Finite Group Databasebeta

← #25129033

Subgroups — #25129033

Order 11008.

1228 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×#14583588C211yesmaximal, characteristic
2C2×#14583055C211yesmaximal, characteristic, complemented
3#19137954C211yesmaximal, characteristic
4#19135744C212yesmaximal, complemented
5#19135604C212yesmaximal, complemented
6#19135028C211yesmaximal, characteristic, complemented
7#19134933C212yesmaximal, complemented
8#19134899C212yesmaximal, complemented
9#19134892C211yesmaximal, characteristic
10#19134690C211yesmaximal, characteristic, complemented
11C2×C43×#419C211yesmaximal, characteristic, complemented
12C22×#10621885C2212yes—
13#14583588—24no—
14#14583588—24no—
15C2×#13063318—21no—
16C2×#13063317—21no—
17C2×#13063316C2211yescharacteristic
18C2×#13063307—21no—
19C2×#13063305C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063301C2212yes—
22C2×#13063290C2211yescharacteristic
23C2×C4×C22⋊D43C2211yescharacteristic
24C2×#13063282—21no—
25C2×C4⋊C4×D43C2211yescharacteristic
26#14583055—24no—
27C2×#13063250C2212yes—
28C2×#13063249C2212yes—
29C2×C22⋊(C43⋊C8)C2211yescharacteristic
30C2×(C2×D43)⋊C8C2212yes—
31#14582818—21no—
32#14582810—21no—
33#14582806C2212yes—
34#14582778—21no—
35#14582772—21no—
36#14582759C2211yescharacteristic
37#14582662C2212yes—
38#14582661C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C23×Q8×C43C2211yescharacteristic
42C22×M16×C43C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C43×#419—24no—
45C2×#103×C43C2212yes—
46C2×#103×C43C2212yes—
47C22×Dic86C2311yescharacteristic
48C22×C22⋊D43D411yescharacteristic
49C22×C4×D43—21no—
50C22×C4×D43C2311yescharacteristic
51C2×#10621885—24no—
52C2×#10621885—24no—
53C2×#10621885—42no—
54C22×C43⋊C8C2312yes—
55#13063318—28no—
56#13063317—28no—
57#13063316—22no—
58#13063316—22no—
59#13063307—28no—
60#13063305—22no—
61#13063305—22no—
62#13063304—22no—
63#13063304D414yes—
64#13063301—24no—
65#13063301—42no—
66#13063290—22no—
67#13063290—22no—
68C4×C22⋊D43—22no—
69C4×C22⋊D43—22no—
70#13063282—28no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2312yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4D411yescharacteristic
81C4⋊C4×D43—22no—
82C4⋊C4×D43—22no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43D411yescharacteristic
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91#13063250—42no—
92#13063249—24no—
93C22⋊(C43⋊C8)—22no—
94(C2×D43)⋊C8—42no—
95C43⋊#95—21no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×Q8×C43—21no—
99C22×Q8×C43—24no—
100C22×Q8×C43—22no—
101C22×Q8×C43—22no—
102C22×Q8×C43—42no—
103C22×Q8×C43C2312yes—
104C23×C4×C43—21no—
105C23×C4×C43C2311yescharacteristic
106C2×M16×C43—22no—
107C2×M16×C43—42no—
108C22×C8×C43C2312yes—
109#117×C43—22no—
110#117×C43D414yes—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115#103×C43—24no—
116#103×C43—24no—
117C24×C43C2×D411yescharacteristic
118C23×D43C2×D411yescharacteristic
119C2×Q8×C43—22no—
120C2×Q8×C43—28no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—44no—
126C2×Q8×C43—48no—
127C2×Q8×C43—44no—
128C2×Q8×C43—42no—
129C2×Q8×C43#4114yes—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—44no—
136C22×C4×C43—42no—
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—22no—
142C2×C22⋊D43—22no—
143C2×C22⋊D43—41no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C2×C4×D43—24no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—42no—
156C2×C4×D43—42no—
157C2×Dic86—22no—
158C2×Dic86—22no—
159C2×Dic86—21no—
160C2×Dic86C2×D412yes—
161M16×C43—44no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43C2×D412yes—
168C4⋊C4×C43C2×D412yes—
169C22⋊C4×C43—24no—
170C42×C43—24no—
171C22⋊Dic43—24no—
172C22⋊Dic43—22no—
173C22⋊Dic43—42no—
174#10621885—48no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—22no—
177(C2×D43)⋊C4—44no—
178C4⋊Dic43—24no—
179C4⋊Dic43—24no—
180C4⋊Dic43—21no—
181C4⋊Dic43—22no—
182C4⋊Dic43—22no—
183C4⋊Dic43C2×D412yes—
184Dic43⋊C4—24no—
185Dic43⋊C4—24no—
186Dic43⋊C4—24no—
187Dic43⋊C4—24no—
188Dic43⋊C4—22no—
189Dic43⋊C4—44no—
190C4×Dic43—24no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C23×C43—22no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—22no—
200C23×C43#12012yes—
201C23×C43C22×D411yescharacteristic
202C22×D43—21no—
203C22×D43—22no—
204C22×D43—21no—
205C22×D43—22no—
206C22×D43#13712yes—
207Q8×C43—24no—
208Q8×C43—24no—
209Q8×C43—48no—
210Q8×C43—42no—
211Q8×C43—42no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—24no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—24no—
219C2×C4×C43—48no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—42no—
225C2×C4×C43#12012yes—
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4112yes—
229C2×C4×C43H(5,𝔽2)12yes—
230C22⋊D43—44no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—22no—
234C2×Dic43—21no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—22no—
240C2×Dic43—42no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C4×D43—48no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—42no—
250Dic86—24no—
251Dic86—41no—
252Dic86—41no—
253C8×C43—42no—
254C43⋊C8—42no—
255#23983—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43C2×#12011yescharacteristic
262C22×C43#54612yes—
263C22×C43C2×#13711yescharacteristic
264C22×C43#57511yescharacteristic
265C22×C43#57812yes—
266C2×D43—22no—
267C2×D43—24no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—42no—
271C4×C43—22no—
272C4×C43—44no—
273C4×C43—42no—
274C4×C43—42no—
275C4×C43#52511yescharacteristic
276C4×C43#53511yescharacteristic
277C4×C43#54612yes—
278Dic43—42no—
279Dic43—41no—
280Dic43—42no—
281Dic43—41no—
282Dic43—41no—
283Dic43—82no—
284C2×#552—431no—
285C2×#451—431no—
286C2×#419D4311yescharacteristic, complemented
287#2409—431no—
288#2026—432no—
289#2001—432no—
290#1894—431no—
291#1878—432no—
292#1872—432no—
293#1870—431no—
294#1825—431no—
295C2×C43—42no—
296C2×C43#240411yescharacteristic
297C2×C43#300711yescharacteristic
298C2×C43#301111yescharacteristic
299C2×C43#331212yes—
300C2×C43#332712yes—
301D43—42no—
302C23×Q8C2×D4311yescharacteristic
303C22×Q16—432no—
304C22×M16C2×D4311yescharacteristic
305#552—864no—
306#552—864no—
307C2×#126—861no—
308C2×#125—431no—
309C2×#125—861no—
310C2×#123—861no—
311C2×C22⋊Q8—431no—
312C2×C22⋊Q8—432no—
313C2×C22⋊Q8—431no—
314C2×C4×Q8—431no—
315C2×C4×D4—431no—
316C2×#117—861no—
317C2×#117C2×D4311yescharacteristic
318C22×C4⋊C4—431no—
319#451—864no—
320#419—24no—
321C2×#103—432no—
322C2×#103—432no—
323C2×#103C2×D4312yes—
324C2×#103C2×D4312yes—
325C2×C22⋊C8—431no—
326C2×C22⋊C8—432no—
327#395—861no—
328#393—861no—
329#391—432no—
330#386—861no—
331#385—861no—
332#380—431no—
333#340—432no—
334#340—432no—
335#340—432no—
336#336—432no—
337C43#2398311yescharacteristic, complemented, Sylow
338C22×Q8—21no—
339C22×Q8—24no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—42no—
343C22×Q8—431no—
344C22×Q8C22×D4312yes—
345C22×D4—431no—
346C23×C4—21no—
347C23×C4—431no—
348C23×C4—861no—
349C23×C4C22×D4311yescharacteristic
350C2×Q16—864no—
351C2×Q16—864no—
352C2×Q16—1722no—
353C2×M16—22no—
354C2×M16—42no—
355C22×C8—432no—
356C22×C8C22×D4312yes—
357#126—868no—
358#125—868no—
359#125—862no—
360#125—862no—
361#123—868no—
362C22⋊Q8—434no—
363C22⋊Q8—862no—
364C22⋊Q8—862no—
365C22⋊Q8—862no—
366C22⋊Q8—864no—
367C22⋊Q8—1722no—
368C4×Q8—862no—
369C4×Q8—862no—
370C4×D4—862no—
371C4×D4—862no—
372#117—22no—
373#117—868no—
374#117C22⋊D4314yes—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—432no—
378C2×C4⋊C4—862no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4C22×D4311yescharacteristic
388C2×C4⋊C4C22×D4311yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—431no—
391C2×C22⋊C4—431no—
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—861no—
396C2×C42—21no—
397C2×C42—431no—
398C2×C42—861no—
399#103—24no—
400#103—24no—
401#103—864no—
402#103—1722no—
403C22⋊C8—862no—
404C22⋊C8—1722no—
405#95—862no—
406#95—862no—
407#95—861no—
408C24—431no—
409C24D4×D4311yescharacteristic
410C2×Q8—22no—
411C2×Q8—28no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—44no—
417C2×Q8—48no—
418C2×Q8—44no—
419C2×Q8—42no—
420C2×Q8—432no—
421C2×Q8—861no—
422C2×Q8—862no—
423C2×Q8—862no—
424C2×Q8#1062189814yes—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4—1721no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—44no—
434C22×C4—42no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—864no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—1722no—
447C22×C4—1722no—
448C22×C4D4×D4311yescharacteristic
449C22×C4D4×D4312yes—
450C22×C4C2×C22⋊D4312yes—
451C22×C4C23×D4311yescharacteristic
452Q16—1728no—
453M16—44no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—22no—
457C2×C8—862no—
458C2×C8—862no—
459C2×C8—862no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—432no—
463C4⋊C4—864no—
464C4⋊C4—864no—
465C4⋊C4—864no—
466C4⋊C4—864no—
467C4⋊C4—864no—
468C4⋊C4—862no—
469C4⋊C4—864no—
470C4⋊C4—861no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—1724no—
474C4⋊C4C2×C22⋊D4312yes—
475C4⋊C4C2×C22⋊D4312yes—
476C22⋊C4—24no—
477C22⋊C4—864no—
478C22⋊C4—862no—
479C22⋊C4—864no—
480C22⋊C4—862no—
481C22⋊C4—1724no—
482C22⋊C4—1722no—
483C42—24no—
484C42—864no—
485C42—861no—
486C42—861no—
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—432no—
492C23—861no—
493C23—861no—
494C23—862no—
495C23—862no—
496C23#1306329312yes—
497C23C2×D4×D4311yescharacteristic
498Q8—24no—
499Q8—24no—
500Q8—48no—
501Q8—42no—
502Q8—42no—
503Q8—864no—
504Q8—1721no—
505Q8—1721no—
506D4—1724no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—48no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—861no—
521C2×C4—862no—
522C2×C4—861no—
523C2×C4—862no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—1728no—
530C2×C4—1722no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1722no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1722no—
539C2×C4#1306329312yes—
540C2×C4C2×D4×D4311yescharacteristic
541C2×C4C22×C22⋊D4311yescharacteristic
542C2×C4C2×#1062189812yes—
543C2×C4#1306337012yes—
544C8—42no—
545C8—1722no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—864no—
552C22—862no—
553C22—1722no—
554C22—1721no—
555C22—1721no—
556C22C2×#1306329311yescharacteristic
557C22#1458353912yes—
558C22#137×D4311yescharacteristic
559C22#1458369811yescharacteristic
560C22#1458371512yes—
561C4—22no—
562C4—44no—
563C4—42no—
564C4—42no—
565C4—3442no—
566C4—1721no—
567C4—1722no—
568C4—1721no—
569C4—1722no—
570C4—1721no—
571C4#1458341011yescharacteristic
572C4#1458346611yescharacteristic
573C4#1458353912yes—
574C2—42no—
575C2—1722no—
576C2#1913791411yescharacteristic
577C2#1914385111yescharacteristic
578C2#1914388911yescharacteristic
579C2#1914664712yes—
580C2#1914685912yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#419C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC2×#419D43
hypocenterC43#23983
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×#14583055C2semidirect
4. #19135744C2semidirect
5. #19135604C2semidirect
6. #19135028C2semidirect
7. #19134933C2semidirect
8. #19134899C2semidirect
10. #19134690C2semidirect
11. C2×C43×#419C2semidirect
286. C2×#419D43semidirect
337. C43#23983semidirect

Maximal subgroups

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

subgroupindex
C2×#145835882
C2×#145830552
#191379542
#191357442
#191356042
#191350282
#191349332
#191348992
#191348922
#191346902
C2×C43×#4192
#2398343