Finite Group Databasebeta

← #25068632

Subgroups — #25068632

Order 11008.

644 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145171C211yesmaximal, characteristic
2#19143660C211yesmaximal, characteristic, complemented
3#19143658C211yesmaximal, characteristic, complemented
4#19133507C211yesmaximal, characteristic, complemented
5#19133506C211yesmaximal, characteristic, complemented
6#19133426C211yesmaximal, characteristic, complemented
7#19133425C211yesmaximal, characteristic, complemented
8#19133423C211yesmaximal, characteristic, complemented
9#19133417C211yesmaximal, characteristic, complemented
10#19133416C211yesmaximal, characteristic, complemented
11#19133342C211yesmaximal, characteristic, complemented
12#19133010C211yesmaximal, characteristic, complemented
13#19133010C211yesmaximal, characteristic, complemented
14#19132883C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, characteristic, complemented
16#14583446C2211yescharacteristic
17#14583446C2211yescharacteristic
18#14583303C411yescharacteristic
19#14583274C411yescharacteristic
20#14583244C411yescharacteristic
21#14583244C411yescharacteristic
22#14583136C411yescharacteristic
23#14583134C411yescharacteristic
24#14583134C411yescharacteristic
25#14583132C411yescharacteristic
26C4×D344C2211yescharacteristic
27C4×#10621882C2211yescharacteristic
28C4×#10621882C2211yescharacteristic
29#14582978C2211yescharacteristic
30#14582977C2211yescharacteristic
31#14582976C2211yescharacteristic
32#14582975—21no—
33#14582974—21no—
34C8×D172C2211yescharacteristic
35D4×C43⋊C8C2211yescharacteristic
36#14582964C2211yescharacteristic
37C8×C22⋊D43—21no—
38(C22⋊D43)⋊C8—21no—
39#14582951C2211yescharacteristic
40#14582951C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582867—21no—
43#14582865—21no—
44#14582864—21no—
45#14582864—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582628C2211yescharacteristic
52#14582628C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582621C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898—21no—
69C2×D344C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8—21no—
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79C2×C8×D43C2×C411yescharacteristic
80C2×C8×D43C2×C411yescharacteristic
81#13063324C2×C411yescharacteristic
82#13063324C2×C411yescharacteristic
83#13063321C2×C411yescharacteristic
84#13063321C2×C411yescharacteristic
85#13063311—21no—
86#13063311—21no—
87#13063300C2×C411yescharacteristic
88#13063300C2×C411yescharacteristic
89#13063298—21no—
90#13063298—21no—
91#13063296C2×C411yescharacteristic
92#13063296C2×C411yescharacteristic
93C4×D172C2311yescharacteristic
94C4×D172C2311yescharacteristic
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97C42×D43C2311yescharacteristic
98#13063259C2×C411yescharacteristic
99#13063258C2×C411yescharacteristic
100#13063258C2×C411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063247C2×C411yescharacteristic
106#13063247C2×C411yescharacteristic
107#13063246C2×C411yescharacteristic
108#13063246C2×C411yescharacteristic
109#13063245C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119(C2×D43)⋊C8D411yescharacteristic
120(C2×D43)⋊C8D411yescharacteristic
121#13063235—21no—
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43C2×C411yescharacteristic
128C8×Dic43C2×C411yescharacteristic
129C2×D8×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43C2×C411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×D4×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—21no—
154#10621898—81no—
155#10621898—81no—
156#10621898—81no—
157#10621898—81no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172C22×C411yescharacteristic
161C2×D172C22×C411yescharacteristic
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43C22×C411yescharacteristic
165C2×C4×D43C2×D411yescharacteristic
166C2×C4×D43#4111yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169D8×C43—41no—
170M16×C43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—81no—
175C2×C8×C43C22×C411yescharacteristic
176C2×C8×C43C22×C411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C2×C8×C43C2×D411yescharacteristic
179C4⋊C4×C43C22×C411yescharacteristic
180C4⋊C4×C43C22×C411yescharacteristic
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185C22⋊Dic43—21no—
186#10621882—22no—
187#10621882—22no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43C22×C411yescharacteristic
193C4⋊Dic43C22×C411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199#10621877—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—81no—
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208D344—41no—
209#10621872—42no—
210#10621872—81no—
211#10621872—81no—
212C8×D43—22no—
213C8×D43—41no—
214C8×D43—81no—
215C8×D43—81no—
216C23×C43—21no—
217C23×C43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43C4×D411yescharacteristic
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224D4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C22⋊D43—42no—
235C22⋊D43—42no—
236C22⋊D43—81no—
237C22⋊D43—81no—
238C22⋊D43—81no—
239C22⋊D43—81no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43C4×D411yescharacteristic
243C2×Dic43C4×D411yescharacteristic
244C2×Dic43C4×D411yescharacteristic
245D172—21no—
246D172—21no—
247D172—21no—
248D172—21no—
249D172—81no—
250D172—81no—
251C4×D43—21no—
252C4×D43—21no—
253C4×D43—21no—
254C4×D43—21no—
255C4×D43—22no—
256C4×D43—41no—
257C4×D43—41no—
258C4×D43—41no—
259C4×D43—41no—
260Dic86—81no—
261Dic86—81no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—21no—
266C8×C43—41no—
267C8×C43—41no—
268C8×C43—41no—
269C43⋊C8—21no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275C43⋊C8#13112yes—
276#18091—431nomaximal, Sylow
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43—41no—
283C22×C43C2×C4×D411yescharacteristic
284C2×D43—21no—
285C2×D43—21no—
286C2×D43—21no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—41no—
292C2×D43—41no—
293C4×C43—21no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43C2×#13111yescharacteristic
297C4×C43#56811yescharacteristic
298C4×C43#57611yescharacteristic
299C4×C43#57611yescharacteristic
300Dic43—21no—
301Dic43—21no—
302Dic43—41no—
303Dic43—41no—
304Dic43#44412yes—
305#3169—431no—
306#2979—431no—
307#2979—431no—
308#1594—431no—
309#1594—431no—
310#1581—431no—
311#1581—431no—
312#1581—431no—
313#1581D4311yescharacteristic, complemented
314#1580—431no—
315#1580—431no—
316#1564—431no—
317#1484—431no—
318#1484—431no—
319#1451—431no—
320C2×C43—81no—
321C2×C43—81no—
322C2×C43#293511yescharacteristic
323C2×C43#294811yescharacteristic
324C2×C43C2×#44411yescharacteristic
325D43—41no—
326D43—81no—
327D43—81no—
328#532—431no—
329#532—431no—
330#500—431no—
331#493—431no—
332#486—431no—
333#486—431no—
334#466—431no—
335#466—431no—
336#466—431no—
337#466—431no—
338C4×D8—431no—
339C4×D8—431no—
340C4×D8—431no—
341C4×D8C2×D4311yescharacteristic
342#436—431no—
343#436—431no—
344#436—431no—
345#436—861no—
346#436—861no—
347#436C2×D4311yescharacteristic
348C8×D4—431no—
349C8×D4—431no—
350C8×D4—431no—
351C8×D4—861no—
352C8×D4—861no—
353C8×D4C2×D4311yescharacteristic
354#431—431no—
355#431—431no—
356#431—431no—
357#408—861no—
358#408—861no—
359#408—861no—
360#408—861no—
361C4×M16—431no—
362C2×C4×C8—431no—
363#335—431no—
364#335C2×D4311yescharacteristic
365#334—431no—
366#334—431no—
367D4⋊C8—431no—
368D4⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8C2×D4311yescharacteristic
374D4⋊C8C2×D4311yescharacteristic
375#322—431no—
376#322—431no—
377#322—431no—
378#322C2×D4311yescharacteristic
379C43#1809111yescharacteristic, complemented, Sylow
380C2×#41—861no—
381C2×#41—861no—
382C2×D8—431no—
383C2×D8—431no—
384C2×D8—431no—
385C2×D8C4×D4311yescharacteristic
386C2×M16—21no—
387C2×M16—861no—
388C2×M16—861no—
389C2×M16—861no—
390C2×M16—861no—
391C22×C8—21no—
392C22×C8—431no—
393C22×C8—431no—
394C22×C8—861no—
395C22×C8—861no—
396C22×C8—861no—
397C4⋊Q8—431no—
398C4⋊Q8—431no—
399#127—431no—
400#127—431no—
401#124—861no—
402#124—861no—
403#121—431no—
404#121—431no—
405#121—431no—
406#121—431no—
407#121—861no—
408#121—861no—
409C4×D4—431no—
410C4×D4—431no—
411C4×D4—861no—
412C4×D4—861no—
413C4×D4C22×D4311yescharacteristic
414C4×D4C22×D4311yescharacteristic
415C2×C42—431no—
416#107—431no—
417#107—431no—
418#107—431no—
419#107C4×D4311yescharacteristic
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—431no—
423C4⋊C8—431no—
424C4⋊C8C22×D4311yescharacteristic
425C4⋊C8C22×D4311yescharacteristic
426#102—431no—
427#102—431no—
428#102—431no—
429#102—431no—
430#102—431no—
431#102—431no—
432#102C4×D4311yescharacteristic
433#102C4×D4311yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—431no—
437C22⋊C8—431no—
438C22⋊C8—861no—
439C22⋊C8—861no—
440C22⋊C8—861no—
441C22⋊C8—861no—
442C22⋊C8—861no—
443C22⋊C8—861no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446#97—861no—
447C4×C8—431no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8—431no—
452C4×C8—861no—
453C4×C8—861no—
454C4×C8C22×D4311yescharacteristic
455C4×C8C22×D4311yescharacteristic
456C4×C8C22×D4311yescharacteristic
457#41—3441no—
458#41—3441no—
459#41—3441no—
460#41—3441no—
461C2×Q8—861no—
462C2×Q8—861no—
463C2×D4—431no—
464C2×D4—431no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4C2×C4×D4311yescharacteristic
474C2×D4C2×C4×D4311yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—861no—
481C22×C4—861no—
482D8—41no—
483D8—862no—
484D8—862no—
485D8—1721no—
486M16—81no—
487M16—3441no—
488M16—3441no—
489M16—3441no—
490M16—1722no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—81no—
495C2×C8—431no—
496C2×C8—431no—
497C2×C8—431no—
498C2×C8—431no—
499C2×C8—862no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—3441no—
504C2×C8—3441no—
505C2×C8—3441no—
506C2×C8—1721no—
507C2×C8C2×C4×D4311yescharacteristic
508C2×C8C2×C4×D4311yescharacteristic
509C2×C8D4×D4311yescharacteristic
510C2×C8D4×D4311yescharacteristic
511C4⋊C4—431no—
512C4⋊C4—431no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4C2×C4×D4311yescharacteristic
516C4⋊C4C2×C4×D4311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—861no—
520C22⋊C4—861no—
521C22⋊C4—861no—
522C22⋊C4—861no—
523C22⋊C4—861no—
524C22⋊C4—861no—
525C42—431no—
526C42—431no—
527C42—431no—
528C42C23×D4311yescharacteristic
529C23—21no—
530C23—21no—
531C23—431no—
532C23—861no—
533C23—861no—
534Q8—3441no—
535Q8—3441no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—861no—
541D4—861no—
542D4—861no—
543D4—861no—
544D4—3441no—
545D4—3441no—
546D4—3441no—
547D4—3441no—
548D4—3441no—
549D4—3441no—
550D4—1722no—
551D4—1722no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—431no—
559C2×C4—431no—
560C2×C4—431no—
561C2×C4—862no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4#41×D4311yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—432no—
583C8—861no—
584C8—861no—
585C8—861no—
586C8—1721no—
587C8—1721no—
588C8—1721no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—861no—
596C22—861no—
597C22—861no—
598C22—1721no—
599C22—1721no—
600C22—1721no—
601C22—1721no—
602C22—1721no—
603C22—1721no—
604C22C4×D4×D4311yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—432no—
609C4—861no—
610C4—861no—
611C4—1721no—
612C4—1721no—
613C4#131×D4311yescharacteristic
614C4#1458366511yescharacteristic
615C4#1458370011yescharacteristic
616C4#1458370111yescharacteristic
617C2—81no—
618C2—81no—
619C2—3441no—
620C2—3441no—
621C2—1721no—
622C2#1914333611yescharacteristic
623C2#1914344211yescharacteristic
624C2#444×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1581C2
socleC22×C43C2×C4×D4
prime radical#19145171C2
cosocleC42×C43C24
hypercenter#1581D43
hypocenterC43#18091
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #19143660C2semidirect
3. #19143658C2semidirect
4. #19133507C2semidirect
5. #19133506C2semidirect
6. #19133426C2semidirect
7. #19133425C2semidirect
8. #19133423C2semidirect
9. #19133417C2semidirect
10. #19133416C2semidirect
11. #19133342C2semidirect
12. #19133010C2semidirect
13. #19133010C2semidirect
14. #19132883C2semidirect
15. C43×#1581C2semidirect
313. #1581D43semidirect
379. C43#18091semidirect

Maximal subgroups

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

subgroupindex
#191451712
#191436602
#191436582
#191335072
#191335062
#191334262
#191334252
#191334232
#191334172
#191334162
#191333422
#191330102
#191328832
C43×#15812
#1809143