Finite Group Databasebeta

← #35463150

Subgroups — #35463150

Order 21248.

838 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128109C211yesmaximal, characteristic, complemented
2#24911181C211yesmaximal, characteristic
3#24911159C211yesmaximal, characteristic
4#24908947C211yesmaximal, characteristic, complemented
5#24908937C211yesmaximal, characteristic, complemented
6#24908799C211yesmaximal, characteristic, complemented
7#24908789C211yesmaximal, characteristic, complemented
8#24908204C211yesmaximal, characteristic, complemented
9#24908202C211yesmaximal, characteristic, complemented
10#24907656C211yesmaximal, characteristic
11#24907651C211yesmaximal, characteristic
12#24907630C211yesmaximal, characteristic, complemented
13#24907488C211yesmaximal, characteristic
14#24907239C211yesmaximal, characteristic
15C22×#107×C83C211yesmaximal, characteristic
16C2×#14581791C2211yescharacteristic
17C2×#14581783C2211yescharacteristic
18C2×#14581771—21no—
19#19128109—24no—
20C2×#14581725C2211yescharacteristic
21C2×#14581725C2211yescharacteristic
22C2×#14581724C2211yescharacteristic
23C2×#14581724C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×#14581723C2211yescharacteristic
26C2×C22⋊(C83⋊C8)C2211yescharacteristic
27C2×#14581702C2211yescharacteristic
28C2×#14581702C2211yescharacteristic
29#19127640—21no—
30#19127634—21no—
31#19127634—21no—
32#19127621—21no—
33#19127600C2211yescharacteristic
34#19127600C2211yescharacteristic
35#19127597C2211yescharacteristic
36#19127597C2211yescharacteristic
37#19127574—21no—
38#19127574—21no—
39#19127570C2211yescharacteristic
40#19127566C2211yescharacteristic
41#19127561—21no—
42#19127561C2211yescharacteristic
43#19127561C2211yescharacteristic
44C4×C22⋊Dic83C2211yescharacteristic
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53C23×C8×C83C2211yescharacteristic
54C22×C4⋊C4×C83C2211yescharacteristic
55C22×C4⋊C4×C83C2211yescharacteristic
56C2×#107×C83—24no—
57C2×#107×C83C2211yescharacteristic
58C2×#107×C83C2211yescharacteristic
59C2×#107×C83C2211yescharacteristic
60C2×#107×C83C2211yescharacteristic
61C22×Dic166—21no—
62C22×C83⋊C8C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64#14581791—22no—
65#14581791—41no—
66#14581783—22no—
67#14581783—41no—
68#14581771—44no—
69C2×C4⋊Dic83—21no—
70C2×C4⋊Dic83—21no—
71C2×C4⋊Dic83—21no—
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×Dic83⋊C4—21no—
77C2×Dic83⋊C4—21no—
78C2×Dic83⋊C4—21no—
79C2×Dic83⋊C4—21no—
80C2×Dic83⋊C4—21no—
81C2×Dic83⋊C4—21no—
82C2×C22⋊Dic83—21no—
83C2×C22⋊Dic83—21no—
84C2×C22⋊Dic83D411yescharacteristic
85C2×C22⋊Dic83D411yescharacteristic
86C2×C4×Dic83C2311yescharacteristic
87C2×C4×Dic83C2311yescharacteristic
88#14581725—22no—
89#14581725—41no—
90#14581724—22no—
91#14581724—22no—
92#14581723—22no—
93#14581723—41no—
94C22⋊(C83⋊C8)Q814yescomplemented
95#14581702—22no—
96#14581702—22no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C83⋊#95—21no—
103C83⋊#95—21no—
104C83⋊#95—21no—
105C83⋊#95D411yescharacteristic
106C83⋊#95D411yescharacteristic
107C23×C4×C83—21no—
108C23×C4×C83—21no—
109C23×C4×C83C2311yescharacteristic
110C22×C8×C83—22no—
111C22×C8×C83—22no—
112C22×C8×C83Q814yescomplemented
113C22×C8×C83C2311yescharacteristic
114C22×C8×C83C2311yescharacteristic
115C2×C4⋊C4×C83—22no—
116C2×C4⋊C4×C83—22no—
117C2×C4⋊C4×C83—21no—
118C2×C4⋊C4×C83—21no—
119C2×C4⋊C4×C83—41no—
120C2×C4⋊C4×C83—41no—
121C2×C4⋊C4×C83C2311yescharacteristic
122C2×C4⋊C4×C83C2311yescharacteristic
123C2×C4⋊C4×C83C2311yescharacteristic
124C2×C4⋊C4×C83C2311yescharacteristic
125#107×C83—22no—
126#107×C83—22no—
127#107×C83—22no—
128#107×C83D414yes—
129C2×Dic166—42no—
130C2×Dic166—42no—
131C2×Dic166—81no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83C2×D411yescharacteristic
137C22×Dic83C2×D411yescharacteristic
138C22×Dic83C2×D411yescharacteristic
139C22×Dic83C2×D411yescharacteristic
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8—21no—
143C2×C83⋊C8—21no—
144C2×C83⋊C8C2×Q812yes—
145C2×C83⋊C8C2×Q812yes—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152C4⋊Dic83—21no—
153C4⋊Dic83—21no—
154C4⋊Dic83—42no—
155C4⋊Dic83—42no—
156C4⋊Dic83—81no—
157Dic83⋊C4—42no—
158Dic83⋊C4—42no—
159Dic83⋊C4—42no—
160Dic83⋊C4—42no—
161Dic83⋊C4—81no—
162Dic83⋊C4—81no—
163C22⋊Dic83—22no—
164C22⋊Dic83—22no—
165C22⋊Dic83—42no—
166C22⋊Dic83—42no—
167C4×Dic83—21no—
168C4×Dic83—21no—
169C4×Dic83—21no—
170C4×Dic83—21no—
171C24×C83C2×D411yescharacteristic
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—42no—
181C22×C4×C83—42no—
182C22×C4×C83—42no—
183C22×C4×C83—42no—
184C22×C4×C83—81no—
185C22×C4×C83—81no—
186C22×C4×C83C2×D411yescharacteristic
187C22×C4×C83C2×Q812yes—
188C22×C4×C83C2×Q812yes—
189C22×C4×C83C2411yescharacteristic
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C2×C8×C83—28no—
193C2×C8×C83C2×D412yes—
194C2×C8×C83C2×Q812yes—
195C2×C8×C83C2×Q812yes—
196C2×C8×C83#4112yes—
197C4⋊C4×C83—21no—
198C4⋊C4×C83—21no—
199C4⋊C4×C83—21no—
200C4⋊C4×C83—21no—
201C4⋊C4×C83—21no—
202C4⋊C4×C83—21no—
203C4⋊C4×C83—42no—
204C4⋊C4×C83—42no—
205C4⋊C4×C83C2×D412yes—
206C4⋊C4×C83C2×D412yes—
207C23×C83—21no—
208C23×C83—21no—
209C23×C83—21no—
210C23×C83—21no—
211C23×C83C4⋊Q812yes—
212C23×C83AGL(1,ℤ/8)12yes—
213C23×C83#13712yes—
214C23×C83C22×D411yescharacteristic
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—22no—
221C2×C4×C83—22no—
222C2×C4×C83—22no—
223C2×C4×C83—41no—
224C2×C4×C83—41no—
225C2×C4×C83—41no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—84no—
234C2×C4×C83—84no—
235C2×C4×C83C4⋊Q812yes—
236C2×C4×C83C22×D411yescharacteristic
237C2×C4×C83C22×Q811yescharacteristic
238C2×C4×C83C22×Q811yescharacteristic
239C2×C4×C83C2×#4111yescharacteristic
240C2×C4×C83H(5,𝔽2)11yescharacteristic
241C2×C4×C832−1+411yescharacteristic
242C2×Dic83—21no—
243C2×Dic83—21no—
244C2×Dic83—21no—
245C2×Dic83—21no—
246C2×Dic83—21no—
247C2×Dic83—21no—
248C2×Dic83—21no—
249C2×Dic83—21no—
250C2×Dic83—21no—
251C2×Dic83—21no—
252C2×Dic83—21no—
253C2×Dic83—21no—
254C2×Dic83—41no—
255C2×Dic83—41no—
256C2×Dic83—41no—
257C2×Dic83—41no—
258C2×Dic83—41no—
259C2×Dic83—41no—
260C2×Dic83—41no—
261C2×Dic83—41no—
262C2×Dic83—41no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265C2×Dic83—41no—
266Dic166—84no—
267C8×C83—22no—
268C8×C83C22⋊Q814yescomplemented
269C83⋊C8—22no—
270C83⋊C8—22no—
271C22×C83—22no—
272C22×C83—22no—
273C22×C83—22no—
274C22×C83—22no—
275C22×C83—22no—
276C22×C83—22no—
277C22×C83#50114yescomplemented
278C22×C83C2×C4⋊Q811yescharacteristic
279C22×C83D4211yescharacteristic
280C22×C83#54711yescharacteristic
281C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C83C2×#13711yescharacteristic
283C22×C83#57611yescharacteristic
284C22×C83#57811yescharacteristic
285C4×C83—22no—
286C4×C83—42no—
287C4×C83—42no—
288C4×C83—81no—
289C4×C83—81no—
290C4×C83C2×C22⋊Q811yescharacteristic
291C4×C83#54411yescharacteristic
292C4×C83D4×Q811yescharacteristic
293C4×C83#55411yescharacteristic
294Dic83—41no—
295Dic83—41no—
296Dic83—41no—
297Dic83—41no—
298Dic83—81no—
299Dic83—81no—
300Dic83—81no—
301Dic83—81no—
302#26071—831nomaximal, Sylow
303C2×C83—24no—
304C2×C83#244011yescharacteristic
305C2×C83C2×#50111yescharacteristic
306C2×C83#316411yescharacteristic
307C2×C83#326411yescharacteristic
308C2×C83#327011yescharacteristic
309C2×C83#334311yescharacteristic
310C2×C83#334611yescharacteristic
311C2×#501—831no—
312C22×#107D8311yescharacteristic
313#2442—831no—
314#2440—831no—
315#2085—831no—
316#2083—831no—
317#2059—831no—
318#2057—831no—
319#1944—831no—
320#1943—831no—
321#1853—831no—
322#1852—831no—
323#1847—831no—
324#1807—831no—
325#1752—831no—
326C83#2607111yescharacteristic, complemented, Sylow
327C23×C8C2×D8311yescharacteristic
328C2×C4⋊Q8—831no—
329C2×#125—831no—
330C2×C22⋊Q8—1661no—
331C22×C4⋊C4C2×D8311yescharacteristic
332C22×C4⋊C4C2×D8311yescharacteristic
333#501—1664no—
334C2×#107—24no—
335C2×#107—831no—
336C2×#107—831no—
337C2×#107C2×D8311yescharacteristic
338C2×#107C2×D8311yescharacteristic
339C2×#107C2×D8311yescharacteristic
340C2×#107C2×D8311yescharacteristic
341C2×#106—831no—
342C2×#106—831no—
343C2×#106—831no—
344C2×#106—831no—
345C2×C22⋊C8—831no—
346C2×#97—831no—
347C2×#97—831no—
348#400—1661no—
349#398—1661no—
350#398—1661no—
351#395—1661no—
352#389—831no—
353#389—831no—
354#389—831no—
355#389—831no—
356#385—1661no—
357#385—1661no—
358#384—831no—
359#382—831no—
360#380—831no—
361#380—831no—
362#380—1661no—
363C4×C22⋊C4—831no—
364#340—831no—
365#340—831no—
366#340—831no—
367#340—831no—
368#340—831no—
369#340—831no—
370#336—831no—
371#336—831no—
372C22×Q8—1661no—
373C23×C4—21no—
374C23×C4—21no—
375C23×C4C22×D8311yescharacteristic
376C22×C8—22no—
377C22×C8—22no—
378C22×C8—831no—
379C22×C8—831no—
380C22×C8Dic16614yescomplemented
381C22×C8C22×D8311yescharacteristic
382C22×C8C22×D8311yescharacteristic
383C4⋊Q8—3321no—
384C4⋊Q8—1662no—
385#125—3321no—
386#125—1662no—
387C22⋊Q8—3324no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—831no—
395C2×C4⋊C4—831no—
396C2×C4⋊C4—831no—
397C2×C4⋊C4—831no—
398C2×C4⋊C4—1661no—
399C2×C4⋊C4—1661no—
400C2×C4⋊C4—1661no—
401C2×C4⋊C4—1661no—
402C2×C4⋊C4—1661no—
403C2×C4⋊C4—1661no—
404C2×C4⋊C4—1661no—
405C2×C4⋊C4—1661no—
406C2×C4⋊C4—1661no—
407C2×C4⋊C4C22×D8311yescharacteristic
408C2×C4⋊C4C22×D8311yescharacteristic
409C2×C4⋊C4C22×D8311yescharacteristic
410C2×C4⋊C4C22×D8311yescharacteristic
411C2×C22⋊C4—831no—
412C2×C22⋊C4—831no—
413C2×C22⋊C4—1661no—
414C2×C22⋊C4—1661no—
415C2×C42—831no—
416C2×C42—831no—
417#107—22no—
418#107—22no—
419#107—22no—
420#107—3321no—
421#107—1662no—
422#107C22⋊D8314yes—
423#106—3321no—
424#106—1662no—
425#106—1662no—
426#106—1662no—
427C22⋊C8—834no—
428#97—1662no—
429#97—1662no—
430#95—831no—
431#95—831no—
432#95—1661no—
433#95—1661no—
434#95—1661no—
435#95—1661no—
436#95—1661no—
437#95—1661no—
438#95—1661no—
439#95—1661no—
440C24D4×D8311yescharacteristic
441C2×Q8—3322no—
442C2×Q8—3322no—
443C2×Q8—6641no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—81no—
457C22×C4—81no—
458C22×C4—831no—
459C22×C4—831no—
460C22×C4—831no—
461C22×C4—831no—
462C22×C4—1661no—
463C22×C4—1661no—
464C22×C4—1661no—
465C22×C4—1661no—
466C22×C4D4×D8311yescharacteristic
467C22×C4Q8×D8312yes—
468C22×C4C2×Dic16612yes—
469C22×C4C23×D8311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—28no—
473C2×C8—832no—
474C2×C8—832no—
475C2×C8—1661no—
476C2×C8—1661no—
477C2×C8—1661no—
478C2×C8—1661no—
479C2×C8C2×C22⋊D8312yes—
480C2×C8C2×Dic16612yes—
481C2×C8C2×Dic16612yes—
482C2×C8#1305059012yes—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—42no—
490C4⋊C4—42no—
491C4⋊C4—3322no—
492C4⋊C4—3322no—
493C4⋊C4—3322no—
494C4⋊C4—3322no—
495C4⋊C4—3322no—
496C4⋊C4—3322no—
497C4⋊C4—6641no—
498C4⋊C4—6641no—
499C4⋊C4—6641no—
500C4⋊C4—1661no—
501C4⋊C4—1661no—
502C4⋊C4—1661no—
503C4⋊C4—1661no—
504C4⋊C4—1661no—
505C4⋊C4—1661no—
506C4⋊C4—1661no—
507C4⋊C4—1661no—
508C4⋊C4C2×C22⋊D8312yes—
509C4⋊C4C2×C22⋊D8312yes—
510C22⋊C4—3322no—
511C22⋊C4—3322no—
512C22⋊C4—1662no—
513C22⋊C4—1662no—
514C42—1661no—
515C42—1661no—
516C42—1661no—
517C42—1661no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23#1458179112yes—
523C23#1458181612yes—
524C23#1458182412yes—
525C23C2×D4×D8311yescharacteristic
526Q8—6644no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—84no—
547C2×C4—3321no—
548C2×C4—3321no—
549C2×C4—3321no—
550C2×C4—3321no—
551C2×C4—3321no—
552C2×C4—3321no—
553C2×C4—3321no—
554C2×C4—3321no—
555C2×C4—3321no—
556C2×C4—3321no—
557C2×C4—3321no—
558C2×C4—3321no—
559C2×C4—1661no—
560C2×C4—1661no—
561C2×C4—1661no—
562C2×C4—1661no—
563C2×C4—1661no—
564C2×C4—1661no—
565C2×C4—1661no—
566C2×C4—1661no—
567C2×C4—1661no—
568C2×C4—1661no—
569C2×C4—1661no—
570C2×C4—1661no—
571C2×C4#1458179112yes—
572C2×C4C22×C22⋊D8311yescharacteristic
573C2×C4C2×Q8×D8311yescharacteristic
574C2×C4C22×Dic16611yescharacteristic
575C2×C4C2×#1305059011yescharacteristic
576C2×C4#1458183711yescharacteristic
577C2×C4#1458184011yescharacteristic
578C8—22no—
579C8—1662no—
580C8—1662no—
581C8#1458177114yescomplemented
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22#1912810914yescomplemented
589C22C2×#1458179111yescharacteristic
590C22D4×C22⋊D8311yescharacteristic
591C22#1912835211yescharacteristic
592C22C2×#1458181611yescharacteristic
593C22C2×#1458182411yescharacteristic
594C22#1912850211yescharacteristic
595C22#1912851411yescharacteristic
596C4—22no—
597C4—42no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—3321no—
602C4—3321no—
603C4—3321no—
604C4—3321no—
605C4—6641no—
606C4—6641no—
607C4—6641no—
608C4—6641no—
609C4C2×#1458177111yescharacteristic
610C4#1912833211yescharacteristic
611C4Q8×C22⋊D8311yescharacteristic
612C4#1912840611yescharacteristic
613C2—24no—
614C2#2491115911yescharacteristic
615C2C2×#1912810911yescharacteristic
616C2#2491799911yescharacteristic
617C2#2491894311yescharacteristic
618C2#2491903311yescharacteristic
619C2#2491989911yescharacteristic
620C2#2491994411yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC22×#107×C83C2
socleC23×C83C22×D4
prime radicalC24×C83C2×D4
hypercenterC22×#107D83
hypocenterC83#26071
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
1. C2×#19128109C2semidirect
4. #24908947C2semidirect
5. #24908937C2semidirect
6. #24908799C2semidirect
7. #24908789C2semidirect
8. #24908204C2semidirect
9. #24908202C2semidirect
12. #24907630C2semidirect
94. C22⋊(C83⋊C8)Q8semidirect
112. C22×C8×C83Q8semidirect
268. C8×C83C22⋊Q8semidirect
277. C22×C83#501semidirect
326. C83#26071semidirect
380. C22×C8Dic166semidirect
581. C8#14581771semidirect
588. C22#19128109semidirect

Maximal subgroups

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

subgroupindex
C2×#191281092
#249111812
#249111592
#249089472
#249089372
#249087992
#249087892
#249082042
#249082022
#249076562
#249076512
#249076302
#249074882
#249072392
C22×#107×C832
#2607183