Finite Group Databasebeta

← #35310778

Subgroups — #35310778

Order 21248.

994 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
1C22×#14581720C211yesmaximal, characteristic
2#24915980C211yesmaximal, characteristic
3C2×#19127674C211yesmaximal, characteristic
4C2×#19127471C211yesmaximal, characteristic, complemented
5#24907172C211yesmaximal, characteristic, complemented
6C2×#19127461C211yesmaximal, characteristic, complemented
7C4×#117×C83C211yesmaximal, characteristic, complemented
8C22×#13050590C2211yescharacteristic
9C22×#13050574C2211yescharacteristic
10C22×#13050574C2211yescharacteristic
11C2×#14581751C2211yescharacteristic
12C2×#14581720—22no—
13C2×#14581720—21no—
14C2×#14581720—21no—
15C2×#14581720C414yescomplemented
16#19127709C412yescomplemented
17#19127705C412yescomplemented
18#19127700—22no—
19#19127695—22no—
20#19127674—22no—
21#19127674C414yescomplemented
22C2×#14581706—22no—
23#19127471—22no—
24#19127461—22no—
25#19127460—22no—
26C2×#117×C83C2211yescharacteristic
27C2×#117×C83C2211yescharacteristic
28C22×C42×C83C2211yescharacteristic
29C4×C4⋊C4×C83—22no—
30C4×C22⋊C4×C83—22no—
31#376×C83—21no—
32C43×C83—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×#13050590—21no—
42C2×#13050590—21no—
43C2×#13050590C2×C412yes—
44C2×#13050590C2×C412yes—
45C22×Dic166C2×C411yescharacteristic
46C22×D332C2×C411yescharacteristic
47C22×C22⋊D83—21no—
48C22×C4×D83—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×#13050574—21no—
59C2×#13050574C2×C412yes—
60C2×#13050574C2×C412yes—
61C22×C83⋊C8—21no—
62C22×C83⋊C8—21no—
63#14581751—21no—
64#14581751—21no—
65#14581751—21no—
66#14581751C2×C412yes—
67C2×C4⋊Dic83—21no—
68C2×C22⋊Dic83—21no—
69C2×C4×Dic83—21no—
70#14581720—24no—
71#14581720—24no—
72#14581715—24no—
73#14581712—24no—
74#14581706—28no—
75C23×C4×C83—21no—
76C23×C4×C83C2311yescharacteristic
77#117×C83—21no—
78#117×C83—21no—
79#117×C83—21no—
80#117×C83—21no—
81#117×C83C2×C412yes—
82#117×C83C2×C412yes—
83#117×C83D412yes—
84#117×C83D412yes—
85C2×C4⋊C4×C83—21no—
86C2×C4⋊C4×C83D412yes—
87C2×C22⋊C4×C83—21no—
88C2×C22⋊C4×C83D412yes—
89C2×C42×C83—21no—
90C2×C42×C83—21no—
91C2×C42×C83—21no—
92C2×C42×C83—21no—
93C2×C42×C83—21no—
94C2×C42×C83—24no—
95C2×C42×C83C2×C412yes—
96C2×C42×C83D412yes—
97C2×C42×C83D411yescharacteristic
98C2×C42×C83D411yescharacteristic
99#95×C83—24no—
100C23×D83—21no—
101#13050590—22no—
102#13050590—22no—
103#13050590—22no—
104#13050590—22no—
105#13050590—22no—
106#13050590—22no—
107#13050590—22no—
108#13050590—22no—
109#13050590—41no—
110#13050590—41no—
111#13050590—41no—
112#13050590—41no—
113#13050590—41no—
114#13050590—41no—
115#13050590—41no—
116#13050590—41no—
117C2×Dic166—21no—
118C2×Dic166—21no—
119C2×Dic166—21no—
120C2×Dic166—21no—
121C2×Dic166—21no—
122C2×Dic166C4212yescomplemented
123C2×D332—21no—
124C2×D332—21no—
125C2×D332—21no—
126C2×D332—21no—
127C2×D332—21no—
128C2×D332C4212yescomplemented
129C2×C22⋊D83—22no—
130C2×C22⋊D83—22no—
131C2×C22⋊D83—41no—
132C2×C22⋊D83—41no—
133C2×C22⋊D83—41no—
134C2×C22⋊D83—41no—
135C22×Dic83—21no—
136C22×Dic83—41no—
137C2×C4×D83—22no—
138C2×C4×D83—22no—
139C2×C4×D83—41no—
140C2×C4×D83—41no—
141C2×C4×D83—41no—
142C2×C4×D83—41no—
143#13050574—22no—
144#13050574—22no—
145#13050574—22no—
146#13050574—22no—
147#13050574—41no—
148#13050574—41no—
149#13050574—41no—
150#13050574—41no—
151C2×C83⋊C8—22no—
152C2×C83⋊C8—22no—
153C2×C83⋊C8—41no—
154C2×C83⋊C8—41no—
155C2×C83⋊C8—41no—
156C2×C83⋊C8—41no—
157C4⋊Dic83—22no—
158C4⋊Dic83—41no—
159C22⋊Dic83—22no—
160C22⋊Dic83—41no—
161C4×Dic83—22no—
162C4×Dic83—41no—
163C24×C83C2×D411yescharacteristic
164C22×C4×C83—21no—
165C22×C4×C83—22no—
166C22×C4×C83—21no—
167C22×C4×C83—22no—
168C22×C4×C83—22no—
169C22×C4×C83—22no—
170C22×C4×C83—44no—
171C22×C4×C83C22×C411yescharacteristic
172C22×C4×C83C22×C411yescharacteristic
173C22×C4×C83C22×C411yescharacteristic
174C22×C4×C83C2×D411yescharacteristic
175C22×C4×C83C2×D411yescharacteristic
176C22×C4×C83C2×D411yescharacteristic
177C22×C4×C83C2×D411yescharacteristic
178C22×C4×C83C2×D411yescharacteristic
179C22×C4×C83#4111yescharacteristic
180C22×C4×C83#4111yescharacteristic
181C22×C4×C83#4111yescharacteristic
182C22×C4×C83#4111yescharacteristic
183C22×C4×C83#4111yescharacteristic
184C22×C4×C83#4111yescharacteristic
185C4⋊C4×C83—22no—
186C4⋊C4×C83—22no—
187C4⋊C4×C83—22no—
188C4⋊C4×C83C22⋊C414yes—
189C22⋊C4×C83—22no—
190C22⋊C4×C83—22no—
191C22⋊C4×C83—22no—
192C22⋊C4×C83C22⋊C414yes—
193C42×C83—22no—
194C42×C83—22no—
195C42×C83—22no—
196C42×C83—22no—
197C42×C83—22no—
198C42×C83—22no—
199C42×C83—21no—
200C42×C83—21no—
201C42×C83—48no—
202C42×C83C22⋊C412yes—
203C42×C83C22⋊C412yes—
204C23×C83—42no—
205C23×C83C2×C22⋊C411yescharacteristic
206C23×C83C4×D411yescharacteristic
207C23×C83C4×D411yescharacteristic
208C23×C83#12011yescharacteristic
209C23×C83#12111yescharacteristic
210C23×C83#12111yescharacteristic
211C23×C83#12311yescharacteristic
212C22×D83—22no—
213C22×D83—41no—
214C22×D83—41no—
215C22×D83—82no—
216C2×C4×C83—24no—
217C2×C4×C83—22no—
218C2×C4×C83—22no—
219C2×C4×C83—24no—
220C2×C4×C83—24no—
221C2×C4×C83—44no—
222C2×C4×C83—44no—
223C2×C4×C83—44no—
224C2×C4×C83—44no—
225C2×C4×C83—42no—
226C2×C4×C83C2×C4211yescharacteristic
227C2×C4×C83C2×C22⋊C411yescharacteristic
228C2×C4×C83C2×C22⋊C411yescharacteristic
229C2×C4×C83#11711yescharacteristic
230C2×C4×C83#11711yescharacteristic
231C2×C4×C83#11711yescharacteristic
232C2×C4×C83C4×D411yescharacteristic
233C2×C4×C83C4×D411yescharacteristic
234C2×C4×C83C4×D411yescharacteristic
235C2×C4×C83C4×D411yescharacteristic
236C2×C4×C83C4×D411yescharacteristic
237C2×C4×C83C4×D411yescharacteristic
238C2×C4×C83C4×D411yescharacteristic
239C2×C4×C83C4×D411yescharacteristic
240C2×C4×C83C4×D411yescharacteristic
241C2×C4×C83C4×D411yescharacteristic
242C2×C4×C83#12111yescharacteristic
243C2×C4×C83#12111yescharacteristic
244C2×C4×C83#12111yescharacteristic
245C2×C4×C83#12111yescharacteristic
246C2×C4×C83#12311yescharacteristic
247C2×C4×C83#12311yescharacteristic
248C2×C4×C83#12411yescharacteristic
249C2×C4×C83#12411yescharacteristic
250C2×C4×C83#12411yescharacteristic
251C2×C4×C83#12611yescharacteristic
252C2×C4×C83#12611yescharacteristic
253C2×C4×C83#12711yescharacteristic
254C22⋊D83—42no—
255C22⋊D83—42no—
256C22⋊D83—42no—
257C22⋊D83—42no—
258C2×Dic83—22no—
259C2×Dic83—41no—
260C2×Dic83—41no—
261C2×Dic83—42no—
262C2×Dic83—82no—
263D332—22no—
264D332—22no—
265D332—41no—
266D332—41no—
267C4×D83—42no—
268C4×D83—42no—
269C4×D83—42no—
270C4×D83—42no—
271Dic166—22no—
272Dic166—22no—
273Dic166—41no—
274Dic166—41no—
275C83⋊C8—42no—
276C83⋊C8—42no—
277C22×C83—22no—
278C22×C83—22no—
279C22×C83—22no—
280C22×C83—41no—
281C22×C83—41no—
282C22×C83—41no—
283C22×C83—41no—
284C22×C83C4×C22⋊C411yescharacteristic
285C22×C83#38611yescharacteristic
286C22×C83#38611yescharacteristic
287C22×C83#38611yescharacteristic
288C22×C83#38811yescharacteristic
289C22×C83#38811yescharacteristic
290C22×C83#39011yescharacteristic
291C2×D83—42no—
292C2×D83—82no—
293C2×D83—82no—
294C2×D83—82no—
295C4×C83—24no—
296C4×C83—44no—
297C4×C83—42no—
298C4×C83—44no—
299C4×C83C4×C22⋊C411yescharacteristic
300C4×C83C4×C22⋊C411yescharacteristic
301C4×C83#38811yescharacteristic
302C4×C83#38811yescharacteristic
303C4×C83#38811yescharacteristic
304C4×C83#38811yescharacteristic
305C4×C83#39011yescharacteristic
306C4×C83#39011yescharacteristic
307Dic83—42no—
308Dic83—82no—
309#10945—831nomaximal, Sylow
310C2×C83—21no—
311C2×C83—21no—
312C2×C83—21no—
313C2×C83—21no—
314C2×C83—21no—
315C2×C83—21no—
316C2×C83#143711yescharacteristic
317C2×C83#190612yes—
318D83—82no—
319C22×#104—831no—
320#2896—831no—
321C2×#410—831no—
322C4×#117D8311yescharacteristic, complemented
323C2×#344—831no—
324#1733—831no—
325C2×#339—831no—
326C83#1094511yescharacteristic, complemented, Sylow
327C22×#41—831no—
328C22×M16—831no—
329C22×M16—831no—
330C2×#117—831no—
331C2×#117C2×D8311yescharacteristic
332C2×#117C2×D8311yescharacteristic
333C22×C42C2×D8311yescharacteristic
334C2×#104—834no—
335C2×#104—1662no—
336C2×#104—1661no—
337C2×#104—1661no—
338#419—832no—
339#418—832no—
340#417—1662no—
341#416—1662no—
342#410—834no—
343#410—1662no—
344C2×#99—1662no—
345C4×C4⋊C4—22no—
346C4×C22⋊C4—22no—
347#376—21no—
348C43—21no—
349#344—1662no—
350#339—1662no—
351#339—1662no—
352C2×#41—832no—
353C2×#41—832no—
354C2×#41—1661no—
355C2×#41—1661no—
356C2×#41—1661no—
357C2×#41—1661no—
358C2×#41—1661no—
359C2×#41—1661no—
360C2×#41—1661no—
361C2×#41—1661no—
362C2×#41—1661no—
363C2×#41—1661no—
364C22×Q8—831no—
365C22×D4—831no—
366C22×D4—1661no—
367C23×C4—21no—
368C23×C4—1661no—
369C23×C4C22×D8311yescharacteristic
370C2×M16—832no—
371C2×M16—832no—
372C2×M16—1661no—
373C2×M16—1661no—
374C2×M16—1661no—
375C2×M16—1661no—
376C2×M16—1661no—
377C2×M16—1661no—
378C2×M16—1661no—
379C2×M16—1661no—
380C2×M16—1661no—
381C2×M16—1661no—
382C22×C8—1661no—
383C22×C8—1661no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—832no—
389#117—1661no—
390#117—1661no—
391#117—1661no—
392#117C4×D8312yes—
393#117C4×D8312yes—
394#117D33212yes—
395#117D33212yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—1661no—
398C2×C4⋊C4C22⋊D8312yes—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—1661no—
401C2×C22⋊C4C22⋊D8312yes—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—24no—
408C2×C42—1661no—
409C2×C42C4×D8312yes—
410C2×C42D33212yes—
411C2×C42C22⋊D8311yescharacteristic
412C2×C42C22⋊D8311yescharacteristic
413#104—1664no—
414#104—1664no—
415#103—1664no—
416#102—1664no—
417#99—1668no—
418#95—24no—
419C24—1661no—
420C24C2×C22⋊D8311yescharacteristic
421#41—3321no—
422#41—3321no—
423#41—3321no—
424#41—3321no—
425#41—3321no—
426#41—3321no—
427#41—3321no—
428#41—3321no—
429#41—1662no—
430#41—1662no—
431#41—1662no—
432#41—1662no—
433#41—1662no—
434#41—1662no—
435#41—1662no—
436#41—1662no—
437C2×Q8—832no—
438C2×Q8—1661no—
439C2×Q8—1661no—
440C2×Q8—1661no—
441C2×Q8—1661no—
442C2×Q8—1661no—
443C2×D4—3321no—
444C2×D4—3321no—
445C2×D4—3321no—
446C2×D4—3321no—
447C2×D4—832no—
448C2×D4—1662no—
449C2×D4—1662no—
450C2×D4—1661no—
451C2×D4—1661no—
452C2×D4—1661no—
453C2×D4—1661no—
454C2×D4—1661no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—44no—
462C22×C4—3321no—
463C22×C4—3321no—
464C22×C4—3321no—
465C22×C4—3321no—
466C22×C4—3321no—
467C22×C4—1661no—
468C22×C4—1662no—
469C22×C4—1662no—
470C22×C4C2×C4×D8311yescharacteristic
471C22×C4C2×C4×D8311yescharacteristic
472C22×C4C2×C4×D8311yescharacteristic
473C22×C4C2×C22⋊D8311yescharacteristic
474C22×C4C2×C22⋊D8311yescharacteristic
475C22×C4C2×D33211yescharacteristic
476C22×C4C2×D33211yescharacteristic
477C22×C4C2×D33211yescharacteristic
478C22×C4#1305059011yescharacteristic
479C22×C4#1305059011yescharacteristic
480C22×C4#1305059011yescharacteristic
481C22×C4#1305059011yescharacteristic
482C22×C4#1305059011yescharacteristic
483C22×C4#1305059011yescharacteristic
484M16—3321no—
485M16—3321no—
486M16—3321no—
487M16—3321no—
488M16—1662no—
489M16—1662no—
490M16—1662no—
491M16—1662no—
492C2×C8—3321no—
493C2×C8—3321no—
494C2×C8—3321no—
495C2×C8—3321no—
496C2×C8—1662no—
497C2×C8—1662no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—3321no—
502C4⋊C4—1662no—
503C4⋊C4(C2×D83)⋊C414yes—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—3321no—
508C22⋊C4—1662no—
509C22⋊C4(C2×D83)⋊C414yes—
510C42—22no—
511C42—22no—
512C42—22no—
513C42—21no—
514C42—21no—
515C42—22no—
516C42—22no—
517C42—22no—
518C42—48no—
519C42—3321no—
520C42—1662no—
521C42(C2×D83)⋊C412yes—
522C42(C2×D83)⋊C412yes—
523C23—42no—
524C23—3321no—
525C23—3321no—
526C23—6642no—
527C23—1662no—
528C23C2×(C2×D83)⋊C411yescharacteristic
529C23C4×C22⋊D8311yescharacteristic
530C23C4×C22⋊D8311yescharacteristic
531C23#1458176111yescharacteristic
532C23#1458176611yescharacteristic
533C23#1458176611yescharacteristic
534C23#1458177511yescharacteristic
535Q8—3321no—
536Q8—3321no—
537Q8—1662no—
538Q8—1662no—
539D4—3322no—
540D4—3322no—
541D4—3322no—
542D4—3322no—
543D4—3321no—
544D4—3321no—
545D4—1662no—
546D4—1662no—
547C2×C4—24no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—44no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—44no—
556C2×C4—42no—
557C2×C4—3321no—
558C2×C4—3321no—
559C2×C4—3322no—
560C2×C4—3322no—
561C2×C4—3322no—
562C2×C4—3322no—
563C2×C4—3322no—
564C2×C4—6642no—
565C2×C4—1662no—
566C2×C4C42×D8311yescharacteristic
567C2×C4C2×(C2×D83)⋊C411yescharacteristic
568C2×C4C2×(C2×D83)⋊C411yescharacteristic
569C2×C4#1458174911yescharacteristic
570C2×C4#1458174911yescharacteristic
571C2×C4#1458174911yescharacteristic
572C2×C4C4×C22⋊D8311yescharacteristic
573C2×C4C4×C22⋊D8311yescharacteristic
574C2×C4C4×C22⋊D8311yescharacteristic
575C2×C4C4×C22⋊D8311yescharacteristic
576C2×C4C4×D33211yescharacteristic
577C2×C4C4×D33211yescharacteristic
578C2×C4C4×D33211yescharacteristic
579C2×C4C4×D33211yescharacteristic
580C2×C4C4×D33211yescharacteristic
581C2×C4C4×D33211yescharacteristic
582C2×C4#1458176611yescharacteristic
583C2×C4#1458176611yescharacteristic
584C2×C4#1458176611yescharacteristic
585C2×C4#1458176611yescharacteristic
586C2×C4#1458177511yescharacteristic
587C2×C4#1458177511yescharacteristic
588C2×C4#1458178011yescharacteristic
589C2×C4#1458178011yescharacteristic
590C2×C4#1458178011yescharacteristic
591C2×C4#1458178611yescharacteristic
592C2×C4#1458178611yescharacteristic
593C2×C4#1458178911yescharacteristic
594C8—3322no—
595C8—3322no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—3322no—
604C22—6642no—
605C22—6642no—
606C22—6642no—
607C22C4×(C2×D83)⋊C411yescharacteristic
608C22#1912758011yescharacteristic
609C22#1912758011yescharacteristic
610C22#1912758011yescharacteristic
611C22#1912759211yescharacteristic
612C22#1912759211yescharacteristic
613C22#1912760311yescharacteristic
614C4—24no—
615C4—42no—
616C4—44no—
617C4—44no—
618C4—3322no—
619C4—6642no—
620C4C4×(C2×D83)⋊C411yescharacteristic
621C4C4×(C2×D83)⋊C411yescharacteristic
622C4#1912759211yescharacteristic
623C4#1912759211yescharacteristic
624C4#1912759211yescharacteristic
625C4#1912759211yescharacteristic
626C4#1912760311yescharacteristic
627C4#1912760311yescharacteristic
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—21no—
634C2—6642no—
635C2#2490570111yescharacteristic
636C2#2490796412yes—
subgroupG/H
centerC2×C4#14581766
commutatorC2×C4×C83C2×C42
FrattiniC23×C4C22×D83
FittingC4×#117×C83C2
socleC22×C83#386
prime radicalC22×#13050590C22
cosocleC23×C4×C83C23
hypercenterC4×#117D83
hypocenterC83#10945
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
4. C2×#19127471C2semidirect
5. #24907172C2semidirect
6. C2×#19127461C2semidirect
7. C4×#117×C83C2semidirect
15. C2×#14581720C4semidirect
16. #19127709C4semidirect
17. #19127705C4semidirect
21. #19127674C4semidirect
122. C2×Dic166C42semidirect
128. C2×D332C42semidirect
322. C4×#117D83semidirect
326. C83#10945semidirect

Maximal subgroups

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

subgroupindex
C22×#145817202
#249159802
C2×#191276742
C2×#191274712
#249071722
C2×#191274612
C4×#117×C832
#1094583