Finite Group Databasebeta

← #25115994

Subgroups — #25115994

Order 11008.

894 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×#14583000C211yesmaximal, characteristic
2#19137559C211yesmaximal, characteristic, complemented
3D4×Dic43⋊C4C211yesmaximal, characteristic
4#19135282C211yesmaximal, characteristic, complemented
5#19135274C211yesmaximal, characteristic, complemented
6#19135186C211yesmaximal, characteristic, complemented
7#19135167C211yesmaximal, characteristic, complemented
8#19134931C211yesmaximal, characteristic
9#19134727C211yesmaximal, characteristic, complemented
10#19134603C211yesmaximal, characteristic
11#19134598C211yesmaximal, characteristic, complemented
12#19134466C211yesmaximal, characteristic, complemented
13#19134422C211yesmaximal, characteristic
14C4×#13063246C211yesmaximal, characteristic
15C43×#1877C211yesmaximal, characteristic
16C2×Q8×Dic43C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C22×Dic43⋊C4—21no—
20#14583000C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063235C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582806C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582795C2211yescharacteristic
33#14582784—21no—
34#14582782—21no—
35#14582772—21no—
36#14582771—21no—
37#14582768C2211yescharacteristic
38#14582766—21no—
39#14582764C2211yescharacteristic
40#14582757—21no—
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582744—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C23×Dic43—21no—
61C23×Dic43—21no—
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64Q8×Dic43—22no—
65Q8×Dic43C2×C414yescomplemented
66D4×Dic43—22no—
67D4×Dic43—22no—
68D4×Dic43—41no—
69D4×Dic43C2×C414yes—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—44no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063259C2×C414yescomplemented
90Dic43⋊C8—22no—
91#13063249—41no—
92#13063249C2×C414yescomplemented
93#13063246—22no—
94#13063246C2×C414yes—
95#13063235—41no—
96#13063235C2×C414yescomplemented
97C4×C43⋊C8—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43C2×C414yes—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4×D4×C43—22no—
117C4×D4×C43—41no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#103×C43—41no—
123#102×C43—22no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43C22×C412yes—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43C22×C412yes—
137C2×D4×C43#4112yes—
138C2×D4×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—24no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—81no—
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162SD16×C43—28no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C22×C412yes—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C22⋊C4×C43—42no—
174C42×C43—21no—
175C42×C43—21no—
176C22⋊Dic43—24no—
177C22⋊Dic43—42no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—24no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C22×C412yes—
186C4⋊Dic43C22×C412yes—
187Dic43⋊C4—22no—
188Dic43⋊C4—41no—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—24no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C4×Dic43C22×C412yes—
199C4×Dic43#4112yes—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C22×C412yes—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—22no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43C22×D411yescharacteristic
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—41no—
217Q8×C43—41no—
218D4×C43—22no—
219D4×C43—22no—
220D4×C43—22no—
221D4×C43#11714yes—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—84no—
237C2×C4×C43AGL(1,ℤ/8)12yes—
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C432−1+411yescharacteristic
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—48no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—84no—
268C2×Dic43C4×D412yes—
269C2×Dic43C4×D412yes—
270C8×C43—22no—
271C8×C43—41no—
272C43⋊C8—22no—
273C43⋊C8—41no—
274#22778—431nomaximal, Sylow
275C22×C43—24no—
276C22×C43—42no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—42no—
282C22×C43C2×C4×D411yescharacteristic
283C22×C43#54611yescharacteristic
284C22×C43#54811yescharacteristic
285C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C43#57511yescharacteristic
287C22×C43#57711yescharacteristic
288C22×C43#57811yescharacteristic
289C4×C43—22no—
290C4×C43—42no—
291C4×C43—41no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43C2×#11711yescharacteristic
295C4×C43#52011yescharacteristic
296C4×C43#55211yescharacteristic
297C4×C43#55311yescharacteristic
298Dic43—22no—
299Dic43—22no—
300Dic43—42no—
301Dic43—42no—
302Dic43—41no—
303Dic43—41no—
304Dic43—81no—
305Dic43—81no—
306C2×#440—431no—
307#2356—431no—
308D4×C4⋊C4—431no—
309#1935—431no—
310#1933—431no—
311#1921—431no—
312#1918—431no—
313#1877—431no—
314#1877D4311yescharacteristic
315#1836—431no—
316#1804—431no—
317#1803—431no—
318#1771—431no—
319#1762—431no—
320C4×#102—431no—
321C2×C43—44no—
322C2×C43#235211yescharacteristic
323C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
324C2×C43#294711yescharacteristic
325C2×C43#331011yescharacteristic
326C2×C43#331511yescharacteristic
327C2×C43#336711yescharacteristic
328C2×C43#337611yescharacteristic
329C22×SD16C2×D4311yescharacteristic
330C2×C4×Q8—431no—
331C2×C4×D4—431no—
332C2×C4×D4—431no—
333C2×C4×D4C2×D4311yescharacteristic
334C22×C4⋊C4—861no—
335#440—438no—
336C2×#107—431no—
337C2×C4⋊C8—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103C2×D4311yescharacteristic
341C2×#102—431no—
342C2×#102—431no—
343C2×#102C2×D4311yescharacteristic
344C2×#97—431no—
345C2×#97—431no—
346C2×C4×C8—431no—
347#391—431no—
348#391C2×D4311yescharacteristic
349#389—431no—
350#389—431no—
351#387—861no—
352#387—861no—
353#385—861no—
354#385—861no—
355#384—431no—
356#383—861no—
357#382—431no—
358#380—861no—
359C4×C4⋊C4—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—431no—
362#376—861no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#336—431no—
372#336C2×D4311yescharacteristic
373C43#2277811yescharacteristic, complemented, Sylow
374C22×Q8C22×D4311yescharacteristic
375C22×D4C22×D4311yescharacteristic
376C23×C4—21no—
377C23×C4—861no—
378C23×C4—861no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16C4×D4314yes—
382C22×C8—431no—
383C22×C8—431no—
384C22×C8C22×D4311yescharacteristic
385C22×C8C22×D4311yescharacteristic
386C4×Q8—434no—
387C4×Q8—862no—
388C4×D4—22no—
389C4×D4—41no—
390C4×D4—434no—
391C4×D4—862no—
392C4×D4—862no—
393C4×D4—1721no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—1724no—
406C2×C4⋊C4C22×D4311yescharacteristic
407C2×C4⋊C4C22×D4311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—431no—
412C2×C42—431no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42C22×D4311yescharacteristic
417#107—434no—
418C4⋊C8—862no—
419#103—41no—
420#103—434no—
421#103—1721no—
422#102—22no—
423#102—434no—
424#102—862no—
425#97—434no—
426#97—1721no—
427C4×C8—1721no—
428#95—21no—
429#95—21no—
430#95—431no—
431#95—431no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C2×C4×D4312yes—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×C4×D4312yes—
451C2×D4#1062190012yes—
452C2×D4#1062190012yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—81no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—431no—
463C22×C4—864no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—3441no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4C23×D4311yescharacteristic
476SD16—28no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—432no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8C2×C4×D4312yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—432no—
494C4⋊C4—432no—
495C4⋊C4—864no—
496C4⋊C4—862no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—3441no—
504C4⋊C4—1721no—
505C4⋊C4—1722no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C22⋊C4—42no—
509C22⋊C4—864no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—432no—
514C42—432no—
515C42—864no—
516C42—861no—
517C42—861no—
518C42—1722no—
519C42—1722no—
520C23—22no—
521C23—22no—
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23C2×D4×D4311yescharacteristic
528Q8—22no—
529Q8—22no—
530Q8—41no—
531Q8—41no—
532D4—22no—
533D4—22no—
534D4—22no—
535D4#1306328114yes—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—84no—
551C2×C4—432no—
552C2×C4—432no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—3444no—
566C2×C4—1728no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4#1306335212yes—
578C2×C4C22×C4×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4C2×#1062190011yescharacteristic
581C2×C4C2×#1062190011yescharacteristic
582C2×C4#1306337011yescharacteristic
583C2×C4#1306337211yescharacteristic
584C8—22no—
585C8—41no—
586C8—862no—
587C8—1721no—
588C22—24no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22C4×D4×D4311yescharacteristic
596C22#1458353611yescharacteristic
597C22#1458355511yescharacteristic
598C22C2×#1306335211yescharacteristic
599C22#1458369611yescharacteristic
600C22#1458370911yescharacteristic
601C22#1458371511yescharacteristic
602C4—22no—
603C4—41no—
604C4—42no—
605C4—81no—
606C4—81no—
607C4—862no—
608C4—862no—
609C4—3441no—
610C4—3441no—
611C4—1721no—
612C4—1721no—
613C4—1722no—
614C4—1722no—
615C4C2×#1306328111yescharacteristic
616C4#1458337811yescharacteristic
617C4#1458358611yescharacteristic
618C4#1458359211yescharacteristic
619C2—44no—
620C2#1913752211yescharacteristic
621C2C4×#1306335211yescharacteristic
622C2#1914343511yescharacteristic
623C2#1914662011yescharacteristic
624C2#1914669511yescharacteristic
625C2#1914731711yescharacteristic
626C2#1914742611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1877C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1877D43
hypocenterC43#22778
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
2. #19137559C2semidirect
4. #19135282C2semidirect
5. #19135274C2semidirect
6. #19135186C2semidirect
7. #19135167C2semidirect
9. #19134727C2semidirect
11. #19134598C2semidirect
12. #19134466C2semidirect
20. #14583000C4semidirect
65. Q8×Dic43C2×C4semidirect
89. #13063259C2×C4semidirect
92. #13063249C2×C4semidirect
96. #13063235C2×C4semidirect
373. C43#22778semidirect

Maximal subgroups

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

subgroupindex
C2×#145830002
#191375592
D4×Dic43⋊C42
#191352822
#191352742
#191351862
#191351672
#191349312
#191347272
#191346032
#191345982
#191344662
#191344222
C4×#130632462
C43×#18772
#2277843