Finite Group Databasebeta

← #35422107

Subgroups — #35422107

Order 21248.

810 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D83C211yesmaximal, characteristic
2#24910339C211yesmaximal, characteristic
3#24910336C211yesmaximal, characteristic
4#24908200C211yesmaximal, characteristic, complemented
5#24908198C211yesmaximal, characteristic, complemented
6#24908036C211yesmaximal, characteristic, complemented
7#24908035C211yesmaximal, characteristic, complemented
8#24908033C211yesmaximal, characteristic, complemented
9#24907552C211yesmaximal, characteristic
10#24907552C211yesmaximal, characteristic
11#24907487C211yesmaximal, characteristic
12#24907361C211yesmaximal, characteristic, complemented
13#24907359C211yesmaximal, characteristic, complemented
14#24907238C211yesmaximal, characteristic
15C83×#1918C211yesmaximal, characteristic, complemented
16C22×C8×D83C2211yescharacteristic
17C2×C4⋊C4×D83C2211yescharacteristic
18C2×C4⋊C4×D83C2211yescharacteristic
19C2×#14581726C2211yescharacteristic
20C2×#14581725C2211yescharacteristic
21C2×#14581725C2211yescharacteristic
22#107×D83C418yescomplemented
23C2×#14581723C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×(C2×D83)⋊C8C2211yescharacteristic
26C2×#14581703C2211yescharacteristic
27C2×#14581702C2211yescharacteristic
28#19127600C2211yescharacteristic
29#19127599C2211yescharacteristic
30#19127597C2211yescharacteristic
31#19127588—21no—
32#19127585—21no—
33#19127583—21no—
34#19127582—21no—
35#19127560—21no—
36#19127558—21no—
37#19127558C2211yescharacteristic
38#19127558C2211yescharacteristic
39C4⋊C4×Dic83C2211yescharacteristic
40C4⋊C4×Dic83C2211yescharacteristic
41C4×C4⋊Dic83C2211yescharacteristic
42C4×(C2×D83)⋊C4—21no—
43C4×(C2×D83)⋊C4C2211yescharacteristic
44#19127548—21no—
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51#19127463C2211yescharacteristic
52#19127455C2211yescharacteristic
53C2×#107×C83C2211yescharacteristic
54#389×C83C2211yescharacteristic
55C4×C4⋊C4×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#340×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60C22×C4×D83—21no—
61C22×C4×D83—21no—
62C22×C4×D83C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65C2×C8×D83—22no—
66C2×C8×D83—22no—
67C2×C8×D83C2×C414yes—
68C2×C4⋊Dic83—21no—
69C2×C4⋊Dic83C2311yescharacteristic
70C2×C4⋊Dic83C2311yescharacteristic
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×Dic83⋊C4—21no—
74C2×Dic83⋊C4—21no—
75C2×Dic83⋊C4—21no—
76C2×Dic83⋊C4—21no—
77C4⋊C4×D83—22no—
78C4⋊C4×D83—22no—
79C4⋊C4×D83C2×C414yes—
80C4⋊C4×D83C2×C414yes—
81C2×(C2×D83)⋊C4—21no—
82C2×(C2×D83)⋊C4—21no—
83C2×(C2×D83)⋊C4D411yescharacteristic
84C2×(C2×D83)⋊C4D411yescharacteristic
85C2×C4×Dic83—21no—
86C2×C4×Dic83—21no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83C2311yescharacteristic
89#14581726C2×C414yes—
90#14581725C2×C414yes—
91#14581725C2×C414yes—
92#14581723—22no—
93#14581723—22no—
94(C2×D83)⋊C8—22no—
95#14581703—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
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109C2×C4⋊C4×C83—21no—
110C2×C4⋊C4×C83C2311yescharacteristic
111C2×C4⋊C4×C83C2311yescharacteristic
112C2×C4⋊C4×C83C2311yescharacteristic
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C42×C83—21no—
115C2×C42×C83C2311yescharacteristic
116#107×C83C2×C414yes—
117#95×C83—21no—
118#95×C83—21no—
119C23×D83C2×D411yescharacteristic
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83C2×D411yescharacteristic
125C22×Dic83C2×D411yescharacteristic
126C22×Dic83C2×D411yescharacteristic
127C2×C4×D83—21no—
128C2×C4×D83—21no—
129C2×C4×D83—21no—
130C2×C4×D83—21no—
131C2×C4×D83—24no—
132C2×C4×D83—24no—
133C2×C4×D83—81no—
134C2×C4×D83—81no—
135C2×C4×D83—81no—
136C2×C4×D83—81no—
137C2×C4×D83C22×C412yes—
138C2×C4×D83#4112yes—
139C2×C83⋊C8—21no—
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8C22×C412yes—
143C2×C83⋊C8#4112yes—
144C2×C83⋊C8#4112yes—
145C8×D83—28no—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—21no—
151C4⋊Dic83—21no—
152C4⋊Dic83—81no—
153C4⋊Dic83C22×C412yes—
154C4⋊Dic83C22×C412yes—
155Dic83⋊C4—24no—
156Dic83⋊C4—24no—
157Dic83⋊C4—81no—
158Dic83⋊C4—81no—
159(C2×D83)⋊C4—22no—
160(C2×D83)⋊C4—22no—
161(C2×D83)⋊C4—42no—
162(C2×D83)⋊C4—42no—
163C4×Dic83—21no—
164C4×Dic83—21no—
165C4×Dic83—81no—
166C4×Dic83—81no—
167C4×Dic83—81no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83C2411yescharacteristic
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83C22×C412yes—
181C4⋊C4×C83—21no—
182C4⋊C4×C83—21no—
183C4⋊C4×C83—21no—
184C4⋊C4×C83—21no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—81no—
188C4⋊C4×C83C22×C412yes—
189C4⋊C4×C83C22×C412yes—
190C42×C83—21no—
191C42×C83—21no—
192C42×C83—81no—
193C23×C83C22×D411yescharacteristic
194C22×D83—21no—
195C22×D83—21no—
196C22×D83—21no—
197C22×D83—21no—
198C22×D83C4×D412yes—
199C22×D83#13712yes—
200C22×D83#13712yes—
201C2×C4×C83—22no—
202C2×C4×C83—22no—
203C2×C4×C83—21no—
204C2×C4×C83—21no—
205C2×C4×C83—21no—
206C2×C4×C83—21no—
207C2×C4×C83—21no—
208C2×C4×C83—21no—
209C2×C4×C83—41no—
210C2×C4×C83—41no—
211C2×C4×C83—41no—
212C2×C4×C83—41no—
213C2×C4×C83—41no—
214C2×C4×C83—41no—
215C2×C4×C83—41no—
216C2×C4×C83—41no—
217C2×C4×C83—41no—
218C2×C4×C83—41no—
219C2×C4×C83C23×C411yescharacteristic
220C2×C4×C83C2×#4111yescharacteristic
221C2×C4×C83C2×#4111yescharacteristic
222C2×C4×C83C2×#4111yescharacteristic
223C2×C4×C832−1+411yescharacteristic
224C2×C4×C832−1+411yescharacteristic
225C2×Dic83—21no—
226C2×Dic83—21no—
227C2×Dic83—22no—
228C2×Dic83—22no—
229C2×Dic83—21no—
230C2×Dic83—21no—
231C2×Dic83—21no—
232C2×Dic83—21no—
233C2×Dic83—21no—
234C2×Dic83—21no—
235C2×Dic83—41no—
236C2×Dic83—41no—
237C2×Dic83—41no—
238C2×Dic83—41no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245C2×Dic83C4×D412yes—
246C4×D83—22no—
247C4×D83—22no—
248C4×D83—22no—
249C4×D83—22no—
250C4×D83—84no—
251C4×D83—84no—
252C8×C83—22no—
253C8×C83—41no—
254C83⋊C8—41no—
255C83⋊C8#11714yes—
256C22×C83C2×C4×D411yescharacteristic
257C22×C83#54711yescharacteristic
258C22×C83#54711yescharacteristic
259C22×C83C2×#13711yescharacteristic
260C22×C83C2×#13711yescharacteristic
261C22×C83#57611yescharacteristic
262C22×C83#57611yescharacteristic
263C2×D83—22no—
264C2×D83—22no—
265C2×D83—22no—
266C2×D83—22no—
267C2×D83—22no—
268C2×D83—22no—
269C2×D83#44114yes—
270C4×C83—41no—
271C4×C83—41no—
272C4×C83—42no—
273C4×C83—42no—
274C4×C83—81no—
275C4×C83—81no—
276C4×C83C2×#11711yescharacteristic
277C4×C83#51911yescharacteristic
278C4×C83#55211yescharacteristic
279C4×C83#55211yescharacteristic
280Dic83—22no—
281Dic83—41no—
282Dic83—41no—
283Dic83—42no—
284Dic83—42no—
285Dic83—81no—
286Dic83—81no—
287#22618—831nomaximal, Sylow
288C2×C83#234411yescharacteristic
289C2×C83C2×#44111yescharacteristic
290C2×C83#294811yescharacteristic
291C2×C83#334611yescharacteristic
292C2×C83#334611yescharacteristic
293C2×C83#334611yescharacteristic
294C2×C83#334611yescharacteristic
295D83—24no—
296C22×#107—831no—
297#2345—831no—
298#2345—831no—
299#1943—831no—
300#1943—831no—
301#1918—831no—
302#1918—831no—
303#1918—831no—
304#1918D8311yescharacteristic, complemented
305#1824—831no—
306#1824—831no—
307#1807—831no—
308#1776—831no—
309#1776—831no—
310#1752—831no—
311C83#2261811yescharacteristic, complemented, Sylow
312C23×C8—831no—
313C22×C4⋊C4—831no—
314C22×C4⋊C4—831no—
315C2×#107—831no—
316C2×#107—831no—
317C2×#107—831no—
318C2×#107—838no—
319C2×#107C2×D8311yescharacteristic
320C2×#106—831no—
321C2×#106—831no—
322C2×C22⋊C8—831no—
323C2×#97—831no—
324C2×#97—831no—
325#389—831no—
326#389—831no—
327#389—831no—
328#389C2×D8311yescharacteristic
329#387—1661no—
330#387—1661no—
331#387—1661no—
332#387—1661no—
333#380—831no—
334#380—831no—
335#380—1661no—
336#380—1661no—
337C4×C4⋊C4—831no—
338C4×C4⋊C4—831no—
339C4×C4⋊C4—831no—
340C4×C4⋊C4C2×D8311yescharacteristic
341C4×C22⋊C4—831no—
342C4×C22⋊C4—1661no—
343C4×C22⋊C4—1661no—
344#340—831no—
345#340—831no—
346#340—831no—
347#340—831no—
348#340—831no—
349#340—831no—
350#340—831no—
351#340C2×D8311yescharacteristic
352#340C2×D8311yescharacteristic
353#340C2×D8311yescharacteristic
354#336—831no—
355#336C2×D8311yescharacteristic
356C23×C4—831no—
357C23×C4—1661no—
358C23×C4—1661no—
359C22×C8—831no—
360C22×C8—834no—
361C22×C8—831no—
362C22×C8—1662no—
363C22×C8—1662no—
364C22×C8C22×D8311yescharacteristic
365C22×C8C22×D8311yescharacteristic
366C2×C4⋊C4—21no—
367C2×C4⋊C4—831no—
368C2×C4⋊C4—831no—
369C2×C4⋊C4—834no—
370C2×C4⋊C4—834no—
371C2×C4⋊C4—831no—
372C2×C4⋊C4—831no—
373C2×C4⋊C4—1662no—
374C2×C4⋊C4—1662no—
375C2×C4⋊C4—1661no—
376C2×C4⋊C4—1661no—
377C2×C4⋊C4—1661no—
378C2×C4⋊C4—1661no—
379C2×C4⋊C4—1661no—
380C2×C4⋊C4C22×D8311yescharacteristic
381C2×C4⋊C4C22×D8311yescharacteristic
382C2×C4⋊C4C22×D8311yescharacteristic
383C2×C4⋊C4C22×D8311yescharacteristic
384C2×C22⋊C4—831no—
385C2×C22⋊C4—831no—
386C2×C22⋊C4—1661no—
387C2×C22⋊C4—1661no—
388C2×C42—21no—
389C2×C42—831no—
390C2×C42—1661no—
391C2×C42—1661no—
392C2×C42—1661no—
393C2×C42C22×D8311yescharacteristic
394#107—834no—
395#107—834no—
396#107—834no—
397#107C4×D8314yes—
398#106—1662no—
399#106—1662no—
400C22⋊C8—1662no—
401#97—1662no—
402#97—1662no—
403#95—21no—
404#95—21no—
405#95—831no—
406#95—831no—
407#95—1661no—
408#95—1661no—
409#95—1661no—
410#95—1661no—
411#95—1661no—
412#95—1661no—
413#95—1661no—
414#95—1661no—
415C24—831no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—831no—
421C22×C4—832no—
422C22×C4—832no—
423C22×C4—831no—
424C22×C4—831no—
425C22×C4—6641no—
426C22×C4—6641no—
427C22×C4—6641no—
428C22×C4—6641no—
429C22×C4—1664no—
430C22×C4—1664no—
431C22×C4—1661no—
432C22×C4—1661no—
433C22×C4—1661no—
434C22×C4—1661no—
435C22×C4—1661no—
436C22×C4—1661no—
437C22×C4—1661no—
438C22×C4—1661no—
439C22×C4D4×D8311yescharacteristic
440C22×C4D4×D8311yescharacteristic
441C22×C4C23×D8311yescharacteristic
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—832no—
448C2×C8—832no—
449C2×C8—832no—
450C2×C8—1668no—
451C2×C8—1661no—
452C2×C8—1661no—
453C2×C8—1661no—
454C2×C8C2×C4×D8312yes—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—81no—
462C4⋊C4—832no—
463C4⋊C4—832no—
464C4⋊C4—6641no—
465C4⋊C4—6641no—
466C4⋊C4—6641no—
467C4⋊C4—1664no—
468C4⋊C4—1664no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4C2×C4×D8312yes—
476C4⋊C4C2×C4×D8312yes—
477C22⋊C4—3322no—
478C22⋊C4—3322no—
479C22⋊C4—1662no—
480C22⋊C4—1662no—
481C42—21no—
482C42—21no—
483C42—81no—
484C42—6641no—
485C42—6641no—
486C42—6641no—
487C42—1661no—
488C42—1661no—
489C23—832no—
490C23—832no—
491C23—832no—
492C23—1661no—
493C23—1661no—
494C23—1661no—
495C23—1661no—
496C23C2×D4×D8311yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—3321no—
516C2×C4—3321no—
517C2×C4—3321no—
518C2×C4—3321no—
519C2×C4—3321no—
520C2×C4—3321no—
521C2×C4—3321no—
522C2×C4—3321no—
523C2×C4—3321no—
524C2×C4—3321no—
525C2×C4—832no—
526C2×C4—6644no—
527C2×C4—6644no—
528C2×C4—1661no—
529C2×C4—1661no—
530C2×C4—1662no—
531C2×C4—1662no—
532C2×C4—1661no—
533C2×C4—1661no—
534C2×C4—1661no—
535C2×C4—1661no—
536C2×C4—1661no—
537C2×C4—1661no—
538C2×C4—1662no—
539C2×C4—1662no—
540C2×C4—1662no—
541C2×C4—1662no—
542C2×C4C22×C4×D8311yescharacteristic
543C2×C4#41×D8311yescharacteristic
544C2×C4#41×D8311yescharacteristic
545C2×C4#41×D8311yescharacteristic
546C2×C4#1458183911yescharacteristic
547C2×C4#1458184011yescharacteristic
548C8—22no—
549C8—41no—
550C8—3321no—
551C8—834no—
552C22—834no—
553C22—1662no—
554C22—1662no—
555C22—1662no—
556C22—1662no—
557C22—1662no—
558C22—1662no—
559C22C4×D4×D8311yescharacteristic
560C22#1912834911yescharacteristic
561C22#1912835311yescharacteristic
562C22#137×D8311yescharacteristic
563C22#137×D8311yescharacteristic
564C22#1912850211yescharacteristic
565C22#1912850311yescharacteristic
566C4—42no—
567C4—42no—
568C4—41no—
569C4—41no—
570C4—81no—
571C4—81no—
572C4—3322no—
573C4—3322no—
574C4—3321no—
575C4—3321no—
576C4—6641no—
577C4—6641no—
578C4—1662no—
579C4#117×D8311yescharacteristic
580C4#1912817711yescharacteristic
581C4#1912838311yescharacteristic
582C4#1912838711yescharacteristic
583C2—1664no—
584C2#2491032911yescharacteristic
585C2#441×D8311yescharacteristic
586C2#2491631011yescharacteristic
587C2#2491994111yescharacteristic
588C2#2491994511yescharacteristic
589C2#2491995111yescharacteristic
590C2#2491995511yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1918C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
cosocleC22×C4×C83C24
hypercenter#1918D83
hypocenterC83#22618
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #24908200C2semidirect
5. #24908198C2semidirect
6. #24908036C2semidirect
7. #24908035C2semidirect
8. #24908033C2semidirect
12. #24907361C2semidirect
13. #24907359C2semidirect
15. C83×#1918C2semidirect
22. #107×D83C4semidirect
304. #1918D83semidirect
311. C83#22618semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D832
#249103392
#249103362
#249082002
#249081982
#249080362
#249080352
#249080332
#249075522
#249074872
#249073612
#249073592
#249072382
C83×#19182
#2261883