Finite Group Databasebeta

← #25105683

Subgroups — #25105683

Order 11008.

1558 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583406C211yesmaximal, characteristic
2C2×#14582861C211yesmaximal, characteristic, complemented
3#380×D43C211yesmaximal, characteristic, complemented
4#19135030C212yesmaximal, complemented
5#19135025C212yesmaximal, complemented
6#19134909C212yesmaximal, complemented
7#19134899C212yesmaximal, complemented
8#19134691C211yesmaximal, characteristic, complemented
9#19134687C211yesmaximal, characteristic, complemented
10#19134535C211yesmaximal, characteristic, complemented
11C43×#1788C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×#10621872C2212yes—
14#14583406—24no—
15#14583406C418yescomplemented
16C2×#13063306—21no—
17C2×#13063301C2211yescharacteristic
18C2×#13063301C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×#13063293—21no—
22C2×C4×C22⋊D43—21no—
23C2×C4×C22⋊D43—21no—
24C2×#13063284C2211yescharacteristic
25C2×C4⋊C4×D43C2212yes—
26C2×C22⋊C4×D43—21no—
27C2×#13063249C2212yescomplemented
28C2×#13063246C2212yescomplemented
29#14582861—24no—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×(C2×D43)⋊C8C2212yes—
32#14582759C2211yescharacteristic
33#14582758—21no—
34#14582757—21no—
35#14582756C2212yes—
36#95×D43—21no—
37#14582662C2212yescomplemented
38#14582662C2212yescomplemented
39#14582661C2212yescomplemented
40#14582661C2212yescomplemented
41C22×#41×C43C2211yescharacteristic
42C2×#103×C43C2212yescomplemented
43C2×#102×C43C2212yescomplemented
44C2×C22⋊C8×C43C2211yescharacteristic
45C43×#380C2211yescharacteristic
46C24×D43D411yescharacteristic
47C22×C22⋊D43—21no—
48C22×C22⋊D43—21no—
49C23×Dic43D411yescharacteristic
50C22×C4×D43—22no—
51C22×C4×D43—42no—
52C22×C4×D43—42no—
53C22×C4×D43C2×C414yes—
54C22×C4×D43D411yescharacteristic
55C22×C4×D43D411yescharacteristic
56C22×C4×D43D414yes—
57C22×C4×D43C2311yescharacteristic
58C22×C4×D43C2311yescharacteristic
59C2×#10621872—24no—
60C2×#10621872—42no—
61C2×#10621872—42no—
62C22×C43⋊C8C2312yes—
63#13063306—28no—
64#13063301—22no—
65#13063301—22no—
66#13063301C2×C414yes—
67#13063301C2×C414yescomplemented
68#13063296—22no—
69#13063296—22no—
70#13063296C2×C414yes—
71#13063296C2×C414yescomplemented
72#13063293—28no—
73C4×C22⋊D43—28no—
74C4×C22⋊D43—28no—
75#13063284—22no—
76#13063284C2×C414yescomplemented
77C2×C4⋊Dic43C2312yes—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—22no—
83C4⋊C4×D43—42no—
84C4⋊C4×D43—42no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—22no—
92C22⋊C4×D43—44no—
93C2×C4×Dic43—21no—
94#13063249—42no—
95#13063246—42no—
96C22⋊(C43⋊C8)—22no—
97(C2×D43)⋊C8—24no—
98C43⋊#95—21no—
99C43⋊#95—22no—
100C2×#41×C43—22no—
101C2×#41×C43—42no—
102C2×#41×C43—42no—
103C2×#41×C43C2×C414yescomplemented
104C22×Q8×C43C2311yescharacteristic
105C22×D4×C43—21no—
106C22×D4×C43C2311yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2312yes—
110C2×C4⋊C4×C43C2312yes—
111C2×C22⋊C4×C43—21no—
112#103×C43—42no—
113#102×C43—42no—
114C22⋊C8×C43—22no—
115#95×C43—21no—
116C24×C43—21no—
117C24×C43C2×D411yescharacteristic
118C23×D43—22no—
119C23×D43—22no—
120C23×D43—42no—
121C23×D43—42no—
122C23×D43C22⋊C414yes—
123C23×D43C2×D411yescharacteristic
124C23×D43C2×D411yescharacteristic
125#41×C43—44no—
126#41×C43—44no—
127#41×C43—48no—
128C2×Q8×C43—21no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43C22×C412yes—
132C2×D4×C43—21no—
133C2×D4×C43—24no—
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—44no—
137C2×D4×C43C22×C412yes—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—24no—
141C22×C4×C43—21no—
142C22×C4×C43—22no—
143C22×C4×C43—44no—
144C22×C4×C43C22×C412yes—
145C22×C4×C43C2×D412yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—24no—
149C2×C22⋊D43—24no—
150C2×C22⋊D43—44no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—42no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—22no—
156C22×Dic43—42no—
157C22×Dic43C22⋊C414yes—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—42no—
165C2×C4×D43—42no—
166C2×C4×D43—44no—
167C2×C4×D43—44no—
168C2×C4×D43—44no—
169C2×C4×D43—44no—
170C2×C4×D43—48no—
171C2×C4×D43—44no—
172C2×C4×D43C22⋊C414yes—
173C2×C4×D43C22⋊C414yes—
174C2×C4×D43C22×C412yes—
175C2×C4×D43C22×C412yes—
176C2×C4×D43C2×D412yes—
177C2×C4×D43C2×D412yes—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C2×C8×C43—22no—
181C4⋊C4×C43—22no—
182C4⋊C4×C43—22no—
183C22⋊C4×C43—42no—
184C22⋊Dic43—24no—
185C22⋊Dic43—24no—
186C22⋊Dic43—24no—
187C22⋊Dic43—42no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—44no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—22no—
194C4⋊Dic43—22no—
195C4⋊Dic43C22×C412yes—
196C4⋊Dic43C22×C412yes—
197Dic43⋊C4—24no—
198Dic43⋊C4—24no—
199Dic43⋊C4—44no—
200C4×Dic43—24no—
201C2×C43⋊C8—22no—
202C2×C43⋊C8—22no—
203C2×C43⋊C8—22no—
204#10621872—48no—
205C23×C43—22no—
206C23×C43—21no—
207C23×C43—21no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—42no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—42no—
214C23×C43C2×C22⋊C412yes—
215C23×C43C22×D411yescharacteristic
216C22×D43—22no—
217C22×D43—22no—
218C22×D43—22no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—22no—
222C22×D43—28no—
223C22×D43—44no—
224C22×D43—44no—
225C22×D43—48no—
226C22×D43—48no—
227C22×D43C2×C22⋊C412yes—
228C22×D43C2×C22⋊C412yes—
229C22×D43AGL(1,ℤ/8)12yes—
230C22×D43#13712yes—
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—42no—
234D4×C43—22no—
235D4×C43—22no—
236D4×C43—48no—
237D4×C43—42no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—24no—
242C2×C4×C43—22no—
243C2×C4×C43—48no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43—42no—
247C2×C4×C43—42no—
248C2×C4×C43C2×C22⋊C412yes—
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43H(5,𝔽2)12yes—
252C2×C4×C43H(5,𝔽2)12yes—
253C22⋊D43—48no—
254C22⋊D43—48no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—44no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43C2×C22⋊C412yes—
267C2×Dic43C2×C22⋊C412yes—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—24no—
273C4×D43—24no—
274C4×D43—44no—
275C4×D43—44no—
276C4×D43—88no—
277C8×C43—42no—
278C43⋊C8—42no—
279#21769—431nomaximal, Sylow
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—22no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—82no—
289C22×C43—82no—
290C22×C43C22×C22⋊C411yescharacteristic
291C22×C43#53412yes—
292C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
293C22×C43C2×#13711yescharacteristic
294C22×C43#57512yes—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—24no—
298C2×D43—24no—
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—416no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43#41714yes—
306C4×C43—22no—
307C4×C43—42no—
308C4×C43—82no—
309C4×C43#51811yescharacteristic
310C4×C43#51811yescharacteristic
311C4×C43#53412yes—
312Dic43—22no—
313Dic43—22no—
314Dic43—42no—
315Dic43—42no—
316Dic43—82no—
317C2×#525—431no—
318C2×#407—431no—
319C2×#380—431no—
320#1895—432no—
321#1894—432no—
322#1874—432no—
323#1872—432no—
324#1825—431no—
325#1825—431no—
326#1788—431no—
327#1788D4311yescharacteristic, complemented
328C2×C43—42no—
329C2×C43—82no—
330C2×C43#230811yescharacteristic
331C2×C43C2×#41711yescharacteristic
332C2×C43#289611yescharacteristic
333C2×C43#319412yes—
334C2×C43#319612yes—
335D43—24no—
336D43—42no—
337C22×#41C2×D4311yescharacteristic
338C24×C4—431no—
339C22×M16—432no—
340#525—438no—
341#525—864no—
342C2×#123—861no—
343C2×C22⋊Q8—431no—
344C2×C22⋊Q8—431no—
345C2×#121—431no—
346C2×#121—431no—
347C2×#120—861no—
348C2×C4×D4—861no—
349C2×C4×D4—861no—
350C2×#117—431no—
351C22×C4⋊C4—432no—
352C22×C22⋊C4—861no—
353C2×#103—432no—
354C2×#103C2×D4312yescomplemented
355C2×#102—432no—
356C2×#102C2×D4312yescomplemented
357#407—864no—
358C2×C22⋊C8—431no—
359C2×C22⋊C8—432no—
360C2×C22⋊C8C2×D4311yescharacteristic
361#380—431no—
362#380—432no—
363#380—861no—
364#380—861no—
365#380C2×D4311yescharacteristic
366C2×#95—861no—
367#340—432no—
368#340—432no—
369#340—432no—
370#340—432no—
371C43#2176911yescharacteristic, complemented, Sylow
372C25—431no—
373C2×#41—22no—
374C2×#41—42no—
375C2×#41—42no—
376C2×#41C4×D4314yescomplemented
377C22×Q8C22×D4311yescharacteristic
378C22×D4—21no—
379C22×D4—861no—
380C22×D4—861no—
381C22×D4C22×D4311yescharacteristic
382C23×C4—21no—
383C23×C4—431no—
384C23×C4—431no—
385C23×C4—431no—
386C23×C4—434no—
387C23×C4—431no—
388C23×C4—431no—
389C23×C4—434no—
390C23×C4—862no—
391C23×C4—1722no—
392C23×C4—1722no—
393C23×C4C22×D4311yescharacteristic
394C2×M16—864no—
395C2×M16—1722no—
396C2×M16—1722no—
397C22×C8—432no—
398C22×C8C22×D4312yes—
399#123—868no—
400C22⋊Q8—434no—
401C22⋊Q8—434no—
402C22⋊Q8—862no—
403C22⋊Q8—862no—
404#121—434no—
405#121—434no—
406#121—862no—
407#121—862no—
408#120—868no—
409C4×D4—868no—
410C4×D4—868no—
411#117—434no—
412#117—862no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—432no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—1722no—
420C2×C4⋊C4—1722no—
421C2×C4⋊C4C22×D4312yes—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—862no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—1724no—
431C2×C42—861no—
432#103—42no—
433#103—1722no—
434#102—42no—
435#102—1722no—
436C22⋊C8—22no—
437C22⋊C8—864no—
438C22⋊C8—862no—
439#95—21no—
440#95—862no—
441#95—861no—
442C24—21no—
443C24—431no—
444C24—431no—
445C24—434no—
446C24—862no—
447C24—862no—
448C24—1722no—
449C24—1722no—
450C24D4×D4311yescharacteristic
451#41—44no—
452#41—44no—
453#41—48no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8C2×C4×D4312yes—
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—44no—
463C2×D4—864no—
464C2×D4—864no—
465C2×D4—1722no—
466C2×D4—1722no—
467C2×D4—1724no—
468C2×D4C2×C4×D4312yes—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—44no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—434no—
478C22×C4—432no—
479C22×C4—432no—
480C22×C4—432no—
481C22×C4—432no—
482C22×C4—434no—
483C22×C4—434no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4—862no—
491C22×C4—1724no—
492C22×C4—1724no—
493C22×C4—1728no—
494C22×C4—1722no—
495C22×C4—1722no—
496C22×C4—1724no—
497C22×C4—1724no—
498C22×C4—1724no—
499C22×C4—1722no—
500C22×C4C2×C4×D4312yes—
501C22×C4D4×D4311yescharacteristic
502C22×C4D4×D4312yes—
503C22×C4C23×D4311yescharacteristic
504M16—1728no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—862no—
509C2×C8—862no—
510C2×C8—862no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—864no—
516C4⋊C4—864no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—1724no—
522C22⋊C4—42no—
523C22⋊C4—864no—
524C22⋊C4—864no—
525C22⋊C4—864no—
526C22⋊C4—864no—
527C22⋊C4—864no—
528C22⋊C4—1724no—
529C22⋊C4—1722no—
530C42—864no—
531C23—21no—
532C23—21no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—42no—
540C23—432no—
541C23—432no—
542C23—432no—
543C23—432no—
544C23—868no—
545C23—862no—
546C23—862no—
547C23—861no—
548C23—861no—
549C23—862no—
550C23—862no—
551C23—1724no—
552C23—1724no—
553C23—1728no—
554C23—1728no—
555C23C22⋊C4×D4312yes—
556C23C2×D4×D4311yescharacteristic
557Q8—22no—
558Q8—22no—
559Q8—42no—
560D4—22no—
561D4—22no—
562D4—48no—
563D4—42no—
564D4—1728no—
565D4—1728no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—48no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—432no—
577C2×C4—432no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—864no—
585C2×C4—864no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—3448no—
589C2×C4—1724no—
590C2×C4—1724no—
591C2×C4—1724no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1722no—
598C2×C4C22⋊C4×D4312yes—
599C2×C4C22×C4×D4311yescharacteristic
600C2×C4C2×D4×D4311yescharacteristic
601C2×C4#1306337012yes—
602C2×C4#1306337012yes—
603C8—42no—
604C8—1722no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—82no—
614C22—82no—
615C22—434no—
616C22—862no—
617C22—864no—
618C22—862no—
619C22—864no—
620C22—862no—
621C22—862no—
622C22—862no—
623C22—17216no—
624C22—1722no—
625C22—1722no—
626C22C2×C22⋊C4×D4311yescharacteristic
627C22#1458345912yes—
628C22AGL(1,ℤ/8)×D4311yescharacteristic
629C22#137×D4311yescharacteristic
630C22#1458369612yes—
631C4—22no—
632C4—42no—
633C4—82no—
634C4—862no—
635C4—862no—
636C4—3442no—
637C4—1722no—
638C4—1722no—
639C4#1458337211yescharacteristic
640C4#1458337211yescharacteristic
641C4#1458345912yes—
642C2—42no—
643C2—82no—
644C2—864no—
645C2—1722no—
646C2#1913717111yescharacteristic
647C2#417×D4311yescharacteristic
648C2#1914311011yescharacteristic
649C2#1914540712yes—
650C2#1914542312yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583406C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#21769
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582861C2semidirect
3. #380×D43C2semidirect
4. #19135030C2semidirect
5. #19135025C2semidirect
6. #19134909C2semidirect
7. #19134899C2semidirect
8. #19134691C2semidirect
9. #19134687C2semidirect
10. #19134535C2semidirect
11. C43×#1788C2semidirect
15. #14583406C4semidirect
27. C2×#13063249C22semidirect
28. C2×#13063246C22semidirect
37. #14582662C22semidirect
38. #14582662C22semidirect
39. #14582661C22semidirect
40. #14582661C22semidirect
42. C2×#103×C43C22semidirect
43. C2×#102×C43C22semidirect
67. #13063301C2×C4semidirect
71. #13063296C2×C4semidirect
76. #13063284C2×C4semidirect
103. C2×#41×C43C2×C4semidirect
327. #1788D43semidirect
354. C2×#103C2×D43semidirect
356. C2×#102C2×D43semidirect
371. C43#21769semidirect
376. C2×#41C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834062
C2×#145828612
#380×D432
#191350302
#191350252
#191349092
#191348992
#191346912
#191346872
#191345352
C43×#17882
#2176943