Finite Group Databasebeta

← #35462648

Subgroups — #35462648

Order 21248.

736 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912484C211yesmaximal, characteristic, complemented
2#24910410C211yesmaximal, characteristic
3#24908850C211yesmaximal, characteristic
4#24908850C211yesmaximal, characteristic
5#24908610C211yesmaximal, characteristic
6#24908600C211yesmaximal, characteristic
7#24908418C211yesmaximal, characteristic, complemented
8#24908410C211yesmaximal, characteristic, complemented
9#24908222C211yesmaximal, characteristic, complemented
10#24908056C211yesmaximal, characteristic, complemented
11#24908035C211yesmaximal, characteristic, complemented
12#24907597C211yesmaximal, characteristic, complemented
13#24907474C211yesmaximal, characteristic
14#24907289C211yesmaximal, characteristic
15C83×#1940C211yesmaximal, characteristic, complemented
16C2×#14581792C2211yescharacteristic
17C2×#14581784C2211yescharacteristic
18C2×C4×D332C2211yescharacteristic
19C2×#14581750—21no—
20C2×#14581726C2211yescharacteristic
21C2×#14581726C2211yescharacteristic
22C2×#14581714C2211yescharacteristic
23C2×#14581714C2211yescharacteristic
24C2×#14581714C2211yescharacteristic
25C2×#14581714C2211yescharacteristic
26#19127634—21no—
27#19127621—21no—
28#19127605—21no—
29#19127603C2211yescharacteristic
30#19127603C2211yescharacteristic
31#19127599C2211yescharacteristic
32#19127599C2211yescharacteristic
33#19127598—21no—
34#19127593—21no—
35#19127593—21no—
36#19127571C2211yescharacteristic
37#19127567C2211yescharacteristic
38#19127558—21no—
39C4×C4⋊Dic83C2211yescharacteristic
40C4×C4⋊Dic83C2211yescharacteristic
41C4×C4⋊Dic83C2211yescharacteristic
42#19127464C2211yescharacteristic
43#19127464C2211yescharacteristic
44#19127464C2211yescharacteristic
45#19127464C2211yescharacteristic
46#19127464C2211yescharacteristic
47#19127464C2211yescharacteristic
48#19127464C2211yescharacteristic
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127464C2211yescharacteristic
52C2×C4⋊C8×C83C2211yescharacteristic
53C2×C4⋊C8×C83C2211yescharacteristic
54C2×C4⋊C8×C83C2211yescharacteristic
55C2×#97×C83C2211yescharacteristic
56C4×C4⋊C4×C83C2211yescharacteristic
57#336×C83C2211yescharacteristic
58#336×C83C2211yescharacteristic
59C22×Dic166—21no—
60C22×D332C2311yescharacteristic
61C22×C4×D83—21no—
62#14581792—22no—
63#14581792—41no—
64#14581784—22no—
65#14581784—41no—
66C4×D332—22no—
67C4×D332Q814yescomplemented
68#14581750—44no—
69C2×C4⋊Dic83—21no—
70C2×C4⋊Dic83—21no—
71C2×C4⋊Dic83—21no—
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×C4⋊Dic83C2311yescharacteristic
76C2×C4⋊Dic83C2311yescharacteristic
77C2×C4⋊Dic83C2311yescharacteristic
78C2×C4⋊Dic83C2311yescharacteristic
79C2×Dic83⋊C4—21no—
80C2×Dic83⋊C4—21no—
81C2×Dic83⋊C4—21no—
82C2×Dic83⋊C4—21no—
83C2×(C2×D83)⋊C4—21no—
84C2×(C2×D83)⋊C4—21no—
85C2×(C2×D83)⋊C4—21no—
86C2×(C2×D83)⋊C4—21no—
87C2×(C2×D83)⋊C4—21no—
88C2×C4×Dic83—21no—
89C2×C4×Dic83—21no—
90C2×C4×Dic83—21no—
91#14581726—22no—
92#14581726—22no—
93#14581714—22no—
94#14581714—22no—
95#14581714—41no—
96#14581714—41no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C83⋊#95—21no—
100C83⋊#95—21no—
101C83⋊#95—21no—
102C83⋊#95—21no—
103C83⋊#95—21no—
104C22×C8×C83C2311yescharacteristic
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C2×C4⋊C4×C83D411yescharacteristic
109C2×C4⋊C4×C83D411yescharacteristic
110C2×C42×C83C2311yescharacteristic
111C2×C42×C83C2311yescharacteristic
112C2×C42×C83C2311yescharacteristic
113C4⋊C8×C83—22no—
114C4⋊C8×C83—41no—
115C4⋊C8×C83—41no—
116#97×C83—22no—
117#95×C83D411yescharacteristic
118#95×C83D411yescharacteristic
119C23×D83—21no—
120C2×Dic166—42no—
121C2×Dic166—42no—
122C2×Dic166—81no—
123C2×D332—21no—
124C2×D332—21no—
125C2×D332—21no—
126C2×D332—21no—
127C2×D332—21no—
128C2×D332C2×Q812yes—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C2×C4×D83—24no—
137C2×C4×D83—42no—
138C2×C4×D83—42no—
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—81no—
153C4⋊Dic83C2×Q812yes—
154C4⋊Dic83#4112yes—
155C4⋊Dic83#4112yes—
156Dic83⋊C4—42no—
157Dic83⋊C4—42no—
158Dic83⋊C4—42no—
159Dic83⋊C4—81no—
160(C2×D83)⋊C4—24no—
161(C2×D83)⋊C4—42no—
162(C2×D83)⋊C4—42no—
163(C2×D83)⋊C4—81no—
164(C2×D83)⋊C4—81no—
165C4×Dic83—42no—
166C4×Dic83—42no—
167C4×Dic83—81no—
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2×D411yescharacteristic
171C22×C4×C83C2×D411yescharacteristic
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×C83—21no—
181C2×C8×C83—21no—
182C2×C8×C83—21no—
183C2×C8×C83—21no—
184C2×C8×C83—21no—
185C2×C8×C83—21no—
186C2×C8×C83—21no—
187C4⋊C4×C83—22no—
188C4⋊C4×C83—41no—
189C42×C83—21no—
190C42×C83—21no—
191C42×C83—21no—
192C42×C83—21no—
193C42×C83C2×Q812yes—
194C42×C83#4112yes—
195C23×C83C22×D411yescharacteristic
196C22×D83—22no—
197C22×D83—41no—
198C22×D83—41no—
199C22×D83—41no—
200C22×D83—41no—
201C22×D83—41no—
202C22×D83—41no—
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—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—21no—
218C2×C4×C83C22⋊Q812yes—
219C2×C4×C83C22⋊Q812yes—
220C2×C4×C83AGL(1,ℤ/8)12yes—
221C2×C4×C83C22×Q811yescharacteristic
222C2×C4×C83C2×#4111yescharacteristic
223C2×C4×C83C2×#4111yescharacteristic
224C2×C4×C83C2×#4111yescharacteristic
225C2×C4×C83H(5,𝔽2)11yescharacteristic
226C2×C4×C832−1+411yescharacteristic
227C2×Dic83—22no—
228C2×Dic83—22no—
229C2×Dic83—22no—
230C2×Dic83—41no—
231C2×Dic83—41no—
232C2×Dic83—41no—
233C2×Dic83—41no—
234C2×Dic83—41no—
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×Dic83—41no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248D332—22no—
249D332—22no—
250D332—41no—
251D332—41no—
252C4×D83—48no—
253Dic166—84no—
254C8×C83—41no—
255C8×C83—41no—
256C8×C83—41no—
257C8×C83—41no—
258C22×C83C2×C22⋊Q811yescharacteristic
259C22×C83#54611yescharacteristic
260C22×C83#54811yescharacteristic
261C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C83#57511yescharacteristic
263C22×C83#57611yescharacteristic
264C22×C83#57811yescharacteristic
265C2×D83—42no—
266C2×D83—42no—
267C2×D83—42no—
268C2×D83—81no—
269C2×D83—81no—
270C2×D83—81no—
271C2×D83—81no—
272C4×C83—22no—
273C4×C83—22no—
274C4×C83—22no—
275C4×C83—41no—
276C4×C83—41no—
277C4×C83—41no—
278C4×C83#53311yescharacteristic
279C4×C83#54411yescharacteristic
280C4×C83#55511yescharacteristic
281C4×C83#55611yescharacteristic
282Dic83—42no—
283Dic83—42no—
284Dic83—42no—
285Dic83—81no—
286Dic83—81no—
287Dic83—81no—
288Dic83—81no—
289#26033—831nomaximal, Sylow
290C2×C83#243911yescharacteristic
291C2×C83#307711yescharacteristic
292C2×C83#308311yescharacteristic
293C2×C83#330811yescharacteristic
294C2×C83#331911yescharacteristic
295C2×C83#336611yescharacteristic
296C2×C83#337711yescharacteristic
297D83—82no—
298#2550—831no—
299#2354—831no—
300#2067—831no—
301#2067—831no—
302#2025—831no—
303#2023—831no—
304#1989—831no—
305#1987—831no—
306#1947—831no—
307#1940D8311yescharacteristic, complemented
308#1921—831no—
309#1918—831no—
310#1836—831no—
311#1804—831no—
312#1762—831no—
313C83#2603311yescharacteristic, complemented, Sylow
314C2×C4⋊Q8—831no—
315C2×#125—831no—
316C2×C4×D4—831no—
317C2×#117—1661no—
318C2×#107—831no—
319C2×#107—831no—
320C2×C4⋊C8C2×D8311yescharacteristic
321C2×C4⋊C8C2×D8311yescharacteristic
322C2×C4⋊C8C2×D8311yescharacteristic
323C2×#102—831no—
324C2×#102—831no—
325C2×#102—831no—
326C2×#102—831no—
327C2×#97C2×D8311yescharacteristic
328#398—1661no—
329#395—1661no—
330#391—1661no—
331#390—831no—
332#390—831no—
333#389—831no—
334#389—831no—
335#389—1661no—
336#388—1661no—
337#388—1661no—
338#384—831no—
339#382—831no—
340#380—1661no—
341C4×C4⋊C4—831no—
342C4×C4⋊C4—831no—
343C4×C4⋊C4—831no—
344C4×C4⋊C4C2×D8311yescharacteristic
345#340—831no—
346#340—831no—
347#340—831no—
348#340—831no—
349#340—831no—
350#340—831no—
351#340—831no—
352#340—831no—
353#340—831no—
354#340—831no—
355#336C2×D8311yescharacteristic
356#336C2×D8311yescharacteristic
357C22×Q8—1661no—
358C22×D4—831no—
359C23×C4—1661no—
360C22×C8C22×D8311yescharacteristic
361C22×C8C22×D8311yescharacteristic
362C22×C8C22×D8311yescharacteristic
363C22×C8C22×D8311yescharacteristic
364C4⋊Q8—3321no—
365C4⋊Q8—1662no—
366#125—3321no—
367#125—1662no—
368C4×D4—834no—
369C4×D4—1662no—
370#117—3324no—
371C2×C4⋊C4—831no—
372C2×C4⋊C4—831no—
373C2×C4⋊C4—831no—
374C2×C4⋊C4—831no—
375C2×C4⋊C4—831no—
376C2×C4⋊C4—831no—
377C2×C4⋊C4—831no—
378C2×C4⋊C4—1661no—
379C2×C4⋊C4—1661no—
380C2×C4⋊C4—1661no—
381C2×C4⋊C4—1661no—
382C2×C4⋊C4—1661no—
383C2×C4⋊C4—1661no—
384C2×C4⋊C4—1661no—
385C2×C4⋊C4D33211yescharacteristic
386C2×C4⋊C4D33211yescharacteristic
387C2×C22⋊C4—1661no—
388C2×C22⋊C4—1661no—
389C2×C22⋊C4—1661no—
390C2×C22⋊C4—1661no—
391C2×C22⋊C4—1661no—
392C2×C42—1661no—
393C2×C42—1661no—
394C2×C42—1661no—
395C2×C42C22×D8311yescharacteristic
396C2×C42C22×D8311yescharacteristic
397C2×C42C22×D8311yescharacteristic
398#107—1662no—
399#107—1662no—
400C4⋊C8—22no—
401C4⋊C8—41no—
402C4⋊C8—41no—
403#102—3321no—
404#102—3321no—
405#102—1662no—
406#102—1662no—
407#97—22no—
408#95—1661no—
409#95—1661no—
410#95—1661no—
411#95—1661no—
412#95—1661no—
413#95—1661no—
414#95—1661no—
415#95D33211yescharacteristic
416#95D33211yescharacteristic
417C24—1661no—
418C2×Q8—3322no—
419C2×Q8—3322no—
420C2×Q8—6641no—
421C2×D4—832no—
422C2×D4—1661no—
423C2×D4—1661no—
424C2×D4—1661no—
425C2×D4—1661no—
426C2×D4—1661no—
427C22×C4—3322no—
428C22×C4—3322no—
429C22×C4—1661no—
430C22×C4—1661no—
431C22×C4—1661no—
432C22×C4—1661no—
433C22×C4—1661no—
434C22×C4—1661no—
435C22×C4—1661no—
436C22×C4—1664no—
437C22×C4C2×D33211yescharacteristic
438C22×C4C2×D33211yescharacteristic
439C22×C4C2×D33211yescharacteristic
440C22×C4C2×D33211yescharacteristic
441C22×C4C2×D33211yescharacteristic
442C22×C4C2×D33211yescharacteristic
443C22×C4C23×D8311yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C4⋊C4—22no—
457C4⋊C4—41no—
458C4⋊C4—3322no—
459C4⋊C4—3322no—
460C4⋊C4—3322no—
461C4⋊C4—3322no—
462C4⋊C4—3322no—
463C4⋊C4—832no—
464C4⋊C4—832no—
465C4⋊C4—832no—
466C4⋊C4—6641no—
467C4⋊C4—6641no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4—1661no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C22⋊C4—3322no—
480C22⋊C4—3322no—
481C22⋊C4—6641no—
482C22⋊C4—6641no—
483C22⋊C4—1664no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—3322no—
489C42—3322no—
490C42—6641no—
491C42Q8×D8312yes—
492C42#1305058912yes—
493C23—3321no—
494C23—3321no—
495C23—3321no—
496C23—3321no—
497C23—3321no—
498C23—3321no—
499C23—1662no—
500C23C22×D33211yescharacteristic
501Q8—6644no—
502D4—3321no—
503D4—3321no—
504D4—1662no—
505D4—1662no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
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—3328no—
522C2×C4—3321no—
523C2×C4—3321no—
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—3321no—
535C2×C4—3321no—
536C2×C4—3321no—
537C2×C4—3321no—
538C2×C4—3321no—
539C2×C4—3321no—
540C2×C4—1662no—
541C2×C4—1662no—
542C2×C4—1662no—
543C2×C4#1458177212yes—
544C2×C4#1458177212yes—
545C2×C4#1458182012yes—
546C2×C4C2×Q8×D8311yescharacteristic
547C2×C4#41×D8311yescharacteristic
548C2×C4#41×D8311yescharacteristic
549C2×C4C2×#1305058911yescharacteristic
550C2×C4#1458183711yescharacteristic
551C2×C4#1458184011yescharacteristic
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C22—3322no—
557C22—3322no—
558C22—3322no—
559C22—6641no—
560C22—6641no—
561C22—6641no—
562C22—6641no—
563C22C2×#1458177211yescharacteristic
564C22#1912834611yescharacteristic
565C22#1912836311yescharacteristic
566C22C2×#1458182011yescharacteristic
567C22#1912850111yescharacteristic
568C22#1912850611yescharacteristic
569C22#1912851811yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—3322no—
577C4—3322no—
578C4—3322no—
579C4—6641no—
580C4—6641no—
581C4—6641no—
582C4—6641no—
583C4#1912825711yescharacteristic
584C4#1912832811yescharacteristic
585C4#1912841511yescharacteristic
586C4#1912842211yescharacteristic
587C2—6642no—
588C2#2491115211yescharacteristic
589C2#2491726211yescharacteristic
590C2#2491731611yescharacteristic
591C2#2491945611yescharacteristic
592C2#2491962111yescharacteristic
593C2#2492017211yescharacteristic
594C2#2492030711yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#1940C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenter#1940D83
hypocenterC83#26033
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
1. #24912484C2semidirect
7. #24908418C2semidirect
8. #24908410C2semidirect
9. #24908222C2semidirect
10. #24908056C2semidirect
11. #24908035C2semidirect
12. #24907597C2semidirect
15. C83×#1940C2semidirect
67. C4×D332Q8semidirect
307. #1940D83semidirect
313. C83#26033semidirect

Maximal subgroups

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

subgroupindex
#249124842
#249104102
#249088502
#249086102
#249086002
#249084182
#249084102
#249082222
#249080562
#249080352
#249075972
#249074742
#249072892
C83×#19402
#2603383