Finite Group Databasebeta

← #25069019

Subgroups — #25069019

Order 11008.

962 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583496C211yesmaximal, characteristic
2#19144543C211yesmaximal, characteristic, complemented
3#19144535C211yesmaximal, characteristic
4#19133624C214yesmaximal, complemented
5#19133590C214yesmaximal, complemented
6#19133127C211yesmaximal, characteristic, complemented
7#19133123C211yesmaximal, characteristic
8#19132925C211yesmaximal, characteristic, complemented
9C43×#2484C211yesmaximal, 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#14583240—22no—
23#14583234C2212yescomplemented
24#14583229C2212yescomplemented
25#14583223—22no—
26#14583217C2212yes—
27#14583212C2212yes—
28#14582942—21no—
29#14582942—21no—
30#14582907—21no—
31#14582903—21no—
32#14582863C2211yescharacteristic
33#14582863C2211yescharacteristic
34#14582635C2214yescomplemented
35#14582632C2214yes—
36#14582625C2214yescomplemented
37C2×#117×C43C2211yescharacteristic
38C22×C4⋊C4×C43C2211yescharacteristic
39C43×#400C2212yescomplemented
40C43×#398C2212yescomplemented
41C43×#387—22no—
42C43×#385—21no—
43C43×#381—21no—
44C43×#381C2211yescharacteristic
45C22×Dic86D411yescharacteristic
46C22×D172D411yescharacteristic
47C22×C22⋊D43—21no—
48C22×C4×D43—21no—
49C2×#10621877—21no—
50C2×#10621877—21no—
51#13063320—24no—
52#13063320—24no—
53#13063315—24no—
54#13063315—24no—
55#13063310—24no—
56#13063310—24no—
57#13063308—24no—
58#13063308—24no—
59#13063304—21no—
60#13063304—21no—
61#13063304D412yes—
62#13063304C2312yes—
63#13063303—24no—
64#13063303—24no—
65#13063299—21no—
66#13063299—21no—
67#13063299D412yes—
68#13063299C2312yes—
69C4×C22⋊D43—24no—
70C4×C22⋊D43—24no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43D411yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×C4×Dic43—21no—
83#13063258—22no—
84#13063258—22no—
85#13063256—22no—
86#13063256—22no—
87#13063248—22no—
88#13063248—22no—
89#13063245—22no—
90#13063245—22no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)—21no—
93C22⋊(C43⋊C8)C2312yes—
94C22⋊(C43⋊C8)C2312yes—
95C23×C4×C43D411yescharacteristic
96C23×C4×C43D411yescharacteristic
97C23×C4×C43C2311yescharacteristic
98#117×C43—21no—
99#117×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—22no—
107C2×C4⋊C4×C43D412yes—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C4⋊C4×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2312yes—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C42×C43—21no—
114#95×C43—22no—
115#95×C43—22no—
116#95×C43—21no—
117#95×C43—22no—
118#95×C43C2312yes—
119C24×C43C2×D411yescharacteristic
120C23×D43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—42no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D412yes—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2411yescharacteristic
139C2×C22⋊D43—22no—
140C2×C22⋊D43—22no—
141C2×C22⋊D43—44no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C2×D172—21no—
146C2×D172—42no—
147C2×D172C2×D412yes—
148C2×C4×D43—24no—
149C2×C4×D43—82no—
150C2×Dic86—21no—
151C2×Dic86—42no—
152C2×Dic86C2×D412yes—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—44no—
162C22⋊C4×C43—42no—
163C22⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C42×C43—41no—
166C42×C43—41no—
167C22⋊Dic43—22no—
168C22⋊Dic43—22no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—24no—
171(C2×D43)⋊C4—24no—
172(C2×D43)⋊C4—22no—
173(C2×D43)⋊C4—22no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43C2×D412yes—
177C4⋊Dic43C2×D412yes—
178Dic43⋊C4—24no—
179Dic43⋊C4—24no—
180Dic43⋊C4—24no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183C4×Dic43—24no—
184#10621877—42no—
185#10621877—42no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—41no—
191C23×C43#12011yescharacteristic
192C23×C43#12011yescharacteristic
193C23×C43C22×D411yescharacteristic
194C22×D43—22no—
195C22×D43—42no—
196C22×D43—42no—
197C22×D43—42no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—81no—
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C22⋊D43—44no—
225C22⋊D43—44no—
226C2×Dic43—22no—
227C2×Dic43—22no—
228C2×Dic43—22no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232D172—42no—
233D172—81no—
234C4×D43—84no—
235Dic86—42no—
236Dic86—81no—
237C43⋊C8—42no—
238C43⋊C8—42no—
239#18139—431nomaximal, Sylow
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—44no—
248C22×C43#45812yes—
249C22×C43C2×#12011yescharacteristic
250C22×C43#57512yes—
251C2×D43—42no—
252C2×D43—42no—
253C2×D43—42no—
254C2×D43—84no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—42no—
260C4×C43—42no—
261C4×C43—82no—
262C4×C43—81no—
263C4×C43—81no—
264Dic43—42no—
265Dic43—42no—
266Dic43—42no—
267C2×#539—431no—
268#3095—431no—
269#3094—431no—
270#2484D4311yescharacteristic, complemented
271#1615—434no—
272#1609—434no—
273#1511—431no—
274#1510—431no—
275#1463—431no—
276C2×C43—22no—
277C2×C43—22no—
278C2×C43—41no—
279C2×C43#300511yescharacteristic
280C2×C43#302011yescharacteristic
281C2×C43C2×#45811yescharacteristic
282D43—82no—
283#539—434no—
284#539—862no—
285#539—862no—
286#539—862no—
287C2×#126—861no—
288C2×#125—861no—
289C2×#123—861no—
290C2×#123—861no—
291C2×C22⋊Q8—431no—
292C2×C22⋊Q8—861no—
293C2×#121—431no—
294C2×C4×D4—861no—
295C2×#117C2×D4311yescharacteristic
296C22×C4⋊C4C2×D4311yescharacteristic
297#485—862no—
298#484—432no—
299#483—432no—
300#482—862no—
301#481—432no—
302#480—432no—
303#428—861no—
304#428—861no—
305#419—861no—
306#418—861no—
307#407—431no—
308#407—431no—
309#400C2×D4312yescomplemented
310#398C2×D4312yescomplemented
311#387—22no—
312#385—21no—
313#381—21no—
314#381C2×D4311yescharacteristic
315#328—434no—
316#327—434no—
317#324—434no—
318C43#1813911yescharacteristic, complemented, Sylow
319C22×Q8—431no—
320C22×D4—431no—
321C22×D4—861no—
322C23×C4—861no—
323C23×C4C22⋊D4311yescharacteristic
324C23×C4C22⋊D4311yescharacteristic
325C23×C4C22×D4311yescharacteristic
326C2×M16—861no—
327C2×M16—861no—
328#126—864no—
329#126—864no—
330#125—864no—
331#125—864no—
332#123—864no—
333#123—864no—
334#123—864no—
335#123—864no—
336C22⋊Q8—432no—
337C22⋊Q8—432no—
338C22⋊Q8—864no—
339C22⋊Q8—864no—
340C22⋊Q8—861no—
341C22⋊Q8—861no—
342#121—432no—
343#121—432no—
344#121—861no—
345#121—861no—
346C4×D4—864no—
347C4×D4—864no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—431no—
358C2×C4⋊C4—431no—
359C2×C4⋊C4—861no—
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4C22⋊D4312yes—
364C2×C4⋊C4C22×D4311yescharacteristic
365C2×C4⋊C4C22×D4311yescharacteristic
366C2×C4⋊C4C22×D4312yes—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—861no—
370C2×C22⋊C4—861no—
371C2×C22⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C42—21no—
375C2×C42—861no—
376#107—862no—
377#107—862no—
378#106—862no—
379#106—862no—
380#103—862no—
381#103—862no—
382#102—862no—
383#102—862no—
384C22⋊C8—432no—
385C22⋊C8—432no—
386C22⋊C8—861no—
387C22⋊C8—861no—
388#95—22no—
389#95—22no—
390#95—21no—
391#95—22no—
392#95C22×D4312yes—
393C24—861no—
394C24C2×C22⋊D4311yescharacteristic
395C2×Q8—432no—
396C2×Q8—861no—
397C2×Q8—1722no—
398C2×D4—432no—
399C2×D4—862no—
400C2×D4—862no—
401C2×D4—861no—
402C2×D4—1722no—
403C2×D4—1724no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—864no—
415C22×C4—861no—
416C22×C4—861no—
417C22×C4—861no—
418C22×C4—3442no—
419C22×C4D4×D4311yescharacteristic
420C22×C4D4×D4311yescharacteristic
421C22×C4D4×D4311yescharacteristic
422C22×C4D4×D4311yescharacteristic
423C22×C4C2×C22⋊D4312yes—
424C22×C4C2×C22⋊D4312yes—
425C22×C4C2×C22⋊D4311yescharacteristic
426C22×C4C23×D4311yescharacteristic
427M16—1722no—
428M16—1722no—
429C2×C8—862no—
430C2×C8—862no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—44no—
440C4⋊C4—432no—
441C4⋊C4—432no—
442C4⋊C4—864no—
443C4⋊C4—864no—
444C4⋊C4—864no—
445C4⋊C4—861no—
446C4⋊C4—861no—
447C4⋊C4—862no—
448C4⋊C4—862no—
449C22⋊C4—42no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—864no—
453C22⋊C4—864no—
454C22⋊C4—864no—
455C22⋊C4—862no—
456C22⋊C4—862no—
457C22⋊C4—862no—
458C22⋊C4—862no—
459C42—41no—
460C42—41no—
461C42—864no—
462C23—22no—
463C23—22no—
464C23—41no—
465C23—862no—
466C23—1722no—
467C23—1722no—
468C23—1722no—
469C23#1306329311yescharacteristic
470C23#1306329311yescharacteristic
471C23C22×C22⋊D4311yescharacteristic
472Q8—3441no—
473Q8—1722no—
474D4—3441no—
475D4—1722no—
476D4—1724no—
477D4—1724no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—81no—
500C2×C4—862no—
501C2×C4—862no—
502C2×C4—862no—
503C2×C4—3444no—
504C2×C4—1722no—
505C2×C4—1722no—
506C2×C4—1722no—
507C2×C4#1306329311yescharacteristic
508C2×C4#1306329311yescharacteristic
509C2×C4C2×D4×D4311yescharacteristic
510C2×C4C2×D4×D4311yescharacteristic
511C8—1722no—
512C8—1722no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—44no—
521C22—3444no—
522C22—1722no—
523C22—1722no—
524C22—1722no—
525C22#1458308812yes—
526C22C2×#1306329311yescharacteristic
527C22#1458369712yes—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—1722no—
538C4—1722no—
539C4—1722no—
540C2—22no—
541C2—22no—
542C2—41no—
543C2—3442no—
544C2#1914383511yescharacteristic
545C2#1914395811yescharacteristic
546C2C2×#1458308811yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2484C2
socleC22×C43C2×#120
prime radicalC2×#13063299C22
hypercenter#2484D43
hypocenterC43#18139
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2484

Complements

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

NH ≅ G/Ntype
2. #19144543C2semidirect
4. #19133624C2semidirect
5. #19133590C2semidirect
6. #19133127C2semidirect
8. #19132925C2semidirect
9. C43×#2484C2semidirect
23. #14583234C22semidirect
24. #14583229C22semidirect
34. #14582635C22semidirect
36. #14582625C22semidirect
39. C43×#400C22semidirect
40. C43×#398C22semidirect
270. #2484D43semidirect
309. #400C2×D43semidirect
310. #398C2×D43semidirect
318. C43#18139semidirect

Maximal subgroups

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

subgroupindex
C2×#145834962
#191445432
#191445352
#191336242
#191335902
#191331272
#191331232
#191329252
C43×#24842
#1813943