Finite Group Databasebeta

← #35374361

Subgroups — #35374361

Order 21248.

626 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#24917481C211yesmaximal, characteristic
2#24916438C211yesmaximal, characteristic, complemented
3#24906341C211yesmaximal, characteristic, complemented
4#24906334C211yesmaximal, characteristic, complemented
5#24906327C211yesmaximal, characteristic, complemented
6#24906320C211yesmaximal, characteristic, complemented
7#24906285C211yesmaximal, characteristic, complemented
8#24906280C211yesmaximal, characteristic, complemented
9#24906275C211yesmaximal, characteristic, complemented
10#24906273C211yesmaximal, characteristic, complemented
11#24906241C211yesmaximal, characteristic, complemented
12#24905897C211yesmaximal, characteristic, complemented
13#24905869C211yesmaximal, characteristic, complemented
14#24905755C211yesmaximal, characteristic, complemented
15C8×#41×C83C211yesmaximal, characteristic, complemented
16#19128235C2211yescharacteristic
17#19128042C411yescharacteristic
18#19128025C411yescharacteristic
19#19128008C411yescharacteristic
20#19128001C411yescharacteristic
21#19127923C411yescharacteristic
22#19127916C411yescharacteristic
23#19127863C411yescharacteristic
24#19127846C411yescharacteristic
25#19127831C2211yescharacteristic
26C8×Dic166C2211yescharacteristic
27C4×#13050580C2211yescharacteristic
28C4×#13050577C2211yescharacteristic
29C4×#13050578C2211yescharacteristic
30C4×#13050575C2211yescharacteristic
31#19127780C2211yescharacteristic
32#19127772—21no—
33C8×D332C2211yescharacteristic
34C8×C22⋊D83—21no—
35#19127760—21no—
36#19127758C2211yescharacteristic
37#19127754C2211yescharacteristic
38#19127754C2211yescharacteristic
39#19127655—21no—
40#19127453C2211yescharacteristic
41#19127453C2211yescharacteristic
42#19127451C2211yescharacteristic
43#19127451C2211yescharacteristic
44Q8⋊(C83⋊C8)C2211yescharacteristic
45Q8⋊(C83⋊C8)C2211yescharacteristic
46#19127431C2211yescharacteristic
47#19127431C2211yescharacteristic
48D4⋊(C83⋊C8)C2211yescharacteristic
49D4⋊(C83⋊C8)C2211yescharacteristic
50#19127428C2211yescharacteristic
51#19127428C2211yescharacteristic
52#19127423C2211yescharacteristic
53#19127423C2211yescharacteristic
54#19127423C2211yescharacteristic
55#19127423C2211yescharacteristic
56C4×#41×C83C2211yescharacteristic
57C8×Q8×C83C2211yescharacteristic
58C8×Q8×C83C2211yescharacteristic
59C8×D4×C83—21no—
60C8×D4×C83—21no—
61C8×D4×C83C2211yescharacteristic
62C8×D4×C83C2211yescharacteristic
63#431×C83—21no—
64#431×C83C2211yescharacteristic
65C2×C4×C8×C83—21no—
66C2×C4×C8×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050578C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050575C2×C411yescharacteristic
71C2×#13050573—21no—
72C2×C8×D83—21no—
73#14581786—21no—
74#14581784C2×C411yescharacteristic
75#14581780C2×C411yescharacteristic
76#14581775—21no—
77#14581771C2×C411yescharacteristic
78#14581766C2×C411yescharacteristic
79C4×Dic166C2311yescharacteristic
80C4×D332C2311yescharacteristic
81C4×C22⋊D83—21no—
82#14581749—21no—
83#14581725C2×C411yescharacteristic
84#14581725C2×C411yescharacteristic
85#14581723C2×C411yescharacteristic
86#14581723C2×C411yescharacteristic
87C4⋊(C83⋊C8)—21no—
88C4⋊(C83⋊C8)C2×C411yescharacteristic
89C4⋊(C83⋊C8)C2×C411yescharacteristic
90C4⋊(C83⋊C8)C2311yescharacteristic
91C4⋊(C83⋊C8)C2311yescharacteristic
92Dic83⋊C8—21no—
93Dic83⋊C8—21no—
94#14581716C2×C411yescharacteristic
95#14581716C2×C411yescharacteristic
96#14581715C2×C411yescharacteristic
97#14581715C2×C411yescharacteristic
98#14581713C2×C411yescharacteristic
99#14581713C2×C411yescharacteristic
100#14581712C2×C411yescharacteristic
101#14581712C2×C411yescharacteristic
102C22⋊(C83⋊C8)—21no—
103C22⋊(C83⋊C8)—21no—
104C22⋊(C83⋊C8)C2×C411yescharacteristic
105C22⋊(C83⋊C8)C2×C411yescharacteristic
106(C2×D83)⋊C8—21no—
107(C2×D83)⋊C8—21no—
108#14581703—21no—
109#14581702—21no—
110C4×C83⋊C8C2311yescharacteristic
111C4×C83⋊C8C2311yescharacteristic
112C4×C83⋊C8C2311yescharacteristic
113C4×C83⋊C8C2311yescharacteristic
114C8×Dic83—21no—
115C2×#41×C83C2×C411yescharacteristic
116C22×C8×C83—21no—
117C22×C8×C83—21no—
118C22×C8×C83D411yescharacteristic
119C22×C8×C83D411yescharacteristic
120C4×Q8×C83C2×C411yescharacteristic
121C4×Q8×C83C2311yescharacteristic
122C4×D4×C83—21no—
123C4×D4×C83—21no—
124C4×D4×C83C2×C411yescharacteristic
125C4×D4×C83C2311yescharacteristic
126#117×C83—21no—
127#117×C83C2×C411yescharacteristic
128C2×C42×C83—21no—
129C2×C42×C83C2311yescharacteristic
130C4⋊C8×C83—21no—
131C4⋊C8×C83—21no—
132C4⋊C8×C83C2311yescharacteristic
133C4⋊C8×C83C2311yescharacteristic
134C22⋊C8×C83—21no—
135C22⋊C8×C83—21no—
136C22⋊C8×C83—21no—
137C4×C8×C83—21no—
138C4×C8×C83—21no—
139C4×C8×C83—21no—
140C4×C8×C83D411yescharacteristic
141C4×C8×C83D411yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166C22×C411yescharacteristic
145C2×D332C22×C411yescharacteristic
146C2×C22⋊D83—21no—
147C2×C4×D83—21no—
148#13050580—22no—
149#13050578—22no—
150#13050577—22no—
151#13050575—22no—
152#13050573—42no—
153C2×C83⋊C8—21no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8C22×C411yescharacteristic
158C2×C83⋊C8C22×C411yescharacteristic
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C8×D83—42no—
162C4⋊Dic83C22×C411yescharacteristic
163C4⋊Dic83C22×C411yescharacteristic
164Dic83⋊C4—21no—
165Dic83⋊C4—21no—
166Dic83⋊C4—21no—
167Dic83⋊C4—21no—
168C22⋊Dic83—21no—
169(C2×D83)⋊C4—21no—
170(C2×D83)⋊C4—21no—
171(C2×D83)⋊C4—21no—
172(C2×D83)⋊C4—21no—
173C4×Dic83—21no—
174#41×C83—22no—
175#41×C83—22no—
176C2×Q8×C83C22×C411yescharacteristic
177C2×D4×C83—21no—
178C2×D4×C83C22×C411yescharacteristic
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83C22×C411yescharacteristic
183C22×C4×C83C2×D411yescharacteristic
184C22×C4×C83#4111yescharacteristic
185C2×C8×C83—21no—
186C2×C8×C83—21no—
187C2×C8×C83—41no—
188C2×C8×C83—41no—
189C2×C8×C83—42no—
190C2×C8×C83—42no—
191C2×C8×C83C2×D411yescharacteristic
192C2×C8×C83C2×D411yescharacteristic
193C2×C8×C83C2×D411yescharacteristic
194C2×C8×C83C2×D411yescharacteristic
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83C22×C411yescharacteristic
198C4⋊C4×C83C22×C411yescharacteristic
199C22⋊C4×C83—21no—
200C22⋊C4×C83—21no—
201C22⋊C4×C83—21no—
202C42×C83—21no—
203C42×C83—21no—
204C42×C83—21no—
205C42×C83C22×C411yescharacteristic
206C42×C83C2×D411yescharacteristic
207C42×C83#4111yescharacteristic
208C42×C83C2411yescharacteristic
209C23×C83—21no—
210C23×C83C4×D411yescharacteristic
211C22×D83—21no—
212Q8×C83—21no—
213Q8×C83#13112yes—
214D4×C83—24no—
215D4×C83—21no—
216D4×C83#13112yes—
217C2×C4×C83—24no—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—41no—
226C2×C4×C83—42no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83C4×D411yescharacteristic
230C2×C4×C83C4×D411yescharacteristic
231C2×C4×C83C4×D411yescharacteristic
232C2×C4×C83C23×C411yescharacteristic
233C2×C4×C83C22×D411yescharacteristic
234C2×C4×C83C2×#4111yescharacteristic
235C22⋊D83—42no—
236C2×Dic83—21no—
237C2×Dic83—21no—
238C2×Dic83—21no—
239D332—21no—
240D332—21no—
241C4×D83—41no—
242C4×D83—41no—
243Dic166—21no—
244Dic166—21no—
245C8×C83—21no—
246C8×C83—21no—
247C8×C83—21no—
248C8×C83—21no—
249C8×C83—41no—
250C8×C83—41no—
251C83⋊C8—21no—
252C83⋊C8—21no—
253C83⋊C8—21no—
254C83⋊C8—21no—
255C83⋊C8—41no—
256C83⋊C8—41no—
257C83⋊C8—41no—
258C83⋊C8—41no—
259C22×C83—21no—
260C22×C83—22no—
261C22×C83—21no—
262C22×C83—21no—
263C22×C83—41no—
264C22×C83—41no—
265C22×C83C2×C4×D411yescharacteristic
266C2×D83—41no—
267C2×D83—41no—
268C2×D83—41no—
269C4×C83—21no—
270C4×C83—22no—
271C4×C83—21no—
272C4×C83—21no—
273C4×C83—21no—
274C4×C83—41no—
275C4×C83—41no—
276C4×C83C2×#13111yescharacteristic
277C4×C83C2×#13111yescharacteristic
278C4×C83#57511yescharacteristic
279C4×C83#57511yescharacteristic
280Dic83—41no—
281Dic83—41no—
282Dic83—41no—
283#17909—831nomaximal, Sylow
284C2×C83—41no—
285C2×C83—42no—
286C2×C83#292911yescharacteristic
287C2×C83#294311yescharacteristic
288C2×C83#295511yescharacteristic
289D83—81no—
290#3102—831no—
291#2966—831no—
292C8×#41D8311yescharacteristic, complemented
293#1588—831no—
294#1587—831no—
295#1586—831no—
296#1585—831no—
297#1580—831no—
298#1579—831no—
299SD16⋊C8—831no—
300SD16⋊C8—831no—
301#1572—831no—
302#1488—831no—
303#1482—831no—
304#1452—831no—
305C83#1790911yescharacteristic, complemented, Sylow
306#529—831no—
307C4×#41C2×D8311yescharacteristic
308#485—831no—
309#482—831no—
310#479—831no—
311#478—831no—
312#464—831no—
313#463—831no—
314#452—831no—
315#449—831no—
316#446—831no—
317C8×Q8—831no—
318C8×Q8C2×D8311yescharacteristic
319C8×Q8C2×D8311yescharacteristic
320C4×Q16—831no—
321C4×SD16—831no—
322C4×SD16—831no—
323C4×D8—831no—
324#436—831no—
325#435—1661no—
326C8×D4—21no—
327C8×D4—21no—
328C8×D4—831no—
329C8×D4—1661no—
330C8×D4C2×D8311yescharacteristic
331C8×D4C2×D8311yescharacteristic
332#433—1661no—
333#432—831no—
334#431—21no—
335#431—831no—
336#431—831no—
337#431C2×D8311yescharacteristic
338#405—1661no—
339C2×C4×C8—21no—
340C2×C4×C8C2×D8311yescharacteristic
341#335—831no—
342#335—831no—
343#334—831no—
344#334—831no—
345Q8⋊C8—831no—
346Q8⋊C8—831no—
347Q8⋊C8—831no—
348Q8⋊C8—831no—
349D4⋊C8—831no—
350D4⋊C8—831no—
351D4⋊C8—831no—
352D4⋊C8—831no—
353#322—831no—
354#322—831no—
355#322—831no—
356#322—831no—
357C2×#41C4×D8311yescharacteristic
358C2×Q16—831no—
359C2×SD16—831no—
360C2×SD16—831no—
361C2×D8—831no—
362C2×M16—1661no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—1661no—
366C22×C8C22⋊D8311yescharacteristic
367C22×C8C22⋊D8311yescharacteristic
368#126—1661no—
369#125—831no—
370#124—831no—
371#123—1661no—
372C22⋊Q8—831no—
373#121—831no—
374C4×Q8—831no—
375C4×Q8C4×D8311yescharacteristic
376C4×Q8C22×D8311yescharacteristic
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—831no—
380C4×D4—1661no—
381C4×D4C4×D8311yescharacteristic
382C4×D4C22×D8311yescharacteristic
383#117—21no—
384#117—1661no—
385#117C4×D8311yescharacteristic
386C2×C42—21no—
387C2×C42C22×D8311yescharacteristic
388#107—831no—
389#107—831no—
390#106—831no—
391#106—831no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—831no—
395C4⋊C8—831no—
396C4⋊C8—831no—
397C4⋊C8—831no—
398C4⋊C8—1661no—
399C4⋊C8—1661no—
400C4⋊C8—1661no—
401C4⋊C8C22×D8311yescharacteristic
402C4⋊C8C22×D8311yescharacteristic
403#103—831no—
404#103—831no—
405#103—831no—
406#103—831no—
407#102—831no—
408#102—831no—
409#102—831no—
410#102—831no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—831no—
415C22⋊C8—831no—
416C22⋊C8—1661no—
417C22⋊C8—1661no—
418C22⋊C8—1661no—
419C22⋊C8—1661no—
420#97—1661no—
421#97—1661no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8—831no—
426C4×C8—831no—
427C4×C8—831no—
428C4×C8—831no—
429C4×C8—1661no—
430C4×C8C22⋊D8311yescharacteristic
431C4×C8C22⋊D8311yescharacteristic
432C4×C8C22×D8311yescharacteristic
433C4×C8C22×D8311yescharacteristic
434#41—22no—
435#41—22no—
436C2×Q8—831no—
437C2×Q8C2×C4×D8311yescharacteristic
438C2×D4—21no—
439C2×D4—831no—
440C2×D4—1661no—
441C2×D4C2×C4×D8311yescharacteristic
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—1661no—
446C22×C4C2×C4×D8311yescharacteristic
447C22×C4C2×C22⋊D8311yescharacteristic
448C22×C4#1305059011yescharacteristic
449Q16—1662no—
450SD16—1662no—
451SD16—1662no—
452D8—1662no—
453M16—3322no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—41no—
457C2×C8—41no—
458C2×C8—42no—
459C2×C8—42no—
460C2×C8—3322no—
461C2×C8—831no—
462C2×C8—831no—
463C2×C8—831no—
464C2×C8—831no—
465C2×C8—1661no—
466C2×C8—1661no—
467C2×C8—1661no—
468C2×C8—1661no—
469C2×C8C2×C22⋊D8311yescharacteristic
470C2×C8C2×C22⋊D8311yescharacteristic
471C2×C8C2×C22⋊D8311yescharacteristic
472C2×C8C2×C22⋊D8311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—831no—
476C4⋊C4—831no—
477C4⋊C4—1661no—
478C4⋊C4—1661no—
479C4⋊C4—1661no—
480C4⋊C4—1661no—
481C4⋊C4C2×C4×D8311yescharacteristic
482C4⋊C4C2×C4×D8311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—1661no—
487C22⋊C4—1661no—
488C22⋊C4—1661no—
489C22⋊C4—1661no—
490C22⋊C4—1661no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—1661no—
495C42C2×C4×D8311yescharacteristic
496C42C2×C22⋊D8311yescharacteristic
497C42#1305059011yescharacteristic
498C42C23×D8311yescharacteristic
499C23—21no—
500C23—1661no—
501C23C4×C22⋊D8311yescharacteristic
502Q8—21no—
503Q8—1661no—
504Q8—1661no—
505Q8#1458179812yes—
506D4—24no—
507D4—21no—
508D4—3322no—
509D4—1661no—
510D4—1661no—
511D4#1458179812yes—
512C2×C4—24no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—3321no—
525C2×C4—3321no—
526C2×C4—1661no—
527C2×C4—1661no—
528C2×C4—1661no—
529C2×C4C4×C22⋊D8311yescharacteristic
530C2×C4C4×C22⋊D8311yescharacteristic
531C2×C4C4×C22⋊D8311yescharacteristic
532C2×C4C22×C4×D8311yescharacteristic
533C2×C4C22×C22⋊D8311yescharacteristic
534C2×C4C2×#1305059011yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—3321no—
542C8—3321no—
543C8—3321no—
544C8—3321no—
545C8—1661no—
546C8—1661no—
547C8—1661no—
548C8—1661no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—3321no—
556C22—3321no—
557C22—3321no—
558C22C2×C4×C22⋊D8311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—22no—
564C4—41no—
565C4—41no—
566C4—3321no—
567C4—3321no—
568C4—3321no—
569C4C2×#1458179811yescharacteristic
570C4C2×#1458179811yescharacteristic
571C4#1912849911yescharacteristic
572C4#1912849911yescharacteristic
573C2—41no—
574C2—42no—
575C2—6641no—
576C2#2491615711yescharacteristic
577C2#2491626111yescharacteristic
578C2#2491636411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC8×#41×C83C2
socleC22×C83C2×C4×D4
prime radical#19127846C4
cosocleC42×C83C24
hypercenterC8×#41D83
hypocenterC83#17909
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C4×C8 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
2. #24916438C2semidirect
3. #24906341C2semidirect
4. #24906334C2semidirect
5. #24906327C2semidirect
6. #24906320C2semidirect
7. #24906285C2semidirect
8. #24906280C2semidirect
9. #24906275C2semidirect
10. #24906273C2semidirect
11. #24906241C2semidirect
12. #24905897C2semidirect
13. #24905869C2semidirect
14. #24905755C2semidirect
15. C8×#41×C83C2semidirect
292. C8×#41D83semidirect
305. C83#17909semidirect

Maximal subgroups

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

subgroupindex
#249174812
#249164382
#249063412
#249063342
#249063272
#249063202
#249062852
#249062802
#249062752
#249062732
#249062412
#249058972
#249058692
#249057552
C8×#41×C832
#1790983