Finite Group Databasebeta

← #25135322

Subgroups — #25135322

Order 11008.

1188 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583049C211yesmaximal, characteristic
2C2×#14582953C211yesmaximal, characteristic, complemented
3#19142929C211yesmaximal, characteristic, complemented
4C2×#14582800C211yesmaximal, characteristic
5#19135984C212yesmaximal, complemented
6#19135909C212yesmaximal, complemented
7#19135473C212yesmaximal, complemented
8#19135290C212yesmaximal, complemented
9#19134783C211yesmaximal, characteristic, complemented
10#19134527C211yesmaximal, characteristic
11C43×#1872C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C22×#10621884C2212yes—
14C22×(C2×D43)⋊C4—21no—
15C22×(C2×D43)⋊C4—21no—
16C22×C4×Dic43C2211yescharacteristic
17#14583049—24no—
18#14582953—24no—
19C2×#13063258C2212yescomplemented
20C2×Dic43⋊C8C2212yescomplemented
21C2×#13063247C2212yes—
22C2×#13063247C2212yes—
23C2×#13063245C2212yes—
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063235C2212yescomplemented
26#14582806C2211yescharacteristic, complemented
27#14582806C2211yescharacteristic, complemented
28#14582800—21no—
29#14582800—21no—
30#14582800C2212yes—
31#14582800C2212yes—
32#14582795C2211yescharacteristic, complemented
33#14582795C2211yescharacteristic, complemented
34#14582780—21no—
35#14582780—21no—
36#14582771—21no—
37#14582760—21no—
38#14582759C2211yescharacteristic
39#14582661C2212yescomplemented
40C2×C22⋊Q8×C43C2211yescharacteristic
41C22×C4⋊C4×C43C2211yescharacteristic
42C2×#103×C43C2212yescomplemented
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#340C2212yescomplemented
45C24×D43—21no—
46C22×D172—21no—
47C22×D172—24no—
48C22×D172—22no—
49C22×D172—22no—
50C22×D172—42no—
51C22×D172C2312yes—
52C23×Dic43D411yescharacteristic
53C23×Dic43D411yescharacteristic
54C2×#10621884—24no—
55C2×#10621884—24no—
56C2×#10621884—42no—
57C22×C43⋊C8C2312yes—
58C2×C4⋊Dic43C2311yescharacteristic
59C2×C4⋊Dic43C2311yescharacteristic
60C2×Dic43⋊C4—21no—
61C2×Dic43⋊C4—21no—
62C2×C22⋊Dic43—21no—
63C2×(C2×D43)⋊C4—22no—
64C2×(C2×D43)⋊C4—22no—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4—44no—
68C2×(C2×D43)⋊C4—44no—
69C2×C4×Dic43—22no—
70C2×C4×Dic43—22no—
71C2×C4×Dic43D411yescharacteristic
72C2×C4×Dic43D411yescharacteristic
73C2×C4×Dic43C2311yescharacteristic
74C2×C4×Dic43C2311yescharacteristic
75#13063258—42no—
76Dic43⋊C8—24no—
77#13063247—24no—
78#13063247—42no—
79#13063245—24no—
80C22⋊(C43⋊C8)D414yes—
81#13063235—24no—
82C43⋊#95—21no—
83C43⋊#95—21no—
84C43⋊#95—21no—
85C43⋊#95—21no—
86C43⋊#95—21no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C22×Q8×C43C2311yescharacteristic
90C23×C4×C43—21no—
91C23×C4×C43C2311yescharacteristic
92C22×C8×C43C2312yes—
93C22⋊Q8×C43—22no—
94C22⋊Q8×C43—22no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—42no—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2312yes—
100C2×C22⋊C4×C43—21no—
101#103×C43—42no—
102C22⋊C8×C43—22no—
103C24×C43C2×D411yescharacteristic
104C23×D43—24no—
105C23×D43—22no—
106C23×D43—42no—
107C23×D43—42no—
108C23×D43—42no—
109C23×D43—42no—
110C23×D43—42no—
111C23×D43—42no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C2×D412yes—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43#4112yes—
127C22×C4×C43C2411yescharacteristic
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—41no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×D172—24no—
141C2×D172—22no—
142C2×D172—22no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172—48no—
147C2×D172—48no—
148C2×D172—42no—
149C2×D172—42no—
150C2×D172#4114yes—
151C2×C8×C43—22no—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—42no—
159C4⋊C4×C43—42no—
160C22⋊C4×C43—42no—
161C22⋊Dic43—42no—
162#10621884—48no—
163(C2×D43)⋊C4—44no—
164(C2×D43)⋊C4—44no—
165(C2×D43)⋊C4—44no—
166(C2×D43)⋊C4—44no—
167C4⋊Dic43—22no—
168C4⋊Dic43—22no—
169Dic43⋊C4—42no—
170Dic43⋊C4—42no—
171C4×Dic43—22no—
172C4×Dic43—22no—
173C4×Dic43—21no—
174C4×Dic43—21no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8C2×D414yes—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43#12112yes—
185C23×C43AGL(1,ℤ/8)12yes—
186C23×C43#13712yes—
187C23×C43C22×D411yescharacteristic
188C22×D43—24no—
189C22×D43—48no—
190C22×D43—48no—
191C22×D43—48no—
192C22×D43—42no—
193C22×D43—42no—
194C22×D43—42no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—42no—
198C22×D43—84no—
199C22×D43—84no—
200C22×D43—84no—
201C22×D43—84no—
202Q8×C43—42no—
203Q8×C43—42no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—24no—
207C2×C4×C43—24no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—42no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—84no—
218C2×C4×C43#12112yes—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4112yes—
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43H(5,𝔽2)12yes—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—44no—
235C2×Dic43—44no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43AGL(1,ℤ/8)12yes—
243D172—24no—
244D172—24no—
245D172—48no—
246D172—42no—
247D172—42no—
248C8×C43—42no—
249C43⋊C8—24no—
250#24507—431nomaximal, Sylow
251C22×C43—22no—
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—22no—
257C22×C43#46814yes—
258C22×C43C2×#12111yescharacteristic
259C22×C43#52511yescharacteristic
260C22×C43#53511yescharacteristic
261C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C43C2×#13711yescharacteristic
264C22×C43#57511yescharacteristic
265C2×D43—44no—
266C2×D43—44no—
267C2×D43—44no—
268C2×D43—816no—
269C2×D43—82no—
270C2×D43—82no—
271C2×D43—82no—
272C2×D43—82no—
273C4×C43—22no—
274C4×C43—81no—
275C4×C43—82no—
276C4×C43—81no—
277C4×C43#54612yes—
278C4×C43#55112yes—
279Dic43—22no—
280Dic43—41no—
281Dic43—41no—
282Dic43—41no—
283Dic43—81no—
284Dic43—81no—
285C2×#450—431no—
286C2×#432—431no—
287#2855—431no—
288C2×#390—431no—
289#2067—432no—
290#2055—432no—
291#1973—432no—
292#1936—432no—
293#1872D4311yescharacteristic, complemented
294#1852—431no—
295#1786—431no—
296C2×C43—24no—
297C2×C43#241111yescharacteristic
298C2×C43C2×#46811yescharacteristic
299C2×C43#305511yescharacteristic
300C2×C43#311011yescharacteristic
301C2×C43#311411yescharacteristic
302C2×C43#321511yescharacteristic
303C2×C43#321711yescharacteristic
304D43—84no—
305C23×D4—431no—
306C22×SD16—432no—
307C2×C22⋊Q8C2×D4311yescharacteristic
308C22×C4⋊C4C2×D4311yescharacteristic
309C22×C22⋊C4—861no—
310C22×C22⋊C4—861no—
311C22×C42—431no—
312#450—864no—
313#432—864no—
314C2×#107—432no—
315C2×C4⋊C8—432no—
316C2×#103C2×D4312yescomplemented
317C2×#102—432no—
318C2×#102—432no—
319C2×#102—432no—
320C2×C22⋊C8—431no—
321C2×C22⋊C8C2×D4311yescharacteristic
322C2×#97—432no—
323#391—431no—
324#391—431no—
325#390—432no—
326#390—432no—
327#390—861no—
328#390—861no—
329#389—431no—
330#389—431no—
331#387—861no—
332#387—861no—
333#385—861no—
334#381—861no—
335#380—431no—
336#340—432no—
337#340C2×D4312yescomplemented
338C43#2450711yescharacteristic, complemented, Sylow
339C25—861no—
340C22×Q8C22×D4311yescharacteristic
341C22×D4—432no—
342C22×D4—864no—
343C22×D4—862no—
344C22×D4—861no—
345C22×D4—862no—
346C22×D4—1722no—
347C23×C4—21no—
348C23×C4—431no—
349C23×C4—431no—
350C23×C4C22×D4311yescharacteristic
351C2×SD16—864no—
352C2×SD16—864no—
353C2×SD16—1722no—
354C22×C8—432no—
355C22×C8C22×D4312yes—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4C22×D4312yes—
366C2×C4⋊C4C22×D4311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—862no—
369C2×C22⋊C4—862no—
370C2×C22⋊C4—862no—
371C2×C22⋊C4—862no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—1724no—
374C2×C22⋊C4—1724no—
375C2×C42—431no—
376C2×C42—431no—
377C2×C42—431no—
378C2×C42—431no—
379C2×C42—862no—
380C2×C42—862no—
381#107—1722no—
382C4⋊C8—864no—
383#103—42no—
384#102—864no—
385#102—864no—
386#102—1722no—
387C22⋊C8—22no—
388C22⋊C8—434no—
389#97—864no—
390#95—861no—
391#95—861no—
392#95—861no—
393#95—861no—
394#95—861no—
395#95—861no—
396#95—861no—
397C24—864no—
398C24—862no—
399C24—1722no—
400C24—1722no—
401C24—1722no—
402C24—1722no—
403C24—1722no—
404C24—1722no—
405C24D4×D4311yescharacteristic
406C2×Q8—21no—
407C2×Q8—22no—
408C2×Q8—21no—
409C2×Q8—22no—
410C2×D4—434no—
411C2×D4—864no—
412C2×D4—862no—
413C2×D4—862no—
414C2×D4—862no—
415C2×D4—862no—
416C2×D4—862no—
417C2×D4—1728no—
418C2×D4—1728no—
419C2×D4—1722no—
420C2×D4—1722no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—1721no—
441C22×C4#1062189812yes—
442C22×C4D4×D4311yescharacteristic
443C22×C4D4×D4312yes—
444C22×C4C23×D4311yescharacteristic
445SD16—1728no—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—434no—
450C2×C8—862no—
451C2×C8—862no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—42no—
457C4⋊C4—42no—
458C4⋊C4—862no—
459C4⋊C4—862no—
460C4⋊C4—1722no—
461C4⋊C4—1722no—
462C22⋊C4—42no—
463C22⋊C4—1724no—
464C22⋊C4—1724no—
465C22⋊C4—1724no—
466C22⋊C4—1724no—
467C22⋊C4—1722no—
468C42—862no—
469C42—862no—
470C42—861no—
471C42—861no—
472C42—861no—
473C42—861no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—864no—
479C23—3444no—
480C23—3444no—
481C23—3444no—
482C23—3444no—
483C23—1728no—
484C23—1728no—
485C23—1728no—
486C23—1722no—
487C23—1722no—
488C23—1722no—
489C23—1722no—
490C23—1722no—
491C23—1722no—
492C23#1306329812yes—
493C23#1306335212yes—
494C23#1306335712yes—
495C23C2×D4×D4311yescharacteristic
496Q8—42no—
497Q8—42no—
498D4—864no—
499D4—864no—
500D4—1728no—
501D4—1722no—
502D4—1722no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—41no—
516C2×C4—84no—
517C2×C4—432no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—1724no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1724no—
537C2×C4#1306329812yes—
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4#41×D4312yes—
540C2×C4C2×#1062189811yescharacteristic
541C2×C4#1306337012yes—
542C8—42no—
543C8—864no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—34416no—
551C22—3442no—
552C22—3442no—
553C22—3442no—
554C22—3442no—
555C22—1724no—
556C22—1724no—
557C22—1724no—
558C22#1458314814yes—
559C22C2×#1306329811yescharacteristic
560C22#1458340711yescharacteristic
561C22#1458346411yescharacteristic
562C22AGL(1,ℤ/8)×D4311yescharacteristic
563C22C2×#1306335211yescharacteristic
564C22C2×#1306335711yescharacteristic
565C22#1458369811yescharacteristic
566C4—22no—
567C4—81no—
568C4—82no—
569C4—81no—
570C4—862no—
571C4—3441no—
572C4—3441no—
573C4—1721no—
574C4—1721no—
575C4—1721no—
576C4#1458353812yes—
577C4#1458357812yes—
578C2—24no—
579C2—3444no—
580C2#1913798311yescharacteristic
581C2C2×#1458314811yescharacteristic
582C2#1914421711yescharacteristic
583C2#1914469111yescharacteristic
584C2#1914473611yescharacteristic
585C2#1914559711yescharacteristic
586C2#1914561611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC23×D172C22
hypercenter#1872D43
hypocenterC43#24507
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#14582953C2semidirect
3. #19142929C2semidirect
5. #19135984C2semidirect
6. #19135909C2semidirect
7. #19135473C2semidirect
8. #19135290C2semidirect
9. #19134783C2semidirect
11. C43×#1872C2semidirect
19. C2×#13063258C22semidirect
20. C2×Dic43⋊C8C22semidirect
25. C2×#13063235C22semidirect
26. #14582806C22semidirect
27. #14582806C22semidirect
32. #14582795C22semidirect
33. #14582795C22semidirect
39. #14582661C22semidirect
42. C2×#103×C43C22semidirect
44. C43×#340C22semidirect
293. #1872D43semidirect
316. C2×#103C2×D43semidirect
337. #340C2×D43semidirect
338. C43#24507semidirect

Maximal subgroups

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

subgroupindex
C2×#145830492
C2×#145829532
#191429292
C2×#145828002
#191359842
#191359092
#191354732
#191352902
#191347832
#191345272
C43×#18722
#2450743