Finite Group Databasebeta

← #35462691

Subgroups — #35462691

Order 21248.

744 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910434C211yesmaximal, characteristic
2#24908848C211yesmaximal, characteristic
3#24908834C211yesmaximal, characteristic
4#24908596C211yesmaximal, characteristic
5#24908596C211yesmaximal, characteristic
6#24908416C211yesmaximal, characteristic, complemented
7#24908412C211yesmaximal, characteristic, complemented
8#24908231C211yesmaximal, characteristic, complemented
9#24908187C211yesmaximal, characteristic, complemented
10#24908052C211yesmaximal, characteristic, complemented
11#24908038C211yesmaximal, characteristic, complemented
12#24907598C211yesmaximal, characteristic, complemented
13#24907460C211yesmaximal, characteristic
14#24907291C211yesmaximal, characteristic
15C83×#2551C211yesmaximal, characteristic, complemented
16C2×C4×D332C2211yescharacteristic
17C2×#14581725C2211yescharacteristic
18C2×#14581723C2211yescharacteristic
19C2×C4⋊(C83⋊C8)C2211yescharacteristic
20C2×C4⋊(C83⋊C8)C2211yescharacteristic
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22C2×#14581712C2211yescharacteristic
23C2×#14581712C2211yescharacteristic
24C2×#14581712C2211yescharacteristic
25C2×#14581712C2211yescharacteristic
26C2×#14581703C2211yescharacteristic
27#19127603C2211yescharacteristic
28#19127603C2211yescharacteristic
29#19127591—21no—
30#19127591—21no—
31#19127567C2211yescharacteristic
32#19127563—21no—
33C4×C4⋊Dic83C2211yescharacteristic
34C4×C4⋊Dic83C2211yescharacteristic
35#19127548—21no—
36#19127463C2211yescharacteristic
37#19127463C2211yescharacteristic
38#19127463C2211yescharacteristic
39#19127463C2211yescharacteristic
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127456C2211yescharacteristic
47#19127456C2211yescharacteristic
48C2×C4⋊Q8×C83—21no—
49C2×C4⋊Q8×C83C2211yescharacteristic
50C2×C4⋊Q8×C83C2211yescharacteristic
51#395×C83—21no—
52#395×C83—21no—
53#389×C83—21no—
54#389×C83C2211yescharacteristic
55#389×C83C2211yescharacteristic
56#384×C83C2211yescharacteristic
57C4×C4⋊C4×C83C2211yescharacteristic
58C4×C4⋊C4×C83C2211yescharacteristic
59C22×D332C2311yescharacteristic
60C22×C4×D83—21no—
61C22×C83⋊C8C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65C4×D332—22no—
66C4×D332Q814yescomplemented
67C2×C4⋊Dic83C2311yescharacteristic
68C2×C4⋊Dic83C2311yescharacteristic
69C2×C4⋊Dic83C2311yescharacteristic
70C2×(C2×D83)⋊C4—21no—
71C2×(C2×D83)⋊C4—21no—
72C2×(C2×D83)⋊C4—21no—
73C2×(C2×D83)⋊C4—21no—
74C2×(C2×D83)⋊C4—21no—
75C2×C4×Dic83—21no—
76C2×C4×Dic83—21no—
77#14581725—22no—
78#14581723—22no—
79C4⋊(C83⋊C8)—22no—
80C4⋊(C83⋊C8)—41no—
81C4⋊(C83⋊C8)—41no—
82#14581712—22no—
83#14581712—22no—
84#14581712—41no—
85#14581712—41no—
86#14581703—22no—
87C83⋊#95—21no—
88C83⋊#95—21no—
89C83⋊#95—21no—
90C83⋊#95—21no—
91C22×Q8×C83—21no—
92C22×Q8×C83—21no—
93C4⋊Q8×C83—22no—
94C4⋊Q8×C83—22no—
95C4⋊Q8×C83—41no—
96C4⋊Q8×C83—41no—
97C4⋊Q8×C83—44no—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83—21no—
100C2×C4⋊C4×C83—21no—
101C2×C4⋊C4×C83—21no—
102C2×C4⋊C4×C83—21no—
103C2×C4⋊C4×C83—21no—
104C2×C4⋊C4×C83D411yescharacteristic
105C2×C4⋊C4×C83D411yescharacteristic
106C2×C4⋊C4×C83C2311yescharacteristic
107C2×C4⋊C4×C83C2311yescharacteristic
108C2×C4⋊C4×C83C2311yescharacteristic
109C2×C4⋊C4×C83C2311yescharacteristic
110C2×C42×C83—21no—
111C2×C42×C83C2311yescharacteristic
112C2×C42×C83C2311yescharacteristic
113C2×C42×C83C2311yescharacteristic
114#95×C83—21no—
115#95×C83—21no—
116#95×C83—21no—
117#95×C83D411yescharacteristic
118#95×C83D411yescharacteristic
119C23×D83—21no—
120C2×D332—21no—
121C2×D332—21no—
122C2×D332—21no—
123C2×D332—21no—
124C2×D332—21no—
125C2×D332C2×Q812yes—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—21no—
129C2×C4×D83—24no—
130C2×C4×D83—81no—
131C2×C4×D83—81no—
132C2×C83⋊C8—21no—
133C2×C83⋊C8—21no—
134C2×C83⋊C8—21no—
135C2×C83⋊C8—21no—
136C2×C83⋊C8—21no—
137C2×C83⋊C8—21no—
138C2×C83⋊C8—21no—
139C2×C83⋊C8—21no—
140C2×C83⋊C8—21no—
141C2×C83⋊C8—21no—
142C2×C83⋊C8—21no—
143C2×C83⋊C8—21no—
144C4⋊Dic83—21no—
145C4⋊Dic83—21no—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83C2×Q812yes—
150(C2×D83)⋊C4—24no—
151(C2×D83)⋊C4—42no—
152(C2×D83)⋊C4—42no—
153(C2×D83)⋊C4—81no—
154(C2×D83)⋊C4—81no—
155C4×Dic83—81no—
156C4×Dic83—81no—
157C2×Q8×C83—42no—
158C2×Q8×C83—42no—
159C2×Q8×C83—42no—
160C2×Q8×C83—42no—
161C2×Q8×C83—81no—
162C2×Q8×C83—81no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2×D411yescharacteristic
171C22×C4×C83C2×D411yescharacteristic
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2411yescharacteristic
174C4⋊C4×C83—22no—
175C4⋊C4×C83—22no—
176C4⋊C4×C83—21no—
177C4⋊C4×C83—21no—
178C4⋊C4×C83—21no—
179C4⋊C4×C83—21no—
180C4⋊C4×C83—21no—
181C4⋊C4×C83—21no—
182C4⋊C4×C83—42no—
183C4⋊C4×C83—42no—
184C4⋊C4×C83—42no—
185C4⋊C4×C83—42no—
186C4⋊C4×C83—42no—
187C4⋊C4×C83—81no—
188C4⋊C4×C83#4112yes—
189C4⋊C4×C83#4112yes—
190C42×C83—21no—
191C42×C83—21no—
192C42×C83—21no—
193C42×C83—21no—
194C42×C83—42no—
195C42×C83C2×Q812yes—
196C42×C83#4112yes—
197C23×C83C22×D411yescharacteristic
198C22×D83—22no—
199C22×D83—41no—
200C22×D83—41no—
201C22×D83—41no—
202C22×D83—41no—
203C22×D83—41no—
204C22×D83—41no—
205Q8×C83—84no—
206Q8×C83—84no—
207C2×C4×C83—21no—
208C2×C4×C83—21no—
209C2×C4×C83—21no—
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—22no—
218C2×C4×C83—22no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
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×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83C22⋊Q812yes—
234C2×C4×C83C22⋊Q812yes—
235C2×C4×C83AGL(1,ℤ/8)12yes—
236C2×C4×C83#13712yes—
237C2×C4×C83C22×Q811yescharacteristic
238C2×C4×C83C2×#4111yescharacteristic
239C2×C4×C83C2×#4111yescharacteristic
240C2×C4×C83C2×#4111yescharacteristic
241C2×C4×C83H(5,𝔽2)11yescharacteristic
242C2×C4×C832−1+411yescharacteristic
243C2×Dic83—22no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C2×Dic83—41no—
251C2×Dic83—41no—
252D332—22no—
253D332—22no—
254D332—41no—
255D332—41no—
256C4×D83—84no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C83⋊C8—41no—
260C83⋊C8—41no—
261C22×C83C2×C22⋊Q811yescharacteristic
262C22×C83#54611yescharacteristic
263C22×C83#54811yescharacteristic
264C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C83C2×#13711yescharacteristic
266C22×C83#57611yescharacteristic
267C22×C83#57711yescharacteristic
268C2×D83—42no—
269C2×D83—42no—
270C2×D83—42no—
271C2×D83—81no—
272C2×D83—81no—
273C2×D83—81no—
274C2×D83—81no—
275C4×C83—22no—
276C4×C83—22no—
277C4×C83—22no—
278C4×C83—22no—
279C4×C83—42no—
280C4×C83—41no—
281C4×C83—42no—
282C4×C83—41no—
283C4×C83—81no—
284C4×C83—81no—
285C4×C83#53311yescharacteristic
286C4×C83#54411yescharacteristic
287C4×C83#55511yescharacteristic
288C4×C83#55611yescharacteristic
289Dic83—42no—
290Dic83—81no—
291Dic83—81no—
292#26036—831nomaximal, Sylow
293C2×C83#243911yescharacteristic
294C2×C83#307911yescharacteristic
295C2×C83#308111yescharacteristic
296C2×C83#331811yescharacteristic
297C2×C83#332011yescharacteristic
298C2×C83#337311yescharacteristic
299C2×C83#337511yescharacteristic
300D83—82no—
301#2551D8311yescharacteristic, complemented
302#2357—831no—
303#2067—831no—
304#2065—831no—
305#2023—831no—
306#2023—831no—
307#1988—831no—
308#1987—831no—
309#1949—831no—
310#1940—831no—
311#1921—831no—
312#1919—831no—
313#1836—831no—
314#1802—831no—
315#1762—831no—
316C83#2603611yescharacteristic, complemented, Sylow
317C2×C4⋊Q8—21no—
318C2×C4⋊Q8C2×D8311yescharacteristic
319C2×C4⋊Q8C2×D8311yescharacteristic
320C2×C4×D4—831no—
321C2×#107—831no—
322C2×#106—831no—
323C2×C4⋊C8—831no—
324C2×C4⋊C8—831no—
325C2×C4⋊C8—831no—
326C2×#102—831no—
327C2×#102—831no—
328C2×#102—831no—
329C2×#102—831no—
330C2×#97—831no—
331#395—21no—
332#395—21no—
333#390—831no—
334#390—831no—
335#389—21no—
336#389C2×D8311yescharacteristic
337#389C2×D8311yescharacteristic
338#388—1661no—
339#388—1661no—
340#384C2×D8311yescharacteristic
341#382—831no—
342#381—1661no—
343C4×C4⋊C4—831no—
344C4×C4⋊C4—831no—
345C4×C4⋊C4C2×D8311yescharacteristic
346C4×C4⋊C4C2×D8311yescharacteristic
347C4×C22⋊C4—1661no—
348#340—831no—
349#340—831no—
350#340—831no—
351#340—831no—
352#340—831no—
353#340—831no—
354#340—831no—
355#340—831no—
356#340—831no—
357#340—831no—
358#336—831no—
359#336—831no—
360C22×Q8—21no—
361C22×Q8—21no—
362C22×D4—831no—
363C23×C4—1661no—
364C22×C8—831no—
365C22×C8—831no—
366C22×C8—831no—
367C22×C8—831no—
368C4⋊Q8—22no—
369C4⋊Q8—22no—
370C4⋊Q8—41no—
371C4⋊Q8—41no—
372C4⋊Q8—44no—
373C4×D4—834no—
374C4×D4—1662no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—831no—
382C2×C4⋊C4—831no—
383C2×C4⋊C4—831no—
384C2×C4⋊C4C22⋊D8311yescharacteristic
385C2×C4⋊C4C22⋊D8311yescharacteristic
386C2×C4⋊C4C22×D8311yescharacteristic
387C2×C4⋊C4C22×D8311yescharacteristic
388C2×C4⋊C4C22×D8311yescharacteristic
389C2×C4⋊C4C22×D8311yescharacteristic
390C2×C22⋊C4—1661no—
391C2×C22⋊C4—1661no—
392C2×C22⋊C4—1661no—
393C2×C22⋊C4—1661no—
394C2×C22⋊C4—1661no—
395C2×C42—21no—
396C2×C42—1661no—
397C2×C42—1661no—
398C2×C42C22×D8311yescharacteristic
399C2×C42C22×D8311yescharacteristic
400C2×C42C22×D8311yescharacteristic
401#107—1662no—
402#106—1662no—
403C4⋊C8—3321no—
404C4⋊C8—3321no—
405C4⋊C8—1662no—
406#102—3321no—
407#102—3321no—
408#102—1662no—
409#102—1662no—
410#97—1662no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—1661no—
415#95—1661no—
416#95—1661no—
417#95—1661no—
418#95C22⋊D8311yescharacteristic
419#95C22⋊D8311yescharacteristic
420C24—1661no—
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—42no—
425C2×Q8—81no—
426C2×Q8—81no—
427C2×D4—832no—
428C2×D4—1661no—
429C2×D4—1661no—
430C2×D4—1661no—
431C2×D4—1661no—
432C2×D4—1661no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—6641no—
438C22×C4—6641no—
439C22×C4—1661no—
440C22×C4—1661no—
441C22×C4—1661no—
442C22×C4—1664no—
443C22×C4C2×C22⋊D8311yescharacteristic
444C22×C4C2×C22⋊D8311yescharacteristic
445C22×C4C2×C22⋊D8311yescharacteristic
446C22×C4C2×C22⋊D8311yescharacteristic
447C22×C4C2×C22⋊D8311yescharacteristic
448C22×C4C2×C22⋊D8311yescharacteristic
449C22×C4C23×D8311yescharacteristic
450C2×C8—1661no—
451C2×C8—1661no—
452C2×C8—1661no—
453C2×C8—1661no—
454C2×C8—1661no—
455C2×C8—1661no—
456C2×C8—1661no—
457C2×C8—1661no—
458C2×C8—1661no—
459C2×C8—1661no—
460C2×C8—1661no—
461C2×C8—1661no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—81no—
476C4⋊C4—832no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4—1661no—
482C4⋊C4#1305058912yes—
483C4⋊C4#1305059112yes—
484C22⋊C4—3322no—
485C22⋊C4—3322no—
486C22⋊C4—6641no—
487C22⋊C4—6641no—
488C22⋊C4—1664no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—42no—
494C42—6641no—
495C42—6641no—
496C42Q8×D8312yes—
497C42#1305059112yes—
498C23—3321no—
499C23—3321no—
500C23—3321no—
501C23—3321no—
502C23—3321no—
503C23—3321no—
504C23—1662no—
505C23C22×C22⋊D8311yescharacteristic
506Q8—84no—
507Q8—84no—
508D4—3321no—
509D4—3321no—
510D4—1662no—
511D4—1662no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—3321no—
539C2×C4—3321no—
540C2×C4—3321no—
541C2×C4—3321no—
542C2×C4—3321no—
543C2×C4—3321no—
544C2×C4—3321no—
545C2×C4—3321no—
546C2×C4—6644no—
547C2×C4—1662no—
548C2×C4#1458176812yes—
549C2×C4#1458176812yes—
550C2×C4#1458181812yes—
551C2×C4#1458182312yes—
552C2×C4C2×Q8×D8311yescharacteristic
553C2×C4C2×#1305058911yescharacteristic
554C2×C4C2×#1305059111yescharacteristic
555C2×C4C2×#1305059111yescharacteristic
556C2×C4#1458183711yescharacteristic
557C2×C4#1458184011yescharacteristic
558C8—3321no—
559C8—3321no—
560C8—3321no—
561C8—3321no—
562C22—3322no—
563C22—3322no—
564C22—3322no—
565C22—6641no—
566C22—6641no—
567C22—6641no—
568C22—6641no—
569C22C2×#1458176811yescharacteristic
570C22#1912834511yescharacteristic
571C22#1912836211yescharacteristic
572C22C2×#1458181811yescharacteristic
573C22C2×#1458182311yescharacteristic
574C22#1912850411yescharacteristic
575C22#1912850911yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—22no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—3322no—
587C4—6641no—
588C4—6641no—
589C4#1912825611yescharacteristic
590C4#1912832811yescharacteristic
591C4#1912841711yescharacteristic
592C4#1912842511yescharacteristic
593C2—6642no—
594C2#2491115011yescharacteristic
595C2#2491727211yescharacteristic
596C2#2491728811yescharacteristic
597C2#2491960411yescharacteristic
598C2#2491963411yescharacteristic
599C2#2492025511yescharacteristic
600C2#2492027711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2551C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenter#2551D83
hypocenterC83#26036
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
6. #24908416C2semidirect
7. #24908412C2semidirect
8. #24908231C2semidirect
9. #24908187C2semidirect
10. #24908052C2semidirect
11. #24908038C2semidirect
12. #24907598C2semidirect
15. C83×#2551C2semidirect
66. C4×D332Q8semidirect
301. #2551D83semidirect
316. C83#26036semidirect

Maximal subgroups

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

subgroupindex
#249104342
#249088482
#249088342
#249085962
#249084162
#249084122
#249082312
#249081872
#249080522
#249080382
#249075982
#249074602
#249072912
C83×#25512
#2603683