Finite Group Databasebeta

← #25068418

Subgroups — #25068418

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145171C211yesmaximal, characteristic
2#19143340C211yesmaximal, characteristic, complemented
3#19143334C211yesmaximal, characteristic, complemented
4#19133507C211yesmaximal, characteristic, complemented
5#19133506C211yesmaximal, characteristic, complemented
6#19133461C211yesmaximal, characteristic, complemented
7#19133460C211yesmaximal, characteristic, complemented
8#19133458C211yesmaximal, characteristic, complemented
9#19133417C211yesmaximal, characteristic, complemented
10#19133416C211yesmaximal, characteristic, complemented
11#334×D43C211yesmaximal, characteristic, complemented
12#19132992C211yesmaximal, characteristic, complemented
13#19132992C211yesmaximal, characteristic, complemented
14#19132883C211yesmaximal, characteristic, complemented
15C43×#1586C211yesmaximal, characteristic, complemented
16C2×#13063333—21no—
17C2×#13063331—21no—
18#14583446C2211yescharacteristic
19#14583446C2211yescharacteristic
20#14583303C411yescharacteristic
21#14583274C411yescharacteristic
22#14583244C411yescharacteristic
23#14583244C411yescharacteristic
24#14583136C411yescharacteristic
25#14583134C411yescharacteristic
26#14583134C411yescharacteristic
27#14583132C411yescharacteristic
28C4×D344C2211yescharacteristic
29C4×#10621882C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582977C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582973—21no—
35#14582970—21no—
36#14582968—21no—
37#14582967—21no—
38C8×D172C2211yescharacteristic
39D4×C43⋊C8C2211yescharacteristic
40#14582964C2211yescharacteristic
41#14582950C2211yescharacteristic
42C4⋊C8×D43C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44#14582864—21no—
45#14582864—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582650C2211yescharacteristic
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×#334C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898—21no—
69C2×D344C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621882C2×C411yescharacteristic
72#13063333—44no—
73#13063331—44no—
74C2×#10621877—21no—
75C2×#10621872—21no—
76C2×#10621872—21no—
77C2×#10621872D411yescharacteristic
78C2×#10621872D411yescharacteristic
79C22×C43⋊C8—21no—
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83C2×C8×D43—21no—
84C2×C8×D43C2×C411yescharacteristic
85C2×C8×D43C2×C411yescharacteristic
86#13063324C2×C411yescharacteristic
87#13063324C2×C411yescharacteristic
88#13063321C2×C411yescharacteristic
89#13063321C2×C411yescharacteristic
90#13063311—21no—
91#13063311—21no—
92#13063300C2×C411yescharacteristic
93#13063300C2×C411yescharacteristic
94#13063298—21no—
95#13063298—21no—
96#13063296C2×C411yescharacteristic
97#13063296C2×C411yescharacteristic
98C4×D172C2311yescharacteristic
99C4×D172C2311yescharacteristic
100C4×C22⋊D43—21no—
101C4×C22⋊D43—21no—
102C42×D43C2311yescharacteristic
103#13063259C2×C411yescharacteristic
104#13063258C2×C411yescharacteristic
105#13063258C2×C411yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063247C2×C411yescharacteristic
112#13063247C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116#13063245C2×C411yescharacteristic
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊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#13063235D411yescharacteristic
125#13063235D411yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C4×C43⋊C8C2311yescharacteristic
128C4×C43⋊C8C2311yescharacteristic
129C8×Dic43C2×C411yescharacteristic
130C8×Dic43C2×C411yescharacteristic
131C2×D8×C43C2×C411yescharacteristic
132C2×M16×C43—21no—
133C22×C8×C43—21no—
134C4×D4×C43C2311yescharacteristic
135C4×D4×C43C2311yescharacteristic
136#107×C43C2×C411yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139#102×C43C2×C411yescharacteristic
140#102×C43C2×C411yescharacteristic
141C22⋊C8×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C4×C8×C43C2311yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C2×D4×C43C22×C411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152C2×C22⋊D43—21no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—21no—
155C2×C22⋊D43—21no—
156#10621898—42no—
157#10621898—42no—
158#10621898—42no—
159#10621898—42no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172C22×C411yescharacteristic
163C2×D172C22×C411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43C22×C411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43#4111yescharacteristic
169C2×Dic86—21no—
170C2×Dic86—21no—
171D8×C43—41no—
172M16×C43—42no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—42no—
177C2×C8×C43C22×C411yescharacteristic
178C2×C8×C43C22×C411yescharacteristic
179C2×C8×C43C2×D411yescharacteristic
180C2×C8×C43C2×D411yescharacteristic
181C4⋊C4×C43C22×C411yescharacteristic
182C4⋊C4×C43C22×C411yescharacteristic
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43C2411yescharacteristic
186C22⋊Dic43—21no—
187C22⋊Dic43—21no—
188#10621882—22no—
189#10621882—22no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194C4⋊Dic43C22×C411yescharacteristic
195C4⋊Dic43C22×C411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198C4×Dic43C22×C411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201#10621877—42no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—42no—
206C2×C43⋊C8C22×C411yescharacteristic
207C2×C43⋊C8C22×C411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C2×C43⋊C8C2×D411yescharacteristic
210D344—41no—
211#10621872—22no—
212#10621872—22no—
213#10621872—42no—
214#10621872—42no—
215C8×D43—22no—
216C8×D43—41no—
217C8×D43—42no—
218C8×D43—42no—
219C8×D43—42no—
220C8×D43—42no—
221C23×C43—21no—
222C23×C43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43C4×D411yescharacteristic
226D4×C43—21no—
227D4×C43—21no—
228D4×C43—21no—
229D4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C22⋊D43—42no—
240C22⋊D43—42no—
241C22⋊D43—42no—
242C22⋊D43—42no—
243C22⋊D43—81no—
244C22⋊D43—81no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43C4×D411yescharacteristic
248C2×Dic43C4×D411yescharacteristic
249C2×Dic43C4×D411yescharacteristic
250D172—21no—
251D172—21no—
252D172—21no—
253D172—21no—
254D172—42no—
255D172—42no—
256C4×D43—21no—
257C4×D43—21no—
258C4×D43—41no—
259C4×D43—41no—
260C4×D43—41no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43AGL(1,ℤ/8)12yes—
264C4×D43AGL(1,ℤ/8)12yes—
265Dic86—42no—
266Dic86—42no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—21no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43—41no—
274C43⋊C8—21no—
275C43⋊C8—21no—
276C43⋊C8—21no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280C43⋊C8#13112yescomplemented
281#18073—431nomaximal, Sylow
282C22×C43—41no—
283C22×C43—41no—
284C22×C43—41no—
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43C2×C4×D411yescharacteristic
289C2×D43—21no—
290C2×D43—21no—
291C2×D43—41no—
292C2×D43—41no—
293C2×D43—41no—
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43#44212yes—
298C4×C43—21no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43C2×#13111yescharacteristic
302C4×C43#56811yescharacteristic
303C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
304C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
305Dic43—21no—
306Dic43—21no—
307Dic43—41no—
308Dic43—41no—
309Dic43#44212yes—
310#3169—431no—
311#2935—431no—
312#2935—431no—
313#1594—431no—
314#1594—431no—
315#1586—431no—
316#1586—431no—
317#1586—431no—
318#1586D4311yescharacteristic, complemented
319#1580—431no—
320#1580—431no—
321C2×#334—431no—
322#1480—431no—
323#1480—431no—
324#1451—431no—
325C2×C43—81no—
326C2×C43—81no—
327C2×C43#293511yescharacteristic
328C2×C43C2×#44211yescharacteristic
329C2×C43#295711yescharacteristic
330D43—22no—
331D43—81no—
332D43—81no—
333C2×#131—861no—
334C2×#131—861no—
335#532—431no—
336#532—431no—
337#500—431no—
338#493—431no—
339#486—431no—
340#486—431no—
341#466—431no—
342#466—431no—
343#466—431no—
344#466—431no—
345C4×D8—431no—
346C4×D8—431no—
347C4×D8—431no—
348C4×D8C2×D4311yescharacteristic
349#436—431no—
350#436—431no—
351#436—431no—
352#436C2×D4311yescharacteristic
353#435—861no—
354#435—861no—
355#435—861no—
356#435—861no—
357C8×D4—431no—
358C8×D4—431no—
359C8×D4—431no—
360C8×D4C2×D4311yescharacteristic
361#431—431no—
362C2×C4⋊C8—431no—
363C2×C4⋊C8—431no—
364#408—861no—
365#408—861no—
366C4×M16—431no—
367C2×C4×C8—431no—
368#334—431no—
369#334—431no—
370#334—431no—
371#334C2×D4311yescharacteristic
372D4⋊C8—431no—
373D4⋊C8—431no—
374D4⋊C8—431no—
375D4⋊C8—431no—
376D4⋊C8—431no—
377D4⋊C8—431no—
378D4⋊C8C2×D4311yescharacteristic
379D4⋊C8C2×D4311yescharacteristic
380#322—431no—
381#322—431no—
382#322—431no—
383#322C2×D4311yescharacteristic
384C43#1807311yescharacteristic, complemented, Sylow
385C2×#41—861no—
386C2×#41—861no—
387C2×D8—431no—
388C2×D8—431no—
389C2×D8—431no—
390C2×D8C4×D4311yescharacteristic
391#131—1724no—
392#131—1724no—
393C2×M16—21no—
394C2×M16—431no—
395C2×M16—431no—
396C2×M16—861no—
397C2×M16—861no—
398C2×M16—861no—
399C22×C8—21no—
400C22×C8—431no—
401C22×C8—431no—
402C22×C8—861no—
403C22×C8—861no—
404C22×C8—861no—
405C22×C8—861no—
406C22×C8—861no—
407C4⋊Q8—431no—
408C4⋊Q8—431no—
409#127—431no—
410#127—431no—
411#124—861no—
412#124—861no—
413#121—431no—
414#121—431no—
415#121—431no—
416#121—431no—
417#121—861no—
418#121—861no—
419C4×D4—431no—
420C4×D4—431no—
421C4×D4—861no—
422C4×D4—861no—
423C4×D4C22×D4311yescharacteristic
424C4×D4C22×D4311yescharacteristic
425C2×C42—431no—
426#107—431no—
427#107—431no—
428#107—431no—
429#107C4×D4311yescharacteristic
430C4⋊C8—431no—
431C4⋊C8—431no—
432C4⋊C8—861no—
433C4⋊C8—861no—
434C4⋊C8—861no—
435C4⋊C8C22×D4311yescharacteristic
436C4⋊C8C22×D4311yescharacteristic
437#102—431no—
438#102—431no—
439#102—431no—
440#102—431no—
441#102—431no—
442#102—431no—
443#102C4×D4311yescharacteristic
444#102C4×D4311yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447C22⋊C8—861no—
448C22⋊C8—861no—
449C22⋊C8—861no—
450C22⋊C8—861no—
451C22⋊C8—861no—
452C22⋊C8—861no—
453C22⋊C8—861no—
454#97—431no—
455#97—431no—
456C4×C8—431no—
457C4×C8—431no—
458C4×C8—431no—
459C4×C8—431no—
460C4×C8—431no—
461C4×C8C22×D4311yescharacteristic
462C4×C8C22×D4311yescharacteristic
463C4×C8C22×D4311yescharacteristic
464#41—1722no—
465#41—1722no—
466#41—1722no—
467#41—1722no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×D4—431no—
471C2×D4—431no—
472C2×D4—861no—
473C2×D4—861no—
474C2×D4—861no—
475C2×D4—861no—
476C2×D4—861no—
477C2×D4—861no—
478C2×D4—861no—
479C2×D4—861no—
480C2×D4C2×C4×D4311yescharacteristic
481C2×D4C2×C4×D4311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—861no—
488C22×C4—861no—
489D8—41no—
490D8—862no—
491D8—862no—
492D8—1721no—
493M16—42no—
494M16—862no—
495M16—862no—
496M16—1722no—
497M16—1722no—
498M16—1722no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—42no—
503C2×C8—431no—
504C2×C8—431no—
505C2×C8—431no—
506C2×C8—431no—
507C2×C8—862no—
508C2×C8—861no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—1721no—
512C2×C8—1722no—
513C2×C8—1722no—
514C2×C8—1722no—
515C2×C8—1722no—
516C2×C8—1722no—
517C2×C8C2×C4×D4311yescharacteristic
518C2×C8C2×C4×D4311yescharacteristic
519C2×C8D4×D4311yescharacteristic
520C2×C8D4×D4311yescharacteristic
521C4⋊C4—431no—
522C4⋊C4—431no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4C2×C4×D4311yescharacteristic
526C4⋊C4C2×C4×D4311yescharacteristic
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—861no—
530C22⋊C4—861no—
531C22⋊C4—861no—
532C22⋊C4—861no—
533C22⋊C4—861no—
534C22⋊C4—861no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42C23×D4311yescharacteristic
539C23—21no—
540C23—21no—
541C23—431no—
542C23—861no—
543C23—861no—
544Q8—1722no—
545Q8—1722no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—861no—
551D4—861no—
552D4—861no—
553D4—861no—
554D4—3441no—
555D4—3441no—
556D4—1722no—
557D4—1722no—
558D4—1722no—
559D4—1722no—
560D4—1722no—
561D4—1722no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—431no—
569C2×C4—432no—
570C2×C4—432no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4C22×C4×D4311yescharacteristic
583C2×C4C2×D4×D4311yescharacteristic
584C2×C4#41×D4311yescharacteristic
585C8—21no—
586C8—21no—
587C8—21no—
588C8—21no—
589C8—41no—
590C8—41no—
591C8—41no—
592C8—432no—
593C8—861no—
594C8—861no—
595C8—861no—
596C8—1721no—
597C8—1721no—
598C8—1721no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—432no—
606C22—861no—
607C22—861no—
608C22—1721no—
609C22—1721no—
610C22—1721no—
611C22—1721no—
612C22—1721no—
613C22—1721no—
614C22C4×D4×D4311yescharacteristic
615C4—21no—
616C4—41no—
617C4—41no—
618C4—432no—
619C4—861no—
620C4—861no—
621C4—1721no—
622C4—1721no—
623C4#131×D4311yescharacteristic
624C4#1458366511yescharacteristic
625C4AGL(1,ℤ/8)×D4311yescharacteristic
626C4AGL(1,ℤ/8)×D4311yescharacteristic
627C2—81no—
628C2—81no—
629C2—862no—
630C2—3441no—
631C2—3441no—
632C2#1914333611yescharacteristic
633C2#442×D4311yescharacteristic
634C2#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#18073
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. #19143340C2semidirect
3. #19143334C2semidirect
4. #19133507C2semidirect
5. #19133506C2semidirect
6. #19133461C2semidirect
7. #19133460C2semidirect
8. #19133458C2semidirect
9. #19133417C2semidirect
10. #19133416C2semidirect
11. #334×D43C2semidirect
12. #19132992C2semidirect
13. #19132992C2semidirect
14. #19132883C2semidirect
15. C43×#1586C2semidirect
280. C43⋊C8#131semidirect
318. #1586D43semidirect
384. C43#18073semidirect

Maximal subgroups

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

subgroupindex
#191451712
#191433402
#191433342
#191335072
#191335062
#191334612
#191334602
#191334582
#191334172
#191334162
#334×D432
#191329922
#191328832
C43×#15862
#1807343