Finite Group Databasebeta

← #35407909

Subgroups — #35407909

Order 21248.

990 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127742C211yesmaximal, characteristic
2C2×#19127738C211yesmaximal, characteristic
3C2×#19127726C211yesmaximal, characteristic
4#24910084C211yesmaximal, characteristic
5#24909817C211yesmaximal, characteristic
6#24908234C211yesmaximal, characteristic, complemented
7#24908233C211yesmaximal, characteristic, complemented
8#24908231C211yesmaximal, characteristic, complemented
9#24908228C211yesmaximal, characteristic, complemented
10#24908225C211yesmaximal, characteristic, complemented
11#24908224C211yesmaximal, characteristic, complemented
12#24908218C211yesmaximal, characteristic, complemented
13#24907181C211yesmaximal, characteristic
14#340×D83C211yesmaximal, characteristic
15C83×#1947C211yesmaximal, characteristic, complemented
16C22×#13050573C2211yescharacteristic
17C22×C8×D83C2211yescharacteristic
18C2×#14581750C2211yescharacteristic
19C2×#14581750C2211yescharacteristic
20C2×#14581749C2211yescharacteristic
21C2×C4⋊C4×D83C2211yescharacteristic
22C2×C4⋊C4×D83C2211yescharacteristic
23#19127742—24no—
24#19127738—24no—
25C2×#14581726C2211yescharacteristic
26C2×#14581725C2211yescharacteristic
27C2×#14581724C2211yescharacteristic
28C2×#14581723C2211yescharacteristic
29C2×#14581723C2211yescharacteristic
30C2×#14581723C2211yescharacteristic
31#19127726C418yescomplemented
32C2×C4⋊(C83⋊C8)C2211yescharacteristic
33C2×Dic83⋊C8C2211yescharacteristic
34C2×Dic83⋊C8C2211yescharacteristic
35#19127596—21no—
36#19127596—21no—
37#19127572—21no—
38#19127572—21no—
39#19127570C2211yescharacteristic
40#19127567C2211yescharacteristic
41#19127566C2211yescharacteristic
42C4⋊C4×Dic83C2211yescharacteristic
43C4⋊C4×Dic83C2211yescharacteristic
44C4×Dic83⋊C4—21no—
45C4×C4⋊Dic83C2211yescharacteristic
46#19127552—21no—
47C4×(C2×D83)⋊C4—21no—
48#19127548—21no—
49#19127464C2211yescharacteristic
50#19127464C2211yescharacteristic
51#19127463C2211yescharacteristic
52#19127463C2211yescharacteristic
53#19127463C2211yescharacteristic
54#19127463C2211yescharacteristic
55C2×#107×C83C2211yescharacteristic
56C2×#107×C83C2211yescharacteristic
57C2×C4⋊C8×C83C2211yescharacteristic
58#384×C83C2211yescharacteristic
59C4×C4⋊C4×C83C2211yescharacteristic
60#340×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic
62C22×C4×D83—21no—
63C22×C4×D83—21no—
64C22×C4×D83C2311yescharacteristic
65C2×#13050573—22no—
66C2×#13050573—22no—
67C2×#13050573C2×C414yes—
68C22×C83⋊C8C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C2×C8×D83—22no—
71C2×C8×D83—22no—
72C2×C8×D83C2×C414yes—
73#14581750—22no—
74#14581750—22no—
75#14581750—22no—
76#14581750D414yes—
77#14581749C2×C414yes—
78#14581749Q814yes—
79C2×C4⋊Dic83C2311yescharacteristic
80C2×C4⋊Dic83C2311yescharacteristic
81C2×C4⋊Dic83C2311yescharacteristic
82C2×C4⋊Dic83C2311yescharacteristic
83C2×Dic83⋊C4—21no—
84C2×Dic83⋊C4—21no—
85C2×Dic83⋊C4—21no—
86C2×Dic83⋊C4—21no—
87C2×Dic83⋊C4D411yescharacteristic
88C2×Dic83⋊C4D411yescharacteristic
89C4⋊C4×D83—22no—
90C4⋊C4×D83—22no—
91C4⋊C4×D83—22no—
92C4⋊C4×D83Q814yes—
93C2×(C2×D83)⋊C4—21no—
94C2×(C2×D83)⋊C4—21no—
95C2×(C2×D83)⋊C4D411yescharacteristic
96C2×(C2×D83)⋊C4D411yescharacteristic
97C2×C4×Dic83—21no—
98C2×C4×Dic83—21no—
99C2×C4×Dic83—21no—
100C2×C4×Dic83—21no—
101C2×C4×Dic83—21no—
102C2×C4×Dic83C2311yescharacteristic
103#14581726—22no—
104#14581725—22no—
105#14581724—22no—
106#14581723—22no—
107#14581723—22no—
108#14581723—22no—
109C4⋊(C83⋊C8)C2×C414yescomplemented
110Dic83⋊C8C2×C414yescomplemented
111Dic83⋊C8C2×C414yescomplemented
112C83⋊#95—21no—
113C83⋊#95—21no—
114C83⋊#95—21no—
115C83⋊#95—21no—
116C83⋊#95—21no—
117C83⋊#95—21no—
118C83⋊#95—21no—
119C22×C8×C83C2311yescharacteristic
120C22×C8×C83C2311yescharacteristic
121C2×C4⋊C4×C83—21no—
122C2×C4⋊C4×C83—21no—
123C2×C4⋊C4×C83C2311yescharacteristic
124C2×C4⋊C4×C83C2311yescharacteristic
125C2×C4⋊C4×C83C2311yescharacteristic
126C2×C4⋊C4×C83C2311yescharacteristic
127C2×C42×C83—21no—
128C2×C42×C83C2311yescharacteristic
129#107×C83—22no—
130#107×C83—22no—
131C4⋊C8×C83C2×C414yescomplemented
132#95×C83—21no—
133C23×D83C2×D411yescharacteristic
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83C2×D411yescharacteristic
139C22×Dic83C2×D411yescharacteristic
140C22×Dic83C2×D411yescharacteristic
141C2×C4×D83—24no—
142C2×C4×D83—42no—
143C2×C4×D83—81no—
144C2×C4×D83—81no—
145C2×C4×D83—81no—
146C2×C4×D83—81no—
147C2×C4×D83C22×C412yes—
148C2×C4×D83C2×D412yes—
149C2×C4×D83C2×Q812yes—
150C2×C4×D83C2×Q812yes—
151C2×C4×D83#4112yes—
152C2×C4×D83#4112yes—
153#13050573—28no—
154C2×C83⋊C8—21no—
155C2×C83⋊C8—21no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8C22×C412yes—
159C2×C83⋊C8C22×C412yes—
160C8×D83—28no—
161C4⋊Dic83—21no—
162C4⋊Dic83—21no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—21no—
166C4⋊Dic83—21no—
167C4⋊Dic83C2×D412yes—
168C4⋊Dic83C2×Q812yes—
169Dic83⋊C4—24no—
170Dic83⋊C4—42no—
171Dic83⋊C4—81no—
172Dic83⋊C4—81no—
173Dic83⋊C4C4⋊C414yes—
174Dic83⋊C4C4⋊C414yes—
175(C2×D83)⋊C4—24no—
176(C2×D83)⋊C4—42no—
177(C2×D83)⋊C4C4⋊C414yes—
178(C2×D83)⋊C4C4⋊C414yes—
179C4×Dic83—24no—
180C4×Dic83—42no—
181C4×Dic83—81no—
182C4×Dic83—81no—
183C4×Dic83—81no—
184C4×Dic83C22×C412yes—
185C4×Dic83C2×Q812yes—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83C2×D411yescharacteristic
191C22×C4×C83C2×D411yescharacteristic
192C22×C4×C83C2411yescharacteristic
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83C22×C412yes—
198C2×C8×C83C22×C412yes—
199C4⋊C4×C83—21no—
200C4⋊C4×C83—21no—
201C4⋊C4×C83—21no—
202C4⋊C4×C83—21no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83—21no—
205C4⋊C4×C83—81no—
206C4⋊C4×C83—81no—
207C4⋊C4×C83C2×D412yes—
208C4⋊C4×C83C2×Q812yes—
209C42×C83—81no—
210C42×C83C22×C412yes—
211C42×C83C2×Q812yes—
212C23×C83C22×D411yescharacteristic
213C22×D83—21no—
214C22×D83—21no—
215C22×D83—21no—
216C22×D83—21no—
217C22×D83C2×C4⋊C412yes—
218C22×D83#12112yes—
219C22×D83C22⋊Q812yes—
220C2×C4×C83—21no—
221C2×C4×C83—21no—
222C2×C4×C83—21no—
223C2×C4×C83—21no—
224C2×C4×C83—22no—
225C2×C4×C83—22no—
226C2×C4×C83—41no—
227C2×C4×C83—41no—
228C2×C4×C83—41no—
229C2×C4×C83—41no—
230C2×C4×C83—41no—
231C2×C4×C83—41no—
232C2×C4×C83—41no—
233C2×C4×C83—41no—
234C2×C4×C83—41no—
235C2×C4×C83—41no—
236C2×C4×C83C2×C4⋊C412yes—
237C2×C4×C83C2×C4⋊C412yes—
238C2×C4×C83C23×C411yescharacteristic
239C2×C4×C83C22×D411yescharacteristic
240C2×C4×C83C22×Q811yescharacteristic
241C2×C4×C83C22×Q811yescharacteristic
242C2×C4×C83C2×#4111yescharacteristic
243C2×C4×C83C2×#4111yescharacteristic
244C2×Dic83—21no—
245C2×Dic83—21no—
246C2×Dic83—21no—
247C2×Dic83—21no—
248C2×Dic83—22no—
249C2×Dic83—22no—
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—41no—
259C2×Dic83—41no—
260C2×Dic83C2×C4⋊C412yes—
261C2×Dic83C2×C4⋊C412yes—
262C2×Dic83C2×C4⋊C412yes—
263C2×Dic83#12112yes—
264C2×Dic83C22⋊Q812yes—
265C4×D83—84no—
266C4×D83—84no—
267C4×D83C4×D414yes—
268C4×D83C4×Q814yes—
269C4×D83#12514yes—
270C4×D83C4⋊Q814yes—
271C8×C83—22no—
272C8×C83—22no—
273C83⋊C8—22no—
274C83⋊C8—22no—
275C22×C83C22×C4⋊C411yescharacteristic
276C22×C83C2×#12111yescharacteristic
277C22×C83C2×C22⋊Q811yescharacteristic
278C22×C83#57611yescharacteristic
279C22×C83#57711yescharacteristic
280C22×C83#57711yescharacteristic
281C22×C83#57811yescharacteristic
282C2×D83—22no—
283C2×D83—22no—
284C2×D83—22no—
285C2×D83—22no—
286C2×D83—22no—
287C2×D83—22no—
288C2×D83#38914yes—
289C4×C83—22no—
290C4×C83—22no—
291C4×C83—42no—
292C4×C83—42no—
293C4×C83—81no—
294C4×C83—81no—
295C4×C83C2×C4×D411yescharacteristic
296C4×C83C2×C4×Q811yescharacteristic
297C4×C83C2×#12511yescharacteristic
298C4×C83C2×C4⋊Q811yescharacteristic
299Dic83—22no—
300Dic83—22no—
301Dic83—42no—
302Dic83—42no—
303Dic83—81no—
304Dic83—81no—
305Dic83#38914yes—
306#21175—831nomaximal, Sylow
307C2×C83C2×#38911yescharacteristic
308C2×C83#291211yescharacteristic
309C2×C83#291311yescharacteristic
310C2×C83#304511yescharacteristic
311C2×C83#304611yescharacteristic
312C2×C83#308111yescharacteristic
313C2×C83#308211yescharacteristic
314D83—24no—
315C2×#428—831no—
316C2×#427—831no—
317C2×#424—831no—
318#2317—831no—
319#2274—831no—
320#1949—831no—
321#1949—831no—
322#1949—831no—
323#1949—831no—
324#1948—831no—
325#1948—831no—
326#1947—831no—
327#1947D8311yescharacteristic, complemented
328#1736—831no—
329C2×#340—831no—
330C83#2117511yescharacteristic, complemented, Sylow
331C22×M16—831no—
332C23×C8—831no—
333C2×#117—831no—
334C2×#117—831no—
335C2×#117—831no—
336C22×C4⋊C4—831no—
337C22×C4⋊C4—831no—
338#428—1664no—
339#427—1664no—
340C2×#107—831no—
341C2×#107—831no—
342C2×#107C2×D8311yescharacteristic
343C2×#107C2×D8311yescharacteristic
344C2×#106—831no—
345C2×#106—831no—
346C2×#106—831no—
347C2×#106—831no—
348#424—838no—
349C2×C4⋊C8—831no—
350C2×C4⋊C8—831no—
351C2×C4⋊C8—831no—
352C2×C4⋊C8C2×D8311yescharacteristic
353#389—1661no—
354#389—1661no—
355#385—1661no—
356#385—1661no—
357#384—831no—
358#384C2×D8311yescharacteristic
359#382—831no—
360#382—831no—
361C4×C4⋊C4—831no—
362C4×C4⋊C4—831no—
363C4×C4⋊C4—831no—
364C4×C4⋊C4—1661no—
365C4×C4⋊C4—1661no—
366C4×C4⋊C4C2×D8311yescharacteristic
367C4×C22⋊C4—1661no—
368C4×C22⋊C4—1661no—
369#340—831no—
370#340—831no—
371#340—831no—
372#340—831no—
373#340—831no—
374#340—831no—
375#340C2×D8311yescharacteristic
376#340C2×D8311yescharacteristic
377C23×C4—831no—
378C23×C4—1661no—
379C23×C4—1661no—
380C2×M16—834no—
381C2×M16—1662no—
382C2×M16—1662no—
383C22×C8—831no—
384C22×C8—831no—
385C22×C8—834no—
386C22×C8—1662no—
387C22×C8—1662no—
388C22×C8C22×D8311yescharacteristic
389C22×C8C22×D8311yescharacteristic
390#117—834no—
391#117—834no—
392#117—834no—
393#117—1662no—
394#117—1662no—
395#117—1662no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—831no—
399C2×C4⋊C4—831no—
400C2×C4⋊C4—831no—
401C2×C4⋊C4—831no—
402C2×C4⋊C4—834no—
403C2×C4⋊C4—831no—
404C2×C4⋊C4—831no—
405C2×C4⋊C4—1662no—
406C2×C4⋊C4—1662no—
407C2×C4⋊C4—1662no—
408C2×C4⋊C4—1661no—
409C2×C4⋊C4—1661no—
410C2×C4⋊C4—1661no—
411C2×C4⋊C4—1661no—
412C2×C4⋊C4C22×D8311yescharacteristic
413C2×C4⋊C4C22×D8311yescharacteristic
414C2×C4⋊C4C22×D8311yescharacteristic
415C2×C4⋊C4C22×D8311yescharacteristic
416C2×C22⋊C4—831no—
417C2×C22⋊C4—831no—
418C2×C22⋊C4—1661no—
419C2×C22⋊C4—1661no—
420C2×C42—21no—
421C2×C42—831no—
422C2×C42—1661no—
423C2×C42—1661no—
424C2×C42—1661no—
425C2×C42—1661no—
426C2×C42—1661no—
427C2×C42C22×D8311yescharacteristic
428#107—22no—
429#107—22no—
430#107—1662no—
431#107—1662no—
432#106—1662no—
433#106—1662no—
434#106—1662no—
435#106—1662no—
436C4⋊C8—834no—
437C4⋊C8—834no—
438C4⋊C8—834no—
439C4⋊C8C4×D8314yescomplemented
440#95—21no—
441#95—1661no—
442#95—1661no—
443#95—1661no—
444#95—1661no—
445#95—1661no—
446#95—1661no—
447#95—1661no—
448C24—831no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—3322no—
454C22×C4—831no—
455C22×C4—832no—
456C22×C4—832no—
457C22×C4—832no—
458C22×C4—832no—
459C22×C4—832no—
460C22×C4—832no—
461C22×C4—831no—
462C22×C4—831no—
463C22×C4—6641no—
464C22×C4—6641no—
465C22×C4—6641no—
466C22×C4—6641no—
467C22×C4—1664no—
468C22×C4—1661no—
469C22×C4—1661no—
470C22×C4—1661no—
471C22×C4—1661no—
472C22×C4D4×D8311yescharacteristic
473C22×C4D4×D8311yescharacteristic
474C22×C4C23×D8311yescharacteristic
475M16—1668no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—832no—
481C2×C8—832no—
482C2×C8—1668no—
483C2×C8—1661no—
484C2×C8—1661no—
485C2×C8—1661no—
486C2×C8—1661no—
487C2×C8C2×C4×D8312yes—
488C2×C8C2×C4×D8312yes—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—81no—
496C4⋊C4—81no—
497C4⋊C4—3322no—
498C4⋊C4—834no—
499C4⋊C4—834no—
500C4⋊C4—832no—
501C4⋊C4—832no—
502C4⋊C4—6641no—
503C4⋊C4—6641no—
504C4⋊C4—1664no—
505C4⋊C4—1661no—
506C4⋊C4—1661no—
507C4⋊C4—1661no—
508C4⋊C4—1661no—
509C4⋊C4—1661no—
510C4⋊C4—1661no—
511C4⋊C4D4×D8312yes—
512C4⋊C4Q8×D8312yes—
513C22⋊C4—3322no—
514C22⋊C4—834no—
515C22⋊C4—834no—
516C22⋊C4—1664no—
517C42—81no—
518C42—3322no—
519C42—832no—
520C42—832no—
521C42—6641no—
522C42—6641no—
523C42—6641no—
524C42—1664no—
525C42C2×C4×D8312yes—
526C42Q8×D8312yes—
527C23—832no—
528C23—832no—
529C23—832no—
530C23—1661no—
531C23—1661no—
532C23—1661no—
533C23—1661no—
534C23C2×D4×D8311yescharacteristic
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—3321no—
552C2×C4—3321no—
553C2×C4—3321no—
554C2×C4—3321no—
555C2×C4—3321no—
556C2×C4—3321no—
557C2×C4—3321no—
558C2×C4—3321no—
559C2×C4—3321no—
560C2×C4—3321no—
561C2×C4—832no—
562C2×C4—832no—
563C2×C4—832no—
564C2×C4—834no—
565C2×C4—834no—
566C2×C4—834no—
567C2×C4—834no—
568C2×C4—832no—
569C2×C4—832no—
570C2×C4—6644no—
571C2×C4—6644no—
572C2×C4—1662no—
573C2×C4—1662no—
574C2×C4—1661no—
575C2×C4—1661no—
576C2×C4—1661no—
577C2×C4—1661no—
578C2×C4C4⋊C4×D8312yes—
579C2×C4C4⋊C4×D8312yes—
580C2×C4C22×C4×D8311yescharacteristic
581C2×C4C2×D4×D8311yescharacteristic
582C2×C4C2×Q8×D8311yescharacteristic
583C2×C4C2×Q8×D8311yescharacteristic
584C2×C4#41×D8311yescharacteristic
585C2×C4#41×D8311yescharacteristic
586C8—22no—
587C8—22no—
588C8—1662no—
589C8—1662no—
590C22—834no—
591C22—1662no—
592C22—1662no—
593C22—1662no—
594C22—1662no—
595C22—1662no—
596C22—1662no—
597C22C2×C4⋊C4×D8311yescharacteristic
598C22#121×D8311yescharacteristic
599C22C22⋊Q8×D8311yescharacteristic
600C22#1912850211yescharacteristic
601C22#1912851011yescharacteristic
602C22#1912851111yescharacteristic
603C22#1912851411yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—3322no—
611C4—3322no—
612C4—834no—
613C4—6641no—
614C4—6641no—
615C4—1662no—
616C4—1662no—
617C4C4×D4×D8311yescharacteristic
618C4C4×Q8×D8311yescharacteristic
619C4#125×D8311yescharacteristic
620C4C4⋊Q8×D8311yescharacteristic
621C2—1664no—
622C2#389×D8311yescharacteristic
623C2#2491605711yescharacteristic
624C2#2491605911yescharacteristic
625C2#2491699711yescharacteristic
626C2#2491701011yescharacteristic
627C2#2491728711yescharacteristic
628C2#2491730011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
FittingC83×#1947C2
socleC23×C83C22×D4
prime radicalC23×D83C2×D4
cosocleC22×C4×C83C24
hypercenter#1947D83
hypocenterC83#21175
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
6. #24908234C2semidirect
7. #24908233C2semidirect
8. #24908231C2semidirect
9. #24908228C2semidirect
10. #24908225C2semidirect
11. #24908224C2semidirect
12. #24908218C2semidirect
15. C83×#1947C2semidirect
31. #19127726C4semidirect
109. C4⋊(C83⋊C8)C2×C4semidirect
110. Dic83⋊C8C2×C4semidirect
111. Dic83⋊C8C2×C4semidirect
131. C4⋊C8×C83C2×C4semidirect
327. #1947D83semidirect
330. C83#21175semidirect
439. C4⋊C8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191277422
C2×#191277382
C2×#191277262
#249100842
#249098172
#249082342
#249082332
#249082312
#249082282
#249082252
#249082242
#249082182
#249071812
#340×D832
C83×#19472
#2117583