Finite Group Databasebeta

← #35310835

Subgroups — #35310835

Order 21248.

966 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127719C211yesmaximal, characteristic
2C2×#19127700C211yesmaximal, characteristic
3C2×#19127674C211yesmaximal, characteristic
4C2×#19127471C211yesmaximal, characteristic, complemented
5#24907182C211yesmaximal, characteristic, complemented
6C2×#19127457C211yesmaximal, characteristic, complemented
7C83×#2274C211yesmaximal, characteristic, complemented
8C22×#13050590C2211yescharacteristic
9C22×#13050574C2211yescharacteristic
10C22×#13050574C2211yescharacteristic
11C2×#14581751C2211yescharacteristic
12#19127719—22no—
13#19127719C414yescomplemented
14C2×#14581720—22no—
15#19127700—22no—
16#19127700—22no—
17C2×#14581715C412yescomplemented
18C2×#14581712C412yescomplemented
19#19127674—22no—
20#19127674C414yescomplemented
21C2×#14581706—22no—
22#19127471—22no—
23#19127463—22no—
24#19127457—22no—
25C2×#117×C83C2211yescharacteristic
26C2×#117×C83C2211yescharacteristic
27C22×C4⋊C4×C83C2211yescharacteristic
28C4×C4⋊C4×C83—22no—
29C4×C4⋊C4×C83—22no—
30C4×C22⋊C4×C83—22no—
31C2×#13050590—21no—
32C2×#13050590—21no—
33C2×#13050590—21no—
34C2×#13050590—21no—
35C2×#13050590—21no—
36C2×#13050590—21no—
37C2×#13050590—21no—
38C2×#13050590—21no—
39C2×#13050590—21no—
40C2×#13050590—21no—
41C2×#13050590C2×C412yes—
42C2×#13050590C2×C412yes—
43C22×Dic166C2×C411yescharacteristic
44C22×D332C2×C411yescharacteristic
45C22×C22⋊D83—21no—
46C22×C4×D83—21no—
47C2×#13050574—21no—
48C2×#13050574—21no—
49C2×#13050574—21no—
50C2×#13050574—21no—
51C2×#13050574—21no—
52C2×#13050574—21no—
53C2×#13050574—21no—
54C2×#13050574—21no—
55C2×#13050574—21no—
56C2×#13050574—21no—
57C2×#13050574—21no—
58C2×#13050574C2×C412yes—
59C22×C83⋊C8—21no—
60C22×C83⋊C8C2×C412yes—
61#14581751—21no—
62#14581751—21no—
63#14581751—21no—
64#14581751C2×C412yes—
65C2×C4⋊Dic83—21no—
66C2×C22⋊Dic83—21no—
67C2×C4×Dic83—21no—
68#14581720—28no—
69#14581715—24no—
70#14581712—24no—
71#14581706—28no—
72C23×C4×C83—21no—
73C23×C4×C83C2311yescharacteristic
74#117×C83—21no—
75#117×C83—21no—
76#117×C83—21no—
77#117×C83—21no—
78#117×C83C2×C412yes—
79#117×C83C2×C412yes—
80#117×C83D412yes—
81#117×C83D412yes—
82C2×C4⋊C4×C83—21no—
83C2×C4⋊C4×C83—21no—
84C2×C4⋊C4×C83—21no—
85C2×C4⋊C4×C83—21no—
86C2×C4⋊C4×C83—21no—
87C2×C4⋊C4×C83C2×C412yes—
88C2×C4⋊C4×C83D412yes—
89C2×C4⋊C4×C83D412yes—
90C2×C22⋊C4×C83—21no—
91C2×C22⋊C4×C83D412yes—
92C2×C42×C83—21no—
93C2×C42×C83—24no—
94C2×C42×C83D412yes—
95#95×C83—24no—
96C23×D83—21no—
97#13050590—22no—
98#13050590—22no—
99#13050590—22no—
100#13050590—22no—
101#13050590—22no—
102#13050590—22no—
103#13050590—22no—
104#13050590—22no—
105#13050590—41no—
106#13050590—41no—
107#13050590—41no—
108#13050590—41no—
109#13050590—41no—
110#13050590—41no—
111#13050590—41no—
112#13050590—41no—
113C2×Dic166—21no—
114C2×Dic166—21no—
115C2×Dic166—21no—
116C2×Dic166—21no—
117C2×Dic166—21no—
118C2×Dic166C4212yescomplemented
119C2×D332—21no—
120C2×D332—21no—
121C2×D332—21no—
122C2×D332—21no—
123C2×D332—21no—
124C2×D332C4212yescomplemented
125C2×C22⋊D83—22no—
126C2×C22⋊D83—22no—
127C2×C22⋊D83—41no—
128C2×C22⋊D83—41no—
129C2×C22⋊D83—41no—
130C2×C22⋊D83—41no—
131C22×Dic83—21no—
132C22×Dic83—41no—
133C2×C4×D83—22no—
134C2×C4×D83—22no—
135C2×C4×D83—41no—
136C2×C4×D83—41no—
137C2×C4×D83—41no—
138C2×C4×D83—41no—
139#13050574—22no—
140#13050574—22no—
141#13050574—41no—
142#13050574—41no—
143#13050574—41no—
144#13050574—41no—
145#13050574—41no—
146#13050574—41no—
147C2×C83⋊C8—22no—
148C2×C83⋊C8—22no—
149C2×C83⋊C8—22no—
150C2×C83⋊C8—22no—
151C2×C83⋊C8—41no—
152C2×C83⋊C8—41no—
153C4⋊Dic83—22no—
154C4⋊Dic83—41no—
155C22⋊Dic83—22no—
156C22⋊Dic83—41no—
157C4×Dic83—22no—
158C4×Dic83—41no—
159C24×C83C2×D411yescharacteristic
160C22×C4×C83—22no—
161C22×C4×C83—22no—
162C22×C4×C83—22no—
163C22×C4×C83—22no—
164C22×C4×C83—22no—
165C22×C4×C83—82no—
166C22×C4×C83C22×C411yescharacteristic
167C22×C4×C83C22×C411yescharacteristic
168C22×C4×C83C22×C411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2×D411yescharacteristic
171C22×C4×C83C2×D411yescharacteristic
172C22×C4×C83C2×D411yescharacteristic
173C22×C4×C83C2×D411yescharacteristic
174C22×C4×C83#4111yescharacteristic
175C22×C4×C83#4111yescharacteristic
176C22×C4×C83#4111yescharacteristic
177C22×C4×C83#4111yescharacteristic
178C22×C4×C83#4111yescharacteristic
179C22×C4×C83#4111yescharacteristic
180C4⋊C4×C83—22no—
181C4⋊C4×C83—22no—
182C4⋊C4×C83—22no—
183C4⋊C4×C83—22no—
184C4⋊C4×C83—22no—
185C4⋊C4×C83—22no—
186C4⋊C4×C83—22no—
187C4⋊C4×C83C22⋊C414yes—
188C22⋊C4×C83—22no—
189C22⋊C4×C83—22no—
190C22⋊C4×C83—22no—
191C22⋊C4×C83C22⋊C414yes—
192C42×C83—22no—
193C42×C83—22no—
194C42×C83—22no—
195C42×C83—84no—
196C42×C83C22⋊C414yes—
197C23×C83—41no—
198C23×C83—41no—
199C23×C83C2×C22⋊C411yescharacteristic
200C23×C83C4×D411yescharacteristic
201C23×C83C4×D411yescharacteristic
202C23×C83#12011yescharacteristic
203C23×C83#12111yescharacteristic
204C23×C83#12111yescharacteristic
205C23×C83#12311yescharacteristic
206C22×D83—22no—
207C22×D83—41no—
208C22×D83—41no—
209C22×D83—81no—
210C22×D83—81no—
211C2×C4×C83—24no—
212C2×C4×C83—24no—
213C2×C4×C83—24no—
214C2×C4×C83—42no—
215C2×C4×C83—42no—
216C2×C4×C83—44no—
217C2×C4×C83—42no—
218C2×C4×C83—42no—
219C2×C4×C83—82no—
220C2×C4×C83—82no—
221C2×C4×C83C2×C4211yescharacteristic
222C2×C4×C83C2×C22⋊C411yescharacteristic
223C2×C4×C83C2×C22⋊C411yescharacteristic
224C2×C4×C83#11711yescharacteristic
225C2×C4×C83#11711yescharacteristic
226C2×C4×C83#11711yescharacteristic
227C2×C4×C83C4×D411yescharacteristic
228C2×C4×C83C4×D411yescharacteristic
229C2×C4×C83C4×D411yescharacteristic
230C2×C4×C83C4×D411yescharacteristic
231C2×C4×C83C4×D411yescharacteristic
232C2×C4×C83C4×D411yescharacteristic
233C2×C4×C83C4×D411yescharacteristic
234C2×C4×C83C4×D411yescharacteristic
235C2×C4×C83C4×D411yescharacteristic
236C2×C4×C83C4×D411yescharacteristic
237C2×C4×C83#12111yescharacteristic
238C2×C4×C83#12111yescharacteristic
239C2×C4×C83#12111yescharacteristic
240C2×C4×C83#12111yescharacteristic
241C2×C4×C83#12311yescharacteristic
242C2×C4×C83#12311yescharacteristic
243C2×C4×C83#12411yescharacteristic
244C2×C4×C83#12411yescharacteristic
245C2×C4×C83#12411yescharacteristic
246C2×C4×C83#12611yescharacteristic
247C2×C4×C83#12611yescharacteristic
248C2×C4×C83#12711yescharacteristic
249C22⋊D83—42no—
250C22⋊D83—42no—
251C22⋊D83—42no—
252C22⋊D83—42no—
253C2×Dic83—22no—
254C2×Dic83—41no—
255C2×Dic83—41no—
256C2×Dic83—42no—
257C2×Dic83—81no—
258C2×Dic83—81no—
259D332—22no—
260D332—22no—
261D332—41no—
262D332—41no—
263C4×D83—42no—
264C4×D83—42no—
265C4×D83—42no—
266C4×D83—42no—
267Dic166—22no—
268Dic166—22no—
269Dic166—41no—
270Dic166—41no—
271C83⋊C8—42no—
272C83⋊C8—42no—
273C22×C83—21no—
274C22×C83—21no—
275C22×C83—21no—
276C22×C83—21no—
277C22×C83—21no—
278C22×C83—21no—
279C22×C83—41no—
280C22×C83—41no—
281C22×C83—41no—
282C22×C83—41no—
283C22×C83C4×C22⋊C411yescharacteristic
284C22×C83#38611yescharacteristic
285C22×C83#38611yescharacteristic
286C22×C83#38611yescharacteristic
287C22×C83#38811yescharacteristic
288C22×C83#38811yescharacteristic
289C22×C83#39011yescharacteristic
290C2×D83—42no—
291C2×D83—82no—
292C2×D83—81no—
293C2×D83—81no—
294C2×D83—82no—
295C4×C83—44no—
296C4×C83—44no—
297C4×C83—44no—
298C4×C83C4×C22⋊C411yescharacteristic
299C4×C83C4×C22⋊C411yescharacteristic
300C4×C83#38811yescharacteristic
301C4×C83#38811yescharacteristic
302C4×C83#38811yescharacteristic
303C4×C83#38811yescharacteristic
304C4×C83#39011yescharacteristic
305C4×C83#39011yescharacteristic
306Dic83—42no—
307Dic83—82no—
308#10954—831nomaximal, Sylow
309C2×C83—21no—
310C2×C83—21no—
311C2×C83—21no—
312C2×C83—21no—
313C2×C83—21no—
314C2×C83—21no—
315C2×C83#143711yescharacteristic
316C2×C83#190411yescharacteristic
317C2×C83#190511yescharacteristic
318D83—82no—
319C2×#421—831no—
320C2×#417—831no—
321C2×#410—831no—
322#2274D8311yescharacteristic, complemented
323C2×#344—831no—
324#1736—831no—
325C2×H(3,ℤ/4)—831no—
326C83#1095411yescharacteristic, complemented, Sylow
327C22×#41—831no—
328C22×M16—831no—
329C22×M16—831no—
330C2×#117—831no—
331C2×#117C2×D8311yescharacteristic
332C2×#117C2×D8311yescharacteristic
333C22×C4⋊C4C2×D8311yescharacteristic
334#421—834no—
335#421—1662no—
336C2×#104—1662no—
337#417—1662no—
338#417—1662no—
339C2×#103—832no—
340C2×#102—832no—
341#410—834no—
342#410—1662no—
343C2×#99—1662no—
344C4×C4⋊C4—22no—
345C4×C4⋊C4—22no—
346C4×C22⋊C4—22no—
347#344—1662no—
348#340—1662no—
349H(3,ℤ/4)—1662no—
350C2×#41—832no—
351C2×#41—832no—
352C2×#41—1661no—
353C2×#41—1661no—
354C2×#41—1661no—
355C2×#41—1661no—
356C2×#41—1661no—
357C2×#41—1661no—
358C2×#41—1661no—
359C2×#41—1661no—
360C2×#41—1661no—
361C2×#41—1661no—
362C22×Q8—831no—
363C22×D4—831no—
364C22×D4—1661no—
365C23×C4—21no—
366C23×C4—1661no—
367C23×C4C22×D8311yescharacteristic
368C2×M16—832no—
369C2×M16—1661no—
370C2×M16—1661no—
371C2×M16—1661no—
372C2×M16—1661no—
373C2×M16—1661no—
374C2×M16—1661no—
375C2×M16—1661no—
376C2×M16—1661no—
377C2×M16—1661no—
378C2×M16—1661no—
379C2×M16—1661no—
380C22×C8—832no—
381C22×C8—1661no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—832no—
387#117—1661no—
388#117—1661no—
389#117—1661no—
390#117C4×D8312yes—
391#117C4×D8312yes—
392#117D33212yes—
393#117D33212yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—1661no—
400C2×C4⋊C4C4×D8312yes—
401C2×C4⋊C4D33212yes—
402C2×C4⋊C4C22⋊D8312yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—1661no—
405C2×C22⋊C4C22⋊D8312yes—
406C2×C42—21no—
407C2×C42—24no—
408C2×C42—1661no—
409C2×C42C22⋊D8312yes—
410#104—1668no—
411#103—1664no—
412#102—1664no—
413#99—1668no—
414#95—24no—
415C24—1661no—
416C24C2×C22⋊D8311yescharacteristic
417#41—3321no—
418#41—3321no—
419#41—3321no—
420#41—3321no—
421#41—3321no—
422#41—3321no—
423#41—3321no—
424#41—3321no—
425#41—1662no—
426#41—1662no—
427#41—1662no—
428#41—1662no—
429#41—1662no—
430#41—1662no—
431#41—1662no—
432#41—1662no—
433C2×Q8—832no—
434C2×Q8—1661no—
435C2×Q8—1661no—
436C2×Q8—1661no—
437C2×Q8—1661no—
438C2×Q8—1661no—
439C2×D4—3321no—
440C2×D4—3321no—
441C2×D4—3321no—
442C2×D4—3321no—
443C2×D4—832no—
444C2×D4—1662no—
445C2×D4—1662no—
446C2×D4—1661no—
447C2×D4—1661no—
448C2×D4—1661no—
449C2×D4—1661no—
450C2×D4—1661no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—82no—
457C22×C4—3321no—
458C22×C4—3321no—
459C22×C4—3321no—
460C22×C4—3321no—
461C22×C4—3321no—
462C22×C4—1661no—
463C22×C4—1662no—
464C22×C4—1662no—
465C22×C4C2×C4×D8311yescharacteristic
466C22×C4C2×C4×D8311yescharacteristic
467C22×C4C2×C4×D8311yescharacteristic
468C22×C4C2×C22⋊D8311yescharacteristic
469C22×C4C2×C22⋊D8311yescharacteristic
470C22×C4C2×D33211yescharacteristic
471C22×C4C2×D33211yescharacteristic
472C22×C4C2×D33211yescharacteristic
473C22×C4#1305059011yescharacteristic
474C22×C4#1305059011yescharacteristic
475C22×C4#1305059011yescharacteristic
476C22×C4#1305059011yescharacteristic
477C22×C4#1305059011yescharacteristic
478C22×C4#1305059011yescharacteristic
479M16—3321no—
480M16—3321no—
481M16—3321no—
482M16—3321no—
483M16—3321no—
484M16—3321no—
485M16—1662no—
486M16—1662no—
487C2×C8—3321no—
488C2×C8—3321no—
489C2×C8—1662no—
490C2×C8—1662no—
491C2×C8—1662no—
492C2×C8—1662no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—3321no—
501C4⋊C4—1662no—
502C4⋊C4(C2×D83)⋊C414yes—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—3321no—
507C22⋊C4—1662no—
508C22⋊C4(C2×D83)⋊C414yes—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—84no—
513C42—3321no—
514C42—1662no—
515C42(C2×D83)⋊C414yes—
516C23—41no—
517C23—41no—
518C23—3321no—
519C23—3321no—
520C23—6641no—
521C23—6641no—
522C23—1662no—
523C23C2×(C2×D83)⋊C411yescharacteristic
524C23C4×C22⋊D8311yescharacteristic
525C23C4×C22⋊D8311yescharacteristic
526C23#1458176111yescharacteristic
527C23#1458176611yescharacteristic
528C23#1458176611yescharacteristic
529C23#1458177511yescharacteristic
530Q8—3321no—
531Q8—3321no—
532Q8—1662no—
533Q8—1662no—
534D4—3322no—
535D4—3322no—
536D4—3322no—
537D4—3322no—
538D4—3321no—
539D4—3321no—
540D4—1662no—
541D4—1662no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—3321no—
553C2×C4—3321no—
554C2×C4—3322no—
555C2×C4—3322no—
556C2×C4—3322no—
557C2×C4—3322no—
558C2×C4—3322no—
559C2×C4—6641no—
560C2×C4—6641no—
561C2×C4—1662no—
562C2×C4C42×D8311yescharacteristic
563C2×C4C2×(C2×D83)⋊C411yescharacteristic
564C2×C4C2×(C2×D83)⋊C411yescharacteristic
565C2×C4#1458174911yescharacteristic
566C2×C4#1458174911yescharacteristic
567C2×C4#1458174911yescharacteristic
568C2×C4C4×C22⋊D8311yescharacteristic
569C2×C4C4×C22⋊D8311yescharacteristic
570C2×C4C4×C22⋊D8311yescharacteristic
571C2×C4C4×C22⋊D8311yescharacteristic
572C2×C4C4×D33211yescharacteristic
573C2×C4C4×D33211yescharacteristic
574C2×C4C4×D33211yescharacteristic
575C2×C4C4×D33211yescharacteristic
576C2×C4C4×D33211yescharacteristic
577C2×C4C4×D33211yescharacteristic
578C2×C4#1458176611yescharacteristic
579C2×C4#1458176611yescharacteristic
580C2×C4#1458176611yescharacteristic
581C2×C4#1458176611yescharacteristic
582C2×C4#1458177511yescharacteristic
583C2×C4#1458177511yescharacteristic
584C2×C4#1458178011yescharacteristic
585C2×C4#1458178011yescharacteristic
586C2×C4#1458178011yescharacteristic
587C2×C4#1458178611yescharacteristic
588C2×C4#1458178611yescharacteristic
589C2×C4#1458178911yescharacteristic
590C8—3322no—
591C8—3322no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—3322no—
603C22—6642no—
604C22—6642no—
605C22—6641no—
606C22—6641no—
607C22C4×(C2×D83)⋊C411yescharacteristic
608C22#1912758011yescharacteristic
609C22#1912758011yescharacteristic
610C22#1912758011yescharacteristic
611C22#1912759211yescharacteristic
612C22#1912759211yescharacteristic
613C22#1912760311yescharacteristic
614C4—44no—
615C4—44no—
616C4—44no—
617C4—3322no—
618C4—6642no—
619C4C4×(C2×D83)⋊C411yescharacteristic
620C4C4×(C2×D83)⋊C411yescharacteristic
621C4#1912759211yescharacteristic
622C4#1912759211yescharacteristic
623C4#1912759211yescharacteristic
624C4#1912759211yescharacteristic
625C4#1912760311yescharacteristic
626C4#1912760311yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—6642no—
634C2#2490570111yescharacteristic
635C2#2490795011yescharacteristic
636C2#2490795711yescharacteristic
subgroupG/H
centerC22#19127580
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC83×#2274C2
socleC22×C83#386
prime radicalC22×#13050590C22
cosocleC23×C4×C83C23
hypercenter#2274D83
hypocenterC83#10954
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2274

Complements

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

NH ≅ G/Ntype
4. C2×#19127471C2semidirect
5. #24907182C2semidirect
6. C2×#19127457C2semidirect
7. C83×#2274C2semidirect
13. #19127719C4semidirect
17. C2×#14581715C4semidirect
18. C2×#14581712C4semidirect
20. #19127674C4semidirect
118. C2×Dic166C42semidirect
124. C2×D332C42semidirect
322. #2274D83semidirect
326. C83#10954semidirect

Maximal subgroups

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

subgroupindex
C2×#191277192
C2×#191277002
C2×#191276742
C2×#191274712
#249071822
C2×#191274572
C83×#22742
#1095483