Finite Group Databasebeta

← #25128580

Subgroups — #25128580

Order 11008.

1382 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583516C211yesmaximal, characteristic, complemented
2C2×#14583050C211yesmaximal, characteristic, complemented
3#19137177C211yesmaximal, characteristic, complemented
4#19135729C212yesmaximal, complemented
5#19135670C212yesmaximal, complemented
6#19134947C212yesmaximal, complemented
7#19134945C212yesmaximal, complemented
8#19134918C211yesmaximal, characteristic, complemented
9#19134905C211yesmaximal, characteristic, complemented
10#19134664C211yesmaximal, characteristic, complemented
11C2×C43×#447C211yesmaximal, characteristic
12C22×#10621883C2212yes—
13#14583516—24no—
14#14583516—24no—
15C2×#13063324C2211yescharacteristic, complemented
16C2×#13063318—21no—
17C2×#13063312—21no—
18C2×#13063312C2211yescharacteristic, complemented
19C2×#13063306—21no—
20C2×#13063304C2211yescharacteristic
21C2×#13063302—21no—
22C2×#13063290C2211yescharacteristic, complemented
23C2×D4×Dic43C2211yescharacteristic, complemented
24C2×#13063284C2211yescharacteristic
25C2×#13063284C2211yescharacteristic
26#14583050—24no—
27C2×#13063250C2212yescomplemented
28C2×#13063246C2212yes—
29C2×#13063246C2212yescomplemented
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31#14582802—21no—
32#14582802—21no—
33#14582802C2212yes—
34#14582802C2212yes—
35#14582755—21no—
36#14582755—21no—
37#14582662C2212yescomplemented
38#14582661C2212yescomplemented
39#14582653C2212yescomplemented
40#14582653C2212yescomplemented
41C23×D4×C43C2211yescharacteristic
42C22×D8×C43C2212yes—
43C2×#121×C43C2211yescharacteristic
44C43×#447—24no—
45C2×#102×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C23×Dic43—21no—
50C2×#10621883—24no—
51C2×#10621883—24no—
52C2×#10621883—42no—
53C22×C43⋊C8C2312yes—
54#13063324—22no—
55#13063324—22no—
56#13063318—28no—
57#13063312—28no—
58#13063312—22no—
59#13063312—22no—
60#13063306—28no—
61#13063304—22no—
62#13063304D414yes—
63#13063302—28no—
64#13063290—22no—
65#13063290—22no—
66D4×Dic43—22no—
67D4×Dic43—22no—
68#13063284—22no—
69#13063284—22no—
70#13063284—42no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43C2312yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—22no—
84C2×C22⋊Dic43—22no—
85C2×C22⋊Dic43—22no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43D411yescharacteristic
88C2×C22⋊Dic43D411yescharacteristic
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92C2×C4×Dic43C2311yescharacteristic
93#13063250—42no—
94#13063246—24no—
95#13063246—42no—
96C22⋊(C43⋊C8)—22no—
97C25×C43—21no—
98C22×D4×C43—21no—
99C22×D4×C43—24no—
100C22×D4×C43—21no—
101C22×D4×C43—22no—
102C22×D4×C43—22no—
103C22×D4×C43—42no—
104C22×D4×C43C2311yescharacteristic
105C22×D4×C43C2312yes—
106C23×C4×C43C2311yescharacteristic
107C2×D8×C43—24no—
108C2×D8×C43—24no—
109C2×D8×C43—42no—
110C22×C8×C43C2312yes—
111#121×C43—22no—
112#121×C43D414yes—
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C22⋊C4×C43—21no—
115#102×C43—24no—
116C22⋊C8×C43—22no—
117C24×C43—24no—
118C24×C43—21no—
119C24×C43—22no—
120C24×C43—42no—
121C24×C43—42no—
122C24×C43—82no—
123C24×C43—82no—
124C24×C43C2×D411yescharacteristic
125C2×D4×C43—24no—
126C2×D4×C43—21no—
127C2×D4×C43—22no—
128C2×D4×C43—24no—
129C2×D4×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—48no—
136C2×D4×C43—48no—
137C2×D4×C43—42no—
138C2×D4×C43—42no—
139C2×D4×C43—82no—
140C2×D4×C43C2×D412yes—
141C2×D4×C43#4114yes—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—21no—
145C22×C4×C43C2×D412yes—
146C22×C4×C43C2×D412yes—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—24no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—22no—
153C22×Dic43—82no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157C22×Dic43C2×D411yescharacteristic
158C2×Dic86—22no—
159C2×Dic86—22no—
160C2×Dic86—21no—
161C2×Dic86—24no—
162C2×Dic86—82no—
163C2×Dic86C2×D412yes—
164D8×C43—48no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C2×D412yes—
170C22⋊C4×C43—24no—
171C22⋊Dic43—24no—
172C22⋊Dic43—24no—
173C22⋊Dic43—24no—
174C22⋊Dic43—24no—
175C22⋊Dic43—22no—
176C22⋊Dic43—22no—
177C22⋊Dic43—42no—
178C22⋊Dic43—82no—
179C22⋊Dic43—82no—
180C22⋊Dic43—82no—
181C22⋊Dic43—82no—
182#10621883—48no—
183C4⋊Dic43—22no—
184C4⋊Dic43—22no—
185C4⋊Dic43—21no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4⋊Dic43C2×D412yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—24no—
191Dic43⋊C4—24no—
192C4×Dic43—24no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—22no—
206C23×C43—24no—
207C23×C43—48no—
208C23×C43—42no—
209C23×C43—41no—
210C23×C43—42no—
211C23×C43—41no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43—84no—
219C23×C43—84no—
220C23×C43—88no—
221C23×C43—88no—
222C23×C43#12012yes—
223C23×C43C22×D411yescharacteristic
224D4×C43—24no—
225D4×C43—24no—
226D4×C43—24no—
227D4×C43—48no—
228D4×C43—42no—
229D4×C43—42no—
230D4×C43—42no—
231D4×C43—84no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—22no—
237C2×C4×C43—42no—
238C2×C4×C43#12012yes—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×D411yescharacteristic
241C2×C4×C43C2×#4112yes—
242C2×C4×C43H(5,𝔽2)12yes—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—84no—
260Dic86—24no—
261Dic86—42no—
262Dic86—84no—
263C8×C43—42no—
264C43⋊C8—42no—
265#23945—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—44no—
272C22×C43—44no—
273C22×C43—44no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—42no—
277C22×C43—816no—
278C22×C43—82no—
279C22×C43—82no—
280C22×C43—82no—
281C22×C43—82no—
282C22×C43—82no—
283C22×C43—82no—
284C22×C43C2×#12011yescharacteristic
285C22×C43#52511yescharacteristic
286C22×C43#53511yescharacteristic
287C22×C43#57612yes—
288C22×C43#57712yes—
289C4×C43—22no—
290C4×C43—42no—
291C4×C43#54612yes—
292C4×C43#54612yes—
293Dic43—42no—
294Dic43—41no—
295Dic43—42no—
296Dic43—41no—
297Dic43—41no—
298Dic43—41no—
299Dic43—82no—
300C2×#542—431no—
301C2×#450—431no—
302C2×#447D4311yescharacteristic
303#2309—431no—
304#2023—432no—
305#2012—432no—
306#1880—432no—
307#1879—432no—
308#1875—431no—
309#1873—431no—
310#1818—431no—
311C2×C43—42no—
312C2×C43—82no—
313C2×C43—84no—
314C2×C43#240411yescharacteristic
315C2×C43#300811yescharacteristic
316C2×C43#301011yescharacteristic
317C2×C43#311812yes—
318C2×C43#322412yes—
319C23×D4C2×D4311yescharacteristic
320C22×SD16—432no—
321C22×D8C2×D4312yes—
322#542—864no—
323#542—864no—
324C2×C4⋊Q8—431no—
325C2×#126—861no—
326C2×#124—431no—
327C2×#124—861no—
328C2×#123—861no—
329C2×C22⋊Q8—431no—
330C2×C22⋊Q8—861no—
331C2×#121C2×D4311yescharacteristic
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×#117—431no—
335C2×#117—431no—
336#450—864no—
337#447—24no—
338C2×#103—432no—
339C2×#102—432no—
340C2×#102—432no—
341C2×#102C2×D4312yes—
342C2×C22⋊C8—431no—
343C2×C22⋊C8C2×D4311yescharacteristic
344#390—432no—
345#390—432no—
346#390—861no—
347#390—861no—
348#379—861no—
349#379—861no—
350#340—432no—
351#340—432no—
352#336—432no—
353#336—432no—
354C43#2394511yescharacteristic, complemented, Sylow
355C25—21no—
356C22×Q8—431no—
357C22×Q8—861no—
358C22×D4—21no—
359C22×D4—24no—
360C22×D4—21no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—42no—
364C22×D4C22×D4312yes—
365C22×D4C22×D4311yescharacteristic
366C23×C4—861no—
367C23×C4C22×D4311yescharacteristic
368C2×SD16—864no—
369C2×SD16—864no—
370C2×SD16—1722no—
371C2×D8—24no—
372C2×D8—24no—
373C2×D8—42no—
374C22×C8—432no—
375C22×C8C22×D4312yes—
376C4⋊Q8—862no—
377C4⋊Q8—862no—
378#126—868no—
379#124—862no—
380#124—868no—
381#124—862no—
382#123—868no—
383C22⋊Q8—434no—
384C22⋊Q8—868no—
385C22⋊Q8—862no—
386#121—22no—
387#121C22⋊D4314yes—
388C4×Q8—862no—
389C4×Q8—862no—
390C4×D4—862no—
391C4×D4—862no—
392#117—862no—
393#117—862no—
394#117—1722no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—432no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—431no—
405C2×C22⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—862no—
411C2×C22⋊C4—862no—
412C2×C22⋊C4—862no—
413C2×C22⋊C4—862no—
414C2×C22⋊C4—861no—
415C2×C42—431no—
416C2×C42—431no—
417C2×C42—861no—
418C2×C42—861no—
419#103—1722no—
420#102—24no—
421#102—864no—
422#102—1722no—
423C22⋊C8—22no—
424C22⋊C8—862no—
425C24—24no—
426C24—21no—
427C24—22no—
428C24—42no—
429C24—42no—
430C24—82no—
431C24—82no—
432C24D4×D4311yescharacteristic
433C2×Q8—432no—
434C2×Q8—864no—
435C2×Q8—861no—
436C2×Q8—862no—
437C2×Q8—862no—
438C2×Q8—3442no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—82no—
454C2×D4#1062190014yes—
455C2×D4C2×C22⋊D4312yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—864no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—862no—
467C22×C4—3442no—
468C22×C4D4×D4311yescharacteristic
469C22×C4D4×D4312yes—
470C22×C4C2×C22⋊D4312yes—
471C22×C4C23×D4311yescharacteristic
472SD16—1728no—
473D8—48no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—862no—
478C2×C8—862no—
479C2×C8—862no—
480C4⋊C4—21no—
481C4⋊C4—432no—
482C4⋊C4—864no—
483C4⋊C4—864no—
484C4⋊C4—862no—
485C4⋊C4—862no—
486C4⋊C4—864no—
487C4⋊C4—861no—
488C4⋊C4—862no—
489C4⋊C4—862no—
490C4⋊C4C2×C22⋊D4312yes—
491C22⋊C4—24no—
492C22⋊C4—864no—
493C22⋊C4—864no—
494C22⋊C4—864no—
495C22⋊C4—862no—
496C22⋊C4—862no—
497C22⋊C4—864no—
498C22⋊C4—3442no—
499C22⋊C4—3442no—
500C22⋊C4—3442no—
501C22⋊C4—3442no—
502C22⋊C4—1722no—
503C42—864no—
504C42—861no—
505C42—861no—
506C42—861no—
507C42—861no—
508C42—1722no—
509C23—21no—
510C23—22no—
511C23—22no—
512C23—21no—
513C23—22no—
514C23—24no—
515C23—48no—
516C23—42no—
517C23—41no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—41no—
526C23—84no—
527C23—84no—
528C23—88no—
529C23—88no—
530C23#1306329312yes—
531C23C2×D4×D4311yescharacteristic
532Q8—864no—
533Q8—3444no—
534Q8—1722no—
535D4—24no—
536D4—24no—
537D4—24no—
538D4—48no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—84no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—42no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—862no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—862no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—3444no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1721no—
564C2×C4—1722no—
565C2×C4—1721no—
566C2×C4#1306329312yes—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C22×C22⋊D4311yescharacteristic
569C2×C4C2×#1062190012yes—
570C2×C4#1306337012yes—
571C8—42no—
572C8—1722no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—816no—
585C22—82no—
586C22—82no—
587C22—82no—
588C22—82no—
589C22—82no—
590C22—82no—
591C22C2×#1306329311yescharacteristic
592C22#1458340511yescharacteristic
593C22#1458346411yescharacteristic
594C22#1458370012yes—
595C22#1458370912yes—
596C4—22no—
597C4—42no—
598C4—3442no—
599C4—1722no—
600C4—1721no—
601C4—1721no—
602C4—1722no—
603C4—1721no—
604C4—1721no—
605C4#1458353612yes—
606C4#1458354312yes—
607C2—42no—
608C2—84no—
609C2—82no—
610C2#1913791111yescharacteristic
611C2#1914385911yescharacteristic
612C2#1914388011yescharacteristic
613C2#1914477212yes—
614C2#1914568512yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#447C2
socleC23×C43C22×D4
hypercenterC2×#447D43
hypocenterC43#23945
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#14583516C2semidirect
2. C2×#14583050C2semidirect
3. #19137177C2semidirect
4. #19135729C2semidirect
5. #19135670C2semidirect
6. #19134947C2semidirect
7. #19134945C2semidirect
8. #19134918C2semidirect
9. #19134905C2semidirect
10. #19134664C2semidirect
15. C2×#13063324C22semidirect
18. C2×#13063312C22semidirect
22. C2×#13063290C22semidirect
23. C2×D4×Dic43C22semidirect
27. C2×#13063250C22semidirect
29. C2×#13063246C22semidirect
37. #14582662C22semidirect
38. #14582661C22semidirect
39. #14582653C22semidirect
40. #14582653C22semidirect
354. C43#23945semidirect

Maximal subgroups

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

subgroupindex
C2×#145835162
C2×#145830502
#191371772
#191357292
#191356702
#191349472
#191349452
#191349182
#191349052
#191346642
C2×C43×#4472
#2394543