Finite Group Databasebeta

← #25068352

Subgroups — #25068352

Order 11008.

722 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#19133478C211yesmaximal, characteristic, complemented
5#19133477C211yesmaximal, characteristic, complemented
6#19133426C211yesmaximal, characteristic, complemented
7#19133425C211yesmaximal, characteristic, complemented
8#19133423C211yesmaximal, characteristic, complemented
9C8×#10621882C211yesmaximal, characteristic, complemented
10#19133387C211yesmaximal, characteristic, complemented
11#335×D43C211yesmaximal, characteristic, complemented
12#19132992C211yesmaximal, characteristic, complemented
13#19132992C211yesmaximal, characteristic, complemented
14#19132874C211yesmaximal, characteristic, complemented
15C43×#1581C211yesmaximal, 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#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582651C2211yescharacteristic
51#14582628C2211yescharacteristic
52#14582628C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
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
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—42no—
213#10621872—42no—
214#10621872D814yescomplemented
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×D43C2×D812yes—
264C4×D43#13512yes—
265Dic86—42no—
266Dic86—42no—
267C8×C43—21no—
268C8×C43—21no—
269C8×C43—21no—
270C8×C43—41no—
271C8×C43—41no—
272C8×C43—41no—
273C8×C43C2×D812yes—
274C43⋊C8—21no—
275C43⋊C8—21no—
276C43⋊C8—41no—
277C43⋊C8—41no—
278C43⋊C8—41no—
279C43⋊C8#13112yescomplemented
280C43⋊C8C2×D812yes—
281#18066—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×D43C4×D812yes—
298C4×C43—21no—
299C4×C43—41no—
300C4×C43—41no—
301C4×C43C2×#13111yescharacteristic
302C4×C43#56811yescharacteristic
303C4×C43C22×D811yescharacteristic
304C4×C43C2×#13511yescharacteristic
305Dic43—21no—
306Dic43—21no—
307Dic43—41no—
308Dic43—41no—
309Dic43C4×D812yes—
310#3169—431no—
311#2935—431no—
312#2935—431no—
313#1589—431no—
314#1589—431no—
315#1581—431no—
316#1581—431no—
317#1581—431no—
318#1581D4311yescharacteristic, complemented
319C8×D8—431no—
320C8×D8—431no—
321C2×#335—431no—
322#1480—431no—
323#1480—431no—
324C8×M16—431no—
325C2×C43—81no—
326C2×C43—81no—
327C2×C43#293511yescharacteristic
328C2×C43C2×C4×D811yescharacteristic
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#335—431no—
369#335—431no—
370#335—431no—
371#335C2×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#322C2×D4311yescharacteristic
382C82—431no—
383C82—431no—
384C43#1806611yescharacteristic, 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—434no—
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—41no—
589C8—41no—
590C8—41no—
591C8—432no—
592C8—432no—
593C8—861no—
594C8—861no—
595C8—1721no—
596C8—1721no—
597C8—1721no—
598C8D8×D4312yes—
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
625C4C2×D8×D4311yescharacteristic
626C4#135×D4311yescharacteristic
627C2—81no—
628C2—81no—
629C2—862no—
630C2—3441no—
631C2—3441no—
632C2#1914333611yescharacteristic
633C2C4×D8×D4311yescharacteristic
634C2#1914350911yescharacteristic
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#18066
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. #19143340C2semidirect
3. #19143334C2semidirect
4. #19133478C2semidirect
5. #19133477C2semidirect
6. #19133426C2semidirect
7. #19133425C2semidirect
8. #19133423C2semidirect
9. C8×#10621882C2semidirect
10. #19133387C2semidirect
11. #335×D43C2semidirect
12. #19132992C2semidirect
13. #19132992C2semidirect
14. #19132874C2semidirect
15. C43×#1581C2semidirect
214. #10621872D8semidirect
279. C43⋊C8#131semidirect
318. #1581D43semidirect
384. C43#18066semidirect

Maximal subgroups

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

subgroupindex
#191451712
#191433402
#191433342
#191334782
#191334772
#191334262
#191334252
#191334232
C8×#106218822
#191333872
#335×D432
#191329922
#191328742
C43×#15812
#1806643