Finite Group Databasebeta

← #25106271

Subgroups — #25106271

Order 11008.

1502 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583446C211yesmaximal, characteristic
2C2×#14582951C211yesmaximal, characteristic, complemented
3#384×D43C211yesmaximal, characteristic, complemented
4#19135554C212yesmaximal, complemented
5#19135399C212yesmaximal, complemented
6#19134911C212yesmaximal, complemented
7#19134909C212yesmaximal, complemented
8#19134596C211yesmaximal, characteristic, complemented
9#19134595C211yesmaximal, characteristic, complemented
10#19134592C211yesmaximal, characteristic, complemented
11C43×#1802C211yesmaximal, characteristic, complemented
12C22×#10621898—21no—
13#14583446—24no—
14#14583446C418yescomplemented
15C2×#13063324C2211yescharacteristic
16C2×#13063321C2211yescharacteristic
17C2×#13063311—21no—
18C2×#13063300C2211yescharacteristic
19C2×#13063298—21no—
20C2×#13063296C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×C22⋊D43—21no—
23C2×C4⋊C4×D43—21no—
24C2×C4⋊C4×D43—21no—
25C2×C4⋊C4×D43C2212yes—
26C2×C42×D43C2211yescharacteristic
27#14582951—24no—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063247C2212yes—
30C2×#13063246C2212yes—
31C2×#13063245C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33C2×C8×Dic43C2212yes—
34#14582769C2211yescharacteristic
35#14582768—21no—
36#14582768—21no—
37#14582768C2212yes—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×D4×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic
43C2×#102×C43C2212yes—
44C43×#384C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621898—28no—
47C2×#10621898—44no—
48C2×#10621898—44no—
49C22×Dic86—21no—
50C22×D172—21no—
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C22×C22⋊D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43—22no—
57C22×C4×D43D411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C22×C43⋊C8C2312yes—
61#13063324—22no—
62#13063324C2×C414yescomplemented
63#13063321—22no—
64#13063321C2×C414yescomplemented
65#13063311—28no—
66#13063300—22no—
67#13063300C2×C414yes—
68#13063298—28no—
69#13063296—22no—
70#13063296C2×C414yes—
71C4×D172—22no—
72C4×D172C2×C414yescomplemented
73C4×C22⋊D43—28no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43—21no—
76C2×C4⋊Dic43C2312yes—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—22no—
82C4⋊C4×D43—42no—
83C4⋊C4×D43—42no—
84C4⋊C4×D43—44no—
85C4⋊C4×D43—44no—
86C2×C22⋊Dic43—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43D411yescharacteristic
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43C2311yescharacteristic
92C42×D43C2×C414yes—
93C42×D43D414yes—
94C4⋊(C43⋊C8)—22no—
95#13063247—42no—
96#13063246—42no—
97#13063245—42no—
98(C2×D43)⋊C8—24no—
99C8×Dic43—24no—
100C22×D4×C43C2311yescharacteristic
101C23×C4×C43—21no—
102C22×C8×C43C2312yes—
103C4×D4×C43—22no—
104C4×D4×C43C2×C414yescomplemented
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43C2312yes—
108C2×C4⋊C4×C43C2311yescharacteristic
109C2×C22⋊C4×C43—21no—
110C2×C42×C43C2311yescharacteristic
111C4⋊C8×C43—22no—
112#102×C43—42no—
113C24×C43—21no—
114C23×D43—21no—
115C23×D43C2×D411yescharacteristic
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43C22×C412yes—
122C22×C4×C43—24no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C2×C22⋊D43—24no—
131C2×C22⋊D43—24no—
132C2×C22⋊D43—24no—
133C2×C22⋊D43—42no—
134C2×C22⋊D43—42no—
135C2×C22⋊D43—42no—
136C2×C22⋊D43—42no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144#10621898—432no—
145C2×D172—21no—
146C2×D172—24no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172—42no—
152C2×D172—42no—
153C2×D172C22×C412yes—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—22no—
159C2×C4×D43—22no—
160C2×C4×D43—24no—
161C2×C4×D43—44no—
162C2×C4×D43—44no—
163C2×C4×D43—42no—
164C2×C4×D43—42no—
165C2×C4×D43—44no—
166C2×C4×D43C22⋊C414yes—
167C2×C4×D43C22⋊C414yes—
168C2×C4×D43D814yes—
169C2×C4×D43SD1614yes—
170C2×C4×D43C22×C412yes—
171C2×C4×D43C2×D412yes—
172C2×Dic86—24no—
173C2×Dic86—42no—
174C2×Dic86—42no—
175C2×C8×C43—22no—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—42no—
182C4⋊C4×C43—42no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—24no—
185C42×C43C22×C412yes—
186C42×C43C2×D412yes—
187C22⋊Dic43—24no—
188(C2×D43)⋊C4—24no—
189(C2×D43)⋊C4—24no—
190C4⋊Dic43—21no—
191C4⋊Dic43—22no—
192C4⋊Dic43—22no—
193C4⋊Dic43—42no—
194C4⋊Dic43—42no—
195C4⋊Dic43C22×C412yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—44no—
198Dic43⋊C4—44no—
199Dic43⋊C4—44no—
200C4×Dic43C22⋊C414yes—
201C4×Dic43C22⋊C414yes—
202C4×Dic43C22×C412yes—
203C4×Dic43C2×D412yes—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—22no—
206C2×C43⋊C8—22no—
207C23×C43—22no—
208C23×C43—41no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43C22×D411yescharacteristic
215C22×D43—21no—
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43C2×C22⋊C412yes—
227C22×D43C2×D812yes—
228C22×D43C2×SD1612yes—
229D4×C43—22no—
230D4×C43—22no—
231D4×C43—41no—
232D4×C43—41no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—22no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—48no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43C2×C22⋊C412yes—
243C2×C4×C43C2×C22⋊C412yes—
244C2×C4×C43C2×D812yes—
245C2×C4×C43C2×SD1612yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C2×C4×C43H(5,𝔽2)11yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C2×C4×C432−1+411yescharacteristic
252C22⋊D43—48no—
253C22⋊D43—48no—
254C22⋊D43—48no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43C2×C22⋊C412yes—
264C2×Dic43C2×C22⋊C412yes—
265C2×Dic43C2×C22⋊C412yes—
266C2×Dic43C2×D812yes—
267C2×Dic43C2×SD1612yes—
268C2×Dic43AGL(1,ℤ/8)12yes—
269C2×Dic43#13712yes—
270D172—22no—
271D172—22no—
272D172—48no—
273D172—41no—
274D172—41no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—28no—
280C4×D43—48no—
281C4×D43—88no—
282C4×D43#102116yescomplemented
283Dic86—48no—
284C8×C43—42no—
285C43⋊C8—42no—
286#21859—431nomaximal, Sylow
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43C22×C22⋊C411yescharacteristic
295C22×C43#53511yescharacteristic
296C22×C43#53611yescharacteristic
297C22×C43C22×D811yescharacteristic
298C22×C43C22×SD1611yescharacteristic
299C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C43C2×#13711yescharacteristic
301C2×D43—22no—
302C2×D43—22no—
303C2×D43—22no—
304C2×D43—22no—
305C2×D43—22no—
306C2×D43—22no—
307C2×D43—42no—
308C2×D43—42no—
309C2×D43—42no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43C2×#10214yes—
315C4×C43—22no—
316C4×C43—42no—
317C4×C43—82no—
318C4×C43C2×#10214yes—
319C4×C43#52011yescharacteristic
320C4×C43#52011yescharacteristic
321C4×C43#53711yescharacteristic
322C4×C43#53711yescharacteristic
323Dic43—22no—
324Dic43—42no—
325Dic43—82no—
326Dic43C2×#10214yes—
327Dic43#41714yes—
328C2×#532—431no—
329C2×#431—431no—
330C2×#384—431no—
331#1990—432no—
332#1957—432no—
333#1874—432no—
334#1874—432no—
335#1802—431no—
336#1802—431no—
337#1802—431no—
338#1802D4311yescharacteristic, complemented
339C2×C43—82no—
340C2×C43#231111yescharacteristic
341C2×C43C22×#10211yescharacteristic
342C2×C43C2×#41711yescharacteristic
343C2×C43#320511yescharacteristic
344C2×C43#320611yescharacteristic
345C2×C43#322611yescharacteristic
346C2×C43#322711yescharacteristic
347D43—24no—
348D43—82no—
349C22×#41—861no—
350#532—438no—
351#532—864no—
352C2×C4⋊Q8—431no—
353C2×#127—431no—
354C2×#124—861no—
355C2×#121—431no—
356C2×#121—431no—
357C2×#121—861no—
358C2×C4×D4—431no—
359C2×C4×D4—861no—
360C2×C4×D4C2×D4311yescharacteristic
361C22×C4⋊C4—432no—
362C22×C4⋊C4—861no—
363C22×C4⋊C4—861no—
364C22×C42—431no—
365#431—864no—
366C2×C4⋊C8—431no—
367C2×C4⋊C8C2×D4311yescharacteristic
368C2×#102—432no—
369C2×#102—432no—
370C2×#102—432no—
371C2×#102C2×D4312yes—
372C2×C22⋊C8—432no—
373C2×C4×C8—432no—
374#384—432no—
375#384—431no—
376#384—861no—
377#384—861no—
378#384C2×D4311yescharacteristic
379#340—432no—
380#340—432no—
381#340—432no—
382#340C2×D4312yes—
383C43#2185911yescharacteristic, complemented, Sylow
384C2×#41—868no—
385C2×#41—1724no—
386C2×#41—1724no—
387C22×Q8—861no—
388C22×D4—431no—
389C22×D4—861no—
390C22×D4—861no—
391C22×D4—861no—
392C22×D4—861no—
393C22×D4C22×D4311yescharacteristic
394C23×C4—21no—
395C23×C4—431no—
396C23×C4—431no—
397C23×C4—431no—
398C23×C4—862no—
399C23×C4—861no—
400C22×C8—432no—
401C22×C8C22×D4312yes—
402C4⋊Q8—434no—
403C4⋊Q8—862no—
404#127—434no—
405#127—862no—
406#124—868no—
407#121—434no—
408#121—434no—
409#121—868no—
410#121—862no—
411#121—862no—
412C4×D4—22no—
413C4×D4—434no—
414C4×D4—868no—
415C4×D4—862no—
416C4×D4C4×D4314yescomplemented
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—862no—
423C2×C4⋊C4—862no—
424C2×C4⋊C4—862no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4—1722no—
428C2×C4⋊C4—1722no—
429C2×C4⋊C4—1724no—
430C2×C4⋊C4—1724no—
431C2×C4⋊C4C22×D4312yes—
432C2×C4⋊C4C22×D4311yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—861no—
435C2×C22⋊C4—861no—
436C2×C22⋊C4—861no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—434no—
441C2×C42—434no—
442C2×C42C22×D4311yescharacteristic
443C4⋊C8—22no—
444C4⋊C8—862no—
445#102—42no—
446#102—1722no—
447#102—1722no—
448#102—1722no—
449C22⋊C8—864no—
450C4×C8—864no—
451C24—21no—
452C24—431no—
453C24—861no—
454#41—17232no—
455C2×Q8—864no—
456C2×Q8—1722no—
457C2×Q8—1722no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—432no—
464C2×D4—864no—
465C2×D4—864no—
466C2×D4—864no—
467C2×D4—864no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—861no—
472C2×D4—861no—
473C2×D4—1722no—
474C2×D4—1722no—
475C2×D4—1722no—
476C2×D4—1722no—
477C2×D4—1722no—
478C2×D4—1722no—
479C2×D4—1722no—
480C2×D4—1722no—
481C2×D4C2×C4×D4312yes—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—434no—
490C22×C4—434no—
491C22×C4—434no—
492C22×C4—431no—
493C22×C4—434no—
494C22×C4—432no—
495C22×C4—432no—
496C22×C4—862no—
497C22×C4—862no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—861no—
501C22×C4—861no—
502C22×C4—861no—
503C22×C4—864no—
504C22×C4—862no—
505C22×C4—1724no—
506C22×C4—1724no—
507C22×C4—1724no—
508C22×C4—1722no—
509C22×C4—1722no—
510C22×C4D4×D4311yescharacteristic
511C22×C4D4×D4311yescharacteristic
512C22×C4C23×D4311yescharacteristic
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—862no—
517C2×C8—862no—
518C2×C8—862no—
519C4⋊C4—21no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—432no—
525C4⋊C4—864no—
526C4⋊C4—861no—
527C4⋊C4—862no—
528C4⋊C4—862no—
529C4⋊C4—1722no—
530C4⋊C4—1724no—
531C4⋊C4—1724no—
532C4⋊C4—1724no—
533C4⋊C4—1722no—
534C4⋊C4C2×C4×D4312yes—
535C22⋊C4—24no—
536C22⋊C4—864no—
537C22⋊C4—864no—
538C22⋊C4—864no—
539C42—434no—
540C42—434no—
541C42—432no—
542C42—432no—
543C42C2×C4×D4312yes—
544C42D4×D4312yes—
545C23—22no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—432no—
553C23—432no—
554C23—432no—
555C23—861no—
556C23—861no—
557C23—861no—
558C23—861no—
559C23—862no—
560C23—1721no—
561C23—1721no—
562C23—1721no—
563C23—1721no—
564C23—1721no—
565C23—1721no—
566C23C2×D4×D4311yescharacteristic
567Q8—1728no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572D4—862no—
573D4—862no—
574D4—1728no—
575D4—1728no—
576D4—1728no—
577D4—1728no—
578D4—1721no—
579D4—1721no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—48no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—432no—
590C2×C4—432no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—432no—
595C2×C4—4316no—
596C2×C4—432no—
597C2×C4—868no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—3448no—
606C2×C4—1722no—
607C2×C4—1722no—
608C2×C4—1722no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1728no—
612C2×C4C22⋊C4×D4312yes—
613C2×C4C22⋊C4×D4312yes—
614C2×C4D8×D4312yes—
615C2×C4SD16×D4312yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#1306337011yescharacteristic
619C2×C4#1306337111yescharacteristic
620C2×C4#1306337211yescharacteristic
621C2×C4#1306337311yescharacteristic
622C8—42no—
623C8—1722no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—434no—
632C22—862no—
633C22—862no—
634C22—862no—
635C22—862no—
636C22—862no—
637C22—862no—
638C22—3441no—
639C22—3441no—
640C22—3441no—
641C22—3441no—
642C22—1722no—
643C22—1722no—
644C22—1722no—
645C22C2×C22⋊C4×D4311yescharacteristic
646C22#1458346511yescharacteristic
647C22#1458347211yescharacteristic
648C22C2×D8×D4311yescharacteristic
649C22C2×SD16×D4311yescharacteristic
650C22AGL(1,ℤ/8)×D4311yescharacteristic
651C22#137×D4311yescharacteristic
652C4—22no—
653C4—42no—
654C4—82no—
655C4—434no—
656C4—434no—
657C4—862no—
658C4—3442no—
659C4—1722no—
660C4#102×D4314yes—
661C4#1458337911yescharacteristic
662C4#1458338011yescharacteristic
663C4#1458347811yescharacteristic
664C4#1458347911yescharacteristic
665C2—82no—
666C2—864no—
667C2—3442no—
668C2#1913718411yescharacteristic
669C2C2×#102×D4311yescharacteristic
670C2#417×D4311yescharacteristic
671C2#1914551211yescharacteristic
672C2#1914551911yescharacteristic
673C2#1914571511yescharacteristic
674C2#1914572211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC2×#14583446C2
cosocleC22×C4×C43C24
hypercenter#1802D43
hypocenterC43#21859
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. C2×#14582951C2semidirect
3. #384×D43C2semidirect
4. #19135554C2semidirect
5. #19135399C2semidirect
6. #19134911C2semidirect
7. #19134909C2semidirect
8. #19134596C2semidirect
9. #19134595C2semidirect
10. #19134592C2semidirect
11. C43×#1802C2semidirect
14. #14583446C4semidirect
62. #13063324C2×C4semidirect
64. #13063321C2×C4semidirect
72. C4×D172C2×C4semidirect
104. C4×D4×C43C2×C4semidirect
282. C4×D43#102semidirect
338. #1802D43semidirect
383. C43#21859semidirect
416. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834462
C2×#145829512
#384×D432
#191355542
#191353992
#191349112
#191349092
#191345962
#191345952
#191345922
C43×#18022
#2185943