Finite Group Databasebeta

← #35463002

Subgroups — #35463002

Order 21248.

820 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128001C211yesmaximal, characteristic
2C2×#19128001C211yesmaximal, characteristic
3#24912498C211yesmaximal, characteristic, complemented
4#24908964C211yesmaximal, characteristic, complemented
5#24908954C211yesmaximal, characteristic, complemented
6#24908801C211yesmaximal, characteristic, complemented
7#24908801C211yesmaximal, characteristic, complemented
8#24908229C211yesmaximal, characteristic, complemented
9#24908187C211yesmaximal, characteristic, complemented
10#24907724C211yesmaximal, characteristic
11#24907710C211yesmaximal, characteristic
12#24907632C211yesmaximal, characteristic, complemented
13#24907463C211yesmaximal, characteristic
14#24907288C211yesmaximal, characteristic
15C83×#2349C211yesmaximal, characteristic
16C2×#14581784C2211yescharacteristic
17C2×#14581784C2211yescharacteristic
18#19128001—24no—
19#19128001—24no—
20C2×#14581725C2211yescharacteristic
21C2×#14581725C2211yescharacteristic
22C2×#14581725C2211yescharacteristic
23C2×#14581723C2211yescharacteristic
24C2×#14581723C2211yescharacteristic
25C2×#14581723C2211yescharacteristic
26C2×C4⋊(C83⋊C8)C2211yescharacteristic
27C2×C4⋊(C83⋊C8)C2211yescharacteristic
28C2×C4⋊(C83⋊C8)C2211yescharacteristic
29C2×#14581713C2211yescharacteristic
30C2×#14581713C2211yescharacteristic
31C2×#14581713C2211yescharacteristic
32C2×#14581713C2211yescharacteristic
33C2×#14581703C2211yescharacteristic
34#19127635—21no—
35#19127635—21no—
36#19127599C2211yescharacteristic
37#19127599C2211yescharacteristic
38#19127597—21no—
39#19127571C2211yescharacteristic
40#19127570—21no—
41C4×C4⋊Dic83C2211yescharacteristic
42#19127463C2211yescharacteristic
43#19127463C2211yescharacteristic
44#19127463C2211yescharacteristic
45#19127463C2211yescharacteristic
46#19127463C2211yescharacteristic
47#19127463C2211yescharacteristic
48#19127456C2211yescharacteristic
49#19127456C2211yescharacteristic
50C2×C4×D4×C83C2211yescharacteristic
51C2×C4×D4×C83C2211yescharacteristic
52C2×C4×D4×C83C2211yescharacteristic
53#389×C83C2211yescharacteristic
54#389×C83C2211yescharacteristic
55#385×C83—21no—
56#385×C83—21no—
57#382×C83C2211yescharacteristic
58#380×C83—21no—
59C4×C4⋊C4×C83C2211yescharacteristic
60C2×#95×C83—21no—
61C22×C83⋊C8C2311yescharacteristic
62C22×C83⋊C8C2311yescharacteristic
63C22×C83⋊C8C2311yescharacteristic
64C22×C83⋊C8C2311yescharacteristic
65#14581784—22no—
66#14581784—22no—
67#14581784—41no—
68#14581784—41no—
69C2×C4⋊Dic83—21no—
70C2×C4⋊Dic83—21no—
71C2×C4⋊Dic83C2311yescharacteristic
72C2×C4⋊Dic83C2311yescharacteristic
73C2×C4⋊Dic83C2311yescharacteristic
74C2×C4⋊Dic83C2311yescharacteristic
75C2×Dic83⋊C4—21no—
76C2×Dic83⋊C4—21no—
77C2×Dic83⋊C4—21no—
78C2×Dic83⋊C4—21no—
79C2×Dic83⋊C4—21no—
80C2×Dic83⋊C4—21no—
81C2×C4×Dic83—21no—
82#14581725—22no—
83#14581725—22no—
84#14581725—41no—
85#14581723—22no—
86#14581723—22no—
87#14581723—41no—
88C4⋊(C83⋊C8)—22no—
89C4⋊(C83⋊C8)—22no—
90C4⋊(C83⋊C8)—22no—
91#14581713—22no—
92#14581713—22no—
93#14581713D414yes—
94#14581713Q814yes—
95#14581703—22no—
96C83⋊#95—21no—
97C83⋊#95—21no—
98C83⋊#95—21no—
99C22×D4×C83C2311yescharacteristic
100C23×C4×C83—21no—
101C23×C4×C83—21no—
102C23×C4×C83—21no—
103C4×D4×C83—22no—
104C4×D4×C83—22no—
105C4×D4×C83—22no—
106C4×D4×C83—41no—
107C4×D4×C83—41no—
108C4×D4×C83Q814yes—
109C2×C4⋊C4×C83—21no—
110C2×C4⋊C4×C83—21no—
111C2×C4⋊C4×C83D411yescharacteristic
112C2×C4⋊C4×C83D411yescharacteristic
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C4⋊C4×C83C2311yescharacteristic
116C2×C22⋊C4×C83—21no—
117C2×C22⋊C4×C83—21no—
118C2×C22⋊C4×C83—21no—
119C2×C42×C83C2311yescharacteristic
120C2×C42×C83C2311yescharacteristic
121C2×C42×C83C2311yescharacteristic
122#95×C83—21no—
123#95×C83—21no—
124#95×C83—21no—
125#95×C83—21no—
126#95×C83D411yescharacteristic
127#95×C83D411yescharacteristic
128C22×Dic83—21no—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—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—21no—
142C2×C83⋊C8C2×D412yes—
143C2×C83⋊C8C2×Q812yes—
144C4⋊Dic83—21no—
145C4⋊Dic83—21no—
146C4⋊Dic83—21no—
147C4⋊Dic83—21no—
148C4⋊Dic83—21no—
149C4⋊Dic83—21no—
150C4⋊Dic83—42no—
151C4⋊Dic83—81no—
152C4⋊Dic83C2×D412yes—
153C4⋊Dic83C2×Q812yes—
154Dic83⋊C4—42no—
155Dic83⋊C4—42no—
156Dic83⋊C4—42no—
157Dic83⋊C4—42no—
158Dic83⋊C4—81no—
159Dic83⋊C4—81no—
160C4×Dic83—42no—
161C24×C83—21no—
162C2×D4×C83—21no—
163C2×D4×C83—21no—
164C2×D4×C83—21no—
165C2×D4×C83C2×D412yes—
166C2×D4×C83C2×Q812yes—
167C2×D4×C83C2×Q812yes—
168C22×C4×C83—21no—
169C22×C4×C83—24no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83—42no—
173C22×C4×C83—42no—
174C22×C4×C83—42no—
175C22×C4×C83—42no—
176C22×C4×C83—81no—
177C22×C4×C83—81no—
178C22×C4×C83—81no—
179C22×C4×C83—81no—
180C22×C4×C83C2×D411yescharacteristic
181C22×C4×C83C2×D411yescharacteristic
182C22×C4×C83C2×D411yescharacteristic
183C22×C4×C83C2×D411yescharacteristic
184C22×C4×C83C2×D411yescharacteristic
185C22×C4×C83C2×D411yescharacteristic
186C22×C4×C83C2411yescharacteristic
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—41no—
193C4⋊C4×C83—41no—
194C4⋊C4×C83—81no—
195C4⋊C4×C83—81no—
196C4⋊C4×C83C2×Q812yes—
197C22⋊C4×C83—24no—
198C22⋊C4×C83—42no—
199C22⋊C4×C83—42no—
200C42×C83—21no—
201C42×C83—21no—
202C42×C83—21no—
203C42×C83—21no—
204C42×C83C2×Q812yes—
205C42×C83#4112yes—
206C23×C83—22no—
207C23×C83—22no—
208C23×C83—22no—
209C23×C83—41no—
210C23×C83—41no—
211C23×C83—41no—
212C23×C83—41no—
213C23×C83C22×D411yescharacteristic
214D4×C83—22no—
215D4×C83—22no—
216D4×C83—22no—
217D4×C83C4⋊Q814yes—
218C2×C4×C83—21no—
219C2×C4×C83—21no—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—22no—
223C2×C4×C83—21no—
224C2×C4×C83—21no—
225C2×C4×C83—21no—
226C2×C4×C83—21no—
227C2×C4×C83—21no—
228C2×C4×C83—21no—
229C2×C4×C83—21no—
230C2×C4×C83—21no—
231C2×C4×C83—21no—
232C2×C4×C83—21no—
233C2×C4×C83—21no—
234C2×C4×C83—21no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—41no—
240C2×C4×C83—41no—
241C2×C4×C83—41no—
242C2×C4×C83—41no—
243C2×C4×C83—84no—
244C2×C4×C83—84no—
245C2×C4×C83—84no—
246C2×C4×C83C22⋊Q812yes—
247C2×C4×C83C22⋊Q812yes—
248C2×C4×C83C22×D411yescharacteristic
249C2×C4×C83C22×Q811yescharacteristic
250C2×C4×C83C22×Q811yescharacteristic
251C2×C4×C83C2×#4111yescharacteristic
252C2×C4×C83H(5,𝔽2)11yescharacteristic
253C2×C4×C832−1+411yescharacteristic
254C2×Dic83—22no—
255C2×Dic83—22no—
256C2×Dic83—41no—
257C2×Dic83—41no—
258C2×Dic83—41no—
259C2×Dic83—41no—
260C2×Dic83—41no—
261C2×Dic83—41no—
262C2×Dic83—41no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265C2×Dic83—41no—
266C83⋊C8—22no—
267C83⋊C8—22no—
268C83⋊C8—41no—
269C83⋊C8—41no—
270C22×C83—24no—
271C22×C83—42no—
272C22×C83—42no—
273C22×C83—42no—
274C22×C83—42no—
275C22×C83—42no—
276C22×C83—42no—
277C22×C83C2×C22⋊Q811yescharacteristic
278C22×C83D4211yescharacteristic
279C22×C83D4×Q811yescharacteristic
280C22×C83#57511yescharacteristic
281C22×C83#57511yescharacteristic
282C22×C83#57611yescharacteristic
283C22×C83#57711yescharacteristic
284C4×C83—22no—
285C4×C83—22no—
286C4×C83—42no—
287C4×C83—41no—
288C4×C83—41no—
289C4×C83—41no—
290C4×C83—41no—
291C4×C83—81no—
292C4×C83—81no—
293C4×C83C2×C4⋊Q811yescharacteristic
294C4×C83#54411yescharacteristic
295C4×C83#54711yescharacteristic
296C4×C83#55411yescharacteristic
297Dic83—42no—
298Dic83—42no—
299Dic83—81no—
300Dic83—81no—
301#26059—831nomaximal, Sylow
302C2×C83—44no—
303C2×C83#244011yescharacteristic
304C2×C83#308011yescharacteristic
305C2×C83#308111yescharacteristic
306C2×C83#326711yescharacteristic
307C2×C83#326811yescharacteristic
308C2×C83#338811yescharacteristic
309C2×C83#338911yescharacteristic
310C2×#478—831no—
311C2×#478—831no—
312#2552—831no—
313#2349D8311yescharacteristic
314#2088—831no—
315#2086—831no—
316#2059—831no—
317#2059—831no—
318#1949—831no—
319#1940—831no—
320#1864—831no—
321#1862—831no—
322#1847—831no—
323#1802—831no—
324#1762—831no—
325C83#2605911yescharacteristic, complemented, Sylow
326C2×#125—831no—
327C2×#125—831no—
328C2×C4×D4C2×D8311yescharacteristic
329C2×C4×D4C2×D8311yescharacteristic
330C2×C4×D4C2×D8311yescharacteristic
331#478—1664no—
332#478—1664no—
333C2×#107—831no—
334C2×#107—831no—
335C2×#107—831no—
336C2×#106—831no—
337C2×#106—831no—
338C2×#106—831no—
339C2×C4⋊C8—831no—
340C2×C4⋊C8—831no—
341C2×C4⋊C8—831no—
342C2×#102—831no—
343C2×#102—831no—
344C2×#102—831no—
345C2×#102—831no—
346C2×#97—831no—
347#398—1661no—
348#398—1661no—
349#389—831no—
350#389—831no—
351#389—1661no—
352#389C2×D8311yescharacteristic
353#389C2×D8311yescharacteristic
354#385—21no—
355#385—21no—
356#384—831no—
357#384—1661no—
358#382C2×D8311yescharacteristic
359#380—21no—
360C4×C4⋊C4—831no—
361C4×C4⋊C4C2×D8311yescharacteristic
362C2×#95—21no—
363#340—831no—
364#340—831no—
365#340—831no—
366#340—831no—
367#340—831no—
368#340—831no—
369#336—831no—
370#336—831no—
371C22×D4C22×D8311yescharacteristic
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—21no—
375C22×C8—831no—
376C22×C8—831no—
377C22×C8—831no—
378C22×C8—831no—
379#125—3321no—
380#125—3321no—
381#125—1662no—
382#125—1662no—
383C4×D4—22no—
384C4×D4—22no—
385C4×D4—22no—
386C4×D4—41no—
387C4×D4—41no—
388C4×D4Dic16614yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—831no—
392C2×C4⋊C4—831no—
393C2×C4⋊C4—831no—
394C2×C4⋊C4—831no—
395C2×C4⋊C4—1661no—
396C2×C4⋊C4—1661no—
397C2×C4⋊C4—1661no—
398C2×C4⋊C4—1661no—
399C2×C4⋊C4—1661no—
400C2×C4⋊C4—1661no—
401C2×C4⋊C4—1661no—
402C2×C4⋊C4—1661no—
403C2×C4⋊C4C22⋊D8311yescharacteristic
404C2×C4⋊C4C22⋊D8311yescharacteristic
405C2×C4⋊C4C22×D8311yescharacteristic
406C2×C4⋊C4C22×D8311yescharacteristic
407C2×C4⋊C4C22×D8311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C42—1661no—
412C2×C42C22×D8311yescharacteristic
413C2×C42C22×D8311yescharacteristic
414C2×C42C22×D8311yescharacteristic
415#107—3321no—
416#107—1662no—
417#107—1662no—
418#106—3321no—
419#106—1662no—
420#106—1662no—
421C4⋊C8—1662no—
422C4⋊C8—1662no—
423C4⋊C8—1662no—
424#102—834no—
425#102—834no—
426#102—1662no—
427#102—1662no—
428#97—1662no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—1661no—
434#95—1661no—
435#95—1661no—
436#95C22⋊D8311yescharacteristic
437#95C22⋊D8311yescharacteristic
438C24—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4D4×D8312yes—
443C2×D4Q8×D8312yes—
444C2×D4C2×Dic16612yes—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4—81no—
456C22×C4—81no—
457C22×C4—1661no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4—1661no—
461C22×C4C2×C22⋊D8311yescharacteristic
462C22×C4C2×C22⋊D8311yescharacteristic
463C22×C4C2×C22⋊D8311yescharacteristic
464C22×C4C2×C22⋊D8311yescharacteristic
465C22×C4C2×C22⋊D8311yescharacteristic
466C22×C4C2×C22⋊D8311yescharacteristic
467C22×C4C23×D8311yescharacteristic
468C2×C8—832no—
469C2×C8—832no—
470C2×C8—1661no—
471C2×C8—1661no—
472C2×C8—1661no—
473C2×C8—1661no—
474C2×C8—1661no—
475C2×C8—1661no—
476C2×C8—1661no—
477C2×C8—1661no—
478C2×C8—1661no—
479C2×C8—1661no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—81no—
488C4⋊C4—81no—
489C4⋊C4—3322no—
490C4⋊C4—3322no—
491C4⋊C4—3322no—
492C4⋊C4—3322no—
493C4⋊C4—3322no—
494C4⋊C4—832no—
495C4⋊C4—832no—
496C4⋊C4—6641no—
497C4⋊C4—6641no—
498C4⋊C4—6641no—
499C4⋊C4—1661no—
500C4⋊C4—1661no—
501C4⋊C4—1661no—
502C4⋊C4—1661no—
503C4⋊C4—1661no—
504C4⋊C4—1661no—
505C4⋊C4C2×Dic16612yes—
506C22⋊C4—24no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—3322no—
514C42C2×Dic16612yes—
515C42#1305059012yes—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C22×C22⋊D8311yescharacteristic
524D4—22no—
525D4—22no—
526D4—22no—
527D4#1458179114yes—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—84no—
554C2×C4—84no—
555C2×C4—84no—
556C2×C4—3321no—
557C2×C4—3321no—
558C2×C4—3321no—
559C2×C4—3321no—
560C2×C4—3321no—
561C2×C4—3321no—
562C2×C4—3321no—
563C2×C4—3321no—
564C2×C4—3321no—
565C2×C4—3321no—
566C2×C4—1662no—
567C2×C4—1662no—
568C2×C4#1458177112yes—
569C2×C4#1458177112yes—
570C2×C4C2×D4×D8311yescharacteristic
571C2×C4C2×Q8×D8311yescharacteristic
572C2×C4C22×Dic16611yescharacteristic
573C2×C4C2×#1305059011yescharacteristic
574C2×C4#1458183711yescharacteristic
575C2×C4#1458184011yescharacteristic
576C8—3321no—
577C8—3321no—
578C8—1662no—
579C8—1662no—
580C22—24no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22C2×#1458177111yescharacteristic
588C22D4×C22⋊D8311yescharacteristic
589C22Q8×C22⋊D8311yescharacteristic
590C22#1912849911yescharacteristic
591C22#1912849911yescharacteristic
592C22#1912850411yescharacteristic
593C22#1912851211yescharacteristic
594C4—22no—
595C4—22no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—81no—
602C4—81no—
603C4—3322no—
604C4—3322no—
605C4—6641no—
606C4—6641no—
607C4C2×#1458179111yescharacteristic
608C4#1912833211yescharacteristic
609C4#1912835211yescharacteristic
610C4#1912840611yescharacteristic
611C2—44no—
612C2#2491115911yescharacteristic
613C2#2491728511yescharacteristic
614C2#2491729411yescharacteristic
615C2#2491898411yescharacteristic
616C2#2491899911yescharacteristic
617C2#2492040811yescharacteristic
618C2#2492041711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC83×#2349C2
socleC23×C83C22×D4
prime radicalC22×D4×C83C23
hypercenter#2349D83
hypocenterC83#26059
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #24912498C2semidirect
4. #24908964C2semidirect
5. #24908954C2semidirect
6. #24908801C2semidirect
7. #24908801C2semidirect
8. #24908229C2semidirect
9. #24908187C2semidirect
12. #24907632C2semidirect
325. C83#26059semidirect

Maximal subgroups

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

subgroupindex
C2×#191280012
#249124982
#249089642
#249089542
#249088012
#249082292
#249081872
#249077242
#249077102
#249076322
#249074632
#249072882
C83×#23492
#2605983