Finite Group Databasebeta

← #25067231

Subgroups — #25067231

Order 11008.

622 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#19145190C211yesmaximal, characteristic
2#19143746C211yesmaximal, characteristic, complemented
3#19143670C211yesmaximal, characteristic, complemented
4#19133510C211yesmaximal, characteristic, complemented
5#19133499C211yesmaximal, characteristic, complemented
6#19133487C211yesmaximal, characteristic, complemented
7#19133481C211yesmaximal, characteristic, complemented
8#19133420C211yesmaximal, characteristic, complemented
9#19133409C211yesmaximal, characteristic, complemented
10C8×#10621873C211yesmaximal, characteristic, complemented
11C8×D344C211yesmaximal, characteristic, complemented
12#19133362C211yesmaximal, characteristic, complemented
13#19133056C211yesmaximal, characteristic, complemented
14#19133047C211yesmaximal, characteristic, complemented
15C8×M16×C43C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583308C411yescharacteristic
19#14583288C411yescharacteristic
20#14583264C411yescharacteristic
21#14583259C411yescharacteristic
22#14583152C411yescharacteristic
23#14583152C411yescharacteristic
24#14583145C411yescharacteristic
25#14583145C411yescharacteristic
26#14583029C2211yescharacteristic
27C8×Dic86C2211yescharacteristic
28C4×#10621873C2211yescharacteristic
29C4×#10621873C2211yescharacteristic
30C4×D344C2211yescharacteristic
31C4×D344C2211yescharacteristic
32#14582978C2211yescharacteristic
33#14582978C2211yescharacteristic
34#14582978C2211yescharacteristic
35#14582974—21no—
36#14582973—21no—
37#14582969—21no—
38#14582969—21no—
39C8×D172C2211yescharacteristic
40C8×D172C2211yescharacteristic
41C8×D172C2211yescharacteristic
42#14582959—21no—
43#14582956C2211yescharacteristic
44#14582924—21no—
45#14582923C2211yescharacteristic
46#14582864—21no—
47#14582864—21no—
48#14582652C2211yescharacteristic
49#14582652C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582650C2211yescharacteristic
52#14582631C2211yescharacteristic
53#14582631C2211yescharacteristic
54#14582628C2211yescharacteristic
55#14582628C2211yescharacteristic
56#14582628C2211yescharacteristic
57#14582628C2211yescharacteristic
58#14582628C2211yescharacteristic
59#14582628C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C4×M16×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×#322C2211yescharacteristic
64C43×#322C2211yescharacteristic
65C82×C43C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×D344C2×C411yescharacteristic
71C2×D344C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79#13063325C2×C411yescharacteristic
80#13063322C2×C411yescharacteristic
81#13063319—21no—
82#13063317C2×C411yescharacteristic
83#13063313—21no—
84#13063313C2×C411yescharacteristic
85#13063308—21no—
86#13063304C2×C411yescharacteristic
87#13063299—21no—
88#13063299C2×C411yescharacteristic
89#13063299C2×C411yescharacteristic
90#13063299C2×C411yescharacteristic
91C4×Dic86C2311yescharacteristic
92C4×D172—21no—
93C4×D172C2311yescharacteristic
94C4×D172C2311yescharacteristic
95C4×D172C2311yescharacteristic
96C4×C22⋊D43—21no—
97#13063282—21no—
98#13063259C2×C411yescharacteristic
99#13063259C2×C411yescharacteristic
100#13063257C2×C411yescharacteristic
101#13063257C2×C411yescharacteristic
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250C2×C411yescharacteristic
110#13063250C2×C411yescharacteristic
111#13063247C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063247C2×C411yescharacteristic
115#13063247C2×C411yescharacteristic
116#13063247C2×C411yescharacteristic
117C22⋊(C43⋊C8)—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124#13063236—21no—
125#13063235—21no—
126C8×Dic43—21no—
127C2×M16×C43C2×C411yescharacteristic
128C2×M16×C43C2×C411yescharacteristic
129C22×C8×C43—21no—
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43D411yescharacteristic
133C22⋊C8×C43D411yescharacteristic
134C22⋊C8×C43D411yescharacteristic
135#97×C43C2×C411yescharacteristic
136#97×C43C2×C411yescharacteristic
137C4×C8×C43—21no—
138C4×C8×C43C2311yescharacteristic
139C4×C8×C43C2311yescharacteristic
140C4×C8×C43C2311yescharacteristic
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C22×C411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150#10621898—81no—
151#10621898—81no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C22×C411yescharacteristic
155C2×D172C22×C411yescharacteristic
156C2×D172C22×C411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×Dic86—21no—
161C2×Dic86C22×C411yescharacteristic
162M16×C43—22no—
163M16×C43—22no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—42no—
167C2×C8×C43C22×C411yescharacteristic
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C42×C43C22×C411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43#4111yescharacteristic
178C42×C43C2411yescharacteristic
179C22⋊Dic43—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C22×C411yescharacteristic
190C4⋊Dic43C22×C411yescharacteristic
191C4⋊Dic43C22×C411yescharacteristic
192C4⋊Dic43C22×C411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197C4×Dic43—21no—
198#10621877—81no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203D344—22no—
204D344—22no—
205#10621873—22no—
206#10621873—22no—
207#10621872—81no—
208#10621872—81no—
209#10621872—81no—
210C8×D43—81no—
211C8×D43—81no—
212C8×D43—81no—
213C23×C43C4×D411yescharacteristic
214C22×D43—21no—
215C22×D43—21no—
216C22×D43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43C4×D411yescharacteristic
223C2×C4×C43C4×D411yescharacteristic
224C2×C4×C43C4×D411yescharacteristic
225C2×C4×C43C23×C411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—81no—
229C22⋊D43—81no—
230C22⋊D43—81no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236D172—21no—
237D172—21no—
238D172—21no—
239D172—21no—
240D172—21no—
241D172—21no—
242D172—81no—
243D172—81no—
244C4×D43—41no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—41no—
250Dic86—21no—
251Dic86—21no—
252Dic86—81no—
253C8×C43—22no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43#13112yes—
262C8×C43#13112yes—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8—41no—
267#17968—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43C2×C4×D411yescharacteristic
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C4×C43—21no—
282C4×C43—21no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43C2×#13111yescharacteristic
286C4×C43C2×#13111yescharacteristic
287C4×C43#57611yescharacteristic
288C4×C43#57711yescharacteristic
289Dic43—41no—
290Dic43—41no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294#3171—431no—
295#2993—431no—
296#2981—431no—
297#1594—431no—
298#1592—431no—
299#1590—431no—
300#1589—431no—
301#1580—431no—
302SD16⋊C8—431no—
303C8×SD16—431no—
304C8×D8—431no—
305#1569—431no—
306#1494—431no—
307#1492—431no—
308C8×M16D4311yescharacteristic, complemented
309C2×C43—41no—
310C2×C43#293111yescharacteristic
311C2×C43#294611yescharacteristic
312C2×C43#295611yescharacteristic
313D43—81no—
314D43—81no—
315D43—81no—
316#532—431no—
317#529—431no—
318#501—431no—
319#496—431no—
320#490—431no—
321#489—431no—
322#469—431no—
323#469—431no—
324#468—431no—
325#468—431no—
326#446—431no—
327C8×Q8—431no—
328C4×SD16—431no—
329C4×SD16—431no—
330C4×D8—431no—
331C4×D8—431no—
332#436—431no—
333#436—431no—
334#436—431no—
335#436—861no—
336#435—861no—
337#435—861no—
338#435—861no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—431no—
342#433—861no—
343#432—431no—
344#431C2×D4311yescharacteristic
345#424—861no—
346#423—431no—
347#408—861no—
348#408—861no—
349C4×M16C2×D4311yescharacteristic
350C2×C4×C8C2×D4311yescharacteristic
351#335—431no—
352#335—431no—
353#334—431no—
354#334—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8—431no—
362D4⋊C8—431no—
363#322C2×D4311yescharacteristic
364#322C2×D4311yescharacteristic
365C82C2×D4311yescharacteristic
366C82C2×D4311yescharacteristic
367C43#1796811yescharacteristic, complemented, Sylow
368C2×#41—861no—
369C2×SD16—431no—
370C2×SD16—431no—
371C2×D8—431no—
372C2×D8—431no—
373C2×M16—861no—
374C2×M16—861no—
375C2×M16—861no—
376C2×M16—861no—
377C2×M16C4×D4311yescharacteristic
378C2×M16C4×D4311yescharacteristic
379C22×C8—21no—
380C22×C8—861no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8—431no—
384#127—431no—
385#126—861no—
386#125—431no—
387#124—431no—
388#124—861no—
389#123—861no—
390C22⋊Q8—431no—
391#121—431no—
392#121—431no—
393#121—431no—
394#121—861no—
395C4×Q8—431no—
396C4×D4—431no—
397C4×D4—431no—
398C4×D4—431no—
399C4×D4—861no—
400C4×D4—861no—
401#117—861no—
402C2×C42C22×D4311yescharacteristic
403#107—431no—
404#107—431no—
405#106—431no—
406#106—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8D17211yescharacteristic
415C4⋊C8D17211yescharacteristic
416#103—431no—
417#103—431no—
418#102—431no—
419#102—431no—
420#102—431no—
421#102—431no—
422#102—431no—
423#102—431no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8D17211yescharacteristic
432C22⋊C8D17211yescharacteristic
433#97—861no—
434#97—861no—
435#97C4×D4311yescharacteristic
436#97C4×D4311yescharacteristic
437C4×C8—21no—
438C4×C8—861no—
439C4×C8C22×D4311yescharacteristic
440C4×C8C22×D4311yescharacteristic
441C4×C8C22×D4311yescharacteristic
442C4×C8C22×D4311yescharacteristic
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445#41—3441no—
446#41—3441no—
447C2×Q8—431no—
448C2×Q8—861no—
449C2×D4—431no—
450C2×D4—431no—
451C2×D4—431no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4C2×C4×D4311yescharacteristic
461C22×C4C2×D17211yescharacteristic
462C22×C4#1062189811yescharacteristic
463SD16—862no—
464SD16—862no—
465D8—862no—
466D8—862no—
467M16—22no—
468M16—22no—
469M16—3441no—
470M16—3441no—
471M16—3441no—
472M16—3441no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—42no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—3441no—
481C2×C8—3441no—
482C2×C8—3441no—
483C2×C8C2×C4×D4311yescharacteristic
484C2×C8C2×C4×D4311yescharacteristic
485C2×C8C2×C4×D4311yescharacteristic
486C2×C8C2×C4×D4311yescharacteristic
487C2×C8C2×D17211yescharacteristic
488C2×C8C2×D17211yescharacteristic
489C2×C8C2×D17211yescharacteristic
490C2×C8C2×D17211yescharacteristic
491C4⋊C4—431no—
492C4⋊C4—431no—
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C42—861no—
510C42C2×C4×D4311yescharacteristic
511C42C2×D17211yescharacteristic
512C42#1062189811yescharacteristic
513C42C23×D4311yescharacteristic
514C23—861no—
515C23—861no—
516C23—861no—
517C23C4×D17211yescharacteristic
518Q8—861no—
519Q8—861no—
520Q8—3441no—
521D4—861no—
522D4—861no—
523D4—861no—
524D4—861no—
525D4—861no—
526D4—861no—
527D4—3441no—
528D4—3441no—
529D4—3441no—
530D4—3441no—
531D4—3441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4C4×D17211yescharacteristic
549C2×C4C4×D17211yescharacteristic
550C2×C4C4×D17211yescharacteristic
551C2×C4C22×C4×D4311yescharacteristic
552C2×C4C22×D17211yescharacteristic
553C2×C4C2×#1062189811yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—1721no—
563C8—1721no—
564C8—1721no—
565C8—1721no—
566C8#1306333112yes—
567C8#1306333112yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—1721no—
572C22—1721no—
573C22—1721no—
574C22—1721no—
575C22—1721no—
576C22—1721no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22C2×C4×D17211yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—1721no—
586C4—1721no—
587C4—1721no—
588C4—1721no—
589C4—1721no—
590C4C2×#1306333111yescharacteristic
591C4C2×#1306333111yescharacteristic
592C4#1458370411yescharacteristic
593C4#1458371111yescharacteristic
594C2—41no—
595C2—3441no—
596C2—3441no—
597C2—3441no—
598C2#1914330811yescharacteristic
599C2#1914342911yescharacteristic
600C2#1914350611yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×M16×C43C2
socleC22×C43C2×C4×D4
prime radical#19145190C2
cosocleC42×C43C24
hypercenterC8×M16D43
hypocenterC43#17968
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #431 ◁ C8×M16

Complements

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

NH ≅ G/Ntype
2. #19143746C2semidirect
3. #19143670C2semidirect
4. #19133510C2semidirect
5. #19133499C2semidirect
6. #19133487C2semidirect
7. #19133481C2semidirect
8. #19133420C2semidirect
9. #19133409C2semidirect
10. C8×#10621873C2semidirect
11. C8×D344C2semidirect
12. #19133362C2semidirect
13. #19133056C2semidirect
14. #19133047C2semidirect
15. C8×M16×C43C2semidirect
308. C8×M16D43semidirect
367. C43#17968semidirect

Maximal subgroups

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

subgroupindex
#191451902
#191437462
#191436702
#191335102
#191334992
#191334872
#191334812
#191334202
#191334092
C8×#106218732
C8×D3442
#191333622
#191330562
#191330472
C8×M16×C432
#1796843