Finite Group Databasebeta

← #25153251

Subgroups — #25153251

Order 11008.

1320 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063324C211yesmaximal, characteristic, complemented
2C2×#14583260C212yesmaximal, complemented
3#19142898C211yesmaximal, characteristic
4#19135734C212yesmaximal, complemented
5#19135730C212yesmaximal, complemented
6#19135566C212yesmaximal, complemented
7#19134912C211yesmaximal, characteristic
8#19134910C211yesmaximal, characteristic
9#19134903C211yesmaximal, characteristic, complemented
10#19134359C211yesmaximal, characteristic, complemented
11C43×#1872C211yesmaximal, characteristic, complemented
12C23×Dic86—21no—
13C2×#13063324—28no—
14C2×#13063324—21no—
15C2×#13063324—21no—
16C2×#13063324C2212yes—
17C2×#13063324C2212yes—
18C2×#13063314C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×Dic43⋊C4—21no—
22C22×C4×Dic43C2211yescharacteristic
23#14583260—28no—
24C2×#13063249C2212yes—
25C2×#13063247C2212yes—
26C2×#13063245C2212yes—
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063235C2212yes—
29#14582806C2211yescharacteristic
30#14582800C2211yescharacteristic
31#14582789—21no—
32#14582789—21no—
33#14582776—21no—
34#14582776—21no—
35#14582764C2211yescharacteristic
36#14582662C2212yes—
37#14582661C2212yes—
38#14582661C2212yes—
39#14582653C2212yes—
40C2×C22⋊Q8×C43C2211yescharacteristic
41C22×C4⋊C4×C43C2211yescharacteristic
42C2×#103×C43C2212yes—
43C2×C22⋊C8×C43C2211yescharacteristic
44C43×#340C2212yes—
45C22×Dic86—28no—
46C22×Dic86—22no—
47C22×Dic86—22no—
48C22×Dic86—44no—
49C22×Dic86—44no—
50C22×D172C2311yescharacteristic
51C22×C22⋊D43—21no—
52C23×Dic43—21no—
53C23×Dic43D411yescharacteristic
54C23×Dic43D411yescharacteristic
55C22×C43⋊C8C2312yes—
56#13063324—28no—
57#13063324—28no—
58#13063324—24no—
59#13063324—24no—
60#13063324—24no—
61#13063324D418yescomplemented
62#13063314—24no—
63#13063299—22no—
64#13063299—22no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—24no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2312yes—
69C2×Dic43⋊C4—28no—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×C4×Dic43—24no—
78C2×C4×Dic43D411yescharacteristic
79C2×C4×Dic43D411yescharacteristic
80C2×C4×Dic43C2311yescharacteristic
81C2×C4×Dic43C2311yescharacteristic
82#13063249—24no—
83#13063247—24no—
84#13063245—24no—
85C22⋊(C43⋊C8)—22no—
86#13063235—24no—
87C43⋊#95—21no—
88C43⋊#95—21no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×Q8×C43C2311yescharacteristic
92C23×C4×C43—21no—
93C23×C4×C43C2311yescharacteristic
94C22×C8×C43C2312yes—
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43—22no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—24no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2312yes—
102C2×C22⋊C4×C43—21no—
103#103×C43—24no—
104C22⋊C8×C43—22no—
105C24×C43C2×D411yescharacteristic
106C23×D43—21no—
107C2×Q8×C43—22no—
108C2×Q8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—24no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—42no—
118C22×C4×C43—42no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43#4112yes—
121C22×C4×C43#4112yes—
122C22×C4×C43C2411yescharacteristic
123C2×C22⋊D43—42no—
124C2×C22⋊D43—42no—
125C2×C22⋊D43—42no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—24no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—42no—
136C22×Dic43—42no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×D172—22no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—22no—
145C2×Dic86—28no—
146C2×Dic86—28no—
147C2×Dic86—432no—
148C2×Dic86—44no—
149C2×Dic86—44no—
150C2×Dic86—44no—
151C2×Dic86—44no—
152C2×C8×C43—22no—
153C2×C8×C43—22no—
154C2×C8×C43—22no—
155C4⋊C4×C43—24no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43C2×D414yes—
161C22⋊C4×C43—42no—
162(C2×D43)⋊C4—42no—
163(C2×D43)⋊C4—42no—
164(C2×D43)⋊C4—42no—
165(C2×D43)⋊C4—42no—
166(C2×D43)⋊C4—42no—
167C4⋊Dic43—24no—
168C4⋊Dic43—22no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43C2×D414yes—
172Dic43⋊C4—28no—
173Dic43⋊C4—28no—
174C4×Dic43—22no—
175C4×Dic43—22no—
176C4×Dic43—22no—
177C4×Dic43C2×D414yes—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C23×C43—21no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—21no—
185C23×C43#12412yes—
186C23×C43AGL(1,ℤ/8)12yes—
187C23×C43#13712yes—
188C23×C43C22×D411yescharacteristic
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196Q8×C43—42no—
197Q8×C43—42no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—24no—
201C2×C4×C43—24no—
202C2×C4×C43—24no—
203C2×C4×C43—48no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43#12412yes—
213C2×C4×C43C22×D412yes—
214C2×C4×C43C2×#4111yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C2×C4×C432−1+412yes—
217C22⋊D43—84no—
218C2×Dic43—28no—
219C2×Dic43—28no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—24no—
229C2×Dic43—48no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43#12012yes—
236C2×Dic43#12012yes—
237C2×Dic43AGL(1,ℤ/8)12yes—
238C2×Dic43#13712yes—
239D172—42no—
240D172—42no—
241Dic86—416no—
242Dic86—416no—
243C8×C43—42no—
244C43⋊C8—42no—
245#25908—431nomaximal, Sylow
246C22×C43—22no—
247C22×C43—22no—
248C22×C43—22no—
249C22×C43—22no—
250C22×C43—22no—
251C22×C43—22no—
252C22×C43#48914yescomplemented
253C22×C43C2×#12011yescharacteristic
254C22×C43C2×#12411yescharacteristic
255C22×C43#53611yescharacteristic
256C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
257C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C43C2×#13711yescharacteristic
259C22×C43C2×#13711yescharacteristic
260C2×D43—81no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C4×C43—22no—
268C4×C43—44no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43#54812yes—
272C4×C43#54812yes—
273Dic43—22no—
274Dic43—22no—
275Dic43—22no—
276Dic43—22no—
277Dic43—44no—
278Dic43—81no—
279C22×C4⋊Q8—431no—
280C2×#489—432no—
281#2850—431no—
282#2024—432no—
283#2023—432no—
284#1993—432no—
285#1874—431no—
286#1874—431no—
287#1872—431no—
288#1872D4311yescharacteristic, complemented
289#1749—431no—
290C2×C43—24no—
291C2×C43#243611yescharacteristic
292C2×C43#300311yescharacteristic
293C2×C43#300411yescharacteristic
294C2×C43C2×#48911yescharacteristic
295C2×C43#314111yescharacteristic
296C2×C43#323811yescharacteristic
297C2×C43#323911yescharacteristic
298D43—161no—
299C23×Q8—861no—
300C2×C4⋊Q8—432no—
301C2×C4⋊Q8—432no—
302C2×C4⋊Q8—861no—
303C2×C4⋊Q8—861no—
304C2×C4⋊Q8—868no—
305C2×#124—431no—
306C2×C22⋊Q8C2×D4311yescharacteristic
307C2×#121—431no—
308C22×C4⋊C4—431no—
309C22×C4⋊C4—861no—
310C22×C4⋊C4C2×D4311yescharacteristic
311C22×C42—431no—
312#489—868no—
313C2×#103—432no—
314C2×#103C2×D4312yes—
315C2×#102—432no—
316C2×#102—432no—
317C2×C22⋊C8—431no—
318C2×C22⋊C8C2×D4311yescharacteristic
319C2×#97—432no—
320#391—431no—
321#390—431no—
322#388—861no—
323#388—861no—
324#386—861no—
325#386—861no—
326#382—431no—
327#340—432no—
328#340—432no—
329#340—432no—
330#340C2×D4312yes—
331#336—432no—
332C43#2590811yescharacteristic, complemented, Sylow
333C22×Q8—862no—
334C22×Q8—862no—
335C22×Q8—868no—
336C22×Q8—1724no—
337C22×Q8—1724no—
338C22×Q8C22×D4311yescharacteristic
339C22×D4—431no—
340C22×D4—861no—
341C23×C4—21no—
342C23×C4—431no—
343C23×C4—431no—
344C23×C4—861no—
345C23×C4C22×D4311yescharacteristic
346C22×C8—432no—
347C22×C8C22×D4312yes—
348C4⋊Q8—438no—
349C4⋊Q8—864no—
350C4⋊Q8—864no—
351C4⋊Q8—868no—
352C4⋊Q8—868no—
353C4⋊Q8—864no—
354#124—864no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357#121—862no—
358#121—862no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—432no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—864no—
365C2×C4⋊C4—862no—
366C2×C4⋊C4—862no—
367C2×C4⋊C4—868no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4C22×D4311yescharacteristic
370C2×C4⋊C4C22×D4312yes—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—861no—
377C2×C42—431no—
378C2×C42—431no—
379C2×C42—431no—
380C2×C42—431no—
381C2×C42—864no—
382#103—24no—
383#103—864no—
384#102—864no—
385#102—864no—
386C22⋊C8—22no—
387C22⋊C8—862no—
388#97—864no—
389#95—861no—
390#95—861no—
391#95—861no—
392#95—861no—
393C24—861no—
394C24D4×D4311yescharacteristic
395C2×Q8—22no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—868no—
400C2×Q8—868no—
401C2×Q8—1724no—
402C2×Q8—17232no—
403C2×Q8—1724no—
404C2×Q8—1724no—
405C2×Q8—1724no—
406C2×D4—862no—
407C2×D4—861no—
408C2×D4—861no—
409C2×D4—862no—
410C2×D4—1722no—
411C2×D4—1722no—
412C2×D4—1722no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—431no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—864no—
432C22×C4—862no—
433C22×C4—861no—
434C22×C4—1722no—
435C22×C4—1722no—
436C22×C4#1062189812yes—
437C22×C4D4×D4311yescharacteristic
438C22×C4#1062190012yes—
439C22×C4C23×D4311yescharacteristic
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—862no—
444C2×C8—862no—
445C2×C8—862no—
446C4⋊C4—24no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—42no—
451C4⋊C4—434no—
452C4⋊C4—868no—
453C4⋊C4—868no—
454C4⋊C4—864no—
455C4⋊C4—862no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4D4×D4314yes—
459C22⋊C4—42no—
460C22⋊C4—1722no—
461C22⋊C4—1722no—
462C22⋊C4—1722no—
463C22⋊C4—1722no—
464C22⋊C4—1722no—
465C42—434no—
466C42—862no—
467C42—862no—
468C42—862no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—1721no—
474C23—1721no—
475C23—1721no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23#1306331112yes—
481C23#1306335212yes—
482C23#1306335712yes—
483C23C2×D4×D4311yescharacteristic
484Q8—42no—
485Q8—42no—
486Q8—17216no—
487Q8—17216no—
488D4—3444no—
489D4—1722no—
490D4—1722no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—48no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—432no—
506C2×C4—432no—
507C2×C4—432no—
508C2×C4—432no—
509C2×C4—868no—
510C2×C4—868no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—864no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1728no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4#1306331112yes—
527C2×C4C2×D4×D4312yes—
528C2×C4C2×#1062190011yescharacteristic
529C2×C4C2×#1062189811yescharacteristic
530C2×C4#1306337212yes—
531C8—42no—
532C8—1722no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—3441no—
540C22—3441no—
541C22—3441no—
542C22—3441no—
543C22—3441no—
544C22—3441no—
545C22—3441no—
546C22#1458326014yescomplemented
547C22#120×D4311yescharacteristic
548C22C2×#1306331111yescharacteristic
549C22#1458347111yescharacteristic
550C22AGL(1,ℤ/8)×D4311yescharacteristic
551C22C2×#1306335211yescharacteristic
552C22#137×D4311yescharacteristic
553C22C2×#1306335711yescharacteristic
554C4—22no—
555C4—44no—
556C4—81no—
557C4—81no—
558C4—862no—
559C4—862no—
560C4—862no—
561C4—862no—
562C4—3441no—
563C4—1724no—
564C4#1458355512yes—
565C4#1458355812yes—
566C2—24no—
567C2—6881no—
568C2#1913825111yescharacteristic
569C2#1914382311yescharacteristic
570C2#1914383011yescharacteristic
571C2C2×#1458326011yescharacteristic
572C2#1914498611yescharacteristic
573C2#1914581911yescharacteristic
574C2#1914582811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1872C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#1872D43
hypocenterC43#25908
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
1. C22×#13063324C2semidirect
2. C2×#14583260C2semidirect
4. #19135734C2semidirect
5. #19135730C2semidirect
6. #19135566C2semidirect
9. #19134903C2semidirect
10. #19134359C2semidirect
11. C43×#1872C2semidirect
61. #13063324D4semidirect
252. C22×C43#489semidirect
288. #1872D43semidirect
332. C43#25908semidirect
546. C22#14583260semidirect

Maximal subgroups

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

subgroupindex
C22×#130633242
C2×#145832602
#191428982
#191357342
#191357302
#191355662
#191349122
#191349102
#191349032
#191343592
C43×#18722
#2590843