Finite Group Databasebeta

← #25070738

Subgroups — #25070738

Order 11008.

982 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583494C211yesmaximal, characteristic
2#19145416C211yesmaximal, characteristic, complemented
3#19139976C211yesmaximal, characteristic, complemented
4#19133589C214yesmaximal, complemented
5#19133555C214yesmaximal, complemented
6#19133116C211yesmaximal, characteristic, complemented
7#19133111C211yesmaximal, characteristic
8#19132924C211yesmaximal, characteristic, complemented
9C43×#3193C211yesmaximal, characteristic
10#14583494—22no—
11#14583494—22no—
12#14583494—22no—
13#14583494C2214yes—
14C2×#13063318—21no—
15C2×#13063315—21no—
16C2×#13063306—21no—
17C2×#13063306—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063302—21no—
20C2×D4×Dic43—21no—
21C22×Dic43⋊C4C2211yescharacteristic
22#14583229C2212yescomplemented
23#14583227—21no—
24#14583155—22no—
25#14583055C2212yescomplemented
26#14583054—21no—
27#14582863C2211yescharacteristic
28#14582830C2212yescomplemented
29#14582818C2212yescomplemented
30#14582794—22no—
31#14582771—21no—
32#14582771—21no—
33C4×C22⋊Dic43C2211yescharacteristic
34#14582637C2214yescomplemented
35#14582633C2214yes—
36#14582624C2214yescomplemented
37C2×C22⋊Q8×C43C2211yescharacteristic
38C2×#121×C43C2211yescharacteristic
39C43×#484—21no—
40C43×#480C2212yes—
41C43×#468—22no—
42C43×#450—21no—
43C43×#448C2212yes—
44C43×#407C2211yescharacteristic
45C22×Dic86D411yescharacteristic
46C23×Dic43—21no—
47C23×Dic43D411yescharacteristic
48C23×Dic43D411yescharacteristic
49C2×#10621885—22no—
50C2×#10621877—21no—
51#13063318—24no—
52#13063318—24no—
53#13063315—24no—
54#13063315—24no—
55#13063306—24no—
56#13063306—24no—
57#13063306—24no—
58#13063306—24no—
59#13063304—21no—
60#13063304—21no—
61#13063304D412yes—
62#13063304C2312yes—
63#13063302—24no—
64#13063302—24no—
65D4×Dic43—24no—
66D4×Dic43—24no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×Dic43⋊C4—21no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—22no—
78C2×Dic43⋊C4D412yes—
79C2×Dic43⋊C4C2312yes—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87#13063256—22no—
88#13063249—22no—
89#13063248—22no—
90C22⋊(C43⋊C8)—21no—
91C22⋊(C43⋊C8)C2312yes—
92C43⋊#95—22no—
93C43⋊#95—22no—
94C43⋊#95C2312yes—
95C22×Q8×C43C2311yescharacteristic
96C22×D4×C43—21no—
97C22×D4×C43D411yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C2×SD16×C43—22no—
100C2×M16×C43—21no—
101C22⋊Q8×C43—21no—
102C22⋊Q8×C43—21no—
103C22⋊Q8×C43—21no—
104C22⋊Q8×C43—21no—
105#121×C43—21no—
106#121×C43—21no—
107#121×C43D412yes—
108#121×C43C2312yes—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D411yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114#107×C43—22no—
115#103×C43—22no—
116#102×C43—22no—
117C22⋊C8×C43—21no—
118C22⋊C8×C43C2312yes—
119C24×C43—21no—
120C24×C43C2×D411yescharacteristic
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—81no—
124C2×D4×C43—21no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—44no—
128C2×D4×C43—81no—
129C2×D4×C43C2×D412yes—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—81no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—24no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—81no—
150C22×Dic43—82no—
151C22×Dic43C2×D412yes—
152C22×Dic43C2×D412yes—
153C2×Dic86—21no—
154C2×Dic86—81no—
155C2×Dic86C2×D412yes—
156SD16×C43—82no—
157M16×C43—81no—
158C2×C8×C43—22no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—41no—
163C4⋊C4×C43—41no—
164C4⋊C4×C43C2×D412yes—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C22⋊Dic43—24no—
170C22⋊Dic43—24no—
171C22⋊Dic43—24no—
172C22⋊Dic43—24no—
173C22⋊Dic43—22no—
174C22⋊Dic43—22no—
175#10621885—82no—
176C4⋊Dic43—24no—
177C4⋊Dic43—21no—
178C4⋊Dic43C2×D412yes—
179Dic43⋊C4—24no—
180Dic43⋊C4—24no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4—22no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187Dic43⋊C4—44no—
188Dic43⋊C4—82no—
189C4×Dic43—24no—
190C4×Dic43—81no—
191#10621877—81no—
192C2×C43⋊C8—22no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—41no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43#12011yescharacteristic
201C23×C43#12011yescharacteristic
202C23×C43C22×D411yescharacteristic
203Q8×C43—42no—
204Q8×C43—42no—
205D4×C43—42no—
206D4×C43—44no—
207D4×C43—44no—
208D4×C43—81no—
209C2×C4×C43—22no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—42no—
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×Dic43—24no—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—81no—
241C2×Dic43—84no—
242Dic86—42no—
243Dic86—81no—
244C8×C43—42no—
245C43⋊C8—42no—
246#18321—431nomaximal, Sylow
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—21no—
251C22×C43—21no—
252C22×C43—21no—
253C22×C43—21no—
254C22×C43—44no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—84no—
259C22×C43#45612yes—
260C22×C43C2×#12011yescharacteristic
261C22×C43#57512yes—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—42no—
267C4×C43—81no—
268C4×C43—81no—
269Dic43—44no—
270Dic43—42no—
271Dic43—42no—
272Dic43—42no—
273Dic43—42no—
274C2×#539—431no—
275#3195—431no—
276#3193D4311yescharacteristic
277#2583—431no—
278#1609—434no—
279#1603—434no—
280#1508—431no—
281#1507—431no—
282#1463—431no—
283C2×C43—22no—
284C2×C43—22no—
285C2×C43—41no—
286C2×C43—82no—
287C2×C43#300511yescharacteristic
288C2×C43C2×#45611yescharacteristic
289C2×C43#302611yescharacteristic
290#539—434no—
291#539—862no—
292#539—862no—
293#539—862no—
294C2×#126—861no—
295C2×#125—861no—
296C2×#123—861no—
297C2×#123—861no—
298C2×C22⋊Q8—431no—
299C2×C22⋊Q8—861no—
300C2×C22⋊Q8C2×D4311yescharacteristic
301C2×#121C2×D4311yescharacteristic
302C2×C4×D4—861no—
303C22×C4⋊C4—431no—
304#484—21no—
305#483—432no—
306#483—861no—
307#480C2×D4312yes—
308#470—862no—
309#468—22no—
310#451—432no—
311#451—861no—
312#450—21no—
313#448C2×D4312yes—
314#407—431no—
315#407C2×D4311yescharacteristic
316#398—432no—
317#395—432no—
318#389—862no—
319#385—861no—
320#385—861no—
321C4×C22⋊C4—431no—
322#328—434no—
323#327—434no—
324#324—434no—
325C43#1832111yescharacteristic, complemented, Sylow
326C22×Q8—431no—
327C22×Q8C22×D4311yescharacteristic
328C22×D4—21no—
329C22×D4C22⋊D4311yescharacteristic
330C23×C4—431no—
331C23×C4—431no—
332C23×C4—861no—
333C23×C4C22×D4311yescharacteristic
334C2×Q16—862no—
335C2×SD16—22no—
336C2×M16—21no—
337C2×M16—861no—
338#126—864no—
339#126—864no—
340#125—864no—
341#125—864no—
342#123—864no—
343#123—864no—
344#123—864no—
345#123—864no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—432no—
351C22⋊Q8—432no—
352C22⋊Q8—864no—
353C22⋊Q8—864no—
354C22⋊Q8—861no—
355C22⋊Q8—861no—
356#121—21no—
357#121—21no—
358#121C22⋊D4312yes—
359#121C22×D4312yes—
360C4×D4—864no—
361C4×D4—864no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—432no—
365C2×C4⋊C4—432no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—862no—
376C2×C4⋊C4C22⋊D4311yescharacteristic
377C2×C4⋊C4C22×D4311yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C42—861no—
386C2×C42—861no—
387#107—22no—
388#106—862no—
389#103—22no—
390#103—862no—
391#103—862no—
392#102—22no—
393C22⋊C8—21no—
394C22⋊C8—432no—
395C22⋊C8—861no—
396C22⋊C8C22×D4312yes—
397#95—432no—
398#95—862no—
399#95—862no—
400C24—21no—
401C24D4×D4311yescharacteristic
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—81no—
405C2×Q8—432no—
406C2×Q8—861no—
407C2×Q8—3441no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—21no—
411C2×D4—44no—
412C2×D4—81no—
413C2×D4C2×C22⋊D4312yes—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—81no—
418C22×C4—432no—
419C22×C4—432no—
420C22×C4—864no—
421C22×C4—861no—
422C22×C4—861no—
423C22×C4—861no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—862no—
428C22×C4—3442no—
429C22×C4—3441no—
430C22×C4—1722no—
431C22×C4D4×D4311yescharacteristic
432C22×C4D4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C23×D4311yescharacteristic
437Q16—3442no—
438SD16—82no—
439M16—81no—
440M16—3441no—
441C2×C8—22no—
442C2×C8—862no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—432no—
449C4⋊C4—864no—
450C4⋊C4—864no—
451C4⋊C4—864no—
452C4⋊C4—862no—
453C4⋊C4—862no—
454C4⋊C4—861no—
455C4⋊C4—862no—
456C4⋊C4—862no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—3442no—
460C4⋊C4—1724no—
461C4⋊C4C2×C22⋊D4312yes—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—864no—
467C22⋊C4—864no—
468C22⋊C4—864no—
469C22⋊C4—864no—
470C22⋊C4—862no—
471C22⋊C4—862no—
472C42—864no—
473C42—3441no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—41no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23#1306329311yescharacteristic
482C23#1306329311yescharacteristic
483C23C2×D4×D4311yescharacteristic
484Q8—42no—
485Q8—42no—
486Q8—3441no—
487Q8—1722no—
488D4—42no—
489D4—44no—
490D4—44no—
491D4—81no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—864no—
505C2×C4—862no—
506C2×C4—862no—
507C2×C4—862no—
508C2×C4—862no—
509C2×C4—862no—
510C2×C4—862no—
511C2×C4—3441no—
512C2×C4—3444no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4#1306329311yescharacteristic
522C2×C4#1306329311yescharacteristic
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C22×C22⋊D4311yescharacteristic
525C8—42no—
526C8—1722no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—44no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—84no—
539C22#1458308012yes—
540C22C2×#1306329311yescharacteristic
541C22#1458369512yes—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—42no—
547C4—81no—
548C4—81no—
549C4—1724no—
550C4—1722no—
551C4—1722no—
552C4—1722no—
553C4—1722no—
554C2—22no—
555C2—22no—
556C2—41no—
557C2—82no—
558C2#1914383411yescharacteristic
559C2C2×#1458308011yescharacteristic
560C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3193C2
socleC22×C43C2×#120
prime radicalC2×#121×C43C22
hypercenter#3193D43
hypocenterC43#18321
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3193

Complements

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

NH ≅ G/Ntype
2. #19145416C2semidirect
3. #19139976C2semidirect
4. #19133589C2semidirect
5. #19133555C2semidirect
6. #19133116C2semidirect
8. #19132924C2semidirect
22. #14583229C22semidirect
25. #14583055C22semidirect
28. #14582830C22semidirect
29. #14582818C22semidirect
34. #14582637C22semidirect
36. #14582624C22semidirect
325. C43#18321semidirect

Maximal subgroups

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

subgroupindex
C2×#145834942
#191454162
#191399762
#191335892
#191335552
#191331162
#191331112
#191329242
C43×#31932
#1832143