Finite Group Databasebeta

← #25149957

Subgroups — #25149957

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2C2×#14583267C211yesmaximal, characteristic, complemented
3C2×#14583106C211yesmaximal, characteristic, complemented
4#19135603C212yesmaximal, complemented
5#19135603C212yesmaximal, complemented
6#19135552C211yesmaximal, characteristic, complemented
7#19135394C211yesmaximal, characteristic
8#19134908C212yesmaximal, complemented
9#19134903C212yesmaximal, complemented
10#19134428C211yesmaximal, characteristic, complemented
11C43×#2542C211yesmaximal, characteristic
12C22×#10621885C2212yes—
13#14583589—24no—
14#14583589—24no—
15C2×#13063318—21no—
16C2×#13063317C2211yescharacteristic
17C2×#13063315—21no—
18C2×#13063306—21no—
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23C2×#13063281—21no—
24C22×C4⋊Dic43C2211yescharacteristic
25#14583267—24no—
26#14583106—24no—
27C2×C4⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063249C2212yes—
29C2×#13063249C2212yes—
30C2×#13063249C2212yes—
31C2×#13063248C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×C22⋊(C43⋊C8)C2212yes—
34C2×#13063236C2211yescharacteristic
35#14582661C2212yes—
36#14582661C2212yes—
37#14582661C2212yes—
38C2×C4⋊Q8×C43C2211yescharacteristic
39C2×C22⋊Q8×C43C2212yes—
40C2×C22⋊Q8×C43C2212yes—
41C2×C4×D4×C43C2211yescharacteristic
42C43×#399—21no—
43C43×#399—21no—
44C43×#390—21no—
45C43×#384—21no—
46C4×C4⋊C4×C43C2211yescharacteristic
47C22×Dic86C2311yescharacteristic
48C23×Dic43—21no—
49C2×#10621885—24no—
50C2×#10621885—42no—
51C2×#10621885—42no—
52C22×C43⋊C8C2312yes—
53C22×C43⋊C8C2312yes—
54#13063318—28no—
55#13063317—22no—
56#13063317D414yes—
57#13063315—28no—
58#13063306—28no—
59#13063304—22no—
60#13063304—22no—
61#13063304—22no—
62#13063304—22no—
63C4×Dic86—22no—
64C4×Dic86D414yes—
65#13063284—22no—
66#13063284—22no—
67#13063281—28no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—22no—
70C2×C4⋊Dic43—22no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C4⋊(C43⋊C8)—22no—
85#13063249—24no—
86#13063249—24no—
87#13063249—24no—
88#13063248—24no—
89C22⋊(C43⋊C8)—42no—
90C22⋊(C43⋊C8)—42no—
91#13063236—22no—
92C22×Q8×C43C2312yes—
93C22×D4×C43D411yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2311yescharacteristic
96C4⋊Q8×C43—22no—
97C4⋊Q8×C43—22no—
98C22⋊Q8×C43—24no—
99C22⋊Q8×C43—24no—
100C22⋊Q8×C43—42no—
101C22⋊Q8×C43—42no—
102C4×D4×C43—22no—
103C4×D4×C43—22no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43—22no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43C2312yes—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#95×C43—21no—
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C2×Q8×C43—22no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—41no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—24no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C2×Dic86—22no—
151C2×Dic86—22no—
152C2×Dic86—21no—
153C2×Dic86C2×D412yes—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—44no—
157C4⋊C4×C43—44no—
158C4⋊C4×C43—42no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43#4114yes—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—44no—
164C22⋊C4×C43—44no—
165C42×C43—42no—
166C42×C43C2×D412yes—
167C42×C43C2×D412yes—
168C22⋊Dic43—24no—
169C22⋊Dic43—24no—
170C22⋊Dic43—24no—
171#10621885—48no—
172C4⋊Dic43—24no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43C2×D412yes—
177C4⋊Dic43C2×D412yes—
178C4⋊Dic43C2×D412yes—
179Dic43⋊C4—24no—
180Dic43⋊C4—24no—
181Dic43⋊C4—24no—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184C4×Dic43—24no—
185C4×Dic43—24no—
186C2×C43⋊C8—22no—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C23×C43—21no—
193C23×C43—22no—
194C23×C43—21no—
195C23×C43—22no—
196C23×C43—21no—
197C23×C43—22no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—22no—
201C23×C43#13712yes—
202C23×C43C22×D411yescharacteristic
203Q8×C43—42no—
204Q8×C43—42no—
205Q8×C43—42no—
206Q8×C43—42no—
207D4×C43—44no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43#12012yes—
228C2×C4×C43#12012yes—
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4112yes—
232C2×C4×C43H(5,𝔽2)12yes—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—22no—
237C2×Dic43—48no—
238C2×Dic43—42no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—42no—
244Dic86—22no—
245Dic86—22no—
246Dic86—42no—
247C43⋊C8—42no—
248C43⋊C8—42no—
249#25584—431nomaximal, Sylow
250C22×C43—22no—
251C22×C43—24no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43—42no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43C2×#12011yescharacteristic
261C22×C43#54612yes—
262C22×C43C2×#13711yescharacteristic
263C22×C43#57511yescharacteristic
264C22×C43#57812yes—
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—44no—
270C4×C43—82no—
271C4×C43#53211yescharacteristic
272C4×C43#53511yescharacteristic
273C4×C43#55012yes—
274Dic43—42no—
275Dic43—42no—
276Dic43—42no—
277Dic43—42no—
278C2×#552—431no—
279C2×#491—431no—
280C2×#462—431no—
281#2542D4311yescharacteristic
282#2001—432no—
283#2001—432no—
284#1989—431no—
285#1955—431no—
286#1873—432no—
287#1872—432no—
288#1763—431no—
289C2×C43—42no—
290C2×C43—81no—
291C2×C43#243111yescharacteristic
292C2×C43#300711yescharacteristic
293C2×C43#301111yescharacteristic
294C2×C43#331212yes—
295C2×C43#331512yes—
296C22×Q16—432no—
297#552—864no—
298#552—864no—
299C2×C4⋊Q8C2×D4311yescharacteristic
300C2×#126—861no—
301C2×#125—431no—
302C2×#125—861no—
303C2×#123—861no—
304C2×C22⋊Q8—431no—
305C2×C22⋊Q8—431no—
306C2×C22⋊Q8C2×D4312yes—
307C2×C22⋊Q8C2×D4312yes—
308C2×C4×Q8—431no—
309C2×C4×D4C2×D4311yescharacteristic
310C2×#117—431no—
311C2×#117—861no—
312C22×C4⋊C4—431no—
313#491—864no—
314#462—864no—
315C2×C4⋊C8—431no—
316C2×#103—432no—
317C2×#103—432no—
318C2×#103—432no—
319C2×#103—432no—
320C2×C22⋊C8—432no—
321C2×C22⋊C8—432no—
322C2×#97—431no—
323#399—21no—
324#399—21no—
325#390—21no—
326#384—21no—
327C4×C4⋊C4C2×D4311yescharacteristic
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2558411yescharacteristic, complemented, Sylow
332C22×Q8—431no—
333C22×Q8C22×D4312yes—
334C22×D4C22⋊D4311yescharacteristic
335C23×C4—861no—
336C23×C4C22×D4311yescharacteristic
337C23×C4C22×D4311yescharacteristic
338C2×Q16—864no—
339C2×Q16—1722no—
340C2×Q16—1722no—
341C22×C8—432no—
342C22×C8—432no—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345#126—868no—
346#125—434no—
347#125—868no—
348#125—862no—
349#123—868no—
350C22⋊Q8—24no—
351C22⋊Q8—24no—
352C22⋊Q8—42no—
353C22⋊Q8—42no—
354C22⋊Q8—862no—
355C22⋊Q8—862no—
356C22⋊Q8—862no—
357C22⋊Q8—862no—
358C4×Q8—434no—
359C4×Q8—862no—
360C4×D4—22no—
361C4×D4—22no—
362#117—868no—
363#117—862no—
364#117—862no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4C22⋊D4311yescharacteristic
381C2×C4⋊C4C22×D4312yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
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×C42—861no—
392C2×C42C22×D4311yescharacteristic
393C4⋊C8—862no—
394#103—864no—
395#103—864no—
396#103—864no—
397#103—864no—
398C22⋊C8—1722no—
399C22⋊C8—1722no—
400#97—862no—
401#95—21no—
402C24C2×C22⋊D4311yescharacteristic
403C24C2×C22⋊D4311yescharacteristic
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—432no—
411C2×Q8—861no—
412C2×Q8—862no—
413C2×Q8—862no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—41no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—864no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—1722no—
433C22×C4—1722no—
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C23×D4311yescharacteristic
439Q16—1728no—
440C2×C8—862no—
441C2×C8—862no—
442C2×C8—862no—
443C2×C8—862no—
444C2×C8—862no—
445C2×C8—862no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—42no—
451C4⋊C4—42no—
452C4⋊C4—432no—
453C4⋊C4—432no—
454C4⋊C4—432no—
455C4⋊C4—864no—
456C4⋊C4—864no—
457C4⋊C4—864no—
458C4⋊C4—864no—
459C4⋊C4—864no—
460C4⋊C4—864no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4#1062190014yes—
465C22⋊C4—22no—
466C22⋊C4—22no—
467C22⋊C4—44no—
468C22⋊C4—44no—
469C22⋊C4—864no—
470C22⋊C4—864no—
471C22⋊C4—864no—
472C42—42no—
473C42—864no—
474C42—864no—
475C42D4×D4312yes—
476C42D4×D4312yes—
477C23—21no—
478C23—21no—
479C23—22no—
480C23—22no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—22no—
485C23—22no—
486C23#1306335612yes—
487C23C22×C22⋊D4311yescharacteristic
488Q8—42no—
489Q8—42no—
490Q8—42no—
491Q8—42no—
492Q8—862no—
493Q8—862no—
494Q8—1722no—
495D4—44no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—1728no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4#1306329312yes—
527C2×C4#1306329312yes—
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4C2×#1062190012yes—
531C2×C4#1306337012yes—
532C8—1722no—
533C8—1722no—
534C22—24no—
535C22—22no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22C2×#1306329311yescharacteristic
545C22#1458354312yes—
546C22C2×#1306335611yescharacteristic
547C22#1458369711yescharacteristic
548C22#1458371412yes—
549C4—22no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—44no—
554C4—82no—
555C4—1722no—
556C4—1722no—
557C4—1722no—
558C4—1722no—
559C4#1458344711yescharacteristic
560C4#1458346211yescharacteristic
561C4#1458356912yes—
562C2—42no—
563C2—81no—
564C2#1913821111yescharacteristic
565C2#1914385311yescharacteristic
566C2#1914388811yescharacteristic
567C2#1914664612yes—
568C2#1914669112yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2542C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#2542D43
hypocenterC43#25584
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
2. C2×#14583267C2semidirect
3. C2×#14583106C2semidirect
4. #19135603C2semidirect
5. #19135603C2semidirect
6. #19135552C2semidirect
8. #19134908C2semidirect
9. #19134903C2semidirect
10. #19134428C2semidirect
331. C43#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145832672
C2×#145831062
#191356032
#191355522
#191353942
#191349082
#191349032
#191344282
C43×#25422
#2558443