Finite Group Databasebeta

← #25128782

Subgroups — #25128782

Order 11008.

1500 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583601C211yesmaximal, characteristic, complemented
2C22×#13063246C211yesmaximal, characteristic, complemented
3#19137945C211yesmaximal, characteristic, complemented
4#19135739C212yesmaximal, complemented
5#19135590C212yesmaximal, complemented
6#19135024C211yesmaximal, characteristic, complemented
7#19134945C212yesmaximal, complemented
8#19134914C212yesmaximal, complemented
9#19134885C211yesmaximal, characteristic, complemented
10#19134686C211yesmaximal, characteristic, complemented
11C2×C43×#447C211yesmaximal, characteristic, complemented
12C23×C43⋊C8C2211yescharacteristic
13#14583601—24no—
14#14583601—24no—
15C2×#13063318—21no—
16C2×#13063316C2211yescharacteristic, complemented
17C2×#13063309—21no—
18C2×#13063297—21no—
19C2×#13063296C2212yes—
20C2×#13063296C2211yescharacteristic, complemented
21C2×#13063294—21no—
22C2×D4×Dic43—21no—
23C2×D4×Dic43C2211yescharacteristic, complemented
24C2×C4×C22⋊D43C2211yescharacteristic
25C2×#13063283C2211yescharacteristic, complemented
26C22×C4⋊Dic43C2211yescharacteristic
27C2×#13063246—24no—
28C2×#13063246C2212yes—
29C2×#13063246C2212yes—
30C2×#13063246C2212yescomplemented
31C2×(C2×D43)⋊C8C2212yescomplemented
32#14582813—21no—
33#14582807—21no—
34#14582802C2212yes—
35#14582759C2211yescharacteristic
36#14582755—21no—
37#14582662C2212yescomplemented
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582653C2212yescomplemented
41C23×D4×C43C2211yescharacteristic
42C22×D8×C43C2212yes—
43C2×#121×C43C2211yescharacteristic
44C43×#447—24no—
45C2×#102×C43C2212yes—
46C2×C22⋊C8×C43C2211yescharacteristic
47C22×C22⋊D43—21no—
48C22×C22⋊D43—22no—
49C22×C22⋊D43D411yescharacteristic
50C23×Dic43—21no—
51C23×Dic43—21no—
52C22×C4×D43C2311yescharacteristic
53C22×C43⋊C8—22no—
54C22×C43⋊C8—42no—
55C22×C43⋊C8C2312yes—
56#13063318—28no—
57#13063316—22no—
58#13063316—22no—
59#13063309—28no—
60#13063297—28no—
61#13063296—22no—
62#13063296—24no—
63#13063296—22no—
64#13063296—42no—
65#13063294—44no—
66D4×Dic43—28no—
67D4×Dic43—22no—
68D4×Dic43—22no—
69C4×C22⋊D43—22no—
70C4×C22⋊D43—22no—
71#13063283—22no—
72#13063283—22no—
73C2×C4⋊Dic43—22no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43D414yescomplemented
77C2×C4⋊Dic43C2312yes—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—22no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—22no—
88C2×C22⋊Dic43D411yescharacteristic
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063246—24no—
94#13063246—24no—
95#13063246—42no—
96(C2×D43)⋊C8—42no—
97C43⋊#95—21no—
98C25×C43—21no—
99C22×D4×C43—24no—
100C22×D4×C43—21no—
101C22×D4×C43—22no—
102C22×D4×C43—22no—
103C22×D4×C43—21no—
104C22×D4×C43—42no—
105C22×D4×C43C2311yescharacteristic
106C22×D4×C43C2312yes—
107C23×C4×C43C2311yescharacteristic
108C2×D8×C43—24no—
109C2×D8×C43—24no—
110C2×D8×C43—42no—
111C22×C8×C43C2312yes—
112#121×C43—22no—
113#121×C43D414yescomplemented
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C22⋊C4×C43—21no—
116#102×C43—24no—
117C22⋊C8×C43—22no—
118C24×C43—21no—
119C24×C43—22no—
120C24×C43—44no—
121C24×C43—42no—
122C24×C43—42no—
123C24×C43—42no—
124C24×C43—82no—
125C24×C43C2×D411yescharacteristic
126C23×D43C2×D411yescharacteristic
127C2×D4×C43—21no—
128C2×D4×C43—22no—
129C2×D4×C43—24no—
130C2×D4×C43—28no—
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—44no—
138C2×D4×C43—48no—
139C2×D4×C43—44no—
140C2×D4×C43—42no—
141C2×D4×C43—42no—
142C2×D4×C43—42no—
143C2×D4×C43C2×D412yes—
144C2×D4×C43#4114yes—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—24no—
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—44no—
157C2×C22⋊D43—44no—
158C2×C22⋊D43—82no—
159C2×C22⋊D43—82no—
160C22×Dic43—24no—
161C22×Dic43—24no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—22no—
165C22×Dic43—82no—
166C22×Dic43—82no—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—22no—
173C2×C4×D43—22no—
174D8×C43—48no—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43C2×D412yes—
180C22⋊C4×C43—24no—
181C22⋊Dic43—24no—
182C22⋊Dic43—24no—
183C22⋊Dic43—22no—
184C22⋊Dic43—44no—
185C22⋊Dic43—44no—
186C22⋊Dic43—42no—
187C22⋊Dic43—82no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—22no—
190C4⋊Dic43—24no—
191C4⋊Dic43—24no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—22no—
195C4⋊Dic43—22no—
196C4⋊Dic43C2×D412yes—
197C4⋊Dic43C2×D412yes—
198Dic43⋊C4—24no—
199Dic43⋊C4—22no—
200C4×Dic43—24no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—44no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—24no—
211C23×C43—48no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—41no—
216C23×C43—42no—
217C23×C43—42no—
218C23×C43—41no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43—88no—
223C23×C43—88no—
224C23×C43—84no—
225C23×C43—84no—
226C23×C43#12012yes—
227C23×C43#13512yes—
228C23×C43AGL(1,ℤ/8)12yes—
229C23×C43C22×D411yescharacteristic
230C22×D43—21no—
231C22×D43—22no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—22no—
235D4×C43—24no—
236D4×C43—24no—
237D4×C43—24no—
238D4×C43—48no—
239D4×C43—48no—
240D4×C43—41no—
241D4×C43—41no—
242D4×C43—42no—
243D4×C43—42no—
244C2×C4×C43—22no—
245C2×C4×C43—22no—
246C2×C4×C43—22no—
247C2×C4×C43—24no—
248C2×C4×C43—22no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43#12012yes—
252C2×C4×C43C22×D411yescharacteristic
253C2×C4×C43C22×D411yescharacteristic
254C2×C4×C43C2×#4112yes—
255C2×C4×C43H(5,𝔽2)12yes—
256C22⋊D43—44no—
257C22⋊D43—84no—
258C22⋊D43—88no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—22no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—22no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—84no—
274C2×Dic43—84no—
275C4×D43—41no—
276C4×D43—41no—
277C4×D43—42no—
278C8×C43—42no—
279C43⋊C8—42no—
280#23963—431nomaximal, Sylow
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—24no—
284C22×C43—24no—
285C22×C43—44no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—44no—
290C22×C43—44no—
291C22×C43—816no—
292C22×C43—82no—
293C22×C43—82no—
294C22×C43—82no—
295C22×C43—82no—
296C22×C43—82no—
297C22×C43—82no—
298C22×C43#44914yes—
299C22×C43C2×#12011yescharacteristic
300C22×C43#54612yes—
301C22×C43C2×#13511yescharacteristic
302C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C43#57612yes—
304C2×D43—41no—
305C2×D43—41no—
306C2×D43—41no—
307C2×D43—42no—
308C2×D43—42no—
309C4×C43—22no—
310C4×C43—42no—
311C4×C43#52511yescharacteristic
312C4×C43#53511yescharacteristic
313C4×C43#54612yes—
314Dic43—41no—
315Dic43—41no—
316Dic43—41no—
317Dic43—42no—
318Dic43—42no—
319Dic43—82no—
320C2×#553—431no—
321C2×#447D4311yescharacteristic, complemented
322C22×#102—431no—
323#2408—431no—
324#2025—432no—
325#1999—432no—
326#1893—431no—
327#1879—432no—
328#1875—432no—
329#1869—431no—
330#1824—431no—
331C2×C43—24no—
332C2×C43—82no—
333C2×C43—84no—
334C2×C43#240411yescharacteristic
335C2×C43C2×#44911yescharacteristic
336C2×C43#300811yescharacteristic
337C2×C43#329712yes—
338C2×C43#331812yes—
339D43—81no—
340C23×D4C2×D4311yescharacteristic
341C22×D8C2×D4312yes—
342C23×C8—431no—
343#553—864no—
344#553—864no—
345C2×#126—861no—
346C2×#125—431no—
347C2×#123—861no—
348C2×#121—431no—
349C2×#121—432no—
350C2×#121—861no—
351C2×#121C2×D4311yescharacteristic
352C2×#120—861no—
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4—861no—
356C2×#117—431no—
357C22×C4⋊C4—431no—
358#447—24no—
359C2×#102—432no—
360C2×#102—432no—
361C2×#102—432no—
362C2×#102—864no—
363C2×#102C2×D4312yes—
364C2×C22⋊C8—432no—
365C2×C22⋊C8C2×D4311yescharacteristic
366#394—861no—
367#392—861no—
368#390—432no—
369#380—431no—
370#379—861no—
371#340—432no—
372#340—432no—
373#340—432no—
374#336—432no—
375C43#2396311yescharacteristic, complemented, Sylow
376C25—21no—
377C22×D4—24no—
378C22×D4—21no—
379C22×D4—22no—
380C22×D4—21no—
381C22×D4—22no—
382C22×D4—42no—
383C22×D4—431no—
384C22×D4—861no—
385C22×D4—862no—
386C22×D4C22×D4312yes—
387C22×D4C22×D4311yescharacteristic
388C23×C4—431no—
389C23×C4—861no—
390C23×C4—861no—
391C23×C4C22×D4311yescharacteristic
392C2×D8—24no—
393C2×D8—24no—
394C2×D8—42no—
395C22×C8—432no—
396C22×C8—862no—
397C22×C8—1722no—
398C22×C8C22×D4312yes—
399#126—868no—
400#125—862no—
401#125—862no—
402#123—868no—
403#121—22no—
404#121—862no—
405#121—868no—
406#121—862no—
407#121—864no—
408#121—1722no—
409#121C22⋊D4314yescomplemented
410#120—1724no—
411C4×D4—862no—
412C4×D4—868no—
413C4×D4—862no—
414C4×D4—862no—
415C4×D4—862no—
416#117—862no—
417#117—862no—
418C2×C4⋊C4—434no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—862no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—431no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—862no—
435C2×C22⋊C4—862no—
436C2×C22⋊C4—862no—
437C2×C22⋊C4—861no—
438C2×C42—431no—
439C2×C42—861no—
440#102—24no—
441#102—864no—
442#102—864no—
443#102—1722no—
444C22⋊C8—22no—
445C22⋊C8—1722no—
446#95—861no—
447C24—21no—
448C24—22no—
449C24—44no—
450C24—42no—
451C24—42no—
452C24—42no—
453C24—82no—
454C24—431no—
455C24D4×D4311yescharacteristic
456C2×D4—28no—
457C2×D4—24no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—48no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4—864no—
473C2×D4—862no—
474C2×D4—862no—
475C2×D4—862no—
476C2×D4—3442no—
477C2×D4—3442no—
478C2×D4—1724no—
479C2×D4—1724no—
480C2×D4#1062190014yes—
481C2×D4C2×C22⋊D4312yes—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—864no—
489C22×C4—864no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—862no—
497C22×C4—3442no—
498C22×C4—3442no—
499C22×C4D4×D4311yescharacteristic
500C22×C4D4×D4312yes—
501C22×C4C2×C22⋊D4312yes—
502C22×C4C23×D4311yescharacteristic
503D8—48no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—862no—
508C2×C8—862no—
509C2×C8—862no—
510C2×C8—1724no—
511C4⋊C4—21no—
512C4⋊C4—432no—
513C4⋊C4—432no—
514C4⋊C4—864no—
515C4⋊C4—864no—
516C4⋊C4—864no—
517C4⋊C4—862no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—862no—
521C4⋊C4—862no—
522C4⋊C4C2×C22⋊D4312yes—
523C22⋊C4—24no—
524C22⋊C4—864no—
525C22⋊C4—864no—
526C22⋊C4—864no—
527C22⋊C4—862no—
528C22⋊C4—862no—
529C22⋊C4—3442no—
530C22⋊C4—1724no—
531C22⋊C4—1724no—
532C22⋊C4—1722no—
533C42—864no—
534C42—861no—
535C42—861no—
536C23—22no—
537C23—22no—
538C23—22no—
539C23—24no—
540C23—48no—
541C23—42no—
542C23—41no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—88no—
552C23—88no—
553C23—84no—
554C23—84no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—862no—
559C23—862no—
560C23#1306329312yes—
561C23#1306334412yes—
562C23#1306334912yes—
563C23C2×D4×D4311yescharacteristic
564D4—24no—
565D4—24no—
566D4—24no—
567D4—48no—
568D4—48no—
569D4—41no—
570D4—42no—
571D4—41no—
572D4—42no—
573D4—3448no—
574D4—3444no—
575D4—1724no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—861no—
584C2×C4—862no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—862no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—3444no—
593C2×C4—3444no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1722no—
602C2×C4#1306329312yes—
603C2×C4C2×D4×D4311yescharacteristic
604C2×C4C22×C22⋊D4311yescharacteristic
605C2×C4C2×#1062190012yes—
606C2×C4#1306337012yes—
607C8—42no—
608C8—1722no—
609C22—22no—
610C22—22no—
611C22—24no—
612C22—24no—
613C22—42no—
614C22—44no—
615C22—42no—
616C22—42no—
617C22—44no—
618C22—44no—
619C22—816no—
620C22—82no—
621C22—82no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22—1722no—
630C22—1722no—
631C22#1458304114yes—
632C22C2×#1306329311yescharacteristic
633C22#1458353612yes—
634C22C2×#1306334411yescharacteristic
635C22C2×#1306334911yescharacteristic
636C22#1458370312yes—
637C4—22no—
638C4—42no—
639C4—3442no—
640C4—1721no—
641C4—1721no—
642C4—1721no—
643C4—1722no—
644C4—1722no—
645C4#1458340511yescharacteristic
646C4#1458346411yescharacteristic
647C4#1458354312yes—
648C2—24no—
649C2—84no—
650C2—82no—
651C2—3441no—
652C2#1913791111yescharacteristic
653C2C2×#1458304111yescharacteristic
654C2#1914386211yescharacteristic
655C2#1914644912yes—
656C2#1914674012yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#447C2
socleC23×C43C22×D4
hypercenterC2×#447D43
hypocenterC43#23963
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#14583601C2semidirect
2. C22×#13063246C2semidirect
3. #19137945C2semidirect
4. #19135739C2semidirect
5. #19135590C2semidirect
6. #19135024C2semidirect
7. #19134945C2semidirect
8. #19134914C2semidirect
9. #19134885C2semidirect
10. #19134686C2semidirect
11. C2×C43×#447C2semidirect
16. C2×#13063316C22semidirect
20. C2×#13063296C22semidirect
23. C2×D4×Dic43C22semidirect
25. C2×#13063283C22semidirect
30. C2×#13063246C22semidirect
31. C2×(C2×D43)⋊C8C22semidirect
37. #14582662C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582653C22semidirect
76. C2×C4⋊Dic43D4semidirect
113. #121×C43D4semidirect
321. C2×#447D43semidirect
375. C43#23963semidirect
409. #121C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836012
C22×#130632462
#191379452
#191357392
#191355902
#191350242
#191349452
#191349142
#191348852
#191346862
C2×C43×#4472
#2396343