Finite Group Databasebeta

← #35408745

Subgroups — #35408745

Order 21248.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127799C211yesmaximal, characteristic
2#24909927C211yesmaximal, characteristic
3#24908347C211yesmaximal, characteristic
4#24908320C211yesmaximal, characteristic
5#24908198C211yesmaximal, characteristic, complemented
6#24908193C211yesmaximal, characteristic, complemented
7#24908159C211yesmaximal, characteristic
8#24908156C211yesmaximal, characteristic, complemented
9#24908145C211yesmaximal, characteristic
10#24908142C211yesmaximal, characteristic, complemented
11#24907361C211yesmaximal, characteristic, complemented
12#24907293C211yesmaximal, characteristic, complemented
13#24907291C211yesmaximal, characteristic
14C4×#14581703C211yesmaximal, characteristic, complemented
15C83×#2295C211yesmaximal, characteristic, complemented
16C22×#13050577C2211yescharacteristic
17C2×C4×D332C2211yescharacteristic
18C2×#14581749—21no—
19#19127799C418yescomplemented
20C2×#14581725C2211yescharacteristic
21C2×#14581725C2211yescharacteristic
22C2×#14581723C2211yescharacteristic
23C2×#14581716C2211yescharacteristic
24C2×#14581716C2211yescharacteristic
25C2×#14581716C2211yescharacteristic
26C2×#14581712C2211yescharacteristic
27C2×#14581712C2211yescharacteristic
28C2×#14581712C2211yescharacteristic
29C2×#14581703C2211yescharacteristic
30C2×#14581703C2211yescharacteristic
31C2×#14581703C2211yescharacteristic
32C2×#14581703C2211yescharacteristic
33C2×C4×C83⋊C8C2211yescharacteristic
34C2×C4×C83⋊C8C2211yescharacteristic
35#19127603C2211yescharacteristic
36#19127603C2211yescharacteristic
37#19127599C2211yescharacteristic
38#19127599C2211yescharacteristic
39#19127592—21no—
40#19127592—21no—
41C4×C4⋊Dic83C2211yescharacteristic
42C4×(C2×D83)⋊C4—21no—
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49C2×C4×Q8×C83C2211yescharacteristic
50#391×C83C2211yescharacteristic
51#391×C83C2211yescharacteristic
52#389×C83C2211yescharacteristic
53#389×C83C2211yescharacteristic
54#387×C83—21no—
55#387×C83—21no—
56C4×C4⋊C4×C83—21no—
57C4×C4⋊C4×C83C2211yescharacteristic
58#376×C83—21no—
59C43×C83C2211yescharacteristic
60C22×D332C2311yescharacteristic
61C22×C4×D83—21no—
62C2×#13050577—22no—
63C2×#13050577—22no—
64C2×#13050577C2×C414yes—
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67C22×C83⋊C8C2311yescharacteristic
68C22×C83⋊C8C2311yescharacteristic
69C4×D332—22no—
70C4×D332C2×C414yes—
71#14581749—44no—
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×Dic83⋊C4—21no—
76C2×Dic83⋊C4—21no—
77C2×(C2×D83)⋊C4—21no—
78C2×(C2×D83)⋊C4—21no—
79C2×(C2×D83)⋊C4—21no—
80C2×(C2×D83)⋊C4—21no—
81C2×(C2×D83)⋊C4—21no—
82C2×C4×Dic83—21no—
83#14581725—22no—
84#14581725C2×C414yes—
85#14581723—22no—
86#14581716—22no—
87#14581716—22no—
88#14581716C2×C414yes—
89#14581712—22no—
90#14581712—22no—
91#14581712C2×C414yes—
92#14581703—22no—
93#14581703—22no—
94#14581703—22no—
95#14581703C2×C414yes—
96C4×C83⋊C8—22no—
97C4×C83⋊C8—22no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C22×Q8×C83C2311yescharacteristic
102C4×Q8×C83—22no—
103C4×Q8×C83C2×C414yes—
104C2×C4⋊C4×C83—21no—
105C2×C4⋊C4×C83—21no—
106C2×C4⋊C4×C83—21no—
107C2×C4⋊C4×C83C2311yescharacteristic
108C2×C4⋊C4×C83C2311yescharacteristic
109C2×C4⋊C4×C83C2311yescharacteristic
110C2×C42×C83—21no—
111C2×C42×C83—21no—
112C2×C42×C83D411yescharacteristic
113C2×C42×C83D411yescharacteristic
114C2×C42×C83D411yescharacteristic
115C2×C42×C83D411yescharacteristic
116C2×C42×C83C2311yescharacteristic
117C2×C42×C83C2311yescharacteristic
118C2×C42×C83C2311yescharacteristic
119#95×C83—21no—
120#95×C83—21no—
121#95×C83—21no—
122#95×C83—21no—
123#95×C83—21no—
124#95×C83—21no—
125#95×C83—21no—
126C23×D83—21no—
127C2×D332—21no—
128C2×D332—21no—
129C2×D332—21no—
130C2×D332—21no—
131C2×D332—21no—
132C2×D332C22×C412yes—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C2×C4×D83—24no—
137C2×C4×D83—42no—
138C2×C4×D83—42no—
139#13050577—28no—
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8—21no—
143C2×C83⋊C8—21no—
144C2×C83⋊C8—21no—
145C2×C83⋊C8—21no—
146C2×C83⋊C8C22×C412yes—
147C2×C83⋊C8C22×C412yes—
148C2×C83⋊C8#4112yes—
149C2×C83⋊C8#4112yes—
150C2×C83⋊C8#4112yes—
151C2×C83⋊C8#4112yes—
152C4⋊Dic83—21no—
153C4⋊Dic83—21no—
154C4⋊Dic83—21no—
155C4⋊Dic83—21no—
156C4⋊Dic83—21no—
157C4⋊Dic83C22×C412yes—
158Dic83⋊C4—42no—
159Dic83⋊C4—42no—
160(C2×D83)⋊C4—24no—
161(C2×D83)⋊C4—42no—
162(C2×D83)⋊C4—42no—
163(C2×D83)⋊C4—42no—
164(C2×D83)⋊C4—42no—
165C4×Dic83—42no—
166C2×Q8×C83—21no—
167C2×Q8×C83—21no—
168C2×Q8×C83—21no—
169C2×Q8×C83—21no—
170C2×Q8×C83—21no—
171C2×Q8×C83C22×C412yes—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2×D411yescharacteristic
178C22×C4×C83C2×D411yescharacteristic
179C22×C4×C83C2×D411yescharacteristic
180C22×C4×C83C2×D411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83C2411yescharacteristic
183C4⋊C4×C83—24no—
184C4⋊C4×C83—21no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—42no—
190C4⋊C4×C83—42no—
191C4⋊C4×C83C22×C412yes—
192C42×C83—24no—
193C42×C83—22no—
194C42×C83—22no—
195C42×C83—21no—
196C42×C83—21no—
197C42×C83—21no—
198C42×C83—21no—
199C42×C83—41no—
200C42×C83—41no—
201C42×C83—42no—
202C42×C83C22×C412yes—
203C42×C83#4112yes—
204C23×C83C22×D411yescharacteristic
205C22×D83—22no—
206C22×D83—41no—
207C22×D83—41no—
208C22×D83—41no—
209C22×D83—41no—
210C22×D83—41no—
211C22×D83—41no—
212Q8×C83—22no—
213Q8×C83—22no—
214Q8×C83—41no—
215Q8×C83—41no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—22no—
225C2×C4×C83—22no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83C4×D412yes—
243C2×C4×C83C4×D412yes—
244C2×C4×C83AGL(1,ℤ/8)12yes—
245C2×C4×C83#13712yes—
246C2×C4×C83C23×C411yescharacteristic
247C2×C4×C83C2×#4111yescharacteristic
248C2×C4×C83C2×#4111yescharacteristic
249C2×C4×C83C2×#4111yescharacteristic
250C2×C4×C83C2×#4111yescharacteristic
251C2×C4×C83C2×#4111yescharacteristic
252C2×Dic83—22no—
253C2×Dic83—41no—
254C2×Dic83—41no—
255C2×Dic83—41no—
256C2×Dic83—41no—
257C2×Dic83—41no—
258C2×Dic83—41no—
259C2×Dic83—41no—
260C2×Dic83—41no—
261D332—22no—
262D332—22no—
263D332—41no—
264D332—41no—
265C4×D83—48no—
266C83⋊C8—22no—
267C83⋊C8—22no—
268C83⋊C8—22no—
269C83⋊C8#11714yescomplemented
270C22×C83C2×C4×D411yescharacteristic
271C22×C83#53211yescharacteristic
272C22×C83#53211yescharacteristic
273C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C83C2×#13711yescharacteristic
275C22×C83#57511yescharacteristic
276C22×C83#57511yescharacteristic
277C2×D83—42no—
278C2×D83—42no—
279C2×D83—42no—
280C2×D83—81no—
281C2×D83—81no—
282C2×D83—81no—
283C2×D83—81no—
284C4×C83—22no—
285C4×C83—22no—
286C4×C83—22no—
287C4×C83—22no—
288C4×C83—41no—
289C4×C83—41no—
290C4×C83—42no—
291C4×C83—42no—
292C4×C83—81no—
293C4×C83—81no—
294C4×C83C2×#11711yescharacteristic
295C4×C83C4×#4111yescharacteristic
296C4×C83#52911yescharacteristic
297C4×C83#52911yescharacteristic
298Dic83—42no—
299Dic83—81no—
300Dic83—81no—
301#21288—831nomaximal, Sylow
302C2×C83#229311yescharacteristic
303C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
304C2×C83C4×#13711yescharacteristic
305C2×C83#318011yescharacteristic
306C2×C83#318111yescharacteristic
307C2×C83#318211yescharacteristic
308C2×C83#318311yescharacteristic
309D83—82no—
310C2×#440—831no—
311#2295D8311yescharacteristic, complemented
312#2293—831no—
313#1973—831no—
314#1968—831no—
315#1943—831no—
316#1942—831no—
317#1936—831no—
318#1935—831no—
319#1934—831no—
320#1933—831no—
321#1776—831no—
322#1763—831no—
323#1762—831no—
324C4×#97—831no—
325C83#2128811yescharacteristic, complemented, Sylow
326C22×SD16—831no—
327C2×C4×Q8C2×D8311yescharacteristic
328C2×C4×D4—831no—
329C2×#117—1661no—
330#440—838no—
331C2×#107—831no—
332C2×#107—831no—
333C2×#106—831no—
334C2×#103—831no—
335C2×#103—831no—
336C2×#103—831no—
337C2×#102—831no—
338C2×#102—831no—
339C2×#102—831no—
340C2×#97—831no—
341C2×#97—831no—
342C2×#97—831no—
343C2×#97—831no—
344C2×C4×C8—831no—
345C2×C4×C8—831no—
346#391C2×D8311yescharacteristic
347#391C2×D8311yescharacteristic
348#390—831no—
349#390—831no—
350#389—831no—
351#389—831no—
352#389C2×D8311yescharacteristic
353#389C2×D8311yescharacteristic
354#388—1661no—
355#388—1661no—
356#387—21no—
357#387—21no—
358C4×C4⋊C4—21no—
359C4×C4⋊C4—831no—
360C4×C4⋊C4C2×D8311yescharacteristic
361C4×C22⋊C4—1661no—
362#376—21no—
363C43C2×D8311yescharacteristic
364#340—831no—
365#340—831no—
366#340—831no—
367#340—831no—
368#340—831no—
369#340—831no—
370C22×Q8C22×D8311yescharacteristic
371C22×D4—831no—
372C23×C4—1661no—
373C2×SD16—834no—
374C2×SD16—1662no—
375C2×SD16—1662no—
376C22×C8—831no—
377C22×C8—831no—
378C22×C8—831no—
379C22×C8—831no—
380C4×Q8—22no—
381C4×Q8C4×D8314yes—
382C4×D4—834no—
383C4×D4—1662no—
384#117—3324no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—831no—
389C2×C4⋊C4—831no—
390C2×C4⋊C4—831no—
391C2×C4⋊C4—1661no—
392C2×C4⋊C4—1661no—
393C2×C4⋊C4C22×D8311yescharacteristic
394C2×C4⋊C4C22×D8311yescharacteristic
395C2×C4⋊C4C22×D8311yescharacteristic
396C2×C22⋊C4—1661no—
397C2×C22⋊C4—1661no—
398C2×C22⋊C4—1661no—
399C2×C22⋊C4—1661no—
400C2×C22⋊C4—1661no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—1661no—
404C2×C42C22⋊D8311yescharacteristic
405C2×C42C22⋊D8311yescharacteristic
406C2×C42C22⋊D8311yescharacteristic
407C2×C42C22⋊D8311yescharacteristic
408C2×C42C22×D8311yescharacteristic
409C2×C42C22×D8311yescharacteristic
410C2×C42C22×D8311yescharacteristic
411#107—834no—
412#107—1662no—
413#106—1662no—
414#103—834no—
415#103—1662no—
416#103—1662no—
417#102—834no—
418#102—1662no—
419#102—1662no—
420#97—834no—
421#97—1662no—
422#97—1662no—
423#97—1662no—
424C4×C8—1662no—
425C4×C8—1662no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—1661no—
434#95—1661no—
435#95—1661no—
436C24—1661no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×C4×D8312yes—
443C2×D4—832no—
444C2×D4—1661no—
445C2×D4—1661no—
446C2×D4—1661no—
447C2×D4—1661no—
448C2×D4—1661no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—3322no—
454C22×C4—3322no—
455C22×C4—1661no—
456C22×C4—1661no—
457C22×C4—1661no—
458C22×C4—1664no—
459C22×C4C2×C22⋊D8311yescharacteristic
460C22×C4C2×C22⋊D8311yescharacteristic
461C22×C4C2×C22⋊D8311yescharacteristic
462C22×C4C2×C22⋊D8311yescharacteristic
463C22×C4C2×C22⋊D8311yescharacteristic
464C22×C4C2×C22⋊D8311yescharacteristic
465C22×C4C23×D8311yescharacteristic
466SD16—1668no—
467C2×C8—832no—
468C2×C8—832no—
469C2×C8—832no—
470C2×C8—832no—
471C2×C8—832no—
472C2×C8—832no—
473C2×C8—1661no—
474C2×C8—1661no—
475C2×C8—1661no—
476C2×C8—1661no—
477C2×C8—1661no—
478C2×C8—1661no—
479C4⋊C4—21no—
480C4⋊C4—24no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—3322no—
488C4⋊C4—3322no—
489C4⋊C4—832no—
490C4⋊C4—1661no—
491C4⋊C4—1661no—
492C4⋊C4—1661no—
493C4⋊C4—1661no—
494C4⋊C4—1661no—
495C4⋊C4C2×C4×D8312yes—
496C22⋊C4—3322no—
497C22⋊C4—3322no—
498C22⋊C4—3322no—
499C22⋊C4—3322no—
500C22⋊C4—1664no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—24no—
508C42—41no—
509C42—41no—
510C42—42no—
511C42—3322no—
512C42C2×C4×D8312yes—
513C42#1305059012yes—
514C23—3321no—
515C23—3321no—
516C23—3321no—
517C23—3321no—
518C23—3321no—
519C23—3321no—
520C23—1662no—
521C23C22×C22⋊D8311yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—3321no—
527D4—3321no—
528D4—1662no—
529D4—1662no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—3328no—
557C2×C4—3321no—
558C2×C4—3321no—
559C2×C4—3321no—
560C2×C4—3321no—
561C2×C4—3321no—
562C2×C4—3321no—
563C2×C4—3321no—
564C2×C4—3321no—
565C2×C4—1662no—
566C2×C4C4×C22⋊D8312yes—
567C2×C4C4×C22⋊D8312yes—
568C2×C4#1458181712yes—
569C2×C4#1458182312yes—
570C2×C4C22×C4×D8311yescharacteristic
571C2×C4#41×D8311yescharacteristic
572C2×C4#41×D8311yescharacteristic
573C2×C4#41×D8311yescharacteristic
574C2×C4#41×D8311yescharacteristic
575C2×C4C2×#1305059011yescharacteristic
576C8—834no—
577C8—1662no—
578C8—1662no—
579C8—1662no—
580C22—3322no—
581C22—3322no—
582C22—3322no—
583C22—6641no—
584C22—6641no—
585C22—6641no—
586C22—6641no—
587C22C2×C4×C22⋊D8311yescharacteristic
588C22#1912824711yescharacteristic
589C22#1912824711yescharacteristic
590C22C2×#1458181711yescharacteristic
591C22C2×#1458182311yescharacteristic
592C22#1912849911yescharacteristic
593C22#1912849911yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—42no—
599C4—42no—
600C4—41no—
601C4—41no—
602C4—81no—
603C4—81no—
604C4—3322no—
605C4—6641no—
606C4—6641no—
607C4#117×D8311yescharacteristic
608C4#1912816911yescharacteristic
609C4#1912822911yescharacteristic
610C4#1912822911yescharacteristic
611C2—6642no—
612C2#2490992211yescharacteristic
613C2C4×#1458181711yescharacteristic
614C2C4×#1458182311yescharacteristic
615C2#2491816211yescharacteristic
616C2#2491816611yescharacteristic
617C2#2491818211yescharacteristic
618C2#2491818611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2295C2
socleC23×C83C22×D4
prime radicalC22×D332C23
cosocleC22×C4×C83C24
hypercenter#2295D83
hypocenterC83#21288
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C43 ◁ #2295

Complements

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

NH ≅ G/Ntype
5. #24908198C2semidirect
6. #24908193C2semidirect
8. #24908156C2semidirect
10. #24908142C2semidirect
11. #24907361C2semidirect
12. #24907293C2semidirect
14. C4×#14581703C2semidirect
15. C83×#2295C2semidirect
19. #19127799C4semidirect
269. C83⋊C8#117semidirect
311. #2295D83semidirect
325. C83#21288semidirect

Maximal subgroups

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

subgroupindex
C2×#191277992
#249099272
#249083472
#249083202
#249081982
#249081932
#249081592
#249081562
#249081452
#249081422
#249073612
#249072932
#249072912
C4×#145817032
C83×#22952
#2128883