Finite Group Databasebeta

← #25063811

Subgroups — #25063811

Order 11008.

974 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148689C211yesmaximal, characteristic
2#19143682C211yesmaximal, characteristic, complemented
3#19136958C211yesmaximal, characteristic, complemented
4#19133120C211yesmaximal, characteristic
5#19133117C212yesmaximal
6#19133106C211yesmaximal, characteristic, complemented
7#19133105C212yesmaximal, complemented
8#19133095C211yesmaximal, characteristic, complemented
9#19133092C212yesmaximal, complemented
10#19133078C212yesmaximal
11C43×#1500C211yesmaximal, characteristic
12#14583628C411yescharacteristic, complemented
13#14583627C411yescharacteristic, complemented
14#14583626C412yescomplemented
15#14583619C411yescharacteristic, complemented
16#14583618C412yescomplemented
17#14583589—21no—
18#14583586—22no—
19D4×Dic86—21no—
20D4×Dic86C411yescharacteristic, complemented
21#14583511—21no—
22#14583506—22no—
23#14583456C2211yescharacteristic
24#14583451C2212yes—
25#14583430C2212yes—
26#14583376—21no—
27C2×C4×Dic86—21no—
28C2×C4×Dic86C2211yescharacteristic
29#14583029—21no—
30#14583028—22no—
31C8×Dic86—21no—
32#14582956C2211yescharacteristic
33#14582953C2212yes—
34#14582949C2212yes—
35C4×C4⋊Dic43—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37#14582750—22no—
38#14582750C2212yes—
39#14582744C2212yes—
40#14582637C2212yes—
41#14582637C2212yes—
42#14582636C2212yes—
43#14582635C2212yes—
44#14582635C2212yes—
45#14582633C2212yes—
46C43×#529C2211yescharacteristic
47C43×#431C2211yescharacteristic
48C43×#376C2211yescharacteristic
49C43×#328C2211yescharacteristic
50C43×#328C2211yescharacteristic
51C43×#327C2211yescharacteristic
52C43×#327C2211yescharacteristic
53C22×Dic86—21no—
54C22×Dic86D411yescharacteristic
55#13063325—21no—
56#13063325C2×C411yescharacteristic
57#13063325C2×C411yescharacteristic
58#13063324—22no—
59#13063324C2×C412yes—
60#13063323C2×C412yes—
61#13063318—22no—
62#13063318—22no—
63#13063318—22no—
64#13063318—22no—
65#13063317—21no—
66#13063317—21no—
67#13063316—22no—
68#13063316C2×C412yes—
69#13063315—22no—
70#13063315—22no—
71#13063315—22no—
72#13063315—22no—
73#13063312C2×C412yes—
74#13063306—22no—
75#13063304—21no—
76#13063304—21no—
77#13063304—21no—
78#13063304C2312yes—
79#13063302—22no—
80#13063302—22no—
81#13063302—22no—
82Q8×Dic43C2×C412yes—
83C4×Dic86—28no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×Dic86—21no—
87C4×Dic86C2×C412yes—
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86C2×C412yes—
90C4×Dic86C2×C411yescharacteristic
91C4×Dic86D411yescharacteristic
92C4×Dic86D412yes—
93C4×Dic86D411yescharacteristic
94#13063290—22no—
95#13063290—22no—
96#13063290C2×C412yes—
97#13063290C2×C412yes—
98D4×Dic43—22no—
99D4×Dic43C2×C412yes—
100#13063284—21no—
101#13063284—21no—
102#13063281—22no—
103#13063281—22no—
104#13063281—22no—
105C2×C4⋊Dic43—21no—
106C2×C4⋊Dic43D411yescharacteristic
107C2×Dic43⋊C4—22no—
108C2×Dic43⋊C4D412yes—
109C2×C4×Dic43—22no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—22no—
112C2×C4×Dic43C2312yes—
113C4⋊(C43⋊C8)—21no—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116C22⋊(C43⋊C8)C2312yes—
117#13063236—21no—
118#13063235—22no—
119C8×Dic43—22no—
120C43⋊#95—22no—
121C43⋊#95C2312yes—
122#126×C43—21no—
123#125×C43C2×C411yescharacteristic
124#124×C43C2×C411yescharacteristic
125#123×C43—21no—
126C22⋊Q8×C43C2311yescharacteristic
127#121×C43C2311yescharacteristic
128C4×Q8×C43C2×C411yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2×C411yescharacteristic
131#117×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C22⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43C2311yescharacteristic
137C4×C8×C43—21no—
138#95×C43—21no—
139#95×C43C2311yescharacteristic
140#95×C43C2311yescharacteristic
141C2×Q8×C43C22×C411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43C22×C411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43C2×D412yes—
153C22×Dic43C2×D412yes—
154C2×Dic86—24no—
155C2×Dic86—21no—
156C2×Dic86—22no—
157C2×Dic86—44no—
158C2×Dic86C22⋊C412yes—
159C2×Dic86C22⋊C411yescharacteristic
160C2×Dic86C22⋊C411yescharacteristic
161C2×Dic86C22×C412yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43C22×C411yescharacteristic
169C4⋊C4×C43C22×C411yescharacteristic
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43—24no—
176C42×C43—21no—
177C42×C43C22×C411yescharacteristic
178C42×C43C22×C411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43C2×D411yescharacteristic
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183C22⋊Dic43—22no—
184C22⋊Dic43—22no—
185C4⋊Dic43—24no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—22no—
190C4⋊Dic43—22no—
191C4⋊Dic43C22⋊C411yescharacteristic
192C4⋊Dic43C22⋊C411yescharacteristic
193C4⋊Dic43C22⋊C412yes—
194C4⋊Dic43C22×C412yes—
195Dic43⋊C4—28no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4C22⋊C412yes—
205Dic43⋊C4C22⋊C412yes—
206Dic43⋊C4C22⋊C412yes—
207Dic43⋊C4C22⋊C412yes—
208C4×Dic43—28no—
209C4×Dic43—22no—
210C4×Dic43—22no—
211C4×Dic43—22no—
212C4×Dic43—22no—
213C4×Dic43—82no—
214C4×Dic43—81no—
215C4×Dic43C22×C412yes—
216C4×Dic43C22×C412yes—
217C4×Dic43C2×D412yes—
218C4×Dic43C2×D412yes—
219C2×C43⋊C8—22no—
220C23×C43—21no—
221C23×C43C22×D411yescharacteristic
222Q8×C43—41no—
223D4×C43—41no—
224D4×C43—41no—
225D4×C43—41no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C2×Dic43—22no—
247C2×Dic43—22no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—44no—
255C2×Dic43C2×C22⋊C412yes—
256C2×Dic43C2×C22⋊C412yes—
257C2×Dic43C2×C22⋊C412yes—
258C2×Dic43C2×C22⋊C412yes—
259Dic86—22no—
260Dic86—24no—
261Dic86—42no—
262Dic86—44no—
263Dic86—42no—
264Dic86#10414yes—
265C8×C43—41no—
266C8×C43—41no—
267C43⋊C8—42no—
268#17549—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43C22×C22⋊C411yescharacteristic
275C22×C43#57711yescharacteristic
276C22×C43#57811yescharacteristic
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—42no—
283C4×C43—42no—
284C4×C43—41no—
285C4×C43—41no—
286C4×C43—41no—
287C4×C43C2×#10412yes—
288Dic43—22no—
289Dic43—22no—
290Dic43—22no—
291Dic43—44no—
292Dic43—42no—
293Dic43—42no—
294Dic43C2×#10414yes—
295#3523—431no—
296#2984—431no—
297#2276—431no—
298#1509—432no—
299#1509—431no—
300#1506—431no—
301#1506—432no—
302#1503—431no—
303#1503—432no—
304#1500—432no—
305#1500D4311yescharacteristic
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—81no—
309C2×C43#288411yescharacteristic
310C2×C43#289811yescharacteristic
311C2×C43C22×#10411yescharacteristic
312#557—432no—
313#557—431no—
314#557—431no—
315#556—432no—
316#556—431no—
317#552—861no—
318#552—862no—
319D4×Q8—431no—
320D4×Q8—861no—
321#541—861no—
322#541—862no—
323#533—432no—
324#533—431no—
325#529—432no—
326#529C2×D4311yescharacteristic
327#519—861no—
328C2×C4×Q8—431no—
329C2×C4×Q8—861no—
330#446—861no—
331#446—862no—
332C8×Q8—861no—
333#432—431no—
334#432—432no—
335#431—432no—
336#431C2×D4311yescharacteristic
337C4×C4⋊C4—431no—
338C4×C4⋊C4—432no—
339C4×C4⋊C4—862no—
340C4×C4⋊C4—861no—
341#376—432no—
342#376C2×D4311yescharacteristic
343#328—432no—
344#328—432no—
345#328—432no—
346#328—432no—
347#328—432no—
348#328C2×D4311yescharacteristic
349#328C2×D4311yescharacteristic
350#327—432no—
351#327C2×D4311yescharacteristic
352#327C2×D4311yescharacteristic
353C43#1754911yescharacteristic, complemented, Sylow
354C22×Q8—431no—
355C22×Q8—861no—
356C4⋊Q8—432no—
357C4⋊Q8—432no—
358C4⋊Q8—431no—
359C4⋊Q8—431no—
360C4⋊Q8—861no—
361C4⋊Q8—862no—
362#126—21no—
363#126—862no—
364#126—862no—
365#126—862no—
366#126—862no—
367#125—432no—
368#125—861no—
369#125—862no—
370#125—862no—
371#125—862no—
372#125—862no—
373#125—862no—
374#125—861no—
375#125C4×D4311yescharacteristic
376#124—432no—
377#124C4×D4311yescharacteristic
378#123—21no—
379#123—862no—
380C22⋊Q8—432no—
381C22⋊Q8—862no—
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387C22⋊Q8C22×D4311yescharacteristic
388#121C22×D4311yescharacteristic
389C4×Q8—431no—
390C4×Q8—432no—
391C4×Q8—431no—
392C4×Q8—431no—
393C4×Q8—432no—
394C4×Q8—431no—
395C4×Q8—432no—
396C4×Q8—432no—
397C4×Q8—432no—
398C4×Q8—432no—
399C4×Q8—861no—
400C4×Q8—861no—
401C4×Q8—868no—
402C4×Q8—862no—
403C4×Q8—862no—
404C4×Q8—861no—
405C4×Q8C4×D4311yescharacteristic
406C4×D4—21no—
407C4×D4—432no—
408C4×D4—862no—
409C4×D4C4×D4311yescharacteristic
410#117—21no—
411#117—862no—
412#117—862no—
413#117—862no—
414#117—861no—
415#117—861no—
416C2×C4⋊C4—432no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—861no—
420C2×C42—21no—
421C2×C42—432no—
422C2×C42—862no—
423C2×C42—862no—
424C2×C42—861no—
425C2×C42C22×D4311yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—862no—
428C4⋊C8—862no—
429C4⋊C8—861no—
430C22⋊C8—432no—
431C22⋊C8C22×D4311yescharacteristic
432C22⋊C8C22×D4311yescharacteristic
433#97—862no—
434#97—861no—
435C4×C8—21no—
436C4×C8—862no—
437#95—21no—
438#95—432no—
439#95—862no—
440#95C22×D4311yescharacteristic
441#95C22×D4311yescharacteristic
442C2×Q8—431no—
443C2×Q8—432no—
444C2×Q8—431no—
445C2×Q8—432no—
446C2×Q8—862no—
447C2×Q8—864no—
448C2×Q8—861no—
449C2×Q8—1724no—
450C2×Q8C2×C4×D4311yescharacteristic
451C2×D4—21no—
452C2×D4C2×C4×D4311yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4C23×D4311yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—862no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—432no—
471C4⋊C4—431no—
472C4⋊C4—432no—
473C4⋊C4—431no—
474C4⋊C4—432no—
475C4⋊C4—432no—
476C4⋊C4—432no—
477C4⋊C4—432no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4—862no—
485C4⋊C4—862no—
486C4⋊C4—868no—
487C4⋊C4—864no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—862no—
492C4⋊C4—862no—
493C4⋊C4C2×C4×D4311yescharacteristic
494C4⋊C4C2×C4×D4311yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—862no—
501C22⋊C4—862no—
502C22⋊C4—862no—
503C22⋊C4—862no—
504C42—24no—
505C42—21no—
506C42—432no—
507C42—432no—
508C42—432no—
509C42—432no—
510C42—862no—
511C42—862no—
512C42—862no—
513C42—868no—
514C42—862no—
515C42—3441no—
516C42—3442no—
517C42C2×C4×D4311yescharacteristic
518C42C2×C4×D4311yescharacteristic
519C42D4×D4311yescharacteristic
520C42D4×D4311yescharacteristic
521C23—21no—
522C23C2×D4×D4311yescharacteristic
523Q8—41no—
524Q8—434no—
525Q8—864no—
526Q8—862no—
527Q8—1722no—
528Q8—1724no—
529Q8—1722no—
530D4—41no—
531D4—41no—
532D4—41no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—432no—
548C2×C4—432no—
549C2×C4—432no—
550C2×C4—432no—
551C2×C4—864no—
552C2×C4—862no—
553C2×C4—862no—
554C2×C4—864no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—1724no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4C22⋊C4×D4311yescharacteristic
561C2×C4C22⋊C4×D4311yescharacteristic
562C2×C4C22⋊C4×D4311yescharacteristic
563C2×C4C22⋊C4×D4311yescharacteristic
564C2×C4C22×C4×D4311yescharacteristic
565C2×C4C2×D4×D4311yescharacteristic
566C8—41no—
567C8—41no—
568C8—1722no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22C2×C22⋊C4×D4311yescharacteristic
575C22#1458370611yescharacteristic
576C22#1458371311yescharacteristic
577C4—21no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—42no—
583C4—42no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—434no—
588C4—862no—
589C4—862no—
590C4—862no—
591C4—1724no—
592C4—1722no—
593C4—1722no—
594C4#104×D4312yes—
595C2—21no—
596C2—21no—
597C2—81no—
598C2#1914305711yescharacteristic
599C2#1914312411yescharacteristic
600C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1500C2
socleC22×C43C22×C22⋊C4
prime radical#121×C43C23
cosocleC22×C4×C43C24
hypercenter#1500D43
hypocenterC43#17549
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1500

Complements

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

NH ≅ G/Ntype
2. #19143682C2semidirect
3. #19136958C2semidirect
6. #19133106C2semidirect
7. #19133105C2semidirect
8. #19133095C2semidirect
9. #19133092C2semidirect
12. #14583628C4semidirect
13. #14583627C4semidirect
14. #14583626C4semidirect
15. #14583619C4semidirect
16. #14583618C4semidirect
20. D4×Dic86C4semidirect
353. C43#17549semidirect

Maximal subgroups

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

subgroupindex
#191486892
#191436822
#191369582
#191331202
#191331172
#191331062
#191331052
#191330952
#191330922
#191330782
C43×#15002
#1754943