Finite Group Databasebeta

← #25130950

Subgroups — #25130950

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×#14583450C211yesmaximal, characteristic
2C2×#14583099C211yesmaximal, characteristic, complemented
3C4×#13063301C211yesmaximal, characteristic, complemented
4#19135786C212yesmaximal, complemented
5#19135597C212yesmaximal, complemented
6#19135548C211yesmaximal, characteristic, complemented
7#19135521C211yesmaximal, characteristic, complemented
8#19134926C212yesmaximal, complemented
9#19134853C212yesmaximal, complemented
10#19134572C211yesmaximal, characteristic, complemented
11C2×C43×#475C211yesmaximal, characteristic, complemented
12C22×#10621902—21no—
13C22×#10621884C2212yes—
14#14583450—24no—
15#14583450—24no—
16C2×#13063322C2211yescharacteristic
17C2×#13063314—21no—
18C2×#13063301C2211yescharacteristic
19C2×#13063300—21no—
20C2×#13063300C2212yes—
21C2×#13063287—21no—
22C2×#13063287C2212yes—
23C2×C42×D43C2211yescharacteristic
24#14583099—24no—
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063247C2212yes—
27C2×#13063247C2212yes—
28C2×#13063245C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30#14582806C2211yescharacteristic
31#14582795C2211yescharacteristic
32#14582780—21no—
33#14582770—21no—
34#14582756C2211yescharacteristic
35C4×Dic43⋊C4—21no—
36C4×C4⋊Dic43C2211yescharacteristic
37C4×(C2×D43)⋊C4—21no—
38#14582661C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C2×C4⋊Q8×C43C2211yescharacteristic
42C2×C4×Q8×C43C2211yescharacteristic
43C43×#475—24no—
44C2×#106×C43C2212yes—
45C2×C4⋊C8×C43C2211yescharacteristic
46C2×#103×C43C2212yes—
47C2×#10621902—28no—
48C2×#10621902—44no—
49C2×#10621902—44no—
50C22×D172—22no—
51C22×D172—21no—
52C22×D172—21no—
53C22×D172C2312yes—
54C22×C4×D43—22no—
55C22×C4×D43D411yescharacteristic
56C22×C4×D43D411yescharacteristic
57C22×C4×D43C2311yescharacteristic
58C2×#10621884—24no—
59C2×#10621884—24no—
60C2×#10621884—42no—
61C22×C43⋊C8C2312yes—
62#13063322—22no—
63#13063322D414yes—
64#13063314—28no—
65#13063301—22no—
66#13063301—22no—
67#13063300—28no—
68#13063300—24no—
69#13063300—24no—
70#13063287—28no—
71#13063287—24no—
72#13063287—24no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43D411yescharacteristic
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85C42×D43—22no—
86C42×D43—22no—
87C4⋊(C43⋊C8)—22no—
88#13063247—24no—
89#13063247—42no—
90#13063245—24no—
91(C2×D43)⋊C8—42no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×Q8×C43—21no—
98C22×Q8×C43C2311yescharacteristic
99C22×C8×C43C2312yes—
100C4⋊Q8×C43—22no—
101C4⋊Q8×C43D414yes—
102C4×Q8×C43—22no—
103C4×Q8×C43—22no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C4⋊C4×C43C2312yes—
108C2×C42×C43—21no—
109C2×C42×C43C2311yescharacteristic
110#106×C43—24no—
111C4⋊C8×C43—22no—
112#103×C43—24no—
113C23×D43—22no—
114C23×D43C2×D411yescharacteristic
115C2×Q8×C43—24no—
116C2×Q8×C43—21no—
117C2×Q8×C43—21no—
118C2×Q8×C43—21no—
119C2×Q8×C43—21no—
120C2×Q8×C43—21no—
121C2×Q8×C43—42no—
122C2×Q8×C43—42no—
123C2×Q8×C43#4112yescomplemented
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C22×Dic43—21no—
131C22×Dic43—21no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135#10621902—432no—
136C2×D172—28no—
137C2×D172—24no—
138C2×D172—24no—
139C2×D172—22no—
140C2×D172—22no—
141C2×D172—22no—
142C2×D172—22no—
143C2×D172—22no—
144C2×D172—44no—
145C2×D172—42no—
146C2×D172—42no—
147C2×D172—42no—
148C2×D172—42no—
149C2×D172—44no—
150C2×D172C2×D414yes—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—28no—
154C2×C4×D43—22no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×C4×D43—41no—
163C2×C4×D43—44no—
164C2×C4×D43—44no—
165C2×C4×D43SD1614yescomplemented
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C4⋊C4×C43—24no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—42no—
174C4⋊C4×C43C2×D414yes—
175C42×C43—42no—
176C42×C43C2×D412yes—
177C42×C43C2×D412yes—
178#10621884—48no—
179(C2×D43)⋊C4—28no—
180(C2×D43)⋊C4—28no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—42no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43#4112yescomplemented
187Dic43⋊C4—24no—
188Dic43⋊C4—42no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—42no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C23×C43C22×D411yescharacteristic
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—24no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43C2×SD1612yes—
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—48no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
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×C43AGL(1,ℤ/8)12yes—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—22no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43C2×SD1612yes—
253D172—24no—
254D172—24no—
255D172—48no—
256D172—416no—
257D172—42no—
258D172—42no—
259D172—48no—
260C4×D43—28no—
261C4×D43—416no—
262C4×D43—44no—
263C4×D43—41no—
264C4×D43—41no—
265C4×D43—41no—
266C4×D43—41no—
267C8×C43—42no—
268C43⋊C8—42no—
269#24154—431nomaximal, Sylow
270C22×C43C2×#12011yescharacteristic
271C22×C43#52511yescharacteristic
272C22×C43#53711yescharacteristic
273C22×C43C22×SD1611yescharacteristic
274C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C43#57511yescharacteristic
276C22×C43#57511yescharacteristic
277C2×D43—22no—
278C2×D43—22no—
279C2×D43—22no—
280C2×D43—41no—
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
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—42no—
293C4×C43—44no—
294C4×C43—81no—
295C4×C43#45014yes—
296C4×C43#54611yescharacteristic
297C4×C43#54711yescharacteristic
298C4×C43#54811yescharacteristic
299C4×C43#55011yescharacteristic
300Dic43—22no—
301Dic43—42no—
302Dic43—41no—
303Dic43—41no—
304Dic43—81no—
305C2×#532—431no—
306C2×#475D4311yescharacteristic, complemented
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#1797—431no—
316C2×C43#240711yescharacteristic
317C2×C43C2×#45011yescharacteristic
318C2×C43#300511yescharacteristic
319C2×C43#310311yescharacteristic
320C2×C43#311511yescharacteristic
321C2×C43#324611yescharacteristic
322C2×C43#325111yescharacteristic
323D43—42no—
324D43—84no—
325C22×#41—861no—
326C22×SD16—432no—
327#532—864no—
328#532—864no—
329C2×C4⋊Q8C2×D4311yescharacteristic
330C2×#127—431no—
331C2×#124—861no—
332C2×C22⋊Q8—431no—
333C2×#121—432no—
334C2×#121—861no—
335C2×C4×Q8C2×D4311yescharacteristic
336C2×C4×D4—432no—
337C2×C4×D4—861no—
338C22×C42—431no—
339#475—24no—
340#460—864no—
341C2×#106C2×D4312yes—
342C2×C4⋊C8—431no—
343C2×C4⋊C8C2×D4311yescharacteristic
344C2×#103C2×D4312yes—
345C2×#102—432no—
346C2×#102—432no—
347C2×#102—432no—
348C2×C22⋊C8—432no—
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#336—432no—
360C43#2415411yescharacteristic, complemented, Sylow
361C2×#41—868no—
362C2×#41—1724no—
363C2×#41—1724no—
364C22×Q8—21no—
365C22×Q8C22×D4311yescharacteristic
366C22×D4—432no—
367C22×D4—862no—
368C22×D4—861no—
369C22×D4—861no—
370C23×C4—431no—
371C23×C4—431no—
372C23×C4—431no—
373C23×C4—862no—
374C2×SD16—864no—
375C2×SD16—864no—
376C2×SD16—1722no—
377C22×C8—432no—
378C22×C8C22×D4312yes—
379C4⋊Q8—22no—
380C4⋊Q8C22⋊D4314yes—
381#127—434no—
382#127—862no—
383#124—868no—
384C22⋊Q8—862no—
385C22⋊Q8—862no—
386#121—864no—
387#121—868no—
388#121—864no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×D4—864no—
392C4×D4—868no—
393C4×D4—864no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4312yes—
402C2×C22⋊C4—862no—
403C2×C22⋊C4—862no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C42—21no—
407C2×C42—431no—
408C2×C42—431no—
409C2×C42—431no—
410C2×C42—862no—
411C2×C42—862no—
412C2×C42—861no—
413C2×C42C22×D4311yescharacteristic
414#106—24no—
415C4⋊C8—22no—
416C4⋊C8—862no—
417#103—24no—
418#102—864no—
419#102—864no—
420#102—1722no—
421C22⋊C8—1722no—
422#95—861no—
423#95—861no—
424#95—861no—
425#95—861no—
426#95—861no—
427C24—431no—
428C24—862no—
429#41—17232no—
430C2×Q8—24no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8#1062190212yescomplemented
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—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—431no—
458C22×C4—434no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—868no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—861no—
465C22×C4—862no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—1721no—
474C22×C4—1721no—
475C22×C4—1724no—
476C22×C4—1724no—
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479C22×C4C23×D4311yescharacteristic
480SD16—1728no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—862no—
487C4⋊C4—24no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—42no—
492C4⋊C4—432no—
493C4⋊C4—864no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1722no—
498C4⋊C4C2×C22⋊D4314yes—
499C22⋊C4—868no—
500C22⋊C4—868no—
501C22⋊C4—864no—
502C22⋊C4—1722no—
503C42—42no—
504C42—862no—
505C42—862no—
506C42—861no—
507C42—861no—
508C42—1722no—
509C42D4×D4312yes—
510C42C2×C22⋊D4312yes—
511C23—432no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—861no—
516C23—861no—
517C23—861no—
518C23—864no—
519C23—1722no—
520C23—1722no—
521C23—1722no—
522C23—1722no—
523C23—1722no—
524C23—1722no—
525C23C2×D4×D4311yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—48no—
529Q8—41no—
530Q8—41no—
531D4—864no—
532D4—864no—
533D4—1728no—
534D4—17216no—
535D4—1728no—
536D4—1722no—
537D4—1722no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—432no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—868no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—862no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—1724no—
561C2×C4—17216no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4#1306329312yes—
572C2×C4#1306329312yes—
573C2×C4SD16×D4312yes—
574C2×C4#1306335212yes—
575C2×C4C2×D4×D4311yescharacteristic
576C2×C4C22×C22⋊D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4C2×#1062190211yescharacteristic
579C2×C4#1306337111yescharacteristic
580C2×C4#1306337311yescharacteristic
581C8—42no—
582C8—1722no—
583C22—862no—
584C22—862no—
585C22—862no—
586C22—3442no—
587C22—3442no—
588C22—3442no—
589C22—3442no—
590C22—1724no—
591C22—1724no—
592C22—1724no—
593C22—1721no—
594C22—1721no—
595C22—1721no—
596C22—1721no—
597C22C2×#1306329311yescharacteristic
598C22#1458341211yescharacteristic
599C22#1458347911yescharacteristic
600C22C2×SD16×D4311yescharacteristic
601C22C2×#1306335211yescharacteristic
602C22#1458369811yescharacteristic
603C22#1458369811yescharacteristic
604C4—22no—
605C4—44no—
606C4—42no—
607C4—81no—
608C4—862no—
609C4—3441no—
610C4—1722no—
611C4—1721no—
612C4—1721no—
613C4#1458304814yes—
614C4#1458354011yescharacteristic
615C4#1458355111yescharacteristic
616C4#1458356011yescharacteristic
617C4#1458356811yescharacteristic
618C2—3444no—
619C2—1722no—
620C2#1913794211yescharacteristic
621C2C2×#1458304811yescharacteristic
622C2#1914383611yescharacteristic
623C2#1914462811yescharacteristic
624C2#1914474911yescharacteristic
625C2#1914591011yescharacteristic
626C2#1914596011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#475C2
socleC23×C43C22×D4
prime radicalC2×#14583450C2
hypercenterC2×#475D43
hypocenterC43#24154
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
2. C2×#14583099C2semidirect
3. C4×#13063301C2semidirect
4. #19135786C2semidirect
5. #19135597C2semidirect
6. #19135548C2semidirect
7. #19135521C2semidirect
8. #19134926C2semidirect
9. #19134853C2semidirect
10. #19134572C2semidirect
11. C2×C43×#475C2semidirect
123. C2×Q8×C43#41semidirect
165. C2×C4×D43SD16semidirect
186. C4⋊Dic43#41semidirect
306. C2×#475D43semidirect
360. C43#24154semidirect
438. C2×Q8#10621902semidirect

Maximal subgroups

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

subgroupindex
C2×#145834502
C2×#145830992
C4×#130633012
#191357862
#191355972
#191355482
#191355212
#191349262
#191348532
#191345722
C2×C43×#4752
#2415443