Finite Group Databasebeta

← #35341126

Subgroups — #35341126

Order 21248.

1566 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127633C211yesmaximal, characteristic
2C2×#19127632C211yesmaximal, characteristic
3C2×#19127631C211yesmaximal, characteristic
4C2×#19127596C211yesmaximal, characteristic
5C2×#19127570C212yesmaximal
6C2×#19127570C211yesmaximal, characteristic
7#24905727C212yesmaximal
8#24905726C212yesmaximal
9Dic83⋊#95C212yesmaximal
10#95×Dic83C211yesmaximal, characteristic
11C2×#398×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2212yes—
14C22×Dic83⋊C4C2212yes—
15C22×Dic83⋊C4C2211yescharacteristic
16C22×Dic83⋊C4C2211yescharacteristic
17C22×Dic83⋊C4C2212yes—
18C22×Dic83⋊C4C2212yes—
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2212yes—
21C22×C4×Dic83C2211yescharacteristic
22C22×C4×Dic83C2212yes—
23#19127633—24no—
24#19127632—24no—
25#19127631—24no—
26#19127596—24no—
27#19127570—28no—
28#19127570—24no—
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2211yescharacteristic
35C2×C83⋊#95C2212yes—
36C22×C4⋊C4×C83C2211yescharacteristic
37C22×C4⋊C4×C83C2211yescharacteristic
38C22×C4⋊C4×C83C2212yes—
39#398×C83—24no—
40C2×#95×C83C2212yes—
41C2×#95×C83C2211yescharacteristic
42C23×Dic83C2312yes—
43C23×Dic83C2311yescharacteristic
44C23×Dic83C2311yescharacteristic
45C23×Dic83C2312yes—
46C23×Dic83C2311yescharacteristic
47C23×Dic83C2311yescharacteristic
48C2×C4⋊Dic83—24no—
49C2×C4⋊Dic83—22no—
50C2×C4⋊Dic83—22no—
51C2×C4⋊Dic83—22no—
52C2×C4⋊Dic83—24no—
53C2×C4⋊Dic83—42no—
54C2×Dic83⋊C4—22no—
55C2×Dic83⋊C4—22no—
56C2×Dic83⋊C4—24no—
57C2×Dic83⋊C4—24no—
58C2×Dic83⋊C4—24no—
59C2×Dic83⋊C4—24no—
60C2×Dic83⋊C4—22no—
61C2×Dic83⋊C4—24no—
62C2×Dic83⋊C4—24no—
63C2×Dic83⋊C4—24no—
64C2×Dic83⋊C4—24no—
65C2×Dic83⋊C4—24no—
66C2×Dic83⋊C4—22no—
67C2×Dic83⋊C4—22no—
68C2×Dic83⋊C4—22no—
69C2×Dic83⋊C4—42no—
70C2×Dic83⋊C4—42no—
71C2×Dic83⋊C4—42no—
72C2×Dic83⋊C4—42no—
73C2×Dic83⋊C4D414yes—
74C2×C4×Dic83—24no—
75C2×C4×Dic83—24no—
76C2×C4×Dic83—24no—
77C2×C4×Dic83D414yes—
78C2×C4×Dic83Q818yes—
79C83⋊#95—22no—
80C83⋊#95—22no—
81C83⋊#95—24no—
82C83⋊#95—24no—
83C83⋊#95—24no—
84C83⋊#95D414yes—
85C83⋊#95Q818yes—
86C23×C4×C83C2312yes—
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2312yes—
91C2×C4⋊C4×C83—24no—
92C2×C4⋊C4×C83—22no—
93C2×C4⋊C4×C83—22no—
94C2×C4⋊C4×C83—22no—
95C2×C4⋊C4×C83—22no—
96C2×C4⋊C4×C83—24no—
97C2×C4⋊C4×C83—22no—
98C2×C4⋊C4×C83—22no—
99C2×C4⋊C4×C83—42no—
100#95×C83—24no—
101#95×C83D414yes—
102C22×Dic83—22no—
103C22×Dic83—22no—
104C22×Dic83—22no—
105C22×Dic83—21no—
106C22×Dic83—21no—
107C22×Dic83—22no—
108C22×Dic83—22no—
109C22×Dic83—21no—
110C22×Dic83—21no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—21no—
116C22×Dic83—21no—
117C22×Dic83—21no—
118C22×Dic83—22no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—22no—
123C22×Dic83—22no—
124C22×Dic83—22no—
125C22×Dic83—22no—
126C22×Dic83—22no—
127C22×Dic83C2×D412yes—
128C22×Dic83C2×D414yes—
129C22×Dic83C2×D412yes—
130C22×Dic83C2×D412yes—
131C22×Dic83C2×D412yes—
132C22×Dic83C2×Q814yes—
133C22×Dic83C2×Q814yes—
134C22×Dic83C2×Q814yes—
135C22×Dic83C2×Q814yes—
136C22×Dic83#4112yes—
137C22×Dic83#4114yes—
138C4⋊Dic83—48no—
139C4⋊Dic83—44no—
140Dic83⋊C4—28no—
141Dic83⋊C4—48no—
142Dic83⋊C4—48no—
143Dic83⋊C4—48no—
144Dic83⋊C4—44no—
145Dic83⋊C4—48no—
146Dic83⋊C4—44no—
147C4×Dic83—216no—
148C4×Dic83—28no—
149C24×C83C2411yescharacteristic
150C22×C4×C83—22no—
151C22×C4×C83—22no—
152C22×C4×C83—22no—
153C22×C4×C83—22no—
154C22×C4×C83—22no—
155C22×C4×C83—22no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—22no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—22no—
171C22×C4×C83—22no—
172C22×C4×C83—22no—
173C22×C4×C83—22no—
174C22×C4×C83C2×D412yes—
175C22×C4×C83C2×D412yes—
176C22×C4×C83C2×D412yes—
177C22×C4×C83C2×D412yes—
178C22×C4×C83C2×D414yes—
179C22×C4×C83C2×Q814yes—
180C22×C4×C83C2×Q814yes—
181C4⋊C4×C83—48no—
182C4⋊C4×C83—44no—
183C4⋊C4×C83—44no—
184C23×C83C22×D411yescharacteristic
185C23×C83C22×D411yescharacteristic
186C23×C83C22×D411yescharacteristic
187C23×C83C22×D411yescharacteristic
188C23×C83C22×Q812yes—
189C23×C83C22×Q812yes—
190C23×C83C2×#4111yescharacteristic
191C23×C83C2×#4112yes—
192C23×C83H(5,𝔽2)11yescharacteristic
193C23×C83H(5,𝔽2)11yescharacteristic
194C23×C832−1+412yes—
195C2×C4×C83—24no—
196C2×C4×C83—22no—
197C2×C4×C83—22no—
198C2×C4×C83—24no—
199C2×C4×C83—24no—
200C2×C4×C83—24no—
201C2×C4×C83—24no—
202C2×C4×C83—24no—
203C2×C4×C83—24no—
204C2×C4×C83—24no—
205C2×C4×C83—22no—
206C2×C4×C83—22no—
207C2×C4×C83—22no—
208C2×C4×C83—41no—
209C2×C4×C83—41no—
210C2×C4×C83—41no—
211C2×C4×C83—41no—
212C2×C4×C83—42no—
213C2×C4×C83—41no—
214C2×C4×C83—41no—
215C2×C4×C83—42no—
216C2×C4×C83—42no—
217C2×C4×C83—41no—
218C2×C4×C83—42no—
219C2×C4×C83—42no—
220C2×C4×C83—42no—
221C2×C4×C83—42no—
222C2×C4×C83—42no—
223C2×C4×C83—42no—
224C2×C4×C83#12714yes—
225C2×C4×C83C4⋊Q818yes—
226C2×Dic83—24no—
227C2×Dic83—22no—
228C2×Dic83—22no—
229C2×Dic83—24no—
230C2×Dic83—24no—
231C2×Dic83—24no—
232C2×Dic83—24no—
233C2×Dic83—24no—
234C2×Dic83—24no—
235C2×Dic83—24no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—22no—
239C2×Dic83—41no—
240C2×Dic83—41no—
241C2×Dic83—41no—
242C2×Dic83—41no—
243C2×Dic83—42no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—42no—
247C2×Dic83—42no—
248C2×Dic83—41no—
249C2×Dic83—42no—
250C2×Dic83—42no—
251C2×Dic83—42no—
252C2×Dic83—42no—
253C2×Dic83—42no—
254C2×Dic83—42no—
255C2×Dic83#12114yes—
256C2×Dic83C22⋊Q818yes—
257C2×Dic83#12314yes—
258C2×Dic83#12518yes—
259C2×Dic83C4⋊Q818yes—
260C2×Dic83C4⋊Q814yes—
261C2×Dic83C4⋊Q814yes—
262C22×C83C2×#12111yescharacteristic
263C22×C83C2×C22⋊Q812yes—
264C22×C83C2×#12311yescharacteristic
265C22×C83C2×#12512yes—
266C22×C83C2×#12711yescharacteristic
267C22×C83C2×C4⋊Q811yescharacteristic
268C22×C83C2×C4⋊Q812yes—
269C22×C83C2×C4⋊Q811yescharacteristic
270C22×C83C2×C4⋊Q812yes—
271C22×C83#53511yescharacteristic
272C22×C83#53611yescharacteristic
273C22×C83#54412yes—
274C22×C83#54412yes—
275C22×C83D4211yescharacteristic
276C22×C83D4211yescharacteristic
277C22×C83#54712yes—
278C22×C83#54712yes—
279C22×C83D4×Q812yes—
280C22×C83#55011yescharacteristic
281C22×C83#55011yescharacteristic
282C22×C83#55412yes—
283C22×C83#55412yes—
284C22×C83#55712yes—
285C4×C83—28no—
286C4×C83—24no—
287C4×C83—42no—
288C4×C83—81no—
289C4×C83—82no—
290Dic83—28no—
291Dic83—24no—
292Dic83—42no—
293Dic83—81no—
294Dic83—82no—
295Dic83#39818yescomplemented
296#15145—831nomaximal, Sylow
297C2×C83C2×#39811yescharacteristic
298C2×C83#244012yes—
299C2×C83#244012yes—
300C2×C83#250111yescharacteristic
301C2×C83#250211yescharacteristic
302C2×C83#254111yescharacteristic
303C2×C83#254611yescharacteristic
304C2×C83#255212yes—
305C2×C83#255212yes—
306C2×C83#266011yescharacteristic
307C2×C83#286811yescharacteristic
308C2×#398—831no—
309C2×#398—831no—
310C2×#398—831no—
311C2×#398D8311yescharacteristic
312C2×#389—831no—
313C2×#384—831no—
314C2×#384—832no—
315#1444—832no—
316#1444—832no—
317C4⋊#95—832no—
318C4×#95—831no—
319C83#1514511yescharacteristic, complemented, Sylow
320C22×C4⋊C4—832no—
321C22×C4⋊C4—832no—
322C22×C4⋊C4—832no—
323C22×C4⋊C4—832no—
324C22×C4⋊C4—831no—
325C22×C4⋊C4—831no—
326C22×C4⋊C4—831no—
327C22×C4⋊C4—831no—
328C22×C4⋊C4—832no—
329C22×C4⋊C4C2×D8311yescharacteristic
330C22×C4⋊C4C2×D8311yescharacteristic
331C22×C4⋊C4C2×D8312yes—
332C22×C42—832no—
333C22×C42—831no—
334#398—24no—
335#398—1664no—
336#398—1664no—
337#398—1664no—
338#389—1664no—
339#384—1664no—
340#384—1668no—
341C2×#95—831no—
342C2×#95—832no—
343C2×#95—832no—
344C2×#95—832no—
345C2×#95—832no—
346C2×#95—831no—
347C2×#95—831no—
348C2×#95C2×D8312yes—
349C2×#95C2×D8311yescharacteristic
350C23×C4—831no—
351C23×C4—832no—
352C23×C4—831no—
353C23×C4—831no—
354C23×C4—832no—
355C23×C4—831no—
356C23×C4C22×D8312yes—
357C23×C4C22×D8311yescharacteristic
358C23×C4C22×D8311yescharacteristic
359C23×C4C22×D8311yescharacteristic
360C23×C4C22×D8312yes—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—3322no—
371C2×C4⋊C4—3322no—
372C2×C4⋊C4—3322no—
373C2×C4⋊C4—3322no—
374C2×C4⋊C4—3322no—
375C2×C4⋊C4—834no—
376C2×C4⋊C4—1664no—
377C2×C4⋊C4—1664no—
378C2×C4⋊C4—1664no—
379C2×C4⋊C4—1664no—
380C2×C4⋊C4—1664no—
381C2×C4⋊C4—1662no—
382C2×C4⋊C4—1664no—
383C2×C4⋊C4—1664no—
384C2×C4⋊C4—1664no—
385C2×C4⋊C4—1664no—
386C2×C4⋊C4—1664no—
387C2×C4⋊C4—1662no—
388C2×C4⋊C4—1662no—
389C2×C4⋊C4—1662no—
390C2×C4⋊C4—1662no—
391C2×C4⋊C4—1662no—
392C2×C4⋊C4—1664no—
393C2×C4⋊C4—1662no—
394C2×C4⋊C4—1662no—
395C2×C4⋊C4—1662no—
396C2×C42—834no—
397C2×C42—838no—
398C2×C42—1664no—
399C2×C42—1664no—
400C2×C42—1664no—
401#95—24no—
402#95—834no—
403#95—838no—
404#95—1662no—
405#95—1662no—
406#95—1664no—
407#95—1664no—
408#95—1664no—
409#95C22⋊D8314yes—
410C24C23×D8311yescharacteristic
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—832no—
436C22×C4—832no—
437C22×C4—834no—
438C22×C4—834no—
439C22×C4—832no—
440C22×C4—834no—
441C22×C4—832no—
442C22×C4—834no—
443C22×C4—834no—
444C22×C4—834no—
445C22×C4—832no—
446C22×C4—1661no—
447C22×C4—1662no—
448C22×C4—1661no—
449C22×C4—1662no—
450C22×C4—1662no—
451C22×C4—1661no—
452C22×C4—1662no—
453C22×C4—1662no—
454C22×C4—1662no—
455C22×C4—1662no—
456C22×C4—1662no—
457C22×C4—1662no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4—1661no—
461C22×C4—1661no—
462C22×C4—1661no—
463C22×C4—1661no—
464C22×C4—1662no—
465C22×C4—1662no—
466C22×C4—1662no—
467C22×C4—1661no—
468C22×C4—1662no—
469C22×C4—1661no—
470C22×C4—1662no—
471C22×C4D4×D8312yes—
472C22×C4D4×D8312yes—
473C22×C4D4×D8312yes—
474C22×C4C2×C22⋊D8312yes—
475C22×C4C2×C22⋊D8314yes—
476C22×C4Q8×D8314yes—
477C22×C4Q8×D8314yes—
478C4⋊C4—48no—
479C4⋊C4—44no—
480C4⋊C4—44no—
481C4⋊C4—3328no—
482C4⋊C4—3328no—
483C4⋊C4—3328no—
484C4⋊C4—3324no—
485C4⋊C4—3328no—
486C4⋊C4—3328no—
487C4⋊C4—3324no—
488C4⋊C4—3324no—
489C4⋊C4—1668no—
490C42—16616no—
491C42—1668no—
492C23C2×D4×D8311yescharacteristic
493C23C2×D4×D8311yescharacteristic
494C23C2×D4×D8311yescharacteristic
495C23C22×C22⋊D8311yescharacteristic
496C23C2×Q8×D8312yes—
497C23C2×Q8×D8312yes—
498C23#41×D8312yes—
499C23#41×D8311yescharacteristic
500C23#1458183711yescharacteristic
501C23#1458183811yescharacteristic
502C23#1458183912yes—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—3321no—
533C2×C4—3321no—
534C2×C4—3321no—
535C2×C4—3321no—
536C2×C4—3322no—
537C2×C4—3322no—
538C2×C4—3322no—
539C2×C4—3322no—
540C2×C4—3322no—
541C2×C4—3322no—
542C2×C4—3322no—
543C2×C4—3321no—
544C2×C4—3322no—
545C2×C4—3321no—
546C2×C4—3322no—
547C2×C4—3321no—
548C2×C4—834no—
549C2×C4—838no—
550C2×C4—834no—
551C2×C4—838no—
552C2×C4—834no—
553C2×C4—838no—
554C2×C4—834no—
555C2×C4—1662no—
556C2×C4—1662no—
557C2×C4—1662no—
558C2×C4—1664no—
559C2×C4—1664no—
560C2×C4—1664no—
561C2×C4—1664no—
562C2×C4—1664no—
563C2×C4—1664no—
564C2×C4—1664no—
565C2×C4—1664no—
566C2×C4—1662no—
567C2×C4—1662no—
568C2×C4#1458178814yes—
569C2×C4#1458179018yes—
570C22#121×D8311yescharacteristic
571C22C22⋊Q8×D8312yes—
572C22#123×D8311yescharacteristic
573C22#125×D8312yes—
574C22C2×#1458178811yescharacteristic
575C22C4⋊Q8×D8312yes—
576C22C4⋊Q8×D8311yescharacteristic
577C22C4⋊Q8×D8311yescharacteristic
578C22C2×#1458179012yes—
579C22#1912826711yescharacteristic
580C22#1912827311yescharacteristic
581C22#1912833012yes—
582C22#1912833112yes—
583C22D4×C22⋊D8311yescharacteristic
584C22#1912833511yescharacteristic
585C22#1912834912yes—
586C22#1912835012yes—
587C22#1912836412yes—
588C22#1912836911yescharacteristic
589C22#1912837011yescharacteristic
590C22#1912840512yes—
591C22#1912840712yes—
592C22#1912842812yes—
593C4—28no—
594C4—24no—
595C4—42no—
596C4—82no—
597C4—81no—
598C4—3322no—
599C4—838no—
600C4—6642no—
601C4—6641no—
602C4—1668no—
603C4—1664no—
604C2#398×D8311yescharacteristic
605C2#2491116012yes—
606C2#2491116212yes—
607C2#2491193211yescharacteristic
608C2#2491193611yescharacteristic
609C2#2491240611yescharacteristic
610C2#2491244711yescharacteristic
611C2#2491249312yes—
612C2#2491249512yes—
613C2#2491358611yescharacteristic
614C2#2491585911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutator, socle, prime radical, cosocleC24×C83C24
FittingC2×#398×C83C2
hypercenterC2×#398D83
hypocenterC83#15145
LCSG ▷ C24×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
295. Dic83#398semidirect
319. C83#15145semidirect

Maximal subgroups

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

subgroupindex
C2×#191276332
C2×#191276322
C2×#191276312
C2×#191275962
C2×#191275702
#249057272
#249057262
Dic83⋊#952
#95×Dic832
C2×#398×C832
#1514583