no—
542C42C2×C4×D4311yescharacteristic
543C42D4×D4311yescharacteristic
544C42D4×D4311yescharacteristic
545C42C23×D4311yescharacteristic
546C23—22no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—431no—
551C23—431no—
552C23—862no—
553C23—862no—
554C23—1721no—
555C23C22⋊C4×D4311yescharacteristic
556Q8—42no—
557Q8—42no—
558D4—42no—
559D4—42no—
560D4—1724no—
561D4—1724no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—431no—
568C2×C4—431no—
569C2×C4—431no—
570C2×C4—431no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—862no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4C22⋊C4×D4311yescharacteristic
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22×C4×D4311yescharacteristic
598C2×C4C2×D4×D4311yescharacteristic
599C2×C4C2×D4×D4311yescharacteristic
600C8—42no—
601C8—42no—
602C8—1722no—
603C8—1722no—
604C22—21no—
605C22—21no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—84no—
610C22—432no—
611C22—861no—
612C22—861no—
613C22—861no—
614C22—861no—
615C22—861no—
616C22—1724no—
617C22#1458291412yes—
618C22C2×C22⋊C4×D4311yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—42no—
625C4—861no—
626C4—861no—
627C4—861no—
628C4—861no—
629C4—861no—
630C4—861no—
631C4—1722no—
632C4—1722no—
633C4#1458288012yes—
634C2—22no—
635C2—82no—
636C2—862no—
637C2—1721no—
638C2C2×#1458288011yescharacteristic
639C2#421×D4311yescharacteristic
640C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1527C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063296C4
cosocleC42×C43C24
hypercenter#1527D43
hypocenterC43#17668
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1527

Complements

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

NH ≅ G/Ntype
2. #19143226C2semidirect
3. #432×D43C2semidirect
4. #19133223C2semidirect
5. #19133212C2semidirect
6. #19133198C2semidirect
7. #19133196C2semidirect
8. #19133193C2semidirect
9. C43×#1527C2semidirect
30. #14582954C22semidirect
31. #14582954C22semidirect
32. #14582954C22semidirect
41. #97×D43C22semidirect
42. #14582640C22semidirect
43. #14582640C22semidirect
44. #14582639C22semidirect
48. C43×#329C22semidirect
322. #1527D43semidirect
368. #329C2×D43semidirect
369. C43#17668semidirect

Maximal subgroups

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

subgroupindex
C2×#145834282
#191432262
#432×D432
#191332232
#191332122
#191331982
#191331962
#191331932
C43×#15272
#1766843