Finite Group Databasebeta

← #35330460

Subgroups — #35330460

Order 21248.

1678 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127626C211yesmaximal, characteristic
2C2×#19127599C211yesmaximal, characteristic, complemented
3C2×#19127595C212yesmaximal
4#24905730C211yesmaximal, characteristic, complemented
5#24905719C211yesmaximal, characteristic, complemented
6#24905708C211yesmaximal, characteristic
7#24905698C212yesmaximal, complemented
8#24905690C212yesmaximal, complemented
9#24905686C212yesmaximal
10C4×C83⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×Dic83⋊C4C2212yes—
15C22×C22⋊Dic83C2212yes—
16C22×C22⋊Dic83C2212yes—
17C22×C4×Dic83C2212yes—
18#19127626C418yescomplemented
19#19127599—24no—
20#19127595—28no—
21C2×C83⋊#95C2212yes—
22C2×C83⋊#95C2211yescharacteristic
23C2×C83⋊#95C2212yes—
24C2×C83⋊#95C2212yes—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2212yes—
31C24×C4×C83C2211yescharacteristic
32C22×C22⋊C4×C83C2211yescharacteristic
33C22×C22⋊C4×C83C2211yescharacteristic
34C22×C42×C83C2211yescharacteristic
35C22×C42×C83C2211yescharacteristic
36C4×C22⋊C4×C83—24no—
37C2×#95×C83C2211yescharacteristic
38C2×#95×C83C2211yescharacteristic
39C23×Dic83C2312yes—
40C23×Dic83C2312yes—
41C23×Dic83C2312yes—
42C23×Dic83C2312yes—
43C2×C4⋊Dic83—22no—
44C2×C4⋊Dic83—22no—
45C2×C4⋊Dic83—22no—
46C2×C4⋊Dic83—42no—
47C2×C4⋊Dic83C2×C414yescomplemented
48C2×Dic83⋊C4—24no—
49C2×Dic83⋊C4—24no—
50C2×Dic83⋊C4—24no—
51C2×C22⋊Dic83—24no—
52C2×C22⋊Dic83—24no—
53C2×C22⋊Dic83—24no—
54C2×C22⋊Dic83—24no—
55C2×C22⋊Dic83—42no—
56C2×C22⋊Dic83C2×C418yes—
57C2×C4×Dic83—24no—
58C2×C4×Dic83—24no—
59C2×C4×Dic83—42no—
60C83⋊#95—24no—
61C83⋊#95—24no—
62C83⋊#95—24no—
63C83⋊#95—24no—
64C83⋊#95—24no—
65C83⋊#95—24no—
66C83⋊#95—22no—
67C83⋊#95—42no—
68C83⋊#95C2×C418yescomplemented
69C83⋊#95C2×C414yescomplemented
70C25×C83C2311yescharacteristic
71C23×C4×C83—22no—
72C23×C4×C83—22no—
73C23×C4×C83—22no—
74C23×C4×C83—24no—
75C23×C4×C83—42no—
76C23×C4×C83C2311yescharacteristic
77C23×C4×C83C2311yescharacteristic
78C23×C4×C83C2311yescharacteristic
79C23×C4×C83C2311yescharacteristic
80C23×C4×C83C2311yescharacteristic
81C23×C4×C83C2311yescharacteristic
82C2×C22⋊C4×C83—22no—
83C2×C22⋊C4×C83—22no—
84C2×C22⋊C4×C83—22no—
85C2×C22⋊C4×C83—22no—
86C2×C22⋊C4×C83C2×C414yes—
87C2×C22⋊C4×C83D414yes—
88C2×C42×C83—22no—
89C2×C42×C83—24no—
90C2×C42×C83—42no—
91C2×C42×C83D414yes—
92#95×C83—22no—
93#95×C83—22no—
94C22×Dic83—22no—
95C22×Dic83—22no—
96C22×Dic83—22no—
97C22×Dic83—22no—
98C22×Dic83—22no—
99C22×Dic83—22no—
100C22×Dic83—22no—
101C22×Dic83—22no—
102C22×Dic83—22no—
103C22×Dic83—22no—
104C22×Dic83—22no—
105C22×Dic83—22no—
106C22×Dic83—22no—
107C22×Dic83—22no—
108C22×Dic83—22no—
109C22×Dic83—22no—
110C22×Dic83—22no—
111C22×Dic83—22no—
112C22×Dic83—22no—
113C22×Dic83—22no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—22no—
118C22×Dic83—22no—
119C22×Dic83C22×C414yes—
120C22×Dic83C22×C414yes—
121C22×Dic83#4114yes—
122C4⋊Dic83—28no—
123C4⋊Dic83—44no—
124Dic83⋊C4—48no—
125C22⋊Dic83—216no—
126C22⋊Dic83—48no—
127C4×Dic83—48no—
128C24×C83—21no—
129C24×C83—21no—
130C24×C83—21no—
131C24×C83—22no—
132C24×C83—21no—
133C24×C83—22no—
134C24×C83—22no—
135C24×C83—22no—
136C24×C83C22×C412yes—
137C24×C83C2×D412yes—
138C24×C83#4112yes—
139C24×C83C2411yescharacteristic
140C22×C4×C83—21no—
141C22×C4×C83—21no—
142C22×C4×C83—22no—
143C22×C4×C83—22no—
144C22×C4×C83—22no—
145C22×C4×C83—22no—
146C22×C4×C83—22no—
147C22×C4×C83—28no—
148C22×C4×C83—21no—
149C22×C4×C83—21no—
150C22×C4×C83—21no—
151C22×C4×C83—22no—
152C22×C4×C83—22no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—22no—
156C22×C4×C83—21no—
157C22×C4×C83—22no—
158C22×C4×C83—22no—
159C22×C4×C83—22no—
160C22×C4×C83—48no—
161C22×C4×C83—48no—
162C22×C4×C83—44no—
163C22×C4×C83—44no—
164C22×C4×C83C22×C412yes—
165C22×C4×C83C22×C412yes—
166C22×C4×C83C2×D412yes—
167C22×C4×C83C2×D412yes—
168C22×C4×C83C2×D412yes—
169C22×C4×C83C2×D412yes—
170C22×C4×C83C2×D412yes—
171C22×C4×C83#4114yes—
172C22×C4×C83#4112yes—
173C22×C4×C83#4112yes—
174C22×C4×C83#4112yes—
175C22⋊C4×C83—28no—
176C22⋊C4×C83—28no—
177C42×C83—44no—
178C42×C83—44no—
179C23×C83—22no—
180C23×C83—24no—
181C23×C83—22no—
182C23×C83—24no—
183C23×C83—22no—
184C23×C83—22no—
185C23×C83—22no—
186C23×C83—22no—
187C23×C83—24no—
188C23×C83—24no—
189C23×C83—24no—
190C23×C83—24no—
191C23×C83—41no—
192C23×C83—42no—
193C23×C83—41no—
194C23×C83—41no—
195C23×C83—41no—
196C23×C83—42no—
197C23×C83—42no—
198C23×C83—42no—
199C23×C83—42no—
200C23×C83—42no—
201C23×C83C4×D414yes—
202C23×C83C23×C411yescharacteristic
203C23×C83C22×D411yescharacteristic
204C23×C83C22×D411yescharacteristic
205C23×C83C2×#4112yes—
206C23×C83C2×#4112yes—
207C23×C83C2×#4111yescharacteristic
208C23×C83C2×#4111yescharacteristic
209C23×C83C2×#4111yescharacteristic
210C23×C83C2×#4111yescharacteristic
211C23×C83H(5,𝔽2)12yes—
212C23×C832−1+412yes—
213C2×C4×C83—24no—
214C2×C4×C83—22no—
215C2×C4×C83—22no—
216C2×C4×C83—22no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—22no—
220C2×C4×C83—24no—
221C2×C4×C83—24no—
222C2×C4×C83—24no—
223C2×C4×C83—24no—
224C2×C4×C83—24no—
225C2×C4×C83—22no—
226C2×C4×C83—24no—
227C2×C4×C83—22no—
228C2×C4×C83—22no—
229C2×C4×C83—24no—
230C2×C4×C83—24no—
231C2×C4×C83—416no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—42no—
236C2×C4×C83—41no—
237C2×C4×C83—41no—
238C2×C4×C83—41no—
239C2×C4×C83—42no—
240C2×C4×C83—42no—
241C2×C4×C83C4×D414yes—
242C2×C4×C83#12114yes—
243C2×C4×C83#12414yes—
244C2×Dic83—24no—
245C2×Dic83—24no—
246C2×Dic83—24no—
247C2×Dic83—24no—
248C2×Dic83—24no—
249C2×Dic83—24no—
250C2×Dic83—24no—
251C2×Dic83—24no—
252C2×Dic83—24no—
253C2×Dic83—42no—
254C2×Dic83—42no—
255C2×Dic83—42no—
256C2×Dic83—42no—
257C2×Dic83—42no—
258C2×Dic83—42no—
259C2×Dic83—42no—
260C2×Dic83—42no—
261C2×Dic83—42no—
262C2×Dic83—42no—
263C2×Dic83—42no—
264C2×Dic83—42no—
265C2×Dic83—42no—
266C2×Dic83—42no—
267C2×Dic83—42no—
268C2×Dic83—42no—
269C2×Dic83—42no—
270C2×Dic83—42no—
271C2×Dic83—42no—
272C22×C83—28no—
273C22×C83—24no—
274C22×C83—42no—
275C22×C83—44no—
276C22×C83—42no—
277C22×C83—42no—
278C22×C83—44no—
279C22×C83—42no—
280C22×C83—42no—
281C22×C83—44no—
282C22×C83—42no—
283C22×C83C2×C4×D411yescharacteristic
284C22×C83C2×C4×D411yescharacteristic
285C22×C83C4×#4112yes—
286C22×C83C4×#4111yescharacteristic
287C22×C83#52012yes—
288C22×C83C2×#12111yescharacteristic
289C22×C83#52511yescharacteristic
290C22×C83C2×#12411yescharacteristic
291C22×C83#52912yes—
292C22×C83#52911yescharacteristic
293C22×C83#53211yescharacteristic
294C22×C83#53211yescharacteristic
295C22×C83#53411yescharacteristic
296C22×C83#53611yescharacteristic
297C22×C83#53912yes—
298C22×C83#54612yes—
299C22×C83#54712yes—
300C22×C83#55112yes—
301C22×C83#55112yes—
302C22×C83#55212yes—
303C22×C83#55212yes—
304C22×C83#55312yes—
305C22×C83#55612yes—
306C4×C83—24no—
307C4×C83—24no—
308C4×C83—24no—
309C4×C83—42no—
310C4×C83—42no—
311C4×C83—42no—
312Dic83—44no—
313Dic83—44no—
314Dic83—44no—
315Dic83—82no—
316#14229—831nomaximal, Sylow
317C2×C83—44no—
318C2×C83C4×#12111yescharacteristic
319C2×C83C4×#12411yescharacteristic
320C2×C83#232211yescharacteristic
321C2×C83#235912yes—
322C2×C83#237312yes—
323C2×C83#254311yescharacteristic
324C2×C83#254711yescharacteristic
325C2×C83#255312yes—
326C2×C83#256111yescharacteristic
327C2×C83#257312yes—
328C2×C83#261111yescharacteristic
329C2×#397—831no—
330C2×#389—831no—
331C2×#388—832no—
332C2×C4×C22⋊C4D8311yescharacteristic
333#1445—831no—
334#1442—831no—
335#1439—831no—
336#1436—832no—
337#1434—832no—
338C22⋊#95—832no—
339C4×#95—831no—
340C83#1422911yescharacteristic, complemented, Sylow
341C24×C4C2×D8311yescharacteristic
342C22×C4⋊C4—831no—
343C22×C4⋊C4—831no—
344C22×C4⋊C4—832no—
345C22×C22⋊C4—832no—
346C22×C22⋊C4—832no—
347C22×C22⋊C4C2×D8311yescharacteristic
348C22×C22⋊C4C2×D8311yescharacteristic
349C22×C42—832no—
350C22×C42C2×D8311yescharacteristic
351C22×C42C2×D8311yescharacteristic
352#397—838no—
353#389—1664no—
354#388—1668no—
355C4×C22⋊C4—24no—
356C2×#95—832no—
357C2×#95—831no—
358C2×#95—832no—
359C2×#95—832no—
360C2×#95—831no—
361C2×#95—832no—
362C2×#95—832no—
363C2×#95—832no—
364C2×#95—832no—
365C2×#95—832no—
366C2×#95C2×D8311yescharacteristic
367C2×#95C2×D8311yescharacteristic
368C25C22×D8311yescharacteristic
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—24no—
373C23×C4—42no—
374C23×C4—832no—
375C23×C4—832no—
376C23×C4—832no—
377C23×C4—832no—
378C23×C4C22×D8311yescharacteristic
379C23×C4C22×D8311yescharacteristic
380C23×C4C22×D8311yescharacteristic
381C23×C4C22×D8311yescharacteristic
382C23×C4C22×D8311yescharacteristic
383C23×C4C22×D8311yescharacteristic
384C2×C4⋊C4—3322no—
385C2×C4⋊C4—834no—
386C2×C4⋊C4—1664no—
387C2×C4⋊C4—1662no—
388C2×C4⋊C4—1664no—
389C2×C4⋊C4—1664no—
390C2×C4⋊C4—1662no—
391C2×C4⋊C4—1662no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—3322no—
397C2×C22⋊C4—838no—
398C2×C22⋊C4—1664no—
399C2×C22⋊C4—1664no—
400C2×C22⋊C4—1664no—
401C2×C22⋊C4—1664no—
402C2×C22⋊C4C4×D8314yes—
403C2×C22⋊C4D33214yes—
404C2×C42—22no—
405C2×C42—24no—
406C2×C42—42no—
407C2×C42—3322no—
408C2×C42—1664no—
409C2×C42—1664no—
410C2×C42C22⋊D8314yes—
411#95—22no—
412#95—22no—
413#95—3322no—
414#95—834no—
415#95—838no—
416#95—1664no—
417#95—1664no—
418#95—1664no—
419#95—1664no—
420#95—1664no—
421#95—1664no—
422#95—1662no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—22no—
431C24C2×C4×D8312yes—
432C24C2×D33212yes—
433C24#1305059012yes—
434C24C23×D8311yescharacteristic
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—28no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—48no—
456C22×C4—48no—
457C22×C4—44no—
458C22×C4—44no—
459C22×C4—834no—
460C22×C4—834no—
461C22×C4—834no—
462C22×C4—1662no—
463C22×C4—1662no—
464C22×C4—1662no—
465C22×C4—1662no—
466C22×C4—1662no—
467C22×C4—1662no—
468C22×C4—1662no—
469C22×C4—1662no—
470C22×C4—1662no—
471C22×C4—1662no—
472C22×C4—1662no—
473C22×C4—1662no—
474C22×C4—1662no—
475C22×C4—1662no—
476C22×C4—1662no—
477C22×C4—1662no—
478C22×C4—1662no—
479C22×C4—1662no—
480C22×C4—1662no—
481C22×C4—1662no—
482C22×C4—1662no—
483C22×C4—1662no—
484C22×C4—1662no—
485C22×C4—1662no—
486C22×C4—1662no—
487C22×C4C2×C4×D8312yes—
488C22×C4C2×C4×D8312yes—
489C22×C4C2×C22⋊D8312yes—
490C22×C4C2×C22⋊D8312yes—
491C22×C4C2×C22⋊D8312yes—
492C22×C4C2×D33212yes—
493C22×C4C2×D33212yes—
494C22×C4#1305058914yes—
495C22×C4#1305059012yes—
496C22×C4#1305059012yes—
497C22×C4#1305059012yes—
498C4⋊C4—3324no—
499C4⋊C4—3328no—
500C4⋊C4—1668no—
501C22⋊C4—28no—
502C22⋊C4—28no—
503C22⋊C4—3328no—
504C22⋊C4—16616no—
505C42—44no—
506C42—44no—
507C42—3328no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—24no—
514C23—22no—
515C23—24no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—41no—
525C23—42no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23C4×D33214yes—
531C23C22×C4×D8311yescharacteristic
532C23C22×C22⋊D8311yescharacteristic
533C23C22×D33211yescharacteristic
534C23#41×D8312yes—
535C23C2×#1305058912yes—
536C23C2×#1305059011yescharacteristic
537C23C2×#1305059011yescharacteristic
538C23C2×#1305059011yescharacteristic
539C23C2×#1305059011yescharacteristic
540C23#1458183712yes—
541C23#1458183912yes—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—416no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—3322no—
571C2×C4—3322no—
572C2×C4—3322no—
573C2×C4—3322no—
574C2×C4—3322no—
575C2×C4—3322no—
576C2×C4—3322no—
577C2×C4—3322no—
578C2×C4—3322no—
579C2×C4—3322no—
580C2×C4—3322no—
581C2×C4—3322no—
582C2×C4—3322no—
583C2×C4—3322no—
584C2×C4—3322no—
585C2×C4—3322no—
586C2×C4—3322no—
587C2×C4—3322no—
588C2×C4—3322no—
589C2×C4—1664no—
590C2×C4—1664no—
591C2×C4—1664no—
592C2×C4—1664no—
593C2×C4—1664no—
594C2×C4—1664no—
595C2×C4—1664no—
596C2×C4—1664no—
597C2×C4—1664no—
598C2×C4C4×C22⋊D8314yes—
599C2×C4#1458176614yes—
600C2×C4#1458177914yes—
601C22—28no—
602C22—24no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—44no—
608C22—44no—
609C22—42no—
610C22—42no—
611C22—44no—
612C22C2×C4×C22⋊D8311yescharacteristic
613C22C2×C4×D33211yescharacteristic
614C22C4×#1305058912yes—
615C22C4×#1305059011yescharacteristic
616C22#1912818012yes—
617C22C2×#1458176611yescharacteristic
618C22#1912821211yescharacteristic
619C22C2×#1458177911yescharacteristic
620C22#1912823312yes—
621C22#1912823511yescharacteristic
622C22#1912824711yescharacteristic
623C22#1912825111yescharacteristic
624C22#1912826011yescharacteristic
625C22#1912827211yescharacteristic
626C22#1912829312yes—
627C22#1912834612yes—
628C22#1912835512yes—
629C22#1912837712yes—
630C22#1912837712yes—
631C22#1912838412yes—
632C22#1912839012yes—
633C22#1912840012yes—
634C22#1912842112yes—
635C4—24no—
636C4—24no—
637C4—24no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—3324no—
642C4—3324no—
643C4—3324no—
644C4—6642no—
645C2—44no—
646C2C4×#1458176611yescharacteristic
647C2C4×#1458177911yescharacteristic
648C2#2491012811yescharacteristic
649C2#2491045712yes—
650C2#2491058412yes—
651C2#2491241911yescharacteristic
652C2#2491245511yescharacteristic
653C2#2491250212yes—
654C2#2491262111yescharacteristic
655C2#2491272212yes—
656C2#2491316111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×C4×C22⋊C4D83
hypocenterC83#14229
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#19127599C2semidirect
4. #24905730C2semidirect
5. #24905719C2semidirect
7. #24905698C2semidirect
8. #24905690C2semidirect
10. C4×C83⋊#95C2semidirect
18. #19127626C4semidirect
47. C2×C4⋊Dic83C2×C4semidirect
68. C83⋊#95C2×C4semidirect
69. C83⋊#95C2×C4semidirect
340. C83#14229semidirect

Maximal subgroups

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

subgroupindex
C2×#191276262
C2×#191275992
C2×#191275952
#249057302
#249057192
#249057082
#249056982
#249056902
#249056862
C4×C83⋊#952
C2×C4×C22⋊C4×C832
#1422983