Finite Group Databasebeta

← #35341112

Subgroups — #35341112

Order 21248.

1934 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581790C211yesmaximal, characteristic
2C2×#19127622C211yesmaximal, characteristic
3C2×#19127621C211yesmaximal, characteristic
4C2×#19127620C211yesmaximal, characteristic
5C2×#19127596C211yesmaximal, characteristic
6C2×#19127570C212yesmaximal
7#24905727C212yesmaximal
8#24905726C212yesmaximal
9Dic83⋊#95C212yesmaximal
10#95×Dic83C211yesmaximal, characteristic
11C2×#395×C83C211yesmaximal, characteristic
12C23×Dic166C2211yescharacteristic
13C2×#14581790—28no—
14C2×#14581790—24no—
15C22×C4⋊Dic83C2212yes—
16C22×Dic83⋊C4C2211yescharacteristic
17C22×Dic83⋊C4C2211yescharacteristic
18C22×Dic83⋊C4C2212yes—
19C22×Dic83⋊C4C2212yes—
20C22×Dic83⋊C4C2212yes—
21C22×Dic83⋊C4C2212yes—
22C22×Dic83⋊C4C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24C22×C4×Dic83C2212yes—
25#19127622—24no—
26#19127621—24no—
27#19127620—24no—
28#19127596—24no—
29#19127570—28no—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2211yescharacteristic
34C2×C83⋊#95C2211yescharacteristic
35C2×C83⋊#95C2211yescharacteristic
36C2×C83⋊#95C2212yes—
37C23×Q8×C83C2211yescharacteristic
38C22×C4⋊C4×C83C2211yescharacteristic
39C22×C4⋊C4×C83C2212yes—
40#395×C83—24no—
41C2×#95×C83C2212yes—
42C2×#95×C83C2211yescharacteristic
43C22×Dic166—24no—
44C22×Dic166—22no—
45C22×Dic166—22no—
46C22×Dic166—22no—
47C22×Dic166—42no—
48C23×Dic83C2311yescharacteristic
49C23×Dic83C2312yes—
50C23×Dic83C2311yescharacteristic
51C23×Dic83C2311yescharacteristic
52C23×Dic83C2312yes—
53C23×Dic83C2311yescharacteristic
54#14581790—232no—
55C2×C4⋊Dic83—24no—
56C2×C4⋊Dic83—24no—
57C2×C4⋊Dic83—42no—
58C2×Dic83⋊C4—22no—
59C2×Dic83⋊C4—24no—
60C2×Dic83⋊C4—24no—
61C2×Dic83⋊C4—24no—
62C2×Dic83⋊C4—24no—
63C2×Dic83⋊C4—22no—
64C2×Dic83⋊C4—24no—
65C2×Dic83⋊C4—24no—
66C2×Dic83⋊C4—22no—
67C2×Dic83⋊C4—24no—
68C2×Dic83⋊C4—24no—
69C2×Dic83⋊C4—24no—
70C2×Dic83⋊C4—24no—
71C2×Dic83⋊C4—22no—
72C2×Dic83⋊C4—22no—
73C2×Dic83⋊C4—22no—
74C2×Dic83⋊C4—42no—
75C2×Dic83⋊C4—42no—
76C2×Dic83⋊C4D418yes—
77C2×Dic83⋊C4Q814yescomplemented
78C2×C4×Dic83—24no—
79C2×C4×Dic83—24no—
80C2×C4×Dic83—24no—
81C2×C4×Dic83D414yes—
82C2×C4×Dic83Q818yescomplemented
83C83⋊#95—22no—
84C83⋊#95—22no—
85C83⋊#95—24no—
86C83⋊#95—24no—
87C83⋊#95—24no—
88C83⋊#95D414yes—
89C83⋊#95Q818yescomplemented
90C22×Q8×C83—24no—
91C22×Q8×C83—22no—
92C22×Q8×C83—22no—
93C22×Q8×C83—22no—
94C22×Q8×C83—42no—
95C23×C4×C83C2311yescharacteristic
96C23×C4×C83C2312yes—
97C23×C4×C83C2311yescharacteristic
98C23×C4×C83C2311yescharacteristic
99C23×C4×C83C2312yes—
100C2×C4⋊C4×C83—24no—
101C2×C4⋊C4×C83—22no—
102C2×C4⋊C4×C83—22no—
103C2×C4⋊C4×C83—24no—
104C2×C4⋊C4×C83—22no—
105C2×C4⋊C4×C83—42no—
106#95×C83—24no—
107#95×C83D414yes—
108C2×Dic166—28no—
109C2×Dic166—48no—
110C2×Dic166—48no—
111C2×Dic166—44no—
112C2×Dic166—44no—
113C22×Dic83—22no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—21no—
118C22×Dic83—21no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—22no—
123C22×Dic83—22no—
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—22no—
129C22×Dic83—22no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—22no—
135C22×Dic83—21no—
136C22×Dic83—22no—
137C22×Dic83C2×D414yes—
138C22×Dic83C2×D412yes—
139C22×Dic83C2×D414yes—
140C22×Dic83C2×D414yes—
141C22×Dic83C2×D412yes—
142C22×Dic83C2×Q812yes—
143C22×Dic83C2×Q814yes—
144C22×Dic83C2×Q814yes—
145C22×Dic83C2×Q814yes—
146C22×Dic83C2×Q814yes—
147C22×Dic83C2×Q812yes—
148C22×Dic83#4112yes—
149C4⋊Dic83—48no—
150Dic83⋊C4—216no—
151Dic83⋊C4—216no—
152Dic83⋊C4—28no—
153Dic83⋊C4—48no—
154Dic83⋊C4—48no—
155Dic83⋊C4—44no—
156Dic83⋊C4—44no—
157C4×Dic83—28no—
158C4×Dic83—216no—
159C24×C83C2411yescharacteristic
160C2×Q8×C83—28no—
161C2×Q8×C83—48no—
162C2×Q8×C83—48no—
163C2×Q8×C83—44no—
164C2×Q8×C83—44no—
165C22×C4×C83—22no—
166C22×C4×C83—22no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—22no—
171C22×C4×C83—21no—
172C22×C4×C83—22no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—22no—
176C22×C4×C83—22no—
177C22×C4×C83—22no—
178C22×C4×C83—21no—
179C22×C4×C83—22no—
180C22×C4×C83—22no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—22no—
186C22×C4×C83—21no—
187C22×C4×C83—22no—
188C22×C4×C83C2×D414yes—
189C22×C4×C83C2×D412yes—
190C22×C4×C83C2×D412yes—
191C22×C4×C83C2×D412yes—
192C22×C4×C83C2×D414yes—
193C22×C4×C83C2×Q812yes—
194C22×C4×C83C2×Q814yes—
195C22×C4×C83C2×Q814yes—
196C4⋊C4×C83—48no—
197C4⋊C4×C83—44no—
198C23×C83C22×D411yescharacteristic
199C23×C83C22×D412yes—
200C23×C83C22×D411yescharacteristic
201C23×C83C22×D411yescharacteristic
202C23×C83C22×Q812yes—
203C23×C83C22×Q811yescharacteristic
204C23×C83C22×Q812yes—
205C23×C83C2×#4111yescharacteristic
206C23×C83H(5,𝔽2)12yes—
207C23×C832−1+411yescharacteristic
208C23×C832−1+411yescharacteristic
209Q8×C83—416no—
210C2×C4×C83—22no—
211C2×C4×C83—24no—
212C2×C4×C83—22no—
213C2×C4×C83—24no—
214C2×C4×C83—24no—
215C2×C4×C83—24no—
216C2×C4×C83—24no—
217C2×C4×C83—24no—
218C2×C4×C83—24no—
219C2×C4×C83—24no—
220C2×C4×C83—24no—
221C2×C4×C83—22no—
222C2×C4×C83—24no—
223C2×C4×C83—24no—
224C2×C4×C83—22no—
225C2×C4×C83—22no—
226C2×C4×C83—41no—
227C2×C4×C83—42no—
228C2×C4×C83—42no—
229C2×C4×C83—41no—
230C2×C4×C83—42no—
231C2×C4×C83—42no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83—41no—
237C2×C4×C83—42no—
238C2×C4×C83—42no—
239C2×C4×C83#12714yes—
240C2×C4×C83C4⋊Q818yescomplemented
241C2×Dic83—22no—
242C2×Dic83—24no—
243C2×Dic83—22no—
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—22no—
253C2×Dic83—24no—
254C2×Dic83—24no—
255C2×Dic83—22no—
256C2×Dic83—22no—
257C2×Dic83—41no—
258C2×Dic83—42no—
259C2×Dic83—42no—
260C2×Dic83—41no—
261C2×Dic83—42no—
262C2×Dic83—42no—
263C2×Dic83—41no—
264C2×Dic83—41no—
265C2×Dic83—41no—
266C2×Dic83—41no—
267C2×Dic83—41no—
268C2×Dic83—42no—
269C2×Dic83—42no—
270C2×Dic83#12014yes—
271C2×Dic83C22⋊Q818yes—
272C2×Dic83C22⋊Q814yes—
273C2×Dic83C4⋊Q814yes—
274C2×Dic83C4⋊Q814yes—
275C2×Dic83C4⋊Q818yes—
276C2×Dic83C4⋊Q818yescomplemented
277Dic166—416no—
278C22×C83C2×#12011yescharacteristic
279C22×C83C2×C22⋊Q811yescharacteristic
280C22×C83C2×C22⋊Q812yes—
281C22×C83C2×#12711yescharacteristic
282C22×C83C2×C4⋊Q811yescharacteristic
283C22×C83C2×C4⋊Q811yescharacteristic
284C22×C83C2×C4⋊Q812yes—
285C22×C83C2×C4⋊Q812yes—
286C22×C83C2×C4⋊Q812yes—
287C22×C83#53511yescharacteristic
288C22×C83#53611yescharacteristic
289C22×C83#54412yes—
290C22×C83#54412yes—
291C22×C83D4212yes—
292C22×C83D4212yes—
293C22×C83#54711yescharacteristic
294C22×C83#54711yescharacteristic
295C22×C83D4×Q812yes—
296C22×C83D4×Q811yescharacteristic
297C22×C83D4×Q811yescharacteristic
298C22×C83D4×Q812yes—
299C22×C83#55412yes—
300C22×C83Q8212yes—
301C4×C83—24no—
302C4×C83—28no—
303C4×C83—44no—
304C4×C83—42no—
305C4×C83—81no—
306Dic83—24no—
307Dic83—28no—
308Dic83—44no—
309Dic83—42no—
310Dic83—81no—
311Dic83#39518yescomplemented
312#15143—831nomaximal, Sylow
313C2×C83C2×#39511yescharacteristic
314C2×C83#243311yescharacteristic
315C2×C83#243411yescharacteristic
316C2×C83#244012yes—
317C2×C83#244012yes—
318C2×C83#254211yescharacteristic
319C2×C83#255112yes—
320C2×C83#255112yes—
321C2×C83#256711yescharacteristic
322C2×C83#266011yescharacteristic
323C2×C83#286811yescharacteristic
324C22×C4⋊Q8—831no—
325C2×#395—831no—
326C2×#395—831no—
327C2×#395—831no—
328C2×#395D8311yescharacteristic
329C2×#389—831no—
330C2×#384—832no—
331#1444—832no—
332#1444—832no—
333C4⋊#95—832no—
334C4×#95—831no—
335C83#1514311yescharacteristic, complemented, Sylow
336C23×Q8—831no—
337C23×Q8C2×D8311yescharacteristic
338C2×C4⋊Q8—1664no—
339C2×C4⋊Q8—1668no—
340C22×C4⋊C4—832no—
341C22×C4⋊C4—832no—
342C22×C4⋊C4—832no—
343C22×C4⋊C4—832no—
344C22×C4⋊C4—831no—
345C22×C4⋊C4—831no—
346C22×C4⋊C4—832no—
347C22×C4⋊C4—831no—
348C22×C4⋊C4C2×D8311yescharacteristic
349C22×C4⋊C4C2×D8312yes—
350C22×C42—831no—
351C22×C42—832no—
352#395—24no—
353#395—1664no—
354#395—1664no—
355#395—1664no—
356#389—1664no—
357#384—1668no—
358C2×#95—831no—
359C2×#95—832no—
360C2×#95—832no—
361C2×#95—832no—
362C2×#95—832no—
363C2×#95—831no—
364C2×#95—831no—
365C2×#95C2×D8312yes—
366C2×#95C2×D8311yescharacteristic
367C22×Q8—24no—
368C22×Q8—22no—
369C22×Q8—22no—
370C22×Q8—22no—
371C22×Q8—42no—
372C22×Q8—3322no—
373C22×Q8—1664no—
374C22×Q8—1662no—
375C22×Q8—1662no—
376C22×Q8—1662no—
377C23×C4—831no—
378C23×C4—832no—
379C23×C4—831no—
380C23×C4—832no—
381C23×C4—831no—
382C23×C4—831no—
383C23×C4C22×D8311yescharacteristic
384C23×C4C22×D8312yes—
385C23×C4C22×D8311yescharacteristic
386C23×C4C22×D8311yescharacteristic
387C23×C4C22×D8312yes—
388C4⋊Q8—16632no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—3322no—
396C2×C4⋊C4—3322no—
397C2×C4⋊C4—3322no—
398C2×C4⋊C4—838no—
399C2×C4⋊C4—834no—
400C2×C4⋊C4—1664no—
401C2×C4⋊C4—1664no—
402C2×C4⋊C4—1664no—
403C2×C4⋊C4—1662no—
404C2×C4⋊C4—1664no—
405C2×C4⋊C4—1664no—
406C2×C4⋊C4—1664no—
407C2×C4⋊C4—1662no—
408C2×C4⋊C4—1662no—
409C2×C4⋊C4—1662no—
410C2×C4⋊C4—1664no—
411C2×C4⋊C4—1664no—
412C2×C4⋊C4—1664no—
413C2×C4⋊C4—1664no—
414C2×C4⋊C4—1664no—
415C2×C4⋊C4—1662no—
416C2×C4⋊C4—1662no—
417C2×C4⋊C4—1664no—
418C2×C42—834no—
419C2×C42—838no—
420C2×C42—1664no—
421C2×C42—1664no—
422C2×C42—1664no—
423#95—24no—
424#95—834no—
425#95—838no—
426#95—1662no—
427#95—1662no—
428#95—1664no—
429#95—1664no—
430#95—1664no—
431#95C22⋊D8314yes—
432C24C23×D8311yescharacteristic
433C2×Q8—28no—
434C2×Q8—48no—
435C2×Q8—48no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—3324no—
439C2×Q8—3328no—
440C2×Q8—3328no—
441C2×Q8—3324no—
442C2×Q8—1668no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—832no—
467C22×C4—834no—
468C22×C4—834no—
469C22×C4—832no—
470C22×C4—832no—
471C22×C4—834no—
472C22×C4—832no—
473C22×C4—834no—
474C22×C4—834no—
475C22×C4—834no—
476C22×C4—834no—
477C22×C4—832no—
478C22×C4—1661no—
479C22×C4—1661no—
480C22×C4—1662no—
481C22×C4—1661no—
482C22×C4—1662no—
483C22×C4—1661no—
484C22×C4—1661no—
485C22×C4—1662no—
486C22×C4—1662no—
487C22×C4—1662no—
488C22×C4—1661no—
489C22×C4—1662no—
490C22×C4—1661no—
491C22×C4—1662no—
492C22×C4—1662no—
493C22×C4—1661no—
494C22×C4—1661no—
495C22×C4—1662no—
496C22×C4—1662no—
497C22×C4—1662no—
498C22×C4—1662no—
499C22×C4—1661no—
500C22×C4—1662no—
501C22×C4—1661no—
502C22×C4D4×D8314yes—
503C22×C4D4×D8312yes—
504C22×C4D4×D8312yes—
505C22×C4C2×C22⋊D8312yes—
506C22×C4C2×C22⋊D8314yes—
507C22×C4Q8×D8312yes—
508C22×C4Q8×D8314yes—
509C22×C4Q8×D8314yes—
510C4⋊C4—48no—
511C4⋊C4—44no—
512C4⋊C4—3328no—
513C4⋊C4—3328no—
514C4⋊C4—3324no—
515C4⋊C4—3328no—
516C4⋊C4—3324no—
517C4⋊C4—16616no—
518C4⋊C4—1668no—
519C4⋊C4—16616no—
520C42—1668no—
521C42—16616no—
522C23C2×D4×D8311yescharacteristic
523C23C2×D4×D8312yes—
524C23C2×D4×D8311yescharacteristic
525C23C22×C22⋊D8311yescharacteristic
526C23C2×Q8×D8312yes—
527C23C2×Q8×D8311yescharacteristic
528C23C2×Q8×D8312yes—
529C23#41×D8311yescharacteristic
530C23#1458183712yes—
531C23#1458183911yescharacteristic
532C23#1458184011yescharacteristic
533Q8—416no—
534Q8—33216no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—3322no—
565C2×C4—3322no—
566C2×C4—3321no—
567C2×C4—3321no—
568C2×C4—3321no—
569C2×C4—3322no—
570C2×C4—3322no—
571C2×C4—3321no—
572C2×C4—3322no—
573C2×C4—3322no—
574C2×C4—3321no—
575C2×C4—3321no—
576C2×C4—3321no—
577C2×C4—834no—
578C2×C4—838no—
579C2×C4—834no—
580C2×C4—838no—
581C2×C4—834no—
582C2×C4—834no—
583C2×C4—838no—
584C2×C4—1664no—
585C2×C4—1664no—
586C2×C4—1662no—
587C2×C4—1662no—
588C2×C4—1664no—
589C2×C4—1662no—
590C2×C4—1664no—
591C2×C4—1664no—
592C2×C4—1664no—
593C2×C4—1664no—
594C2×C4—1664no—
595C2×C4—1664no—
596C2×C4—1664no—
597C2×C4—1662no—
598C2×C4—1664no—
599C2×C4—1662no—
600C2×C4#1458178814yes—
601C2×C4#1458179018yescomplemented
602C22#120×D8311yescharacteristic
603C22C22⋊Q8×D8311yescharacteristic
604C22C22⋊Q8×D8312yes—
605C22C2×#1458178811yescharacteristic
606C22C4⋊Q8×D8311yescharacteristic
607C22C4⋊Q8×D8312yes—
608C22C4⋊Q8×D8312yes—
609C22C4⋊Q8×D8311yescharacteristic
610C22C2×#1458179012yes—
611C22#1912826611yescharacteristic
612C22#1912827411yescharacteristic
613C22#1912832812yes—
614C22#1912833012yes—
615C22#1912833312yes—
616C22D4×C22⋊D8312yes—
617C22#1912835011yescharacteristic
618C22#1912835311yescharacteristic
619C22#1912836411yescharacteristic
620C22#1912836412yes—
621C22Q8×C22⋊D8311yescharacteristic
622C22#1912836612yes—
623C22#1912840512yes—
624C22#1912843112yes—
625C4—28no—
626C4—24no—
627C4—42no—
628C4—44no—
629C4—81no—
630C4—3322no—
631C4—3324no—
632C4—838no—
633C4—6641no—
634C4—1668no—
635C4—1664no—
636C2#395×D8311yescharacteristic
637C2#2491109811yescharacteristic
638C2#2491110211yescharacteristic
639C2#2491115812yes—
640C2#2491116212yes—
641C2#2491241311yescharacteristic
642C2#2491248812yes—
643C2#2491249012yes—
644C2#2491266711yescharacteristic
645C2#2491358111yescharacteristic
646C2#2491585911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutator, socle, prime radical, cosocleC24×C83C24
FittingC2×#395×C83C2
hypercenterC2×#395D83
hypocenterC83#15143
LCSG ▷ C24×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
77. C2×Dic83⋊C4Q8semidirect
82. C2×C4×Dic83Q8semidirect
89. C83⋊#95Q8semidirect
240. C2×C4×C83C4⋊Q8semidirect
276. C2×Dic83C4⋊Q8semidirect
311. Dic83#395semidirect
335. C83#15143semidirect
601. C2×C4#14581790semidirect

Maximal subgroups

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

subgroupindex
C22×#145817902
C2×#191276222
C2×#191276212
C2×#191276202
C2×#191275962
C2×#191275702
#249057272
#249057262
Dic83⋊#952
#95×Dic832
C2×#395×C832
#1514383