Finite Group Databasebeta

← #25099308

Subgroups — #25099308

Order 11008.

1198 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582900C211yesmaximal, characteristic
2C2×#14582900C211yesmaximal, characteristic
3C2×C4×#10621877C211yesmaximal, characteristic, complemented
4C2×#14582797C211yesmaximal, characteristic, complemented
5#19135295C212yesmaximal, complemented
6#19135288C212yesmaximal, complemented
7#19135281C212yesmaximal, complemented
8#19135274C212yesmaximal, complemented
9#19134316C211yesmaximal, characteristic, complemented
10#19134316C211yesmaximal, characteristic, complemented
11C43×#2297C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C22×C4⋊Dic43C2211yescharacteristic
15C22×C4⋊Dic43C2211yescharacteristic
16C22×Dic43⋊C4—21no—
17#14582900—24no—
18#14582900C418yescomplemented
19C2×#13063249C2212yes—
20C2×#13063249C2212yes—
21C2×#13063246C2212yes—
22C2×#13063246C2212yes—
23C4×#10621877—24no—
24C2×#13063236C2212yes—
25C2×C4×C43⋊C8C2212yes—
26#14582797—21no—
27#14582797—21no—
28#14582797C2212yes—
29#14582797C2212yes—
30C2×C43⋊#95—21no—
31#14582661C2212yes—
32#14582661C2212yes—
33#14582661C2212yes—
34#14582661C2212yes—
35C22×#41×C43C2211yescharacteristic
36C2×#117×C43C2211yescharacteristic
37C22×C42×C43C2211yescharacteristic
38C43×#391C2211yescharacteristic
39C43×#391C2211yescharacteristic
40C43×#390C2211yescharacteristic
41C43×#390C2211yescharacteristic
42C43×#386—21no—
43C43×#386—21no—
44C4×C22⋊C4×C43—21no—
45C4×C22⋊C4×C43—21no—
46C23×Dic43—21no—
47C23×Dic43—21no—
48C2×#10621877—22no—
49C2×#10621877—22no—
50C2×#10621877—22no—
51C2×#10621877—22no—
52C2×#10621877C2×C414yes—
53C2×#10621877D414yes—
54C22×C43⋊C8C2312yes—
55C22×C43⋊C8C2312yes—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—22no—
58C2×C4⋊Dic43—22no—
59C2×C4⋊Dic43—22no—
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43C2×C414yes—
62C2×C4⋊Dic43C2312yes—
63C2×C4⋊Dic43C2312yes—
64C2×Dic43⋊C4—22no—
65C2×Dic43⋊C4—22no—
66C2×Dic43⋊C4—44no—
67#13063249—24no—
68#13063249C2×C418yescomplemented
69#13063246—24no—
70#13063246C2×C418yescomplemented
71#13063236—24no—
72C4×C43⋊C8—24no—
73C43⋊#95—22no—
74C43⋊#95—22no—
75C2×#41×C43—22no—
76C2×#41×C43—22no—
77C2×#41×C43—22no—
78C2×#41×C43—22no—
79C2×#41×C43—22no—
80C2×#41×C43C2×C414yes—
81C22×Q8×C43C2311yescharacteristic
82C22×D4×C43—21no—
83C22×D4×C43C2311yescharacteristic
84C23×C4×C43—21no—
85C23×C4×C43D411yescharacteristic
86C23×C4×C43D411yescharacteristic
87C23×C4×C43C2311yescharacteristic
88#117×C43—22no—
89#117×C43—22no—
90C2×C4⋊C4×C43C2311yescharacteristic
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C42×C43—22no—
98C2×C42×C43—22no—
99C2×C42×C43—21no—
100C2×C42×C43D411yescharacteristic
101C2×C42×C43D411yescharacteristic
102C2×C42×C43C2311yescharacteristic
103C2×C42×C43C2311yescharacteristic
104#95×C43—21no—
105#95×C43—21no—
106#95×C43—21no—
107#95×C43—21no—
108C24×C43—21no—
109C24×C43C2×D411yescharacteristic
110#41×C43—28no—
111#41×C43—28no—
112#41×C43—44no—
113#41×C43—44no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C2×Q8×C43—21no—
119C2×Q8×C43C22×C412yes—
120C2×D4×C43—21no—
121C2×D4×C43—24no—
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—42no—
127C2×D4×C43—42no—
128C2×D4×C43C22×C412yes—
129C22×C4×C43—24no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43—42no—
140C22×C4×C43—42no—
141C22×C4×C43C22×C412yes—
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4112yes—
149C22×C4×C43#4112yes—
150C22×C4×C43#4112yes—
151C22×C4×C43#4112yes—
152C22×C4×C43C2411yescharacteristic
153C22×Dic43—24no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—42no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C22⋊C4×C43—42no—
166C22⋊C4×C43—42no—
167C22⋊C4×C43—42no—
168C22⋊C4×C43—42no—
169C22⋊C4×C43—42no—
170C42×C43—22no—
171C42×C43—22no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—42no—
177C4⋊Dic43—24no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43—22no—
181C4⋊Dic43—42no—
182C4⋊Dic43C22×C414yes—
183Dic43⋊C4—44no—
184Dic43⋊C4—44no—
185#10621877—28no—
186#10621877—28no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8C22×C414yes—
192C2×C43⋊C8C2×D414yes—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—22no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43C4×D412yes—
205C23×C43#12112yes—
206C23×C43#12412yes—
207C23×C43C22×D411yescharacteristic
208Q8×C43—22no—
209Q8×C43—22no—
210Q8×C43—41no—
211Q8×C43—41no—
212D4×C43—22no—
213D4×C43—22no—
214D4×C43—48no—
215D4×C43—41no—
216D4×C43—41no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—22no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—44no—
229C2×C4×C43—44no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—48no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43#11714yes—
240C2×C4×C43C4×D414yes—
241C2×C4×C43C4×D412yes—
242C2×C4×C43#12112yes—
243C2×C4×C43#12314yes—
244C2×C4×C43#12412yes—
245C2×C4×C43#12614yes—
246C2×C4×C43AGL(1,ℤ/8)12yes—
247C2×C4×C43#13712yes—
248C2×C4×C43C23×C411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×C4×C43C2×#4111yescharacteristic
254C2×Dic43—24no—
255C2×Dic43—48no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—84no—
262C43⋊C8—24no—
263C43⋊C8—24no—
264#21093—431nomaximal, Sylow
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—22no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—42no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43#38814yes—
279C22×C43C2×C4×D411yescharacteristic
280C22×C43C2×#12111yescharacteristic
281C22×C43C2×#12411yescharacteristic
282C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
283C22×C43C2×#13711yescharacteristic
284C22×C43#57511yescharacteristic
285C22×C43#57511yescharacteristic
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—41no—
289C4×C43—41no—
290C4×C43—42no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43#38814yes—
294C4×C43C2×#11711yescharacteristic
295C4×C43C2×C4×D411yescharacteristic
296C4×C43C2×#12311yescharacteristic
297C4×C43C2×#12611yescharacteristic
298Dic43—44no—
299Dic43—82no—
300C2×#417—431no—
301C2×#417—431no—
302C2×C4×M16—431no—
303#2297D4311yescharacteristic
304C2×#389—431no—
305#1936—432no—
306#1935—432no—
307#1934—432no—
308#1933—432no—
309#1736—431no—
310#1736—431no—
311C2×C43—24no—
312C2×C43—82no—
313C2×C43C2×#38811yescharacteristic
314C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
315C2×C43C4×#13711yescharacteristic
316C2×C43#305511yescharacteristic
317C2×C43#305611yescharacteristic
318C2×C43#314111yescharacteristic
319C2×C43#314211yescharacteristic
320C22×#41C2×D4311yescharacteristic
321C22×M16—431no—
322C22×M16—431no—
323C2×#117C2×D4311yescharacteristic
324C22×C4⋊C4—431no—
325C22×C4⋊C4—431no—
326C22×C4⋊C4—861no—
327C22×C42C2×D4311yescharacteristic
328#417—438no—
329#417—864no—
330C2×#103—432no—
331C2×#103—432no—
332C2×#102—432no—
333C2×#102—432no—
334C4×M16—864no—
335C2×#97—432no—
336C2×C4×C8—432no—
337#391C2×D4311yescharacteristic
338#391C2×D4311yescharacteristic
339#390C2×D4311yescharacteristic
340#390C2×D4311yescharacteristic
341#389—432no—
342#389—432no—
343#389—861no—
344#389—861no—
345#386—21no—
346#386—21no—
347C4×C22⋊C4—21no—
348C4×C22⋊C4—21no—
349C2×#95—861no—
350#340—432no—
351#340—432no—
352#340—432no—
353#340—432no—
354C43#2109311yescharacteristic, complemented, Sylow
355C2×#41—22no—
356C2×#41—22no—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41C4×D4314yes—
361C22×Q8C22×D4311yescharacteristic
362C22×D4—21no—
363C22×D4C22×D4311yescharacteristic
364C23×C4—21no—
365C23×C4—861no—
366C23×C4—861no—
367C23×C4C22⋊D4311yescharacteristic
368C23×C4C22⋊D4311yescharacteristic
369C23×C4C22×D4311yescharacteristic
370C2×M16—434no—
371C2×M16—434no—
372C2×M16—862no—
373C2×M16—862no—
374C2×M16—862no—
375C2×M16—862no—
376C22×C8—432no—
377C22×C8—432no—
378#117—22no—
379#117—22no—
380C2×C4⋊C4—434no—
381C2×C4⋊C4—432no—
382C2×C4⋊C4—432no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—862no—
389C2×C4⋊C4—862no—
390C2×C4⋊C4—1724no—
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C4⋊C4C22×D4311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42C22⋊D4311yescharacteristic
402C2×C42C22⋊D4311yescharacteristic
403C2×C42C22×D4311yescharacteristic
404C2×C42C22×D4311yescharacteristic
405#103—438no—
406#103—864no—
407#102—438no—
408#102—864no—
409#97—864no—
410C4×C8—864no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—862no—
416#95—862no—
417C24—21no—
418C24C2×C22⋊D4311yescharacteristic
419#41—28no—
420#41—28no—
421#41—44no—
422#41—44no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×C4×D4312yes—
429C2×D4—24no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4C2×C4×D4312yes—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—864no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—1722no—
454C22×C4—1722no—
455C22×C4—1722no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4C2×C4×D4312yes—
459C22×C4#1062189812yes—
460C22×C4D4×D4312yes—
461C22×C4#1062190012yes—
462C22×C4#1062190012yes—
463C22×C4#1062190012yes—
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C2×C22⋊D4311yescharacteristic
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C23×D4311yescharacteristic
470M16—868no—
471M16—868no—
472C2×C8—434no—
473C2×C8—434no—
474C2×C8—862no—
475C2×C8—862no—
476C2×C8—862no—
477C2×C8—862no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—434no—
483C4⋊C4—864no—
484C4⋊C4—862no—
485C4⋊C4—862no—
486C4⋊C4—862no—
487C4⋊C4—1724no—
488C4⋊C4—1722no—
489C4⋊C4—1724no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C42—22no—
496C42—22no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—42no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—22no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23C4×C22⋊D4312yes—
514C23#1306329712yes—
515C23#1306331212yes—
516C23C22×C22⋊D4311yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521D4—22no—
522D4—22no—
523D4—48no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—48no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—864no—
549C2×C4—3444no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1728no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4#1306328114yes—
557C2×C4(C22⋊D43)⋊C414yes—
558C2×C4C4×C22⋊D4312yes—
559C2×C4#1306329712yes—
560C2×C4#1306330714yes—
561C2×C4#1306331212yes—
562C2×C4#1306331814yes—
563C2×C4#1306335012yes—
564C2×C4#1306335512yes—
565C2×C4C22×C4×D4311yescharacteristic
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4C2×#1062190011yescharacteristic
568C2×C4C2×#1062190011yescharacteristic
569C2×C4C2×#1062190011yescharacteristic
570C2×C4C2×#1062189811yescharacteristic
571C8—864no—
572C8—864no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22#1458279314yes—
587C22C2×C4×C22⋊D4311yescharacteristic
588C22C2×#1306329711yescharacteristic
589C22C2×#1306331211yescharacteristic
590C22C2×#1306335011yescharacteristic
591C22C2×#1306335511yescharacteristic
592C22#1458369711yescharacteristic
593C22#1458369711yescharacteristic
594C4—22no—
595C4—22no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—81no—
600C4—81no—
601C4—3442no—
602C4—1724no—
603C4#1458279314yes—
604C4C2×#1306328111yescharacteristic
605C4C2×(C22⋊D43)⋊C411yescharacteristic
606C4C2×#1306330711yescharacteristic
607C4C2×#1306331811yescharacteristic
608C2—24no—
609C2—82no—
610C2C2×#1458279311yescharacteristic
611C2C4×#1306335011yescharacteristic
612C2C4×#1306335511yescharacteristic
613C2#1914421611yescharacteristic
614C2#1914422711yescharacteristic
615C2#1914498811yescharacteristic
616C2#1914499511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2297C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenter#2297D43
hypocenterC43#21093
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
3. C2×C4×#10621877C2semidirect
4. C2×#14582797C2semidirect
5. #19135295C2semidirect
6. #19135288C2semidirect
7. #19135281C2semidirect
8. #19135274C2semidirect
9. #19134316C2semidirect
10. #19134316C2semidirect
18. #14582900C4semidirect
68. #13063249C2×C4semidirect
70. #13063246C2×C4semidirect
354. C43#21093semidirect

Maximal subgroups

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

subgroupindex
C2×#145829002
C2×C4×#106218772
C2×#145827972
#191352952
#191352882
#191352812
#191352742
#191343162
C43×#22972
#2109343