Finite Group Databasebeta

← #25064629

Subgroups — #25064629

Order 11008.

984 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583434C211yesmaximal, characteristic
2#19143225C211yesmaximal, characteristic, complemented
3#432×D43C211yesmaximal, characteristic, complemented
4#19133225C214yesmaximal, complemented
5#19133222C211yesmaximal, characteristic, complemented
6#19133218C211yesmaximal, characteristic, complemented
7#19133218C211yesmaximal, characteristic, complemented
8#19133182C214yesmaximal, complemented
9C43×#1534C211yesmaximal, characteristic, complemented
10#14583434—21no—
11#14583434—21no—
12#14583434—21no—
13#14583434—21no—
14#14583434C412yes—
15#14583434C412yes—
16#14583434C2212yes—
17#14583434C2212yes—
18C2×#13063320—21no—
19C2×#13063313C2211yescharacteristic
20C2×#13063310—21no—
21C2×#13063305C411yescharacteristic
22C2×#13063300C411yescharacteristic
23C2×#13063290C411yescharacteristic
24C2×#13063287—21no—
25C2×#13063287C411yescharacteristic
26C2×#13063283—21no—
27C2×C42×D43C2211yescharacteristic
28#14582956C2211yescharacteristic
29#14582956C2211yescharacteristic
30#14582955—21no—
31#14582954C2212yescomplemented
32#14582954C2212yescomplemented
33#14582953—21no—
34#14582951—21no—
35#14582949—21no—
36#14582921—21no—
37C4⋊C8×D43—21no—
38#14582861—21no—
39C22⋊C8×D43—21no—
40#14582851C2212yescomplemented
41#97×D43C2212yescomplemented
42#14582641C2214yescomplemented
43#14582638C2214yescomplemented
44#14582638C2214yescomplemented
45C2×#125×C43C2211yescharacteristic
46C43×#432C2211yescharacteristic
47C43×#432C2211yescharacteristic
48C43×#330C2214yescomplemented
49C22×Dic86C2×C411yescharacteristic
50C22×D172—21no—
51C22×D172C2×C411yescharacteristic
52C22×C4×D43—21no—
53C22×C4×D43C2×C411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C4×D43D411yescharacteristic
56C2×#10621872—22no—
57C2×C8×D43—22no—
58#13063320—22no—
59#13063320—22no—
60#13063320—22no—
61#13063320—22no—
62#13063313—21no—
63#13063313—21no—
64#13063313C2×C412yes—
65#13063313C2312yes—
66#13063310—22no—
67#13063310—22no—
68#13063310—22no—
69#13063310—22no—
70#13063305—21no—
71#13063305—21no—
72#13063305C2×C412yes—
73#13063305C2×C412yes—
74#13063300—21no—
75#13063300—21no—
76#13063300C2×C412yes—
77#13063300C2×C412yes—
78#13063290—21no—
79#13063290—21no—
80#13063290C2×C412yes—
81#13063290C2×C412yes—
82#13063287—22no—
83#13063287—22no—
84#13063287—22no—
85#13063287—22no—
86#13063287—21no—
87#13063287—21no—
88#13063287C2×C412yes—
89#13063287C2×C412yes—
90#13063283—22no—
91#13063283—22no—
92#13063283—22no—
93#13063283—22no—
94C2×C4⋊Dic43—21no—
95C2×Dic43⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—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—
114C4⋊(C43⋊C8)—21no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)—21no—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063236C2312yes—
122#13063236C2312yes—
123#13063235—22no—
124C8×Dic43—22no—
125#125×C43—21no—
126#125×C43—21no—
127#125×C43C2×C412yes—
128#125×C43C2312yes—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43C2×C411yescharacteristic
132C2×C4⋊C4×C43C2×C411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43C2312yes—
139#97×C43C2312yes—
140C23×D43—21no—
141C23×D43C22⋊C411yescharacteristic
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×Dic43—21no—
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22⋊C411yescharacteristic
150C22×Dic43C22⋊C411yescharacteristic
151C2×D172—21no—
152C2×D172—22no—
153C2×D172—22no—
154C2×D172—44no—
155C2×D172—42no—
156C2×D172C22×C412yes—
157C2×C4×D43—22no—
158C2×C4×D43—22no—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—44no—
163C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
172C2×C4×D43C2×D411yescharacteristic
173C2×C4×D43C2×D411yescharacteristic
174C2×C4×D43C2×D411yescharacteristic
175C2×Dic86—21no—
176C2×Dic86—42no—
177C2×Dic86C22×C412yes—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×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—
188C42×C43C22×C411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C42×C43C2×D411yescharacteristic
191C42×C43C2411yescharacteristic
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
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—22no—
203C4⋊Dic43—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43C22⋊C411yescharacteristic
209C4×Dic43C22⋊C411yescharacteristic
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22×C411yescharacteristic
215C4×Dic43C22×C411yescharacteristic
216C4×Dic43C2×D411yescharacteristic
217C4×Dic43C2×D411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222#10621872—44no—
223C8×D43—44no—
224C23×C43C2×C22⋊C411yescharacteristic
225C22×D43—22no—
226C22×D43—22no—
227C22×D43—22no—
228C22×D43—41no—
229C22×D43—42no—
230C22×D43—42no—
231C22×D43—42no—
232C22×D43C2×C22⋊C411yescharacteristic
233C22×D43C2×C22⋊C411yescharacteristic
234C2×C4×C43—22no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—41no—
251C2×Dic43—42no—
252C2×Dic43C2×C22⋊C411yescharacteristic
253C2×Dic43C2×C22⋊C411yescharacteristic
254C2×Dic43C2×C22⋊C411yescharacteristic
255C2×Dic43C2×C22⋊C411yescharacteristic
256C2×Dic43C2×C22⋊C411yescharacteristic
257C2×Dic43C2×C22⋊C411yescharacteristic
258D172—42no—
259D172—42no—
260D172—44no—
261D172—44no—
262C4×D43—22no—
263C4×D43—22no—
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—41no—
269C4×D43—41no—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—44no—
275C4×D43—44no—
276Dic86—42no—
277Dic86—42no—
278C8×C43—42no—
279C8×C43—42no—
280C43⋊C8—42no—
281C43⋊C8—42no—
282#17659—431nomaximal, Sylow
283C22×C43—21no—
284C22×C43—21no—
285C22×C43#41312yes—
286C22×C43C22×C22⋊C411yescharacteristic
287C2×D43—21no—
288C2×D43—21no—
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—21no—
292C2×D43—44no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—84no—
297C2×D43#42112yes—
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43—42no—
306Dic43—21no—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—42no—
312Dic43#42112yes—
313C2×#529—431no—
314#2920—431no—
315C2×#432—431no—
316#1535—434no—
317#1534—431no—
318#1534D4311yescharacteristic, complemented
319#1533—431no—
320#1533—431no—
321#1524—434no—
322C2×C43—22no—
323C2×C43C2×#41311yescharacteristic
324C2×C43C2×#42111yescharacteristic
325C2×C43C2×#42111yescharacteristic
326D43—22no—
327D43—41no—
328D43—82no—
329#529—432no—
330#529—432no—
331#529—432no—
332#529—432no—
333#529—861no—
334#529—861no—
335#529—861no—
336#529—861no—
337C2×#126—861no—
338C2×#125C2×D4311yescharacteristic
339C2×#124—431no—
340C2×#123—861no—
341C2×C22⋊Q8—431no—
342C2×#121—431no—
343C2×C4×Q8—431no—
344C2×C4×D4—431no—
345C2×C4×D4—861no—
346C2×#117—861no—
347C22×C42—431no—
348#432—431no—
349#432—431no—
350#432—432no—
351#432—432no—
352#432—861no—
353#432—861no—
354#432C2×D4311yescharacteristic
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—432no—
363C2×#97—432no—
364#330—434no—
365#330C2×D4314yescomplemented
366#329—434no—
367#329—434no—
368C43#1765911yescharacteristic, complemented, Sylow
369C22×Q8—431no—
370C22×D4—431no—
371C22×D4—861no—
372C23×C4—431no—
373C23×C4—431no—
374C23×C4—431no—
375C23×C4—861no—
376C2×M16—862no—
377C22×C8—862no—
378#126—862no—
379#126—862no—
380#126—862no—
381#126—862no—
382#125—21no—
383#125—21no—
384#125C4×D4312yes—
385#125C22×D4312yes—
386#124—432no—
387#124—432no—
388#124—861no—
389#124—861no—
390#123—862no—
391#123—862no—
392#123—862no—
393#123—862no—
394C22⋊Q8—432no—
395C22⋊Q8—432no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398#121—432no—
399#121—432no—
400#121—861no—
401#121—861no—
402C4×Q8—432no—
403C4×Q8—432no—
404C4×Q8—861no—
405C4×Q8—861no—
406C4×D4—432no—
407C4×D4—432no—
408C4×D4—861no—
409C4×D4—861no—
410C4×D4—862no—
411C4×D4—862no—
412C4×D4—862no—
413C4×D4—862no—
414#117—862no—
415#117—862no—
416#117—862no—
417#117—862no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4C4×D4311yescharacteristic
423C2×C4⋊C4C4×D4311yescharacteristic
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C42—431no—
430C2×C42—431no—
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—861no—
441C2×C42C22×D4311yescharacteristic
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8—862no—
445C4⋊C8—862no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—862no—
451C22⋊C8—862no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454#97—432no—
455#97—432no—
456#97—862no—
457#97C22×D4312yes—
458#97C22×D4312yes—
459C4×C8—862no—
460C24—431no—
461C24—861no—
462C2×Q8—432no—
463C2×Q8—861no—
464C2×Q8—1722no—
465C2×D4—432no—
466C2×D4—862no—
467C2×D4—862no—
468C2×D4—861no—
469C2×D4—1722no—
470C2×D4—1724no—
471C22×C4—21no—
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—1722no—
492C22×C4—1722no—
493C22×C4—1722no—
494C22×C4—1724no—
495C22×C4C2×C4×D4311yescharacteristic
496C22×C4D4×D4311yescharacteristic
497C22×C4D4×D4311yescharacteristic
498M16—1724no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—862no—
502C2×C8—862no—
503C2×C8—1724no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4C2×C4×D4312yes—
515C4⋊C4C2×C4×D4312yes—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C42—431no—
527C42—431no—
528C42—431no—
529C42—431no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—862no—
539C42—862no—
540C42C2×C4×D4311yescharacteristic
541C42D4×D4311yescharacteristic
542C42D4×D4311yescharacteristic
543C42C23×D4311yescharacteristic
544C23—431no—
545C23—431no—
546C23—862no—
547C23—862no—
548C23—862no—
549C23—1721no—
550C23—1722no—
551C23—1722no—
552C23—1722no—
553C23C22⋊C4×D4311yescharacteristic
554Q8—1722no—
555Q8—1722no—
556D4—1722no—
557D4—1722no—
558D4—1724no—
559D4—1724no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
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—1724no—
589C2×C4—1724no—
590C2×C4—1721no—
591C2×C4—1722no—
592C2×C4C22⋊C4×D4311yescharacteristic
593C2×C4C22⋊C4×D4311yescharacteristic
594C2×C4C22⋊C4×D4311yescharacteristic
595C2×C4C22×C4×D4311yescharacteristic
596C2×C4C2×D4×D4311yescharacteristic
597C2×C4C2×D4×D4311yescharacteristic
598C8—42no—
599C8—42no—
600C8—1722no—
601C8—1722no—
602C22—21no—
603C22—21no—
604C22—432no—
605C22—861no—
606C22—861no—
607C22—861no—
608C22—861no—
609C22—861no—
610C22—3444no—
611C22—1724no—
612C22—1722no—
613C22—1722no—
614C22—1722no—
615C22#1458288212yes—
616C22C2×C22⋊C4×D4311yescharacteristic
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—21no—
623C4—42no—
624C4—42no—
625C4—432no—
626C4—861no—
627C4—861no—
628C4—861no—
629C4—861no—
630C4—861no—
631C4—1722no—
632C2—22no—
633C2—862no—
634C2—3442no—
635C2—1721no—
636C2C2×#1458288211yescharacteristic
637C2#421×D4311yescharacteristic
638C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1534C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063300C4
cosocleC42×C43C24
hypercenter#1534D43
hypocenterC43#17659
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1534

Complements

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

NH ≅ G/Ntype
2. #19143225C2semidirect
3. #432×D43C2semidirect
4. #19133225C2semidirect
5. #19133222C2semidirect
6. #19133218C2semidirect
7. #19133218C2semidirect
8. #19133182C2semidirect
9. C43×#1534C2semidirect
31. #14582954C22semidirect
32. #14582954C22semidirect
40. #14582851C22semidirect
41. #97×D43C22semidirect
42. #14582641C22semidirect
43. #14582638C22semidirect
44. #14582638C22semidirect
48. C43×#330C22semidirect
318. #1534D43semidirect
365. #330C2×D43semidirect
368. C43#17659semidirect

Maximal subgroups

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

subgroupindex
C2×#145834342
#191432252
#432×D432
#191332252
#191332222
#191332182
#191331822
C43×#15342
#1765943