Finite Group Databasebeta

← #35466515

Subgroups — #35466515

Order 21248.

784 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912629C211yesmaximal, characteristic
2D4×C4⋊Dic83C211yesmaximal, characteristic
3#24908896C211yesmaximal, characteristic, complemented
4#24908896C211yesmaximal, characteristic, complemented
5#24908891C211yesmaximal, characteristic, complemented
6#24908886C211yesmaximal, characteristic, complemented
7#24908432C211yesmaximal, characteristic, complemented
8#24908418C211yesmaximal, characteristic, complemented
9#24908227C211yesmaximal, characteristic, complemented
10#24907658C211yesmaximal, characteristic, complemented
11#24907658C211yesmaximal, characteristic, complemented
12#24907554C211yesmaximal, characteristic, complemented
13#24907550C211yesmaximal, characteristic, complemented
14#24907360C211yesmaximal, characteristic, complemented
15C83×#1955C211yesmaximal, characteristic
16C2×#14581784C2211yescharacteristic
17C2×D4×Dic83—21no—
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C2×#14581726C2211yescharacteristic
21C2×#14581724C2211yescharacteristic
22C2×#14581724C2211yescharacteristic
23C2×#14581724C2211yescharacteristic
24#19127639—21no—
25#19127615—21no—
26#19127600—21no—
27#19127595—21no—
28#19127595—21no—
29#19127576—21no—
30#19127576—21no—
31#19127571C2211yescharacteristic
32#19127561C2211yescharacteristic
33#19127561C2211yescharacteristic
34#19127561C2211yescharacteristic
35#19127561C2211yescharacteristic
36#19127561C2211yescharacteristic
37#19127561C2211yescharacteristic
38C4×C4⋊Dic83C2211yescharacteristic
39C4×C4⋊Dic83C2211yescharacteristic
40#19127464C2211yescharacteristic
41#19127464C2211yescharacteristic
42#19127464C2211yescharacteristic
43#19127464C2211yescharacteristic
44#19127464C2211yescharacteristic
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127464C2211yescharacteristic
52C2×C4×D4×C83C2211yescharacteristic
53C2×C4⋊C8×C83C2211yescharacteristic
54C2×C22⋊C8×C83C2211yescharacteristic
55C2×C22⋊C8×C83C2211yescharacteristic
56C2×C22⋊C8×C83C2211yescharacteristic
57C2×C22⋊C8×C83C2211yescharacteristic
58C2×#97×C83C2211yescharacteristic
59C23×Dic83—21no—
60C23×Dic83—21no—
61#14581784—22no—
62#14581784—22no—
63D4×Dic83—44no—
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83—21no—
67C2×C4⋊Dic83—21no—
68C2×C4⋊Dic83—21no—
69C2×C4⋊Dic83—21no—
70C2×C4⋊Dic83—41no—
71C2×C4⋊Dic83—41no—
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×C4⋊Dic83C2311yescharacteristic
77C2×C4⋊Dic83C2311yescharacteristic
78C2×C4⋊Dic83C2311yescharacteristic
79C2×C4⋊Dic83C2311yescharacteristic
80C2×Dic83⋊C4—21no—
81C2×Dic83⋊C4—21no—
82C2×C22⋊Dic83—21no—
83C2×C22⋊Dic83—21no—
84C2×C22⋊Dic83—21no—
85C2×C22⋊Dic83—21no—
86C2×C22⋊Dic83—21no—
87C2×C22⋊Dic83—21no—
88C2×C4×Dic83—21no—
89C2×C4×Dic83—21no—
90#14581726—22no—
91#14581724—22no—
92#14581724—41no—
93#14581724—41no—
94C83⋊#95—21no—
95C83⋊#95—21no—
96C83⋊#95—21no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C22×D4×C83D411yescharacteristic
103C23×C4×C83C2311yescharacteristic
104C23×C4×C83C2311yescharacteristic
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109C4×D4×C83—22no—
110C4×D4×C83—22no—
111C2×C4⋊C4×C83D411yescharacteristic
112C2×C22⋊C4×C83D411yescharacteristic
113C2×C22⋊C4×C83D411yescharacteristic
114C2×C42×C83C2311yescharacteristic
115C4⋊C8×C83—22no—
116C22⋊C8×C83—22no—
117C22⋊C8×C83—22no—
118C22⋊C8×C83—41no—
119C22⋊C8×C83—41no—
120#97×C83—22no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—21no—
129C22×Dic83—42no—
130C22×Dic83—42no—
131C22×Dic83—42no—
132C22×Dic83—42no—
133C22×Dic83—81no—
134C22×Dic83—81no—
135C4⋊Dic83—21no—
136C4⋊Dic83—21no—
137C4⋊Dic83—21no—
138C4⋊Dic83—21no—
139C4⋊Dic83—21no—
140C4⋊Dic83—21no—
141C4⋊Dic83—21no—
142C4⋊Dic83—21no—
143C4⋊Dic83—21no—
144C4⋊Dic83—21no—
145C4⋊Dic83—21no—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—42no—
151C4⋊Dic83—42no—
152C4⋊Dic83—42no—
153C4⋊Dic83—81no—
154C4⋊Dic83#4112yes—
155Dic83⋊C4—42no—
156Dic83⋊C4—42no—
157C22⋊Dic83—42no—
158C22⋊Dic83—42no—
159C22⋊Dic83—42no—
160C22⋊Dic83—42no—
161C22⋊Dic83—81no—
162C22⋊Dic83—81no—
163C4×Dic83—42no—
164C4×Dic83—81no—
165C24×C83C2×D411yescharacteristic
166C24×C83C2×D411yescharacteristic
167C2×D4×C83—22no—
168C2×D4×C83—22no—
169C2×D4×C83—22no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
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—21no—
181C22×C4×C83—21no—
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83C2×D411yescharacteristic
184C22×C4×C83C2×D411yescharacteristic
185C22×C4×C83C2×D411yescharacteristic
186C22×C4×C83C2411yescharacteristic
187C2×C8×C83—21no—
188C2×C8×C83—21no—
189C2×C8×C83—21no—
190C2×C8×C83—21no—
191C2×C8×C83—21no—
192C2×C8×C83—21no—
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83#4112yes—
199C4⋊C4×C83—22no—
200C22⋊C4×C83—22no—
201C22⋊C4×C83—22no—
202C42×C83#4112yes—
203C42×C83#4112yes—
204C23×C83—21no—
205C23×C83—21no—
206C23×C83—21no—
207C23×C83—21no—
208C23×C83—21no—
209C23×C83—21no—
210C23×C83—21no—
211C23×C83—21no—
212C23×C83—21no—
213C23×C83—21no—
214C23×C83—21no—
215C23×C83—21no—
216C23×C83AGL(1,ℤ/8)12yes—
217C23×C83#13712yes—
218C23×C83C22×D411yescharacteristic
219D4×C83—28no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
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#12312yes—
239C2×C4×C83#12312yes—
240C2×C4×C83C2×#4111yescharacteristic
241C2×C4×C83C2×#4111yescharacteristic
242C2×C4×C83C2×#4111yescharacteristic
243C2×C4×C83C2×#4111yescharacteristic
244C2×C4×C83H(5,𝔽2)11yescharacteristic
245C2×C4×C832−1+411yescharacteristic
246C2×Dic83—22no—
247C2×Dic83—41no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C2×Dic83—41no—
251C2×Dic83—41no—
252C2×Dic83—41no—
253C2×Dic83—41no—
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—
266C2×Dic83—41no—
267C2×Dic83—41no—
268C2×Dic83—41no—
269C2×Dic83—41no—
270C2×Dic83—84no—
271C2×Dic83—84no—
272C8×C83—22no—
273C8×C83—41no—
274C8×C83—41no—
275C8×C83—41no—
276C22×C83—22no—
277C22×C83—22no—
278C22×C83—22no—
279C22×C83—22no—
280C22×C83—22no—
281C22×C83—22no—
282C22×C83—41no—
283C22×C83—41no—
284C22×C83—41no—
285C22×C83—41no—
286C22×C83—41no—
287C22×C83—41no—
288C22×C83—41no—
289C22×C83—41no—
290C22×C83C2×#12311yescharacteristic
291C22×C83#54611yescharacteristic
292C22×C83#54711yescharacteristic
293C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C83C2×#13711yescharacteristic
295C22×C83#57711yescharacteristic
296C22×C83#57711yescharacteristic
297C4×C83—22no—
298C4×C83—22no—
299C4×C83—41no—
300C4×C83—41no—
301C4×C83#52911yescharacteristic
302C4×C83#54211yescharacteristic
303C4×C83#55611yescharacteristic
304C4×C83#55911yescharacteristic
305Dic83—42no—
306Dic83—81no—
307Dic83—81no—
308Dic83—81no—
309Dic83—81no—
310Dic83—81no—
311Dic83—81no—
312Dic83—81no—
313#26310—831nomaximal, Sylow
314C2×C83—42no—
315C2×C83—42no—
316C2×C83#244711yescharacteristic
317C2×C83#309211yescharacteristic
318C2×C83#309911yescharacteristic
319C2×C83#331011yescharacteristic
320C2×C83#332011yescharacteristic
321C2×C83#334411yescharacteristic
322C2×C83#334511yescharacteristic
323#2562—831no—
324D4×C4⋊C4—831no—
325#2077—831no—
326#2077—831no—
327#2076—831no—
328#2075—831no—
329#1992—831no—
330#1989—831no—
331#1955D8311yescharacteristic
332#1948—831no—
333#1853—831no—
334#1853—831no—
335#1824—831no—
336#1823—831no—
337#1776—831no—
338C83#2631011yescharacteristic, complemented, Sylow
339C2×#125—831no—
340C2×C4×D4—1661no—
341C2×C4×D4C2×D8311yescharacteristic
342C22×C4⋊C4—831no—
343C22×C4⋊C4—831no—
344C2×#107—831no—
345C2×#106—831no—
346C2×#106—831no—
347C2×#106—831no—
348C2×C4⋊C8C2×D8311yescharacteristic
349C2×C22⋊C8C2×D8311yescharacteristic
350C2×C22⋊C8C2×D8311yescharacteristic
351C2×C22⋊C8C2×D8311yescharacteristic
352C2×C22⋊C8C2×D8311yescharacteristic
353C2×#97C2×D8311yescharacteristic
354#400—1661no—
355#394—1661no—
356#389—1661no—
357#388—1661no—
358#388—1661no—
359#385—1661no—
360#385—1661no—
361#384—831no—
362#380—831no—
363#380—831no—
364#380—831no—
365#380—831no—
366#380—831no—
367#380—831no—
368C4×C4⋊C4—831no—
369C4×C4⋊C4—831no—
370#340—831no—
371#340—831no—
372#340—831no—
373#340—831no—
374#340—831no—
375#340—831no—
376#340—831no—
377#340—831no—
378#340—831no—
379#340—831no—
380#340—831no—
381#340—831no—
382C22×D4D33211yescharacteristic
383C23×C4—1661no—
384C23×C4—1661no—
385C23×C4C22×D8311yescharacteristic
386C23×C4C22×D8311yescharacteristic
387C22×C8C22×D8311yescharacteristic
388C22×C8C22×D8311yescharacteristic
389C22×C8C22×D8311yescharacteristic
390C22×C8C22×D8311yescharacteristic
391#125—1662no—
392#125—1662no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—3324no—
396C2×C4⋊C4—3321no—
397C2×C4⋊C4—3321no—
398C2×C4⋊C4—831no—
399C2×C4⋊C4—831no—
400C2×C4⋊C4—831no—
401C2×C4⋊C4—831no—
402C2×C4⋊C4—831no—
403C2×C4⋊C4—831no—
404C2×C4⋊C4—831no—
405C2×C4⋊C4—831no—
406C2×C4⋊C4—1661no—
407C2×C4⋊C4—1661no—
408C2×C4⋊C4—1661no—
409C2×C4⋊C4—1661no—
410C2×C4⋊C4—1661no—
411C2×C4⋊C4—1662no—
412C2×C4⋊C4—1662no—
413C2×C4⋊C4—1661no—
414C2×C4⋊C4D33211yescharacteristic
415C2×C22⋊C4—1661no—
416C2×C22⋊C4—1661no—
417C2×C22⋊C4—1661no—
418C2×C22⋊C4—1661no—
419C2×C22⋊C4—1661no—
420C2×C22⋊C4—1661no—
421C2×C22⋊C4D33211yescharacteristic
422C2×C22⋊C4D33211yescharacteristic
423C2×C42—1661no—
424C2×C42—1661no—
425C2×C42C22×D8311yescharacteristic
426#107—1662no—
427#106—3321no—
428#106—3321no—
429#106—1662no—
430C4⋊C8—22no—
431C22⋊C8—22no—
432C22⋊C8—22no—
433C22⋊C8—41no—
434C22⋊C8—41no—
435#97—22no—
436#95—1661no—
437#95—1661no—
438#95—1661no—
439#95—1661no—
440#95—1661no—
441#95—1661no—
442#95—1661no—
443#95—1661no—
444C24C2×D33211yescharacteristic
445C24C2×D33211yescharacteristic
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—3322no—
462C22×C4—3322no—
463C22×C4—3322no—
464C22×C4—3322no—
465C22×C4—6641no—
466C22×C4—6641no—
467C22×C4—1661no—
468C22×C4—1661no—
469C22×C4—1661no—
470C22×C4—1661no—
471C22×C4—1661no—
472C22×C4—1661no—
473C22×C4—1661no—
474C22×C4—1661no—
475C22×C4C2×D33211yescharacteristic
476C22×C4C2×D33211yescharacteristic
477C22×C4C2×D33211yescharacteristic
478C22×C4C2×D33211yescharacteristic
479C22×C4C23×D8311yescharacteristic
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8#1305058912yes—
492C4⋊C4—22no—
493C4⋊C4—3322no—
494C4⋊C4—3322no—
495C4⋊C4—3322no—
496C4⋊C4—3322no—
497C4⋊C4—3322no—
498C4⋊C4—832no—
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⋊C4—1661no—
509C4⋊C4—1661no—
510C4⋊C4—1661no—
511C4⋊C4—1661no—
512C4⋊C4—1661no—
513C4⋊C4—1661no—
514C4⋊C4—1661no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—3322no—
518C22⋊C4—3322no—
519C22⋊C4—3322no—
520C22⋊C4—3322no—
521C22⋊C4—6641no—
522C22⋊C4—6641no—
523C42—3322no—
524C42—6641no—
525C42#1305058912yes—
526C42#1305058912yes—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23#1458182012yes—
540C23#1458182512yes—
541C23C22×D33211yescharacteristic
542D4—28no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—3321no—
562C2×C4—3321no—
563C2×C4—3321no—
564C2×C4—3321no—
565C2×C4—3321no—
566C2×C4—3321no—
567C2×C4—3321no—
568C2×C4—3321no—
569C2×C4—3321no—
570C2×C4—3321no—
571C2×C4—3321no—
572C2×C4—3321no—
573C2×C4—3321no—
574C2×C4—3321no—
575C2×C4—3321no—
576C2×C4—3321no—
577C2×C4—3321no—
578C2×C4—3321no—
579C2×C4—3321no—
580C2×C4—3321no—
581C2×C4—3321no—
582C2×C4—3321no—
583C2×C4—3321no—
584C2×C4—6644no—
585C2×C4—6644no—
586C2×C4—1662no—
587C2×C4#1458177612yes—
588C2×C4#1458177612yes—
589C2×C4#41×D8311yescharacteristic
590C2×C4C2×#1305058911yescharacteristic
591C2×C4C2×#1305058911yescharacteristic
592C2×C4C2×#1305058911yescharacteristic
593C2×C4#1458183711yescharacteristic
594C2×C4#1458183911yescharacteristic
595C8—22no—
596C8—41no—
597C8—41no—
598C8—41no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22C2×#1458177611yescharacteristic
614C22#1912834611yescharacteristic
615C22#1912835511yescharacteristic
616C22C2×#1458182011yescharacteristic
617C22C2×#1458182511yescharacteristic
618C22#1912851311yescharacteristic
619C22#1912851311yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—3322no—
625C4—6641no—
626C4—6641no—
627C4—6641no—
628C4—6641no—
629C4—6641no—
630C4—6641no—
631C4—6641no—
632C4#1912823211yescharacteristic
633C4#1912831811yescharacteristic
634C4#1912842011yescharacteristic
635C4#1912843711yescharacteristic
636C2—42no—
637C2—42no—
638C2#2491124811yescharacteristic
639C2#2491738811yescharacteristic
640C2#2491745411yescharacteristic
641C2#2491948611yescharacteristic
642C2#2491963611yescharacteristic
643C2#2491992011yescharacteristic
644C2#2491993511yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#1955C2
socleC23×C83C22×D4
prime radicalC22×D4×C83D4
hypercenter#1955D83
hypocenterC83#26310
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1955

Complements

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

NH ≅ G/Ntype
3. #24908896C2semidirect
4. #24908896C2semidirect
5. #24908891C2semidirect
6. #24908886C2semidirect
7. #24908432C2semidirect
8. #24908418C2semidirect
9. #24908227C2semidirect
10. #24907658C2semidirect
11. #24907658C2semidirect
12. #24907554C2semidirect
13. #24907550C2semidirect
14. #24907360C2semidirect
338. C83#26310semidirect

Maximal subgroups

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

subgroupindex
#249126292
D4×C4⋊Dic832
#249088962
#249088912
#249088862
#249084322
#249084182
#249082272
#249076582
#249075542
#249075502
#249073602
C83×#19552
#2631083