Finite Group Databasebeta

← #25152800

Subgroups — #25152800

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063314C211yesmaximal, characteristic
2C2×#14583255C212yesmaximal, complemented
3#19142903C211yesmaximal, characteristic, complemented
4#19135833C212yesmaximal, complemented
5#19135832C212yesmaximal, complemented
6#19135403C212yesmaximal, complemented
7#19134530C211yesmaximal, characteristic, complemented
8#19134527C211yesmaximal, characteristic
9#19134525C211yesmaximal, characteristic
10C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
11C43×#1787C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C2×#13063316C2211yescharacteristic, complemented
14C2×#13063314—28no—
15C2×#13063314—21no—
16C2×#13063314—21no—
17C2×#13063314C2212yes—
18C2×#13063314C2212yes—
19C22×(C2×D43)⋊C4—21no—
20C22×(C2×D43)⋊C4—21no—
21C22×C4×Dic43C2211yescharacteristic
22#14583255—28no—
23C2×#13063249C2212yescomplemented
24C2×#13063249C2212yescomplemented
25C2×#13063247C2212yes—
26C2×#13063247C2212yes—
27C2×#13063245C2212yes—
28C2×#13063245C2212yes—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×C8×Dic43C2212yescomplemented
31#14582798C2211yescharacteristic, complemented
32#14582795C2211yescharacteristic, complemented
33#14582786—21no—
34#14582782—21no—
35#14582774—21no—
36#14582771—21no—
37#14582764C2211yescharacteristic, complemented
38#14582759C2211yescharacteristic
39#14582653C2212yescomplemented
40C23×Q8×C43C2211yescharacteristic
41C2×#103×C43C2212yescomplemented
42C2×#103×C43C2212yescomplemented
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C24×D43—21no—
46C22×D172—21no—
47C22×D172—24no—
48C22×D172—22no—
49C22×D172—22no—
50C22×D172—42no—
51C22×D172C2312yes—
52C23×Dic43D411yescharacteristic
53C23×Dic43D411yescharacteristic
54C22×C43⋊C8C2312yes—
55#13063316—24no—
56#13063314—28no—
57#13063314—28no—
58#13063314—24no—
59#13063314—24no—
60#13063314—24no—
61#13063314D418yes—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2311yescharacteristic
66C2×Dic43⋊C4—21no—
67C2×Dic43⋊C4—21no—
68C2×C22⋊Dic43—21no—
69C2×(C2×D43)⋊C4—28no—
70C2×(C2×D43)⋊C4—28no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—22no—
75C2×C4×Dic43—24no—
76C2×C4×Dic43D411yescharacteristic
77C2×C4×Dic43D411yescharacteristic
78C2×C4×Dic43C2311yescharacteristic
79C2×C4×Dic43C2311yescharacteristic
80#13063249—24no—
81#13063249—42no—
82#13063247—24no—
83#13063247—42no—
84#13063245—24no—
85#13063245—42no—
86C22⋊(C43⋊C8)—22no—
87C8×Dic43—24no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C22×Q8×C43—24no—
94C22×Q8×C43—21no—
95C22×Q8×C43—22no—
96C22×Q8×C43—22no—
97C22×Q8×C43—42no—
98C22×Q8×C43C2312yes—
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101C22×C8×C43C2312yes—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C22⋊C4×C43—21no—
105#103×C43—24no—
106#103×C43—42no—
107C22⋊C8×C43—22no—
108#95×C43—21no—
109C24×C43C2×D411yescharacteristic
110C23×D43—24no—
111C23×D43—22no—
112C23×D43—42no—
113C23×D43—42no—
114C23×D43—42no—
115C23×D43—42no—
116C23×D43—42no—
117C23×D43—42no—
118C2×Q8×C43—24no—
119C2×Q8×C43—22no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—48no—
125C2×Q8×C43—48no—
126C2×Q8×C43—42no—
127C2×Q8×C43—42no—
128C2×Q8×C43C2×D414yes—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—24no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43#4112yes—
139C22×C4×C43#4112yes—
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—41no—
148C22×Dic43—41no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—24no—
154C2×D172—22no—
155C2×D172—22no—
156C2×D172—22no—
157C2×D172—22no—
158C2×D172—22no—
159C2×D172—48no—
160C2×D172—48no—
161C2×D172—42no—
162C2×D172—42no—
163C2×D172C2×D414yes—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C2×C8×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C22⋊C4×C43—42no—
170C22⋊Dic43—42no—
171(C2×D43)⋊C4—28no—
172(C2×D43)⋊C4—28no—
173(C2×D43)⋊C4—28no—
174(C2×D43)⋊C4—28no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—42no—
178C4⋊Dic43—42no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181C4×Dic43—22no—
182C4×Dic43—22no—
183C4×Dic43—22no—
184C4×Dic43C2×D414yes—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C23×C43—21no—
189C23×C43—21no—
190C23×C43—21no—
191C23×C43—21no—
192C23×C43#12412yes—
193C23×C43#13512yes—
194C23×C43#13512yes—
195C23×C43C22×D411yescharacteristic
196C22×D43—24no—
197C22×D43—48no—
198C22×D43—48no—
199C22×D43—48no—
200C22×D43—42no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—84no—
207C22×D43—84no—
208C22×D43—84no—
209C22×D43—84no—
210Q8×C43—24no—
211Q8×C43—24no—
212Q8×C43—48no—
213Q8×C43—42no—
214Q8×C43—42no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—24no—
218C2×C4×C43—24no—
219C2×C4×C43—24no—
220C2×C4×C43—48no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43#12412yes—
230C2×C4×C43C22×D412yes—
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43H(5,𝔽2)12yes—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—44no—
245C2×Dic43—44no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43#12012yes—
253C2×Dic43#12012yes—
254D172—24no—
255D172—24no—
256D172—48no—
257D172—42no—
258D172—42no—
259C8×C43—42no—
260C43⋊C8—42no—
261#25859—431nomaximal, Sylow
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43#48814yescomplemented
269C22×C43C2×#12011yescharacteristic
270C22×C43C2×#12411yescharacteristic
271C22×C43#53511yescharacteristic
272C22×C43C2×#13511yescharacteristic
273C22×C43C2×#13511yescharacteristic
274C22×C43#57511yescharacteristic
275C22×C43#57511yescharacteristic
276C2×D43—44no—
277C2×D43—44no—
278C2×D43—44no—
279C2×D43—816no—
280C2×D43—82no—
281C2×D43—82no—
282C2×D43—82no—
283C2×D43—82no—
284C4×C43—22no—
285C4×C43—44no—
286C4×C43—81no—
287C4×C43—81no—
288C4×C43#54612yes—
289C4×C43#54612yes—
290Dic43—22no—
291Dic43—22no—
292Dic43—41no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296C22×#124—431no—
297C2×#488—432no—
298#2851—431no—
299#2042—432no—
300#2042—432no—
301#1958—432no—
302#1787—431no—
303#1787D4311yescharacteristic, complemented
304#1786—431no—
305#1786—431no—
306C4×C22⋊C8—431no—
307C2×C43—24no—
308C2×C43#243511yescharacteristic
309C2×C43#300211yescharacteristic
310C2×C43#300211yescharacteristic
311C2×C43C2×#48811yescharacteristic
312C2×C43#314011yescharacteristic
313C2×C43#321111yescharacteristic
314C2×C43#321111yescharacteristic
315D43—84no—
316C23×Q8C2×D4311yescharacteristic
317C23×D4—431no—
318C2×#125—431no—
319C2×#124—432no—
320C2×#124—432no—
321C2×#124—861no—
322C2×#124—861no—
323C2×#124—868no—
324C22×C22⋊C4—861no—
325C22×C22⋊C4—861no—
326C22×C42—431no—
327#488—868no—
328C2×#103—432no—
329C2×#103—432no—
330C2×#103C2×D4312yescomplemented
331C2×#103C2×D4312yescomplemented
332C2×#102—432no—
333C2×#102—432no—
334C2×#102—432no—
335C2×#102—432no—
336C2×C22⋊C8—431no—
337C2×C22⋊C8C2×D4311yescharacteristic
338C2×C4×C8—432no—
339#389—431no—
340#389—431no—
341#387—861no—
342#387—861no—
343#385—861no—
344#385—861no—
345#382—431no—
346#380—431no—
347#380C2×D4311yescharacteristic
348#336—432no—
349C43#2585911yescharacteristic, complemented, Sylow
350C25—861no—
351C22×Q8—24no—
352C22×Q8—21no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—42no—
356C22×Q8C22×D4312yes—
357C22×D4—432no—
358C22×D4—864no—
359C22×D4—862no—
360C22×D4—861no—
361C22×D4—862no—
362C22×D4—1722no—
363C23×C4—21no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4C22×D4311yescharacteristic
367C22×C8—432no—
368C22×C8C22×D4312yes—
369#125—864no—
370#124—438no—
371#124—864no—
372#124—864no—
373#124—868no—
374#124—868no—
375#124—864no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4—862no—
387C2×C22⋊C4—862no—
388C2×C22⋊C4—862no—
389C2×C22⋊C4—868no—
390C2×C22⋊C4—868no—
391C2×C22⋊C4—861no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—864no—
397#103—24no—
398#103—42no—
399#103—864no—
400#103—1722no—
401#102—864no—
402#102—864no—
403#102—1722no—
404#102—1722no—
405C22⋊C8—22no—
406C22⋊C8—862no—
407C4×C8—864no—
408#95—21no—
409#95—861no—
410#95—861no—
411#95—861no—
412#95—861no—
413#95—861no—
414C24—864no—
415C24—862no—
416C24—1722no—
417C24—1722no—
418C24—1722no—
419C24—1722no—
420C24—1722no—
421C24—1722no—
422C24D4×D4311yescharacteristic
423C2×Q8—24no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—48no—
430C2×Q8—48no—
431C2×Q8—42no—
432C2×Q8—42no—
433C2×Q8D4×D4314yes—
434C2×D4—434no—
435C2×D4—864no—
436C2×D4—862no—
437C2×D4—862no—
438C2×D4—862no—
439C2×D4—862no—
440C2×D4—862no—
441C2×D4—1728no—
442C2×D4—1728no—
443C2×D4—1722no—
444C2×D4—1722no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—1721no—
464C22×C4—1721no—
465C22×C4#1062189812yes—
466C22×C4D4×D4311yescharacteristic
467C22×C4#1062190012yes—
468C22×C4C23×D4311yescharacteristic
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—862no—
473C2×C8—862no—
474C2×C8—862no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C22⋊C4—42no—
484C22⋊C4—868no—
485C22⋊C4—868no—
486C22⋊C4—868no—
487C22⋊C4—868no—
488C22⋊C4—1722no—
489C42—434no—
490C42—862no—
491C42—862no—
492C42—862no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—864no—
498C23—3444no—
499C23—3444no—
500C23—3444no—
501C23—3444no—
502C23—1728no—
503C23—1728no—
504C23—1728no—
505C23—1722no—
506C23—1722no—
507C23—1722no—
508C23—1722no—
509C23—1722no—
510C23—1722no—
511C23#1306331112yes—
512C23#1306334612yes—
513C23#1306334812yes—
514C23C2×D4×D4311yescharacteristic
515Q8—24no—
516Q8—24no—
517Q8—48no—
518Q8—42no—
519Q8—42no—
520D4—864no—
521D4—864no—
522D4—1728no—
523D4—1722no—
524D4—1722no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—48no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—861no—
549C2×C4—861no—
550C2×C4—861no—
551C2×C4—1724no—
552C2×C4—1724no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4—1721no—
558C2×C4—1721no—
559C2×C4#1306331112yes—
560C2×C4C2×D4×D4312yes—
561C2×C4C2×#1062190011yescharacteristic
562C2×C4C2×#1062189811yescharacteristic
563C2×C4#1306337012yes—
564C8—42no—
565C8—1722no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—34416no—
573C22—3442no—
574C22—3442no—
575C22—3442no—
576C22—3442no—
577C22—1724no—
578C22—1724no—
579C22—1724no—
580C22#1458325514yescomplemented
581C22#120×D4311yescharacteristic
582C22C2×#1306331111yescharacteristic
583C22#1458346411yescharacteristic
584C22C2×#1306334611yescharacteristic
585C22C2×#1306334811yescharacteristic
586C22#1458369811yescharacteristic
587C22#1458369811yescharacteristic
588C4—22no—
589C4—44no—
590C4—81no—
591C4—81no—
592C4—862no—
593C4—862no—
594C4—3441no—
595C4—3441no—
596C4—1721no—
597C4—1721no—
598C4#1458353612yes—
599C4#1458353912yes—
600C2—24no—
601C2—3444no—
602C2#1913824411yescharacteristic
603C2#1914381211yescharacteristic
604C2#1914381811yescharacteristic
605C2C2×#1458325511yescharacteristic
606C2#1914498311yescharacteristic
607C2#1914555911yescharacteristic
608C2#1914556511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1787C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#1787D43
hypocenterC43#25859
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#14583255C2semidirect
3. #19142903C2semidirect
4. #19135833C2semidirect
5. #19135832C2semidirect
6. #19135403C2semidirect
7. #19134530C2semidirect
10. C22⋊C8×Dic43C2semidirect
11. C43×#1787C2semidirect
13. C2×#13063316C22semidirect
23. C2×#13063249C22semidirect
24. C2×#13063249C22semidirect
30. C2×C8×Dic43C22semidirect
31. #14582798C22semidirect
32. #14582795C22semidirect
37. #14582764C22semidirect
39. #14582653C22semidirect
41. C2×#103×C43C22semidirect
42. C2×#103×C43C22semidirect
268. C22×C43#488semidirect
303. #1787D43semidirect
330. C2×#103C2×D43semidirect
331. C2×#103C2×D43semidirect
349. C43#25859semidirect
580. C22#14583255semidirect

Maximal subgroups

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

subgroupindex
C22×#130633142
C2×#145832552
#191429032
#191358332
#191358322
#191354032
#191345302
#191345272
#191345252
C22⋊C8×Dic432
C43×#17872
#2585943