Finite Group Databasebeta

← #35422152

Subgroups — #35422152

Order 21248.

810 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127741C211yesmaximal, characteristic
2#24910354C211yesmaximal, characteristic
3#24908198C211yesmaximal, characteristic, complemented
4#24908193C211yesmaximal, characteristic, complemented
5#24908055C211yesmaximal, characteristic, complemented
6#24908045C211yesmaximal, characteristic, complemented
7#24908038C211yesmaximal, characteristic, complemented
8#24908034C211yesmaximal, characteristic, complemented
9#24907555C211yesmaximal, characteristic
10#24907553C211yesmaximal, characteristic
11#24907494C211yesmaximal, characteristic
12#24907361C211yesmaximal, characteristic, complemented
13C4×#14581723C211yesmaximal, characteristic, complemented
14#24907247C211yesmaximal, characteristic
15C83×#2344C211yesmaximal, characteristic
16C22×#13050574C2211yescharacteristic
17C2×#14581751C2211yescharacteristic
18#19127741C418yescomplemented
19C2×#14581725C2211yescharacteristic
20C2×#14581725C2211yescharacteristic
21C2×#14581725C2211yescharacteristic
22C2×#14581723C2211yescharacteristic
23C2×#14581723C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×C22⋊(C83⋊C8)C2211yescharacteristic
26C2×#14581703C2211yescharacteristic
27C2×C4×C83⋊C8C2211yescharacteristic
28#19127599C2211yescharacteristic
29#19127599C2211yescharacteristic
30#19127595—21no—
31#19127595—21no—
32#19127568—21no—
33#19127561C2211yescharacteristic
34C4×C4⋊Dic83C2211yescharacteristic
35C4×C4⋊Dic83C2211yescharacteristic
36#19127552—21no—
37#19127463C2211yescharacteristic
38#19127463C2211yescharacteristic
39#19127463C2211yescharacteristic
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127456C2211yescharacteristic
48#19127456C2211yescharacteristic
49C2×#117×C83—21no—
50C22×C4⋊C4×C83C2211yescharacteristic
51#389×C83C2211yescharacteristic
52#389×C83C2211yescharacteristic
53#387×C83—21no—
54#387×C83—21no—
55#381×C83—21no—
56#380×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59C4×C22⋊C4×C83C2211yescharacteristic
60C2×#13050574—22no—
61C2×#13050574—22no—
62C2×#13050574C2×C414yes—
63C22×C83⋊C8C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65C22×C83⋊C8C2311yescharacteristic
66C22×C83⋊C8C2311yescharacteristic
67#14581751—22no—
68#14581751C2×C414yes—
69C2×C4⋊Dic83C2311yescharacteristic
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×Dic83⋊C4—21no—
74C2×Dic83⋊C4—21no—
75C2×C22⋊Dic83—21no—
76C2×C22⋊Dic83—21no—
77C2×C4×Dic83—21no—
78C2×C4×Dic83—21no—
79C2×C4×Dic83—21no—
80#14581725—22no—
81#14581725C2×C414yes—
82#14581725C2×C414yes—
83#14581723—22no—
84#14581723C2×C414yes—
85#14581723C2×C414yes—
86C22⋊(C83⋊C8)—22no—
87#14581703—22no—
88C4×C83⋊C8—22no—
89C83⋊#95—21no—
90C83⋊#95—21no—
91C83⋊#95—21no—
92C83⋊#95—21no—
93C83⋊#95—21no—
94C23×C4×C83—21no—
95C23×C4×C83C2311yescharacteristic
96#117×C83—44no—
97C2×C4⋊C4×C83—21no—
98C2×C4⋊C4×C83—22no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83C2×C414yes—
102C2×C4⋊C4×C83C2311yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C4⋊C4×C83C2311yescharacteristic
105C2×C4⋊C4×C83C2311yescharacteristic
106C2×C22⋊C4×C83—21no—
107C2×C22⋊C4×C83D411yescharacteristic
108C2×C22⋊C4×C83D411yescharacteristic
109C2×C42×C83—21no—
110C2×C42×C83—21no—
111C2×C42×C83C2311yescharacteristic
112C2×C42×C83C2311yescharacteristic
113#95×C83—21no—
114#95×C83—21no—
115#95×C83—21no—
116#95×C83—21no—
117#95×C83—21no—
118#95×C83D411yescharacteristic
119#95×C83D411yescharacteristic
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124#13050574—28no—
125C2×C83⋊C8—21no—
126C2×C83⋊C8—21no—
127C2×C83⋊C8—21no—
128C2×C83⋊C8—21no—
129C2×C83⋊C8—21no—
130C2×C83⋊C8—21no—
131C2×C83⋊C8—21no—
132C2×C83⋊C8—21no—
133C2×C83⋊C8C22×C412yes—
134C2×C83⋊C8C22×C412yes—
135C2×C83⋊C8#4112yes—
136C2×C83⋊C8#4112yes—
137C4⋊Dic83—21no—
138C4⋊Dic83—21no—
139C4⋊Dic83—21no—
140C4⋊Dic83—21no—
141C4⋊Dic83—21no—
142C4⋊Dic83—21no—
143C4⋊Dic83C22×C412yes—
144C4⋊Dic83C22×C412yes—
145Dic83⋊C4—42no—
146Dic83⋊C4—42no—
147C22⋊Dic83—24no—
148C22⋊Dic83—81no—
149C4×Dic83—24no—
150C4×Dic83—81no—
151C4×Dic83—81no—
152C24×C83C2×D411yescharacteristic
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—24no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—42no—
163C22×C4×C83—42no—
164C22×C4×C83C22×C412yes—
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83#4112yes—
171C22×C4×C83C2411yescharacteristic
172C4⋊C4×C83—24no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—21no—
177C4⋊C4×C83—21no—
178C4⋊C4×C83—21no—
179C4⋊C4×C83—42no—
180C4⋊C4×C83—42no—
181C4⋊C4×C83C22×C412yes—
182C4⋊C4×C83C22×C412yes—
183C22⋊C4×C83—22no—
184C22⋊C4×C83—41no—
185C22⋊C4×C83—42no—
186C42×C83—21no—
187C42×C83—21no—
188C42×C83—21no—
189C42×C83—21no—
190C42×C83—42no—
191C42×C83—42no—
192C23×C83—21no—
193C23×C83—21no—
194C23×C83—21no—
195C23×C83—21no—
196C23×C83—21no—
197C23×C83—21no—
198C23×C83C4×D412yes—
199C23×C83C22×D411yescharacteristic
200C2×C4×C83—21no—
201C2×C4×C83—21no—
202C2×C4×C83—21no—
203C2×C4×C83—21no—
204C2×C4×C83—22no—
205C2×C4×C83—22no—
206C2×C4×C83—22no—
207C2×C4×C83—22no—
208C2×C4×C83—22no—
209C2×C4×C83—22no—
210C2×C4×C83—21no—
211C2×C4×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83—48no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83—41no—
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×C83C4×D412yes—
231C2×C4×C83AGL(1,ℤ/8)12yes—
232C2×C4×C83C23×C411yescharacteristic
233C2×C4×C83C2×#4111yescharacteristic
234C2×C4×C83C2×#4111yescharacteristic
235C2×C4×C83C2×#4111yescharacteristic
236C2×C4×C832−1+411yescharacteristic
237C2×C4×C832−1+411yescharacteristic
238C2×Dic83—22no—
239C2×Dic83—22no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C83⋊C8—22no—
251C83⋊C8—41no—
252C83⋊C8—41no—
253C83⋊C8#11714yescomplemented
254C22×C83—22no—
255C22×C83—22no—
256C22×C83—22no—
257C22×C83—41no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83C2×C4×D411yescharacteristic
262C22×C83#54711yescharacteristic
263C22×C83#54711yescharacteristic
264C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C83#57511yescharacteristic
266C22×C83#57711yescharacteristic
267C22×C83#57811yescharacteristic
268C4×C83—22no—
269C4×C83—22no—
270C4×C83—41no—
271C4×C83—41no—
272C4×C83—41no—
273C4×C83—42no—
274C4×C83—42no—
275C4×C83—81no—
276C4×C83—81no—
277C4×C83C2×#11711yescharacteristic
278C4×C83#51911yescharacteristic
279C4×C83#55211yescharacteristic
280C4×C83#55211yescharacteristic
281Dic83—42no—
282Dic83—42no—
283Dic83—81no—
284Dic83—81no—
285#22622—831nomaximal, Sylow
286C2×C83—42no—
287C2×C83#234411yescharacteristic
288C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
289C2×C83#294711yescharacteristic
290C2×C83#334511yescharacteristic
291C2×C83#334911yescharacteristic
292C2×C83#335111yescharacteristic
293C2×C83#335311yescharacteristic
294C2×#428—831no—
295#2347—831no—
296#2344D8311yescharacteristic
297#1943—831no—
298#1942—831no—
299#1921—831no—
300#1920—831no—
301#1919—831no—
302#1918—831no—
303#1825—831no—
304#1824—831no—
305#1809—831no—
306#1776—831no—
307C4×#106—831no—
308#1753—831no—
309C83#2262211yescharacteristic, complemented, Sylow
310C22×M16—831no—
311C2×#117—21no—
312C2×#117—831no—
313C22×C4⋊C4C2×D8311yescharacteristic
314#428—838no—
315C2×#107—831no—
316C2×#107—831no—
317C2×#107—831no—
318C2×#106—831no—
319C2×#106—831no—
320C2×#106—831no—
321C2×C22⋊C8—831no—
322C2×#97—831no—
323C2×C4×C8—831no—
324#389—831no—
325#389—831no—
326#389C2×D8311yescharacteristic
327#389C2×D8311yescharacteristic
328#388—1661no—
329#388—1661no—
330#387—21no—
331#387—21no—
332#383—1661no—
333#381—21no—
334#380—831no—
335#380C2×D8311yescharacteristic
336C4×C4⋊C4—831no—
337C4×C4⋊C4—831no—
338C4×C4⋊C4—1661no—
339C4×C4⋊C4C2×D8311yescharacteristic
340C4×C4⋊C4C2×D8311yescharacteristic
341C4×C22⋊C4C2×D8311yescharacteristic
342#340—831no—
343#340—831no—
344#340—831no—
345#340—831no—
346#340—831no—
347#340—831no—
348#340—831no—
349#340—831no—
350#340—831no—
351#340—831no—
352#336—831no—
353#336—831no—
354C23×C4—21no—
355C23×C4C22×D8311yescharacteristic
356C2×M16—834no—
357C2×M16—1662no—
358C2×M16—1662no—
359C22×C8—831no—
360C22×C8—831no—
361C22×C8—831no—
362C22×C8—831no—
363#117—44no—
364#117—834no—
365#117—1662no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—831no—
371C2×C4⋊C4—831no—
372C2×C4⋊C4—831no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—1661no—
375C2×C4⋊C4—1661no—
376C2×C4⋊C4C4×D8314yes—
377C2×C4⋊C4C22×D8311yescharacteristic
378C2×C4⋊C4C22×D8311yescharacteristic
379C2×C4⋊C4C22×D8311yescharacteristic
380C2×C4⋊C4C22×D8311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—1661no—
383C2×C22⋊C4—1661no—
384C2×C22⋊C4C22⋊D8311yescharacteristic
385C2×C22⋊C4C22⋊D8311yescharacteristic
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—1661no—
389C2×C42—1661no—
390C2×C42—1661no—
391C2×C42C22×D8311yescharacteristic
392C2×C42C22×D8311yescharacteristic
393#107—834no—
394#107—834no—
395#107—1662no—
396#106—834no—
397#106—834no—
398#106—1662no—
399C22⋊C8—1662no—
400#97—1662no—
401C4×C8—1662no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—1661no—
408#95—1661no—
409#95—1661no—
410#95—1661no—
411#95—1661no—
412#95C22⋊D8311yescharacteristic
413#95C22⋊D8311yescharacteristic
414C24C2×C22⋊D8311yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—24no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—1661no—
427C22×C4—1661no—
428C22×C4—1661no—
429C22×C4—1661no—
430C22×C4C2×C4×D8312yes—
431C22×C4C2×C22⋊D8311yescharacteristic
432C22×C4C2×C22⋊D8311yescharacteristic
433C22×C4C2×C22⋊D8311yescharacteristic
434C22×C4C2×C22⋊D8311yescharacteristic
435C22×C4C2×C22⋊D8311yescharacteristic
436C22×C4#1305059012yes—
437C22×C4C23×D8311yescharacteristic
438M16—1668no—
439C2×C8—832no—
440C2×C8—832no—
441C2×C8—832no—
442C2×C8—832no—
443C2×C8—1661no—
444C2×C8—1661no—
445C2×C8—1661no—
446C2×C8—1661no—
447C2×C8—1661no—
448C2×C8—1661no—
449C2×C8—1661no—
450C2×C8—1661no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—42no—
459C4⋊C4—42no—
460C4⋊C4—3322no—
461C4⋊C4—3322no—
462C4⋊C4—832no—
463C4⋊C4—832no—
464C4⋊C4—1661no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4C2×C4×D8312yes—
471C4⋊C4C2×C4×D8312yes—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—42no—
475C22⋊C4—6641no—
476C22⋊C4—1664no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—42no—
482C42—42no—
483C42—6641no—
484C42—6641no—
485C42—1664no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23C4×C22⋊D8312yes—
493C23C22×C22⋊D8311yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—48no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—3321no—
525C2×C4—3321no—
526C2×C4—3321no—
527C2×C4—3321no—
528C2×C4—3321no—
529C2×C4—3321no—
530C2×C4—3321no—
531C2×C4—3321no—
532C2×C4—3321no—
533C2×C4—3321no—
534C2×C4—1662no—
535C2×C4—1662no—
536C2×C4C4×C22⋊D8312yes—
537C2×C4#1458181812yes—
538C2×C4C22×C4×D8311yescharacteristic
539C2×C4#41×D8311yescharacteristic
540C2×C4#41×D8311yescharacteristic
541C2×C4C2×#1305059011yescharacteristic
542C2×C4#1458183911yescharacteristic
543C2×C4#1458183911yescharacteristic
544C8—3321no—
545C8—3321no—
546C8—834no—
547C8—1662no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×C4×C22⋊D8311yescharacteristic
556C22#1912835011yescharacteristic
557C22#1912835011yescharacteristic
558C22C2×#1458181811yescharacteristic
559C22#1912849911yescharacteristic
560C22#1912850911yescharacteristic
561C22#1912851611yescharacteristic
562C4—22no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—3322no—
572C4—3322no—
573C4—6641no—
574C4—6641no—
575C4#117×D8311yescharacteristic
576C4#1912817811yescharacteristic
577C4#1912838411yescharacteristic
578C4#1912838411yescharacteristic
579C2—42no—
580C2#2491033311yescharacteristic
581C2C4×#1458181811yescharacteristic
582C2#2491630611yescharacteristic
583C2#2491993311yescharacteristic
584C2#2491999311yescharacteristic
585C2#2492002311yescharacteristic
586C2#2492004711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2344C2
socleC23×C83C22×D4
prime radicalC24×C83C2×D4
cosocleC22×C4×C83C24
hypercenter#2344D83
hypocenterC83#22622
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #24908198C2semidirect
4. #24908193C2semidirect
5. #24908055C2semidirect
6. #24908045C2semidirect
7. #24908038C2semidirect
8. #24908034C2semidirect
12. #24907361C2semidirect
13. C4×#14581723C2semidirect
18. #19127741C4semidirect
253. C83⋊C8#117semidirect
309. C83#22622semidirect

Maximal subgroups

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

subgroupindex
C2×#191277412
#249103542
#249081982
#249081932
#249080552
#249080452
#249080382
#249080342
#249075552
#249075532
#249074942
#249073612
C4×#145817232
#249072472
C83×#23442
#2262283