Finite Group Databasebeta

← #35423878

Subgroups — #35423878

Order 21248.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24916261C211yesmaximal, characteristic
2#24916028C211yesmaximal, characteristic, complemented
3#24908177C211yesmaximal, characteristic, complemented
4#24908170C211yesmaximal, characteristic, complemented
5#24908062C211yesmaximal, characteristic, complemented
6#24908062C211yesmaximal, characteristic, complemented
7#24907793C211yesmaximal, characteristic
8#24907793C211yesmaximal, characteristic
9#24907603C211yesmaximal, characteristic, complemented
10#24907483C211yesmaximal, characteristic, complemented
11#24907480C211yesmaximal, characteristic, complemented
12#24907340C211yesmaximal, characteristic, complemented
13#24907309C211yesmaximal, characteristic, complemented
14#24907302C211yesmaximal, characteristic, complemented
15C83×#2925C211yesmaximal, characteristic, complemented
16C2×#14581812C2211yescharacteristic
17C2×#14581798C2211yescharacteristic
18C2×#14581798C2211yescharacteristic
19C4×#13050590C2211yescharacteristic
20#19127811C411yescharacteristic, complemented
21#19127811C411yescharacteristic, complemented
22#19127806C411yescharacteristic, complemented
23#19127806C411yescharacteristic, complemented
24#19127801C411yescharacteristic, complemented
25#19127801C411yescharacteristic, complemented
26#19127799C411yescharacteristic, complemented
27#19127799C411yescharacteristic, complemented
28#19127737C2211yescharacteristic
29#19127727C2211yescharacteristic
30#19127727C2211yescharacteristic
31#19127726—21no—
32#19127726—21no—
33#19127725C2211yescharacteristic
34#19127723—21no—
35C4⋊C8×D83—21no—
36C2×#14581719C2211yescharacteristic
37C2×#14581719C2211yescharacteristic
38C2×#14581718C2211yescharacteristic
39C2×#14581718C2211yescharacteristic
40#19127697C2211yescharacteristic
41#19127695C2211yescharacteristic
42C2×#14581703C2211yescharacteristic
43C2×#14581702C2211yescharacteristic
44C2×C8×Dic83C2211yescharacteristic
45C4×C4⋊Dic83C2211yescharacteristic
46#19127465C2211yescharacteristic
47#19127465C2211yescharacteristic
48#19127465C2211yescharacteristic
49#19127465C2211yescharacteristic
50#19127462C2211yescharacteristic
51#19127462C2211yescharacteristic
52#19127460C2211yescharacteristic
53#19127460C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C4×#41×C83C2211yescharacteristic
57#433×C83—21no—
58#433×C83—21no—
59#432×C83—21no—
60#431×C83—21no—
61#423×C83C2211yescharacteristic
62C2×C4⋊C8×C83C2211yescharacteristic
63#408×C83C2211yescharacteristic
64#408×C83C2211yescharacteristic
65#405×C83C2211yescharacteristic
66#405×C83C2211yescharacteristic
67C2×#13050590C2311yescharacteristic
68#14581812—22no—
69#14581812—22no—
70C2×#13050580C2×C411yescharacteristic
71C2×#13050578C2×C411yescharacteristic
72C2×#13050577C2×C411yescharacteristic
73C2×#13050575C2×C411yescharacteristic
74#14581798—22no—
75#14581798—22no—
76#14581798—41no—
77#14581798—41no—
78C2×#13050574C2311yescharacteristic
79C2×#13050574C2311yescharacteristic
80C2×#13050573—21no—
81C2×#13050573—21no—
82C22×C83⋊C8C2311yescharacteristic
83C22×C83⋊C8C2311yescharacteristic
84C2×C8×D83—21no—
85C2×C8×D83—21no—
86C4×Dic166C2×C411yescharacteristic
87C4×Dic166C2×C411yescharacteristic
88C4×D332C2×C411yescharacteristic
89C4×D332C2×C411yescharacteristic
90C4×C22⋊D83—21no—
91C4×C22⋊D83—21no—
92#14581751C2311yescharacteristic
93#14581749—21no—
94C2×C4⋊Dic83—21no—
95C2×C4×Dic83C2311yescharacteristic
96C2×C4×Dic83C2311yescharacteristic
97C42×D83—21no—
98#14581725C2×C411yescharacteristic
99#14581725C2×C411yescharacteristic
100#14581723C2×C411yescharacteristic
101#14581723C2×C411yescharacteristic
102C4⋊(C83⋊C8)—21no—
103C4⋊(C83⋊C8)—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
107Dic83⋊C8—21no—
108#14581719—41no—
109#14581719—41no—
110#14581718—22no—
111#14581718—22no—
112#14581716C2×C411yescharacteristic
113#14581716C2×C411yescharacteristic
114#14581715C2×C411yescharacteristic
115#14581715C2×C411yescharacteristic
116#14581713C2×C411yescharacteristic
117#14581713C2×C411yescharacteristic
118#14581712C2×C411yescharacteristic
119#14581712C2×C411yescharacteristic
120#14581703C2×C411yescharacteristic
121#14581703C2×C411yescharacteristic
122#14581703C2×C411yescharacteristic
123#14581703C2×C411yescharacteristic
124#14581702—41no—
125C8×Dic83—41no—
126C83⋊#95—21no—
127C2×#41×C83C2311yescharacteristic
128C2×M16×C83C2311yescharacteristic
129C2×M16×C83C2311yescharacteristic
130C22×C8×C83C2311yescharacteristic
131C22×C8×C83C2311yescharacteristic
132C4×Q8×C83C2×C411yescharacteristic
133C4×Q8×C83C2×C411yescharacteristic
134C4×D4×C83—21no—
135C4×D4×C83—21no—
136C4×D4×C83C2×C411yescharacteristic
137C4×D4×C83C2×C411yescharacteristic
138#117×C83—21no—
139#117×C83C2311yescharacteristic
140C2×C42×C83—21no—
141C2×C42×C83C2311yescharacteristic
142C4⋊C8×C83—21no—
143C4⋊C8×C83—21no—
144C4⋊C8×C83D411yescharacteristic
145C4⋊C8×C83D411yescharacteristic
146C4⋊C8×C83D411yescharacteristic
147C4⋊C8×C83D411yescharacteristic
148C22⋊C8×C83—21no—
149C22⋊C8×C83—21no—
150C22⋊C8×C83—21no—
151C22⋊C8×C83—21no—
152#97×C83—21no—
153#97×C83—21no—
154C4×C8×C83—21no—
155C4×C8×C83—21no—
156#13050590—21no—
157#13050590—21no—
158#13050590#4112yes—
159#13050590#4112yes—
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#13050580—22no—
169#13050578—22no—
170#13050577—22no—
171#13050575—22no—
172#13050574—21no—
173#13050574—21no—
174#13050574—21no—
175#13050574—21no—
176#13050573—42no—
177#13050573—42no—
178C2×C83⋊C8—21no—
179C2×C83⋊C8—21no—
180C2×C83⋊C8—21no—
181C2×C83⋊C8—21no—
182C2×C83⋊C8—21no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8C22×C411yescharacteristic
185C2×C83⋊C8C22×C411yescharacteristic
186C2×C83⋊C8C22×C411yescharacteristic
187C2×C83⋊C8C22×C411yescharacteristic
188C8×D83—42no—
189C8×D83—42no—
190C4⋊Dic83—42no—
191C4⋊Dic83C22×C411yescharacteristic
192C4⋊Dic83C22×C411yescharacteristic
193Dic83⋊C4—21no—
194Dic83⋊C4—21no—
195C22⋊Dic83—21no—
196(C2×D83)⋊C4—21no—
197(C2×D83)⋊C4—21no—
198C4×Dic83—21no—
199C4×Dic83—21no—
200C4×Dic83—21no—
201C4×Dic83—21no—
202C4×Dic83—21no—
203C4×Dic83—21no—
204C4×Dic83—21no—
205#41×C83—21no—
206#41×C83—21no—
207#41×C83—21no—
208#41×C83—21no—
209C2×Q8×C83C22×C411yescharacteristic
210C2×D4×C83—21no—
211C2×D4×C83C22×C411yescharacteristic
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83#4111yescharacteristic
216C22×C4×C83#4111yescharacteristic
217C22×C4×C83C2411yescharacteristic
218M16×C83—21no—
219M16×C83—21no—
220M16×C83—21no—
221M16×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×C83C2×D411yescharacteristic
229C2×C8×C83C2×D411yescharacteristic
230C2×C8×C83C2×D411yescharacteristic
231C2×C8×C83C2×D411yescharacteristic
232C4⋊C4×C83—21no—
233C4⋊C4×C83—21no—
234C4⋊C4×C83C22×C411yescharacteristic
235C4⋊C4×C83C22×C411yescharacteristic
236C22⋊C4×C83—21no—
237C22⋊C4×C83—21no—
238C22⋊C4×C83—21no—
239C42×C83—21no—
240C42×C83—21no—
241C42×C83—21no—
242C42×C83C22×C411yescharacteristic
243C42×C83C22×C411yescharacteristic
244C42×C83C2×D411yescharacteristic
245C42×C83C2×D411yescharacteristic
246C23×C83—21no—
247C23×C83C2×#4111yescharacteristic
248C22×D83—21no—
249Q8×C83—21no—
250Q8×C83—21no—
251D4×C83—21no—
252D4×C83—21no—
253D4×C83—41no—
254D4×C83—41no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—41no—
259C2×C4×C83—41no—
260C2×C4×C83—42no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—81no—
264C2×C4×C83C4×D411yescharacteristic
265C2×C4×C83C4×D411yescharacteristic
266C2×C4×C83C4×D411yescharacteristic
267C2×C4×C83C4×D411yescharacteristic
268C2×C4×C83C23×C411yescharacteristic
269C2×C4×C83C22×D411yescharacteristic
270C2×C4×C83C2×#4111yescharacteristic
271C2×C4×C83C2×#4111yescharacteristic
272C2×C4×C83H(5,𝔽2)11yescharacteristic
273C2×C4×C832−1+411yescharacteristic
274C22⋊D83—22no—
275C22⋊D83—22no—
276C2×Dic83—21no—
277C2×Dic83—22no—
278C2×Dic83—21no—
279C2×Dic83—21no—
280C2×Dic83—41no—
281C2×Dic83—41no—
282C2×Dic83—41no—
283C2×Dic83—41no—
284C2×Dic83—41no—
285D332—21no—
286D332#11712yes—
287C4×D83—22no—
288C4×D83—22no—
289C4×D83—42no—
290C4×D83—81no—
291Dic166—21no—
292Dic166#11712yes—
293C8×C83—21no—
294C8×C83—21no—
295C8×C83—21no—
296C8×C83—21no—
297C8×C83—41no—
298C8×C83—41no—
299C83⋊C8—21no—
300C83⋊C8—21no—
301C83⋊C8—21no—
302C83⋊C8—21no—
303C83⋊C8—41no—
304C83⋊C8—41no—
305C22×C83—21no—
306C22×C83—21no—
307C22×C83—41no—
308C22×C83—41no—
309C22×C83—41no—
310C22×C83C2×C4×D411yescharacteristic
311C22×C83#55211yescharacteristic
312C22×C83#55311yescharacteristic
313C2×D83—22no—
314C2×D83—41no—
315C2×D83—41no—
316C4×C83—21no—
317C4×C83—21no—
318C4×C83—21no—
319C4×C83—21no—
320C4×C83—41no—
321C4×C83—41no—
322C4×C83—41no—
323C4×C83C2×#11711yescharacteristic
324C4×C83#52011yescharacteristic
325C4×C83#54611yescharacteristic
326C4×C83#54811yescharacteristic
327Dic83—22no—
328Dic83—42no—
329Dic83—41no—
330Dic83—41no—
331Dic83—81no—
332#22784—831nomaximal, Sylow
333C2×C83—21no—
334C2×C83—21no—
335C2×C83—81no—
336C2×C83#235211yescharacteristic
337C2×C83#295511yescharacteristic
338C2×C83#295611yescharacteristic
339D83—42no—
340#2943—831no—
341#2925D8311yescharacteristic, complemented
342#2906—831no—
343#1938—831no—
344#1937—831no—
345#1922—831no—
346#1922—831no—
347#1876—831no—
348#1876—831no—
349#1838—831no—
350#1806—831no—
351#1806—831no—
352#1771—831no—
353#1765—831no—
354#1764—831no—
355C83#2278411yescharacteristic, complemented, Sylow
356C2×#135—831no—
357C2×#131—831no—
358C2×#131—831no—
359C4×#41—831no—
360C4×#41C2×D8311yescharacteristic
361#442—831no—
362#442—831no—
363#441—831no—
364#441—831no—
365#440—831no—
366#440—831no—
367#440—831no—
368#440—831no—
369#433—21no—
370#433—21no—
371#432—21no—
372#431—21no—
373#427—831no—
374#424—831no—
375#424—831no—
376#424—1661no—
377#424—1661no—
378#423—831no—
379#423—1661no—
380#423C2×D8311yescharacteristic
381C2×C4⋊C8—1661no—
382C2×C4⋊C8C2×D8311yescharacteristic
383C2×#104—831no—
384C2×#104—831no—
385C2×#104—831no—
386C2×#104—831no—
387#416—831no—
388#416—831no—
389#408C2×D8311yescharacteristic
390#408C2×D8311yescharacteristic
391#405C2×D8311yescharacteristic
392#405C2×D8311yescharacteristic
393C2×#97—831no—
394C2×#97—831no—
395C2×C4×C8—831no—
396C4×C4⋊C4—831no—
397#341—831no—
398#341—831no—
399#341—831no—
400#341—831no—
401#339—831no—
402#339—831no—
403#339—831no—
404#339—831no—
405#336—831no—
406#336—831no—
407C2×#41—831no—
408C2×#41C22×D8311yescharacteristic
409#135—1662no—
410#135—1662no—
411C2×Q16—831no—
412C2×SD16—831no—
413C2×SD16—831no—
414C2×D8—831no—
415#131—3321no—
416#131—3321no—
417#131—1662no—
418#131—1662no—
419C2×M16—831no—
420C2×M16—831no—
421C2×M16—1661no—
422C2×M16—1661no—
423C2×M16C22×D8311yescharacteristic
424C2×M16C22×D8311yescharacteristic
425C22×C8—831no—
426C22×C8—831no—
427C22×C8—1661no—
428C22×C8—1661no—
429C22×C8C22×D8311yescharacteristic
430C22×C8C22×D8311yescharacteristic
431C4×Q8—831no—
432C4×Q8—831no—
433C4×Q8C4×D8311yescharacteristic
434C4×Q8C4×D8311yescharacteristic
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—831no—
438C4×D4—831no—
439C4×D4—1661no—
440C4×D4—1661no—
441C4×D4C4×D8311yescharacteristic
442C4×D4C4×D8311yescharacteristic
443#117—21no—
444#117—831no—
445#117—1661no—
446#117C22×D8311yescharacteristic
447C2×C4⋊C4—1661no—
448C2×C42—21no—
449C2×C42—831no—
450C2×C42—831no—
451C2×C42—1661no—
452C2×C42C22×D8311yescharacteristic
453#107—831no—
454#107—831no—
455#106—831no—
456#106—831no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—1661no—
460C4⋊C8—1661no—
461C4⋊C8—1661no—
462C4⋊C8—1661no—
463C4⋊C8—1661no—
464C4⋊C8—1661no—
465C4⋊C8C22⋊D8311yescharacteristic
466C4⋊C8C22⋊D8311yescharacteristic
467C4⋊C8C22⋊D8311yescharacteristic
468C4⋊C8C22⋊D8311yescharacteristic
469#104—3321no—
470#104—3321no—
471#104—1662no—
472#104—1662no—
473#103—831no—
474#103—831no—
475#103—831no—
476#103—831no—
477#102—831no—
478#102—831no—
479#102—831no—
480#102—831no—
481C22⋊C8—21no—
482C22⋊C8—21no—
483C22⋊C8—21no—
484C22⋊C8—21no—
485#97—21no—
486#97—21no—
487#97—3321no—
488#97—831no—
489#97—831no—
490#97—831no—
491#97—831no—
492C4×C8—21no—
493C4×C8—21no—
494C4×C8—3321no—
495#95—1661no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—832no—
501#41—832no—
502#41—1661no—
503#41—1661no—
504C2×Q8—831no—
505C2×Q8C2×C4×D8311yescharacteristic
506C2×D4—21no—
507C2×D4—831no—
508C2×D4—1661no—
509C2×D4C2×C4×D8311yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—1661no—
514C22×C4—1661no—
515C22×C4—1661no—
516C22×C4—1661no—
517C22×C4—1661no—
518C22×C4#1305059011yescharacteristic
519C22×C4#1305059011yescharacteristic
520C22×C4C23×D8311yescharacteristic
521Q16—1662no—
522SD16—1662no—
523SD16—1662no—
524D8—1662no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—3322no—
530M16—3322no—
531M16—1661no—
532M16—1661no—
533M16—1661no—
534M16—1661no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—3322no—
542C2×C8—3322no—
543C2×C8—831no—
544C2×C8—831no—
545C2×C8—831no—
546C2×C8—831no—
547C2×C8—1661no—
548C2×C8—1661no—
549C2×C8—1661no—
550C2×C8—1661no—
551C2×C8—1661no—
552C2×C8—1661no—
553C2×C8C2×C22⋊D8311yescharacteristic
554C2×C8C2×C22⋊D8311yescharacteristic
555C2×C8C2×C22⋊D8311yescharacteristic
556C2×C8C2×C22⋊D8311yescharacteristic
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—3322no—
560C4⋊C4—831no—
561C4⋊C4—831no—
562C4⋊C4—1661no—
563C4⋊C4—1661no—
564C4⋊C4C2×C4×D8311yescharacteristic
565C4⋊C4C2×C4×D8311yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—1661no—
570C22⋊C4—1661no—
571C22⋊C4—1661no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—1661no—
576C42—1661no—
577C42—1661no—
578C42—1661no—
579C42—1661no—
580C42—1661no—
581C42—1661no—
582C42C2×C4×D8311yescharacteristic
583C42C2×C4×D8311yescharacteristic
584C42C2×C22⋊D8311yescharacteristic
585C42C2×C22⋊D8311yescharacteristic
586C23—21no—
587C23—1661no—
588C23C2×#1305059011yescharacteristic
589Q8—21no—
590Q8—21no—
591Q8—832no—
592Q8—1661no—
593D4—21no—
594D4—21no—
595D4—41no—
596D4—41no—
597D4—832no—
598D4—1662no—
599D4—1662no—
600D4—1661no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—81no—
610C2×C4—3322no—
611C2×C4—3321no—
612C2×C4—3321no—
613C2×C4—3321no—
614C2×C4—3321no—
615C2×C4—3321no—
616C2×C4—6641no—
617C2×C4—1662no—
618C2×C4—1661no—
619C2×C4—1661no—
620C2×C4—1661no—
621C2×C4—1662no—
622C2×C4—1662no—
623C2×C4C4×C22⋊D8311yescharacteristic
624C2×C4C4×C22⋊D8311yescharacteristic
625C2×C4C4×C22⋊D8311yescharacteristic
626C2×C4C4×C22⋊D8311yescharacteristic
627C2×C4C22×C4×D8311yescharacteristic
628C2×C4C22×C22⋊D8311yescharacteristic
629C2×C4#41×D8311yescharacteristic
630C2×C4#41×D8311yescharacteristic
631C2×C4#1458183811yescharacteristic
632C2×C4#1458183911yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—41no—
638C8—41no—
639C8—3321no—
640C8—3321no—
641C8—1661no—
642C8—1661no—
643C8—1661no—
644C8—1661no—
645C22—21no—
646C22—21no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—3321no—
651C22—3321no—
652C22—1662no—
653C22C2×C4×C22⋊D8311yescharacteristic
654C22#1912839011yescharacteristic
655C22#1912839511yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—3322no—
664C4—3321no—
665C4—3321no—
666C4—6641no—
667C4—1662no—
668C4#117×D8311yescharacteristic
669C4#1912818111yescharacteristic
670C4#1912833911yescharacteristic
671C4#1912835811yescharacteristic
672C2—21no—
673C2—21no—
674C2—81no—
675C2—3322no—
676C2#2491039311yescharacteristic
677C2#2491636411yescharacteristic
678C2#2491637011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#2925C2
socleC22×C83C2×C4×D4
prime radicalC2×#14581812C22
cosocleC22×C4×C83C24
hypercenter#2925D83
hypocenterC83#22784
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #24916028C2semidirect
3. #24908177C2semidirect
4. #24908170C2semidirect
5. #24908062C2semidirect
6. #24908062C2semidirect
9. #24907603C2semidirect
10. #24907483C2semidirect
11. #24907480C2semidirect
12. #24907340C2semidirect
13. #24907309C2semidirect
14. #24907302C2semidirect
15. C83×#2925C2semidirect
20. #19127811C4semidirect
21. #19127811C4semidirect
22. #19127806C4semidirect
23. #19127806C4semidirect
24. #19127801C4semidirect
25. #19127801C4semidirect
26. #19127799C4semidirect
27. #19127799C4semidirect
341. #2925D83semidirect
355. C83#22784semidirect

Maximal subgroups

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

subgroupindex
#249162612
#249160282
#249081772
#249081702
#249080622
#249077932
#249076032
#249074832
#249074802
#249073402
#249073092
#249073022
C83×#29252
#2278483