Finite Group Databasebeta

← #25067103

Subgroups — #25067103

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144611C211yesmaximal, characteristic
2#19143739C211yesmaximal, characteristic, complemented
3#19143711C211yesmaximal, characteristic, complemented
4#19133507C211yesmaximal, characteristic, complemented
5#19133502C211yesmaximal, characteristic, complemented
6#19133487C211yesmaximal, characteristic, complemented
7#19133469C211yesmaximal, characteristic, complemented
8#19133456C211yesmaximal, characteristic, complemented
9#19133437C211yesmaximal, characteristic, complemented
10#19133432C211yesmaximal, characteristic, complemented
11#19133364C211yesmaximal, characteristic, complemented
12#19133033C211yesmaximal, characteristic, complemented
13#19133005C211yesmaximal, characteristic, complemented
14#19132889C211yesmaximal, characteristic, complemented
15C43×#1590C211yesmaximal, characteristic, complemented
16#14583431C2211yescharacteristic
17C4×#10621902C2211yescharacteristic
18#14583243C411yescharacteristic
19#14583222C411yescharacteristic
20#14583204C411yescharacteristic
21#14583198C411yescharacteristic
22#14583119C411yescharacteristic
23#14583113C411yescharacteristic
24#14583064C411yescharacteristic
25#14583043C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583029C2211yescharacteristic
28#14583023C2211yescharacteristic
29C4×#10621885C2211yescharacteristic
30C4×#10621873C2211yescharacteristic
31C4×#10621882C2211yescharacteristic
32#14582978C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582975—21no—
35#14582972—21no—
36#14582969—21no—
37#14582967—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582957—21no—
40#14582954—21no—
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582927—21no—
44#14582921—21no—
45#14582921C2211yescharacteristic
46C4⋊C8×D43C2211yescharacteristic
47C4×#10621872C2211yescharacteristic
48#14582650C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582620C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621902C2×C411yescharacteristic
68C2×#10621885C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621872—21no—
72C2×#10621872—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77#13063318—21no—
78#13063316C2×C411yescharacteristic
79#13063312C2×C411yescharacteristic
80#13063307—21no—
81#13063305C2×C411yescharacteristic
82#13063296C2×C411yescharacteristic
83Q8×Dic43C2×C411yescharacteristic
84C4×Dic86C2311yescharacteristic
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87#13063287—21no—
88#13063287C2×C411yescharacteristic
89C4×C22⋊D43—21no—
90#13063284—21no—
91#13063283—21no—
92#13063283C2×C411yescharacteristic
93C42×D43—21no—
94C42×D43C2311yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063257C2×C411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8C2×C411yescharacteristic
106Dic43⋊C8C2×C411yescharacteristic
107Dic43⋊C8D411yescharacteristic
108Dic43⋊C8D411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063249C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063245C2×C411yescharacteristic
115C22⋊(C43⋊C8)—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8C2×C411yescharacteristic
119(C2×D43)⋊C8C2×C411yescharacteristic
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063236—21no—
123#13063235—21no—
124#13063235—21no—
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C8×Dic43—21no—
129C2×SD16×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C2×C22⋊D43—21no—
148#10621902—41no—
149#10621902—41no—
150C2×D172—21no—
151C2×D172C22×C411yescharacteristic
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43C22×C411yescharacteristic
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43#4111yescharacteristic
158C2×Dic86C22×C411yescharacteristic
159SD16×C43—41no—
160M16×C43—81no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C22×C411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C411yescharacteristic
170C4⋊C4×C43C22×C411yescharacteristic
171C22⋊C4×C43—21no—
172C42×C43—21no—
173C42×C43C2411yescharacteristic
174C22⋊Dic43—21no—
175C22⋊Dic43—21no—
176C22⋊Dic43—21no—
177#10621885—41no—
178#10621882—41no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43C22×C411yescharacteristic
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43#4111yescharacteristic
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—81no—
200C2×C43⋊C8C22×C411yescharacteristic
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204#10621873—41no—
205#10621872—42no—
206#10621872—81no—
207#10621872—81no—
208#10621872—81no—
209C8×D43—81no—
210C23×C43—21no—
211C22×D43—21no—
212C22×D43C4×D411yescharacteristic
213Q8×C43—21no—
214Q8×C43—21no—
215D4×C43—21no—
216D4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C23×C411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4111yescharacteristic
225C22⋊D43—81no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43C4×D411yescharacteristic
230C2×Dic43C4×D411yescharacteristic
231C2×Dic43C4×D411yescharacteristic
232D172—21no—
233D172—21no—
234D172—42no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—41no—
240C4×D43—42no—
241C4×D43—41no—
242C4×D43—41no—
243C4×D43—81no—
244Dic86—21no—
245Dic86—21no—
246C8×C43—22no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—21no—
255C43⋊C8—21no—
256C43⋊C8—21no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260#17955—431nomaximal, Sylow
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43C2×C4×D411yescharacteristic
265C2×D43—21no—
266C2×D43—21no—
267C2×D43—21no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43#56811yescharacteristic
276C4×C43#56811yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57711yescharacteristic
279Dic43—21no—
280Dic43—21no—
281Dic43—21no—
282Dic43—41no—
283Dic43—41no—
284Dic43—41no—
285#3102—431no—
286#2993—431no—
287#2989—431no—
288#1594—431no—
289#1593—431no—
290#1590—431no—
291#1590D4311yescharacteristic, complemented
292#1587—431no—
293#1586—431no—
294#1583—431no—
295#1582—431no—
296#1570—431no—
297#1489—431no—
298#1483—431no—
299#1453—431no—
300C2×C43—81no—
301C2×C43#293011yescharacteristic
302C2×C43#295211yescharacteristic
303C2×C43#295611yescharacteristic
304D43—41no—
305D43—81no—
306#529—431no—
307C4×#41—431no—
308#485—431no—
309#482—431no—
310#479—431no—
311#478—431no—
312#464—431no—
313#463—431no—
314#452—431no—
315#449—431no—
316#446—431no—
317#446—431no—
318#446C2×D4311yescharacteristic
319C8×Q8—431no—
320C4×Q16—431no—
321C4×SD16—431no—
322C4×SD16C2×D4311yescharacteristic
323C4×D8—431no—
324#436—431no—
325#436—431no—
326#436—861no—
327#436C2×D4311yescharacteristic
328#435—861no—
329#435—861no—
330#435—861no—
331C8×D4—431no—
332#433—861no—
333#432—861no—
334#431—431no—
335#431—431no—
336#424—861no—
337#423—431no—
338#423—861no—
339C2×C4⋊C8—431no—
340C4×M16—431no—
341#334—431no—
342#334—431no—
343#334—431no—
344#334C2×D4311yescharacteristic
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348Q8⋊C8C2×D4311yescharacteristic
349D4⋊C8—431no—
350D4⋊C8—431no—
351D4⋊C8—431no—
352D4⋊C8C2×D4311yescharacteristic
353#322—431no—
354#322—431no—
355#322—431no—
356C82C2×D4311yescharacteristic
357C43#1795511yescharacteristic, complemented, Sylow
358C2×#41—431no—
359C2×Q16—431no—
360C2×SD16—431no—
361C2×SD16C4×D4311yescharacteristic
362C2×D8—431no—
363C2×M16—21no—
364C2×M16—861no—
365C2×M16—861no—
366C2×M16—861no—
367C2×M16—861no—
368C22×C8—861no—
369C22×C8—861no—
370#126—861no—
371#125—431no—
372#124—431no—
373#123—861no—
374C22⋊Q8—431no—
375#121—431no—
376C4×Q8—431no—
377C4×Q8—431no—
378C4×Q8C22×D4311yescharacteristic
379C4×D4—431no—
380C4×D4—431no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4—861no—
384C4×D4C22×D4311yescharacteristic
385#117—431no—
386#117—861no—
387#117—861no—
388C2×C42—431no—
389C2×C42—861no—
390#107—431no—
391#107—431no—
392#106—431no—
393#106C4×D4311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—431no—
409#103—431no—
410#103—431no—
411#103C4×D4311yescharacteristic
412#102—431no—
413#102—431no—
414#102—431no—
415#102C4×D4311yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—431no—
418C22⋊C8—431no—
419C22⋊C8—431no—
420C22⋊C8—431no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—21no—
425#97—861no—
426#97—861no—
427#97—861no—
428C4×C8—431no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435#41—1721no—
436#41—1721no—
437C2×Q8—431no—
438C2×Q8C2×C4×D4311yescharacteristic
439C2×D4—431no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4C2×C4×D4311yescharacteristic
443C22×C4—21no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—431no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—861no—
450Q16—1721no—
451SD16—41no—
452SD16—1721no—
453D8—1721no—
454M16—81no—
455M16—3441no—
456M16—3441no—
457M16—3441no—
458M16—1722no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—3441no—
470C2×C8—3441no—
471C2×C8C2×C4×D4311yescharacteristic
472C2×C8C2×C4×D4311yescharacteristic
473C2×C8D4×D4311yescharacteristic
474C2×C8D4×D4311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—431no—
477C4⋊C4—431no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4C2×C4×D4311yescharacteristic
484C4⋊C4C2×C4×D4311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C42—21no—
494C42—431no—
495C42—431no—
496C42—431no—
497C42—861no—
498C42—861no—
499C42—861no—
500C42C23×D4311yescharacteristic
501C23—21no—
502C23—431no—
503C23—861no—
504Q8—21no—
505Q8—21no—
506Q8—861no—
507Q8—861no—
508D4—21no—
509D4—21no—
510D4—861no—
511D4—861no—
512D4—3441no—
513D4—1722no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—431no—
520C2×C4—431no—
521C2×C4—431no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—3441no—
530C2×C4—1721no—
531C2×C4—1722no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4C22×C4×D4311yescharacteristic
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4#41×D4311yescharacteristic
537C8—22no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—861no—
545C8—861no—
546C8—861no—
547C8—861no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—861no—
555C22—861no—
556C22—861no—
557C22—1721no—
558C22—1721no—
559C22—1721no—
560C22C4×D4×D4311yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—861no—
566C4—861no—
567C4—861no—
568C4—1721no—
569C4—1721no—
570C4—1721no—
571C4#1458366411yescharacteristic
572C4#1458366511yescharacteristic
573C4#1458370511yescharacteristic
574C4#1458370611yescharacteristic
575C2—81no—
576C2—3441no—
577C2—1721no—
578C2#1914329511yescharacteristic
579C2#1914347311yescharacteristic
580C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1590C2
socleC22×C43C2×C4×D4
prime radical#14583043C4
cosocleC42×C43C24
hypercenter#1590D43
hypocenterC43#17955
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
2. #19143739C2semidirect
3. #19143711C2semidirect
4. #19133507C2semidirect
5. #19133502C2semidirect
6. #19133487C2semidirect
7. #19133469C2semidirect
8. #19133456C2semidirect
9. #19133437C2semidirect
10. #19133432C2semidirect
11. #19133364C2semidirect
12. #19133033C2semidirect
13. #19133005C2semidirect
14. #19132889C2semidirect
15. C43×#1590C2semidirect
291. #1590D43semidirect
357. C43#17955semidirect

Maximal subgroups

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

subgroupindex
#191446112
#191437392
#191437112
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