Finite Group Databasebeta

← #25099303

Subgroups — #25099303

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×#14582898C211yesmaximal, characteristic
2C2×#14582898C211yesmaximal, characteristic
3C2×C4×#10621877C211yesmaximal, characteristic, complemented
4#19137085C211yesmaximal, characteristic
5#19135291C212yesmaximal, complemented
6#19135284C212yesmaximal, complemented
7#19135277C212yesmaximal, complemented
8#19135270C212yesmaximal, complemented
9#19134314C211yesmaximal, characteristic, complemented
10#19134314C211yesmaximal, characteristic, complemented
11C2×C43×#389C211yesmaximal, characteristic, complemented
12C22×#10621898C2211yescharacteristic
13C22×#10621877C2211yescharacteristic
14C22×#10621877C2211yescharacteristic
15C2×#13063284C2211yescharacteristic
16#14582898—24no—
17#14582898C418yescomplemented
18C2×#13063248C2212yes—
19C2×#13063248C2212yes—
20C2×#13063245C2212yes—
21C2×#13063245C2212yes—
22C4×#10621877—24no—
23C2×#13063236C2212yes—
24C2×C4×C43⋊C8C2212yes—
25#14582805C2211yescharacteristic
26#14582805C2211yescharacteristic
27#14582801C2211yescharacteristic
28#14582801C2211yescharacteristic
29#14582778—21no—
30#14582778—21no—
31C4×(C2×D43)⋊C4—21no—
32C4×(C2×D43)⋊C4—21no—
33#14582661C2212yes—
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37C22×C4⋊C4×C43—21no—
38C22×C4⋊C4×C43C2211yescharacteristic
39C22×C4⋊C4×C43C2211yescharacteristic
40C22×C42×C43C2211yescharacteristic
41C43×#389—21no—
42C43×#389—21no—
43C43×#389C2212yes—
44C43×#389C2212yes—
45C2×#95×C43—21no—
46C2×#10621898—22no—
47C2×#10621898—22no—
48C2×#10621898—22no—
49C2×#10621898—22no—
50C2×#10621898—22no—
51C2×#10621898C2×C414yes—
52C22×Dic86C2311yescharacteristic
53C22×D172C2311yescharacteristic
54C22×C22⋊D43—21no—
55C22×C4×D43—21no—
56C2×#10621877—22no—
57C2×#10621877—22no—
58C2×#10621877—22no—
59C2×#10621877—22no—
60C2×#10621877C2×C414yes—
61C2×#10621877D414yes—
62C22×C43⋊C8C2312yes—
63C22×C43⋊C8C2312yes—
64#13063284—22no—
65#13063284—22no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C22⋊Dic43—21no—
69C2×(C2×D43)⋊C4—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×C4×Dic43—21no—
74#13063248—24no—
75#13063248C2×C418yescomplemented
76#13063245—24no—
77#13063245C2×C418yescomplemented
78#13063236—24no—
79C4×C43⋊C8—24no—
80C43⋊#95—21no—
81C43⋊#95—21no—
82C43⋊#95—21no—
83C43⋊#95—21no—
84C23×C4×C43—21no—
85C23×C4×C43—21no—
86C23×C4×C43D411yescharacteristic
87C23×C4×C43D411yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—22no—
91C2×C4⋊C4×C43—22no—
92C2×C4⋊C4×C43—22no—
93C2×C4⋊C4×C43—22no—
94C2×C4⋊C4×C43—22no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—44no—
97C2×C4⋊C4×C43C2×C414yes—
98C2×C4⋊C4×C43C2312yes—
99C2×C4⋊C4×C43C2312yes—
100C2×C42×C43—22no—
101C2×C42×C43—22no—
102C2×C42×C43D411yescharacteristic
103C2×C42×C43D411yescharacteristic
104C2×C42×C43C2311yescharacteristic
105C2×C42×C43C2311yescharacteristic
106#95×C43—22no—
107#95×C43—22no—
108C24×C43C2×D411yescharacteristic
109C23×D43—21no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—24no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—41no—
118C22×C4×C43—41no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C22×C412yes—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43#4112yes—
132C22×C4×C43#4112yes—
133C22×C4×C43#4112yes—
134C22×C4×C43#4112yes—
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—24no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142#10621898—28no—
143#10621898—28no—
144#10621898—44no—
145#10621898—44no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C22×C412yes—
152C2×C4×D43—24no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C22×C412yes—
161C4⋊C4×C43—24no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—44no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43—44no—
168C4⋊C4×C43C22×C414yes—
169C42×C43—22no—
170C42×C43—22no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175C22⋊Dic43—42no—
176(C2×D43)⋊C4—42no—
177(C2×D43)⋊C4—42no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4×Dic43—42no—
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×C43C4×D412yes—
198C23×C43#12112yes—
199C23×C43#12412yes—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—41no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—24no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—44no—
220C2×C4×C43—44no—
221C2×C4×C43—48no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—84no—
228C2×C4×C43#11714yes—
229C2×C4×C43C4×D412yes—
230C2×C4×C43C4×D414yes—
231C2×C4×C43#12112yes—
232C2×C4×C43#12314yes—
233C2×C4×C43#12412yes—
234C2×C4×C43#12614yes—
235C2×C4×C43AGL(1,ℤ/8)12yes—
236C2×C4×C43#13712yes—
237C2×C4×C43C23×C411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C22⋊D43—48no—
244C2×Dic43—22no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253D172—22no—
254D172—22no—
255D172—41no—
256D172—41no—
257C4×D43—48no—
258Dic86—22no—
259Dic86—22no—
260Dic86—41no—
261Dic86—41no—
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#38814yes—
272C22×C43C2×C4×D411yescharacteristic
273C22×C43C2×#12111yescharacteristic
274C22×C43C2×#12411yescharacteristic
275C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C43C2×#13711yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—42no—
282C2×D43—81no—
283C2×D43—81no—
284C2×D43—81no—
285C2×D43—81no—
286C4×C43—22no—
287C4×C43—22no—
288C4×C43—44no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—82no—
292C4×C43#38814yes—
293C4×C43C2×#11711yescharacteristic
294C4×C43C2×C4×D411yescharacteristic
295C4×C43C2×#12311yescharacteristic
296C4×C43C2×#12611yescharacteristic
297Dic43—42no—
298Dic43—81no—
299Dic43—81no—
300C2×#417—431no—
301C2×#417—431no—
302C2×C4×M16—431no—
303#2297—431no—
304C2×#389D4311yescharacteristic, complemented
305#1936—432no—
306#1935—432no—
307#1934—432no—
308#1933—432no—
309#1736—431no—
310#1736—431no—
311C2×C43—24no—
312C2×C43C2×#38811yescharacteristic
313C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
314C2×C43C4×#13711yescharacteristic
315C2×C43#305511yescharacteristic
316C2×C43#305611yescharacteristic
317C2×C43#314111yescharacteristic
318C2×C43#314211yescharacteristic
319D43—82no—
320C22×#41—431no—
321C22×M16—431no—
322C22×M16—431no—
323C2×#117—431no—
324C22×C4⋊C4—21no—
325C22×C4⋊C4C2×D4311yescharacteristic
326C22×C4⋊C4C2×D4311yescharacteristic
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#391—431no—
338#391—431no—
339#390—431no—
340#390—431no—
341#389—21no—
342#389—21no—
343#389C2×D4312yes—
344#389C2×D4312yes—
345#386—861no—
346#386—861no—
347C4×C22⋊C4—861no—
348C4×C22⋊C4—861no—
349C2×#95—21no—
350#340—432no—
351#340—432no—
352#340—432no—
353#340—432no—
354C43#2109311yescharacteristic, complemented, Sylow
355C2×#41—434no—
356C2×#41—862no—
357C2×#41—862no—
358C2×#41—862no—
359C2×#41—862no—
360C2×#41—862no—
361C22×Q8—431no—
362C22×D4—431no—
363C22×D4—861no—
364C23×C4—21no—
365C23×C4—21no—
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—862no—
379#117—862no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—431no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4C4×D4314yes—
391C2×C4⋊C4C22×D4312yes—
392C2×C4⋊C4C22×D4312yes—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—861no—
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—22no—
412#95—22no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417C24—861no—
418C24C2×C22⋊D4311yescharacteristic
419#41—868no—
420#41—868no—
421#41—1724no—
422#41—1724no—
423C2×Q8—432no—
424C2×Q8—861no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×D4—432no—
430C2×D4—864no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—1722no—
437C2×D4—1722no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—861no—
453C22×C4—864no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—1722no—
457C22×C4—1722no—
458C22×C4C2×C4×D4312yes—
459C22×C4#1062189812yes—
460C22×C4D4×D4312yes—
461C22×C4#1062190012yes—
462C22×C4#1062190212yes—
463C22×C4#1062190212yes—
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—24no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—44no—
483C4⋊C4—42no—
484C4⋊C4—44no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4C2×C4×D4314yes—
490C22⋊C4—1722no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C22⋊C4—1722no—
494C22⋊C4—1722no—
495C42—22no—
496C42—22no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—1722no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—862no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23C4×C22⋊D4312yes—
514C23#1306329712yes—
515C23#1306331412yes—
516C23C22×C22⋊D4311yescharacteristic
517Q8—862no—
518Q8—862no—
519Q8—1721no—
520Q8—1721no—
521D4—862no—
522D4—862no—
523D4—1728no—
524D4—1721no—
525D4—1721no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—24no—
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—48no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—84no—
546C2×C4—862no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1728no—
556C2×C4#1306328314yes—
557C2×C4C4×C22⋊D4312yes—
558C2×C4#1306328714yes—
559C2×C4#1306329712yes—
560C2×C4#1306331014yes—
561C2×C4#1306331412yes—
562C2×C4#1306332014yes—
563C2×C4#1306335112yes—
564C2×C4#1306335612yes—
565C2×C4C22×C4×D4311yescharacteristic
566C2×C4C2×D4×D4311yescharacteristic
567C2×C4C2×#1062190011yescharacteristic
568C2×C4C2×#1062189811yescharacteristic
569C2×C4C2×#1062190211yescharacteristic
570C2×C4C2×#1062190211yescharacteristic
571C8—864no—
572C8—864no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—3441no—
580C22—3441no—
581C22—3441no—
582C22—3441no—
583C22—1722no—
584C22—1722no—
585C22—1722no—
586C22#1458278914yes—
587C22C2×C4×C22⋊D4311yescharacteristic
588C22C2×#1306329711yescharacteristic
589C22C2×#1306331411yescharacteristic
590C22C2×#1306335111yescharacteristic
591C22C2×#1306335611yescharacteristic
592C22#1458369711yescharacteristic
593C22#1458369711yescharacteristic
594C4—22no—
595C4—22no—
596C4—41no—
597C4—41no—
598C4—44no—
599C4—82no—
600C4—3441no—
601C4—3441no—
602C4—1722no—
603C4#1458278914yes—
604C4C2×#1306328311yescharacteristic
605C4C2×#1306328711yescharacteristic
606C4C2×#1306331011yescharacteristic
607C4C2×#1306332011yescharacteristic
608C2—24no—
609C2—3442no—
610C2C2×#1458278911yescharacteristic
611C2C4×#1306335111yescharacteristic
612C2C4×#1306335611yescharacteristic
613C2#1914421011yescharacteristic
614C2#1914422111yescharacteristic
615C2#1914499111yescharacteristic
616C2#1914499811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#389C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×#389D43
hypocenterC43#21093
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
3. C2×C4×#10621877C2semidirect
5. #19135291C2semidirect
6. #19135284C2semidirect
7. #19135277C2semidirect
8. #19135270C2semidirect
9. #19134314C2semidirect
10. #19134314C2semidirect
11. C2×C43×#389C2semidirect
17. #14582898C4semidirect
75. #13063248C2×C4semidirect
77. #13063245C2×C4semidirect
304. C2×#389D43semidirect
354. C43#21093semidirect

Maximal subgroups

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

subgroupindex
C2×#145828982
C2×C4×#106218772
#191370852
#191352912
#191352842
#191352772
#191352702
#191343142
C2×C43×#3892
#2109343