Finite Group Databasebeta

← #25130524

Subgroups — #25130524

Order 11008.

1174 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
1C2×#14583622C211yesmaximal, characteristic, complemented
2C2×#14583180C211yesmaximal, characteristic, complemented
3C2×C4×#10621884C211yesmaximal, characteristic, complemented
4#19139511C211yesmaximal, characteristic
5#19135797C212yesmaximal, complemented
6#19135597C212yesmaximal, complemented
7#19135555C211yesmaximal, characteristic, complemented
8#19135388C211yesmaximal, characteristic, complemented
9#19134916C212yesmaximal, complemented
10#19134797C212yesmaximal, complemented
11C43×#1803C211yesmaximal, characteristic, complemented
12C22×#10621884C2211yescharacteristic
13#14583622—24no—
14#14583622—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063320—22no—
17C2×#13063313—21no—
18C2×#13063301C2212yes—
19C2×#13063300—21no—
20C2×#13063300C2212yes—
21C2×C4×Dic86—21no—
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24C2×#13063283C2212yes—
25#14583180—24no—
26C4×#10621884—24no—
27C2×#13063259C2212yes—
28C2×#13063256C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063247C2212yes—
31C2×#13063245C2211yescharacteristic
32C2×(C2×D43)⋊C8C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34C2×C4×C43⋊C8C2211yescharacteristic
35#14582816—22no—
36#14582756—21no—
37#14582756C2212yes—
38#14582661C2212yes—
39#14582661C2212yes—
40C2×C4×Q8×C43C2211yescharacteristic
41C2×C4⋊C8×C43C2211yescharacteristic
42C2×#103×C43C2212yes—
43C43×#384C2211yescharacteristic
44C43×#340C2212yes—
45C22×Dic86—21no—
46C22×D172—22no—
47C22×D172D411yescharacteristic
48C22×D172C2311yescharacteristic
49C22×C4×D43—21no—
50C22×C4×D43C2312yes—
51C2×#10621884—22no—
52C2×#10621884—22no—
53C2×#10621884—22no—
54C22×C43⋊C8C2311yescharacteristic
55C22×C43⋊C8C2311yescharacteristic
56#13063325—22no—
57#13063325D414yescomplemented
58#13063320—216no—
59#13063313—28no—
60#13063301—24no—
61#13063301—24no—
62#13063300—24no—
63#13063300—42no—
64#13063300—44no—
65C4×Dic86—28no—
66C4×D172—22no—
67C4×D172—22no—
68C4×D172—22no—
69C4×D172—22no—
70#13063283—24no—
71#13063283—24no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2312yes—
76C2×Dic43⋊C4—22no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4D412yes—
83C2×C4×Dic43—22no—
84#13063259—24no—
85#13063256—22no—
86#13063249—22no—
87#13063247—24no—
88#13063245—22no—
89(C2×D43)⋊C8—24no—
90(C2×D43)⋊C8—42no—
91C4×C43⋊C8—22no—
92C43⋊#95—22no—
93C22×Q8×C43C2311yescharacteristic
94C22×C8×C43C2312yes—
95C4×Q8×C43—22no—
96C4×Q8×C43D414yescomplemented
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43C2312yes—
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C42×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43—22no—
105#103×C43—42no—
106C23×D43—21no—
107C23×D43C2×D412yes—
108C2×Q8×C43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43C2×D412yes—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2411yescharacteristic
120C22×Dic43—22no—
121C22×Dic43—21no—
122C22×Dic43C2×D412yes—
123C2×D172—22no—
124C2×D172—22no—
125C2×D172—22no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—44no—
132C2×D172—44no—
133C2×D172—82no—
134C2×D172#4112yes—
135C2×C4×D43—22no—
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—42no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×Dic86—24no—
145C2×Dic86—42no—
146C2×Dic86—42no—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C2×C8×C43—22no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—42no—
155C4⋊C4×C43—81no—
156C4⋊C4×C43C2×D412yes—
157C42×C43—24no—
158C42×C43C2×D412yes—
159C42×C43C2×D412yes—
160#10621884—28no—
161(C2×D43)⋊C4—28no—
162(C2×D43)⋊C4—28no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—44no—
165(C2×D43)⋊C4—44no—
166(C2×D43)⋊C4—42no—
167C4⋊Dic43—24no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43C2×D414yes—
173Dic43⋊C4—28no—
174C4×Dic43—28no—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8#4112yes—
181C23×C43C22×D411yescharacteristic
182C22×D43—22no—
183C22×D43—22no—
184C22×D43—22no—
185C22×D43—22no—
186C22×D43—22no—
187C22×D43—22no—
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196Q8×C43—22no—
197Q8×C43—22no—
198Q8×C43—41no—
199Q8×C43—41no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43#12012yes—
212C2×C4×C43#12012yes—
213C2×C4×C43#13512yes—
214C2×C4×C43AGL(1,ℤ/8)12yes—
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C43C2×#4111yescharacteristic
219C2×C4×C43H(5,𝔽2)11yescharacteristic
220C2×C4×C432−1+411yescharacteristic
221C2×Dic43—22no—
222C2×Dic43—24no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230D172—22no—
231D172—22no—
232D172—41no—
233D172—41no—
234D172—44no—
235D172—88no—
236C4×D43—42no—
237C4×D43—42no—
238C4×D43—42no—
239C4×D43—42no—
240C4×D43—84no—
241Dic86—48no—
242C8×C43—42no—
243C43⋊C8—22no—
244C43⋊C8—41no—
245#24119—431nomaximal, Sylow
246C22×C43C2×#12011yescharacteristic
247C22×C43#54611yescharacteristic
248C22×C43#54711yescharacteristic
249C22×C43C2×#13511yescharacteristic
250C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C43#57711yescharacteristic
252C22×C43#57811yescharacteristic
253C2×D43—42no—
254C2×D43—42no—
255C2×D43—42no—
256C2×D43—42no—
257C2×D43—42no—
258C2×D43—42no—
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—81no—
267C4×C43—22no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—82no—
271C4×C43#44914yes—
272C4×C43#52511yescharacteristic
273C4×C43#53711yescharacteristic
274C4×C43#54811yescharacteristic
275C4×C43#55011yescharacteristic
276Dic43—42no—
277Dic43—44no—
278Dic43—81no—
279C2×#556—431no—
280C2×#474—431no—
281C2×C4×SD16—431no—
282#2537—431no—
283#2036—432no—
284#2000—432no—
285#1990—431no—
286#1954—431no—
287#1875—432no—
288#1854—432no—
289#1803D4311yescharacteristic, complemented
290C2×C43#240711yescharacteristic
291C2×C43C2×#44911yescharacteristic
292C2×C43#301311yescharacteristic
293C2×C43#330211yescharacteristic
294C2×C43#332411yescharacteristic
295C2×C43#334011yescharacteristic
296C2×C43#335311yescharacteristic
297D43—82no—
298D43—82no—
299C22×SD16—431no—
300#556—864no—
301#556—864no—
302C2×C4⋊Q8—431no—
303C2×#126—862no—
304C2×#124—861no—
305C2×C22⋊Q8—432no—
306C2×#121—432no—
307C2×#121—861no—
308C2×C4×Q8—861no—
309C2×C4×Q8C2×D4311yescharacteristic
310C2×C4×D4—431no—
311C2×C4×D4—431no—
312C2×#117—432no—
313#474—864no—
314C4×SD16—864no—
315C2×#107—432no—
316C2×#106—431no—
317C2×C4⋊C8C2×D4311yescharacteristic
318C2×#103—431no—
319C2×#103C2×D4312yes—
320C2×#102—432no—
321C2×#102—431no—
322C2×C22⋊C8—432no—
323C2×C22⋊C8—432no—
324C2×C4×C8—431no—
325#394—862no—
326#384C2×D4311yescharacteristic
327#380—432no—
328#380—861no—
329#340—432no—
330#340—432no—
331#340C2×D4312yes—
332C43#2411911yescharacteristic, complemented, Sylow
333C22×Q8—861no—
334C22×Q8C22×D4311yescharacteristic
335C22×D4—431no—
336C22×D4—431no—
337C22×D4—862no—
338C23×C4—432no—
339C23×C4—861no—
340C2×SD16—862no—
341C2×SD16—862no—
342C2×SD16—862no—
343C22×C8—431no—
344C22×C8—431no—
345C22×C8C22×D4312yes—
346C4⋊Q8—434no—
347C4⋊Q8—862no—
348#126—8616no—
349#124—868no—
350C22⋊Q8—864no—
351C22⋊Q8—864no—
352#121—864no—
353#121—1722no—
354#121—1724no—
355C4×Q8—22no—
356C4×Q8—868no—
357C4×Q8D17214yescomplemented
358C4×D4—862no—
359C4×D4—862no—
360C4×D4—862no—
361C4×D4—862no—
362#117—864no—
363#117—864no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—862no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4C22×D4312yes—
373C2×C4⋊C4C22×D4311yescharacteristic
374C2×C22⋊C4—432no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4—862no—
379C2×C22⋊C4—861no—
380C2×C42—21no—
381C2×C42—862no—
382C2×C42C22×D4311yescharacteristic
383#107—864no—
384#106—862no—
385C4⋊C8—22no—
386#103—42no—
387#103—862no—
388#102—864no—
389#102—862no—
390C22⋊C8—864no—
391C22⋊C8—1722no—
392C4×C8—862no—
393#95—862no—
394C24—432no—
395C24—861no—
396C2×Q8—21no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—864no—
402C2×Q8—1722no—
403C2×Q8—1722no—
404C2×Q8C2×D17212yes—
405C2×D4—432no—
406C2×D4—862no—
407C2×D4—862no—
408C2×D4—862no—
409C2×D4—861no—
410C2×D4—861no—
411C2×D4—861no—
412C2×D4—861no—
413C2×D4—861no—
414C2×D4—3442no—
415C2×D4—1724no—
416C2×D4—1724no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—432no—
421C22×C4—862no—
422C22×C4—862no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—861no—
429C22×C4—1722no—
430C22×C4—1722no—
431C22×C4—1722no—
432C22×C4D4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4C23×D4311yescharacteristic
435SD16—868no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—432no—
440C2×C8—861no—
441C2×C8—861no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—81no—
451C4⋊C4—434no—
452C4⋊C4—868no—
453C4⋊C4—862no—
454C4⋊C4—864no—
455C4⋊C4—862no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4C2×D17212yes—
459C22⋊C4—868no—
460C22⋊C4—868no—
461C22⋊C4—864no—
462C22⋊C4—1724no—
463C22⋊C4—1724no—
464C22⋊C4—1722no—
465C42—24no—
466C42—868no—
467C42C2×D17212yes—
468C42D4×D4312yes—
469C23—862no—
470C23—862no—
471C23—862no—
472C23—862no—
473C23—862no—
474C23—862no—
475C23—862no—
476C23—862no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23—1721no—
483C23C2×D4×D4311yescharacteristic
484Q8—22no—
485Q8—22no—
486Q8—41no—
487Q8—41no—
488Q8—1728no—
489D4—862no—
490D4—862no—
491D4—3448no—
492D4—1724no—
493D4—1721no—
494D4—1721no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—862no—
507C2×C4—864no—
508C2×C4—862no—
509C2×C4—862no—
510C2×C4—3444no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4#1306329512yes—
521C2×C4#1306329512yes—
522C2×C4#1306334812yes—
523C2×C4#1306335212yes—
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4C22×D17211yescharacteristic
526C2×C4#41×D4311yescharacteristic
527C2×C4#41×D4311yescharacteristic
528C2×C4#1306337011yescharacteristic
529C2×C4#1306337311yescharacteristic
530C8—42no—
531C8—862no—
532C8—1721no—
533C22—3441no—
534C22—3441no—
535C22—3441no—
536C22—3441no—
537C22—1722no—
538C22—1722no—
539C22—1722no—
540C22—1722no—
541C22—1722no—
542C22—1722no—
543C22—1722no—
544C22—1722no—
545C22—1722no—
546C22—1722no—
547C22C2×#1306329511yescharacteristic
548C22#1458354611yescharacteristic
549C22#1458355111yescharacteristic
550C22C2×#1306334811yescharacteristic
551C22C2×#1306335211yescharacteristic
552C22#1458370911yescharacteristic
553C22#1458371511yescharacteristic
554C4—22no—
555C4—42no—
556C4—42no—
557C4—82no—
558C4—3441no—
559C4—1724no—
560C4—1722no—
561C4#1458304714yes—
562C4#1458341111yescharacteristic
563C4#1458348011yescharacteristic
564C4#1458355911yescharacteristic
565C4#1458356711yescharacteristic
566C2—3442no—
567C2—3442no—
568C2#1913794111yescharacteristic
569C2C2×#1458304711yescharacteristic
570C2#1914391211yescharacteristic
571C2#1914651511yescharacteristic
572C2#1914682911yescharacteristic
573C2#1914701111yescharacteristic
574C2#1914718211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radical#19139511C2
hypercenter#1803D43
hypocenterC43#24119
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
1. C2×#14583622C2semidirect
2. C2×#14583180C2semidirect
3. C2×C4×#10621884C2semidirect
5. #19135797C2semidirect
6. #19135597C2semidirect
7. #19135555C2semidirect
8. #19135388C2semidirect
9. #19134916C2semidirect
10. #19134797C2semidirect
11. C43×#1803C2semidirect
57. #13063325D4semidirect
96. C4×Q8×C43D4semidirect
289. #1803D43semidirect
332. C43#24119semidirect
357. C4×Q8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145836222
C2×#145831802
C2×C4×#106218842
#191395112
#191357972
#191355972
#191355552
#191353882
#191349162
#191347972
C43×#18032
#2411943