Finite Group Databasebeta

← #25169744

Subgroups — #25169744

Order 11008.

840 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139201C211yesmaximal, characteristic, complemented
2#19137660C211yesmaximal, characteristic
3#19136118C211yesmaximal, characteristic, complemented
4#19135908C211yesmaximal, characteristic, complemented
5#19135826C211yesmaximal, characteristic
6#19135451C211yesmaximal, characteristic, complemented
7#19135233C211yesmaximal, characteristic, complemented
8#19135218C211yesmaximal, characteristic, complemented
9#19135174C211yesmaximal, characteristic, complemented
10#19135151C211yesmaximal, characteristic, complemented
11#19134931C211yesmaximal, characteristic, complemented
12#19134931C211yesmaximal, characteristic, complemented
13#19134603C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2014C211yesmaximal, characteristic
16C2×D4×Dic43—21no—
17C2×D4×Dic43C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29C43⋊#401—21no—
30#14582839—21no—
31#14582806C2211yescharacteristic
32#14582806C2211yescharacteristic
33#14582802—21no—
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582786—21no—
38#14582779—21no—
39#14582779—21no—
40#14582766—21no—
41#14582764C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×#127×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C23×Dic43—21no—
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63D4×Dic43—22no—
64D4×Dic43—22no—
65D4×Dic43—41no—
66D4×Dic43—41no—
67D4×Dic43—44no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D411yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43C2311yescharacteristic
84C2×C4×Dic43C2311yescharacteristic
85#13063258—41no—
86#13063257—22no—
87Dic43⋊C8—41no—
88#13063249—22no—
89#13063249—41no—
90#13063246—22no—
91#13063246—22no—
92#13063246—41no—
93#13063246—41no—
94C8×Dic43—41no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95D411yescharacteristic
105C43⋊#95D411yescharacteristic
106C22×Q8×C43C2311yescharacteristic
107C22×D4×C43—21no—
108C22×D4×C43—21no—
109C22×D4×C43C2311yescharacteristic
110C22×D4×C43C2311yescharacteristic
111C2×SD16×C43—22no—
112C2×SD16×C43—22no—
113C2×SD16×C43—22no—
114C2×SD16×C43—41no—
115C2×SD16×C43—41no—
116C2×SD16×C43—41no—
117C22×C8×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119#127×C43—22no—
120#127×C43—22no—
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#102×C43—22no—
124#102×C43—41no—
125#95×C43—21no—
126#95×C43—21no—
127C24×C43—21no—
128C24×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×D4×C43—24no—
136C2×D4×C43—24no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—42no—
148C2×D4×C43—42no—
149C2×D4×C43—81no—
150C2×D4×C43—81no—
151C2×D4×C43#4112yes—
152C2×D4×C43#4112yes—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2411yescharacteristic
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—42no—
163C22×Dic43—42no—
164C22×Dic43—42no—
165C22×Dic43—42no—
166C22×Dic43—81no—
167C22×Dic43—81no—
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172SD16×C43—44no—
173SD16×C43—44no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43#4112yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C22⋊Dic43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187C22⋊Dic43—42no—
188C22⋊Dic43—81no—
189C22⋊Dic43—81no—
190C4⋊Dic43—22no—
191C4⋊Dic43—21no—
192C4⋊Dic43—22no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43#4112yes—
200Dic43⋊C4—42no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—21no—
204C4×Dic43—21no—
205C4×Dic43—42no—
206C4×Dic43—42no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C23×C43—22no—
214C23×C43—22no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43C22×D411yescharacteristic
228Q8×C43—41no—
229Q8×C43—41no—
230Q8×C43—41no—
231Q8×C43—41no—
232D4×C43—22no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—22no—
236D4×C43—48no—
237D4×C43—41no—
238D4×C43—41no—
239D4×C43—41no—
240D4×C43—41no—
241D4×C43—84no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43#13512yes—
254C2×C4×C43C2×#4111yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—22no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—84no—
284C2×Dic43—84no—
285C2×Dic43AGL(1,ℤ/8)12yes—
286C8×C43—22no—
287C8×C43—41no—
288C43⋊C8—41no—
289C43⋊C8—41no—
290#27063—431nomaximal, Sylow
291C22×C43—42no—
292C22×C43—42no—
293C22×C43—42no—
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43—81no—
302C22×C43—81no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43#52511yescharacteristic
306C22×C43#54611yescharacteristic
307C22×C43#55011yescharacteristic
308C22×C43C2×#13511yescharacteristic
309C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
310C22×C43#57711yescharacteristic
311C22×C43#57711yescharacteristic
312C4×C43—22no—
313C4×C43—41no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43#52911yescharacteristic
317C4×C43#53811yescharacteristic
318C4×C43#55111yescharacteristic
319C4×C43#55311yescharacteristic
320Dic43—22no—
321Dic43—41no—
322Dic43—41no—
323Dic43—41no—
324Dic43—42no—
325Dic43—81no—
326Dic43—81no—
327Dic43—81no—
328#2514—431no—
329#2366—431no—
330#2092—431no—
331#2055—431no—
332#2041—431no—
333#2014D4311yescharacteristic
334#1968—431no—
335#1928—431no—
336#1925—431no—
337#1919—431no—
338#1916—431no—
339#1877—431no—
340#1877—431no—
341#1804—431no—
342C4×#102—431no—
343C2×C43—82no—
344C2×C43—82no—
345C2×C43#246711yescharacteristic
346C2×C43#310511yescharacteristic
347C2×C43#312311yescharacteristic
348C2×C43#330411yescharacteristic
349C2×C43#331011yescharacteristic
350C2×C43#339411yescharacteristic
351C2×C43#339711yescharacteristic
352C22×SD16C2×D4311yescharacteristic
353C22×SD16C2×D4311yescharacteristic
354C2×#127C2×D4311yescharacteristic
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4—861no—
358C2×#107—431no—
359C2×#106—431no—
360C2×C4⋊C8—431no—
361C2×#103—431no—
362C2×#103—431no—
363C2×#102—431no—
364C2×#102—431no—
365C2×#102—431no—
366C2×#102—431no—
367C2×#102C2×D4311yescharacteristic
368C2×#102C2×D4311yescharacteristic
369C2×C4×C8—431no—
370#401—861no—
371#400—861no—
372#391—431no—
373#391—431no—
374#391C2×D4311yescharacteristic
375#390—431no—
376#390—431no—
377#390—861no—
378#389—431no—
379#387—861no—
380#386—861no—
381#386—861no—
382#383—861no—
383#382—431no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—431no—
386C4×C4⋊C4—431no—
387#340—431no—
388#340—431no—
389#340—431no—
390#340—431no—
391#336—431no—
392#336—431no—
393#336—431no—
394#336C2×D4311yescharacteristic
395C43#2706311yescharacteristic, complemented, Sylow
396C22×Q8C22×D4311yescharacteristic
397C22×D4—21no—
398C22×D4—21no—
399C22×D4C22×D4311yescharacteristic
400C22×D4C22×D4311yescharacteristic
401C23×C4—861no—
402C23×C4—861no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16—41no—
407C2×SD16—41no—
408C2×SD16—41no—
409C22×C8—431no—
410C22×C8—431no—
411C22×C8C22×D4311yescharacteristic
412C22×C8C22×D4311yescharacteristic
413#127—22no—
414#127—22no—
415C4×D4—862no—
416C4×D4—862no—
417C4×D4—1721no—
418C4×D4—1721no—
419C4×D4—1724no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439#107—1721no—
440#106—862no—
441C4⋊C8—1721no—
442#103—862no—
443#103—1721no—
444#102—22no—
445#102—41no—
446#102—862no—
447#102—862no—
448#102—1721no—
449#102—1721no—
450C4×C8—1721no—
451#95—21no—
452#95—21no—
453#95—431no—
454#95—431no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464C24—21no—
465C24—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×D4—24no—
473C2×D4—24no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4#1062190012yes—
489C2×D4#1062190012yes—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—3441no—
501C22×C4—3441no—
502C22×C4—1722no—
503C22×C4—1722no—
504C22×C4—1722no—
505C22×C4—1722no—
506C22×C4D4×D4311yescharacteristic
507C22×C4D4×D4311yescharacteristic
508C22×C4C23×D4311yescharacteristic
509SD16—44no—
510SD16—44no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—861no—
520C2×C8—861no—
521C2×C8—861no—
522C2×C8#1062190012yes—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—432no—
526C4⋊C4—862no—
527C4⋊C4—862no—
528C4⋊C4—861no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—1722no—
536C22⋊C4—3441no—
537C22⋊C4—3441no—
538C22⋊C4—1722no—
539C22⋊C4—1722no—
540C22⋊C4—1722no—
541C22⋊C4—1722no—
542C42—21no—
543C42—21no—
544C42—861no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42—1722no—
549C42—1722no—
550C23—22no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23C2×D4×D4311yescharacteristic
565Q8—41no—
566Q8—41no—
567Q8—41no—
568Q8—41no—
569D4—22no—
570D4—22no—
571D4—22no—
572D4—22no—
573D4—48no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—84no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—432no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—861no—
602C2×C4—862no—
603C2×C4—3444no—
604C2×C4—3444no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4#1306334612yes—
617C2×C4#41×D4311yescharacteristic
618C2×C4C2×#1062190011yescharacteristic
619C2×C4C2×#1062190011yescharacteristic
620C2×C4C2×#1062190011yescharacteristic
621C2×C4#1306337011yescharacteristic
622C2×C4#1306337011yescharacteristic
623C8—22no—
624C8—41no—
625C8—1721no—
626C8—1721no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22#1458340511yescharacteristic
642C22#1458354611yescharacteristic
643C22#1458356911yescharacteristic
644C22C2×#1306334611yescharacteristic
645C22AGL(1,ℤ/8)×D4311yescharacteristic
646C22#1458370511yescharacteristic
647C22#1458370911yescharacteristic
648C4—22no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—862no—
653C4—3441no—
654C4—3441no—
655C4—3441no—
656C4—1721no—
657C4—1721no—
658C4—1721no—
659C4—1722no—
660C4#1458343011yescharacteristic
661C4#1458348411yescharacteristic
662C4#1458358011yescharacteristic
663C4#1458359211yescharacteristic
664C2—82no—
665C2—82no—
666C2#1913864111yescharacteristic
667C2#1914464311yescharacteristic
668C2#1914484111yescharacteristic
669C2#1914653711yescharacteristic
670C2#1914662311yescharacteristic
671C2#1914759611yescharacteristic
672C2#1914761211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2014C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
hypercenter#2014D43
hypocenterC43#27063
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2014

Complements

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

NH ≅ G/Ntype
1. #19139201C2semidirect
3. #19136118C2semidirect
4. #19135908C2semidirect
6. #19135451C2semidirect
7. #19135233C2semidirect
8. #19135218C2semidirect
9. #19135174C2semidirect
10. #19135151C2semidirect
11. #19134931C2semidirect
12. #19134931C2semidirect
13. #19134603C2semidirect
14. #102×Dic43C2semidirect
395. C43#27063semidirect

Maximal subgroups

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

subgroupindex
#191392012
#191376602
#191361182
#191359082
#191358262
#191354512
#191352332
#191352182
#191351742
#191351512
#191349312
#191346032
#102×Dic432
C43×#20142
#2706343