Finite Group Databasebeta

← #35412251

Subgroups — #35412251

Order 21248.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24917253C211yesmaximal, characteristic
2#24916400C211yesmaximal, characteristic, complemented
3#24915892C211yesmaximal, characteristic
4#24908407C211yesmaximal, characteristic, complemented
5#24908061C211yesmaximal, characteristic, complemented
6#24908061C211yesmaximal, characteristic, complemented
7#24907735C211yesmaximal, characteristic
8#24907735C211yesmaximal, characteristic
9#24907480C211yesmaximal, characteristic
10#24907350C211yesmaximal, characteristic, complemented
11#24907345C211yesmaximal, characteristic, complemented
12#24907340C211yesmaximal, characteristic, complemented
13#24907306C211yesmaximal, characteristic
14#24907299C211yesmaximal, characteristic
15C83×#1950C211yesmaximal, characteristic, complemented
16C2×#14581800C2211yescharacteristic
17C2×#14581800C2211yescharacteristic
18#19128258C2211yescharacteristic
19C4×#13050590C2211yescharacteristic
20#19128009C411yescharacteristic, complemented
21#19128009C411yescharacteristic, complemented
22#19128002C411yescharacteristic, complemented
23#19128002C411yescharacteristic, complemented
24#19127997C411yescharacteristic, complemented
25#19127992C411yescharacteristic, complemented
26#19127987C411yescharacteristic, complemented
27#19127982C411yescharacteristic, complemented
28#19127830—21no—
29#19127830—21no—
30#19127830—21no—
31#19127830—21no—
32#19127739C2211yescharacteristic
33#19127739C2211yescharacteristic
34#19127729C2211yescharacteristic
35#19127729C2211yescharacteristic
36C2×#14581718C2211yescharacteristic
37C2×#14581718C2211yescharacteristic
38#19127698C2211yescharacteristic
39#19127698C2211yescharacteristic
40#19127659C2211yescharacteristic
41#19127659C2211yescharacteristic
42#19127659C2211yescharacteristic
43#19127659C2211yescharacteristic
44#19127655—21no—
45#19127655—21no—
46#19127653—21no—
47C2×#14581703C2211yescharacteristic
48C2×#14581702C2211yescharacteristic
49#97×D83—21no—
50C2×C8×Dic83C2211yescharacteristic
51C4×C4⋊Dic83C2211yescharacteristic
52#19127462C2211yescharacteristic
53#19127462C2211yescharacteristic
54#19127462C2211yescharacteristic
55#19127462C2211yescharacteristic
56#19127462C2211yescharacteristic
57#19127462C2211yescharacteristic
58#19127455C2211yescharacteristic
59#19127455C2211yescharacteristic
60C2×#108×C83C2211yescharacteristic
61C2×#108×C83C2211yescharacteristic
62#423×C83C2211yescharacteristic
63C2×C4⋊C8×C83C2211yescharacteristic
64C4×M16×C83C2211yescharacteristic
65#341×C83C2211yescharacteristic
66#341×C83C2211yescharacteristic
67C2×#13050590C2311yescharacteristic
68#14581800—22no—
69#14581800—22no—
70#14581800—22no—
71#14581800Q814yescomplemented
72C2×#13050573—21no—
73C2×#13050573—21no—
74C22×C83⋊C8C2311yescharacteristic
75C22×C83⋊C8C2311yescharacteristic
76C2×C8×D83—21no—
77C2×C8×D83—21no—
78#14581792C2×C411yescharacteristic
79#14581792C2×C411yescharacteristic
80#14581784C2×C411yescharacteristic
81#14581784C2×C411yescharacteristic
82#14581771—21no—
83#14581771—21no—
84C4×Dic166—21no—
85C4×Dic166—21no—
86C4×Dic166C2×C411yescharacteristic
87C4×Dic166C2×C411yescharacteristic
88C4×D332C2×C411yescharacteristic
89C4×D332C2×C411yescharacteristic
90C4×C22⋊D83—21no—
91C4×C22⋊D83—21no—
92#14581751C2311yescharacteristic
93#14581751C2311yescharacteristic
94#14581751C2311yescharacteristic
95#14581749—21no—
96C2×C4⋊Dic83—21no—
97C2×C4×Dic83C2311yescharacteristic
98C2×C4×Dic83C2311yescharacteristic
99C42×D83—21no—
100#14581726C2×C411yescharacteristic
101#14581726C2×C411yescharacteristic
102#14581726C2×C411yescharacteristic
103#14581726C2×C411yescharacteristic
104#14581724C2×C411yescharacteristic
105#14581724C2×C411yescharacteristic
106#14581724C2×C411yescharacteristic
107#14581724C2×C411yescharacteristic
108Dic83⋊C8—21no—
109Dic83⋊C8—21no—
110Dic83⋊C8—21no—
111Dic83⋊C8—21no—
112#14581718—22no—
113#14581718—22no—
114#14581717C2×C411yescharacteristic
115#14581717C2×C411yescharacteristic
116#14581717C2×C411yescharacteristic
117#14581717C2×C411yescharacteristic
118#14581714C2×C411yescharacteristic
119#14581714C2×C411yescharacteristic
120#14581714C2×C411yescharacteristic
121#14581714C2×C411yescharacteristic
122#14581703D411yescharacteristic
123#14581703D411yescharacteristic
124#14581703D411yescharacteristic
125#14581703D411yescharacteristic
126#14581702—21no—
127#14581702—21no—
128#14581702—21no—
129#14581702—21no—
130#14581702—22no—
131C8×Dic83—21no—
132C8×Dic83—21no—
133C8×Dic83—21no—
134C8×Dic83—21no—
135C8×Dic83—22no—
136C83⋊#95—21no—
137C2×M16×C83C2311yescharacteristic
138C2×M16×C83C2311yescharacteristic
139C2×M16×C83C2311yescharacteristic
140C2×M16×C83C2311yescharacteristic
141C22×C8×C83C2311yescharacteristic
142C22×C8×C83C2311yescharacteristic
143C2×C42×C83C2311yescharacteristic
144#108×C83—22no—
145#108×C83—22no—
146C4⋊C8×C83—21no—
147C4⋊C8×C83—21no—
148C4⋊C8×C83C2×C411yescharacteristic
149C4⋊C8×C83C2×C411yescharacteristic
150C4⋊C8×C83C2×C411yescharacteristic
151C4⋊C8×C83C2×C411yescharacteristic
152#97×C83—21no—
153C4×C8×C83—21no—
154#13050590—21no—
155#13050590—21no—
156#13050590C2×Q812yes—
157#13050590#4112yes—
158C2×Dic166—21no—
159C2×Dic166—21no—
160C2×Dic166C22×C411yescharacteristic
161C2×D332C22×C411yescharacteristic
162C2×C22⋊D83—21no—
163C22×Dic83—21no—
164C22×Dic83—21no—
165C2×C4×D83—21no—
166C2×C4×D83—21no—
167C2×C4×D83—21no—
168#13050573—24no—
169#13050573—24no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8C2×D411yescharacteristic
173C2×C83⋊C8C2×D411yescharacteristic
174C2×C83⋊C8C2×D411yescharacteristic
175C2×C83⋊C8C2×D411yescharacteristic
176C2×C83⋊C8C2×Q812yes—
177C2×C83⋊C8#4112yes—
178C8×D83—24no—
179C8×D83—24no—
180C4⋊Dic83—21no—
181C4⋊Dic83—21no—
182C4⋊Dic83—42no—
183C4⋊Dic83C22×C411yescharacteristic
184C4⋊Dic83C22×C411yescharacteristic
185C4⋊Dic83C22×C411yescharacteristic
186C4⋊Dic83C22×C411yescharacteristic
187C4⋊Dic83C22×C411yescharacteristic
188C4⋊Dic83C22×C411yescharacteristic
189Dic83⋊C4—21no—
190Dic83⋊C4—21no—
191Dic83⋊C4—21no—
192Dic83⋊C4—21no—
193Dic83⋊C4—21no—
194Dic83⋊C4—21no—
195C22⋊Dic83—21no—
196C22⋊Dic83—21no—
197C22⋊Dic83—21no—
198(C2×D83)⋊C4—21no—
199(C2×D83)⋊C4—21no—
200C4×Dic83—21no—
201C4×Dic83—21no—
202C4×Dic83—21no—
203C4×Dic83—21no—
204C4×Dic83—21no—
205C4×Dic83—21no—
206C4×Dic83—21no—
207C4×Dic83—21no—
208C4×Dic83—21no—
209C22×C4×C83#4111yescharacteristic
210C22×C4×C83#4111yescharacteristic
211C22×C4×C83C2411yescharacteristic
212M16×C83—21no—
213M16×C83—21no—
214M16×C83—21no—
215M16×C83—21no—
216M16×C83—21no—
217M16×C83—21no—
218M16×C83C2×Q812yes—
219M16×C83#4112yes—
220C2×C8×C83—21no—
221C2×C8×C83—21no—
222C2×C8×C83—21no—
223C2×C8×C83—21no—
224C2×C8×C83—21no—
225C2×C8×C83—21no—
226C2×C8×C83—21no—
227C2×C8×C83—21no—
228C2×C8×C83C22×C411yescharacteristic
229C2×C8×C83C22×C411yescharacteristic
230C2×C8×C83C22×C411yescharacteristic
231C2×C8×C83C22×C411yescharacteristic
232C42×C83C22×C411yescharacteristic
233C42×C83C22×C411yescharacteristic
234C42×C83C2×D411yescharacteristic
235C42×C83C2×D411yescharacteristic
236C23×C83C2×#4111yescharacteristic
237C22×D83—21no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83C4×D411yescharacteristic
241C2×C4×C83C4×D411yescharacteristic
242C2×C4×C83C4×D411yescharacteristic
243C2×C4×C83C4×D411yescharacteristic
244C2×C4×C83C23×C411yescharacteristic
245C2×C4×C83C22×D411yescharacteristic
246C2×C4×C83C22×Q811yescharacteristic
247C2×C4×C83C2×#4111yescharacteristic
248C2×C4×C83C2×#4111yescharacteristic
249C2×C4×C83C2×#4111yescharacteristic
250C22⋊D83—22no—
251C22⋊D83—22no—
252C2×Dic83—21no—
253C2×Dic83—22no—
254C2×Dic83—21no—
255C2×Dic83—21no—
256C2×Dic83—21no—
257C2×Dic83—21no—
258C2×Dic83—21no—
259C2×Dic83—21no—
260C2×Dic83—41no—
261C2×Dic83—41no—
262C2×Dic83—41no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265D332—21no—
266D332C4×Q812yes—
267C4×D83—22no—
268C4×D83—22no—
269C4×D83—81no—
270C4×D83—81no—
271Dic166—21no—
272Dic166—81no—
273Dic166—81no—
274Dic166C4×Q812yes—
275C8×C83—21no—
276C8×C83—21no—
277C8×C83—21no—
278C8×C83—21no—
279C8×C83—22no—
280C8×C83—22no—
281C8×C83—41no—
282C8×C83—41no—
283C83⋊C8—21no—
284C83⋊C8—21no—
285C83⋊C8C22⋊Q812yes—
286C83⋊C8C22⋊Q812yes—
287C22×C83—21no—
288C22×C83—21no—
289C22×C83C2×C4×D411yescharacteristic
290C22×C83#52911yescharacteristic
291C22×C83#53311yescharacteristic
292C2×D83—22no—
293C2×D83—41no—
294C2×D83—41no—
295C4×C83—21no—
296C4×C83—21no—
297C4×C83—21no—
298C4×C83—21no—
299C4×C83C2×C4×Q811yescharacteristic
300C4×C83C4×#4111yescharacteristic
301C4×C83C2×C22⋊Q811yescharacteristic
302C4×C83#52511yescharacteristic
303Dic83—22no—
304Dic83—42no—
305Dic83—41no—
306Dic83—41no—
307Dic83—41no—
308Dic83—41no—
309Dic83—41no—
310Dic83—41no—
311Dic83—81no—
312#21629—831nomaximal, Sylow
313C2×C83—21no—
314C2×C83—21no—
315C2×C83C4×C22⋊Q811yescharacteristic
316C2×C83#295611yescharacteristic
317C2×C83#295711yescharacteristic
318D83—42no—
319#3076—831no—
320#2961—831no—
321#2875—831no—
322#1986—831no—
323#1950D8311yescharacteristic, complemented
324#1922—831no—
325#1922—831no—
326#1866—831no—
327#1866—831no—
328#1806—831no—
329#1773—831no—
330#1772—831no—
331#1771—831no—
332#1765—831no—
333#1764—831no—
334C83#2162911yescharacteristic, complemented, Sylow
335C2×#131—831no—
336C2×#131—831no—
337#533—831no—
338C4×#41—831no—
339#479—831no—
340#479—831no—
341#478—831no—
342#478—831no—
343#477—831no—
344#476—831no—
345#475—831no—
346#474—831no—
347#446—1661no—
348#446—1661no—
349#446—1661no—
350#446—1661no—
351C2×#108C2×D8311yescharacteristic
352C2×#108C2×D8311yescharacteristic
353#427—831no—
354#427—831no—
355#424—831no—
356#424—831no—
357#423C2×D8311yescharacteristic
358C2×C4⋊C8C2×D8311yescharacteristic
359C2×#104—831no—
360C2×#104—831no—
361#416—831no—
362#416—831no—
363#405—831no—
364#405—831no—
365#405—831no—
366#405—831no—
367#405—1661no—
368#405—1661no—
369C4×M16—1661no—
370C4×M16C2×D8311yescharacteristic
371C2×#97—831no—
372C2×#97—831no—
373C2×#97—1661no—
374C2×C4×C8—831no—
375C4×C4⋊C4—831no—
376#341C2×D8311yescharacteristic
377#341C2×D8311yescharacteristic
378#339—831no—
379#339—831no—
380#339—831no—
381#339—831no—
382#339—831no—
383#339—831no—
384#336—831no—
385#336—831no—
386C2×#41—831no—
387#131—834no—
388#131—1662no—
389#131—1662no—
390#131—1662no—
391C2×M16—1661no—
392C2×M16—1661no—
393C2×M16C22×D8311yescharacteristic
394C2×M16C22×D8311yescharacteristic
395C2×M16C22×D8311yescharacteristic
396C2×M16C22×D8311yescharacteristic
397C22×C8—831no—
398C22×C8—831no—
399C22×C8—1661no—
400C22×C8—1661no—
401C22×C8C22×D8311yescharacteristic
402C22×C8C22×D8311yescharacteristic
403C4⋊Q8—831no—
404C4⋊Q8—831no—
405#125—831no—
406#125—831no—
407C22⋊Q8—1661no—
408C22⋊Q8—1661no—
409C4×Q8—831no—
410C4×Q8—831no—
411C4×Q8—1661no—
412C4×Q8—1661no—
413C4×D4—831no—
414C4×D4—831no—
415C4×D4—1661no—
416C4×D4—1661no—
417#117—831no—
418#117—831no—
419#117—831no—
420#117—1661no—
421C2×C4⋊C4—1661no—
422C2×C42—831no—
423C2×C42—831no—
424C2×C42—1661no—
425C2×C42C22×D8311yescharacteristic
426#108—22no—
427#108—22no—
428#107—831no—
429#107—831no—
430#107—831no—
431#107—831no—
432#106—831no—
433#106—831no—
434#106—831no—
435#106—831no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—1661no—
439C4⋊C8—1661no—
440C4⋊C8—1661no—
441C4⋊C8—1661no—
442C4⋊C8C4×D8311yescharacteristic
443C4⋊C8C4×D8311yescharacteristic
444C4⋊C8C4×D8311yescharacteristic
445C4⋊C8C4×D8311yescharacteristic
446#104—1662no—
447#104—1662no—
448#103—831no—
449#103—831no—
450#103—831no—
451#103—831no—
452#102—831no—
453#102—831no—
454#102—831no—
455#102—831no—
456#97—21no—
457#97—831no—
458#97—831no—
459#97—831no—
460#97—831no—
461#97—1662no—
462#97—1661no—
463#97—1661no—
464#97—1661no—
465#97—1661no—
466C4×C8—21no—
467C4×C8—1662no—
468C4×C8—1661no—
469C4×C8—1661no—
470C4×C8—1661no—
471C4×C8—1661no—
472#95—1661no—
473#41—832no—
474#41—832no—
475#41—1661no—
476#41—1661no—
477C2×Q8—831no—
478C2×Q8—1661no—
479C2×Q8—1661no—
480C2×D4—831no—
481C2×D4—1661no—
482C22×C4—1661no—
483C22×C4—1661no—
484C22×C4—1661no—
485C22×C4—1661no—
486C22×C4—1661no—
487C22×C4#1305059111yescharacteristic
488C22×C4#1305059111yescharacteristic
489C22×C4C23×D8311yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—21no—
496M16—1664no—
497M16—1664no—
498M16Q8×D8312yes—
499M16#1305058912yes—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—831no—
509C2×C8—831no—
510C2×C8—832no—
511C2×C8—832no—
512C2×C8—831no—
513C2×C8—831no—
514C2×C8—1664no—
515C2×C8—1664no—
516C2×C8—1661no—
517C2×C8—1661no—
518C2×C8C2×C4×D8311yescharacteristic
519C2×C8C2×C4×D8311yescharacteristic
520C2×C8C2×C4×D8311yescharacteristic
521C2×C8C2×C4×D8311yescharacteristic
522C4⋊C4—3322no—
523C4⋊C4—831no—
524C4⋊C4—831no—
525C4⋊C4—831no—
526C4⋊C4—831no—
527C4⋊C4—831no—
528C4⋊C4—831no—
529C4⋊C4—1661no—
530C4⋊C4—1661no—
531C4⋊C4—1661no—
532C4⋊C4—1661no—
533C4⋊C4—1661no—
534C4⋊C4—1661no—
535C4⋊C4—1661no—
536C4⋊C4—1661no—
537C22⋊C4—1661no—
538C22⋊C4—1661no—
539C22⋊C4—1661no—
540C22⋊C4—1661no—
541C22⋊C4—1661no—
542C42—1661no—
543C42—1661no—
544C42—1661no—
545C42—1661no—
546C42—1661no—
547C42—1661no—
548C42—1661no—
549C42—1661no—
550C42—1661no—
551C42C2×C4×D8311yescharacteristic
552C42C2×C4×D8311yescharacteristic
553C42D4×D8311yescharacteristic
554C42D4×D8311yescharacteristic
555C23—1661no—
556C23C2×#1305059111yescharacteristic
557Q8—832no—
558Q8—6641no—
559Q8—6641no—
560Q8—1661no—
561D4—832no—
562D4—1662no—
563D4—1662no—
564D4—1661no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—3321no—
568C2×C4—3321no—
569C2×C4—3321no—
570C2×C4—3321no—
571C2×C4—3321no—
572C2×C4—6641no—
573C2×C4—6641no—
574C2×C4—1662no—
575C2×C4—1661no—
576C2×C4—1661no—
577C2×C4—1661no—
578C2×C4—1661no—
579C2×C4—1661no—
580C2×C4—1661no—
581C2×C4—1661no—
582C2×C4—1662no—
583C2×C4—1662no—
584C2×C4#1458175411yescharacteristic
585C2×C4#1458175411yescharacteristic
586C2×C4#1458175411yescharacteristic
587C2×C4#1458175411yescharacteristic
588C2×C4C22×C4×D8311yescharacteristic
589C2×C4C2×D4×D8311yescharacteristic
590C2×C4C2×Q8×D8311yescharacteristic
591C2×C4#41×D8311yescharacteristic
592C2×C4#41×D8311yescharacteristic
593C2×C4C2×#1305058911yescharacteristic
594C8—21no—
595C8—21no—
596C8—21no—
597C8—21no—
598C8—22no—
599C8—22no—
600C8—41no—
601C8—41no—
602C8—832no—
603C8—832no—
604C8—1661no—
605C8—1661no—
606C22—21no—
607C22—21no—
608C22—3321no—
609C22—3321no—
610C22—1662no—
611C22C2×#1458175411yescharacteristic
612C22#1912823611yescharacteristic
613C22#1912825611yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—3322no—
619C4—3321no—
620C4—3321no—
621C4—3321no—
622C4—3321no—
623C4—3321no—
624C4—3321no—
625C4—6641no—
626C4—1662no—
627C4C4×Q8×D8311yescharacteristic
628C4C4×#1305058911yescharacteristic
629C4C22⋊Q8×D8311yescharacteristic
630C4#1912821111yescharacteristic
631C2—21no—
632C2—21no—
633C2—3322no—
634C2#2490999311yescharacteristic
635C2#2491637211yescharacteristic
636C2#2491637911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1950C2
socleC22×C83C2×C4×D4
prime radicalC2×#13050590C23
cosocleC22×C4×C83C24
hypercenter#1950D83
hypocenterC83#21629
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. #24916400C2semidirect
4. #24908407C2semidirect
5. #24908061C2semidirect
6. #24908061C2semidirect
10. #24907350C2semidirect
11. #24907345C2semidirect
12. #24907340C2semidirect
15. C83×#1950C2semidirect
20. #19128009C4semidirect
21. #19128009C4semidirect
22. #19128002C4semidirect
23. #19128002C4semidirect
24. #19127997C4semidirect
25. #19127992C4semidirect
26. #19127987C4semidirect
27. #19127982C4semidirect
71. #14581800Q8semidirect
323. #1950D83semidirect
334. C83#21629semidirect

Maximal subgroups

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

subgroupindex
#249172532
#249164002
#249158922
#249084072
#249080612
#249077352
#249074802
#249073502
#249073452
#249073402
#249073062
#249072992
C83×#19502
#2162983