Finite Group Databasebeta

← #25130445

Subgroups — #25130445

Order 11008.

1068 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583588C211yesmaximal, characteristic
2C2×#14583229C211yesmaximal, characteristic, complemented
3#19138906C211yesmaximal, characteristic
4#19135931C212yesmaximal, complemented
5#19135800C212yesmaximal, complemented
6#19135028C211yesmaximal, characteristic, complemented
7#19134892C211yesmaximal, characteristic
8#19134860C212yesmaximal, complemented
9#19134786C212yesmaximal, complemented
10#19134690C211yesmaximal, characteristic, complemented
11C2×C43×#428C211yesmaximal, characteristic, complemented
12#14583588—24no—
13#14583588—24no—
14C2×#13063318—21no—
15C2×#13063317—21no—
16C2×#13063316C2211yescharacteristic
17C2×#13063307—21no—
18C2×#13063305C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22C2×#13063282—21no—
23C2×C4⋊C4×D43C2211yescharacteristic
24#14583229—24no—
25C2×#13063256C2212yes—
26C2×#13063250C2212yes—
27C2×#13063248C2212yes—
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8C2212yes—
30#14582837—21no—
31#14582834—21no—
32#14582795C2212yes—
33#14582778—21no—
34#14582772—21no—
35#14582759C2211yescharacteristic
36#14582756C2212yes—
37#14582662C2212yes—
38#14582661C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C22×M16×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C22×C4⋊C4×C43C2211yescharacteristic
44C43×#428—24no—
45C2×#107×C43C2212yes—
46C2×#106×C43C2212yes—
47C22×Dic86C2311yescharacteristic
48C22×C22⋊D43D411yescharacteristic
49C22×C4×D43—21no—
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063318—28no—
53#13063317—28no—
54#13063316—22no—
55#13063316—22no—
56#13063307—28no—
57#13063305—22no—
58#13063305—22no—
59#13063304—22no—
60#13063304D414yes—
61#13063290—22no—
62#13063290—22no—
63C4×C22⋊D43—22no—
64C4×C22⋊D43—22no—
65#13063282—28no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2312yes—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—22no—
75C2×Dic43⋊C4D411yescharacteristic
76C4⋊C4×D43—22no—
77C4⋊C4×D43—22no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43D411yescharacteristic
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4D411yescharacteristic
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86#13063256—24no—
87#13063250—24no—
88#13063248—24no—
89C22⋊(C43⋊C8)—22no—
90(C2×D43)⋊C8—24no—
91C43⋊#95—21no—
92C43⋊#95—22no—
93C43⋊#95—22no—
94C23×C4×C43—21no—
95C23×C4×C43C2311yescharacteristic
96C2×M16×C43—22no—
97C2×M16×C43—24no—
98C22×C8×C43C2312yes—
99#117×C43—22no—
100#117×C43D414yes—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C42×C43—21no—
109#107×C43—24no—
110#106×C43—24no—
111C24×C43C2×D411yescharacteristic
112C23×D43C2×D411yescharacteristic
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—42no—
119C22×C4×C43—82no—
120C22×C4×C43C2×D412yes—
121C22×C4×C43C2×D412yes—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2411yescharacteristic
124C2×C22⋊D43—22no—
125C2×C22⋊D43—22no—
126C2×C22⋊D43—41no—
127C22×Dic43—21no—
128C22×Dic43—21no—
129C22×Dic43—22no—
130C22×Dic43C2×D411yescharacteristic
131C22×Dic43C2×D411yescharacteristic
132C22×Dic43C2×D411yescharacteristic
133C2×C4×D43—24no—
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—42no—
139C2×C4×D43—42no—
140C2×Dic86—22no—
141C2×Dic86—22no—
142C2×Dic86—21no—
143C2×Dic86C2×D412yes—
144M16×C43—28no—
145C2×C8×C43—22no—
146C2×C8×C43—22no—
147C2×C8×C43#4114yes—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—42no—
153C4⋊C4×C43C2×D412yes—
154C4⋊C4×C43C2×D412yes—
155C22⋊C4×C43—24no—
156C42×C43—24no—
157C22⋊Dic43—24no—
158C22⋊Dic43—22no—
159C22⋊Dic43—42no—
160(C2×D43)⋊C4—24no—
161(C2×D43)⋊C4—22no—
162(C2×D43)⋊C4—82no—
163C4⋊Dic43—24no—
164C4⋊Dic43—24no—
165C4⋊Dic43—21no—
166C4⋊Dic43—22no—
167C4⋊Dic43—22no—
168C4⋊Dic43C2×D412yes—
169Dic43⋊C4—24no—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173Dic43⋊C4—22no—
174Dic43⋊C4—82no—
175C4×Dic43—24no—
176C4×Dic43—21no—
177C4×Dic43—21no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C23×C43—22no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—22no—
185C23×C43#12012yes—
186C23×C43C22×D411yescharacteristic
187C22×D43—21no—
188C22×D43—22no—
189C22×D43—21no—
190C22×D43—22no—
191C22×D43#13712yes—
192C2×C4×C43—22no—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—24no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—42no—
204C2×C4×C43—84no—
205C2×C4×C43#12012yes—
206C2×C4×C43C22×D411yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C2×#4112yes—
209C2×C4×C432−1+412yes—
210C22⋊D43—44no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—22no—
214C2×Dic43—21no—
215C2×Dic43—22no—
216C2×Dic43—22no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—22no—
220C2×Dic43—42no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—42no—
224C2×Dic43—42no—
225C2×Dic43—42no—
226C4×D43—48no—
227C4×D43—41no—
228C4×D43—41no—
229C4×D43—42no—
230Dic86—24no—
231Dic86—41no—
232Dic86—41no—
233C8×C43—24no—
234C43⋊C8—42no—
235#24111—431nomaximal, Sylow
236C22×C43—22no—
237C22×C43—22no—
238C22×C43—22no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43C2×#12011yescharacteristic
242C22×C43#54712yes—
243C22×C43C2×#13711yescharacteristic
244C22×C43#57511yescharacteristic
245C22×C43#57712yes—
246C2×D43—24no—
247C2×D43—22no—
248C2×D43—42no—
249C2×D43—41no—
250C2×D43—41no—
251C4×C43—22no—
252C4×C43—42no—
253C4×C43—42no—
254C4×C43—82no—
255C4×C43#52511yescharacteristic
256C4×C43#53611yescharacteristic
257C4×C43#54712yes—
258Dic43—42no—
259Dic43—41no—
260Dic43—42no—
261Dic43—41no—
262Dic43—41no—
263Dic43—82no—
264C2×#552—431no—
265C2×#483—431no—
266C2×#428D4311yescharacteristic, complemented
267#2487—431no—
268#2059—432no—
269#2036—432no—
270#1894—431no—
271#1870—431no—
272#1865—432no—
273#1853—432no—
274#1825—431no—
275C2×C43—42no—
276C2×C43#240611yescharacteristic
277C2×C43#300711yescharacteristic
278C2×C43#301011yescharacteristic
279C2×C43#334412yes—
280C2×C43#335112yes—
281D43—42no—
282C22×M16C2×D4311yescharacteristic
283#552—864no—
284#552—864no—
285C2×#126—861no—
286C2×#125—431no—
287C2×#125—861no—
288C2×#123—861no—
289C2×C22⋊Q8—431no—
290C2×C22⋊Q8—431no—
291C2×C4×Q8—431no—
292C2×C4×D4—431no—
293C2×#117—861no—
294C2×#117C2×D4311yescharacteristic
295C22×C4⋊C4—431no—
296C22×C4⋊C4C2×D4311yescharacteristic
297#483—864no—
298#428—24no—
299C2×#107C2×D4312yes—
300C2×#106—432no—
301C2×#106C2×D4312yes—
302C2×#103—432no—
303C2×#103—432no—
304C2×C22⋊C8—431no—
305C2×C22⋊C8—432no—
306#400—861no—
307#399—861no—
308#389—432no—
309#386—861no—
310#385—861no—
311#380—431no—
312#380—432no—
313#340—432no—
314#340—432no—
315#340—432no—
316#336—432no—
317C43#2411111yescharacteristic, complemented, Sylow
318C22×Q8—431no—
319C22×D4—431no—
320C23×C4—21no—
321C23×C4—431no—
322C23×C4—861no—
323C23×C4C22×D4311yescharacteristic
324C2×M16—22no—
325C2×M16—24no—
326C22×C8—432no—
327C22×C8C22×D4312yes—
328#126—868no—
329#125—868no—
330#125—862no—
331#125—862no—
332#123—868no—
333C22⋊Q8—434no—
334C22⋊Q8—862no—
335C22⋊Q8—862no—
336C22⋊Q8—862no—
337C4×Q8—862no—
338C4×Q8—862no—
339C4×D4—862no—
340C4×D4—862no—
341#117—22no—
342#117—868no—
343#117C22⋊D4314yes—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—431no—
348C2×C4⋊C4—431no—
349C2×C4⋊C4—432no—
350C2×C4⋊C4—862no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4—861no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—862no—
358C2×C4⋊C4—862no—
359C2×C4⋊C4C22×D4312yes—
360C2×C4⋊C4C22×D4311yescharacteristic
361C2×C4⋊C4C22×D4311yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—431no—
364C2×C22⋊C4—431no—
365C2×C22⋊C4—861no—
366C2×C22⋊C4—861no—
367C2×C22⋊C4—862no—
368C2×C22⋊C4—861no—
369C2×C42—21no—
370C2×C42—431no—
371C2×C42—861no—
372#107—24no—
373#106—24no—
374#106—864no—
375#103—864no—
376#103—864no—
377C22⋊C8—862no—
378C22⋊C8—864no—
379#95—862no—
380#95—862no—
381#95—861no—
382C24—431no—
383C24D4×D4311yescharacteristic
384C2×Q8—432no—
385C2×Q8—861no—
386C2×Q8—862no—
387C2×Q8—862no—
388C2×D4—862no—
389C2×D4—862no—
390C2×D4—1721no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—42no—
397C22×C4—82no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—431no—
401C22×C4—864no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4—861no—
405C22×C4—861no—
406C22×C4—862no—
407C22×C4—862no—
408C22×C4—862no—
409C22×C4—1722no—
410C22×C4—1722no—
411C22×C4D4×D4311yescharacteristic
412C22×C4D4×D4312yes—
413C22×C4C2×C22⋊D4312yes—
414C22×C4C23×D4311yescharacteristic
415M16—28no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—862no—
419C2×C8—862no—
420C2×C8—862no—
421C2×C8#1062189814yes—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—42no—
427C4⋊C4—432no—
428C4⋊C4—864no—
429C4⋊C4—864no—
430C4⋊C4—864no—
431C4⋊C4—864no—
432C4⋊C4—864no—
433C4⋊C4—862no—
434C4⋊C4—864no—
435C4⋊C4—861no—
436C4⋊C4—862no—
437C4⋊C4—862no—
438C4⋊C4—3442no—
439C4⋊C4C2×C22⋊D4312yes—
440C4⋊C4C2×C22⋊D4312yes—
441C22⋊C4—24no—
442C22⋊C4—864no—
443C22⋊C4—862no—
444C22⋊C4—864no—
445C22⋊C4—862no—
446C22⋊C4—3442no—
447C22⋊C4—1722no—
448C42—24no—
449C42—864no—
450C42—861no—
451C42—861no—
452C23—21no—
453C23—21no—
454C23—22no—
455C23—22no—
456C23—432no—
457C23—861no—
458C23—861no—
459C23—862no—
460C23—862no—
461C23#1306329312yes—
462C23C2×D4×D4311yescharacteristic
463Q8—864no—
464Q8—1721no—
465Q8—1721no—
466D4—1724no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—84no—
480C2×C4—861no—
481C2×C4—862no—
482C2×C4—861no—
483C2×C4—862no—
484C2×C4—861no—
485C2×C4—861no—
486C2×C4—861no—
487C2×C4—862no—
488C2×C4—862no—
489C2×C4—1728no—
490C2×C4—1722no—
491C2×C4—1722no—
492C2×C4—1722no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—1722no—
496C2×C4—1721no—
497C2×C4—1721no—
498C2×C4—1722no—
499C2×C4#1306329312yes—
500C2×C4C2×D4×D4311yescharacteristic
501C2×C4C22×C22⋊D4311yescharacteristic
502C2×C4C2×#1062189812yes—
503C2×C4#1306337312yes—
504C8—24no—
505C8—1722no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—42no—
510C22—42no—
511C22—864no—
512C22—862no—
513C22—1721no—
514C22—1722no—
515C22—1721no—
516C22C2×#1306329311yescharacteristic
517C22#1458355012yes—
518C22#137×D4311yescharacteristic
519C22#1458369811yescharacteristic
520C22#1458370912yes—
521C4—22no—
522C4—42no—
523C4—42no—
524C4—82no—
525C4—3442no—
526C4—1721no—
527C4—1722no—
528C4—1721no—
529C4—1722no—
530C4—1721no—
531C4#1458341011yescharacteristic
532C4#1458347311yescharacteristic
533C4#1458355012yes—
534C2—42no—
535C2—1722no—
536C2#1913793011yescharacteristic
537C2#1914385111yescharacteristic
538C2#1914388011yescharacteristic
539C2#1914705112yes—
540C2#1914715612yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#428D43
hypocenterC43#24111
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. C2×#14583229C2semidirect
4. #19135931C2semidirect
5. #19135800C2semidirect
6. #19135028C2semidirect
8. #19134860C2semidirect
9. #19134786C2semidirect
10. #19134690C2semidirect
11. C2×C43×#428C2semidirect
266. C2×#428D43semidirect
317. C43#24111semidirect

Maximal subgroups

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

subgroupindex
C2×#145835882
C2×#145832292
#191389062
#191359312
#191358002
#191350282
#191348922
#191348602
#191347862
#191346902
C2×C43×#4282
#2411143