Finite Group Databasebeta

← #35327927

Subgroups — #35327927

Order 21248.

1326 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127597C211yesmaximal, characteristic
2C2×#19127566C211yesmaximal, characteristic
3#24905724C212yesmaximal
4#24905721C212yesmaximal
5#24905696C212yesmaximal
6#24905693C211yesmaximal, characteristic
7#24905692C211yesmaximal, characteristic
8#24905692C211yesmaximal, characteristic
9#24905690C212yesmaximal
10C4×C83⋊#95C211yesmaximal, characteristic
11C2×C4×C4⋊C4×C83C211yesmaximal, characteristic
12C22×C4⋊Dic83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×Dic83⋊C4C2212yes—
15C22×C4×Dic83C2211yescharacteristic
16C22×C4×Dic83C2211yescharacteristic
17#19127597—24no—
18#19127566C418yescomplemented
19C2×C83⋊#95C2212yes—
20C2×C83⋊#95C2211yescharacteristic
21C2×C83⋊#95C2211yescharacteristic
22C2×C83⋊#95C2211yescharacteristic
23C2×C83⋊#95C2211yescharacteristic
24C2×C83⋊#95C2212yes—
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C22×C4⋊C4×C83C2211yescharacteristic
33C22×C4⋊C4×C83C2211yescharacteristic
34C22×C42×C83C2212yes—
35C22×C42×C83C2211yescharacteristic
36C4×C4⋊C4×C83—24no—
37C2×#95×C83C2212yes—
38C23×Dic83C2312yes—
39C23×Dic83C2311yescharacteristic
40C23×Dic83C2311yescharacteristic
41C23×Dic83C2312yes—
42C23×Dic83C2311yescharacteristic
43C23×Dic83C2311yescharacteristic
44C2×C4⋊Dic83—22no—
45C2×C4⋊Dic83—22no—
46C2×C4⋊Dic83—22no—
47C2×C4⋊Dic83—22no—
48C2×C4⋊Dic83—22no—
49C2×C4⋊Dic83C2×C414yes—
50C2×Dic83⋊C4—24no—
51C2×Dic83⋊C4—24no—
52C2×Dic83⋊C4—42no—
53C2×C4×Dic83—22no—
54C2×C4×Dic83—22no—
55C2×C4×Dic83—22no—
56C2×C4×Dic83—22no—
57C2×C4×Dic83—22no—
58C2×C4×Dic83C2×C414yes—
59C83⋊#95—22no—
60C83⋊#95—22no—
61C83⋊#95—24no—
62C83⋊#95—24no—
63C83⋊#95—22no—
64C83⋊#95—22no—
65C83⋊#95—24no—
66C83⋊#95—42no—
67C83⋊#95—42no—
68C83⋊#95—42no—
69C83⋊#95—42no—
70C83⋊#95C2×C418yes—
71C83⋊#95C2×C418yes—
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—22no—
80C2×C4⋊C4×C83—22no—
81C2×C4⋊C4×C83C2×C414yes—
82C2×C4⋊C4×C83D414yes—
83C2×C42×C83—22no—
84C2×C42×C83—22no—
85C2×C42×C83—24no—
86C2×C42×C83—24no—
87C2×C42×C83—42no—
88C2×C42×C83Q814yes—
89#95×C83—24no—
90C22×Dic83—21no—
91C22×Dic83—22no—
92C22×Dic83—21no—
93C22×Dic83—21no—
94C22×Dic83—21no—
95C22×Dic83—21no—
96C22×Dic83—21no—
97C22×Dic83—22no—
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—22no—
109C22×Dic83—22no—
110C22×Dic83—21no—
111C22×Dic83—21no—
112C22×Dic83—21no—
113C22×Dic83—22no—
114C22×Dic83—21no—
115C22×Dic83—21no—
116C22×Dic83—21no—
117C22×Dic83—22no—
118C22×Dic83—21no—
119C22×Dic83—21no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—22no—
123C22×Dic83—22no—
124C22×Dic83—22no—
125C22×Dic83—22no—
126C22×Dic83—22no—
127C22×Dic83C22×C412yes—
128C22×Dic83C22×C412yes—
129C22×Dic83C22×C414yes—
130C22×Dic83#4112yes—
131C22×Dic83#4112yes—
132C4⋊Dic83—28no—
133C4⋊Dic83—44no—
134Dic83⋊C4—48no—
135C4×Dic83—28no—
136C4×Dic83—44no—
137C24×C83C2411yescharacteristic
138C22×C4×C83—21no—
139C22×C4×C83—21no—
140C22×C4×C83—21no—
141C22×C4×C83—21no—
142C22×C4×C83—21no—
143C22×C4×C83—22no—
144C22×C4×C83—22no—
145C22×C4×C83—22no—
146C22×C4×C83—21no—
147C22×C4×C83—22no—
148C22×C4×C83—22no—
149C22×C4×C83—22no—
150C22×C4×C83—22no—
151C22×C4×C83—21no—
152C22×C4×C83—21no—
153C22×C4×C83—22no—
154C22×C4×C83—22no—
155C22×C4×C83—22no—
156C22×C4×C83—21no—
157C22×C4×C83—22no—
158C22×C4×C83—22no—
159C22×C4×C83—21no—
160C22×C4×C83C22×C414yes—
161C22×C4×C83C22×C412yes—
162C22×C4×C83C2×D414yes—
163C22×C4×C83C2×D412yes—
164C22×C4×C83C2×Q812yes—
165C22×C4×C83C2×Q812yes—
166C22×C4×C83C2×Q812yes—
167C22×C4×C83#4112yes—
168C22×C4×C83#4112yes—
169C22×C4×C83#4112yes—
170C22×C4×C83#4112yes—
171C22×C4×C83#4112yes—
172C22×C4×C83#4112yes—
173C4⋊C4×C83—28no—
174C4⋊C4×C83—28no—
175C42×C83—28no—
176C42×C83—48no—
177C23×C83C23×C411yescharacteristic
178C23×C83C22×D411yescharacteristic
179C23×C83C22×Q811yescharacteristic
180C23×C83C2×#4111yescharacteristic
181C23×C83C2×#4111yescharacteristic
182C23×C83C2×#4111yescharacteristic
183C23×C83C2×#4111yescharacteristic
184C23×C83C2×#4111yescharacteristic
185C23×C83C2×#4111yescharacteristic
186C23×C83C2×#4111yescharacteristic
187C23×C83C2×#4111yescharacteristic
188C23×C83H(5,𝔽2)11yescharacteristic
189C23×C83H(5,𝔽2)11yescharacteristic
190C23×C832−1+411yescharacteristic
191C23×C832−1+411yescharacteristic
192C2×C4×C83—22no—
193C2×C4×C83—22no—
194C2×C4×C83—22no—
195C2×C4×C83—22no—
196C2×C4×C83—22no—
197C2×C4×C83—22no—
198C2×C4×C83—24no—
199C2×C4×C83—24no—
200C2×C4×C83—24no—
201C2×C4×C83—22no—
202C2×C4×C83—24no—
203C2×C4×C83—22no—
204C2×C4×C83—22no—
205C2×C4×C83—24no—
206C2×C4×C83—24no—
207C2×C4×C83—42no—
208C2×C4×C83—42no—
209C2×C4×C83—42no—
210C2×C4×C83—41no—
211C2×C4×C83—42no—
212C2×C4×C83—41no—
213C2×C4×C83—42no—
214C2×C4×C83—41no—
215C2×C4×C83—42no—
216C2×C4×C83—41no—
217C2×C4×C83—42no—
218C2×C4×C83—42no—
219C2×C4×C83#11714yes—
220C2×C4×C83C4×D414yes—
221C2×C4×C83C4×Q814yes—
222C2×C4×C83C22⋊Q814yes—
223C2×C4×C83#12314yes—
224C2×C4×C83#12514yes—
225C2×C4×C83#12514yes—
226C2×C4×C83#12614yes—
227C2×Dic83—22no—
228C2×Dic83—22no—
229C2×Dic83—24no—
230C2×Dic83—22no—
231C2×Dic83—22no—
232C2×Dic83—24no—
233C2×Dic83—22no—
234C2×Dic83—22no—
235C2×Dic83—24no—
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—42no—
247C2×Dic83—41no—
248C2×Dic83—42no—
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—41no—
260C2×Dic83—41no—
261C2×Dic83—42no—
262C2×Dic83—42no—
263C2×Dic83—42no—
264C2×Dic83—42no—
265C2×Dic83—42no—
266C2×Dic83—42no—
267C2×Dic83—42no—
268C2×Dic83—42no—
269C22×C83C2×#11711yescharacteristic
270C22×C83C2×C4×D411yescharacteristic
271C22×C83C2×C4×Q811yescharacteristic
272C22×C83C4×#4111yescharacteristic
273C22×C83C4×#4111yescharacteristic
274C22×C83#52011yescharacteristic
275C22×C83#52011yescharacteristic
276C22×C83C2×C22⋊Q811yescharacteristic
277C22×C83C2×#12311yescharacteristic
278C22×C83C2×#12511yescharacteristic
279C22×C83C2×#12511yescharacteristic
280C22×C83C2×#12611yescharacteristic
281C22×C83#52911yescharacteristic
282C22×C83#52911yescharacteristic
283C22×C83#53311yescharacteristic
284C22×C83#54011yescharacteristic
285C22×C83#54111yescharacteristic
286C22×C83#54411yescharacteristic
287C22×C83#54411yescharacteristic
288C22×C83#54611yescharacteristic
289C22×C83#54611yescharacteristic
290C22×C83#54811yescharacteristic
291C22×C83#54811yescharacteristic
292C22×C83#55211yescharacteristic
293C22×C83#55211yescharacteristic
294C22×C83#55311yescharacteristic
295C22×C83#55311yescharacteristic
296C22×C83#55511yescharacteristic
297C22×C83#55511yescharacteristic
298C22×C83#55611yescharacteristic
299C22×C83#55611yescharacteristic
300C22×C83#55611yescharacteristic
301C22×C83#55611yescharacteristic
302C22×C83#55911yescharacteristic
303C22×C83#55911yescharacteristic
304C4×C83—24no—
305C4×C83—44no—
306C4×C83—44no—
307C4×C83—42no—
308C4×C83#38718yes—
309Dic83—42no—
310Dic83—42no—
311Dic83—44no—
312Dic83—42no—
313Dic83—42no—
314Dic83—82no—
315#14030—831nomaximal, Sylow
316C2×C83C2×#38711yescharacteristic
317C2×C83C4×#12511yescharacteristic
318C2×C83#233011yescharacteristic
319C2×C83#234611yescharacteristic
320C2×C83#234711yescharacteristic
321C2×C83#236711yescharacteristic
322C2×C83#236711yescharacteristic
323C2×C83#242011yescharacteristic
324C2×C83#242111yescharacteristic
325C2×C83#243911yescharacteristic
326C2×C83#244211yescharacteristic
327C2×C83#251311yescharacteristic
328C2×C83#251411yescharacteristic
329C2×C83#257011yescharacteristic
330C2×C83#257111yescharacteristic
331C2×#389—831no—
332C2×#382—831no—
333C2×C4×C4⋊C4D8311yescharacteristic
334#1443—832no—
335#1442—832no—
336#1436—832no—
337C4⋊#95—831no—
338C4⋊#95—831no—
339C4⋊#95—831no—
340#1434—832no—
341C4×#95—831no—
342C83#1403011yescharacteristic, complemented, Sylow
343C22×C4⋊C4—832no—
344C22×C4⋊C4—831no—
345C22×C4⋊C4—831no—
346C22×C4⋊C4C2×D8311yescharacteristic
347C22×C4⋊C4C2×D8311yescharacteristic
348C22×C42—831no—
349C22×C42—831no—
350C22×C42C2×D8312yes—
351C22×C42C2×D8311yescharacteristic
352#389—1664no—
353#382—838no—
354C4×C4⋊C4—24no—
355C2×#95—832no—
356C2×#95—832no—
357C2×#95—832no—
358C2×#95—832no—
359C2×#95—832no—
360C2×#95—832no—
361C2×#95—831no—
362C2×#95—831no—
363C2×#95—831no—
364C2×#95—831no—
365C2×#95—832no—
366C2×#95—832no—
367C2×#95—832no—
368C2×#95C2×D8312yes—
369C23×C4—832no—
370C23×C4—831no—
371C23×C4—831no—
372C23×C4—831no—
373C23×C4—831no—
374C23×C4—832no—
375C23×C4C22×D8312yes—
376C23×C4C22×D8312yes—
377C23×C4C22×D8311yescharacteristic
378C23×C4C22×D8311yescharacteristic
379C23×C4C22×D8311yescharacteristic
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—3322no—
385C2×C4⋊C4—834no—
386C2×C4⋊C4—1664no—
387C2×C4⋊C4—1664no—
388C2×C4⋊C4—1662no—
389C2×C4⋊C4—1662no—
390C2×C4⋊C4—1662no—
391C2×C4⋊C4—1662no—
392C2×C4⋊C4—1662no—
393C2×C4⋊C4C4×D8314yes—
394C2×C4⋊C4C22⋊D8314yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42—834no—
401C2×C42—1662no—
402C2×C42—1662no—
403C2×C42—1662no—
404C2×C42—1662no—
405C2×C42—1662no—
406C2×C42Dic16614yes—
407#95—24no—
408#95—3322no—
409#95—3322no—
410#95—3322no—
411#95—3322no—
412#95—838no—
413#95—838no—
414#95—1664no—
415#95—1662no—
416#95—1662no—
417#95—1664no—
418#95—1662no—
419#95—1664no—
420#95—1662no—
421C24C23×D8311yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—832no—
445C22×C4—832no—
446C22×C4—834no—
447C22×C4—832no—
448C22×C4—832no—
449C22×C4—1662no—
450C22×C4—1662no—
451C22×C4—1662no—
452C22×C4—1662no—
453C22×C4—1662no—
454C22×C4—1662no—
455C22×C4—1662no—
456C22×C4—1661no—
457C22×C4—1662no—
458C22×C4—1661no—
459C22×C4—1661no—
460C22×C4—1661no—
461C22×C4—1662no—
462C22×C4—1661no—
463C22×C4—1661no—
464C22×C4—1661no—
465C22×C4—1661no—
466C22×C4—1661no—
467C22×C4—1661no—
468C22×C4—1661no—
469C22×C4—1661no—
470C22×C4—1661no—
471C22×C4—1661no—
472C22×C4—1662no—
473C22×C4—1661no—
474C22×C4—1662no—
475C22×C4—1661no—
476C22×C4—1661no—
477C22×C4—1661no—
478C22×C4—1661no—
479C22×C4—1662no—
480C22×C4—1661no—
481C22×C4—1661no—
482C22×C4—1661no—
483C22×C4—1662no—
484C22×C4—1661no—
485C22×C4—1661no—
486C22×C4C2×C4×D8314yes—
487C22×C4C2×C4×D8312yes—
488C22×C4C2×C22⋊D8314yes—
489C22×C4C2×C22⋊D8312yes—
490C22×C4C2×Dic16612yes—
491C22×C4C2×Dic16612yes—
492C22×C4C2×Dic16612yes—
493C22×C4#1305058912yes—
494C22×C4#1305059012yes—
495C22×C4#1305059012yes—
496C22×C4#1305059012yes—
497C22×C4#1305059012yes—
498C22×C4#1305059112yes—
499C4⋊C4—28no—
500C4⋊C4—28no—
501C4⋊C4—3328no—
502C4⋊C4—3324no—
503C4⋊C4—1668no—
504C42—28no—
505C42—48no—
506C42—3324no—
507C42—1668no—
508C23C22×C4×D8311yescharacteristic
509C23C22×C22⋊D8311yescharacteristic
510C23C22×Dic16611yescharacteristic
511C23#41×D8311yescharacteristic
512C23#41×D8311yescharacteristic
513C23C2×#1305058911yescharacteristic
514C23C2×#1305059011yescharacteristic
515C23C2×#1305059011yescharacteristic
516C23C2×#1305059011yescharacteristic
517C23C2×#1305059011yescharacteristic
518C23C2×#1305059111yescharacteristic
519C23#1458183711yescharacteristic
520C23#1458183811yescharacteristic
521C23#1458183911yescharacteristic
522C23#1458184011yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—3322no—
551C2×C4—3321no—
552C2×C4—3321no—
553C2×C4—3322no—
554C2×C4—3321no—
555C2×C4—3321no—
556C2×C4—3321no—
557C2×C4—3321no—
558C2×C4—3321no—
559C2×C4—3321no—
560C2×C4—3321no—
561C2×C4—3321no—
562C2×C4—3322no—
563C2×C4—3321no—
564C2×C4—3321no—
565C2×C4—3322no—
566C2×C4—3321no—
567C2×C4—3321no—
568C2×C4—3321no—
569C2×C4—3321no—
570C2×C4—3322no—
571C2×C4—3322no—
572C2×C4—3322no—
573C2×C4—3322no—
574C2×C4—3322no—
575C2×C4—3322no—
576C2×C4—3322no—
577C2×C4—1662no—
578C2×C4—1662no—
579C2×C4—1662no—
580C2×C4—1662no—
581C2×C4—1662no—
582C2×C4—1662no—
583C2×C4—1664no—
584C2×C4—1662no—
585C2×C4—1662no—
586C2×C4—1664no—
587C2×C4—1662no—
588C2×C4—1662no—
589C2×C4—1664no—
590C2×C4—1662no—
591C2×C4—1662no—
592C2×C4#1458174914yes—
593C2×C4C4×C22⋊D8314yes—
594C2×C4C4×Dic16614yes—
595C2×C4#1458177114yes—
596C2×C4#1458177514yes—
597C2×C4#1458178314yes—
598C2×C4#1458178414yes—
599C2×C4#1458178614yes—
600C22C2×#1458174911yescharacteristic
601C22C2×C4×C22⋊D8311yescharacteristic
602C22C2×C4×Dic16611yescharacteristic
603C22C4×#1305058911yescharacteristic
604C22C4×#1305059111yescharacteristic
605C22#1912818011yescharacteristic
606C22#1912818311yescharacteristic
607C22C2×#1458177111yescharacteristic
608C22C2×#1458177511yescharacteristic
609C22C2×#1458178311yescharacteristic
610C22C2×#1458178411yescharacteristic
611C22C2×#1458178611yescharacteristic
612C22#1912823311yescharacteristic
613C22#1912823811yescharacteristic
614C22#1912825411yescharacteristic
615C22#1912830211yescharacteristic
616C22#1912830911yescharacteristic
617C22#1912832911yescharacteristic
618C22#1912833211yescharacteristic
619C22#1912833911yescharacteristic
620C22#1912834511yescharacteristic
621C22#1912835811yescharacteristic
622C22#1912836211yescharacteristic
623C22#1912838611yescharacteristic
624C22#1912839211yescharacteristic
625C22#1912839911yescharacteristic
626C22#1912840111yescharacteristic
627C22#1912841411yescharacteristic
628C22#1912841611yescharacteristic
629C22#1912841911yescharacteristic
630C22#1912842111yescharacteristic
631C22#1912842311yescharacteristic
632C22#1912842411yescharacteristic
633C22#1912843411yescharacteristic
634C22#1912843611yescharacteristic
635C4—24no—
636C4—42no—
637C4—44no—
638C4—44no—
639C4—3322no—
640C4—3322no—
641C4—3322no—
642C4—3322no—
643C4—3324no—
644C4—6642no—
645C4#1912758518yes—
646C2C2×#1912758511yescharacteristic
647C2C4×#1458178311yescharacteristic
648C2#2491020011yescharacteristic
649C2#2491034411yescharacteristic
650C2#2491035211yescharacteristic
651C2#2491053011yescharacteristic
652C2#2491053611yescharacteristic
653C2#2491094911yescharacteristic
654C2#2491096011yescharacteristic
655C2#2491114811yescharacteristic
656C2#2491118111yescharacteristic
657C2#2491205411yescharacteristic
658C2#2491206511yescharacteristic
659C2#2491269111yescharacteristic
660C2#2491270211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×C4×C4⋊C4×C83C2
socle, prime radical, cosocleC24×C83C24
hypercenterC2×C4×C4⋊C4D83
hypocenterC83#14030
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
18. #19127566C4semidirect
342. C83#14030semidirect

Maximal subgroups

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

subgroupindex
C2×#191275972
C2×#191275662
#249057242
#249057212
#249056962
#249056932
#249056922
#249056902
C4×C83⋊#952
C2×C4×C4⋊C4×C832
#1403083