Finite Group Databasebeta

← #25130513

Subgroups — #25130513

Order 11008.

1218 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583609C211yesmaximal, characteristic, complemented
2C2×#14583190C211yesmaximal, characteristic, complemented
3C2×C4×#10621884C211yesmaximal, characteristic, complemented
4#19139511C211yesmaximal, characteristic
5#19135790C212yesmaximal, complemented
6#19135597C212yesmaximal, complemented
7#19135555C211yesmaximal, characteristic, complemented
8#19135388C211yesmaximal, characteristic, complemented
9#19134911C212yesmaximal, complemented
10#19134789C212yesmaximal, complemented
11C43×#1803C211yesmaximal, characteristic, complemented
12C22×#10621884C2211yescharacteristic
13#14583609—24no—
14#14583609—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063317—21no—
17C2×#13063303—22no—
18C2×#13063301C2212yes—
19C2×#13063300—21no—
20C2×#13063300C2212yes—
21C2×C4×D172—21no—
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24C2×C4⋊C4×D43C2212yes—
25#14583190—24no—
26C4×#10621884—24no—
27C2×#13063257C2212yes—
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—22no—
50C22×C4×D43—21no—
51C22×C4×D43C2312yes—
52C2×#10621884—22no—
53C2×#10621884—22no—
54C2×#10621884—22no—
55C22×C43⋊C8C2311yescharacteristic
56C22×C43⋊C8C2311yescharacteristic
57#13063325—22no—
58#13063325D414yescomplemented
59#13063317—28no—
60#13063303—216no—
61#13063301—24no—
62#13063301—24no—
63#13063300—24no—
64#13063300—42no—
65#13063300—44no—
66C4×D172—28no—
67C4×D172—22no—
68C4×D172—22no—
69C4×D172—22no—
70C4×D172—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2312yes—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—22no—
77C4⋊C4×D43—24no—
78C4⋊C4×D43—24no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4D412yes—
84#13063257—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—21no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—44no—
131C2×D172—44no—
132C2×D172—82no—
133C2×D172SD1614yescomplemented
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—28no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×C4×D43—42no—
145C2×C4×D43—82no—
146C2×C4×D43—82no—
147C2×Dic86—24no—
148C2×Dic86—81no—
149C2×Dic86—81no—
150C2×C8×C43—22no—
151C2×C8×C43—22no—
152C2×C8×C43—22no—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—42no—
158C4⋊C4×C43—81no—
159C4⋊C4×C43C2×D412yes—
160C42×C43—24no—
161C42×C43C2×D412yes—
162C42×C43C2×D412yes—
163#10621884—28no—
164(C2×D43)⋊C4—28no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—44no—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—44no—
169C4⋊Dic43—24no—
170C4⋊Dic43—22no—
171C4⋊Dic43—22no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43C2×D414yes—
175Dic43⋊C4—28no—
176Dic43⋊C4—28no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8#4112yes—
183C23×C43C22×D411yescharacteristic
184C22×D43—22no—
185C22×D43—22no—
186C22×D43—22no—
187C22×D43—22no—
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43C2×SD1614yes—
198Q8×C43—22no—
199Q8×C43—22no—
200Q8×C43—41no—
201Q8×C43—41no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43#12012yes—
214C2×C4×C43#12012yes—
215C2×C4×C43C2×SD1612yes—
216C2×C4×C43#13712yes—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4111yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43H(5,𝔽2)11yescharacteristic
222C2×C4×C432−1+411yescharacteristic
223C2×Dic43—22no—
224C2×Dic43—24no—
225C2×Dic43—22no—
226C2×Dic43—22no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—41no—
232D172—22no—
233D172—22no—
234D172—28no—
235D172—41no—
236D172—41no—
237D172—88no—
238C4×D43—42no—
239C4×D43—42no—
240C4×D43—42no—
241C4×D43—42no—
242C4×D43—88no—
243C4×D43—84no—
244Dic86—84no—
245C8×C43—42no—
246C43⋊C8—22no—
247C43⋊C8—41no—
248#24118—431nomaximal, Sylow
249C22×C43C2×#12011yescharacteristic
250C22×C43#54611yescharacteristic
251C22×C43#54711yescharacteristic
252C22×C43C22×SD1611yescharacteristic
253C22×C43C2×#13711yescharacteristic
254C22×C43#57611yescharacteristic
255C22×C43#57711yescharacteristic
256C2×D43—24no—
257C2×D43—24no—
258C2×D43—24no—
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—81no—
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—22no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43—82no—
274C4×C43#44814yes—
275C4×C43#52511yescharacteristic
276C4×C43#53711yescharacteristic
277C4×C43#54811yescharacteristic
278C4×C43#55011yescharacteristic
279Dic43—42no—
280Dic43—44no—
281Dic43—81no—
282C2×#554—431no—
283C2×#476—431no—
284C2×C4×SD16—431no—
285#2537—431no—
286#2035—432no—
287#2000—432no—
288#1990—431no—
289#1954—431no—
290#1874—432no—
291#1853—432no—
292#1803D4311yescharacteristic, complemented
293C2×C43#240711yescharacteristic
294C2×C43C2×#44811yescharacteristic
295C2×C43#301211yescharacteristic
296C2×C43#329511yescharacteristic
297C2×C43#333111yescharacteristic
298C2×C43#333511yescharacteristic
299C2×C43#335711yescharacteristic
300D43—44no—
301D43—82no—
302C22×SD16—431no—
303#554—864no—
304#554—864no—
305C2×C4⋊Q8—431no—
306C2×#125—861no—
307C2×C22⋊Q8—432no—
308C2×C22⋊Q8—862no—
309C2×#121—432no—
310C2×#121—861no—
311C2×C4×Q8C2×D4311yescharacteristic
312C2×C4×D4—431no—
313C2×C4×D4—431no—
314C2×C4×D4—861no—
315C22×C4⋊C4—432no—
316#476—864no—
317C4×SD16—864no—
318C2×#106—432no—
319C2×#106—431no—
320C2×C4⋊C8C2×D4311yescharacteristic
321C2×#103—431no—
322C2×#103C2×D4312yes—
323C2×#102—432no—
324C2×#102—431no—
325C2×C22⋊C8—432no—
326C2×C22⋊C8—432no—
327C2×C4×C8—431no—
328#394—862no—
329#384C2×D4311yescharacteristic
330#380—432no—
331#380—861no—
332#340—432no—
333#340—432no—
334#340C2×D4312yes—
335C43#2411811yescharacteristic, complemented, Sylow
336C22×Q8—861no—
337C22×Q8C22×D4311yescharacteristic
338C22×D4—431no—
339C22×D4—431no—
340C22×D4—862no—
341C23×C4—432no—
342C23×C4—862no—
343C23×C4—861no—
344C2×SD16—862no—
345C2×SD16—862no—
346C2×SD16—862no—
347C22×C8—431no—
348C22×C8—431no—
349C22×C8C22×D4312yes—
350C4⋊Q8—434no—
351C4⋊Q8—862no—
352#125—868no—
353C22⋊Q8—8616no—
354C22⋊Q8—864no—
355C22⋊Q8—864no—
356#121—864no—
357#121—1722no—
358#121—1724no—
359C4×Q8—22no—
360C4×Q8D17214yescomplemented
361C4×D4—868no—
362C4×D4—862no—
363C4×D4—862no—
364C4×D4—862no—
365C4×D4—862no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—432no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—864no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—864no—
377C2×C4⋊C4C22×D4312yes—
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C22⋊C4—432no—
380C2×C22⋊C4—862no—
381C2×C22⋊C4—862no—
382C2×C22⋊C4—862no—
383C2×C22⋊C4—861no—
384C2×C42—21no—
385C2×C42C22×D4311yescharacteristic
386#106—864no—
387#106—862no—
388C4⋊C8—22no—
389#103—42no—
390#103—862no—
391#102—864no—
392#102—862no—
393C22⋊C8—864no—
394C22⋊C8—1722no—
395C4×C8—862no—
396#95—862no—
397C24—432no—
398C24—861no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—864no—
405C2×Q8—3441no—
406C2×Q8—3441no—
407C2×Q8C2×D17212yes—
408C2×D4—434no—
409C2×D4—432no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—861no—
413C2×D4—861no—
414C2×D4—861no—
415C2×D4—861no—
416C2×D4—861no—
417C2×D4—3442no—
418C2×D4—1724no—
419C2×D4—1724no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—432no—
424C22×C4—868no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—861no—
433C22×C4—3442no—
434C22×C4—3442no—
435C22×C4—1722no—
436C22×C4—1722no—
437C22×C4—1722no—
438C22×C4D4×D4311yescharacteristic
439C22×C4D4×D4311yescharacteristic
440C22×C4C23×D4311yescharacteristic
441SD16—868no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C2×C8—432no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—861no—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—434no—
458C4⋊C4—868no—
459C4⋊C4—868no—
460C4⋊C4—862no—
461C4⋊C4—864no—
462C4⋊C4—862no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4C2×D17212yes—
466C22⋊C4—868no—
467C22⋊C4—864no—
468C22⋊C4—1724no—
469C22⋊C4—1724no—
470C22⋊C4—1722no—
471C42—24no—
472C42C2×D17212yes—
473C42D4×D4312yes—
474C23—434no—
475C23—862no—
476C23—862no—
477C23—862no—
478C23—862no—
479C23—862no—
480C23—862no—
481C23—862no—
482C23—1721no—
483C23—1721no—
484C23—1721no—
485C23—1721no—
486C23—1721no—
487C23—1721no—
488C23C2×D4×D4311yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—41no—
492Q8—41no—
493Q8—3444no—
494D4—862no—
495D4—862no—
496D4—868no—
497D4—3448no—
498D4—1721no—
499D4—1721no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—864no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—3448no—
516C2×C4—3444no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4#1306329512yes—
527C2×C4#1306329512yes—
528C2×C4SD16×D4312yes—
529C2×C4#1306335712yes—
530C2×C4C2×D4×D4311yescharacteristic
531C2×C4C22×D17211yescharacteristic
532C2×C4#41×D4311yescharacteristic
533C2×C4#41×D4311yescharacteristic
534C2×C4#1306337011yescharacteristic
535C2×C4#1306337311yescharacteristic
536C8—42no—
537C8—862no—
538C8—1721no—
539C22—864no—
540C22—864no—
541C22—864no—
542C22—3441no—
543C22—3441no—
544C22—3441no—
545C22—3441no—
546C22—1722no—
547C22—1722no—
548C22—1722no—
549C22—1722no—
550C22—1722no—
551C22—1722no—
552C22—1722no—
553C22C2×#1306329511yescharacteristic
554C22#1458354611yescharacteristic
555C22#1458355111yescharacteristic
556C22C2×SD16×D4311yescharacteristic
557C22C2×#1306335711yescharacteristic
558C22#1458370311yescharacteristic
559C22#1458370811yescharacteristic
560C4—22no—
561C4—42no—
562C4—42no—
563C4—82no—
564C4—3441no—
565C4—1722no—
566C4—1724no—
567C4#1458303914yes—
568C4#1458341111yescharacteristic
569C4#1458348011yescharacteristic
570C4#1458355911yescharacteristic
571C4#1458356711yescharacteristic
572C2—3442no—
573C2—1724no—
574C2#1913794111yescharacteristic
575C2C2×#1458303911yescharacteristic
576C2#1914390111yescharacteristic
577C2#1914642211yescharacteristic
578C2#1914691411yescharacteristic
579C2#1914695511yescharacteristic
580C2#1914721811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radical#19139511C2
hypercenter#1803D43
hypocenterC43#24118
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×#14583609C2semidirect
2. C2×#14583190C2semidirect
3. C2×C4×#10621884C2semidirect
5. #19135790C2semidirect
6. #19135597C2semidirect
7. #19135555C2semidirect
8. #19135388C2semidirect
9. #19134911C2semidirect
10. #19134789C2semidirect
11. C43×#1803C2semidirect
58. #13063325D4semidirect
96. C4×Q8×C43D4semidirect
133. C2×D172SD16semidirect
292. #1803D43semidirect
335. C43#24118semidirect
360. C4×Q8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145836092
C2×#145831902
C2×C4×#106218842
#191395112
#191357902
#191355972
#191355552
#191353882
#191349112
#191347892
C43×#18032
#2411843