Finite Group Databasebeta

← #25067437

Subgroups — #25067437

Order 11008.

624 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145171C211yesmaximal, characteristic
2#19143672C211yesmaximal, characteristic, complemented
3#19143669C211yesmaximal, characteristic, complemented
4#19133461C211yesmaximal, characteristic, complemented
5#19133460C211yesmaximal, characteristic, complemented
6#19133458C211yesmaximal, characteristic, complemented
7#19133427C211yesmaximal, characteristic, complemented
8#19133424C211yesmaximal, characteristic, complemented
9#19133422C211yesmaximal, characteristic, complemented
10#19133421C211yesmaximal, characteristic, complemented
11#19133355C211yesmaximal, characteristic, complemented
12#19133062C211yesmaximal, characteristic, complemented
13#19133062C211yesmaximal, characteristic, complemented
14#19132886C211yesmaximal, characteristic, complemented
15C43×#1586C211yesmaximal, 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#14582973—21no—
33#14582970—21no—
34#14582968—21no—
35#14582967—21no—
36C8×D172C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38#14582964C2211yescharacteristic
39#14582955C2211yescharacteristic
40#14582955C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582950C2211yescharacteristic
43#14582867—21no—
44#14582865—21no—
45#14582864—21no—
46#14582864—21no—
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582650C2211yescharacteristic
51#14582628C2211yescharacteristic
52#14582628C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582620C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C43×#436C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
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—
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43C2×C411yescharacteristic
79C2×C8×D43C2×C411yescharacteristic
80#13063324C2×C411yescharacteristic
81#13063324C2×C411yescharacteristic
82#13063321C2×C411yescharacteristic
83#13063321C2×C411yescharacteristic
84#13063311—21no—
85#13063311—21no—
86#13063300C2×C411yescharacteristic
87#13063300C2×C411yescharacteristic
88#13063298—21no—
89#13063298—21no—
90#13063296C2×C411yescharacteristic
91#13063296C2×C411yescharacteristic
92C4×D172C2311yescharacteristic
93C4×D172C2311yescharacteristic
94C4×C22⋊D43—21no—
95C4×C22⋊D43—21no—
96C42×D43C2311yescharacteristic
97#13063259C2×C411yescharacteristic
98#13063258C2×C411yescharacteristic
99#13063258C2×C411yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102Dic43⋊C8—21no—
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)⋊C8—21no—
120(C2×D43)⋊C8D411yescharacteristic
121(C2×D43)⋊C8D411yescharacteristic
122#13063235—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
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—41no—
187#10621882—41no—
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—81no—
210#10621872—81no—
211C8×D43—41no—
212C8×D43—41no—
213C8×D43—81no—
214C8×D43—81no—
215C23×C43—21no—
216C23×C43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43C4×D411yescharacteristic
220D4×C43—21no—
221D4×C43—21no—
222D4×C43—21no—
223D4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—81no—
234C22⋊D43—81no—
235C22⋊D43—81no—
236C22⋊D43—81no—
237C22⋊D43—81no—
238C22⋊D43—81no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43C4×D411yescharacteristic
242C2×Dic43C4×D411yescharacteristic
243C2×Dic43C4×D411yescharacteristic
244D172—21no—
245D172—21no—
246D172—21no—
247D172—21no—
248D172—81no—
249D172—81no—
250C4×D43—21no—
251C4×D43—21no—
252C4×D43—21no—
253C4×D43—21no—
254C4×D43—41no—
255C4×D43—41no—
256C4×D43—41no—
257C4×D43—41no—
258C4×D43—41no—
259Dic86—81no—
260Dic86—81no—
261C8×C43—21no—
262C8×C43—21no—
263C8×C43—21no—
264C8×C43—21no—
265C8×C43—41no—
266C8×C43—41no—
267C8×C43—41no—
268C43⋊C8—21no—
269C43⋊C8—21no—
270C43⋊C8—21no—
271C43⋊C8—21no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274C43⋊C8—41no—
275#17989—431nomaximal, Sylow
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43—41no—
282C22×C43C2×C4×D411yescharacteristic
283C2×D43—21no—
284C2×D43—21no—
285C2×D43—21no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C2×D43—41no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43#56811yescharacteristic
296C4×C43#56811yescharacteristic
297C4×C43#57611yescharacteristic
298C4×C43#57611yescharacteristic
299Dic43—21no—
300Dic43—21no—
301Dic43—21no—
302Dic43—41no—
303Dic43—41no—
304#3169—431no—
305#2981—431no—
306#2981—431no—
307#1586—431no—
308#1586—431no—
309#1586—431no—
310#1586D4311yescharacteristic, complemented
311#1581—431no—
312#1581—431no—
313#1581—431no—
314#1581—431no—
315#1568—431no—
316#1496—431no—
317#1496—431no—
318#1452—431no—
319C2×C43—81no—
320C2×C43—81no—
321C2×C43#293211yescharacteristic
322C2×C43#294811yescharacteristic
323C2×C43#295711yescharacteristic
324D43—41no—
325D43—81no—
326D43—81no—
327#532—431no—
328#532—431no—
329#500—431no—
330#493—431no—
331#486—431no—
332#486—431no—
333#466—431no—
334#466—431no—
335#466—431no—
336#466—431no—
337C4×D8—431no—
338C4×D8—431no—
339C4×D8—431no—
340C4×D8C2×D4311yescharacteristic
341#436—431no—
342#436—431no—
343#436—431no—
344#436C2×D4311yescharacteristic
345#435—861no—
346#435—861no—
347#435—861no—
348#435—861no—
349C8×D4—431no—
350C8×D4—431no—
351C8×D4—431no—
352C8×D4C2×D4311yescharacteristic
353#432—431no—
354#432—431no—
355#431—431no—
356#431—431no—
357#408—861no—
358#408—861no—
359#408—861no—
360#408—861no—
361C2×C4×C8—431no—
362#335—431no—
363#335—431no—
364#334—431no—
365#334C2×D4311yescharacteristic
366D4⋊C8—431no—
367D4⋊C8—431no—
368D4⋊C8—431no—
369D4⋊C8—431no—
370D4⋊C8—431no—
371D4⋊C8—431no—
372D4⋊C8C2×D4311yescharacteristic
373D4⋊C8C2×D4311yescharacteristic
374#322—431no—
375#322—431no—
376#322—431no—
377#322C2×D4311yescharacteristic
378C43#1798911yescharacteristic, complemented, Sylow
379C2×#41—861no—
380C2×#41—861no—
381C2×D8—431no—
382C2×D8—431no—
383C2×D8—431no—
384C2×D8C4×D4311yescharacteristic
385C2×M16—21no—
386C2×M16—861no—
387C2×M16—861no—
388C2×M16—861no—
389C22×C8—21no—
390C22×C8—431no—
391C22×C8—431no—
392C22×C8—861no—
393C22×C8—861no—
394C22×C8—861no—
395C4⋊Q8—431no—
396C4⋊Q8—431no—
397#127—431no—
398#127—431no—
399#124—861no—
400#124—861no—
401#121—431no—
402#121—431no—
403#121—431no—
404#121—431no—
405#121—861no—
406#121—861no—
407C4×D4—431no—
408C4×D4—431no—
409C4×D4—861no—
410C4×D4—861no—
411C4×D4C22×D4311yescharacteristic
412C4×D4C22×D4311yescharacteristic
413C2×C42—431no—
414#107—431no—
415#107—431no—
416#107—431no—
417#107C4×D4311yescharacteristic
418C4⋊C8—431no—
419C4⋊C8—431no—
420C4⋊C8—431no—
421C4⋊C8—431no—
422C4⋊C8—861no—
423C4⋊C8C22×D4311yescharacteristic
424C4⋊C8C22×D4311yescharacteristic
425#102—431no—
426#102—431no—
427#102—431no—
428#102—431no—
429#102—431no—
430#102—431no—
431#102C4×D4311yescharacteristic
432#102C4×D4311yescharacteristic
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—431no—
436C22⋊C8—431no—
437C22⋊C8—861no—
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—
447#97—861no—
448C4×C8—431no—
449C4×C8—431no—
450C4×C8—431no—
451C4×C8—431no—
452C4×C8—431no—
453C4×C8C22×D4311yescharacteristic
454C4×C8C22×D4311yescharacteristic
455C4×C8C22×D4311yescharacteristic
456#41—3441no—
457#41—3441no—
458#41—3441no—
459#41—3441no—
460C2×Q8—861no—
461C2×Q8—861no—
462C2×D4—431no—
463C2×D4—431no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4C2×C4×D4311yescharacteristic
473C2×D4C2×C4×D4311yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—861no—
480C22×C4—861no—
481D8—41no—
482D8—1721no—
483D8—1721no—
484D8—1721no—
485M16—81no—
486M16—3441no—
487M16—3441no—
488M16—3441no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—81no—
493C2×C8—431no—
494C2×C8—431no—
495C2×C8—431no—
496C2×C8—431no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—3441no—
501C2×C8—3441no—
502C2×C8—3441no—
503C2×C8—1721no—
504C2×C8—1721no—
505C2×C8C2×C4×D4311yescharacteristic
506C2×C8C2×C4×D4311yescharacteristic
507C2×C8D4×D4311yescharacteristic
508C2×C8D4×D4311yescharacteristic
509C4⋊C4—431no—
510C4⋊C4—431no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4C2×C4×D4311yescharacteristic
514C4⋊C4C2×C4×D4311yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—861no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C22⋊C4—861no—
521C22⋊C4—861no—
522C22⋊C4—861no—
523C42—431no—
524C42—431no—
525C42—431no—
526C42C23×D4311yescharacteristic
527C23—21no—
528C23—21no—
529C23—431no—
530C23—861no—
531C23—861no—
532Q8—3441no—
533Q8—3441no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—861no—
539D4—861no—
540D4—861no—
541D4—861no—
542D4—3441no—
543D4—3441no—
544D4—3441no—
545D4—3441no—
546D4—3441no—
547D4—3441no—
548D4—3441no—
549D4—3441no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—431no—
557C2×C4—431no—
558C2×C4—431no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4C22×C4×D4311yescharacteristic
571C2×C4C2×D4×D4311yescharacteristic
572C2×C4#41×D4311yescharacteristic
573C8—21no—
574C8—21no—
575C8—21no—
576C8—21no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—861no—
581C8—861no—
582C8—861no—
583C8—861no—
584C8—1721no—
585C8—1721no—
586C8—1721no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—861no—
594C22—861no—
595C22—861no—
596C22—1721no—
597C22—1721no—
598C22—1721no—
599C22—1721no—
600C22—1721no—
601C22—1721no—
602C22C4×D4×D4311yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—861no—
607C4—861no—
608C4—861no—
609C4—1721no—
610C4—1721no—
611C4#1458366411yescharacteristic
612C4#1458366511yescharacteristic
613C4#1458370311yescharacteristic
614C4#1458370311yescharacteristic
615C2—81no—
616C2—81no—
617C2—3441no—
618C2—3441no—
619C2—1721no—
620C2#1914330911yescharacteristic
621C2#1914344411yescharacteristic
622C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1586C2
socleC22×C43C2×C4×D4
prime radical#19145171C2
cosocleC42×C43C24
hypercenter#1586D43
hypocenterC43#17989
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #19143672C2semidirect
3. #19143669C2semidirect
4. #19133461C2semidirect
5. #19133460C2semidirect
6. #19133458C2semidirect
7. #19133427C2semidirect
8. #19133424C2semidirect
9. #19133422C2semidirect
10. #19133421C2semidirect
11. #19133355C2semidirect
12. #19133062C2semidirect
13. #19133062C2semidirect
14. #19132886C2semidirect
15. C43×#1586C2semidirect
310. #1586D43semidirect
378. C43#17989semidirect

Maximal subgroups

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

subgroupindex
#191451712
#191436722
#191436692
#191334612
#191334602
#191334582
#191334272
#191334242
#191334222
#191334212
#191333552
#191330622
#191328862
C43×#15862
#1798943