Finite Group Databasebeta

← #35313368

Subgroups — #35313368

Order 21248.

1090 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128327C211yesmaximal, characteristic
2C2×#19127468C211yesmaximal, characteristic
3C2×#19127467C211yesmaximal, characteristic
4C2×#19127467C211yesmaximal, characteristic
5C2×#19127467C211yesmaximal, characteristic
6C2×#19127467C211yesmaximal, characteristic
7C2×#342×C83C211yesmaximal, characteristic
8#19128327—22no—
9#19128327—22no—
10#19128327—22no—
11#19128327C414yescomplemented
12C2×#14581771—22no—
13C2×#14581769—22no—
14C2×#14581769—22no—
15C22×C22⋊Dic83C2211yescharacteristic
16C22×C22⋊Dic83C2211yescharacteristic
17C22×C22⋊Dic83C2211yescharacteristic
18C22×C22⋊Dic83C2211yescharacteristic
19#19127468—22no—
20#19127467—22no—
21#19127467—22no—
22#19127467—22no—
23#19127467—22no—
24C22×C22⋊C4×C83C2211yescharacteristic
25C22×C22⋊C4×C83C2211yescharacteristic
26C22×C22⋊C4×C83C2211yescharacteristic
27#342×C83—22no—
28C22×Dic166—22no—
29C23×Dic83—21no—
30C23×Dic83—21no—
31C23×Dic83—21no—
32C23×Dic83Q812yescomplemented
33#14581771—28no—
34#14581771—28no—
35#14581769—28no—
36#14581769—28no—
37#14581769—28no—
38#14581769—28no—
39C2×C4⋊Dic83—22no—
40C2×Dic83⋊C4—24no—
41C2×C22⋊Dic83—21no—
42C2×C22⋊Dic83—21no—
43C2×C22⋊Dic83—21no—
44C2×C22⋊Dic83—21no—
45C2×C22⋊Dic83—21no—
46C2×C22⋊Dic83—21no—
47C2×C22⋊Dic83—21no—
48C2×C22⋊Dic83—21no—
49C2×C22⋊Dic83—21no—
50C2×C22⋊Dic83—21no—
51C2×C22⋊Dic83—21no—
52C2×C22⋊Dic83—21no—
53C2×C22⋊Dic83—21no—
54C2×C22⋊Dic83—21no—
55C2×C22⋊Dic83—21no—
56C2×C22⋊Dic83—21no—
57C2×C22⋊Dic83—21no—
58C2×C22⋊Dic83C2×C412yes—
59C2×C22⋊Dic83C2×C412yes—
60C2×C22⋊Dic83D412yes—
61C2×C22⋊Dic83D412yes—
62C2×C22⋊Dic83D412yes—
63C2×C22⋊Dic83D412yes—
64C2×C22⋊Dic83Q812yescomplemented
65C25×C83C2311yescharacteristic
66C23×C4×C83—21no—
67C23×C4×C83—21no—
68C23×C4×C83—21no—
69C2×C22⋊C4×C83—21no—
70C2×C22⋊C4×C83—21no—
71C2×C22⋊C4×C83—21no—
72C2×C22⋊C4×C83—21no—
73C2×C22⋊C4×C83—21no—
74C2×C22⋊C4×C83—21no—
75C2×C22⋊C4×C83—21no—
76C2×C22⋊C4×C83—21no—
77C2×C22⋊C4×C83—21no—
78C2×C22⋊C4×C83—21no—
79C2×C22⋊C4×C83—21no—
80C2×C22⋊C4×C83—21no—
81C2×C22⋊C4×C83—21no—
82C2×C22⋊C4×C83C2×C412yes—
83C2×C22⋊C4×C83D412yes—
84C2×C22⋊C4×C83D412yes—
85C2×C22⋊C4×C83Q812yescomplemented
86C2×C22⋊C4×C83Q812yescomplemented
87C2×Dic166—28no—
88C2×Dic166—84no—
89C22×Dic83—22no—
90C22×Dic83—22no—
91C22×Dic83—22no—
92C22×Dic83—22no—
93C22×Dic83—22no—
94C22×Dic83—22no—
95C22×Dic83—22no—
96C22×Dic83—22no—
97C22×Dic83—22no—
98C22×Dic83—22no—
99C22×Dic83—41no—
100C22×Dic83—41no—
101C22×Dic83—82no—
102C22×Dic83—82no—
103C22×Dic83—82no—
104C22×Dic83—82no—
105C4⋊Dic83—28no—
106Dic83⋊C4—216no—
107C22⋊Dic83—22no—
108C22⋊Dic83—22no—
109C22⋊Dic83—22no—
110C22⋊Dic83—22no—
111C22⋊Dic83—22no—
112C22⋊Dic83—22no—
113C22⋊Dic83—22no—
114C22⋊Dic83—22no—
115C22⋊Dic83—41no—
116C22⋊Dic83—41no—
117C22⋊Dic83—41no—
118C22⋊Dic83—41no—
119C22⋊Dic83—41no—
120C22⋊Dic83—41no—
121C22⋊Dic83C22⋊C414yes—
122C22⋊Dic83C22⋊C414yes—
123C24×C83—82no—
124C24×C83C22×C411yescharacteristic
125C24×C83C2×D411yescharacteristic
126C24×C83C2×D411yescharacteristic
127C24×C83C2×D411yescharacteristic
128C24×C83C2×D411yescharacteristic
129C24×C83C2×D411yescharacteristic
130C24×C83C2×D411yescharacteristic
131C24×C83C2×Q811yescharacteristic
132C24×C83C2×Q811yescharacteristic
133C24×C83C2×Q811yescharacteristic
134C24×C83C2×Q811yescharacteristic
135C24×C83#4111yescharacteristic
136C24×C83#4111yescharacteristic
137C24×C83#4111yescharacteristic
138C24×C83#4111yescharacteristic
139C22×C4×C83—22no—
140C22×C4×C83—22no—
141C22×C4×C83—22no—
142C22×C4×C83—22no—
143C22×C4×C83—22no—
144C22×C4×C83—41no—
145C22×C4×C83—41no—
146C22×C4×C83—41no—
147C22×C4×C83—41no—
148C22×C4×C83—82no—
149C22×C4×C83—82no—
150C22×C4×C83—82no—
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—41no—
159C22⋊C4×C83—41no—
160C22⋊C4×C83—41no—
161C22⋊C4×C83—41no—
162C22⋊C4×C83C22⋊C414yes—
163C23×C83—42no—
164C23×C83—42no—
165C23×C83—42no—
166C23×C83—42no—
167C23×C83—42no—
168C23×C83—42no—
169C23×C83—42no—
170C23×C83—81no—
171C23×C83—81no—
172C23×C83—81no—
173C23×C83—81no—
174C23×C83—81no—
175C23×C83—81no—
176C23×C83—81no—
177C23×C83—81no—
178C23×C83C2×C22⋊C411yescharacteristic
179C23×C83C2×C22⋊C411yescharacteristic
180C23×C83C2×C22⋊C411yescharacteristic
181C23×C83C4×Q811yescharacteristic
182C23×C83C4×Q811yescharacteristic
183C23×C83C4×Q811yescharacteristic
184C23×C83C4×Q811yescharacteristic
185C23×C83#12011yescharacteristic
186C23×C83#12011yescharacteristic
187C23×C83#12011yescharacteristic
188C23×C83#12011yescharacteristic
189C23×C83C22⋊Q811yescharacteristic
190C23×C83C22⋊Q811yescharacteristic
191C23×C83C22⋊Q811yescharacteristic
192C23×C83C22⋊Q811yescharacteristic
193C23×C83C22⋊Q811yescharacteristic
194C23×C83C22⋊Q811yescharacteristic
195C23×C83C22⋊Q811yescharacteristic
196C23×C83C22⋊Q811yescharacteristic
197C23×C83C22⋊Q811yescharacteristic
198C23×C83C22⋊Q811yescharacteristic
199C23×C83C22⋊Q811yescharacteristic
200C23×C83C22⋊Q811yescharacteristic
201C23×C83#12411yescharacteristic
202C23×C83#12411yescharacteristic
203C23×C83#12411yescharacteristic
204C23×C83#12411yescharacteristic
205C23×C83#12411yescharacteristic
206C23×C83#12411yescharacteristic
207C23×C83C4⋊Q811yescharacteristic
208C23×C83C4⋊Q811yescharacteristic
209C23×C83C4⋊Q811yescharacteristic
210C23×C83C4⋊Q811yescharacteristic
211C23×C83C4⋊Q811yescharacteristic
212C23×C83C4⋊Q811yescharacteristic
213C2×C4×C83—24no—
214C2×C4×C83—44no—
215C2×C4×C83—42no—
216C2×C4×C83—42no—
217C2×C4×C83—82no—
218C2×C4×C83—82no—
219C2×C4×C83—82no—
220C2×C4×C83—82no—
221C2×C4×C83—82no—
222C2×C4×C83—82no—
223C2×C4×C83—82no—
224C2×C4×C83—82no—
225C2×Dic83—24no—
226C2×Dic83—24no—
227C2×Dic83—44no—
228C2×Dic83—44no—
229C2×Dic83—42no—
230C2×Dic83—42no—
231C2×Dic83—82no—
232C2×Dic83—82no—
233C2×Dic83—82no—
234C2×Dic83—82no—
235C2×Dic83—82no—
236C2×Dic83—82no—
237C2×Dic83—82no—
238C2×Dic83—82no—
239C2×Dic83—82no—
240C2×Dic83—82no—
241Dic166—88no—
242C22×C83—22no—
243C22×C83—22no—
244C22×C83—22no—
245C22×C83—22no—
246C22×C83—22no—
247C22×C83—22no—
248C22×C83—22no—
249C22×C83—41no—
250C22×C83—41no—
251C22×C83—41no—
252C22×C83—41no—
253C22×C83—41no—
254C22×C83—41no—
255C22×C83—41no—
256C22×C83—41no—
257C22×C83—41no—
258C22×C83—41no—
259C22×C83—41no—
260C22×C83—41no—
261C22×C83—41no—
262C22×C83—41no—
263C22×C83—41no—
264C22×C83—41no—
265C22×C83—41no—
266C22×C83—41no—
267C22×C83—41no—
268C22×C83—41no—
269C22×C83—41no—
270C22×C83—41no—
271C22×C83—41no—
272C22×C83—41no—
273C22×C83—41no—
274C22×C83—41no—
275C22×C83—41no—
276C22×C83—41no—
277C22×C83#37911yescharacteristic
278C22×C83#39111yescharacteristic
279C22×C83#39111yescharacteristic
280C22×C83#39111yescharacteristic
281C22×C83#39111yescharacteristic
282C22×C83#39111yescharacteristic
283C22×C83#39111yescharacteristic
284C22×C83#39311yescharacteristic
285C22×C83#39311yescharacteristic
286C22×C83#39311yescharacteristic
287C22×C83#39311yescharacteristic
288C22×C83#39511yescharacteristic
289C22×C83#39511yescharacteristic
290C22×C83#39511yescharacteristic
291C22×C83#39511yescharacteristic
292C4×C83—44no—
293C4×C83—82no—
294C4×C83—82no—
295Dic83—44no—
296Dic83—44no—
297Dic83—82no—
298Dic83—82no—
299#11394—831nomaximal, Sylow
300C2×C83—21no—
301C2×C83—21no—
302C2×C83—21no—
303C2×C83—21no—
304C2×C83—21no—
305C2×C83—21no—
306C2×C83—21no—
307C2×C83—21no—
308C2×C83—21no—
309C2×C83—21no—
310C2×C83—21no—
311C2×C83—21no—
312C2×C83—21no—
313C2×C83—21no—
314C2×C83#144611yescharacteristic
315C2×C83#203212yes—
316C2×#543—831no—
317C2×#342—831no—
318C2×#342—831no—
319C2×#342—831no—
320C2×#342—831no—
321C2×#342—831no—
322C2×#342D8311yescharacteristic
323C83#1139411yescharacteristic, complemented, Sylow
324#543—834no—
325#543—1662no—
326#543—1662no—
327#543—1662no—
328C2×C22⋊Q8—1662no—
329C2×C22⋊Q8—1662no—
330C2×C22⋊Q8—1662no—
331C22×C22⋊C4—831no—
332C22×C22⋊C4—831no—
333C22×C22⋊C4—831no—
334C22×C22⋊C4—831no—
335C22×C22⋊C4C2×D8311yescharacteristic
336C22×C22⋊C4C2×D8311yescharacteristic
337C22×C22⋊C4C2×D8311yescharacteristic
338#342—22no—
339#342—1662no—
340#342—1662no—
341#342—1662no—
342#342—1662no—
343#342—1662no—
344C25C22×D8311yescharacteristic
345C22×Q8—1662no—
346C23×C4—21no—
347C23×C4—21no—
348C23×C4—21no—
349C23×C4—832no—
350C23×C4—1661no—
351C23×C4—1661no—
352C23×C4—1661no—
353C22⋊Q8—1668no—
354C22⋊Q8—1668no—
355C22⋊Q8—1668no—
356C22⋊Q8—1668no—
357C22⋊Q8—1668no—
358C22⋊Q8—1668no—
359C2×C4⋊C4—1664no—
360C2×C4⋊C4—1662no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—832no—
375C2×C22⋊C4—832no—
376C2×C22⋊C4—832no—
377C2×C22⋊C4—832no—
378C2×C22⋊C4—832no—
379C2×C22⋊C4—832no—
380C2×C22⋊C4—832no—
381C2×C22⋊C4—1661no—
382C2×C22⋊C4—1661no—
383C2×C22⋊C4—1661no—
384C2×C22⋊C4—1661no—
385C2×C22⋊C4—1661no—
386C2×C22⋊C4—1661no—
387C2×C22⋊C4—1661no—
388C2×C22⋊C4—1661no—
389C2×C22⋊C4—1661no—
390C2×C22⋊C4—1661no—
391C2×C22⋊C4—1661no—
392C2×C22⋊C4—1661no—
393C2×C22⋊C4—1661no—
394C2×C22⋊C4—1661no—
395C2×C22⋊C4—1661no—
396C2×C22⋊C4—1661no—
397C2×C22⋊C4—1661no—
398C2×C22⋊C4Dic16612yescomplemented
399C2×C22⋊C4Dic16612yescomplemented
400C2×C22⋊C4C4×D8312yes—
401C2×C22⋊C4D33212yes—
402C2×C22⋊C4C22⋊D8312yes—
403C24—82no—
404C24C2×C4×D8311yescharacteristic
405C24D4×D8311yescharacteristic
406C24D4×D8311yescharacteristic
407C24D4×D8311yescharacteristic
408C24D4×D8311yescharacteristic
409C24C2×C22⋊D8311yescharacteristic
410C24C2×D33211yescharacteristic
411C24Q8×D8311yescharacteristic
412C24Q8×D8311yescharacteristic
413C24C2×Dic16611yescharacteristic
414C24C2×Dic16611yescharacteristic
415C24#1305058911yescharacteristic
416C24#1305058911yescharacteristic
417C24#1305059011yescharacteristic
418C24#1305059011yescharacteristic
419C2×Q8—6644no—
420C2×Q8—1668no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—82no—
431C22×C4—82no—
432C22×C4—82no—
433C22×C4—3321no—
434C22×C4—3321no—
435C22×C4—6642no—
436C22×C4—6642no—
437C22×C4—6642no—
438C22×C4—6642no—
439C22×C4—1662no—
440C22×C4—1662no—
441C22×C4—1662no—
442C22×C4—1662no—
443C22×C4—1662no—
444C22×C4—1662no—
445C22×C4—1662no—
446C22×C4—1662no—
447C22×C4—1662no—
448C22×C4—1662no—
449C4⋊C4—16616no—
450C4⋊C4—1668no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—3321no—
463C22⋊C4—3321no—
464C22⋊C4—3321no—
465C22⋊C4—3321no—
466C22⋊C4—3321no—
467C22⋊C4—3321no—
468C22⋊C4—834no—
469C22⋊C4—834no—
470C22⋊C4—1662no—
471C22⋊C4—1662no—
472C22⋊C4—1662no—
473C22⋊C4—1662no—
474C22⋊C4—1662no—
475C22⋊C4—1662no—
476C22⋊C4—1662no—
477C22⋊C4—1662no—
478C22⋊C4(C2×D83)⋊C414yes—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—81no—
487C23—81no—
488C23—81no—
489C23—81no—
490C23—81no—
491C23—81no—
492C23—81no—
493C23—81no—
494C23C22⋊C4×D8311yescharacteristic
495C23C22⋊C4×D8311yescharacteristic
496C23C2×(C2×D83)⋊C411yescharacteristic
497C23#1458175711yescharacteristic
498C23#1458175711yescharacteristic
499C23C4×Dic16611yescharacteristic
500C23C4×Dic16611yescharacteristic
501C23#1458176011yescharacteristic
502C23#1458176011yescharacteristic
503C23#1458176211yescharacteristic
504C23#1458176211yescharacteristic
505C23#1458176911yescharacteristic
506C23#1458176911yescharacteristic
507C23#1458176911yescharacteristic
508C23#1458176911yescharacteristic
509C23#1458177011yescharacteristic
510C23#1458177011yescharacteristic
511C23#1458177011yescharacteristic
512C23#1458177011yescharacteristic
513C23#1458177111yescharacteristic
514C23#1458177111yescharacteristic
515C23#1458177211yescharacteristic
516C23#1458177211yescharacteristic
517C23#1458177811yescharacteristic
518C23#1458177811yescharacteristic
519C23#1458177811yescharacteristic
520C23#1458177811yescharacteristic
521C23#1458177911yescharacteristic
522C23#1458178011yescharacteristic
523C23#1458179011yescharacteristic
524C23#1458179111yescharacteristic
525C23#1458179111yescharacteristic
526C23#1458179111yescharacteristic
527C23#1458179111yescharacteristic
528C23#1458179211yescharacteristic
529Q8—6648no—
530C2×C4—24no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—3324no—
543C2×C4—3324no—
544C2×C4—3322no—
545C2×C4—3322no—
546C2×C4—6642no—
547C2×C4—6642no—
548C2×C4—6642no—
549C2×C4—6642no—
550C2×C4—6642no—
551C2×C4—6642no—
552C2×C4—6642no—
553C2×C4—6642no—
554C2×C4—6642no—
555C2×C4—6642no—
556C2×C4—1664no—
557C2×C4—1664no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22#1912755611yescharacteristic
594C22#1912760511yescharacteristic
595C22#1912760511yescharacteristic
596C22#1912760511yescharacteristic
597C22#1912760511yescharacteristic
598C22#1912760611yescharacteristic
599C22#1912760711yescharacteristic
600C22#1912761311yescharacteristic
601C22#1912761311yescharacteristic
602C22#1912761411yescharacteristic
603C22#1912761411yescharacteristic
604C22#1912762111yescharacteristic
605C22#1912762111yescharacteristic
606C22#1912762211yescharacteristic
607C22#1912762211yescharacteristic
608C4—44no—
609C4—82no—
610C4—82no—
611C4—3324no—
612C4—3324no—
613C4—6642no—
614C4—6642no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—21no—
628C2—21no—
629C2#2490573311yescharacteristic
630C2#2490864112yes—
subgroupG/H
centerC22#19127614
commutatorC24×C83C22×C4
FrattiniC25C22×D83
FittingC2×#342×C83C2
socleC22×C83#393
prime radical, cosocleC25×C83C23
hypercenterC2×#342D83
hypocenterC83#11394
LCSG ▷ C24×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
11. #19128327C4semidirect
32. C23×Dic83Q8semidirect
64. C2×C22⋊Dic83Q8semidirect
85. C2×C22⋊C4×C83Q8semidirect
86. C2×C22⋊C4×C83Q8semidirect
323. C83#11394semidirect
398. C2×C22⋊C4Dic166semidirect
399. C2×C22⋊C4Dic166semidirect

Maximal subgroups

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

subgroupindex
C2×#191283272
C2×#191274682
C2×#191274672
C2×#342×C832
#1139483