Finite Group Databasebeta

← #25128594

Subgroups — #25128594

Order 11008.

1222 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic
2C2×#14583055C211yesmaximal, characteristic, complemented
3C2×#14583038C211yesmaximal, characteristic
4#19135736C212yesmaximal, complemented
5#19135688C212yesmaximal, complemented
6#19134939C212yesmaximal, complemented
7#19134932C212yesmaximal, complemented
8#19134917C211yesmaximal, characteristic
9#19134907C211yesmaximal, characteristic, complemented
10#19134666C211yesmaximal, characteristic, complemented
11C43×#2310C211yesmaximal, characteristic, complemented
12C22×#10621885C2212yes—
13C22×#10621884C2212yes—
14#14583520—24no—
15#14583520—24no—
16C2×#13063325C2211yescharacteristic
17C2×#13063320—21no—
18C2×#13063313C2211yescharacteristic
19C2×#13063311—21no—
20C2×#13063307—21no—
21C2×#13063304C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063299C2211yescharacteristic
24C2×C4×Dic86C2211yescharacteristic
25C2×C4×D172C2211yescharacteristic
26#14583055—24no—
27#14583038—24no—
28C2×#13063249C2212yes—
29C2×#13063249C2212yes—
30C2×#13063248C2212yes—
31C2×#13063245C2212yes—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582661C2212yes—
35#14582661C2212yes—
36#14582654C2212yes—
37#14582654C2212yes—
38C23×Q8×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×#391—21no—
42C43×#391—21no—
43C43×#391C2212yes—
44C43×#391C2212yes—
45C43×#381—21no—
46C43×#381—21no—
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C22×D172C2311yescharacteristic
50C22×C22⋊D43—21no—
51C22×C4×D43—21no—
52C2×#10621885—24no—
53C2×#10621885—24no—
54C2×#10621885—42no—
55C2×#10621884—24no—
56C2×#10621884—24no—
57C2×#10621884—42no—
58C22×C43⋊C8C2312yes—
59C22×C43⋊C8C2312yes—
60#13063325—22no—
61#13063325—22no—
62#13063320—28no—
63#13063313—22no—
64#13063313—22no—
65#13063311—28no—
66#13063307—28no—
67#13063304—22no—
68#13063304D414yes—
69#13063303—28no—
70#13063299—22no—
71#13063299D414yes—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C4×D172—22no—
75C4×D172—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87#13063249—24no—
88#13063249—24no—
89#13063248—42no—
90#13063245—42no—
91C22⋊(C43⋊C8)—22no—
92C22⋊(C43⋊C8)—22no—
93C22×Q8×C43—24no—
94C22×Q8×C43—21no—
95C22×Q8×C43—22no—
96C22×Q8×C43—22no—
97C22×Q8×C43—42no—
98C22×Q8×C43C2312yes—
99C23×C4×C43—21no—
100C23×C4×C43C2311yescharacteristic
101#117×C43—22no—
102#117×C43—22no—
103#117×C43—42no—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43C2312yes—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43D411yescharacteristic
109C2×C22⋊C4×C43D411yescharacteristic
110C2×C42×C43—21no—
111C2×C42×C43C2311yescharacteristic
112C2×C42×C43C2311yescharacteristic
113#95×C43—22no—
114#95×C43—22no—
115#95×C43—22no—
116#95×C43—22no—
117C24×C43C2×D411yescharacteristic
118C23×D43—21no—
119C2×Q8×C43—24no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—48no—
126C2×Q8×C43—48no—
127C2×Q8×C43—42no—
128C2×Q8×C43—42no—
129C2×Q8×C43#4114yes—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—24no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—42no—
136C22×C4×C43—42no—
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D412yes—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—24no—
146C2×C22⋊D43—82no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C2×D172—21no—
151C2×D172—22no—
152C2×D172—22no—
153C2×D172C2×D412yes—
154C2×C4×D43—24no—
155C2×C4×D43—82no—
156C2×Dic86—22no—
157C2×Dic86—22no—
158C2×Dic86—21no—
159C2×Dic86—24no—
160C2×Dic86—82no—
161C2×Dic86C2×D412yes—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—42no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—42no—
174C22⋊Dic43—24no—
175#10621885—48no—
176#10621884—48no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—24no—
180(C2×D43)⋊C4—24no—
181C4⋊Dic43—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43C2×D412yes—
185C4⋊Dic43C2×D412yes—
186Dic43⋊C4—24no—
187Dic43⋊C4—24no—
188C4×Dic43—24no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195C23×C43—21no—
196C23×C43—21no—
197C23×C43—22no—
198C23×C43—22no—
199C23×C43#12012yes—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—42no—
205C22×D43—42no—
206Q8×C43—24no—
207Q8×C43—24no—
208Q8×C43—48no—
209Q8×C43—42no—
210Q8×C43—42no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—48no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43#12012yes—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4112yes—
234C2×C4×C43H(5,𝔽2)12yes—
235C22⋊D43—84no—
236C2×Dic43—22no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243D172—24no—
244D172—42no—
245C4×D43—84no—
246Dic86—24no—
247Dic86—42no—
248Dic86—84no—
249C43⋊C8—42no—
250C43⋊C8—42no—
251#23946—431nomaximal, Sylow
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43C2×#12011yescharacteristic
258C22×C43#52511yescharacteristic
259C22×C43#53511yescharacteristic
260C22×C43#57712yes—
261C22×C43#57812yes—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—82no—
266C2×D43—82no—
267C4×C43—22no—
268C4×C43—44no—
269C4×C43—41no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—82no—
274C4×C43#54612yes—
275C4×C43#54612yes—
276Dic43—42no—
277Dic43—42no—
278Dic43—42no—
279C2×#542—431no—
280C2×#451—431no—
281C2×#448—431no—
282#2310D4311yescharacteristic, complemented
283#2024—432no—
284#2015—432no—
285#1878—432no—
286#1877—432no—
287#1875—431no—
288#1873—431no—
289#1818—431no—
290C2×C43—42no—
291C2×C43#240411yescharacteristic
292C2×C43#300911yescharacteristic
293C2×C43#301111yescharacteristic
294C2×C43#312112yes—
295C2×C43#322512yes—
296D43—82no—
297C23×Q8C2×D4311yescharacteristic
298C22×Q16—432no—
299C22×SD16—432no—
300#542—864no—
301#542—864no—
302C2×C4⋊Q8—431no—
303C2×#126—861no—
304C2×#124—431no—
305C2×#124—861no—
306C2×#123—861no—
307C2×C22⋊Q8—431no—
308C2×C22⋊Q8—861no—
309C2×#121—431no—
310C2×C4×Q8—431no—
311C2×C4×D4—431no—
312C2×#117C2×D4311yescharacteristic
313C2×#117C2×D4311yescharacteristic
314#451—864no—
315#448—864no—
316C2×#103—432no—
317C2×#103—432no—
318C2×#103—432no—
319C2×#102—432no—
320C2×C22⋊C8—431no—
321C2×C22⋊C8—431no—
322#391—21no—
323#391—21no—
324#391C2×D4312yes—
325#391C2×D4312yes—
326#381—21no—
327#381—21no—
328#340—432no—
329#340—432no—
330#336—432no—
331#336—432no—
332C43#2394611yescharacteristic, complemented, Sylow
333C22×Q8—24no—
334C22×Q8—21no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—42no—
338C22×Q8—431no—
339C22×Q8—861no—
340C22×Q8C22×D4312yes—
341C22×D4—431no—
342C22×D4—861no—
343C23×C4—21no—
344C23×C4—861no—
345C23×C4C22×D4311yescharacteristic
346C2×Q16—864no—
347C2×Q16—864no—
348C2×Q16—1722no—
349C2×SD16—864no—
350C2×SD16—864no—
351C2×SD16—1722no—
352C22×C8—432no—
353C22×C8—432no—
354C4⋊Q8—862no—
355C4⋊Q8—862no—
356#126—868no—
357#124—862no—
358#124—862no—
359#124—868no—
360#123—868no—
361C22⋊Q8—434no—
362C22⋊Q8—868no—
363C22⋊Q8—862no—
364#121—434no—
365#121—862no—
366C4×Q8—862no—
367C4×Q8—862no—
368C4×D4—862no—
369C4×D4—862no—
370#117—22no—
371#117—22no—
372#117—42no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4C22⋊D4311yescharacteristic
379C2×C4⋊C4C22⋊D4311yescharacteristic
380C2×C4⋊C4C22×D4312yes—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4C22⋊D4311yescharacteristic
388C2×C22⋊C4C22⋊D4311yescharacteristic
389C2×C42—21no—
390C2×C42—861no—
391C2×C42C22×D4311yescharacteristic
392C2×C42C22×D4311yescharacteristic
393#103—864no—
394#103—864no—
395#103—1722no—
396#102—1722no—
397C22⋊C8—862no—
398C22⋊C8—862no—
399#95—22no—
400#95—22no—
401#95—22no—
402#95—22no—
403C24—861no—
404C24C2×C22⋊D4311yescharacteristic
405C2×Q8—24no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—48no—
412C2×Q8—48no—
413C2×Q8—42no—
414C2×Q8—42no—
415C2×Q8—432no—
416C2×Q8—864no—
417C2×Q8—861no—
418C2×Q8—862no—
419C2×Q8—862no—
420C2×Q8—3442no—
421C2×Q8#1062189814yes—
422C2×D4—432no—
423C2×D4—864no—
424C2×D4—861no—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4—3442no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—864no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—3442no—
440C22×C4D4×D4312yes—
441C22×C4D4×D4312yes—
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446C22×C4C2×C22⋊D4311yescharacteristic
447C22×C4C23×D4311yescharacteristic
448Q16—1728no—
449SD16—1728no—
450C2×C8—862no—
451C2×C8—862no—
452C2×C8—862no—
453C2×C8—862no—
454C2×C8—862no—
455C2×C8—862no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—432no—
461C4⋊C4—432no—
462C4⋊C4—864no—
463C4⋊C4—864no—
464C4⋊C4—864no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—42no—
470C22⋊C4—864no—
471C22⋊C4—864no—
472C22⋊C4—864no—
473C22⋊C4—864no—
474C22⋊C4—864no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—864no—
481C23—21no—
482C23—22no—
483C23—22no—
484C23—21no—
485C23—862no—
486C23—1721no—
487C23—1722no—
488C23—1722no—
489C23—1721no—
490C23#1306329312yes—
491C23C22×C22⋊D4311yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—48no—
495Q8—42no—
496Q8—42no—
497Q8—864no—
498Q8—3444no—
499Q8—1722no—
500D4—864no—
501D4—3444no—
502D4—1722no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—48no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—862no—
523C2×C4—862no—
524C2×C4—862no—
525C2×C4—3444no—
526C2×C4—1721no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4—1721no—
530C2×C4#1306329312yes—
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C2×#1062189812yes—
534C2×C4#1306337012yes—
535C8—1722no—
536C8—1722no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—42no—
541C22—42no—
542C22—3442no—
543C22—3442no—
544C22—1722no—
545C22—1722no—
546C22—1722no—
547C22C2×#1306329311yescharacteristic
548C22#1458341011yescharacteristic
549C22#1458346611yescharacteristic
550C22#1458370712yes—
551C22#1458371412yes—
552C4—22no—
553C4—44no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—82no—
559C4—1722no—
560C4—1722no—
561C4—1722no—
562C4#1458353912yes—
563C4#1458353912yes—
564C2—42no—
565C2—3442no—
566C2#1913791411yescharacteristic
567C2#1914387011yescharacteristic
568C2#1914388811yescharacteristic
569C2#1914482412yes—
570C2#1914570412yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2310C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2310D43
hypocenterC43#23946
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. C2×#14583055C2semidirect
4. #19135736C2semidirect
5. #19135688C2semidirect
6. #19134939C2semidirect
7. #19134932C2semidirect
9. #19134907C2semidirect
10. #19134666C2semidirect
11. C43×#2310C2semidirect
282. #2310D43semidirect
332. C43#23946semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145830552
C2×#145830382
#191357362
#191356882
#191349392
#191349322
#191349172
#191349072
#191346662
C43×#23102
#2394643