Finite Group Databasebeta

← #25066721

Subgroups — #25066721

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144624C211yesmaximal, characteristic
2#19143674C211yesmaximal, characteristic, complemented
3#19143669C211yesmaximal, characteristic
4#19133476C211yesmaximal, characteristic, complemented
5#19133470C211yesmaximal, characteristic, complemented
6#19133439C211yesmaximal, characteristic, complemented
7#19133437C211yesmaximal, characteristic, complemented
8#19133407C211yesmaximal, characteristic, complemented
9#19133405C211yesmaximal, characteristic, complemented
10C8×#10621873C211yesmaximal, characteristic, complemented
11#19133372C211yesmaximal, characteristic, complemented
12#19133040C211yesmaximal, characteristic, complemented
13#19133010C211yesmaximal, characteristic
14#19132889C211yesmaximal, characteristic, complemented
15C8×SD16×C43C211yesmaximal, characteristic, complemented
16#14583446C2211yescharacteristic
17C4×Q8×D43C2211yescharacteristic
18#14583219C411yescharacteristic
19#14583216C411yescharacteristic
20#14583183C411yescharacteristic
21#14583182C411yescharacteristic
22#14583098C411yescharacteristic
23#14583097C411yescharacteristic
24#14583039C411yescharacteristic
25#14583036C411yescharacteristic
26Q8×C43⋊C8C2211yescharacteristic
27C8×Dic86—21no—
28C8×Dic86C2211yescharacteristic
29#14583023—21no—
30#14583023C2211yescharacteristic
31C4×#10621873C2211yescharacteristic
32C4×#10621884C2211yescharacteristic
33C4×#10621883C2211yescharacteristic
34#14582977C2211yescharacteristic
35#14582976C2211yescharacteristic
36#14582973—21no—
37#14582970—21no—
38C8×D172C2211yescharacteristic
39#14582955C2211yescharacteristic
40#14582951—21no—
41#14582951C2211yescharacteristic
42#14582950—21no—
43#14582950C2211yescharacteristic
44#14582950C2211yescharacteristic
45#14582865—21no—
46#14582864—21no—
47C4×#10621872C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582620C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×Q8×D43C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621884C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×C8×D43—21no—
76#13063324C2×C411yescharacteristic
77#13063321C2×C411yescharacteristic
78#13063311—21no—
79#13063300C2×C411yescharacteristic
80#13063298—21no—
81#13063296C2×C411yescharacteristic
82Q8×Dic43C2×C411yescharacteristic
83C4×Dic86—21no—
84C4×Dic86C2311yescharacteristic
85#13063290—21no—
86#13063290C2×C411yescharacteristic
87C4×D172C2311yescharacteristic
88C4×C22⋊D43—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43C2×C411yescharacteristic
91C42×D43—21no—
92C42×D43C2311yescharacteristic
93#13063257C2×C411yescharacteristic
94#13063256C2×C411yescharacteristic
95#13063256C2×C411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8C2×C411yescharacteristic
102Dic43⋊C8C2×C411yescharacteristic
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063250C2×C411yescharacteristic
106#13063249C2×C411yescharacteristic
107#13063248C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063246C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8C2×C411yescharacteristic
117(C2×D43)⋊C8C2×C411yescharacteristic
118(C2×D43)⋊C8D411yescharacteristic
119(C2×D43)⋊C8D411yescharacteristic
120#13063235—21no—
121#13063235—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43C2×C411yescharacteristic
130C22×C8×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—
140C4×C8×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—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150Q8×D43—22no—
151Q8×D43—22no—
152#10621898—81no—
153#10621898—81no—
154C2×D172—21no—
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43C22×C411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C22×C411yescharacteristic
165SD16×C43—22no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—81no—
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181#10621884—22no—
182#10621883—22no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43C22×C411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198#10621877—81no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206#10621873—22no—
207#10621872—42no—
208#10621872—81no—
209C8×D43—81no—
210C23×C43—21no—
211C22×D43—21no—
212C22×D43C4×D411yescharacteristic
213Q8×C43—21no—
214Q8×C43#13112yes—
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—
226C22⋊D43—81no—
227C22⋊D43—81no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43C4×D411yescharacteristic
232C2×Dic43C4×D411yescharacteristic
233C2×Dic43C4×D411yescharacteristic
234D172—21no—
235D172—21no—
236D172—81no—
237C4×D43—24no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—21no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—81no—
246Dic86—24no—
247Dic86—21no—
248Dic86—81no—
249Dic86#13112yes—
250C8×C43—22no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—21no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#17923—431nomaximal, Sylow
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43C2×C4×D411yescharacteristic
269C2×D43—21no—
270C2×D43—21no—
271C2×D43—21no—
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43C2×#13111yescharacteristic
280C4×C43C2×#13111yescharacteristic
281C4×C43#57711yescharacteristic
282C4×C43#57711yescharacteristic
283Dic43—21no—
284Dic43—22no—
285Dic43—21no—
286Dic43—21no—
287Dic43—41no—
288Dic43—41no—
289#3103—431no—
290#2982—431no—
291#2981—431no—
292#1588—431no—
293#1588—431no—
294#1583—431no—
295#1583—431no—
296SD16⋊C8—431no—
297SD16⋊C8—431no—
298C8×SD16—431no—
299C8×SD16D4311yescharacteristic, complemented
300#1572—431no—
301#1491—431no—
302#1484—431no—
303#1453—431no—
304C2×C43—81no—
305C2×C43#292911yescharacteristic
306C2×C43#294911yescharacteristic
307C2×C43#295611yescharacteristic
308D43—41no—
309D43—81no—
310#532—431no—
311C2×C4×Q8—431no—
312#481—431no—
313#481—431no—
314#475—431no—
315#475—431no—
316#460—431no—
317#460—431no—
318#448—431no—
319#448—431no—
320C8×Q8—431no—
321C8×Q8—431no—
322C8×Q8—431no—
323C8×Q8—861no—
324C8×Q8—861no—
325C8×Q8C2×D4311yescharacteristic
326C4×SD16—431no—
327C4×SD16—431no—
328C4×SD16—431no—
329C4×SD16C2×D4311yescharacteristic
330#436—431no—
331#436—431no—
332#435—861no—
333#435—861no—
334C8×D4—431no—
335C8×D4C2×D4311yescharacteristic
336#432—431no—
337#431—431no—
338#431—431no—
339#431—431no—
340#431—861no—
341#431—861no—
342#408—861no—
343#408—861no—
344C4×M16—431no—
345#335—431no—
346#335—431no—
347#334—431no—
348#334C2×D4311yescharacteristic
349Q8⋊C8—431no—
350Q8⋊C8—431no—
351Q8⋊C8—431no—
352Q8⋊C8C2×D4311yescharacteristic
353D4⋊C8—431no—
354D4⋊C8—431no—
355D4⋊C8—431no—
356D4⋊C8C2×D4311yescharacteristic
357#322—431no—
358#322—431no—
359#322—431no—
360C82C2×D4311yescharacteristic
361C43#1792311yescharacteristic, complemented, Sylow
362C2×#41—861no—
363C22×Q8—431no—
364C2×SD16—431no—
365C2×SD16—431no—
366C2×SD16—431no—
367C2×SD16C4×D4311yescharacteristic
368C2×M16—861no—
369C2×M16—861no—
370C2×M16—861no—
371C22×C8—21no—
372C22×C8—861no—
373C4⋊Q8—431no—
374#127—431no—
375#124—861no—
376#121—431no—
377#121—431no—
378#121—861no—
379C4×Q8—431no—
380C4×Q8—431no—
381C4×Q8—431no—
382C4×Q8—861no—
383C4×Q8—861no—
384C4×Q8C22×D4311yescharacteristic
385C4×D4—431no—
386C4×D4—861no—
387C4×D4C22×D4311yescharacteristic
388C2×C4⋊C4—431no—
389C2×C4⋊C4—861no—
390C2×C42—431no—
391C2×C42—861no—
392#106—431no—
393#106—431no—
394#106—431no—
395#106C4×D4311yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
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—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—861no—
427#97—861no—
428C4×C8—21no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8C22×D4311yescharacteristic
437C4×C8C22×D4311yescharacteristic
438C4×C8C22×D4311yescharacteristic
439#41—3441no—
440#41—3441no—
441C2×Q8—431no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—862no—
445C2×Q8—862no—
446C2×Q8C2×C4×D4311yescharacteristic
447C2×D4—431no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4C2×C4×D4311yescharacteristic
453C22×C4—21no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—431no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460SD16—22no—
461SD16—862no—
462SD16—862no—
463SD16—862no—
464M16—3441no—
465M16—3441no—
466M16—1722no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—81no—
471C2×C8—431no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—431no—
475C2×C8—861no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—3441no—
479C2×C8C2×C4×D4311yescharacteristic
480C2×C8C2×C4×D4311yescharacteristic
481C2×C8D4×D4311yescharacteristic
482C2×C8D4×D4311yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—431no—
485C4⋊C4—431no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4C2×C4×D4311yescharacteristic
492C4⋊C4C2×C4×D4311yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C42—21no—
498C42—431no—
499C42—431no—
500C42—431no—
501C42—861no—
502C42—861no—
503C42—861no—
504C42C23×D4311yescharacteristic
505C23—21no—
506C23—431no—
507C23—861no—
508Q8—21no—
509Q8—432no—
510Q8—864no—
511Q8—861no—
512Q8—3441no—
513Q8#1306333112yes—
514D4—21no—
515D4—21no—
516D4—861no—
517D4—861no—
518D4—3441no—
519D4—3441no—
520D4—3441no—
521D4—3441no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—431no—
528C2×C4—431no—
529C2×C4—431no—
530C2×C4—864no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—3441no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4C22×C4×D4311yescharacteristic
543C2×C4C2×D4×D4311yescharacteristic
544C2×C4#41×D4311yescharacteristic
545C8—22no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—861no—
553C8—861no—
554C8—861no—
555C8—861no—
556C8—1721no—
557C8—1721no—
558C8—1721no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—861no—
563C22—861no—
564C22—861no—
565C22—1721no—
566C22—1721no—
567C22—1721no—
568C22C4×D4×D4311yescharacteristic
569C4—21no—
570C4—22no—
571C4—41no—
572C4—41no—
573C4—861no—
574C4—861no—
575C4—861no—
576C4—862no—
577C4—1721no—
578C4—1721no—
579C4#131×D4311yescharacteristic
580C4C2×#1306333111yescharacteristic
581C4#1458370511yescharacteristic
582C4#1458370611yescharacteristic
583C2—81no—
584C2—3441no—
585C2—1721no—
586C2#1914328411yescharacteristic
587C2#1914344911yescharacteristic
588C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×SD16×C43C2
socleC22×C43C2×C4×D4
prime radical#14583446C22
cosocleC42×C43C24
hypercenterC8×SD16D43
hypocenterC43#17923
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
2. #19143674C2semidirect
4. #19133476C2semidirect
5. #19133470C2semidirect
6. #19133439C2semidirect
7. #19133437C2semidirect
8. #19133407C2semidirect
9. #19133405C2semidirect
10. C8×#10621873C2semidirect
11. #19133372C2semidirect
12. #19133040C2semidirect
14. #19132889C2semidirect
15. C8×SD16×C43C2semidirect
299. C8×SD16D43semidirect
361. C43#17923semidirect

Maximal subgroups

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

subgroupindex
#191446242
#191436742
#191436692
#191334762
#191334702
#191334392
#191334372
#191334072
#191334052
C8×#106218732
#191333722
#191330402
#191330102
#191328892
C8×SD16×C432
#1792343