Finite Group Databasebeta

← #25130949

Subgroups — #25130949

Order 11008.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583449C211yesmaximal, characteristic
2C2×#14583185C211yesmaximal, characteristic, complemented
3C2×#14583100C211yesmaximal, characteristic, complemented
4C4×#13063304C211yesmaximal, characteristic, complemented
5#19135785C212yesmaximal, complemented
6#19135600C212yesmaximal, complemented
7#19135546C211yesmaximal, characteristic, complemented
8#19135521C211yesmaximal, characteristic, complemented
9#19134928C212yesmaximal, complemented
10#19134859C212yesmaximal, complemented
11C43×#1797C211yesmaximal, characteristic, complemented
12C22×#10621898—21no—
13C22×#10621873C2212yes—
14#14583449—24no—
15#14583449—24no—
16C2×#13063325C2211yescharacteristic
17C2×#13063322C2211yescharacteristic
18C2×#13063313—21no—
19C2×#13063304C2211yescharacteristic
20C2×#13063299—21no—
21C2×#13063299C2212yes—
22C2×C4×Dic86C2211yescharacteristic
23C2×C4×D172—21no—
24C2×C4×D172C2212yes—
25#14583185—24no—
26#14583100—24no—
27C2×#13063257C2212yes—
28C2×#13063250C2212yes—
29C2×#13063247C2212yes—
30C2×#13063247C2212yes—
31C2×#13063247C2212yes—
32#14582805C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582783—21no—
35#14582772—21no—
36#14582759C2211yescharacteristic
37C4×Dic43⋊C4—21no—
38C4×C4⋊Dic43C2211yescharacteristic
39C4×C22⋊Dic43—21no—
40#14582662C2212yes—
41#14582662C2212yes—
42C22×C42×C43C2211yescharacteristic
43C2×C4⋊C8×C43C2211yescharacteristic
44C2×C4⋊C8×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2212yes—
46C43×#336C2212yes—
47C2×#10621898—28no—
48C2×#10621898—44no—
49C2×#10621898—44no—
50C22×Dic86—21no—
51C22×Dic86C2311yescharacteristic
52C22×D172—21no—
53C22×D172—21no—
54C22×D172C2312yes—
55C22×C22⋊D43—22no—
56C22×C4×D43—22no—
57C2×#10621873—24no—
58C2×#10621873—24no—
59C2×#10621873—42no—
60#13063325—22no—
61#13063325D414yes—
62#13063322—22no—
63#13063322D414yes—
64#13063313—28no—
65#13063304—22no—
66#13063304—22no—
67#13063299—28no—
68#13063299—24no—
69#13063299—24no—
70C4×Dic86—22no—
71C4×Dic86—22no—
72C4×D172—28no—
73C4×D172—24no—
74C4×D172—24no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2312yes—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—22no—
86C2×(C2×D43)⋊C4—22no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89#13063257—24no—
90#13063250—24no—
91#13063247—24no—
92#13063247—24no—
93#13063247—42no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C23×C4×C43D411yescharacteristic
100C23×C4×C43D411yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C22×C8×C43C2312yes—
103C22×C8×C43C2312yes—
104C2×C42×C43—22no—
105C2×C42×C43—22no—
106C2×C42×C43D411yescharacteristic
107C2×C42×C43D411yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C2×C42×C43C2311yescharacteristic
110C4⋊C8×C43—22no—
111C4⋊C8×C43—22no—
112C22⋊C8×C43—42no—
113C24×C43C2×D411yescharacteristic
114C23×D43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43SD1614yescomplemented
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2411yescharacteristic
133C2×C22⋊D43—28no—
134C2×C22⋊D43—44no—
135C2×C22⋊D43—44no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141#10621898—432no—
142C2×D172—24no—
143C2×D172—24no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172—22no—
147C2×D172—22no—
148C2×D172—22no—
149C2×D172—42no—
150C2×D172—42no—
151C2×D172—42no—
152C2×D172—42no—
153C2×D172C2×D414yes—
154C2×C4×D43—28no—
155C2×C4×D43—44no—
156C2×C4×D43—44no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—24no—
162C2×Dic86—21no—
163C2×Dic86—42no—
164C2×Dic86—42no—
165C2×Dic86#4112yescomplemented
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C2×C8×C43—22no—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C42×C43—22no—
173C42×C43—22no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43C2×D412yes—
177C42×C43C2×D412yes—
178C22⋊Dic43—24no—
179C22⋊Dic43—42no—
180(C2×D43)⋊C4—28no—
181(C2×D43)⋊C4—28no—
182C4⋊Dic43—24no—
183C4⋊Dic43—22no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×D414yes—
190C4⋊Dic43#4112yescomplemented
191Dic43⋊C4—24no—
192Dic43⋊C4—42no—
193Dic43⋊C4—42no—
194C4×Dic43—42no—
195C4×Dic43—42no—
196#10621873—48no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43C2×SD1612yes—
204C23×C43C22×D411yescharacteristic
205C22×D43—24no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—42no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—28no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—44no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43#12012yes—
229C2×C4×C43#12012yes—
230C2×C4×C43C2×SD1612yes—
231C2×C4×C43C2×SD1612yes—
232C2×C4×C43AGL(1,ℤ/8)12yes—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C22⋊D43—416no—
240C2×Dic43—24no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—41no—
247C2×Dic43—42no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255D172—24no—
256D172—24no—
257D172—48no—
258D172—42no—
259D172—42no—
260D172—48no—
261C4×D43—416no—
262Dic86—22no—
263Dic86—22no—
264Dic86—41no—
265Dic86—41no—
266Dic86—48no—
267C8×C43—42no—
268C8×C43—42no—
269#24154—431nomaximal, Sylow
270C22×C43—22no—
271C22×C43—22no—
272C22×C43—22no—
273C22×C43—41no—
274C22×C43—41no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43C2×#12011yescharacteristic
278C22×C43#52511yescharacteristic
279C22×C43#53711yescharacteristic
280C22×C43C22×SD1611yescharacteristic
281C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C43#57511yescharacteristic
283C22×C43#57511yescharacteristic
284C2×D43—44no—
285C2×D43—44no—
286C2×D43—44no—
287C2×D43—82no—
288C2×D43—82no—
289C2×D43—82no—
290C2×D43—82no—
291C4×C43—22no—
292C4×C43—22no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43#45014yes—
296C4×C43#54611yescharacteristic
297C4×C43#54711yescharacteristic
298C4×C43#54811yescharacteristic
299C4×C43#55011yescharacteristic
300Dic43—42no—
301Dic43—42no—
302Dic43—44no—
303Dic43—81no—
304Dic43—81no—
305C2×#532—431no—
306C2×#475—431no—
307C2×#460—431no—
308C4×C22⋊Q8—431no—
309#2034—432no—
310#2000—432no—
311#1988—431no—
312#1982—431no—
313#1877—432no—
314#1864—432no—
315#1797D4311yescharacteristic, complemented
316C2×C43—42no—
317C2×C43#240711yescharacteristic
318C2×C43C2×#45011yescharacteristic
319C2×C43#300511yescharacteristic
320C2×C43#310311yescharacteristic
321C2×C43#311511yescharacteristic
322C2×C43#324611yescharacteristic
323C2×C43#325111yescharacteristic
324D43—84no—
325C22×#41—861no—
326C22×SD16—432no—
327#532—864no—
328#532—864no—
329C2×C4⋊Q8—431no—
330C2×#127—431no—
331C2×#124—861no—
332C2×C22⋊Q8—431no—
333C2×#121—432no—
334C2×#121—861no—
335C2×C4×Q8—431no—
336C2×C4×D4—432no—
337C2×C4×D4—861no—
338C22×C42C2×D4311yescharacteristic
339#475—864no—
340#460—864no—
341C2×#106—432no—
342C2×C4⋊C8C2×D4311yescharacteristic
343C2×C4⋊C8C2×D4311yescharacteristic
344C2×#103—432no—
345C2×#102—432no—
346C2×#102—432no—
347C2×#102—432no—
348C2×C22⋊C8C2×D4312yes—
349#391—431no—
350#389—431no—
351#387—861no—
352#385—861no—
353#380—431no—
354C4×C4⋊C4—431no—
355C4×C4⋊C4—861no—
356C4×C22⋊C4—861no—
357#340—432no—
358#340—432no—
359#336C2×D4312yes—
360C43#2415411yescharacteristic, complemented, Sylow
361C2×#41—868no—
362C2×#41—1724no—
363C2×#41—1724no—
364C22×Q8—431no—
365C22×Q8—861no—
366C22×D4—432no—
367C22×D4—862no—
368C22×D4—861no—
369C22×D4—861no—
370C23×C4—862no—
371C23×C4D17211yescharacteristic
372C23×C4D17211yescharacteristic
373C23×C4C22×D4311yescharacteristic
374C2×SD16—864no—
375C2×SD16—864no—
376C2×SD16—1722no—
377C22×C8C22×D4312yes—
378C22×C8C22×D4312yes—
379C4⋊Q8—434no—
380C4⋊Q8—862no—
381#127—434no—
382#127—862no—
383#124—868no—
384C22⋊Q8—862no—
385C22⋊Q8—862no—
386#121—864no—
387#121—864no—
388#121—868no—
389C4×Q8—862no—
390C4×Q8—862no—
391C4×D4—864no—
392C4×D4—864no—
393C4×D4—868no—
394C2×C4⋊C4—432no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C22⋊C4—861no—
403C2×C22⋊C4—862no—
404C2×C22⋊C4—862no—
405C2×C22⋊C4—861no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—861no—
409C2×C42—861no—
410C2×C42D17211yescharacteristic
411C2×C42D17211yescharacteristic
412C2×C42C22×D4311yescharacteristic
413C2×C42C22×D4311yescharacteristic
414#106—864no—
415C4⋊C8—22no—
416C4⋊C8—22no—
417#103—864no—
418#102—864no—
419#102—864no—
420#102—1722no—
421C22⋊C8—42no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427C24—862no—
428C24C2×D17211yescharacteristic
429#41—17232no—
430C2×Q8—432no—
431C2×Q8—864no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—1722no—
438C2×Q8—1722no—
439C2×D4—434no—
440C2×D4—868no—
441C2×D4—864no—
442C2×D4—864no—
443C2×D4—862no—
444C2×D4—862no—
445C2×D4—862no—
446C2×D4—862no—
447C2×D4—862no—
448C2×D4—1722no—
449C2×D4—1722no—
450C2×D4—1724no—
451C2×D4—1724no—
452C2×D4—1722no—
453C2×D4—1722no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—868no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—862no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—1724no—
472C22×C4—1724no—
473C22×C4#1062187314yescomplemented
474C22×C4C2×D17211yescharacteristic
475C22×C4C2×D17211yescharacteristic
476C22×C4C2×D17211yescharacteristic
477C22×C4C2×D17211yescharacteristic
478C22×C4C2×D17211yescharacteristic
479C22×C4C23×D4311yescharacteristic
480SD16—1728no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C4⋊C4—434no—
488C4⋊C4—432no—
489C4⋊C4—864no—
490C4⋊C4—864no—
491C4⋊C4—862no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C22⋊C4—868no—
500C22⋊C4—868no—
501C22⋊C4—864no—
502C22⋊C4—1722no—
503C42—22no—
504C42—22no—
505C42—21no—
506C42—21no—
507C42—1722no—
508C42—1722no—
509C42D4×D4312yes—
510C42D4×D4312yes—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—864no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521C23—1722no—
522C23—1722no—
523C23—1722no—
524C23C2×#1062187312yes—
525C23C22×D17211yescharacteristic
526Q8—862no—
527Q8—862no—
528Q8—1728no—
529Q8—1721no—
530Q8—1721no—
531D4—864no—
532D4—864no—
533D4—1728no—
534D4—17216no—
535D4—1722no—
536D4—1728no—
537D4—1722no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—28no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—864no—
555C2×C4—862no—
556C2×C4—862no—
557C2×C4—17216no—
558C2×C4—1721no—
559C2×C4—1721no—
560C2×C4—1721no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1722no—
566C2×C4—1721no—
567C2×C4—1722no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4#1306329512yes—
571C2×C4#1306329512yes—
572C2×C4C2×#1062187312yes—
573C2×C4C2×#1062187312yes—
574C2×C4#1306335312yes—
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C2×D4×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4#41×D4311yescharacteristic
579C2×C4#1306337011yescharacteristic
580C2×C4#1306337311yescharacteristic
581C8—42no—
582C8—42no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—3442no—
591C22—3442no—
592C22—3442no—
593C22—3442no—
594C22—1724no—
595C22—1724no—
596C22—1724no—
597C22C2×#1306329511yescharacteristic
598C22#1458341111yescharacteristic
599C22#1458348011yescharacteristic
600C22C22×#1062187311yescharacteristic
601C22C2×#1306335311yescharacteristic
602C22#1458369911yescharacteristic
603C22#1458369911yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—3441no—
609C4—3441no—
610C4—1722no—
611C4—1724no—
612C4—1722no—
613C4#1458305214yes—
614C4#1458354611yescharacteristic
615C4#1458355111yescharacteristic
616C4#1458355911yescharacteristic
617C4#1458356711yescharacteristic
618C2—42no—
619C2—3444no—
620C2#1913794111yescharacteristic
621C2C2×#1458305211yescharacteristic
622C2#1914384011yescharacteristic
623C2#1914462711yescharacteristic
624C2#1914474711yescharacteristic
625C2#1914591211yescharacteristic
626C2#1914595811yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1797C2
socleC23×C43C22×D4
prime radicalC2×#14583449C2
hypercenter#1797D43
hypocenterC43#24154
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#14583185C2semidirect
3. C2×#14583100C2semidirect
4. C4×#13063304C2semidirect
5. #19135785C2semidirect
6. #19135600C2semidirect
7. #19135546C2semidirect
8. #19135521C2semidirect
9. #19134928C2semidirect
10. #19134859C2semidirect
11. C43×#1797C2semidirect
126. C22×C4×C43SD16semidirect
165. C2×Dic86#41semidirect
190. C4⋊Dic43#41semidirect
315. #1797D43semidirect
360. C43#24154semidirect
473. C22×C4#10621873semidirect

Maximal subgroups

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

subgroupindex
C2×#145834492
C2×#145831852
C2×#145831002
C4×#130633042
#191357852
#191356002
#191355462
#191355212
#191349282
#191348592
C43×#17972
#2415443