Finite Group Databasebeta

← #25132888

Subgroups — #25132888

Order 11008.

1092 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144388C211yesmaximal, characteristic, complemented
2C4×#13063350C211yesmaximal, characteristic
3#19139549C211yesmaximal, characteristic, complemented
4#19135937C212yesmaximal, complemented
5#19135748C212yesmaximal, complemented
6#19135585C211yesmaximal, characteristic, complemented
7#19135540C211yesmaximal, characteristic, complemented
8#19134971C212yesmaximal
9#19134821C212yesmaximal, complemented
10#19134615C211yesmaximal, characteristic, complemented
11C43×#3503C211yesmaximal, characteristic, complemented
12C2×#13063350C2211yescharacteristic
13C2×#13063301—22no—
14C2×C4×D172C2211yescharacteristic
15#14583196—22no—
16#14583186—21no—
17#14583176—21no—
18#14583009—21no—
19#14582997—21no—
20C4×#10621884—21no—
21C4×#10621882—21no—
22#14582942C2212yes—
23#14582942C2211yescharacteristic
24#14582923C2211yescharacteristic
25C2×#13063252C2212yes—
26#14582903C2211yescharacteristic
27#14582903C2212yes—
28#14582900C2211yescharacteristic
29C4×#10621877C2211yescharacteristic
30#14582834—22no—
31#14582800C2212yes—
32#14582768C2212yes—
33C4×C4⋊Dic43C2211yescharacteristic
34#14582668C2212yes—
35#14582668C2212yes—
36#14582658C2212yes—
37#14582658C2212yes—
38#14582658C2212yes—
39Q82×C43—21no—
40C43×#557—21no—
41C43×#554—21no—
42C43×#554—22no—
43D4×Q8×C43—22no—
44D4×Q8×C43—21no—
45C43×#544—22no—
46C43×#544C2212yes—
47C43×#533—21no—
48C43×#533C2211yescharacteristic
49C2×C4⋊Q8×C43—21no—
50C2×C4⋊Q8×C43C2211yescharacteristic
51C43×#520C2212yes—
52C4×#41×C43C2211yescharacteristic
53C22×D172C2311yescharacteristic
54C22×C4×D43—21no—
55#13063350—22no—
56#13063350Q814yescomplemented
57C2×#10621884—21no—
58C2×#10621882—21no—
59C2×#10621877C2311yescharacteristic
60C2×#10621877C2312yes—
61C2×#10621877C2311yescharacteristic
62#13063301—48no—
63C4×D172—21no—
64C4×D172—21no—
65C4×D172—21no—
66C4×D172—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×Dic43⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—21no—
72C2×C4×Dic43C2312yes—
73#13063258—22no—
74#13063258—21no—
75#13063256—22no—
76#13063256—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)—21no—
79#13063252—24no—
80#13063249—21no—
81#13063246—21no—
82#13063245—22no—
83#13063245—22no—
84#13063245—21no—
85#13063245—21no—
86#13063236—21no—
87C4×C43⋊C8—21no—
88C43⋊#95—21no—
89C2×#41×C43C2311yescharacteristic
90C22×Q8×C43—22no—
91C22×Q8×C43D412yes—
92C4⋊Q8×C43—22no—
93C4⋊Q8×C43—22no—
94C4⋊Q8×C43—24no—
95C4⋊Q8×C43—22no—
96C4⋊Q8×C43—22no—
97C4⋊Q8×C43—21no—
98C4⋊Q8×C43—21no—
99C4⋊Q8×C43—21no—
100C4⋊Q8×C43—21no—
101C4⋊Q8×C43D411yescharacteristic
102C4⋊Q8×C43D411yescharacteristic
103#125×C43—24no—
104#125×C43—22no—
105#125×C43—22no—
106#125×C43D412yes—
107C22⋊Q8×C43—22no—
108C22⋊Q8×C43—22no—
109C22⋊Q8×C43—24no—
110C22⋊Q8×C43—24no—
111C22⋊Q8×C43—21no—
112C22⋊Q8×C43—21no—
113C22⋊Q8×C43—24no—
114C4×Q8×C43—22no—
115C4×Q8×C43—22no—
116C4×Q8×C43—22no—
117C4×Q8×C43—21no—
118C4×Q8×C43—21no—
119C4×Q8×C43D411yescharacteristic
120C4×Q8×C43D411yescharacteristic
121C4×D4×C43—22no—
122C4×D4×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43—24no—
125C4×D4×C43D411yescharacteristic
126C4×D4×C43D411yescharacteristic
127#117×C43—22no—
128#117×C43—21no—
129#117×C43C2311yescharacteristic
130#117×C43C2312yes—
131C2×C4⋊C4×C43—22no—
132C2×C4⋊C4×C43—22no—
133C2×C4⋊C4×C43D412yes—
134C2×C4⋊C4×C43C2312yes—
135C2×C42×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C23×D43—21no—
138#41×C43—21no—
139#41×C43—21no—
140#41×C43C2×Q812yes—
141#41×C43#4112yes—
142C2×Q8×C43—24no—
143C2×Q8×C43—21no—
144C2×Q8×C43—22no—
145C2×Q8×C43—21no—
146C2×Q8×C43—22no—
147C2×Q8×C43—44no—
148C2×Q8×C43—84no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—24no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D414yes—
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2411yescharacteristic
160C22×Dic43—22no—
161C22×Dic43—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172C2×Q812yescomplemented
168C2×C4×D43—44no—
169C2×C4×D43—41no—
170C2×C4×D43—41no—
171C4⋊C4×C43—24no—
172C4⋊C4×C43—24no—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—24no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—22no—
185C4⋊C4×C43C2×D412yes—
186C4⋊C4×C43C2×D412yes—
187C4⋊C4×C43C2×D411yescharacteristic
188C4⋊C4×C43C2×D411yescharacteristic
189C22⋊C4×C43—24no—
190C22⋊C4×C43—21no—
191C22⋊C4×C43—21no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—21no—
194C42×C43—24no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43—21no—
198C42×C43—22no—
199C42×C43C2×D411yescharacteristic
200C42×C43C2×D411yescharacteristic
201C42×C43C2×D411yescharacteristic
202C42×C43C2×D411yescharacteristic
203#10621884—24no—
204#10621882—24no—
205(C2×D43)⋊C4—48no—
206(C2×D43)⋊C4—41no—
207(C2×D43)⋊C4—41no—
208C4⋊Dic43—24no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211Dic43⋊C4—48no—
212C4×Dic43—22no—
213C4×Dic43—22no—
214#10621877—21no—
215#10621877—22no—
216#10621877—21no—
217#10621877—21no—
218#10621877—22no—
219#10621877C2×Q812yescomplemented
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—22no—
223C23×C43—21no—
224C23×C43C22×D411yescharacteristic
225C22×D43—22no—
226C22×D43—42no—
227C22×D43—42no—
228C22×D43—41no—
229C22×D43—41no—
230Q8×C43—21no—
231Q8×C43—42no—
232Q8×C43—44no—
233Q8×C43—42no—
234Q8×C43—82no—
235Q8×C43—84no—
236Q8×C43C22⋊Q812yescomplemented
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—21no—
240D4×C43C22⋊Q812yescomplemented
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—24no—
249C2×C4×C43—22no—
250C2×C4×C43—41no—
251C2×C4×C43—42no—
252C2×C4×C43—42no—
253C2×C4×C43—44no—
254C2×C4×C43—84no—
255C2×C4×C43#12011yescharacteristic
256C2×C4×C43#12011yescharacteristic
257C2×C4×C43#12011yescharacteristic
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C22×Q811yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C432−1+411yescharacteristic
264C2×C4×C432−1+411yescharacteristic
265C2×Dic43—24no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—41no—
270D172—22no—
271D172—22no—
272D172—41no—
273D172—41no—
274C4×D43—82no—
275C4×D43—82no—
276C43⋊C8—22no—
277C43⋊C8—41no—
278C43⋊C8—42no—
279#24320—431nomaximal, Sylow
280C22×C43—21no—
281C22×C43—21no—
282C22×C43—22no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43C2×#12011yescharacteristic
286C22×C43#54811yescharacteristic
287C22×C43D4×Q811yescharacteristic
288C2×D43—44no—
289C2×D43—42no—
290C2×D43—82no—
291C2×D43—81no—
292C2×D43—81no—
293C4×C43—22no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—41no—
298C4×C43—44no—
299C4×C43—42no—
300C4×C43—41no—
301C4×C43—42no—
302C4×C43#45312yes—
303C4×C43C2×C22⋊Q811yescharacteristic
304C4×C43#53611yescharacteristic
305C4×C43#54811yescharacteristic
306C4×C43D4×Q811yescharacteristic
307Dic43—44no—
308Dic43—81no—
309#3503D4311yescharacteristic, complemented
310#3077—431no—
311C4×AGL(1,ℤ/8)—431no—
312#2542—431no—
313#2060—432no—
314#2027—432no—
315#1997—431no—
316#1986—431no—
317#1883—432no—
318#1859—432no—
319#1806—431no—
320C2×C43—21no—
321C2×C43—21no—
322C2×C43—42no—
323C2×C43#240911yescharacteristic
324C2×C43C2×#45311yescharacteristic
325C2×C43#302011yescharacteristic
326D43—82no—
327C2×AGL(1,ℤ/8)—431no—
328Q82—21no—
329#557—21no—
330#554—21no—
331#554—22no—
332D4×Q8—22no—
333D4×Q8—21no—
334#544—22no—
335#544C2×D4312yes—
336#533—21no—
337#533C2×D4311yescharacteristic
338C2×C4⋊Q8—21no—
339C2×C4⋊Q8C2×D4311yescharacteristic
340C2×C22⋊Q8—862no—
341#520C2×D4312yes—
342C4×#41C2×D4311yescharacteristic
343C2×C4×D4—431no—
344#478—862no—
345#476—861no—
346#474—861no—
347#442—861no—
348#440—861no—
349C4×SD16—861no—
350C4×D8—861no—
351#428—432no—
352#428—431no—
353#423—431no—
354C2×#104—432no—
355#418—432no—
356#418—431no—
357#417—431no—
358C4×M16—431no—
359#399—862no—
360#390—432no—
361#384—432no—
362C4×C4⋊C4—431no—
363#343—432no—
364#343—432no—
365#339—432no—
366#339—432no—
367#339—432no—
368C43#2432011yescharacteristic, complemented, Sylow
369C2×#41C22×D4311yescharacteristic
370C22×Q8—22no—
371C22×Q8C22⋊D4312yes—
372C22×D4—431no—
373C23×C4—861no—
374AGL(1,ℤ/8)—434no—
375AGL(1,ℤ/8)—862no—
376C2×SD16—861no—
377C2×D8—861no—
378C2×M16—431no—
379C2×M16—431no—
380C2×M16—432no—
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383C4⋊Q8—24no—
384C4⋊Q8—22no—
385C4⋊Q8—22no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8C22⋊D4311yescharacteristic
391C4⋊Q8C22⋊D4311yescharacteristic
392#125—24no—
393#125—22no—
394#125—22no—
395#125C22⋊D4312yes—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—24no—
399C22⋊Q8—24no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—24no—
403C22⋊Q8—1728no—
404C4×Q8—22no—
405C4×Q8—22no—
406C4×Q8—22no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8C22⋊D4311yescharacteristic
410C4×Q8C22⋊D4311yescharacteristic
411C4×D4—22no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—24no—
415C4×D4—861no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4—861no—
419C4×D4C22⋊D4311yescharacteristic
420C4×D4C22⋊D4311yescharacteristic
421#117—22no—
422#117—21no—
423#117C22×D4311yescharacteristic
424#117C22×D4312yes—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—864no—
430C2×C4⋊C4C22⋊D4312yes—
431C2×C4⋊C4C22×D4312yes—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—864no—
434C2×C42—21no—
435C2×C42—432no—
436C2×C42C22×D4311yescharacteristic
437#107—861no—
438#107—862no—
439#106—861no—
440#106—862no—
441C4⋊C8—861no—
442C4⋊C8—861no—
443#104—864no—
444#103—861no—
445#102—861no—
446#102—861no—
447#102—861no—
448#102—862no—
449#102—862no—
450#97—861no—
451C4×C8—861no—
452#95—861no—
453C24—861no—
454#41—21no—
455#41—21no—
456#41Q8×D4312yes—
457#41#1062190212yes—
458C2×Q8—24no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—44no—
464C2×Q8—84no—
465C2×Q8C2×C22⋊D4311yescharacteristic
466C2×D4—21no—
467C2×D4—432no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4C2×C22⋊D4311yescharacteristic
474C22×C4—21no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—862no—
479C22×C4—861no—
480C22×C4—1724no—
481C22×C4—1721no—
482C22×C4—1721no—
483C22×C4C2×C22⋊D4311yescharacteristic
484C22×C4C2×C22⋊D4314yes—
485C22×C4C2×C22⋊D4311yescharacteristic
486C22×C4C23×D4311yescharacteristic
487SD16—864no—
488D8—864no—
489M16—432no—
490M16—861no—
491M16—862no—
492M16—862no—
493M16—861no—
494M16—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—862no—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—24no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—864no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—1728no—
516C4⋊C4C2×C22⋊D4312yes—
517C4⋊C4C2×C22⋊D4311yescharacteristic
518C4⋊C4C2×C22⋊D4312yes—
519C4⋊C4C2×C22⋊D4311yescharacteristic
520C22⋊C4—24no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—1728no—
526C22⋊C4—1721no—
527C22⋊C4—1721no—
528C42—24no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—22no—
533C42—862no—
534C42—862no—
535C42C2×C22⋊D4311yescharacteristic
536C42C2×C22⋊D4311yescharacteristic
537C42C2×C22⋊D4311yescharacteristic
538C42C2×C22⋊D4311yescharacteristic
539C23—21no—
540C23—862no—
541C23—1722no—
542C23—1722no—
543C23—1721no—
544C23—1721no—
545C23C22×C22⋊D4311yescharacteristic
546Q8—21no—
547Q8—42no—
548Q8—44no—
549Q8—42no—
550Q8—82no—
551Q8—84no—
552Q8#1306330112yescomplemented
553D4—22no—
554D4—22no—
555D4—21no—
556D4—862no—
557D4—862no—
558D4—1721no—
559D4—1721no—
560D4#1306330112yescomplemented
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—44no—
574C2×C4—84no—
575C2×C4—864no—
576C2×C4—3442no—
577C2×C4—3442no—
578C2×C4—1722no—
579C2×C4—1721no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4#1306329411yescharacteristic
583C2×C4#1306329411yescharacteristic
584C2×C4#1306329411yescharacteristic
585C2×C4#1306329411yescharacteristic
586C2×C4C22×C22⋊D4311yescharacteristic
587C2×C4C22×C22⋊D4311yescharacteristic
588C2×C4C2×Q8×D4311yescharacteristic
589C2×C4C2×#1062190211yescharacteristic
590C2×C4#1306337311yescharacteristic
591C2×C4#1306337311yescharacteristic
592C8—862no—
593C8—1722no—
594C8—1721no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—41no—
599C22—41no—
600C22—3442no—
601C22—3441no—
602C22—3441no—
603C22—1724no—
604C22—1722no—
605C22C2×#1306329411yescharacteristic
606C22#1458356011yescharacteristic
607C22Q8×C22⋊D4311yescharacteristic
608C4—21no—
609C4—21no—
610C4—22no—
611C4—21no—
612C4—41no—
613C4—42no—
614C4—41no—
615C4—44no—
616C4—42no—
617C4—3441no—
618C4—1724no—
619C4#1458306712yes—
620C4C2×#1306330111yescharacteristic
621C4#1458347311yescharacteristic
622C4#1458356011yescharacteristic
623C4Q8×C22⋊D4311yescharacteristic
624C2—21no—
625C2—21no—
626C2—42no—
627C2—3442no—
628C2#1913795411yescharacteristic
629C2C2×#1458306711yescharacteristic
630C2#1914395911yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3503C2
socleC22×C43C2×#120
prime radicalC2×#13063350C22
hypercenter#3503D43
hypocenterC43#24320
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #19144388C2semidirect
3. #19139549C2semidirect
4. #19135937C2semidirect
5. #19135748C2semidirect
6. #19135585C2semidirect
7. #19135540C2semidirect
9. #19134821C2semidirect
10. #19134615C2semidirect
11. C43×#3503C2semidirect
56. #13063350Q8semidirect
167. C2×D172C2×Q8semidirect
219. #10621877C2×Q8semidirect
236. Q8×C43C22⋊Q8semidirect
240. D4×C43C22⋊Q8semidirect
309. #3503D43semidirect
368. C43#24320semidirect
552. Q8#13063301semidirect
560. D4#13063301semidirect

Maximal subgroups

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

subgroupindex
#191443882
C4×#130633502
#191395492
#191359372
#191357482
#191355852
#191355402
#191349712
#191348212
#191346152
C43×#35032
#2432043