Finite Group Databasebeta

← #25245436

Subgroups — #25245436

Order 11008.

1468 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583109C211yesmaximal, characteristic, complemented
2C2×#14583104C211yesmaximal, characteristic, complemented
3C2×#14583061C212yesmaximal
4#19142947C211yesmaximal, characteristic, complemented
5#19134936C212yesmaximal, complemented
6#19134929C212yesmaximal, complemented
7#19134907C212yesmaximal, complemented
8#19134600C211yesmaximal, characteristic, complemented
9#19134595C211yesmaximal, characteristic, complemented
10#19134575C211yesmaximal, characteristic, complemented
11C2×C4×#41×C43C211yesmaximal, characteristic
12C22×#10621885C2212yes—
13C22×#10621883C2212yes—
14C2×#13063325C2211yescharacteristic
15C2×#13063304C2212yes—
16#14583109—24no—
17#14583104—24no—
18#14583061—28no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063249C2212yes—
22C2×#13063248C2212yes—
23C2×#13063248C2212yes—
24C2×#13063246C2212yes—
25C2×C22⋊(C43⋊C8)C2212yes—
26#14582805C2212yes—
27#14582797—21no—
28#14582797—21no—
29#14582769C2211yescharacteristic
30#14582759—21no—
31#14582759—21no—
32#14582661C2212yes—
33#14582661C2212yes—
34#14582654C2212yes—
35C22×#41×C43C2211yescharacteristic
36C4×#41×C43—24no—
37C4×#41×C43—24no—
38C2×C4×Q8×C43C2211yescharacteristic
39C2×C4×Q8×C43C2211yescharacteristic
40C2×C4×D4×C43—21no—
41C2×C4×D4×C43—21no—
42C2×C4×D4×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C2×#117×C43—21no—
45C2×#117×C43C2211yescharacteristic
46C22×C42×C43—21no—
47C22×C42×C43C2211yescharacteristic
48C22×Dic86C2312yes—
49C2×#10621885—24no—
50C2×#10621885—24no—
51C2×#10621885—24no—
52C2×#10621883—24no—
53C2×#10621883—24no—
54C2×#10621883—24no—
55C22×C43⋊C8C2312yes—
56C22×C43⋊C8C2312yes—
57#13063325—22no—
58#13063325—22no—
59#13063304—24no—
60#13063304—24no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43C2312yes—
66C2×Dic43⋊C4—22no—
67C2×C22⋊Dic43—22no—
68C4⋊(C43⋊C8)—22no—
69C4⋊(C43⋊C8)—22no—
70#13063249—24no—
71#13063248—24no—
72#13063248—24no—
73#13063246—24no—
74C22⋊(C43⋊C8)—24no—
75C43⋊#95—22no—
76C43⋊#95—22no—
77C2×#41×C43—22no—
78C2×#41×C43—22no—
79C2×#41×C43—22no—
80C2×#41×C43—22no—
81C2×#41×C43—22no—
82C2×#41×C43D414yes—
83C22×Q8×C43C2311yescharacteristic
84C22×D4×C43—21no—
85C22×D4×C43C2311yescharacteristic
86C23×C4×C43—21no—
87C23×C4×C43—21no—
88C23×C4×C43—21no—
89C23×C4×C43D411yescharacteristic
90C23×C4×C43D411yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C4×Q8×C43—22no—
93C4×Q8×C43—22no—
94C4×Q8×C43—22no—
95C4×Q8×C43D414yes—
96C4×D4×C43—28no—
97C4×D4×C43—28no—
98C4×D4×C43—22no—
99C4×D4×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43D414yes—
102#117×C43—28no—
103#117×C43—22no—
104#117×C43—22no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2311yescharacteristic
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C42×C43—28no—
113C2×C42×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43—21no—
116C2×C42×C43—22no—
117C2×C42×C43—22no—
118C2×C42×C43D411yescharacteristic
119C2×C42×C43D411yescharacteristic
120C2×C42×C43C2311yescharacteristic
121C2×C42×C43C2311yescharacteristic
122C24×C43—21no—
123C24×C43C2×D411yescharacteristic
124#41×C43—28no—
125#41×C43—28no—
126#41×C43—28no—
127#41×C43—28no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43C2×D412yes—
132C2×Q8×C43C2×D412yes—
133C2×Q8×C43#4112yes—
134C2×D4×C43—24no—
135C2×D4×C43—24no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—24no—
140C2×D4×C43C2×D412yes—
141C2×D4×C43C2×D412yes—
142C2×D4×C43#4112yes—
143C22×C4×C43—24no—
144C22×C4×C43—24no—
145C22×C4×C43—24no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—24no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—24no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—41no—
161C22×C4×C43—42no—
162C22×C4×C43—42no—
163C22×C4×C43—42no—
164C22×C4×C43—42no—
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43#4112yes—
172C22×C4×C43C2411yescharacteristic
173C22×Dic43—22no—
174C22×Dic43—22no—
175C2×Dic86—22no—
176C2×Dic86—22no—
177C2×Dic86—22no—
178C2×Dic86—22no—
179C2×Dic86—22no—
180C2×Dic86—22no—
181C4⋊C4×C43—24no—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C2×D412yes—
186C4⋊C4×C43C2×D412yes—
187C22⋊C4×C43—24no—
188C22⋊C4×C43—24no—
189C22⋊C4×C43—24no—
190C42×C43—24no—
191C42×C43—24no—
192C42×C43—22no—
193C42×C43—24no—
194C42×C43—22no—
195C42×C43—21no—
196C42×C43—21no—
197C42×C43C2×D412yes—
198C42×C43C2×D412yes—
199C22⋊Dic43—44no—
200#10621885—48no—
201#10621883—48no—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43—42no—
205C4⋊Dic43—42no—
206C4⋊Dic43—42no—
207C4⋊Dic43—42no—
208Dic43⋊C4—44no—
209C2×C43⋊C8—22no—
210C2×C43⋊C8—22no—
211C2×C43⋊C8—22no—
212C2×C43⋊C8—22no—
213C2×C43⋊C8—22no—
214C2×C43⋊C8—22no—
215C23×C43—21no—
216C23×C43—22no—
217C23×C43—22no—
218C23×C43—21no—
219C23×C43—22no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43#12112yes—
229C23×C43C22×D411yescharacteristic
230Q8×C43—22no—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43#12114yes—
234D4×C43—216no—
235D4×C43—22no—
236D4×C43—22no—
237D4×C43—22no—
238D4×C43#12114yes—
239C2×C4×C43—216no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—21no—
245C2×C4×C43—22no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—21no—
254C2×C4×C43—22no—
255C2×C4×C43—22no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—44no—
259C2×C4×C43—48no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—44no—
265C2×C4×C43—48no—
266C2×C4×C43#12012yes—
267C2×C4×C43#12012yes—
268C2×C4×C43#12112yes—
269C2×C4×C43#13512yes—
270C2×C4×C43#13712yes—
271C2×C4×C43#13712yes—
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43—42no—
283C2×Dic43—42no—
284Dic86—42no—
285Dic86—42no—
286Dic86—42no—
287Dic86—42no—
288C43⋊C8—42no—
289C43⋊C8—42no—
290#32907—431nomaximal, Sylow
291C22×C43—24no—
292C22×C43—22no—
293C22×C43—22no—
294C22×C43—22no—
295C22×C43—41no—
296C22×C43—42no—
297C22×C43—41no—
298C22×C43—42no—
299C22×C43—41no—
300C22×C43—42no—
301C22×C43—41no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43C2×#12011yescharacteristic
306C22×C43C2×#12111yescharacteristic
307C22×C43#52511yescharacteristic
308C22×C43C2×#13511yescharacteristic
309C22×C43C2×#13711yescharacteristic
310C22×C43C2×#13711yescharacteristic
311C22×C43#57511yescharacteristic
312C4×C43—22no—
313C4×C43—24no—
314C4×C43—22no—
315C4×C43—22no—
316C4×C43—41no—
317C4×C43—42no—
318C4×C43—42no—
319C4×C43#45214yescomplemented
320C4×C43C2×#12111yescharacteristic
321C4×C43C2×#12111yescharacteristic
322C4×C43#52511yescharacteristic
323C4×C43#52511yescharacteristic
324Dic43—82no—
325Dic43—82no—
326C2×C4×#41D4311yescharacteristic
327C2×#462—431no—
328C2×#461—431no—
329C2×#452—432no—
330#2857—431no—
331#1878—432no—
332#1877—432no—
333#1873—432no—
334#1803—431no—
335#1802—431no—
336#1797—431no—
337C2×C43—42no—
338C2×C43—44no—
339C2×C43#284711yescharacteristic
340C2×C43C2×#45211yescharacteristic
341C2×C43#300711yescharacteristic
342C2×C43#303511yescharacteristic
343C2×C43#303911yescharacteristic
344C2×C43#310711yescharacteristic
345C2×C43#311611yescharacteristic
346C22×#41C2×D4311yescharacteristic
347C22×Q16—432no—
348C22×SD16—432no—
349C2×C4⋊Q8—431no—
350C2×C22⋊Q8—432no—
351C4×#41—24no—
352C4×#41—24no—
353C2×C4×Q8C2×D4311yescharacteristic
354C2×C4×Q8C2×D4311yescharacteristic
355C2×C4×D4—21no—
356C2×C4×D4—21no—
357C2×C4×D4C2×D4311yescharacteristic
358C2×C4×D4C2×D4311yescharacteristic
359C2×#117—21no—
360C2×#117C2×D4311yescharacteristic
361C22×C42—21no—
362C22×C42C2×D4311yescharacteristic
363#462—864no—
364#461—864no—
365#452—868no—
366C2×C4⋊C8—431no—
367C2×C4⋊C8—431no—
368C2×#103—432no—
369C2×#103—432no—
370C2×#103—432no—
371C2×#102—432no—
372C2×C22⋊C8—432no—
373#391—432no—
374#389—861no—
375#389—861no—
376#384—431no—
377#380—861no—
378#380—861no—
379#340—432no—
380#340—432no—
381#336—432no—
382C43#3290711yescharacteristic, complemented, Sylow
383C2×#41—22no—
384C2×#41—22no—
385C2×#41—22no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41D17214yes—
389C22×Q8—432no—
390C22×Q8C22×D4311yescharacteristic
391C22×D4—21no—
392C22×D4C22×D4311yescharacteristic
393C23×C4—21no—
394C23×C4—21no—
395C23×C4—21no—
396C23×C4C22⋊D4311yescharacteristic
397C23×C4C22⋊D4311yescharacteristic
398C23×C4C22×D4311yescharacteristic
399C2×Q16—864no—
400C2×Q16—864no—
401C2×Q16—864no—
402C2×SD16—864no—
403C2×SD16—864no—
404C2×SD16—864no—
405C22×C8—432no—
406C22×C8—432no—
407C4⋊Q8—862no—
408C4⋊Q8—862no—
409C22⋊Q8—864no—
410C22⋊Q8—864no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8C22⋊D4314yes—
415C4×D4—28no—
416C4×D4—28no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4C22⋊D4314yes—
421#117—28no—
422#117—22no—
423#117—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—432no—
427C2×C4⋊C4—862no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C4⋊C4C22×D4311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—862no—
438C2×C42—28no—
439C2×C42—21no—
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42C22⋊D4311yescharacteristic
445C2×C42C22⋊D4311yescharacteristic
446C2×C42C22×D4311yescharacteristic
447C2×C42C22×D4311yescharacteristic
448C4⋊C8—862no—
449C4⋊C8—862no—
450#103—864no—
451#103—864no—
452#103—864no—
453#102—864no—
454C22⋊C8—864no—
455#95—862no—
456#95—862no—
457C24—21no—
458C24C2×C22⋊D4311yescharacteristic
459#41—28no—
460#41—28no—
461#41—28no—
462#41—28no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—862no—
467C2×Q8—862no—
468C2×Q8—862no—
469C2×Q8—862no—
470C2×Q8—862no—
471C2×Q8—862no—
472C2×Q8C2×D17212yes—
473C2×Q8#1062189812yes—
474C2×Q8C2×C22⋊D4312yes—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4C2×D17212yes—
482C2×D4#1062189812yes—
483C2×D4C2×C22⋊D4312yes—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—24no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—41no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—862no—
507C22×C4—862no—
508C22×C4C2×D17212yes—
509C22×C4#1062189812yes—
510C22×C4C2×C22⋊D4311yescharacteristic
511C22×C4C2×C22⋊D4311yescharacteristic
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C23×D4311yescharacteristic
516Q16—1728no—
517SD16—1728no—
518C2×C8—862no—
519C2×C8—862no—
520C2×C8—862no—
521C2×C8—862no—
522C2×C8—862no—
523C2×C8—862no—
524C4⋊C4—24no—
525C4⋊C4—24no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—862no—
529C4⋊C4—862no—
530C4⋊C4—1722no—
531C4⋊C4—1722no—
532C4⋊C4—1722no—
533C4⋊C4—1724no—
534C4⋊C4—1722no—
535C4⋊C4C2×C22⋊D4312yes—
536C4⋊C4C2×C22⋊D4312yes—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—24no—
540C22⋊C4—1724no—
541C42—24no—
542C42—24no—
543C42—22no—
544C42—24no—
545C42—22no—
546C42—21no—
547C42—21no—
548C42C2×C22⋊D4312yes—
549C42C2×C22⋊D4312yes—
550C23—21no—
551C23—22no—
552C23—22no—
553C23—21no—
554C23—22no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23#1306329912yes—
564C23C22×C22⋊D4311yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—22no—
568Q8—1722no—
569Q8—1722no—
570Q8—1722no—
571Q8—1722no—
572Q8#1306329914yes—
573D4—216no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4#1306329914yes—
578C2×C4—216no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—44no—
598C2×C4—48no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—44no—
604C2×C4—48no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4#1306329412yes—
612C2×C4#1306329412yes—
613C2×C4#1306329912yes—
614C2×C4#1306334512yes—
615C2×C4#1306335512yes—
616C2×C4#1306335512yes—
617C2×C4C22×C22⋊D4311yescharacteristic
618C2×C4C22×C22⋊D4311yescharacteristic
619C2×C4C22×D17211yescharacteristic
620C2×C4C2×#1062189811yescharacteristic
621C2×C4C2×#1062189811yescharacteristic
622C2×C4C2×#1062189811yescharacteristic
623C8—1722no—
624C8—1722no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—24no—
629C22—41no—
630C22—42no—
631C22—42no—
632C22—41no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—42no—
637C22—41no—
638C22—42no—
639C22C2×#1306329411yescharacteristic
640C22C2×#1306329911yescharacteristic
641C22#1458341011yescharacteristic
642C22C2×#1306334511yescharacteristic
643C22C2×#1306335511yescharacteristic
644C22C2×#1306335511yescharacteristic
645C22#1458369711yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—24no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—3442no—
654C4—3442no—
655C4#1458306114yescomplemented
656C4C2×#1306329911yescharacteristic
657C4C2×#1306329911yescharacteristic
658C4#1458341011yescharacteristic
659C4#1458341011yescharacteristic
660C2—42no—
661C2—44no—
662C2#1914287711yescharacteristic
663C2C2×#1458306111yescharacteristic
664C2#1914385511yescharacteristic
665C2#1914405011yescharacteristic
666C2#1914408211yescharacteristic
667C2#1914466611yescharacteristic
668C2#1914475711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C4×#41×C43C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
hypercenterC2×C4×#41D43
hypocenterC43#32907
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14583109C2semidirect
2. C2×#14583104C2semidirect
4. #19142947C2semidirect
5. #19134936C2semidirect
6. #19134929C2semidirect
7. #19134907C2semidirect
8. #19134600C2semidirect
9. #19134595C2semidirect
10. #19134575C2semidirect
319. C4×C43#452semidirect
382. C43#32907semidirect
655. C4#14583061semidirect

Maximal subgroups

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

subgroupindex
C2×#145831092
C2×#145831042
C2×#145830612
#191429472
#191349362
#191349292
#191349072
#191346002
#191345952
#191345752
C2×C4×#41×C432
#3290743