Finite Group Databasebeta

← #25070739

Subgroups — #25070739

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×#14583496C211yesmaximal, characteristic
2#19145416C211yesmaximal, characteristic, complemented
3#19145397C211yesmaximal, characteristic
4#19133590C214yesmaximal, complemented
5#19133556C214yesmaximal, complemented
6#19133114C211yesmaximal, characteristic, complemented
7#19133110C211yesmaximal, characteristic
8#19132925C211yesmaximal, characteristic, complemented
9C43×#2583C211yesmaximal, characteristic, complemented
10#14583496—22no—
11#14583496—22no—
12#14583496—22no—
13#14583496C2214yes—
14C2×#13063320—21no—
15C2×#13063315—21no—
16C2×#13063310—21no—
17C2×#13063308—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063303—21no—
20C2×#13063299C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22#14583232—21no—
23#14583229C2212yescomplemented
24#14583227—21no—
25#14583212C2212yes—
26#14583155—22no—
27#14583147—22no—
28#14583055C2212yescomplemented
29#14583054—21no—
30#14583049—21no—
31#14583038C2212yes—
32#14582863C2211yescharacteristic
33#14582863C2211yescharacteristic
34#14582635C2214yescomplemented
35#14582632C2214yes—
36#14582625C2214yescomplemented
37C2×C22⋊Q8×C43C2211yescharacteristic
38C22×C4⋊C4×C43C2211yescharacteristic
39C43×#398C2212yescomplemented
40C43×#395C2212yescomplemented
41C43×#389—22no—
42C43×#385—21no—
43C43×#385—21no—
44C4×C22⋊C4×C43C2211yescharacteristic
45C22×Dic86D411yescharacteristic
46C22×D172D411yescharacteristic
47C22×C22⋊D43—21no—
48C22×C4×D43—21no—
49C2×#10621885—22no—
50C2×#10621884—22no—
51C2×#10621877—21no—
52C2×#10621877—21no—
53#13063320—24no—
54#13063320—24no—
55#13063315—24no—
56#13063315—24no—
57#13063310—24no—
58#13063310—24no—
59#13063308—24no—
60#13063308—24no—
61#13063304—21no—
62#13063304—21no—
63#13063304D412yes—
64#13063304C2312yes—
65#13063303—24no—
66#13063303—24no—
67#13063299—21no—
68#13063299—21no—
69#13063299D412yes—
70#13063299C2312yes—
71C4×C22⋊D43—24no—
72C4×C22⋊D43—24no—
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43D411yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85#13063258—22no—
86#13063256—22no—
87#13063249—22no—
88#13063249—22no—
89#13063248—22no—
90#13063245—22no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)—21no—
93C22⋊(C43⋊C8)C2312yes—
94C22⋊(C43⋊C8)C2312yes—
95C22×Q8×C43C2311yescharacteristic
96C23×C4×C43D411yescharacteristic
97C23×C4×C43D411yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C22⋊Q8×C43—21no—
100C22⋊Q8×C43—21no—
101C22⋊Q8×C43—21no—
102C22⋊Q8×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—22no—
109C2×C4⋊C4×C43—22no—
110C2×C4⋊C4×C43D412yes—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2312yes—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43—21no—
116#95×C43—22no—
117#95×C43—22no—
118#95×C43C2312yes—
119C24×C43C2×D411yescharacteristic
120C23×D43—21no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—81no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—42no—
132C22×C4×C43—81no—
133C22×C4×C43—81no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C2×C22⋊D43—22no—
143C2×C22⋊D43—22no—
144C2×C22⋊D43—44no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C2×D172—21no—
149C2×D172—81no—
150C2×D172C2×D412yes—
151C2×C4×D43—24no—
152C2×C4×D43—82no—
153C2×Dic86—21no—
154C2×Dic86—81no—
155C2×Dic86C2×D412yes—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—44no—
163C4⋊C4×C43—41no—
164C4⋊C4×C43—41no—
165C4⋊C4×C43—82no—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C42×C43—81no—
170C22⋊Dic43—22no—
171C22⋊Dic43—22no—
172#10621885—82no—
173#10621884—82no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—22no—
178(C2×D43)⋊C4—22no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43C2×D412yes—
182C4⋊Dic43C2×D412yes—
183Dic43⋊C4—24no—
184Dic43⋊C4—24no—
185Dic43⋊C4—24no—
186Dic43⋊C4—22no—
187Dic43⋊C4—22no—
188C4×Dic43—24no—
189#10621877—81no—
190#10621877—81no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—41no—
196C23×C43#12011yescharacteristic
197C23×C43#12011yescharacteristic
198C23×C43C22×D411yescharacteristic
199C22×D43—22no—
200C22×D43—42no—
201C22×D43—42no—
202C22×D43—42no—
203Q8×C43—42no—
204Q8×C43—42no—
205C2×C4×C43—24no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
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—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—81no—
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C22⋊D43—44no—
232C22⋊D43—44no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239D172—42no—
240D172—81no—
241C4×D43—84no—
242Dic86—42no—
243Dic86—81no—
244C43⋊C8—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#45612yes—
256C22×C43C2×#12011yescharacteristic
257C22×C43#57512yes—
258C2×D43—42no—
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—84no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—44no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—81no—
270C4×C43—81no—
271Dic43—42no—
272Dic43—42no—
273Dic43—42no—
274C2×#539—431no—
275#3195—431no—
276#3193—431no—
277#2583D4311yescharacteristic, complemented
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#300511yescharacteristic
287C2×C43C2×#45611yescharacteristic
288C2×C43#302611yescharacteristic
289D43—82no—
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×#121—431no—
302C2×C4×D4—861no—
303C22×C4⋊C4C2×D4311yescharacteristic
304#484—861no—
305#483—432no—
306#483—861no—
307#480—432no—
308#470—862no—
309#468—862no—
310#451—432no—
311#451—861no—
312#450—861no—
313#448—432no—
314#407—431no—
315#407—431no—
316#398C2×D4312yescomplemented
317#395C2×D4312yescomplemented
318#389—22no—
319#385—21no—
320#385—21no—
321C4×C22⋊C4C2×D4311yescharacteristic
322#328—434no—
323#327—434no—
324#324—434no—
325C43#1832111yescharacteristic, complemented, Sylow
326C22×Q8—431no—
327C22×Q8C22×D4311yescharacteristic
328C22×D4—431no—
329C22×D4—861no—
330C23×C4—861no—
331C23×C4C22⋊D4311yescharacteristic
332C23×C4C22⋊D4311yescharacteristic
333C23×C4C22×D4311yescharacteristic
334C2×Q16—862no—
335C2×SD16—862no—
336C2×M16—861no—
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—432no—
357#121—432no—
358#121—861no—
359#121—861no—
360C4×D4—864no—
361C4×D4—864no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4C22⋊D4312yes—
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C4⋊C4C22×D4312yes—
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—21no—
386C2×C42—861no—
387#107—862no—
388#106—862no—
389#103—862no—
390#103—862no—
391#103—862no—
392#102—862no—
393C22⋊C8—432no—
394C22⋊C8—432no—
395C22⋊C8—861no—
396C22⋊C8—861no—
397#95—22no—
398#95—22no—
399#95C22×D4312yes—
400C24—861no—
401C24C2×C22⋊D4311yescharacteristic
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—81no—
405C2×Q8—432no—
406C2×Q8—861no—
407C2×Q8—3441no—
408C2×D4—432no—
409C2×D4—862no—
410C2×D4—862no—
411C2×D4—861no—
412C2×D4—3441no—
413C2×D4—1724no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—42no—
422C22×C4—81no—
423C22×C4—81no—
424C22×C4—864no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—3442no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4D4×D4311yescharacteristic
432C22×C4D4×D4311yescharacteristic
433C22×C4C2×C22⋊D4312yes—
434C22×C4C2×C22⋊D4312yes—
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C23×D4311yescharacteristic
437Q16—3442no—
438SD16—3442no—
439M16—3441no—
440M16—3441no—
441C2×C8—862no—
442C2×C8—862no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—82no—
453C4⋊C4—432no—
454C4⋊C4—432no—
455C4⋊C4—864no—
456C4⋊C4—864no—
457C4⋊C4—864no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—862no—
461C4⋊C4—862no—
462C22⋊C4—24no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—864no—
466C22⋊C4—864no—
467C22⋊C4—864no—
468C22⋊C4—862no—
469C22⋊C4—862no—
470C22⋊C4—862no—
471C22⋊C4—862no—
472C42—81no—
473C42—864no—
474C23—22no—
475C23—22no—
476C23—41no—
477C23—862no—
478C23—1722no—
479C23—1722no—
480C23—1722no—
481C23#1306329311yescharacteristic
482C23#1306329311yescharacteristic
483C23C22×C22⋊D4311yescharacteristic
484Q8—42no—
485Q8—42no—
486Q8—3441no—
487Q8—1722no—
488D4—3441no—
489D4—1722no—
490D4—1724no—
491D4—1724no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—81no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—3444no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4#1306329311yescharacteristic
522C2×C4#1306329311yescharacteristic
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C8—1722no—
526C8—1722no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—44no—
535C22—3444no—
536C22—1722no—
537C22—1722no—
538C22—1722no—
539C22#1458308112yes—
540C22C2×#1306329311yescharacteristic
541C22#1458369712yes—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—44no—
547C4—42no—
548C4—42no—
549C4—81no—
550C4—81no—
551C4—1722no—
552C4—1722no—
553C4—1722no—
554C2—22no—
555C2—22no—
556C2—41no—
557C2—3442no—
558C2#1914383511yescharacteristic
559C2C2×#1458308111yescharacteristic
560C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2583C2
socleC22×C43C2×#120
prime radicalC2×#13063299C22
hypercenter#2583D43
hypocenterC43#18321
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
2. #19145416C2semidirect
4. #19133590C2semidirect
5. #19133556C2semidirect
6. #19133114C2semidirect
8. #19132925C2semidirect
9. C43×#2583C2semidirect
23. #14583229C22semidirect
28. #14583055C22semidirect
34. #14582635C22semidirect
36. #14582625C22semidirect
39. C43×#398C22semidirect
40. C43×#395C22semidirect
277. #2583D43semidirect
316. #398C2×D43semidirect
317. #395C2×D43semidirect
325. C43#18321semidirect

Maximal subgroups

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

subgroupindex
C2×#145834962
#191454162
#191453972
#191335902
#191335562
#191331142
#191331102
#191329252
C43×#25832
#1832143