Finite Group Databasebeta

← #25063504

Subgroups — #25063504

Order 11008.

1004 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#19148162C211yesmaximal, characteristic
2#19143556C211yesmaximal, characteristic, complemented
3#19143160C211yesmaximal, characteristic, complemented
4#19133059C212yesmaximal, complemented
5#19133050C211yesmaximal, characteristic, complemented
6#19133033C212yesmaximal, complemented
7#19133021C211yesmaximal, characteristic, complemented
8#19133007C212yesmaximal, complemented
9#19132981C212yesmaximal, complemented
10C2×#14582626C211yesmaximal, characteristic, complemented
11C43×#1481C211yesmaximal, characteristic, complemented
12C2×#13063331—21no—
13#14583623C411yescharacteristic
14#14583615C411yescharacteristic
15#14583610C411yescharacteristic
16#14583602—21no—
17#14583591C412yes—
18#14583587—21no—
19#14583576—22no—
20#14583552C411yescharacteristic
21#14583540C412yes—
22#14583436—22no—
23#14583436C2212yes—
24#14583411—21no—
25C4×#10621902C2212yes—
26C4×#10621898C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28#117×D43—21no—
29#14583026—21no—
30#14582976—21no—
31#14582967—22no—
32#14582950C2212yescomplemented
33#14582925—21no—
34#14582924—22no—
35#14582923C2211yescharacteristic
36#14582921C2212yescomplemented
37C4⋊C8×D43C2212yescomplemented
38C4×#10621872C2212yescomplemented
39C2×C4×C43⋊C8C2211yescharacteristic
40Q8⋊(C43⋊C8)C2212yescomplemented
41Q8⋊(C43⋊C8)C2212yescomplemented
42#14582628C2212yes—
43#14582628C2212yes—
44#14582626C2211yescharacteristic
45#14582626C2211yescharacteristic
46#14582626C2211yescharacteristic
47#14582626C2211yescharacteristic
48C43×#533C2211yescharacteristic
49C43×#431C2211yescharacteristic
50C2×C4⋊C8×C43C2211yescharacteristic
51C43×Q8⋊C8C2212yescomplemented
52C43×Q8⋊C8C2212yescomplemented
53C2×#10621902C2×C412yes—
54C2×#10621898D411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C22×C4×D43—21no—
57#13063331—44no—
58C2×#10621877—21no—
59C2×#10621872—22no—
60C2×#10621872—22no—
61C22×C43⋊C8—21no—
62C2×C8×D43—22no—
63#13063320—22no—
64#13063320—22no—
65#13063320—22no—
66#13063316—22no—
67#13063316C2×C412yes—
68#13063314—22no—
69#13063314C2×C412yes—
70#13063310—22no—
71#13063310—22no—
72#13063310—22no—
73#13063309—22no—
74#13063305—21no—
75#13063305—21no—
76#13063301—22no—
77#13063301C2×C412yes—
78#13063300—21no—
79#13063300—21no—
80#13063300—22no—
81#13063300C2×C412yes—
82#13063295—22no—
83Q8×Dic43C2×C412yes—
84C4×Dic86C2×C411yescharacteristic
85C4×Dic86D411yescharacteristic
86C4×D172—22no—
87C4×D172—22no—
88C4×D172—21no—
89C4×D172—21no—
90C4×D172C2×C411yescharacteristic
91C4×D172C2×C411yescharacteristic
92C4×D172C2×C411yescharacteristic
93C4×D172D411yescharacteristic
94C4×D172C2311yescharacteristic
95C4×D172C2311yescharacteristic
96#13063287—22no—
97#13063287C2×C412yes—
98C4×C22⋊D43C2×C412yes—
99C4×C22⋊D43D412yes—
100#13063284D411yescharacteristic
101#13063283—21no—
102#13063283—21no—
103#13063283—22no—
104#13063283C2×C412yes—
105#13063282—22no—
106#13063282D412yes—
107#13063281—22no—
108C2×C4⋊Dic43C2×C411yescharacteristic
109C4⋊C4×D43—21no—
110C4⋊C4×D43—21no—
111C2×(C2×D43)⋊C4—21no—
112C22⋊C4×D43—22no—
113C42×D43—22no—
114C42×D43C2312yes—
115C4⋊(C43⋊C8)—21no—
116C4⋊(C43⋊C8)C2312yes—
117Dic43⋊C8—22no—
118Dic43⋊C8—22no—
119Dic43⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063235—22no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C22×C8×C43—21no—
126C4⋊Q8×C43C2×C411yescharacteristic
127C4⋊Q8×C43C2×C411yescharacteristic
128#125×C43—21no—
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43C2×C412yes—
131C4×Q8×C43—21no—
132C4×Q8×C43C2312yes—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43—21no—
140C4×C8×C43C2312yes—
141C23×D43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43C22×C412yes—
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C2×C22⋊D43C22⋊C412yes—
148C22×Dic43—21no—
149#10621902—24no—
150#10621902—42no—
151#10621898—22no—
152#10621898—22no—
153C2×D172—21no—
154C2×D172—22no—
155C2×D172—22no—
156C2×D172—22no—
157C2×D172—41no—
158C2×D172C22⋊C411yescharacteristic
159C2×D172C22×C411yescharacteristic
160C2×D172C22×C411yescharacteristic
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—42no—
168C2×C4×D43—42no—
169C2×C4×D43C22×C412yes—
170C2×C4×D43C2×D412yes—
171C2×C4×D43C2×D412yes—
172C2×Dic86C22⋊C411yescharacteristic
173C2×C8×C43—22no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—42no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43C22×C412yes—
183C22⋊C4×C43—22no—
184C42×C43—22no—
185C42×C43C22×C411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2411yescharacteristic
189C22⋊Dic43C22⋊C412yes—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
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)⋊C4C22⋊C412yes—
201(C2×D43)⋊C4C22⋊C412yes—
202C4⋊Dic43—21no—
203C4⋊Dic43—22no—
204C4⋊Dic43—22no—
205C4⋊Dic43C22⋊C411yescharacteristic
206C4⋊Dic43C22⋊C411yescharacteristic
207C4⋊Dic43C22×C411yescharacteristic
208C4⋊Dic43C22×C411yescharacteristic
209Dic43⋊C4—22no—
210Dic43⋊C4—22no—
211Dic43⋊C4C22⋊C412yes—
212Dic43⋊C4C22⋊C412yes—
213C4×Dic43—22no—
214C4×Dic43—22no—
215C4×Dic43C22×C412yes—
216C4×Dic43C2×D412yes—
217C4×Dic43C2×D412yes—
218#10621877—42no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—42no—
223#10621872—44no—
224#10621872—44no—
225C8×D43—44no—
226C23×C43C2×C22⋊C411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—42no—
230C22×D43—42no—
231C22×D43—81no—
232C22×D43C2×C22⋊C412yes—
233Q8×C43—22no—
234Q8×C43—22no—
235Q8×C43—81no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43AGL(1,ℤ/8)12yes—
245C2×C4×C43#13712yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C22⋊D43—24no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—42no—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256D172—21no—
257D172—21no—
258D172—21no—
259D172—22no—
260D172—42no—
261D172—44no—
262D172—82no—
263D172#13112yescomplemented
264C4×D43—22no—
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—42no—
269C4×D43—44no—
270C4×D43—41no—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—42no—
275C4×D43—42no—
276C4×D43—82no—
277Dic86—22no—
278C8×C43—42no—
279C8×C43—41no—
280C8×C43—41no—
281C43⋊C8—22no—
282C43⋊C8—41no—
283C43⋊C8—42no—
284#17512—431nomaximal, Sylow
285C22×C43—21no—
286C22×C43—21no—
287C22×C43#41712yes—
288C22×C43C22×C22⋊C411yescharacteristic
289C2×D43—22no—
290C2×D43—22no—
291C2×D43—22no—
292C2×D43—22no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—84no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—42no—
303C4×C43—42no—
304C4×C43#41712yes—
305C4×C43C2×#13111yescharacteristic
306C4×C43#56811yescharacteristic
307C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C43C2×#13711yescharacteristic
309Dic43—22no—
310Dic43—22no—
311Dic43—22no—
312Dic43—41no—
313Dic43—41no—
314#3475—431no—
315#2965—431no—
316#2906—431no—
317#1495—432no—
318#1493—431no—
319#1489—432no—
320#1486—431no—
321#1483—432no—
322#1481D4311yescharacteristic, complemented
323#1477—432no—
324C2×D4⋊C8—431no—
325C2×C43—22no—
326C2×C43#288011yescharacteristic
327C2×C43C2×#41711yescharacteristic
328C2×C43#290111yescharacteristic
329D43—42no—
330D43—42no—
331D43—81no—
332C2×#131—861no—
333#556—431no—
334#555—431no—
335#554—431no—
336#553—861no—
337#552—432no—
338#552—861no—
339#551—862no—
340#547—431no—
341#546—432no—
342#533C2×D4311yescharacteristic
343#529—432no—
344#529—862no—
345#525—861no—
346C4×#41—431no—
347C4×#41—432no—
348C2×C4×D4—431no—
349C2×#117—861no—
350#446—861no—
351#436—861no—
352#435—862no—
353#431—432no—
354#431C2×D4311yescharacteristic
355#424—862no—
356#424—861no—
357#423—431no—
358#423—432no—
359C2×C4⋊C8—432no—
360C2×C4⋊C8C2×D4311yescharacteristic
361C4×M16—432no—
362C2×C4×C8—431no—
363Q8⋊C8—432no—
364Q8⋊C8—432no—
365Q8⋊C8C2×D4312yescomplemented
366Q8⋊C8C2×D4312yescomplemented
367D4⋊C8—431no—
368D4⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—432no—
372D4⋊C8—432no—
373C43#1751211yescharacteristic, complemented, Sylow
374C2×#41—431no—
375C2×#41—432no—
376C22×D4—431no—
377C23×C4—861no—
378#131—1724no—
379C2×M16—862no—
380C2×M16—862no—
381C2×M16—861no—
382C22×C8—21no—
383C22×C8—862no—
384C22×C8—861no—
385C4⋊Q8C4×D4311yescharacteristic
386C4⋊Q8C4×D4311yescharacteristic
387#126—862no—
388#126—862no—
389#126—862no—
390#125—21no—
391#125—432no—
392#125—862no—
393#124—432no—
394#124—862no—
395#123—862no—
396#123—862no—
397#123—862no—
398#123—862no—
399C22⋊Q8—21no—
400C22⋊Q8—432no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C22⋊Q8—862no—
404C22⋊Q8C4×D4312yes—
405#121—432no—
406#121—862no—
407#121—861no—
408#121—861no—
409#120—862no—
410C4×Q8—21no—
411C4×Q8—431no—
412C4×Q8—431no—
413C4×Q8—432no—
414C4×Q8C22×D4312yes—
415C4×D4—432no—
416C4×D4—432no—
417C4×D4—432no—
418C4×D4—431no—
419C4×D4—431no—
420C4×D4—431no—
421C4×D4—431no—
422C4×D4—431no—
423C4×D4—431no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—861no—
428C4×D4—861no—
429#117—21no—
430#117—431no—
431#117—432no—
432#117—432no—
433#117—862no—
434#117—862no—
435#117—862no—
436#117—861no—
437#117—861no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—861no—
440C2×C4⋊C4—861no—
441C2×C22⋊C4—862no—
442C2×C22⋊C4—861no—
443C2×C42—432no—
444C2×C42—862no—
445C2×C42C22×D4311yescharacteristic
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8—432no—
449C4⋊C8—862no—
450C4⋊C8—862no—
451C4⋊C8—862no—
452C4⋊C8—861no—
453C4⋊C8C22×D4311yescharacteristic
454C4⋊C8C22×D4311yescharacteristic
455C22⋊C8—21no—
456C22⋊C8—862no—
457#97—862no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8—861no—
461C4×C8C22×D4312yes—
462C24—861no—
463#41—862no—
464#41—862no—
465#41—864no—
466#41—1722no—
467C2×Q8—21no—
468C2×Q8—431no—
469C2×Q8C2×C4×D4312yes—
470C2×D4—432no—
471C2×D4—431no—
472C2×D4—431no—
473C2×D4—431no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—862no—
477C2×D4—861no—
478C2×D4—1721no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—432no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4C2×C4×D4311yescharacteristic
492C22×C4D4×D4311yescharacteristic
493C22×C4D4×D4311yescharacteristic
494M16—1724no—
495M16—1724no—
496M16—1722no—
497C2×C8—22no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—42no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—862no—
504C2×C8—1724no—
505C2×C8—1722no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—431no—
512C4⋊C4—431no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—431no—
516C4⋊C4—431no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—861no—
522C4⋊C4C2×C4×D4312yes—
523C22⋊C4—22no—
524C22⋊C4—432no—
525C22⋊C4—432no—
526C22⋊C4—432no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C42—22no—
538C42—432no—
539C42—432no—
540C42—432no—
541C42—862no—
542C42—862no—
543C42C2×C4×D4311yescharacteristic
544C42D4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42C23×D4311yescharacteristic
547C23—432no—
548C23—861no—
549C23—861no—
550C23—3441no—
551C23—1722no—
552C23—1722no—
553C23C22⋊C4×D4311yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—81no—
557Q8—862no—
558D4—432no—
559D4—864no—
560D4—861no—
561D4—861no—
562D4—861no—
563D4—862no—
564D4—3442no—
565D4—1722no—
566D4—1724no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—432no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—3442no—
582C2×C4—1722no—
583C2×C4—1724no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4C22⋊C4×D4311yescharacteristic
592C2×C4C22⋊C4×D4311yescharacteristic
593C2×C4C22⋊C4×D4311yescharacteristic
594C2×C4#1306335212yes—
595C2×C4#1306335712yes—
596C2×C4C22×C4×D4311yescharacteristic
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4C2×D4×D4311yescharacteristic
599C8—42no—
600C8—41no—
601C8—41no—
602C8—862no—
603C8—1721no—
604C8—1722no—
605C22—21no—
606C22—21no—
607C22—862no—
608C22—862no—
609C22—862no—
610C22—862no—
611C22—3444no—
612C22—1721no—
613C22—1721no—
614C22—1721no—
615C22—1721no—
616C22—1721no—
617C22#1458289912yes—
618C22C2×C22⋊C4×D4311yescharacteristic
619C4—21no—
620C4—21no—
621C4—21no—
622C4—42no—
623C4—42no—
624C4—862no—
625C4—862no—
626C4—862no—
627C4—1721no—
628C4—1721no—
629C4#1458289912yes—
630C4#131×D4311yescharacteristic
631C4#1458366411yescharacteristic
632C4C2×#1306335211yescharacteristic
633C4C2×#1306335711yescharacteristic
634C2—22no—
635C2—3441no—
636C2—1722no—
637C2—1722no—
638C2#1914304311yescharacteristic
639C2C2×#1458289911yescharacteristic
640C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1481C2
socleC22×C43C22×C22⋊C4
prime radical#19148162C2
cosocleC42×C43C24
hypercenter#1481D43
hypocenterC43#17512
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #19143556C2semidirect
3. #19143160C2semidirect
4. #19133059C2semidirect
5. #19133050C2semidirect
6. #19133033C2semidirect
7. #19133021C2semidirect
8. #19133007C2semidirect
9. #19132981C2semidirect
10. C2×#14582626C2semidirect
11. C43×#1481C2semidirect
32. #14582950C22semidirect
36. #14582921C22semidirect
37. C4⋊C8×D43C22semidirect
38. C4×#10621872C22semidirect
40. Q8⋊(C43⋊C8)C22semidirect
41. Q8⋊(C43⋊C8)C22semidirect
51. C43×Q8⋊C8C22semidirect
52. C43×Q8⋊C8C22semidirect
263. D172#131semidirect
322. #1481D43semidirect
365. Q8⋊C8C2×D43semidirect
366. Q8⋊C8C2×D43semidirect
373. C43#17512semidirect

Maximal subgroups

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

subgroupindex
#191481622
#191435562
#191431602
#191330592
#191330502
#191330332
#191330212
#191330072
#191329812
C2×#145826262
C43×#14812
#1751243