Finite Group Databasebeta

← #35466511

Subgroups — #35466511

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
2#24908900C211yesmaximal, characteristic, complemented
3#24908899C211yesmaximal, characteristic, complemented
4#24908894C211yesmaximal, characteristic, complemented
5#24908889C211yesmaximal, characteristic, complemented
6#24908431C211yesmaximal, characteristic, complemented
7#24908420C211yesmaximal, characteristic, complemented
8#24908262C211yesmaximal, characteristic
9#24908224C211yesmaximal, characteristic, complemented
10#24907656C211yesmaximal, characteristic, complemented
11#24907656C211yesmaximal, characteristic, complemented
12#24907553C211yesmaximal, characteristic, complemented
13#24907549C211yesmaximal, characteristic, complemented
14#24907361C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C83C211yesmaximal, characteristic
16C2×#14581784C2211yescharacteristic
17C2×#14581725C2211yescharacteristic
18C2×#14581723C2211yescharacteristic
19C2×#14581723C2211yescharacteristic
20C2×#14581723C2211yescharacteristic
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×C22⋊(C83⋊C8)C2211yescharacteristic
23C2×C22⋊(C83⋊C8)C2211yescharacteristic
24C2×C22⋊(C83⋊C8)C2211yescharacteristic
25C2×C22⋊(C83⋊C8)C2211yescharacteristic
26C2×#14581703C2211yescharacteristic
27#19127639—21no—
28#19127615—21no—
29#19127595—21no—
30#19127595—21no—
31#19127561C2211yescharacteristic
32#19127561C2211yescharacteristic
33#19127561C2211yescharacteristic
34#19127561C2211yescharacteristic
35C4×C4⋊Dic83C2211yescharacteristic
36#19127463C2211yescharacteristic
37#19127463C2211yescharacteristic
38#19127463C2211yescharacteristic
39#19127463C2211yescharacteristic
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48C2×C4×D4×C83—21no—
49C2×C4×D4×C83C2211yescharacteristic
50C22×C4⋊C4×C83C2211yescharacteristic
51C22×C4⋊C4×C83C2211yescharacteristic
52#389×C83—21no—
53#385×C83—21no—
54#385×C83—21no—
55#384×C83C2211yescharacteristic
56#380×C83C2211yescharacteristic
57#380×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59C22×C83⋊C8C2311yescharacteristic
60C22×C83⋊C8C2311yescharacteristic
61C22×C83⋊C8C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63#14581784—22no—
64#14581784—22no—
65C2×C4⋊Dic83C2311yescharacteristic
66C2×C4⋊Dic83C2311yescharacteristic
67C2×C4⋊Dic83C2311yescharacteristic
68C2×C4⋊Dic83C2311yescharacteristic
69C2×Dic83⋊C4—21no—
70C2×Dic83⋊C4—21no—
71C2×C22⋊Dic83—21no—
72C2×C22⋊Dic83—21no—
73C2×C22⋊Dic83—21no—
74C2×C22⋊Dic83—21no—
75C2×C4×Dic83—21no—
76#14581725—22no—
77#14581723—22no—
78#14581723—41no—
79#14581723—41no—
80C4⋊(C83⋊C8)—22no—
81C22⋊(C83⋊C8)—22no—
82C22⋊(C83⋊C8)—22no—
83C22⋊(C83⋊C8)—41no—
84C22⋊(C83⋊C8)—41no—
85#14581703—22no—
86C83⋊#95—21no—
87C83⋊#95—21no—
88C83⋊#95—21no—
89C83⋊#95—21no—
90C83⋊#95—21no—
91C22×D4×C83D411yescharacteristic
92C23×C4×C83—21no—
93C23×C4×C83—21no—
94C23×C4×C83C2311yescharacteristic
95C23×C4×C83C2311yescharacteristic
96C4×D4×C83—22no—
97C4×D4×C83—22no—
98C4×D4×C83—44no—
99C2×C4⋊C4×C83—22no—
100C2×C4⋊C4×C83—22no—
101C2×C4⋊C4×C83—21no—
102C2×C4⋊C4×C83—21no—
103C2×C4⋊C4×C83—21no—
104C2×C4⋊C4×C83—21no—
105C2×C4⋊C4×C83—41no—
106C2×C4⋊C4×C83—41no—
107C2×C4⋊C4×C83D411yescharacteristic
108C2×C4⋊C4×C83C2311yescharacteristic
109C2×C4⋊C4×C83C2311yescharacteristic
110C2×C4⋊C4×C83C2311yescharacteristic
111C2×C4⋊C4×C83C2311yescharacteristic
112C2×C22⋊C4×C83—21no—
113C2×C22⋊C4×C83—21no—
114C2×C22⋊C4×C83D411yescharacteristic
115C2×C22⋊C4×C83D411yescharacteristic
116C2×C42×C83—21no—
117C2×C42×C83C2311yescharacteristic
118#95×C83—21no—
119#95×C83—21no—
120#95×C83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—21no—
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⋊C8—21no—
134C2×C83⋊C8—21no—
135C2×C83⋊C8—21no—
136C2×C83⋊C8#4112yes—
137C4⋊Dic83—21no—
138C4⋊Dic83—21no—
139C4⋊Dic83—21no—
140C4⋊Dic83—21no—
141C4⋊Dic83—21no—
142C4⋊Dic83—21no—
143C4⋊Dic83—21no—
144C4⋊Dic83—21no—
145Dic83⋊C4—42no—
146Dic83⋊C4—42no—
147C22⋊Dic83—42no—
148C22⋊Dic83—42no—
149C22⋊Dic83—81no—
150C22⋊Dic83—81no—
151C4×Dic83—81no—
152C24×C83C2×D411yescharacteristic
153C24×C83C2×D411yescharacteristic
154C2×D4×C83—22no—
155C2×D4×C83—22no—
156C2×D4×C83—22no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—42no—
174C22×C4×C83—42no—
175C22×C4×C83—42no—
176C22×C4×C83—42no—
177C22×C4×C83—81no—
178C22×C4×C83—81no—
179C22×C4×C83C2×D411yescharacteristic
180C22×C4×C83C2×D411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83C2411yescharacteristic
184C4⋊C4×C83—22no—
185C4⋊C4×C83—21no—
186C4⋊C4×C83—21no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—42no—
193C4⋊C4×C83—42no—
194C4⋊C4×C83—42no—
195C4⋊C4×C83—81no—
196C4⋊C4×C83#4112yes—
197C22⋊C4×C83—22no—
198C22⋊C4×C83—22no—
199C22⋊C4×C83—42no—
200C22⋊C4×C83—42no—
201C42×C83—42no—
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—22no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
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—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—41no—
244C2×C4×C83—41no—
245C2×C4×C83—41no—
246C2×C4×C83—41no—
247C2×C4×C83—41no—
248C2×C4×C83—41no—
249C2×C4×C83—41no—
250C2×C4×C83—84no—
251C2×C4×C83—84no—
252C2×C4×C83#12312yes—
253C2×C4×C83#12312yes—
254C2×C4×C83C2×#4111yescharacteristic
255C2×C4×C83C2×#4111yescharacteristic
256C2×C4×C83C2×#4111yescharacteristic
257C2×C4×C83C2×#4111yescharacteristic
258C2×C4×C83H(5,𝔽2)11yescharacteristic
259C2×C4×C832−1+411yescharacteristic
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—41no—
271C2×Dic83—41no—
272C83⋊C8—22no—
273C83⋊C8—41no—
274C83⋊C8—41no—
275C83⋊C8—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—42no—
302C4×C83—81no—
303C4×C83—81no—
304C4×C83—81no—
305C4×C83#52911yescharacteristic
306C4×C83#54211yescharacteristic
307C4×C83#55611yescharacteristic
308C4×C83#55911yescharacteristic
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⋊C4D8311yescharacteristic
325#2077—831no—
326#2077—831no—
327#2076—831no—
328#2075—831no—
329#1992—831no—
330#1989—831no—
331#1955—831no—
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—21no—
341C2×C4×D4C2×D8311yescharacteristic
342C22×C4⋊C4C2×D8311yescharacteristic
343C22×C4⋊C4C2×D8311yescharacteristic
344C2×#107—831no—
345C2×#106—831no—
346C2×#106—831no—
347C2×#106—831no—
348C2×C4⋊C8—831no—
349C2×C22⋊C8—831no—
350C2×C22⋊C8—831no—
351C2×C22⋊C8—831no—
352C2×C22⋊C8—831no—
353C2×#97—831no—
354#400—1661no—
355#394—1661no—
356#389—21no—
357#388—1661no—
358#388—1661no—
359#385—21no—
360#385—21no—
361#384C2×D8311yescharacteristic
362#380—831no—
363#380—831no—
364#380—831no—
365#380—831no—
366#380C2×D8311yescharacteristic
367#380C2×D8311yescharacteristic
368C4×C4⋊C4—831no—
369C4×C4⋊C4C2×D8311yescharacteristic
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×D4C22⋊D8311yescharacteristic
383C23×C4—21no—
384C23×C4—21no—
385C23×C4C22×D8311yescharacteristic
386C23×C4C22×D8311yescharacteristic
387C22×C8—831no—
388C22×C8—831no—
389C22×C8—831no—
390C22×C8—831no—
391#125—1662no—
392#125—1662no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—44no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4—831no—
405C2×C4⋊C4—831no—
406C2×C4⋊C4—831no—
407C2×C4⋊C4—831no—
408C2×C4⋊C4—1661no—
409C2×C4⋊C4—1661no—
410C2×C4⋊C4C22⋊D8311yescharacteristic
411C2×C4⋊C4C22×D8311yescharacteristic
412C2×C4⋊C4C22×D8311yescharacteristic
413C2×C4⋊C4C22×D8311yescharacteristic
414C2×C4⋊C4C22×D8311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—1661no—
418C2×C22⋊C4—1661no—
419C2×C22⋊C4—1661no—
420C2×C22⋊C4—1661no—
421C2×C22⋊C4C22⋊D8311yescharacteristic
422C2×C22⋊C4C22⋊D8311yescharacteristic
423C2×C42—21no—
424C2×C42—1661no—
425C2×C42C22×D8311yescharacteristic
426#107—1662no—
427#106—3321no—
428#106—3321no—
429#106—1662no—
430C4⋊C8—1662no—
431C22⋊C8—3321no—
432C22⋊C8—3321no—
433C22⋊C8—1662no—
434C22⋊C8—1662no—
435#97—1662no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—1661no—
440#95—1661no—
441#95—1661no—
442#95—1661no—
443#95—1661no—
444C24C2×C22⋊D8311yescharacteristic
445C24C2×C22⋊D8311yescharacteristic
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—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—81no—
470C22×C4—81no—
471C22×C4—1661no—
472C22×C4—1661no—
473C22×C4—1661no—
474C22×C4—1661no—
475C22×C4C2×C22⋊D8311yescharacteristic
476C22×C4C2×C22⋊D8311yescharacteristic
477C22×C4C2×C22⋊D8311yescharacteristic
478C22×C4C2×C22⋊D8311yescharacteristic
479C22×C4C23×D8311yescharacteristic
480C2×C8—832no—
481C2×C8—1661no—
482C2×C8—1661no—
483C2×C8—1661no—
484C2×C8—1661no—
485C2×C8—1661no—
486C2×C8—1661no—
487C2×C8—1661no—
488C2×C8—1661no—
489C2×C8—1661no—
490C2×C8—1661no—
491C2×C8—1661no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—81no—
504C4⋊C4—3322no—
505C4⋊C4—3322no—
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#1305058912yes—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—3322no—
520C22⋊C4—3322no—
521C22⋊C4—6641no—
522C22⋊C4—6641no—
523C42—42no—
524C42—6641no—
525C42#1305059012yes—
526C42#1305059012yes—
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#1458181812yes—
540C23#1458182312yes—
541C23C22×C22⋊D8311yescharacteristic
542D4—28no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4—84no—
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—3321no—
585C2×C4—3321no—
586C2×C4—3321no—
587C2×C4#1458177512yes—
588C2×C4#1458177512yes—
589C2×C4#41×D8311yescharacteristic
590C2×C4C2×#1305058911yescharacteristic
591C2×C4C2×#1305059011yescharacteristic
592C2×C4C2×#1305059011yescharacteristic
593C2×C4#1458183711yescharacteristic
594C2×C4#1458183911yescharacteristic
595C8—3321no—
596C8—3321no—
597C8—3321no—
598C8—1662no—
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×#1458177511yescharacteristic
614C22#1912834511yescharacteristic
615C22#1912835011yescharacteristic
616C22C2×#1458181811yescharacteristic
617C22C2×#1458182311yescharacteristic
618C22#1912850911yescharacteristic
619C22#1912851211yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—81no—
626C4—81no—
627C4—81no—
628C4—6641no—
629C4—6641no—
630C4—6641no—
631C4—6641no—
632C4#1912823311yescharacteristic
633C4#1912831611yescharacteristic
634C4#1912842111yescharacteristic
635C4#1912843411yescharacteristic
636C2—42no—
637C2—42no—
638C2#2491124411yescharacteristic
639C2#2491738611yescharacteristic
640C2#2491745211yescharacteristic
641C2#2491948411yescharacteristic
642C2#2491963411yescharacteristic
643C2#2491991211yescharacteristic
644C2#2491993311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingD4×C4⋊C4×C83C2
socleC23×C83C22×D4
prime radicalC22×D4×C83D4
hypercenterD4×C4⋊C4D83
hypocenterC83#26310
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #24908900C2semidirect
3. #24908899C2semidirect
4. #24908894C2semidirect
5. #24908889C2semidirect
6. #24908431C2semidirect
7. #24908420C2semidirect
9. #24908224C2semidirect
10. #24907656C2semidirect
11. #24907656C2semidirect
12. #24907553C2semidirect
13. #24907549C2semidirect
14. #24907361C2semidirect
338. C83#26310semidirect

Maximal subgroups

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

subgroupindex
#249126292
#249089002
#249088992
#249088942
#249088892
#249084312
#249084202
#249082622
#249082242
#249076562
#249075532
#249075492
#249073612
D4×C4⋊C4×C832
#2631083