Finite Group Databasebeta

← C2×#397×D83 #35570608

Subgroups — C2×#397×D83 #35570608

Order 21248.

5230 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D83C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D83C211yesmaximal, characteristic
3C22×C22⋊C4×D83C212yesmaximal
4C2×#19127630C212yesmaximal, complemented
5C2×#19127629C212yesmaximal, complemented
6C2×#19127628C211yesmaximal, characteristic, complemented
7C2×#19127627C211yesmaximal, characteristic, complemented
8C2×#19127626C211yesmaximal, characteristic, complemented
9#397×D83C2116yesmaximal, direct product factor
10C2×#95×D83C211yesmaximal, characteristic, complemented
11C2×#95×D83C212yesmaximal, complemented
12C2×#397×C83C211yesmaximal, characteristic, complemented
13C25×D83C2211yescharacteristic
14C23×C4×D83C2212yes—
15C23×C4×D83C2212yes—
16C23×C4×D83C2211yescharacteristic
17C23×C4×D83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic, complemented
19C22×Dic83⋊C4C2212yescomplemented
20C2×C4⋊C4×D83—28no—
21C2×C4⋊C4×D83C2218yescomplemented
22C22×C22⋊Dic83C2212yes—
23C22×C22⋊Dic83C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2212yes—
26C22×(C2×D83)⋊C4C2212yes—
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C2×C22⋊C4×D83—216no—
29C2×C22⋊C4×D83—28no—
30C2×C22⋊C4×D83C22116yes—
31C2×C22⋊C4×D83C2218yes—
32#19127630C22116yescomplemented
33#19127629C22116yescomplemented
34#19127628C2218yescomplemented
35#19127627C2218yescomplemented
36#19127626C2218yescomplemented
37C2×C83⋊#95C2211yescharacteristic, complemented
38C2×C83⋊#95C2212yescomplemented
39C2×C83⋊#95C2212yescomplemented
40C2×C83⋊#95C2212yescomplemented
41C2×C83⋊#95C2212yescomplemented
42#95×D83C22116yescomplemented
43#95×D83C2218yescomplemented
44C22×C4⋊C4×C83C2211yescharacteristic, complemented
45C22×C22⋊C4×C83C2211yescharacteristic
46C22×C22⋊C4×C83C2212yes—
47#397×C83C2218yescomplemented
48C2×#95×C83C2211yescharacteristic, complemented
49C2×#95×C83C2212yescomplemented
50C24×D83—24no—
51C24×D83—24no—
52C24×D83—28no—
53C24×D83—28no—
54C24×D83D418yes—
55C24×D83C2314yes—
56C24×D83C2311yescharacteristic
57C24×D83C2311yescharacteristic
58C23×Dic83C2312yes—
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2312yes—
61C23×Dic83C2311yescharacteristic
62C22×C4×D83—28no—
63C22×C4×D83—28no—
64C22×C4×D83—28no—
65C22×C4×D83—24no—
66C22×C4×D83—28no—
67C22×C4×D83—28no—
68C22×C4×D83—28no—
69C22×C4×D83—28no—
70C22×C4×D83—28no—
71C22×C4×D83D418yes—
72C22×C4×D83C2318yes—
73C22×C4×D83C2318yes—
74C22×C4×D83C2314yes—
75C22×C4×D83C2314yes—
76C2×C4⋊Dic83—24no—
77C2×C4⋊Dic83C2314yescomplemented
78C2×Dic83⋊C4—28no—
79C2×Dic83⋊C4C2318yescomplemented
80C4⋊C4×D83—232no—
81C2×C22⋊Dic83—24no—
82C2×C22⋊Dic83—28no—
83C2×C22⋊Dic83C2318yes—
84C2×C22⋊Dic83C2314yes—
85C2×(C2×D83)⋊C4—28no—
86C2×(C2×D83)⋊C4—28no—
87C2×(C2×D83)⋊C4—24no—
88C2×(C2×D83)⋊C4—24no—
89C2×(C2×D83)⋊C4C2314yes—
90C2×(C2×D83)⋊C4C2318yes—
91C2×(C2×D83)⋊C4C2318yes—
92C2×(C2×D83)⋊C4C2314yes—
93C22⋊C4×D83—264no—
94C22⋊C4×D83—232no—
95C83⋊#95C2314yescomplemented
96C83⋊#95C2318yescomplemented
97C83⋊#95C2318yescomplemented
98C83⋊#95C2318yescomplemented
99C83⋊#95C2318yescomplemented
100C25×C83C2311yescharacteristic
101C23×C4×C83C2312yes—
102C23×C4×C83C2311yescharacteristic
103C23×C4×C83C2312yes—
104C23×C4×C83C2311yescharacteristic
105C2×C4⋊C4×C83—24no—
106C2×C4⋊C4×C83C2314yescomplemented
107C2×C22⋊C4×C83—28no—
108C2×C22⋊C4×C83—24no—
109C2×C22⋊C4×C83C2314yes—
110C2×C22⋊C4×C83C2318yes—
111#95×C83C2314yescomplemented
112#95×C83C2318yescomplemented
113C23×D83—22no—
114C23×D83—22no—
115C23×D83—24no—
116C23×D83—24no—
117C23×D83—232no—
118C23×D83—264no—
119C23×D83—28no—
120C23×D83—28no—
121C23×D83—216no—
122C23×D83—216no—
123C23×D83—416no—
124C23×D83—416no—
125C23×D83—432no—
126C23×D83C2×D4116yes—
127C23×D83C2×D414yes—
128C23×D83C2×D414yes—
129C23×D83C2×D414yes—
130C23×D83#4114yes—
131C23×D83#4118yes—
132C23×D83#4118yes—
133C23×D83C2412yes—
134C23×D83C2412yes—
135C22×Dic83—24no—
136C22×Dic83—24no—
137C22×Dic83—24no—
138C22×Dic83—22no—
139C22×Dic83—24no—
140C22×Dic83—24no—
141C22×Dic83—24no—
142C22×Dic83—24no—
143C22×Dic83—24no—
144C22×Dic83C2×D414yes—
145C22×Dic83C2414yes—
146C22×Dic83C2412yes—
147C22×Dic83C2414yes—
148C22×Dic83C2412yes—
149C2×C4×D83—232no—
150C2×C4×D83—216no—
151C2×C4×D83—216no—
152C2×C4×D83—216no—
153C2×C4×D83—28no—
154C2×C4×D83—216no—
155C2×C4×D83—216no—
156C2×C4×D83—216no—
157C2×C4×D83—216no—
158C2×C4×D83—216no—
159C2×C4×D83—432no—
160C2×C4×D83—432no—
161C2×C4×D83—416no—
162C2×C4×D83C2×D4116yes—
163C4⋊Dic83—28no—
164Dic83⋊C4—216no—
165C22⋊Dic83—216no—
166C22⋊Dic83—28no—
167(C2×D83)⋊C4—216no—
168(C2×D83)⋊C4—216no—
169(C2×D83)⋊C4—28no—
170(C2×D83)⋊C4—28no—
171C24×C83—22no—
172C24×C83—22no—
173C24×C83—24no—
174C24×C83—24no—
175C24×C83C2×D414yes—
176C24×C83C2412yes—
177C24×C83C2411yescharacteristic
178C22×C4×C83—24no—
179C22×C4×C83—24no—
180C22×C4×C83—24no—
181C22×C4×C83—22no—
182C22×C4×C83—24no—
183C22×C4×C83—24no—
184C22×C4×C83—24no—
185C22×C4×C83—24no—
186C22×C4×C83—24no—
187C22×C4×C83C2×D414yes—
188C22×C4×C83C2414yes—
189C22×C4×C83C2412yes—
190C22×C4×C83C2414yes—
191C22×C4×C83C2412yes—
192C4⋊C4×C83—28no—
193C22⋊C4×C83—216no—
194C22⋊C4×C83—28no—
195C23×C83—28no—
196C23×C83—216no—
197C23×C83—22no—
198C23×C83—22no—
199C23×C83—24no—
200C23×C83—24no—
201C23×C83—44no—
202C23×C83—44no—
203C23×C83—48no—
204C23×C83C22×D414yes—
205C23×C83C22×D412yes—
206C23×C83C22×D412yes—
207C23×C83C2×#4112yes—
208C23×C83C2×#4114yes—
209C23×C83C2×#4114yes—
210C23×C83C2511yescharacteristic
211C22×D83—28no—
212C22×D83—216no—
213C22×D83—22no—
214C22×D83—22no—
215C22×D83—24no—
216C22×D83—24no—
217C22×D83—232no—
218C22×D83—264no—
219C22×D83—44no—
220C22×D83—44no—
221C22×D83—48no—
222C22×D83—416no—
223C22×D83—416no—
224C22×D83—432no—
225C22×D83—4128no—
226C22×D83#121116yes—
227C22×D83#123116yes—
228C22×D83#123132yes—
229C22×D83#124116yes—
230C22×D83#126132yes—
231C22×D83C22×D414yes—
232C22×D83C22×D414yes—
233C22×D83C22×D414yes—
234C22×D83C2×#4114yes—
235C22×D83C2×#4118yes—
236C22×D83C2×#4118yes—
237C2×C4×C83—28no—
238C2×C4×C83—24no—
239C2×C4×C83—24no—
240C2×C4×C83—24no—
241C2×C4×C83—22no—
242C2×C4×C83—24no—
243C2×C4×C83—24no—
244C2×C4×C83—24no—
245C2×C4×C83—24no—
246C2×C4×C83—24no—
247C2×C4×C83—48no—
248C2×C4×C83—48no—
249C2×C4×C83—44no—
250C2×C4×C83C22×D414yes—
251C2×Dic83—28no—
252C2×Dic83—24no—
253C2×Dic83—24no—
254C2×Dic83—24no—
255C2×Dic83—22no—
256C2×Dic83—24no—
257C2×Dic83—24no—
258C2×Dic83—24no—
259C2×Dic83—24no—
260C2×Dic83—24no—
261C2×Dic83—48no—
262C2×Dic83—48no—
263C2×Dic83—44no—
264C2×Dic83C22×D414yes—
265C4×D83—232no—
266C4×D83—432no—
267C4×D83—432no—
268C4×D83—416no—
269C22×C83—24no—
270C22×C83—28no—
271C22×C83—416no—
272C22×C83—42no—
273C22×C83—42no—
274C22×C83—44no—
275C22×C83C2×#12114yes—
276C22×C83C2×#12314yes—
277C22×C83C2×#12318yes—
278C22×C83C2×#12414yes—
279C22×C83C2×#12618yes—
280C22×C83C23×D411yescharacteristic
281C22×C83C23×D411yescharacteristic
282C22×C83C22×#4111yescharacteristic
283C22×C83C22×#4112yes—
284C22×C83C22×#4112yes—
285C2×D83—24no—
286C2×D83—28no—
287C2×D83—416no—
288C2×D83—42no—
289C2×D83—42no—
290C2×D83—44no—
291C2×D83—464no—
292C2×D83#397164yesdirect product factor
293C2×D83C2×#12118yes—
294C2×D83C2×#12318yes—
295C2×D83C2×#123116yes—
296C2×D83C2×#12418yes—
297C2×D83C2×#126116yes—
298C4×C83—24no—
299C4×C83—44no—
300C4×C83—44no—
301C4×C83—42no—
302Dic83—24no—
303Dic83—44no—
304Dic83—44no—
305Dic83—42no—
306C22×#397—831nomaximal, Sylow
307C2×C83—44no—
308C2×C83C2×#39718yescomplemented
309C2×C83C22×#12111yescharacteristic
310C2×C83C22×#12311yescharacteristic
311C2×C83C22×#12312yes—
312C2×C83C22×#12411yescharacteristic
313C2×C83C22×#12612yes—
314D83—44no—
315D83C2×#397116yesdirect product factor
316C23×C4⋊C4—831no—
317C23×C22⋊C4—831no—
318C23×C22⋊C4—832no—
319C2×#397—8316no—
320C2×#397—831no—
321C2×#397—832no—
322C2×#397—831no—
323C2×#397—831no—
324C2×#397—832no—
325C2×#397D8311yescharacteristic, direct product factor
326C22×#95—831no—
327C22×#95—832no—
328C83C22×#39711yescharacteristic, complemented, Sylow
329C26—831no—
330C24×C4—831no—
331C24×C4—832no—
332C24×C4—831no—
333C24×C4—832no—
334C22×C4⋊C4—832no—
335C22×C4⋊C4—831no—
336C22×C4⋊C4—838no—
337C22×C4⋊C4—1668no—
338C22×C4⋊C4C2×D8311yescharacteristic, complemented
339C22×C22⋊C4—831no—
340C22×C22⋊C4—832no—
341C22×C22⋊C4—831no—
342C22×C22⋊C4—832no—
343C22×C22⋊C4—832no—
344C22×C22⋊C4—831no—
345C22×C22⋊C4—838no—
346C22×C22⋊C4—8316no—
347C22×C22⋊C4—1668no—
348C22×C22⋊C4—16616no—
349C22×C22⋊C4C2×D8312yes—
350C22×C22⋊C4C2×D8311yescharacteristic
351#397—838no—
352#397—838no—
353#397—8316no—
354#397—838no—
355#397—8316no—
356#397C2×D8318yesdirect product factor
357C2×#95—832no—
358C2×#95—832no—
359C2×#95—832no—
360C2×#95—832no—
361C2×#95—831no—
362C2×#95—838no—
363C2×#95—8316no—
364C2×#95C2×D8312yescomplemented
365C2×#95C2×D8311yescharacteristic, complemented
366C25—831no—
367C25—838no—
368C25—834no—
369C25—831no—
370C25—1664no—
371C25—1664no—
372C25—1668no—
373C25—1668no—
374C25C22×D8311yescharacteristic
375C23×C4—831no—
376C23×C4—838no—
377C23×C4—834no—
378C23×C4—832no—
379C23×C4—832no—
380C23×C4—831no—
381C23×C4—838no—
382C23×C4—834no—
383C23×C4—838no—
384C23×C4—1664no—
385C23×C4—1668no—
386C23×C4—1668no—
387C23×C4—1668no—
388C23×C4—1668no—
389C23×C4—1668no—
390C23×C4—1668no—
391C23×C4—1668no—
392C23×C4—1668no—
393C23×C4C22×D8312yes—
394C23×C4C22×D8312yes—
395C23×C4C22×D8311yescharacteristic
396C23×C4C22×D8311yescharacteristic
397C2×C4⋊C4—24no—
398C2×C4⋊C4—838no—
399C2×C4⋊C4—834no—
400C2×C4⋊C4—16632no—
401C2×C4⋊C4—1668no—
402C2×C4⋊C4—1664no—
403C2×C4⋊C4C22×D8314yescomplemented
404C2×C22⋊C4—28no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—834no—
407C2×C22⋊C4—838no—
408C2×C22⋊C4—834no—
409C2×C22⋊C4—838no—
410C2×C22⋊C4—838no—
411C2×C22⋊C4—834no—
412C2×C22⋊C4—16632no—
413C2×C22⋊C4—16664no—
414C2×C22⋊C4—1664no—
415C2×C22⋊C4—1668no—
416C2×C22⋊C4—1668no—
417C2×C22⋊C4—1664no—
418C2×C22⋊C4—1668no—
419C2×C22⋊C4—1664no—
420C2×C22⋊C4C22×D8318yes—
421C2×C22⋊C4C22×D8314yes—
422#95—838no—
423#95—838no—
424#95—834no—
425#95—838no—
426#95—838no—
427#95C22×D8318yescomplemented
428#95C22×D8314yescomplemented
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—33216no—
434C24—33216no—
435C24—33232no—
436C24—834no—
437C24—834no—
438C24—834no—
439C24—838no—
440C24—838no—
441C24—832no—
442C24—8316no—
443C24—834no—
444C24—832no—
445C24—1668no—
446C24—16632no—
447C24—16664no—
448C24—1668no—
449C24—16616no—
450C24—16616no—
451C24—1662no—
452C24—1664no—
453C24—1664no—
454C24—1662no—
455C24D4×D8314yes—
456C24C23×D8312yes—
457C24C23×D8311yescharacteristic
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—33232no—
468C22×C4—33232no—
469C22×C4—33216no—
470C22×C4—834no—
471C22×C4—832no—
472C22×C4—8316no—
473C22×C4—834no—
474C22×C4—832no—
475C22×C4—834no—
476C22×C4—1668no—
477C22×C4—16616no—
478C22×C4—16616no—
479C22×C4—16616no—
480C22×C4—16616no—
481C22×C4—16616no—
482C22×C4—16616no—
483C22×C4—16616no—
484C22×C4—16632no—
485C22×C4—16616no—
486C22×C4—1664no—
487C22×C4—1664no—
488C22×C4—1662no—
489C22×C4—1664no—
490C22×C4—1664no—
491C22×C4—1664no—
492C22×C4—1664no—
493C22×C4—1664no—
494C22×C4—1664no—
495C22×C4D4×D8314yes—
496C22×C4C23×D8314yes—
497C22×C4C23×D8312yes—
498C22×C4C23×D8314yes—
499C22×C4C23×D8312yes—
500C4⋊C4—28no—
501C4⋊C4—16616no—
502C4⋊C4—1668no—
503C22⋊C4—216no—
504C22⋊C4—28no—
505C22⋊C4—1668no—
506C22⋊C4—16616no—
507C22⋊C4—16616no—
508C22⋊C4—1668no—
509C22⋊C4—16616no—
510C22⋊C4—1668no—
511C23—28no—
512C23—216no—
513C23—22no—
514C23—22no—
515C23—24no—
516C23—24no—
517C23—44no—
518C23—44no—
519C23—48no—
520C23—332128no—
521C23—33216no—
522C23—33216no—
523C23—33232no—
524C23—3324no—
525C23—3324no—
526C23—3328no—
527C23—8316no—
528C23—8332no—
529C23—8316no—
530C23—8316no—
531C23—8332no—
532C23—834no—
533C23—834no—
534C23—834no—
535C23—838no—
536C23—838no—
537C23—834no—
538C23—16632no—
539C23—16664no—
540C23—1668no—
541C23—16616no—
542C23—1662no—
543C23—1664no—
544C23—1664no—
545C23—1662no—
546C23C2×D4×D8314yes—
547C23C2×D4×D8312yes—
548C23C2×D4×D8312yes—
549C23#41×D8312yes—
550C23#41×D8314yes—
551C23#41×D8314yes—
552C23C24×D8311yescharacteristic
553C2×C4—28no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—48no—
564C2×C4—48no—
565C2×C4—44no—
566C2×C4—33232no—
567C2×C4—33232no—
568C2×C4—33216no—
569C2×C4—3328no—
570C2×C4—3328no—
571C2×C4—3324no—
572C2×C4—834no—
573C2×C4—16632no—
574C2×C4—1664no—
575C2×C4—1664no—
576C2×C4—1662no—
577C2×C4—1664no—
578C2×C4—1664no—
579C2×C4—1664no—
580C2×C4—1664no—
581C2×C4—1664no—
582C2×C4—1668no—
583C2×C4—1664no—
584C2×C4C2×D4×D8314yes—
585C22—24no—
586C22—28no—
587C22—416no—
588C22—42no—
589C22—42no—
590C22—44no—
591C22—33264no—
592C22—33216no—
593C22—3322no—
594C22—3322no—
595C22—3324no—
596C22—8364no—
597C22—838no—
598C22—8316no—
599C22—838no—
600C22—838no—
601C22—8316no—
602C22—1664no—
603C22—1668no—
604C22#121×D8314yes—
605C22#123×D8314yes—
606C22#123×D8318yes—
607C22#124×D8314yes—
608C22#126×D8318yes—
609C22C22×D4×D8311yescharacteristic
610C22C22×D4×D8311yescharacteristic
611C22C2×#41×D8311yescharacteristic
612C22C2×#41×D8312yes—
613C22C2×#41×D8312yes—
614C4—24no—
615C4—44no—
616C4—44no—
617C4—42no—
618C4—3324no—
619C4—3324no—
620C4—3322no—
621C4—1664no—
622C2—44no—
623C2—3324no—
624C2—8316no—
625C2#397×D8318yesdirect product factor
626C2C2×#121×D8311yescharacteristic
627C2C2×#123×D8311yescharacteristic
628C2C2×#123×D8312yes—
629C2C2×#124×D8311yescharacteristic
630C2C2×#126×D8312yes—
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#397×C83C2
socleC24×C83C24
prime radicalC25×D83C22
hypercenterC2×#397D83
hypocenterC83C22×#397
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×C4⋊C4×D83C2semidirect
4. C2×#19127630C2semidirect
5. C2×#19127629C2semidirect
6. C2×#19127628C2semidirect
7. C2×#19127627C2semidirect
8. C2×#19127626C2semidirect
9. #397×D83C2direct (N × H)
10. C2×#95×D83C2semidirect
11. C2×#95×D83C2semidirect
12. C2×#397×C83C2semidirect
18. C22×C4⋊Dic83C22semidirect
19. C22×Dic83⋊C4C22semidirect
21. C2×C4⋊C4×D83C22semidirect
32. #19127630C22semidirect
33. #19127629C22semidirect
34. #19127628C22semidirect
35. #19127627C22semidirect
36. #19127626C22semidirect
37. C2×C83⋊#95C22semidirect
38. C2×C83⋊#95C22semidirect
39. C2×C83⋊#95C22semidirect
40. C2×C83⋊#95C22semidirect
41. C2×C83⋊#95C22semidirect
42. #95×D83C22semidirect
43. #95×D83C22semidirect
44. C22×C4⋊C4×C83C22semidirect
47. #397×C83C22semidirect
48. C2×#95×C83C22semidirect
49. C2×#95×C83C22semidirect
77. C2×C4⋊Dic83C23semidirect
79. C2×Dic83⋊C4C23semidirect
95. C83⋊#95C23semidirect
96. C83⋊#95C23semidirect
97. C83⋊#95C23semidirect
98. C83⋊#95C23semidirect
99. C83⋊#95C23semidirect
106. C2×C4⋊C4×C83C23semidirect
111. #95×C83C23semidirect
112. #95×C83C23semidirect
292. C2×D83#397direct (N × H)
308. C2×C83C2×#397semidirect
315. D83C2×#397direct (N × H)
325. C2×#397D83direct (N × H)
328. C83C22×#397semidirect
338. C22×C4⋊C4C2×D83semidirect
356. #397C2×D83direct (N × H)
364. C2×#95C2×D83semidirect
365. C2×#95C2×D83semidirect
403. C2×C4⋊C4C22×D83semidirect
427. #95C22×D83semidirect
428. #95C22×D83semidirect
625. C2#397×D83direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D832
C22×C22⋊C4×D832
C2×#191276302
C2×#191276292
C2×#191276282
C2×#191276272
C2×#191276262
#397×D832
C2×#95×D832
C2×#397×C832
C22×#39783