Finite Group Databasebeta

← #35341134

Subgroups — #35341134

Order 21248.

1294 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127640C212yesmaximal
2C2×#19127600C211yesmaximal, characteristic
3#24905722C212yesmaximal
4#24905722C212yesmaximal
5#24905716C212yesmaximal
6#24905693C211yesmaximal, characteristic
7#24905692C211yesmaximal, characteristic
8#24905692C211yesmaximal, characteristic
9#24905692C211yesmaximal, characteristic
10C4×C83⋊#95C211yesmaximal, characteristic
11C2×#384×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×C4⋊Dic83C2212yes—
15C22×C4×Dic83C2211yescharacteristic
16C22×C4×Dic83C2211yescharacteristic
17#19127640—28no—
18#19127600—24no—
19C2×C83⋊#95C2212yes—
20C2×C83⋊#95C2212yes—
21C2×C83⋊#95C2212yes—
22C2×C83⋊#95C2212yes—
23C2×C83⋊#95C2212yes—
24C2×C83⋊#95C2211yescharacteristic
25C2×C83⋊#95C2211yescharacteristic
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2211yescharacteristic
32C22×C4⋊C4×C83C2211yescharacteristic
33C22×C4⋊C4×C83C2212yes—
34C22×C4⋊C4×C83C2212yes—
35C22×C4⋊C4×C83C2211yescharacteristic
36C22×C42×C83C2211yescharacteristic
37#384×C83—24no—
38C23×Dic83C2312yes—
39C23×Dic83C2312yes—
40C23×Dic83C2311yescharacteristic
41C23×Dic83C2311yescharacteristic
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2311yescharacteristic
44C2×C4⋊Dic83—24no—
45C2×C4⋊Dic83—24no—
46C2×C4⋊Dic83—22no—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83—22no—
50C2×C4⋊Dic83—22no—
51C2×C4⋊Dic83—22no—
52C2×C4⋊Dic83—42no—
53C2×C4×Dic83—22no—
54C2×C4×Dic83—22no—
55C2×C4×Dic83—22no—
56C2×C4×Dic83—22no—
57C2×C4×Dic83—22no—
58C2×C4×Dic83—22no—
59C83⋊#95—24no—
60C83⋊#95—24no—
61C83⋊#95—24no—
62C83⋊#95—24no—
63C83⋊#95—24no—
64C83⋊#95—22no—
65C83⋊#95—22no—
66C83⋊#95—24no—
67C83⋊#95—42no—
68C83⋊#95—42no—
69C83⋊#95—42no—
70C83⋊#95D414yes—
71C83⋊#95Q814yes—
72C23×C4×C83C2312yes—
73C23×C4×C83C2312yes—
74C23×C4×C83C2311yescharacteristic
75C23×C4×C83C2311yescharacteristic
76C23×C4×C83C2311yescharacteristic
77C2×C4⋊C4×C83—22no—
78C2×C4⋊C4×C83—22no—
79C2×C4⋊C4×C83—24no—
80C2×C4⋊C4×C83—24no—
81C2×C4⋊C4×C83—24no—
82C2×C4⋊C4×C83—22no—
83C2×C4⋊C4×C83—24no—
84C2×C4⋊C4×C83—22no—
85C2×C4⋊C4×C83—22no—
86C2×C4⋊C4×C83—42no—
87C2×C4⋊C4×C83—42no—
88C2×C4⋊C4×C83D414yes—
89C2×C42×C83—22no—
90C2×C42×C83—22no—
91C2×C42×C83Q814yes—
92C22×Dic83—21no—
93C22×Dic83—21no—
94C22×Dic83—21no—
95C22×Dic83—21no—
96C22×Dic83—21no—
97C22×Dic83—21no—
98C22×Dic83—21no—
99C22×Dic83—21no—
100C22×Dic83—21no—
101C22×Dic83—21no—
102C22×Dic83—21no—
103C22×Dic83—21no—
104C22×Dic83—21no—
105C22×Dic83—21no—
106C22×Dic83—21no—
107C22×Dic83—21no—
108C22×Dic83—21no—
109C22×Dic83—21no—
110C22×Dic83—21no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—21no—
116C22×Dic83—22no—
117C22×Dic83—22no—
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×Dic83—22no—
128C22×Dic83—22no—
129C22×Dic83—22no—
130C22×Dic83C2×D412yes—
131C22×Dic83C2×D412yes—
132C22×Dic83C2×Q812yes—
133C22×Dic83C2×Q812yes—
134C4⋊Dic83—48no—
135C4⋊Dic83—44no—
136C4⋊Dic83—44no—
137C4×Dic83—44no—
138C4×Dic83—44no—
139C24×C83C2411yescharacteristic
140C22×C4×C83—21no—
141C22×C4×C83—21no—
142C22×C4×C83—21no—
143C22×C4×C83—21no—
144C22×C4×C83—21no—
145C22×C4×C83—21no—
146C22×C4×C83—21no—
147C22×C4×C83—21no—
148C22×C4×C83—22no—
149C22×C4×C83—22no—
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—22no—
157C22×C4×C83—22no—
158C22×C4×C83—22no—
159C22×C4×C83—22no—
160C22×C4×C83—22no—
161C22×C4×C83C2×D412yes—
162C22×C4×C83C2×D414yes—
163C22×C4×C83C2×D412yes—
164C22×C4×C83C2×Q812yes—
165C22×C4×C83C2×Q812yes—
166C22×C4×C83C2×Q812yes—
167C22×C4×C83C2×Q812yes—
168C22×C4×C83#4112yes—
169C22×C4×C83#4112yes—
170C22×C4×C83#4112yes—
171C22×C4×C83#4112yes—
172C22×C4×C83#4112yes—
173C22×C4×C83#4112yes—
174C22×C4×C83#4112yes—
175C4⋊C4×C83—28no—
176C4⋊C4×C83—48no—
177C4⋊C4×C83—48no—
178C4⋊C4×C83—44no—
179C42×C83—28no—
180C23×C83C22×D411yescharacteristic
181C23×C83C22×D411yescharacteristic
182C23×C83C22×Q811yescharacteristic
183C23×C83C22×Q811yescharacteristic
184C23×C83C2×#4111yescharacteristic
185C23×C83C2×#4111yescharacteristic
186C23×C83C2×#4111yescharacteristic
187C23×C83C2×#4111yescharacteristic
188C23×C83C2×#4111yescharacteristic
189C23×C83C2×#4111yescharacteristic
190C23×C83C2×#4111yescharacteristic
191C23×C83H(5,𝔽2)11yescharacteristic
192C23×C83H(5,𝔽2)11yescharacteristic
193C23×C832−1+411yescharacteristic
194C23×C832−1+411yescharacteristic
195C2×C4×C83—22no—
196C2×C4×C83—22no—
197C2×C4×C83—22no—
198C2×C4×C83—22no—
199C2×C4×C83—22no—
200C2×C4×C83—22no—
201C2×C4×C83—22no—
202C2×C4×C83—22no—
203C2×C4×C83—22no—
204C2×C4×C83—22no—
205C2×C4×C83—22no—
206C2×C4×C83—22no—
207C2×C4×C83—24no—
208C2×C4×C83—24no—
209C2×C4×C83—24no—
210C2×C4×C83—42no—
211C2×C4×C83—42no—
212C2×C4×C83—42no—
213C2×C4×C83—42no—
214C2×C4×C83—42no—
215C2×C4×C83—42no—
216C2×C4×C83—42no—
217C2×C4×C83—42no—
218C2×C4×C83—42no—
219C2×C4×C83—42no—
220C2×C4×C83—42no—
221C2×C4×C83C22⋊Q814yes—
222C2×C4×C83#12314yes—
223C2×C4×C83#12414yes—
224C2×C4×C83#12514yes—
225C2×C4×C83#12514yes—
226C2×C4×C83#12514yes—
227C2×C4×C83#12614yes—
228C2×C4×C83#12614yes—
229C2×C4×C83C4⋊Q814yes—
230C2×Dic83—22no—
231C2×Dic83—22no—
232C2×Dic83—22no—
233C2×Dic83—22no—
234C2×Dic83—22no—
235C2×Dic83—22no—
236C2×Dic83—22no—
237C2×Dic83—22no—
238C2×Dic83—22no—
239C2×Dic83—22no—
240C2×Dic83—22no—
241C2×Dic83—22no—
242C2×Dic83—41no—
243C2×Dic83—41no—
244C2×Dic83—41no—
245C2×Dic83—41no—
246C2×Dic83—41no—
247C2×Dic83—41no—
248C2×Dic83—41no—
249C2×Dic83—41no—
250C2×Dic83—41no—
251C2×Dic83—41no—
252C2×Dic83—41no—
253C2×Dic83—41no—
254C2×Dic83—41no—
255C2×Dic83—41no—
256C2×Dic83—41no—
257C2×Dic83—41no—
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×C83C2×C22⋊Q811yescharacteristic
273C22×C83C2×#12311yescharacteristic
274C22×C83C2×#12411yescharacteristic
275C22×C83C2×#12511yescharacteristic
276C22×C83C2×#12511yescharacteristic
277C22×C83C2×#12511yescharacteristic
278C22×C83C2×#12611yescharacteristic
279C22×C83C2×#12611yescharacteristic
280C22×C83C2×C4⋊Q811yescharacteristic
281C22×C83#53211yescharacteristic
282C22×C83#53211yescharacteristic
283C22×C83#53311yescharacteristic
284C22×C83#53311yescharacteristic
285C22×C83#54011yescharacteristic
286C22×C83#54111yescharacteristic
287C22×C83#54211yescharacteristic
288C22×C83#54211yescharacteristic
289C22×C83#54411yescharacteristic
290C22×C83#54411yescharacteristic
291C22×C83D4211yescharacteristic
292C22×C83#54611yescharacteristic
293C22×C83#54711yescharacteristic
294C22×C83#54711yescharacteristic
295C22×C83#54811yescharacteristic
296C22×C83D4×Q811yescharacteristic
297C22×C83#55011yescharacteristic
298C22×C83#55211yescharacteristic
299C22×C83#55311yescharacteristic
300C22×C83#55411yescharacteristic
301C22×C83#55411yescharacteristic
302C22×C83#55511yescharacteristic
303C22×C83#55611yescharacteristic
304C22×C83#55611yescharacteristic
305C22×C83#55711yescharacteristic
306C22×C83#55911yescharacteristic
307C4×C83—24no—
308C4×C83—24no—
309C4×C83—44no—
310C4×C83—82no—
311C4×C83#40018yescomplemented
312Dic83—42no—
313Dic83—42no—
314Dic83—42no—
315Dic83—42no—
316Dic83—82no—
317Dic83—82no—
318#15146—831nomaximal, Sylow
319C2×C83C2×#40011yescharacteristic
320C2×C83#244011yescharacteristic
321C2×C83#244211yescharacteristic
322C2×C83#244511yescharacteristic
323C2×C83#244611yescharacteristic
324C2×C83#249111yescharacteristic
325C2×C83#249211yescharacteristic
326C2×C83#249611yescharacteristic
327C2×C83#249711yescharacteristic
328C2×C83#251111yescharacteristic
329C2×C83#251211yescharacteristic
330C2×C83#255211yescharacteristic
331C2×C83#257111yescharacteristic
332C2×C83#264711yescharacteristic
333C2×C83#285911yescharacteristic
334C2×#400—832no—
335C2×#389—831no—
336C2×#384D8311yescharacteristic
337#1442—832no—
338#1442—832no—
339#1441—832no—
340C4⋊#95—831no—
341C4⋊#95—831no—
342C4⋊#95—831no—
343C4⋊#95—831no—
344C4×#95—831no—
345C83#1514611yescharacteristic, complemented, Sylow
346C22×C4⋊C4—832no—
347C22×C4⋊C4—831no—
348C22×C4⋊C4—831no—
349C22×C4⋊C4C2×D8311yescharacteristic
350C22×C4⋊C4C2×D8312yes—
351C22×C4⋊C4C2×D8312yes—
352C22×C4⋊C4C2×D8311yescharacteristic
353C22×C42—831no—
354C22×C42—831no—
355C22×C42C2×D8311yescharacteristic
356#400—1668no—
357#389—1664no—
358#384—24no—
359C2×#95—832no—
360C2×#95—832no—
361C2×#95—832no—
362C2×#95—831no—
363C2×#95—831no—
364C2×#95—832no—
365C2×#95—832no—
366C2×#95—832no—
367C2×#95—832no—
368C2×#95—831no—
369C2×#95—831no—
370C2×#95—832no—
371C2×#95—832no—
372C23×C4—831no—
373C23×C4—831no—
374C23×C4—831no—
375C23×C4—831no—
376C23×C4—832no—
377C23×C4—832no—
378C23×C4C22×D8312yes—
379C23×C4C22×D8312yes—
380C23×C4C22×D8311yescharacteristic
381C23×C4C22×D8311yescharacteristic
382C23×C4C22×D8311yescharacteristic
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—3322no—
395C2×C4⋊C4—1664no—
396C2×C4⋊C4—1664no—
397C2×C4⋊C4—1662no—
398C2×C4⋊C4—1662no—
399C2×C4⋊C4—1662no—
400C2×C4⋊C4—1662no—
401C2×C4⋊C4—1662no—
402C2×C4⋊C4—1662no—
403C2×C4⋊C4C22⋊D8314yes—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—1662no—
407C2×C42—1662no—
408C2×C42—1662no—
409C2×C42—1662no—
410C2×C42—1662no—
411C2×C42—1662no—
412C2×C42Dic16614yes—
413#95—3322no—
414#95—3322no—
415#95—3322no—
416#95—834no—
417#95—834no—
418#95—1664no—
419#95—1664no—
420#95—1664no—
421#95—1664no—
422#95—1664no—
423#95—1662no—
424#95—1664no—
425#95—1662no—
426C24C23×D8311yescharacteristic
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—832no—
449C22×C4—832no—
450C22×C4—832no—
451C22×C4—832no—
452C22×C4—1662no—
453C22×C4—1662no—
454C22×C4—1662no—
455C22×C4—1662no—
456C22×C4—1662no—
457C22×C4—1662no—
458C22×C4—1662no—
459C22×C4—1662no—
460C22×C4—1662no—
461C22×C4—1662no—
462C22×C4—1662no—
463C22×C4—1662no—
464C22×C4—1662no—
465C22×C4—1662no—
466C22×C4—1661no—
467C22×C4—1661no—
468C22×C4—1661no—
469C22×C4—1661no—
470C22×C4—1661no—
471C22×C4—1661no—
472C22×C4—1661no—
473C22×C4—1661no—
474C22×C4—1661no—
475C22×C4—1661no—
476C22×C4—1661no—
477C22×C4—1661no—
478C22×C4—1661no—
479C22×C4—1661no—
480C22×C4—1661no—
481C22×C4—1661no—
482C22×C4—1661no—
483C22×C4—1661no—
484C22×C4—1661no—
485C22×C4—1661no—
486C22×C4—1661no—
487C22×C4—1661no—
488C22×C4—1661no—
489C22×C4—1661no—
490C22×C4D4×D8312yes—
491C22×C4C2×C22⋊D8314yes—
492C22×C4C2×C22⋊D8312yes—
493C22×C4Q8×D8312yes—
494C22×C4C2×Dic16612yes—
495C22×C4C2×Dic16612yes—
496C22×C4C2×Dic16612yes—
497C22×C4#1305058912yes—
498C22×C4#1305058912yes—
499C22×C4#1305058912yes—
500C22×C4#1305059012yes—
501C22×C4#1305059112yes—
502C22×C4#1305059112yes—
503C22×C4#1305059112yes—
504C4⋊C4—28no—
505C4⋊C4—48no—
506C4⋊C4—48no—
507C4⋊C4—44no—
508C4⋊C4—3328no—
509C4⋊C4—3324no—
510C4⋊C4—3324no—
511C42—28no—
512C42—3324no—
513C42—3324no—
514C23C2×D4×D8311yescharacteristic
515C23C22×C22⋊D8311yescharacteristic
516C23C2×Q8×D8311yescharacteristic
517C23C22×Dic16611yescharacteristic
518C23C2×#1305058911yescharacteristic
519C23C2×#1305058911yescharacteristic
520C23C2×#1305058911yescharacteristic
521C23C2×#1305059011yescharacteristic
522C23C2×#1305059111yescharacteristic
523C23C2×#1305059111yescharacteristic
524C23C2×#1305059111yescharacteristic
525C23#1458183711yescharacteristic
526C23#1458183711yescharacteristic
527C23#1458184011yescharacteristic
528C23#1458184011yescharacteristic
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—3321no—
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—3321no—
567C2×C4—3321no—
568C2×C4—3321no—
569C2×C4—3321no—
570C2×C4—3321no—
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—1662no—
586C2×C4—1662no—
587C2×C4—1662no—
588C2×C4—1662no—
589C2×C4—1662no—
590C2×C4—1662no—
591C2×C4—1662no—
592C2×C4—1662no—
593C2×C4—1662no—
594C2×C4—1662no—
595C2×C4—1662no—
596C2×C4—1662no—
597C2×C4#1458177114yes—
598C2×C4#1458177314yes—
599C2×C4#1458178114yes—
600C2×C4#1458178314yes—
601C2×C4#1458178314yes—
602C2×C4#1458178314yes—
603C2×C4#1458178714yes—
604C2×C4#1458178714yes—
605C2×C4#1458179114yes—
606C22C2×#1458177111yescharacteristic
607C22C2×#1458177311yescharacteristic
608C22C2×#1458178111yescharacteristic
609C22C2×#1458178311yescharacteristic
610C22C2×#1458178311yescharacteristic
611C22C2×#1458178311yescharacteristic
612C22C2×#1458178711yescharacteristic
613C22C2×#1458178711yescharacteristic
614C22C2×#1458179111yescharacteristic
615C22#1912824911yescharacteristic
616C22#1912825211yescharacteristic
617C22#1912825611yescharacteristic
618C22#1912825611yescharacteristic
619C22#1912830511yescharacteristic
620C22#1912831211yescharacteristic
621C22#1912832511yescharacteristic
622C22#1912832511yescharacteristic
623C22#1912833211yescharacteristic
624C22#1912833211yescharacteristic
625C22D4×C22⋊D8311yescharacteristic
626C22#1912834511yescharacteristic
627C22#1912835211yescharacteristic
628C22#1912835411yescharacteristic
629C22#1912836211yescharacteristic
630C22Q8×C22⋊D8311yescharacteristic
631C22#1912837111yescharacteristic
632C22#1912838611yescharacteristic
633C22#1912839911yescharacteristic
634C22#1912840611yescharacteristic
635C22#1912841211yescharacteristic
636C22#1912841711yescharacteristic
637C22#1912842511yescharacteristic
638C22#1912842511yescharacteristic
639C22#1912842611yescharacteristic
640C22#1912843711yescharacteristic
641C4—24no—
642C4—24no—
643C4—44no—
644C4—82no—
645C4—3322no—
646C4—3322no—
647C4—3322no—
648C4—3322no—
649C4—6642no—
650C4—6642no—
651C4#1912764018yescomplemented
652C2C2×#1912764011yescharacteristic
653C2#2491115911yescharacteristic
654C2#2491118111yescharacteristic
655C2#2491122411yescharacteristic
656C2#2491123511yescharacteristic
657C2#2491182911yescharacteristic
658C2#2491184011yescharacteristic
659C2#2491188811yescharacteristic
660C2#2491189911yescharacteristic
661C2#2491203411yescharacteristic
662C2#2491204511yescharacteristic
663C2#2491249911yescharacteristic
664C2#2491270511yescharacteristic
665C2#2491344311yescharacteristic
666C2#2491582411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutator, socle, prime radical, cosocleC24×C83C24
FittingC2×#384×C83C2
hypercenterC2×#384D83
hypocenterC83#15146
LCSG ▷ C24×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
311. C4×C83#400semidirect
345. C83#15146semidirect
651. C4#19127640semidirect

Maximal subgroups

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

subgroupindex
C2×#191276402
C2×#191276002
#249057222
#249057162
#249056932
#249056922
C4×C83⋊#952
C2×#384×C832
#1514683