Finite Group Databasebeta

← #25130442

Subgroups — #25130442

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×#14583583C211yesmaximal, characteristic
2C2×#14582939C211yesmaximal, characteristic, complemented
3#19138906C211yesmaximal, characteristic
4#19135935C212yesmaximal, complemented
5#19135796C212yesmaximal, complemented
6#19135029C211yesmaximal, characteristic, complemented
7#19134890C211yesmaximal, characteristic
8#19134861C212yesmaximal, complemented
9#19134786C212yesmaximal, complemented
10#19134691C211yesmaximal, characteristic, complemented
11C2×C43×#483C211yesmaximal, characteristic, complemented
12C22×#10621877C2211yescharacteristic
13#14583583—24no—
14#14583583—24no—
15C2×#13063318—21no—
16C2×#13063316C2211yescharacteristic
17C2×#13063315—21no—
18C2×#13063307—21no—
19C2×#13063301C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×C4×C22⋊D43C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23C2×#13063283—21no—
24C2×C4⋊C4×D43C2211yescharacteristic
25#14582939—24no—
26C2×#13063258C2212yes—
27C2×#13063256C2212yes—
28C2×#13063249C2212yes—
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#14582662C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C2×C22⋊Q8×C43C2211yescharacteristic
42C22×C4⋊C4×C43C2211yescharacteristic
43C43×#483—24no—
44C2×#106×C43C2212yes—
45C2×#103×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C22×C22⋊D43D411yescharacteristic
48C22×C4×D43—21no—
49C22×C4×D43C2311yescharacteristic
50C2×#10621877—22no—
51C2×#10621877—24no—
52C22×C43⋊C8C2312yes—
53#13063318—28no—
54#13063316—22no—
55#13063316—22no—
56#13063315—28no—
57#13063307—28no—
58#13063301—22no—
59#13063301—22no—
60Q8×Dic43—22no—
61Q8×Dic43—22no—
62C4×C22⋊D43—22no—
63C4×C22⋊D43—22no—
64#13063284—22no—
65#13063284D414yes—
66#13063283—28no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43C2312yes—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4D411yescharacteristic
77C4⋊C4×D43—22no—
78C4⋊C4×D43—22no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43D411yescharacteristic
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88#13063258—24no—
89#13063256—24no—
90#13063249—24no—
91(C2×D43)⋊C8—24no—
92C43⋊#95—21no—
93C43⋊#95—22no—
94C43⋊#95—22no—
95C22×Q8×C43C2311yescharacteristic
96C23×C4×C43—21no—
97C23×C4×C43C2311yescharacteristic
98C22×C8×C43C2312yes—
99C22⋊Q8×C43—22no—
100C22⋊Q8×C43D414yes—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108#106×C43—24no—
109#103×C43—24no—
110C22⋊C8×C43—22no—
111C24×C43C2×D411yescharacteristic
112C23×D43C2×D411yescharacteristic
113C2×Q8×C43—21no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43C2×D412yes—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—42no—
123C22×C4×C43—82no—
124C22×C4×C43C2×D412yes—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—22no—
129C2×C22⋊D43—22no—
130C2×C22⋊D43—41no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C2×C4×D43—24no—
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—42no—
143C2×C4×D43—42no—
144C2×C8×C43—22no—
145C2×C8×C43—22no—
146C2×C8×C43—22no—
147C4⋊C4×C43—24no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—42no—
152C4⋊C4×C43C2×D412yes—
153C22⋊C4×C43—24no—
154C22⋊Dic43—24no—
155C22⋊Dic43—22no—
156C22⋊Dic43—42no—
157(C2×D43)⋊C4—24no—
158(C2×D43)⋊C4—22no—
159(C2×D43)⋊C4—82no—
160C4⋊Dic43—24no—
161C4⋊Dic43—24no—
162C4⋊Dic43—21no—
163C4⋊Dic43—21no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43C2×D412yes—
167C4⋊Dic43C2×D412yes—
168Dic43⋊C4—24no—
169Dic43⋊C4—24no—
170Dic43⋊C4—24no—
171Dic43⋊C4—22no—
172Dic43⋊C4—82no—
173C4×Dic43—24no—
174C4×Dic43—24no—
175C4×Dic43—21no—
176C4×Dic43—21no—
177#10621877—28no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8#4114yes—
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—
192Q8×C43—24no—
193Q8×C43—41no—
194Q8×C43—41no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—24no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—42no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—84no—
208C2×C4×C43#12012yes—
209C2×C4×C43C22×D411yescharacteristic
210C2×C4×C43C22×D411yescharacteristic
211C2×C4×C43C2×#4112yes—
212C2×C4×C432−1+412yes—
213C22⋊D43—44no—
214C2×Dic43—21no—
215C2×Dic43—22no—
216C2×Dic43—21no—
217C2×Dic43—22no—
218C2×Dic43—21no—
219C2×Dic43—22no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—22no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43—42no—
229C4×D43—48no—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43—42no—
233C8×C43—42no—
234C43⋊C8—24no—
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—41no—
259Dic43—42no—
260Dic43—41no—
261Dic43—41no—
262Dic43—42no—
263Dic43—82no—
264C2×#552—431no—
265C2×#483D4311yescharacteristic, complemented
266C2×#428—431no—
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×M16—431no—
283#552—864no—
284#552—864no—
285C2×#126—861no—
286C2×#125—431no—
287C2×#125—861no—
288C2×#123—861no—
289C2×C22⋊Q8—431no—
290C2×C22⋊Q8C2×D4311yescharacteristic
291C2×C4×Q8—431no—
292C2×C4×D4—431no—
293C2×#117—431no—
294C2×#117—861no—
295C22×C4⋊C4—431no—
296C22×C4⋊C4C2×D4311yescharacteristic
297#483—24no—
298#428—864no—
299C2×#107—432no—
300C2×#106—432no—
301C2×#106C2×D4312yes—
302C2×#103—432no—
303C2×#103C2×D4312yes—
304C2×C22⋊C8—432no—
305C2×C22⋊C8C2×D4311yescharacteristic
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×Q8C22×D4311yescharacteristic
319C22×D4—431no—
320C23×C4—21no—
321C23×C4—431no—
322C23×C4—861no—
323C23×C4C22×D4311yescharacteristic
324C2×M16—864no—
325C2×M16—862no—
326C22×C8—432no—
327C22×C8C22×D4312yes—
328#126—868no—
329#125—862no—
330#125—868no—
331#125—862no—
332#123—868no—
333C22⋊Q8—22no—
334C22⋊Q8—862no—
335C22⋊Q8—862no—
336C22⋊Q8C22⋊D4314yes—
337C4×Q8—862no—
338C4×Q8—862no—
339C4×D4—862no—
340C4×D4—862no—
341#117—434no—
342#117—868no—
343#117—862no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—431no—
349C2×C4⋊C4—431no—
350C2×C4⋊C4—431no—
351C2×C4⋊C4—432no—
352C2×C4⋊C4—862no—
353C2×C4⋊C4—861no—
354C2×C4⋊C4—861no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—861no—
358C2×C4⋊C4—862no—
359C2×C4⋊C4—862no—
360C2×C4⋊C4C22×D4312yes—
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—431no—
370C2×C42—861no—
371C2×C42—861no—
372#107—864no—
373#106—24no—
374#106—864no—
375#103—24no—
376#103—864no—
377C22⋊C8—22no—
378C22⋊C8—864no—
379#95—862no—
380#95—862no—
381#95—861no—
382C24—431no—
383C24D4×D4311yescharacteristic
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8C2×C22⋊D4312yes—
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—868no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—434no—
420C2×C8—862no—
421C2×C8—862no—
422C4⋊C4—24no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—42no—
427C4⋊C4—432no—
428C4⋊C4—432no—
429C4⋊C4—864no—
430C4⋊C4—864no—
431C4⋊C4—864no—
432C4⋊C4—864no—
433C4⋊C4—864no—
434C4⋊C4—862no—
435C4⋊C4—861no—
436C4⋊C4—861no—
437C4⋊C4—862no—
438C4⋊C4—862no—
439C4⋊C4—3442no—
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—864no—
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—24no—
464Q8—41no—
465Q8—41no—
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—862no—
483C2×C4—861no—
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×C4#41×D4312yes—
503C2×C4#1306337212yes—
504C8—42no—
505C8—864no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—42no—
510C22—42no—
511C22—864no—
512C22—862no—
513C22—1721no—
514C22—1722no—
515C22—1721no—
516C22C2×#1306329311yescharacteristic
517C22#1458354712yes—
518C22#137×D4311yescharacteristic
519C22#1458369811yescharacteristic
520C22#1458370512yes—
521C4—22no—
522C4—42no—
523C4—42no—
524C4—82no—
525C4—3442no—
526C4—1721no—
527C4—1721no—
528C4—1722no—
529C4—1721no—
530C4—1722no—
531C4#1458340711yescharacteristic
532C4#1458347111yescharacteristic
533C4#1458354812yes—
534C2—42no—
535C2—1722no—
536C2#1913792711yescharacteristic
537C2#1914385111yescharacteristic
538C2#1914387711yescharacteristic
539C2#1914705312yes—
540C2#1914715812yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#483C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#483D43
hypocenterC43#24111
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
2. C2×#14582939C2semidirect
4. #19135935C2semidirect
5. #19135796C2semidirect
6. #19135029C2semidirect
8. #19134861C2semidirect
9. #19134786C2semidirect
10. #19134691C2semidirect
11. C2×C43×#483C2semidirect
265. C2×#483D43semidirect
317. C43#24111semidirect

Maximal subgroups

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

subgroupindex
C2×#145835832
C2×#145829392
#191389062
#191359352
#191357962
#191350292
#191348902
#191348612
#191347862
#191346912
C2×C43×#4832
#2411143