Finite Group Databasebeta

← #25153247

Subgroups — #25153247

Order 11008.

1320 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2C2×#14583260C212yesmaximal, complemented
3#19142899C211yesmaximal, characteristic
4#19135736C211yesmaximal, characteristic, complemented
5#19135732C211yesmaximal, characteristic, complemented
6#19135728C211yesmaximal, characteristic, complemented
7#19135566C212yesmaximal, complemented
8#19134911C212yesmaximal
9#19134899C212yesmaximal, complemented
10#19134356C211yesmaximal, characteristic, complemented
11C43×#2024C211yesmaximal, characteristic, complemented
12C22×Q8×D43—21no—
13C2×#13063325C2211yescharacteristic
14C2×#13063324—21no—
15C2×#13063324C2212yes—
16C2×#13063323—21no—
17C4⋊Q8×D43—28no—
18C2×#13063314C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×#13063300C2211yescharacteristic
21C2×C4⋊C4×D43—21no—
22C2×C4⋊C4×D43C2212yes—
23C2×C42×D43C2211yescharacteristic
24#14583260—28no—
25C2×#13063249C2212yes—
26C2×#13063247C2212yes—
27C2×#13063245C2212yes—
28C2×(C2×D43)⋊C8C2212yes—
29C2×#13063235C2212yes—
30#14582801C2211yescharacteristic
31#14582788—21no—
32#14582788—21no—
33#14582777—21no—
34#14582777—21no—
35#14582764C2211yescharacteristic
36#14582662C2212yes—
37#14582661C2212yes—
38#14582661C2212yes—
39#14582654C2211yescharacteristic
40C2×C4⋊Q8×C43C2211yescharacteristic
41C2×#103×C43C2212yes—
42C43×#391C2211yescharacteristic
43C43×#340C2212yes—
44C43×#336C2211yescharacteristic
45C22×Dic86—21no—
46C22×Dic86—22no—
47C2×Q8×D43—28no—
48C2×Q8×D43—44no—
49C2×Q8×D43—44no—
50C22×D172—21no—
51C22×D172C2311yescharacteristic
52C22×C4×D43—22no—
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C22×C43⋊C8C2312yes—
57#13063325—24no—
58#13063324—28no—
59#13063324—24no—
60#13063324D418yescomplemented
61#13063323—28no—
62#13063314—24no—
63#13063301—24no—
64#13063300—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43C2311yescharacteristic
67C2×C4⋊Dic43C2312yes—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4—21no—
71C4⋊C4×D43—28no—
72C4⋊C4×D43—24no—
73C4⋊C4×D43—24no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×C4×Dic43D411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83C42×D43—24no—
84#13063249—24no—
85#13063247—24no—
86#13063245—24no—
87(C2×D43)⋊C8—24no—
88#13063235—24no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C22×Q8×C43—21no—
92C22×Q8×C43C2311yescharacteristic
93C22×C8×C43C2312yes—
94C4⋊Q8×C43—24no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2312yes—
98C2×C42×C43C2311yescharacteristic
99#103×C43—24no—
100#95×C43—21no—
101#95×C43—21no—
102C23×D43—21no—
103C23×D43C2×D411yescharacteristic
104C2×Q8×C43—24no—
105C2×Q8×C43—22no—
106C2×Q8×C43—22no—
107C2×Q8×C43—21no—
108C2×Q8×C43—21no—
109C2×Q8×C43—42no—
110C2×Q8×C43—42no—
111C22×C4×C43—22no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2411yescharacteristic
117C22×Dic43—22no—
118C22×Dic43—21no—
119C22×Dic43C2×D411yescharacteristic
120C22×Dic43C2×D411yescharacteristic
121C22×Dic43C2×D411yescharacteristic
122Q8×D43—432no—
123C2×D172—22no—
124C2×D172—22no—
125C2×D172—21no—
126C2×D172—21no—
127C2×D172—42no—
128C2×D172—42no—
129C2×D172—42no—
130C2×C4×D43—22no—
131C2×C4×D43—22no—
132C2×C4×D43—22no—
133C2×C4×D43—21no—
134C2×C4×D43—21no—
135C2×C4×D43—22no—
136C2×C4×D43—22no—
137C2×C4×D43—28no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—44no—
141C2×C4×D43—44no—
142C2×C4×D43#4114yes—
143C2×Dic86—24no—
144C2×Dic86—28no—
145C2×Dic86—44no—
146C2×Dic86—44no—
147C2×Dic86—42no—
148C2×Dic86—42no—
149C2×C8×C43—22no—
150C2×C8×C43—22no—
151C2×C8×C43—22no—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43C2×D414yes—
156C42×C43—22no—
157(C2×D43)⋊C4—42no—
158(C2×D43)⋊C4—42no—
159(C2×D43)⋊C4—42no—
160(C2×D43)⋊C4—42no—
161(C2×D43)⋊C4—42no—
162(C2×D43)⋊C4—42no—
163C4⋊Dic43—24no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43C2×D414yes—
167Dic43⋊C4—28no—
168Dic43⋊C4—28no—
169Dic43⋊C4—42no—
170C4×Dic43—22no—
171C4×Dic43—22no—
172C4×Dic43C2×D414yes—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C23×C43C22×D411yescharacteristic
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—21no—
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—41no—
187C22×D43—41no—
188C22×D43#12412yes—
189C22×D43AGL(1,ℤ/8)12yes—
190C22×D43#13712yes—
191Q8×C43—48no—
192Q8×C43—42no—
193Q8×C43—42no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—24no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43AGL(1,ℤ/8)12yes—
208C2×C4×C43#13712yes—
209C2×C4×C43C22×D412yes—
210C2×C4×C43C2×#4112yes—
211C2×C4×C432−1+411yescharacteristic
212C2×C4×C432−1+411yescharacteristic
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—24no—
220C2×Dic43—42no—
221C2×Dic43—42no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43#12012yes—
226C2×Dic43#12012yes—
227C2×Dic43#12412yes—
228D172—42no—
229D172—42no—
230D172—84no—
231C4×D43—28no—
232C4×D43—28no—
233C4×D43—24no—
234C4×D43—24no—
235C4×D43—416no—
236Dic86—416no—
237Dic86—48no—
238C8×C43—42no—
239C43⋊C8—42no—
240#25908—431nomaximal, Sylow
241C22×C43C2×#12011yescharacteristic
242C22×C43C2×#12411yescharacteristic
243C22×C43#53611yescharacteristic
244C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
245C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
246C22×C43C2×#13711yescharacteristic
247C22×C43C2×#13711yescharacteristic
248C2×D43—22no—
249C2×D43—22no—
250C2×D43—22no—
251C2×D43—22no—
252C2×D43—22no—
253C2×D43—22no—
254C2×D43—81no—
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—81no—
258C2×D43—81no—
259C2×D43—81no—
260C2×D43—81no—
261C2×D43#48914yescomplemented
262C4×C43—22no—
263C4×C43—22no—
264C4×C43—44no—
265C4×C43—81no—
266C4×C43—81no—
267C4×C43#54812yes—
268C4×C43#54812yes—
269Dic43—22no—
270Dic43—22no—
271Dic43—22no—
272Dic43—44no—
273Dic43—81no—
274C22×C4⋊Q8—431no—
275C2×#489—432no—
276#2850—431no—
277#2024—431no—
278#2024D4311yescharacteristic, complemented
279#2023—431no—
280#2023—431no—
281#1993—432no—
282#1874—432no—
283#1872—432no—
284#1749—431no—
285C2×C43#243611yescharacteristic
286C2×C43#300311yescharacteristic
287C2×C43#300411yescharacteristic
288C2×C43C2×#48911yescharacteristic
289C2×C43#314111yescharacteristic
290C2×C43#323811yescharacteristic
291C2×C43#323911yescharacteristic
292D43—24no—
293D43—161no—
294C23×Q8—861no—
295C2×C4⋊Q8—432no—
296C2×C4⋊Q8—431no—
297C2×C4⋊Q8—861no—
298C2×C4⋊Q8—861no—
299C2×C4⋊Q8—868no—
300C2×C4⋊Q8C2×D4311yescharacteristic
301C2×#124—431no—
302C2×C22⋊Q8—431no—
303C2×#121—431no—
304C22×C4⋊C4—432no—
305C22×C4⋊C4—861no—
306C22×C42—431no—
307#489—868no—
308C2×#103—432no—
309C2×#103C2×D4312yes—
310C2×#102—432no—
311C2×#102—432no—
312C2×C22⋊C8—432no—
313C2×#97—432no—
314#391C2×D4311yescharacteristic
315#390—431no—
316#388—861no—
317#388—861no—
318#386—861no—
319#386—861no—
320#382—431no—
321#340—432no—
322#340—432no—
323#340—432no—
324#340C2×D4312yes—
325#336—431no—
326#336C2×D4311yescharacteristic
327C43#2590811yescharacteristic, complemented, Sylow
328C22×Q8—21no—
329C22×Q8—862no—
330C22×Q8—868no—
331C22×Q8—861no—
332C22×Q8—1724no—
333C22×Q8—1724no—
334C22×Q8C22×D4311yescharacteristic
335C22×D4—431no—
336C22×D4—861no—
337C23×C4—431no—
338C23×C4—431no—
339C23×C4—431no—
340C23×C4—862no—
341C22×C8—432no—
342C22×C8C22×D4312yes—
343C4⋊Q8—24no—
344C4⋊Q8—438no—
345C4⋊Q8—864no—
346C4⋊Q8—864no—
347C4⋊Q8—868no—
348C4⋊Q8—868no—
349#124—864no—
350C22⋊Q8—864no—
351#121—864no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—432no—
354C2×C4⋊C4—431no—
355C2×C4⋊C4—864no—
356C2×C4⋊C4—868no—
357C2×C4⋊C4—862no—
358C2×C4⋊C4—862no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4—864no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4C22×D4311yescharacteristic
363C2×C4⋊C4C22×D4312yes—
364C2×C22⋊C4—861no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—861no—
368C2×C22⋊C4—861no—
369C2×C22⋊C4—861no—
370C2×C42—431no—
371C2×C42—431no—
372C2×C42—431no—
373C2×C42—864no—
374C2×C42C22×D4311yescharacteristic
375#103—24no—
376#103—864no—
377#102—864no—
378#102—864no—
379C22⋊C8—864no—
380#97—864no—
381#95—21no—
382#95—21no—
383#95—861no—
384#95—861no—
385C24—431no—
386C24—861no—
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—42no—
393C2×Q8—42no—
394C2×Q8—868no—
395C2×Q8—864no—
396C2×Q8—1722no—
397C2×Q8—1724no—
398C2×Q8—1724no—
399C2×Q8—17232no—
400C2×Q8—1722no—
401C2×D4—862no—
402C2×D4—862no—
403C2×D4—861no—
404C2×D4—861no—
405C2×D4—1722no—
406C2×D4—1722no—
407C2×D4—1722no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—431no—
412C22×C4—431no—
413C22×C4—431no—
414C22×C4—434no—
415C22×C4—862no—
416C22×C4—862no—
417C22×C4—862no—
418C22×C4—862no—
419C22×C4—868no—
420C22×C4—862no—
421C22×C4—862no—
422C22×C4—862no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—862no—
426C22×C4—861no—
427C22×C4—1724no—
428C22×C4—1724no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4C23×D4311yescharacteristic
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—862no—
436C2×C8—862no—
437C2×C8—862no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—434no—
442C4⋊C4—868no—
443C4⋊C4—868no—
444C4⋊C4—864no—
445C4⋊C4—862no—
446C4⋊C4—862no—
447C4⋊C4—1722no—
448C4⋊C4D4×D4314yes—
449C22⋊C4—1722no—
450C22⋊C4—1722no—
451C22⋊C4—1722no—
452C22⋊C4—1722no—
453C22⋊C4—1722no—
454C22⋊C4—1722no—
455C42—22no—
456C42—434no—
457C42—862no—
458C42—862no—
459C23—432no—
460C23—432no—
461C23—432no—
462C23—861no—
463C23—861no—
464C23—861no—
465C23—861no—
466C23—1721no—
467C23—1721no—
468C23—1721no—
469C23—1721no—
470C23—1721no—
471C23—1721no—
472C23—1721no—
473C23C2×D4×D4311yescharacteristic
474Q8—48no—
475Q8—42no—
476Q8—42no—
477Q8—1728no—
478Q8—17216no—
479D4—3444no—
480D4—1722no—
481D4—1722no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—24no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—432no—
496C2×C4—432no—
497C2×C4—432no—
498C2×C4—868no—
499C2×C4—868no—
500C2×C4—861no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—864no—
507C2×C4—864no—
508C2×C4—864no—
509C2×C4—17216no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4#1306335212yes—
516C2×C4#1306335712yes—
517C2×C4C2×D4×D4312yes—
518C2×C4#41×D4312yes—
519C2×C4#1306337211yescharacteristic
520C2×C4#1306337311yescharacteristic
521C8—42no—
522C8—1722no—
523C22—434no—
524C22—862no—
525C22—862no—
526C22—862no—
527C22—862no—
528C22—862no—
529C22—862no—
530C22—3441no—
531C22—3441no—
532C22—3441no—
533C22—3441no—
534C22—3441no—
535C22—3441no—
536C22—3441no—
537C22#120×D4311yescharacteristic
538C22#124×D4311yescharacteristic
539C22#1458347211yescharacteristic
540C22AGL(1,ℤ/8)×D4311yescharacteristic
541C22C2×#1306335211yescharacteristic
542C22#137×D4311yescharacteristic
543C22C2×#1306335711yescharacteristic
544C4—22no—
545C4—22no—
546C4—44no—
547C4—81no—
548C4—81no—
549C4—862no—
550C4—862no—
551C4—862no—
552C4—3441no—
553C4—1724no—
554C4#1458355712yes—
555C4#1458355912yes—
556C2—864no—
557C2—6881no—
558C2#1913824811yescharacteristic
559C2#1914382311yescharacteristic
560C2#1914383011yescharacteristic
561C2#489×D4311yescharacteristic
562C2#1914499011yescharacteristic
563C2#1914582011yescharacteristic
564C2#1914582911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2024C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#2024D43
hypocenterC43#25908
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D43C2semidirect
2. C2×#14583260C2semidirect
4. #19135736C2semidirect
5. #19135732C2semidirect
6. #19135728C2semidirect
7. #19135566C2semidirect
9. #19134899C2semidirect
10. #19134356C2semidirect
11. C43×#2024C2semidirect
60. #13063324D4semidirect
261. C2×D43#489semidirect
278. #2024D43semidirect
327. C43#25908semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D432
C2×#145832602
#191428992
#191357362
#191357322
#191357282
#191355662
#191349112
#191348992
#191343562
C43×#20242
#2590843