Finite Group Databasebeta

← #35420030

Subgroups — #35420030

Order 21248.

1466 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127779C211yesmaximal, characteristic, complemented
2C2×#19127702C211yesmaximal, characteristic, complemented
3C2×#19127710C211yesmaximal, characteristic, complemented
4#24910392C211yesmaximal, characteristic, complemented
5#24908396C211yesmaximal, characteristic, complemented
6#24908275C211yesmaximal, characteristic, complemented
7#24907902C211yesmaximal, characteristic, complemented
8#24907897C211yesmaximal, characteristic, complemented
9#24907786C211yesmaximal, characteristic, complemented
10#24907771C211yesmaximal, characteristic, complemented
11#24907478C211yesmaximal, characteristic, complemented
12#24907403C211yesmaximal, characteristic, complemented
13#24907398C211yesmaximal, characteristic, complemented
14C4×#14581716C211yesmaximal, characteristic, complemented
15C2×#548×C83C211yesmaximal, characteristic
16C22×#13050574C2211yescharacteristic
17C22×#13050574C2211yescharacteristic
18C2×#14581751C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20#19127779—24no—
21C2×C4⋊(C83⋊C8)C2211yescharacteristic
22#19127710—24no—
23#19127702—24no—
24C2×#14581716C2211yescharacteristic
25C2×#14581716C2211yescharacteristic
26C2×#14581716C2211yescharacteristic
27C2×#14581716C2211yescharacteristic
28C2×#14581716C2211yescharacteristic
29C2×#14581716C2211yescharacteristic
30C2×#14581716C2211yescharacteristic
31C2×#14581716C2211yescharacteristic
32C2×#14581713C2211yescharacteristic
33C2×#14581713C2211yescharacteristic
34C2×#14581713C2211yescharacteristic
35C2×#14581713C2211yescharacteristic
36C2×C22⋊(C83⋊C8)C2211yescharacteristic
37C2×C22⋊(C83⋊C8)C2211yescharacteristic
38C2×C4×C83⋊C8C2211yescharacteristic
39#19127594—21no—
40#19127587—21no—
41#19127581—21no—
42#19127567C2211yescharacteristic
43#19127561C2211yescharacteristic
44#19127561C2211yescharacteristic
45C4×C4⋊Dic83C2211yescharacteristic
46C22⋊C4×Dic83—21no—
47#19127463C2211yescharacteristic
48#19127463C2211yescharacteristic
49#19127463C2211yescharacteristic
50#19127463C2211yescharacteristic
51C22×#41×C83C2211yescharacteristic
52C23×Q8×C83C2211yescharacteristic
53#548×C83—24no—
54#548×C83C418yescomplemented
55C2×#124×C83—21no—
56C2×#124×C83C2211yescharacteristic
57C2×C22⋊Q8×C83—21no—
58C2×C22⋊Q8×C83C2211yescharacteristic
59C2×#121×C83—21no—
60C2×#121×C83C2211yescharacteristic
61C2×C4×Q8×C83C2211yescharacteristic
62C2×C4×D4×C83—21no—
63C2×C4×D4×C83C2211yescharacteristic
64C23×Dic83—21no—
65C2×#13050574—22no—
66C2×#13050574—22no—
67C2×#13050574—22no—
68C2×#13050574—22no—
69C2×#13050574—41no—
70C2×#13050574—41no—
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75#14581751—22no—
76#14581751—41no—
77C2×C4⋊Dic83—22no—
78C2×C4⋊Dic83—21no—
79C2×C4⋊Dic83—41no—
80C2×C4⋊Dic83C2311yescharacteristic
81C2×C4⋊Dic83C2311yescharacteristic
82C2×C4⋊Dic83C2311yescharacteristic
83C2×C4⋊Dic83C2311yescharacteristic
84C2×C22⋊Dic83—21no—
85C2×C22⋊Dic83—21no—
86C2×C22⋊Dic83—21no—
87C2×C4×Dic83—21no—
88C2×C4×Dic83—21no—
89C4⋊(C83⋊C8)—22no—
90#14581716—22no—
91#14581716—22no—
92#14581716—22no—
93#14581716—22no—
94#14581716—22no—
95#14581716—41no—
96#14581716—41no—
97#14581716D414yescomplemented
98#14581713—22no—
99#14581713—22no—
100#14581713—41no—
101#14581713—41no—
102C22⋊(C83⋊C8)—22no—
103C22⋊(C83⋊C8)—22no—
104C4×C83⋊C8—22no—
105C83⋊#95—21no—
106C83⋊#95—21no—
107C83⋊#95—21no—
108C83⋊#95—21no—
109C83⋊#95—21no—
110C2×#41×C83—22no—
111C2×#41×C83—22no—
112C2×#41×C83—22no—
113C2×#41×C83—41no—
114C2×#41×C83—41no—
115C2×#41×C83C2×C414yes—
116C22×Q8×C83—21no—
117C22×Q8×C83—22no—
118C22×Q8×C83—22no—
119C22×Q8×C83—22no—
120C22×Q8×C83—41no—
121C22×Q8×C83—41no—
122C22×Q8×C83C2×C414yescomplemented
123C22×Q8×C83C2311yescharacteristic
124C22×Q8×C83C2311yescharacteristic
125C22×D4×C83—21no—
126C22×D4×C83—21no—
127C22×D4×C83D411yescharacteristic
128C22×D4×C83C2311yescharacteristic
129C23×C4×C83—21no—
130C23×C4×C83—21no—
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133#124×C83—28no—
134#124×C83—22no—
135#124×C83C2×C414yescomplemented
136C22⋊Q8×C83—22no—
137C22⋊Q8×C83—28no—
138C22⋊Q8×C83C2×C414yes—
139#121×C83—28no—
140#121×C83—22no—
141#121×C83C2×C414yescomplemented
142C4×Q8×C83—22no—
143C4×Q8×C83C2×C414yescomplemented
144C4×D4×C83—28no—
145C4×D4×C83C2×C414yes—
146C4×D4×C83D414yes—
147C2×C4⋊C4×C83—21no—
148C2×C4⋊C4×C83—21no—
149C2×C4⋊C4×C83D411yescharacteristic
150C2×C4⋊C4×C83C2311yescharacteristic
151C2×C22⋊C4×C83—21no—
152C2×C22⋊C4×C83—21no—
153C2×C22⋊C4×C83—21no—
154C2×C22⋊C4×C83—21no—
155C2×C22⋊C4×C83D411yescharacteristic
156C2×C22⋊C4×C83D411yescharacteristic
157C2×C42×C83—21no—
158C2×C42×C83C2311yescharacteristic
159C22×Dic83—21no—
160C22×Dic83—21no—
161C22×Dic83—21no—
162C22×Dic83—21no—
163C22×Dic83—42no—
164C22×Dic83—42no—
165C22×Dic83—81no—
166#13050574—44no—
167#13050574—44no—
168C2×C83⋊C8—21no—
169C2×C83⋊C8—21no—
170C2×C83⋊C8—21no—
171C2×C83⋊C8—21no—
172C2×C83⋊C8—21no—
173C2×C83⋊C8—21no—
174C2×C83⋊C8—21no—
175C2×C83⋊C8—21no—
176C2×C83⋊C8—21no—
177C2×C83⋊C8—21no—
178C2×C83⋊C8—21no—
179C2×C83⋊C8C2×D412yes—
180C4⋊Dic83—21no—
181C4⋊Dic83—21no—
182C4⋊Dic83—21no—
183C4⋊Dic83—21no—
184C4⋊Dic83—21no—
185C4⋊Dic83—21no—
186C4⋊Dic83—21no—
187C4⋊Dic83—42no—
188C4⋊Dic83C2×D412yes—
189C22⋊Dic83—42no—
190C22⋊Dic83—42no—
191C22⋊Dic83—81no—
192C4×Dic83—42no—
193C4×Dic83—81no—
194C24×C83—21no—
195C24×C83C2×D411yescharacteristic
196C24×C83C2×D411yescharacteristic
197#41×C83—28no—
198#41×C83—44no—
199#41×C83—44no—
200#41×C83—44no—
201C2×Q8×C83—24no—
202C2×Q8×C83—21no—
203C2×Q8×C83—21no—
204C2×Q8×C83—21no—
205C2×Q8×C83—21no—
206C2×Q8×C83—28no—
207C2×Q8×C83—21no—
208C2×Q8×C83—21no—
209C2×Q8×C83—21no—
210C2×Q8×C83—21no—
211C2×Q8×C83—42no—
212C2×Q8×C83—42no—
213C2×Q8×C83—44no—
214C2×Q8×C83—44no—
215C2×Q8×C83—44no—
216C2×Q8×C83C22×C412yes—
217C2×Q8×C83C22×C412yes—
218C2×Q8×C83C2×D412yes—
219C2×Q8×C83#4112yes—
220C2×D4×C83—24no—
221C2×D4×C83—24no—
222C2×D4×C83—21no—
223C2×D4×C83—21no—
224C2×D4×C83—21no—
225C2×D4×C83—21no—
226C2×D4×C83—21no—
227C2×D4×C83—41no—
228C2×D4×C83—41no—
229C2×D4×C83—42no—
230C2×D4×C83—42no—
231C2×D4×C83—42no—
232C2×D4×C83—42no—
233C2×D4×C83C22⋊C414yes—
234C2×D4×C83C22×C412yes—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—24no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—24no—
248C22×C4×C83—42no—
249C22×C4×C83—42no—
250C22×C4×C83—42no—
251C22×C4×C83—42no—
252C22×C4×C83C22×C412yes—
253C22×C4×C83C22×C412yes—
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2×D411yescharacteristic
258C22×C4×C83C2×D412yes—
259C22×C4×C83C2×D412yes—
260C22×C4×C83C2411yescharacteristic
261C4⋊C4×C83—24no—
262C4⋊C4×C83—24no—
263C4⋊C4×C83—21no—
264C4⋊C4×C83C22⋊C414yes—
265C4⋊C4×C83C22×C412yes—
266C22⋊C4×C83—24no—
267C22⋊C4×C83—24no—
268C22⋊C4×C83—24no—
269C22⋊C4×C83—24no—
270C22⋊C4×C83C22⋊C414yes—
271C22⋊C4×C83C22⋊C414yes—
272C42×C83—24no—
273C42×C83C22×C412yes—
274C42×C83C2×D412yes—
275C23×C83—21no—
276C23×C83—21no—
277C23×C83—21no—
278C23×C83—21no—
279C23×C83—21no—
280C23×C83—21no—
281C23×C83—21no—
282C23×C83—21no—
283C23×C83—21no—
284C23×C83—21no—
285C23×C83—21no—
286C23×C83—21no—
287C23×C83—22no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83C2×C22⋊C412yes—
295C23×C83C2×C22⋊C412yes—
296C23×C83C22×D411yescharacteristic
297Q8×C83—22no—
298Q8×C83—22no—
299Q8×C83—22no—
300Q8×C83—22no—
301Q8×C83—22no—
302Q8×C83—48no—
303Q8×C83—41no—
304Q8×C83—41no—
305Q8×C83C4×D414yes—
306D4×C83—22no—
307D4×C83—22no—
308D4×C83—44no—
309D4×C83—48no—
310D4×C83—48no—
311D4×C83—41no—
312D4×C83—41no—
313C2×C4×C83—22no—
314C2×C4×C83—21no—
315C2×C4×C83—21no—
316C2×C4×C83—22no—
317C2×C4×C83—21no—
318C2×C4×C83—21no—
319C2×C4×C83—22no—
320C2×C4×C83—21no—
321C2×C4×C83—21no—
322C2×C4×C83—21no—
323C2×C4×C83—21no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—48no—
335C2×C4×C83—48no—
336C2×C4×C83—41no—
337C2×C4×C83—41no—
338C2×C4×C83—41no—
339C2×C4×C83—41no—
340C2×C4×C83C2×C22⋊C412yes—
341C2×C4×C83C2×C22⋊C412yes—
342C2×C4×C83C2×C22⋊C412yes—
343C2×C4×C83C2×C22⋊C412yes—
344C2×C4×C83C23×C411yescharacteristic
345C2×C4×C83C22×D411yescharacteristic
346C2×C4×C83C22×D411yescharacteristic
347C2×C4×C83C2×#4111yescharacteristic
348C2×C4×C83H(5,𝔽2)11yescharacteristic
349C2×C4×C83H(5,𝔽2)11yescharacteristic
350C2×Dic83—22no—
351C2×Dic83—41no—
352C2×Dic83—41no—
353C2×Dic83—41no—
354C2×Dic83—41no—
355C2×Dic83—41no—
356C2×Dic83—41no—
357C2×Dic83—41no—
358C2×Dic83—41no—
359C2×Dic83—41no—
360C2×Dic83—41no—
361C2×Dic83—41no—
362C2×Dic83—84no—
363C83⋊C8—22no—
364C83⋊C8—41no—
365C83⋊C8—41no—
366C83⋊C8—41no—
367C22×C83—22no—
368C22×C83—22no—
369C22×C83—22no—
370C22×C83—22no—
371C22×C83—22no—
372C22×C83—22no—
373C22×C83—41no—
374C22×C83—41no—
375C22×C83—41no—
376C22×C83—41no—
377C22×C83—41no—
378C22×C83—41no—
379C22×C83—41no—
380C22×C83—41no—
381C22×C83—42no—
382C22×C83—42no—
383C22×C83—42no—
384C22×C83—81no—
385C22×C83—81no—
386C22×C83—81no—
387C22×C83—81no—
388C22×C83C22×C22⋊C411yescharacteristic
389C22×C83D4211yescharacteristic
390C22×C83#54611yescharacteristic
391C22×C83#57511yescharacteristic
392C22×C83#57511yescharacteristic
393C22×C83#57711yescharacteristic
394C22×C83#57811yescharacteristic
395C4×C83—22no—
396C4×C83—22no—
397C4×C83—24no—
398C4×C83—22no—
399C4×C83—22no—
400C4×C83—42no—
401C4×C83—42no—
402C4×C83C2×C4×D411yescharacteristic
403C4×C83#51811yescharacteristic
404C4×C83D4211yescharacteristic
405C4×C83#54611yescharacteristic
406Dic83—42no—
407Dic83—81no—
408Dic83—81no—
409Dic83—81no—
410#22429—831nomaximal, Sylow
411C2×C83—42no—
412C2×C83—42no—
413C2×C83—82no—
414C2×C83D4×C22⋊C411yescharacteristic
415C2×C83#289611yescharacteristic
416C2×C83#289811yescharacteristic
417C2×C83#327511yescharacteristic
418C2×C83#327711yescharacteristic
419C2×C83#332611yescharacteristic
420C2×C83#332711yescharacteristic
421C2×#548D8311yescharacteristic
422C2×#436—831no—
423C2×#417—831no—
424C2×#419—831no—
425#2352—831no—
426#1983—831no—
427#1958—831no—
428#1895—831no—
429#1894—831no—
430#1875—831no—
431#1872—831no—
432#1805—831no—
433#1788—831no—
434#1787—831no—
435C4×#103—831no—
436C83#2242911yescharacteristic, complemented, Sylow
437C22×#41C2×D8311yescharacteristic
438C23×Q8C2×D8311yescharacteristic
439C22×M16—831no—
440C22×M16—831no—
441#548—24no—
442#548Dic8318yescomplemented
443C2×#124—21no—
444C2×#124C2×D8311yescharacteristic
445C2×C22⋊Q8—21no—
446C2×C22⋊Q8C2×D8311yescharacteristic
447C2×#121—21no—
448C2×#121C2×D8311yescharacteristic
449C2×C4×Q8C2×D8311yescharacteristic
450C2×C4×D4—21no—
451C2×C4×D4C2×D8311yescharacteristic
452C2×#117—831no—
453C22×C4⋊C4—831no—
454#436—1664no—
455C2×C4⋊C8—831no—
456#419—1664no—
457#417—1664no—
458C2×#103—831no—
459C2×#103—831no—
460C2×#103—831no—
461C2×#103—831no—
462C2×#103—831no—
463C2×#103—831no—
464C2×#103—831no—
465C2×#103—831no—
466C2×#102—831no—
467C2×#102—831no—
468C2×#102—831no—
469C2×#102—831no—
470C2×C22⋊C8—831no—
471C2×C22⋊C8—831no—
472C2×C4×C8—831no—
473#388—1661no—
474#387—1661no—
475#386—1661no—
476#382—831no—
477#380—831no—
478#380—831no—
479C4×C4⋊C4—831no—
480C4×C22⋊C4—1661no—
481#340—831no—
482#340—831no—
483#340—831no—
484#340—831no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41C2×Dic8314yes—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—22no—
495C22×Q8—41no—
496C22×Q8—41no—
497C22×Q8C2×Dic8314yescomplemented
498C22×Q8C22×D8311yescharacteristic
499C22×Q8C22×D8311yescharacteristic
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C22⋊D8311yescharacteristic
503C22×D4C22×D8311yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—1661no—
507C23×C4C22×D8311yescharacteristic
508C23×C4C22×D8311yescharacteristic
509C2×M16—3321no—
510C2×M16—3321no—
511C2×M16—1662no—
512C2×M16—1662no—
513C2×M16—1662no—
514C2×M16—1662no—
515C22×C8—831no—
516C22×C8—831no—
517C22×C8—831no—
518C22×C8—831no—
519#124—28no—
520#124—22no—
521#124C2×Dic8314yescomplemented
522C22⋊Q8—22no—
523C22⋊Q8—28no—
524C22⋊Q8C2×Dic8314yes—
525#121—28no—
526#121—22no—
527#121C2×Dic8314yescomplemented
528C4×Q8—22no—
529C4×Q8C2×Dic8314yescomplemented
530C4×D4—28no—
531C4×D4C2×Dic8314yes—
532C4×D4C22⋊D8314yes—
533#117—3321no—
534#117—1662no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—3321no—
538C2×C4⋊C4—831no—
539C2×C4⋊C4—831no—
540C2×C4⋊C4—831no—
541C2×C4⋊C4—831no—
542C2×C4⋊C4—1661no—
543C2×C4⋊C4—1662no—
544C2×C4⋊C4C22⋊D8311yescharacteristic
545C2×C4⋊C4C22×D8311yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1661no—
551C2×C22⋊C4—1661no—
552C2×C22⋊C4—1661no—
553C2×C22⋊C4C22⋊D8311yescharacteristic
554C2×C22⋊C4C22⋊D8311yescharacteristic
555C2×C42—21no—
556C2×C42—1661no—
557C2×C42—1661no—
558C2×C42C22×D8311yescharacteristic
559C4⋊C8—1662no—
560#103—3321no—
561#103—3321no—
562#103—834no—
563#103—1662no—
564#103—1662no—
565#103—1662no—
566#103—1662no—
567#103—1662no—
568#102—3321no—
569#102—3321no—
570#102—1662no—
571#102—1662no—
572C22⋊C8—1662no—
573C22⋊C8—1662no—
574C4×C8—1662no—
575#95—1661no—
576#95—1661no—
577#95—1661no—
578#95—1661no—
579#95—1661no—
580C24—21no—
581C24C2×C22⋊D8311yescharacteristic
582C24C2×C22⋊D8311yescharacteristic
583#41—28no—
584#41—44no—
585#41—44no—
586#41—44no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—24no—
592C2×Q8—28no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8C22×Dic8312yes—
603C2×Q8C22×Dic8312yes—
604C2×Q8D4×D8312yes—
605C2×Q8#1305058912yes—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4C22⋊Dic8314yes—
620C2×D4C22×Dic8312yes—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—3322no—
639C22×C4—3322no—
640C22×C4—6641no—
641C22×C4—1661no—
642C22×C4—1661no—
643C22×C4—1661no—
644C22×C4—1661no—
645C22×C4C22×Dic8312yes—
646C22×C4C22×Dic8312yes—
647C22×C4C2×C22⋊D8312yes—
648C22×C4C2×C22⋊D8312yes—
649C22×C4C2×C22⋊D8311yescharacteristic
650C22×C4C2×C22⋊D8311yescharacteristic
651C22×C4C2×C22⋊D8311yescharacteristic
652C22×C4C2×C22⋊D8311yescharacteristic
653C22×C4C23×D8311yescharacteristic
654M16—3324no—
655M16—3324no—
656C2×C8—832no—
657C2×C8—1661no—
658C2×C8—1661no—
659C2×C8—1661no—
660C2×C8—1661no—
661C2×C8—1661no—
662C2×C8—1661no—
663C2×C8—1661no—
664C2×C8—1661no—
665C2×C8—1661no—
666C2×C8—1661no—
667C2×C8—1661no—
668C4⋊C4—21no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—3322no—
672C4⋊C4—832no—
673C4⋊C4—1661no—
674C4⋊C4—1661no—
675C4⋊C4—1661no—
676C4⋊C4—1661no—
677C4⋊C4—1661no—
678C4⋊C4—1661no—
679C4⋊C4—1661no—
680C4⋊C4C22⋊Dic8314yes—
681C4⋊C4C22×Dic8312yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—3322no—
687C22⋊C4—3322no—
688C22⋊C4—6641no—
689C22⋊C4C22⋊Dic8314yes—
690C22⋊C4C22⋊Dic8314yes—
691C42—24no—
692C42—3322no—
693C42—6641no—
694C42C22×Dic8312yes—
695C42C2×C22⋊D8312yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊Dic8312yes—
716C23C2×C22⋊Dic8312yes—
717C23C22×C22⋊D8311yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8D4×Dic8314yes—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4—41no—
733D4—41no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—48no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—3321no—
762C2×C4—3321no—
763C2×C4—3321no—
764C2×C4—3321no—
765C2×C4—3321no—
766C2×C4—3321no—
767C2×C4—3321no—
768C2×C4—3321no—
769C2×C4—3321no—
770C2×C4—3321no—
771C2×C4—3321no—
772C2×C4—6644no—
773C2×C4—1662no—
774C2×C4C2×C22⋊Dic8312yes—
775C2×C4C2×C22⋊Dic8312yes—
776C2×C4C2×C22⋊Dic8312yes—
777C2×C4C2×C22⋊Dic8312yes—
778C2×C4C23×Dic8311yescharacteristic
779C2×C4C2×D4×D8311yescharacteristic
780C2×C4C22×C22⋊D8311yescharacteristic
781C2×C4C2×#1305058911yescharacteristic
782C2×C4#1458183711yescharacteristic
783C2×C4#1458183711yescharacteristic
784C8—3321no—
785C8—3321no—
786C8—3321no—
787C8—1662no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22C22×C22⋊Dic8311yescharacteristic
810C22D4×C22⋊D8311yescharacteristic
811C22#1912834511yescharacteristic
812C22#1912849911yescharacteristic
813C22#1912849911yescharacteristic
814C22#1912850911yescharacteristic
815C22#1912851611yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—24no—
821C4—42no—
822C4—42no—
823C4—3322no—
824C4—6641no—
825C4—6641no—
826C4—6641no—
827C4C2×D4×Dic8311yescharacteristic
828C4#1912817611yescharacteristic
829C4D4×C22⋊D8311yescharacteristic
830C4#1912834511yescharacteristic
831C2—42no—
832C2—42no—
833C2—82no—
834C2D4×C22⋊Dic8311yescharacteristic
835C2#2491598211yescharacteristic
836C2#2491599611yescharacteristic
837C2#2491909511yescharacteristic
838C2#2491911611yescharacteristic
839C2#2491971611yescharacteristic
840C2#2491973111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutatorC2×C4×C83C23×C4
FrattiniC22×C4C23×D83
Fitting, prime radicalC2×#548×C83C2
socleC23×C83C22×D4
cosocleC22×C4×C83C24
hypercenterC2×#548D83
hypocenterC83#22429
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#19127779C2semidirect
2. C2×#19127702C2semidirect
3. C2×#19127710C2semidirect
4. #24910392C2semidirect
5. #24908396C2semidirect
6. #24908275C2semidirect
7. #24907902C2semidirect
8. #24907897C2semidirect
9. #24907786C2semidirect
10. #24907771C2semidirect
11. #24907478C2semidirect
12. #24907403C2semidirect
13. #24907398C2semidirect
14. C4×#14581716C2semidirect
54. #548×C83C4semidirect
97. #14581716D4semidirect
122. C22×Q8×C83C2×C4semidirect
135. #124×C83C2×C4semidirect
141. #121×C83C2×C4semidirect
143. C4×Q8×C83C2×C4semidirect
436. C83#22429semidirect
442. #548Dic83semidirect
497. C22×Q8C2×Dic83semidirect
521. #124C2×Dic83semidirect
527. #121C2×Dic83semidirect
529. C4×Q8C2×Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191277792
C2×#191277022
C2×#191277102
#249103922
#249083962
#249082752
#249079022
#249078972
#249077862
#249077712
#249074782
#249074032
#249073982
C4×#145817162
C2×#548×C832
#2242983