Finite Group Databasebeta

← #35463449

Subgroups — #35463449

Order 21248.

678 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910434C211yesmaximal, characteristic
2#24908992C211yesmaximal, characteristic
3#24908987C211yesmaximal, characteristic
4#24908834C211yesmaximal, characteristic
5#24908834C211yesmaximal, characteristic
6#24908231C211yesmaximal, characteristic, complemented
7#24908229C211yesmaximal, characteristic, complemented
8#24908224C211yesmaximal, characteristic, complemented
9#24908182C211yesmaximal, characteristic, complemented
10#24908052C211yesmaximal, characteristic, complemented
11#24908031C211yesmaximal, characteristic, complemented
12#24907625C211yesmaximal, characteristic, complemented
13#24907470C211yesmaximal, characteristic
14C4×#14581712C211yesmaximal, characteristic
15C83×#2570C211yesmaximal, characteristic, complemented
16C2×C4×D332C2211yescharacteristic
17C2×#14581725C2211yescharacteristic
18C2×#14581725C2211yescharacteristic
19C2×#14581725C2211yescharacteristic
20C2×#14581723C2211yescharacteristic
21C2×#14581723C2211yescharacteristic
22C2×#14581723C2211yescharacteristic
23C2×C4⋊(C83⋊C8)C2211yescharacteristic
24C2×C4⋊(C83⋊C8)C2211yescharacteristic
25C2×C4⋊(C83⋊C8)C2211yescharacteristic
26C2×#14581712C2211yescharacteristic
27C2×#14581712C2211yescharacteristic
28C2×#14581712C2211yescharacteristic
29C2×#14581712C2211yescharacteristic
30C2×C4×C83⋊C8C2211yescharacteristic
31#19127603C2211yescharacteristic
32#19127603C2211yescharacteristic
33#19127591—21no—
34#19127591—21no—
35#19127567C2211yescharacteristic
36#19127563—21no—
37C4×C4⋊Dic83C2211yescharacteristic
38C4×C4⋊Dic83C2211yescharacteristic
39#19127548—21no—
40#19127463C2211yescharacteristic
41#19127463C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127456C2211yescharacteristic
47#19127456C2211yescharacteristic
48#400×C83—21no—
49#398×C83—21no—
50#389×C83C2211yescharacteristic
51#389×C83C2211yescharacteristic
52#387×C83—21no—
53#387×C83—21no—
54#384×C83C2211yescharacteristic
55#382×C83C2211yescharacteristic
56#382×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×D332Q814yes—
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#14581725—22no—
79#14581725—41no—
80#14581723—41no—
81#14581723—41no—
82#14581723—41no—
83C4⋊(C83⋊C8)—22no—
84C4⋊(C83⋊C8)—22no—
85C4⋊(C83⋊C8)—22no—
86#14581712—22no—
87#14581712—22no—
88#14581712—41no—
89#14581712—41no—
90C4×C83⋊C8—22no—
91C83⋊#95—21no—
92C83⋊#95—21no—
93C83⋊#95—21no—
94C83⋊#95—21no—
95C2×C4⋊C4×C83—21no—
96C2×C4⋊C4×C83—21no—
97C2×C4⋊C4×C83—21no—
98C2×C4⋊C4×C83—21no—
99C2×C4⋊C4×C83D411yescharacteristic
100C2×C4⋊C4×C83D411yescharacteristic
101C2×C4⋊C4×C83C2311yescharacteristic
102C2×C4⋊C4×C83C2311yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C4⋊C4×C83C2311yescharacteristic
105C2×C42×C83—21no—
106C2×C42×C83C2311yescharacteristic
107C2×C42×C83C2311yescharacteristic
108C2×C42×C83C2311yescharacteristic
109#95×C83—21no—
110#95×C83—21no—
111#95×C83—21no—
112#95×C83—21no—
113#95×C83—21no—
114#95×C83—21no—
115#95×C83—21no—
116#95×C83D411yescharacteristic
117#95×C83D411yescharacteristic
118C23×D83—21no—
119C2×D332—21no—
120C2×D332—21no—
121C2×D332—21no—
122C2×D332—21no—
123C2×D332—21no—
124C2×D332C2×Q812yes—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C2×C4×D83—24no—
129C2×C4×D83—81no—
130C2×C4×D83—81no—
131C2×C83⋊C8—21no—
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#4112yes—
142C2×C83⋊C8#4112yes—
143C4⋊Dic83—21no—
144C4⋊Dic83—21no—
145C4⋊Dic83—21no—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83C2×Q812yes—
149(C2×D83)⋊C4—24no—
150(C2×D83)⋊C4—42no—
151(C2×D83)⋊C4—42no—
152(C2×D83)⋊C4—81no—
153(C2×D83)⋊C4—81no—
154C4×Dic83—81no—
155C4×Dic83—81no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83C2×D411yescharacteristic
161C22×C4×C83C2×D411yescharacteristic
162C22×C4×C83C2×D411yescharacteristic
163C22×C4×C83C2×D411yescharacteristic
164C22×C4×C83C2×D411yescharacteristic
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2411yescharacteristic
167C4⋊C4×C83—22no—
168C4⋊C4×C83—21no—
169C4⋊C4×C83—21no—
170C4⋊C4×C83—21no—
171C4⋊C4×C83—21no—
172C4⋊C4×C83—21no—
173C4⋊C4×C83—21no—
174C4⋊C4×C83—21no—
175C4⋊C4×C83—21no—
176C4⋊C4×C83—41no—
177C4⋊C4×C83—42no—
178C4⋊C4×C83—42no—
179C4⋊C4×C83—81no—
180C4⋊C4×C83—81no—
181C42×C83—21no—
182C42×C83—21no—
183C42×C83—21no—
184C42×C83—21no—
185C42×C83—81no—
186C42×C83C2×Q812yes—
187C42×C83#4112yes—
188C23×C83C22×D411yescharacteristic
189C22×D83—22no—
190C22×D83—41no—
191C22×D83—41no—
192C22×D83—41no—
193C22×D83—41no—
194C22×D83—41no—
195C22×D83—41no—
196C2×C4×C83—21no—
197C2×C4×C83—21no—
198C2×C4×C83—21no—
199C2×C4×C83—21no—
200C2×C4×C83—21no—
201C2×C4×C83—21no—
202C2×C4×C83—21no—
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—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×C83—41no—
220C2×C4×C83—41no—
221C2×C4×C83—41no—
222C2×C4×C83—41no—
223C2×C4×C83C22⋊Q812yes—
224C2×C4×C83C22⋊Q812yes—
225C2×C4×C83#13512yes—
226C2×C4×C83C22×Q811yescharacteristic
227C2×C4×C83C2×#4111yescharacteristic
228C2×C4×C83C2×#4111yescharacteristic
229C2×C4×C83C2×#4111yescharacteristic
230C2×C4×C83H(5,𝔽2)11yescharacteristic
231C2×C4×C832−1+411yescharacteristic
232C2×Dic83—22no—
233C2×Dic83—41no—
234C2×Dic83—41no—
235C2×Dic83—41no—
236C2×Dic83—41no—
237C2×Dic83—41no—
238C2×Dic83—41no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241D332—22no—
242D332—22no—
243D332—41no—
244D332—41no—
245C4×D83—84no—
246C83⋊C8—22no—
247C83⋊C8—22no—
248C83⋊C8—41no—
249C83⋊C8—41no—
250C22×C83C2×C22⋊Q811yescharacteristic
251C22×C83#54711yescharacteristic
252C22×C83#55011yescharacteristic
253C22×C83C2×#13511yescharacteristic
254C22×C83#57511yescharacteristic
255C22×C83#57611yescharacteristic
256C22×C83#57711yescharacteristic
257C2×D83—42no—
258C2×D83—42no—
259C2×D83—42no—
260C2×D83—81no—
261C2×D83—81no—
262C2×D83—81no—
263C2×D83—81no—
264C4×C83—22no—
265C4×C83—22no—
266C4×C83—22no—
267C4×C83—41no—
268C4×C83—41no—
269C4×C83—41no—
270C4×C83—81no—
271C4×C83—81no—
272C4×C83—81no—
273C4×C83—81no—
274C4×C83#53311yescharacteristic
275C4×C83#54411yescharacteristic
276C4×C83#55211yescharacteristic
277C4×C83#55311yescharacteristic
278Dic83—42no—
279Dic83—81no—
280Dic83—81no—
281#26094—831nomaximal, Sylow
282C2×C83#244111yescharacteristic
283C2×C83#307611yescharacteristic
284C2×C83#308111yescharacteristic
285C2×C83#333711yescharacteristic
286C2×C83#335511yescharacteristic
287C2×C83#339611yescharacteristic
288C2×C83#340111yescharacteristic
289D83—82no—
290#2570D8311yescharacteristic, complemented
291#2357—831no—
292#2093—831no—
293#2092—831no—
294#2065—831no—
295#2065—831no—
296#1949—831no—
297#1949—831no—
298#1948—831no—
299#1939—831no—
300#1921—831no—
301#1918—831no—
302#1846—831no—
303#1804—831no—
304C4×#102—831no—
305C83#2609411yescharacteristic, complemented, Sylow
306C2×C4×D4—831no—
307C2×#107—831no—
308C2×#107—831no—
309C2×#107—831no—
310C2×#106—831no—
311C2×#106—831no—
312C2×#106—831no—
313C2×C4⋊C8—831no—
314C2×C4⋊C8—831no—
315C2×C4⋊C8—831no—
316C2×#102—831no—
317C2×#102—831no—
318C2×#102—831no—
319C2×#102—831no—
320C2×C4×C8—831no—
321#400—21no—
322#398—21no—
323#390—831no—
324#390—831no—
325#389C2×D8311yescharacteristic
326#389C2×D8311yescharacteristic
327#388—1661no—
328#388—1661no—
329#387—21no—
330#387—21no—
331#384C2×D8311yescharacteristic
332#382—831no—
333#382C2×D8311yescharacteristic
334#382C2×D8311yescharacteristic
335#381—1661no—
336C4×C4⋊C4—831no—
337C4×C4⋊C4—831no—
338C4×C4⋊C4C2×D8311yescharacteristic
339C4×C4⋊C4C2×D8311yescharacteristic
340C4×C22⋊C4—1661no—
341#340—831no—
342#340—831no—
343#340—831no—
344#340—831no—
345#340—831no—
346#340—831no—
347#336—831no—
348#336—831no—
349C22×D4—831no—
350C23×C4—1661no—
351C22×C8—831no—
352C22×C8—831no—
353C22×C8—831no—
354C22×C8—831no—
355C4×D4—834no—
356C4×D4—1662no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—831no—
362C2×C4⋊C4—831no—
363C2×C4⋊C4—831no—
364C2×C4⋊C4C22⋊D8311yescharacteristic
365C2×C4⋊C4C22⋊D8311yescharacteristic
366C2×C4⋊C4C22×D8311yescharacteristic
367C2×C4⋊C4C22×D8311yescharacteristic
368C2×C4⋊C4C22×D8311yescharacteristic
369C2×C4⋊C4C22×D8311yescharacteristic
370C2×C22⋊C4—1661no—
371C2×C22⋊C4—1661no—
372C2×C22⋊C4—1661no—
373C2×C22⋊C4—1661no—
374C2×C22⋊C4—1661no—
375C2×C42—21no—
376C2×C42—1661no—
377C2×C42—1661no—
378C2×C42C22×D8311yescharacteristic
379C2×C42C22×D8311yescharacteristic
380C2×C42C22×D8311yescharacteristic
381#107—3321no—
382#107—1662no—
383#107—1662no—
384#106—3321no—
385#106—3321no—
386#106—3321no—
387C4⋊C8—1662no—
388C4⋊C8—1662no—
389C4⋊C8—1662no—
390#102—3321no—
391#102—3321no—
392#102—1662no—
393#102—1662no—
394C4×C8—1662no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—1661no—
403#95—1661no—
404#95—1661no—
405#95—1661no—
406#95C22⋊D8311yescharacteristic
407#95C22⋊D8311yescharacteristic
408C24—1661no—
409C2×D4—832no—
410C2×D4—1661no—
411C2×D4—1661no—
412C2×D4—1661no—
413C2×D4—1661no—
414C2×D4—1661no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—6641no—
420C22×C4—6641no—
421C22×C4—1661no—
422C22×C4—1661no—
423C22×C4—1661no—
424C22×C4—1664no—
425C22×C4C2×C22⋊D8311yescharacteristic
426C22×C4C2×C22⋊D8311yescharacteristic
427C22×C4C2×C22⋊D8311yescharacteristic
428C22×C4C2×C22⋊D8311yescharacteristic
429C22×C4C2×C22⋊D8311yescharacteristic
430C22×C4C2×C22⋊D8311yescharacteristic
431C22×C4C23×D8311yescharacteristic
432C2×C8—832no—
433C2×C8—832no—
434C2×C8—1661no—
435C2×C8—1661no—
436C2×C8—1661no—
437C2×C8—1661no—
438C2×C8—1661no—
439C2×C8—1661no—
440C2×C8—1661no—
441C2×C8—1661no—
442C2×C8—1661no—
443C2×C8—1661no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—832no—
459C4⋊C4—1661no—
460C4⋊C4—1661no—
461C4⋊C4—1661no—
462C4⋊C4—1661no—
463C4⋊C4—1661no—
464C22⋊C4—3322no—
465C22⋊C4—3322no—
466C22⋊C4—6641no—
467C22⋊C4—6641no—
468C22⋊C4—1664no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—81no—
474C42—6641no—
475C42—6641no—
476C42Q8×D8312yes—
477C42#1305059112yes—
478C23—3321no—
479C23—3321no—
480C23—3321no—
481C23—3321no—
482C23—3321no—
483C23—3321no—
484C23—1662no—
485C23C22×C22⋊D8311yescharacteristic
486D4—3321no—
487D4—3321no—
488D4—1662no—
489D4—1662no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
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—41no—
516C2×C4—41no—
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—6644no—
526C2×C4—1662no—
527C2×C4#1458176812yes—
528C2×C4#1458176812yes—
529C2×C4#1458181212yes—
530C2×C4C2×Q8×D8311yescharacteristic
531C2×C4#41×D8311yescharacteristic
532C2×C4#41×D8311yescharacteristic
533C2×C4C2×#1305059111yescharacteristic
534C2×C4#1458183811yescharacteristic
535C2×C4#1458183911yescharacteristic
536C8—3321no—
537C8—3321no—
538C8—1662no—
539C8—1662no—
540C22—3322no—
541C22—3322no—
542C22—3322no—
543C22—6641no—
544C22—6641no—
545C22—6641no—
546C22—6641no—
547C22C2×#1458176811yescharacteristic
548C22#1912835011yescharacteristic
549C22#1912837011yescharacteristic
550C22C2×#1458181211yescharacteristic
551C22#1912849911yescharacteristic
552C22#1912850411yescharacteristic
553C22#1912850911yescharacteristic
554C4—22no—
555C4—22no—
556C4—22no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—3322no—
565C4—6641no—
566C4—6641no—
567C4#1912825711yescharacteristic
568C4#1912833111yescharacteristic
569C4#1912838911yescharacteristic
570C4#1912840411yescharacteristic
571C2—6642no—
572C2#2491117211yescharacteristic
573C2#2491724511yescharacteristic
574C2#2491728811yescharacteristic
575C2#2491984211yescharacteristic
576C2#2492006311yescharacteristic
577C2#2492047111yescharacteristic
578C2#2492052911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2570C2
socleC23×C83C22×D4
prime radicalC22×D332C23
hypercenter#2570D83
hypocenterC83#26094
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2570

Complements

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

NH ≅ G/Ntype
6. #24908231C2semidirect
7. #24908229C2semidirect
8. #24908224C2semidirect
9. #24908182C2semidirect
10. #24908052C2semidirect
11. #24908031C2semidirect
12. #24907625C2semidirect
15. C83×#2570C2semidirect
290. #2570D83semidirect
305. C83#26094semidirect

Maximal subgroups

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

subgroupindex
#249104342
#249089922
#249089872
#249088342
#249082312
#249082292
#249082242
#249081822
#249080522
#249080312
#249076252
#249074702
C4×#145817122
C83×#25702
#2609483