Finite Group Databasebeta

← C4×#99×D83 #35402048

Subgroups — C4×#99×D83 #35402048

Order 21248.

2242 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D83C211yesmaximal, characteristic
2C2×#99×D83C212yesmaximal
3C4×C22⋊C4×D83C212yesmaximal, complemented
4#99×Dic83C212yesmaximal, complemented
5C4×#14581706C212yesmaximal, complemented
6C4×#14581707C211yesmaximal, characteristic, complemented
7#24907250C212yesmaximal, complemented
8#342×D83C212yesmaximal, complemented
9C4×#99×C83C211yesmaximal, characteristic, complemented
10C22×D4×D83C2211yescharacteristic
11C23×C4×D83C411yescharacteristic, complemented
12C23×C4×D83C2211yescharacteristic
13C2×C4×D332C411yescharacteristic, complemented
14C2×D4×Dic83C2211yescharacteristic
15C2×#14581754C411yescharacteristic, complemented
16C2×C4×C22⋊D83C411yescharacteristic, complemented
17C2×C4×C22⋊D83C2211yescharacteristic
18C2×(C22⋊D83)⋊C4C411yescharacteristic, complemented
19C2×(C22⋊D83)⋊C4C2211yescharacteristic
20C4×D4×D83—22no—
21C4×D4×D83—22no—
22C4×D4×D83—22no—
23C4×D4×D83—22no—
24C2×C4⋊C4×D83C411yescharacteristic, complemented
25C2×C22⋊C4×D83C411yescharacteristic, complemented
26C2×C22⋊C4×D83C2214yes—
27C2×C22⋊C4×D83C2211yescharacteristic
28C2×C42×D83—22no—
29C2×C42×D83C411yescharacteristic, complemented
30C2×#14581707C2212yes—
31C2×#14581706C2214yes—
32#99×D83C4116yesdirect product factor
33C22⋊C4×Dic83C2214yescomplemented
34C4×(C2×D83)⋊C4—22no—
35C4×C22⋊Dic83C2212yescomplemented
36#19127548—22no—
37#95×D83—22no—
38#19127468C2212yescomplemented
39#19127467C2214yescomplemented
40C2×C4×D4×C83C2211yescharacteristic
41C2×#99×C83C2212yes—
42C4×C22⋊C4×C83C2212yescomplemented
43#342×C83C2212yescomplemented
44C24×D83C2×C411yescharacteristic
45C24×D83C2311yescharacteristic
46C22×D332C2×C411yescharacteristic
47C22×C22⋊D83C2×C411yescharacteristic
48C22×C22⋊D83C2311yescharacteristic
49C2×D4×D83—22no—
50C2×D4×D83—22no—
51C2×D4×D83—24no—
52C2×D4×D83C2×C418yes—
53C23×Dic83C2×C411yescharacteristic, complemented
54C23×Dic83C2311yescharacteristic
55C22×C4×D83—24no—
56C22×C4×D83—21no—
57C22×C4×D83—21no—
58C22×C4×D83—21no—
59C22×C4×D83—21no—
60C22×C4×D83—44no—
61C22×C4×D83—44no—
62C22×C4×D83C2×C411yescharacteristic
63C22×C4×D83C2×C411yescharacteristic
64C22×C4×D83C2×C411yescharacteristic
65C22×C4×D83C2×C411yescharacteristic
66C22×C4×D83C2×C411yescharacteristic
67C22×C4×D83C2×C411yescharacteristic
68C22×C4×D83C2×C411yescharacteristic
69C22×C4×D83C2×C411yescharacteristic, complemented
70C22×C4×D83C2×C411yescharacteristic, complemented
71C22×C4×D83D412yes—
72C22×C4×D83D412yes—
73C22×C4×D83D412yes—
74C22×C4×D83D412yes—
75C4×D332—22no—
76C4×D332—22no—
77D4×Dic83—22no—
78D4×Dic83—22no—
79#14581754—22no—
80#14581754—22no—
81C4×C22⋊D83—22no—
82C4×C22⋊D83—22no—
83C4×C22⋊D83—22no—
84C4×C22⋊D83—22no—
85(C22⋊D83)⋊C4—22no—
86(C22⋊D83)⋊C4—22no—
87(C22⋊D83)⋊C4—22no—
88(C22⋊D83)⋊C4—22no—
89C2×C4⋊Dic83C2×C411yescharacteristic, complemented
90C2×Dic83⋊C4C2×C411yescharacteristic, complemented
91C2×Dic83⋊C4C2×C411yescharacteristic, complemented
92C4⋊C4×D83—22no—
93C4⋊C4×D83—22no—
94C2×C22⋊Dic83C2×C411yescharacteristic, complemented
95C2×C22⋊Dic83C2311yescharacteristic
96C2×C22⋊Dic83C2314yes—
97C2×(C2×D83)⋊C4—24no—
98C2×(C2×D83)⋊C4C2×C411yescharacteristic
99C2×(C2×D83)⋊C4C2×C411yescharacteristic
100C2×(C2×D83)⋊C4C2×C411yescharacteristic, complemented
101C2×(C2×D83)⋊C4C2×C411yescharacteristic, complemented
102C22⋊C4×D83—22no—
103C22⋊C4×D83—22no—
104C22⋊C4×D83—28no—
105C22⋊C4×D83—22no—
106C22⋊C4×D83—22no—
107C22⋊C4×D83C2×C4116yescomplemented
108C2×C4×Dic83—24no—
109C2×C4×Dic83—22no—
110C2×C4×Dic83C2×C411yescharacteristic, complemented
111C2×C4×Dic83C2×C411yescharacteristic, complemented
112C2×C4×Dic83C2×C411yescharacteristic, complemented
113C42×D83—21no—
114C42×D83—21no—
115C42×D83—21no—
116C42×D83—21no—
117C42×D83—48no—
118#14581707C2×C418yescomplemented
119#14581706C2×C4116yescomplemented
120C83⋊#95—24no—
121C83⋊#95—22no—
122C22×D4×C83C2311yescharacteristic
123C23×C4×C83C2×C411yescharacteristic, complemented
124C23×C4×C83C2311yescharacteristic
125C4×D4×C83—22no—
126C4×D4×C83—22no—
127C2×C4⋊C4×C83C2×C411yescharacteristic, complemented
128C2×C22⋊C4×C83C2×C411yescharacteristic, complemented
129C2×C22⋊C4×C83C2311yescharacteristic
130C2×C22⋊C4×C83C2314yes—
131C2×C42×C83—22no—
132C2×C42×C83C2×C411yescharacteristic, complemented
133#99×C83C2×C418yescomplemented
134#95×C83—22no—
135C23×D83—21no—
136C23×D83—21no—
137C23×D83—22no—
138C23×D83—42no—
139C23×D83—42no—
140C23×D83—42no—
141C23×D83—42no—
142C23×D83C4214yescomplemented
143C23×D83C22×C411yescharacteristic
144C23×D83C22×C411yescharacteristic
145C23×D83C22×C411yescharacteristic
146C23×D83C22×C414yes—
147C23×D83C2×D412yes—
148C23×D83C2×D412yes—
149C23×D83#4114yes—
150C2×D332—22no—
151C2×D332—22no—
152C2×D332C4214yescomplemented
153C2×C22⋊D83—22no—
154C2×C22⋊D83—22no—
155C2×C22⋊D83—22no—
156C2×C22⋊D83—22no—
157C2×C22⋊D83C4214yescomplemented
158C2×C22⋊D83C22×C414yes—
159D4×D83—216no—
160D4×D83—216no—
161C22×Dic83—24no—
162C22×Dic83—21no—
163C22×Dic83—21no—
164C22×Dic83—42no—
165C22×Dic83—42no—
166C22×Dic83C22×C411yescharacteristic
167C22×Dic83C22×C411yescharacteristic
168C22×Dic83C22×C411yescharacteristic
169C22×Dic83C22×C411yescharacteristic
170C22×Dic83C22×C411yescharacteristic
171C22×Dic83C2×D412yes—
172C22×Dic83C2×D412yes—
173C2×C4×D83—21no—
174C2×C4×D83—21no—
175C2×C4×D83—22no—
176C2×C4×D83—24no—
177C2×C4×D83—28no—
178C2×C4×D83—21no—
179C2×C4×D83—21no—
180C2×C4×D83—21no—
181C2×C4×D83—21no—
182C2×C4×D83—216no—
183C2×C4×D83—21no—
184C2×C4×D83—21no—
185C2×C4×D83—21no—
186C2×C4×D83—21no—
187C2×C4×D83—42no—
188C2×C4×D83—44no—
189C2×C4×D83—42no—
190C2×C4×D83—44no—
191C2×C4×D83—42no—
192C2×C4×D83—44no—
193C2×C4×D83—44no—
194C2×C4×D83—44no—
195C2×C4×D83—44no—
196C2×C4×D83—48no—
197C2×C4×D83—48no—
198C2×C4×D83—44no—
199C2×C4×D83—42no—
200C2×C4×D83—42no—
201C2×C4×D83—42no—
202C2×C4×D83—42no—
203C2×C4×D83C4214yescomplemented
204C2×C4×D83C22⋊C411yescharacteristic
205C2×C4×D83C22⋊C411yescharacteristic
206C2×C4×D83C22⋊C411yescharacteristic
207C2×C4×D83C22⋊C412yes—
208C2×C4×D83C22⋊C412yes—
209C2×C4×D83C22⋊C412yes—
210C2×C4×D83C22⋊C412yes—
211C2×C4×D83C22⋊C412yes—
212C2×C4×D83C22⋊C412yes—
213C2×C4×D83C22⋊C411yescharacteristic
214C4⋊Dic83—22no—
215Dic83⋊C4—22no—
216Dic83⋊C4—22no—
217C22⋊Dic83—22no—
218C22⋊Dic83—24no—
219C22⋊Dic83—22no—
220C22⋊Dic83C22×C418yescomplemented
221(C2×D83)⋊C4—22no—
222(C2×D83)⋊C4—22no—
223(C2×D83)⋊C4—216no—
224(C2×D83)⋊C4—22no—
225(C2×D83)⋊C4—22no—
226C4×Dic83—21no—
227C4×Dic83—21no—
228C4×Dic83—21no—
229C4×Dic83—21no—
230C4×Dic83—21no—
231C4×Dic83—21no—
232C4×Dic83—48no—
233C4×Dic83—44no—
234C24×C83C22×C411yescharacteristic
235C24×C83C2411yescharacteristic
236C2×D4×C83—22no—
237C2×D4×C83—22no—
238C2×D4×C83C22×C414yes—
239C22×C4×C83—24no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—42no—
243C22×C4×C83—42no—
244C22×C4×C83C22×C411yescharacteristic
245C22×C4×C83C22×C411yescharacteristic
246C22×C4×C83C22×C411yescharacteristic
247C22×C4×C83C22×C411yescharacteristic
248C22×C4×C83C22×C411yescharacteristic
249C22×C4×C83C2×D412yes—
250C22×C4×C83C2×D412yes—
251C4⋊C4×C83—22no—
252C22⋊C4×C83—22no—
253C22⋊C4×C83—24no—
254C22⋊C4×C83—22no—
255C22⋊C4×C83C22×C418yescomplemented
256C42×C83—21no—
257C42×C83—21no—
258C42×C83—44no—
259C23×C83—21no—
260C23×C83—21no—
261C23×C83—41no—
262C23×C83—41no—
263C23×C83—41no—
264C23×C83—41no—
265C23×C83C2×C4212yescomplemented
266C23×C83C23×C411yescharacteristic
267C23×C83C23×C412yes—
268C23×C83C22×D412yes—
269C23×C83C2×#4112yes—
270C22×D83—24no—
271C22×D83—22no—
272C22×D83—24no—
273C22×D83—22no—
274C22×D83—21no—
275C22×D83—21no—
276C22×D83—24no—
277C22×D83—24no—
278C22×D83—48no—
279C22×D83—48no—
280C22×D83—41no—
281C22×D83—42no—
282C22×D83—41no—
283C22×D83—42no—
284C22×D83—42no—
285C22×D83—42no—
286C22×D83—48no—
287C22×D83—48no—
288C22×D83—42no—
289C22×D83—42no—
290C22×D83—41no—
291C22×D83—41no—
292C22×D83C2×C4212yes—
293C22×D83C2×C4212yes—
294C22×D83C2×C4212yescomplemented
295C22×D83C2×C22⋊C412yes—
296C22×D83C2×C22⋊C411yescharacteristic
297C22×D83C2×C22⋊C411yescharacteristic
298C22×D83#11712yes—
299C22×D83#11712yes—
300C22×D83C4×D418yes—
301C22×D83C4×D418yes—
302D4×C83—28no—
303C2×C4×C83—21no—
304C2×C4×C83—21no—
305C2×C4×C83—24no—
306C2×C4×C83—22no—
307C2×C4×C83—21no—
308C2×C4×C83—21no—
309C2×C4×C83—28no—
310C2×C4×C83—41no—
311C2×C4×C83—42no—
312C2×C4×C83—42no—
313C2×C4×C83—44no—
314C2×C4×C83—44no—
315C2×C4×C83—42no—
316C2×C4×C83—41no—
317C2×C4×C83—41no—
318C2×C4×C83C2×C4212yescomplemented
319C2×C4×C83C2×C22⋊C411yescharacteristic
320C2×C4×C83C2×C22⋊C412yes—
321C2×C4×C83C2×C22⋊C411yescharacteristic
322C22⋊D83—28no—
323C22⋊D83—28no—
324C2×Dic83—21no—
325C2×Dic83—21no—
326C2×Dic83—24no—
327C2×Dic83—22no—
328C2×Dic83—21no—
329C2×Dic83—21no—
330C2×Dic83—28no—
331C2×Dic83—41no—
332C2×Dic83—42no—
333C2×Dic83—42no—
334C2×Dic83—44no—
335C2×Dic83—44no—
336C2×Dic83—42no—
337C2×Dic83—41no—
338C2×Dic83—41no—
339C2×Dic83C2×C4212yescomplemented
340C2×Dic83C2×C22⋊C411yescharacteristic
341C2×Dic83C2×C22⋊C412yes—
342C2×Dic83C2×C22⋊C411yescharacteristic
343D332—28no—
344C4×D83—24no—
345C4×D83—24no—
346C4×D83—22no—
347C4×D83—24no—
348C4×D83—22no—
349C4×D83—24no—
350C4×D83—22no—
351C4×D83—24no—
352C4×D83—42no—
353C4×D83—42no—
354C4×D83—42no—
355C4×D83—42no—
356C4×D83—42no—
357C4×D83—432no—
358C4×D83—42no—
359C4×D83—42no—
360C4×D83—42no—
361C4×D83—42no—
362C4×D83—42no—
363C4×D83—42no—
364C4×D83#9914yesdirect product factor
365C22×C83—22no—
366C22×C83—21no—
367C22×C83—22no—
368C22×C83—21no—
369C22×C83—22no—
370C22×C83—42no—
371C22×C83—42no—
372C22×C83—42no—
373C22×C83—42no—
374C22×C83—41no—
375C22×C83—41no—
376C22×C83C22×C4211yescharacteristic
377C22×C83C22×C22⋊C411yescharacteristic
378C22×C83C2×#11711yescharacteristic
379C22×C83C2×C4×D414yes—
380C2×D83—21no—
381C2×D83—22no—
382C2×D83—21no—
383C2×D83—22no—
384C2×D83—216no—
385C2×D83—24no—
386C2×D83—24no—
387C2×D83—22no—
388C2×D83—42no—
389C2×D83—42no—
390C2×D83—48no—
391C2×D83—48no—
392C2×D83—42no—
393C2×D83—41no—
394C2×D83—41no—
395C2×D83—48no—
396C2×D83—42no—
397C2×D83C4×C22⋊C412yes—
398C2×D83C4×C22⋊C414yes—
399C2×D83C4×C22⋊C412yes—
400C2×D83C2×#9912yes—
401C2×D83#41012yes—
402C4×C83—21no—
403C4×C83—22no—
404C4×C83—22no—
405C4×C83—48no—
406C4×C83—41no—
407C4×C83—41no—
408C4×C83C2×#9912yescomplemented
409Dic83—21no—
410Dic83—22no—
411Dic83—22no—
412Dic83—48no—
413Dic83—41no—
414Dic83—41no—
415Dic83C2×#9912yescomplemented
416C2×C4×#99—831nomaximal, Sylow
417C2×C83—24no—
418C2×C83—21no—
419C2×C83—21no—
420C2×C83—42no—
421C2×C83C2×C4×C22⋊C411yescharacteristic
422C2×C83C22×#9911yescharacteristic
423C2×C83C2×#41011yescharacteristic
424D83—22no—
425D83—24no—
426D83—42no—
427D83C4×#9914yesdirect product factor
428C22×C4×D4—831no—
429C22×#99—832no—
430C2×C4×C22⋊C4—832no—
431C4×#99—832no—
432C4×#99—832no—
433C4×#99—832no—
434C4×#99—831no—
435C4×#99D8311yescharacteristic, direct product factor
436C2×#342—832no—
437C83C2×C4×#9911yescharacteristic, complemented, Sylow
438C23×D4—831no—
439C24×C4—831no—
440C24×C4—831no—
441C2×C4×D4—831no—
442C2×C4×D4—831no—
443C2×C4×D4—831no—
444C2×C4×D4—831no—
445C2×C4×D4—831no—
446C2×C4×D4—831no—
447C2×C4×D4—831no—
448C2×C4×D4—1662no—
449C2×C4×D4—1662no—
450C2×C4×D4—1662no—
451C2×C4×D4—1662no—
452C2×C4×D4C2×D8311yescharacteristic
453C22×C4⋊C4—831no—
454C22×C22⋊C4—834no—
455C22×C22⋊C4—831no—
456C22×C22⋊C4—831no—
457C22×C42—831no—
458C22×C42—1662no—
459C2×#99—832no—
460C2×#99—834no—
461C2×#99—8316no—
462C2×#99C2×D8312yes—
463C4×C22⋊C4—832no—
464C4×C22⋊C4—834no—
465C4×C22⋊C4—1662no—
466C4×C22⋊C4—1662no—
467C4×C22⋊C4C2×D8312yescomplemented
468C2×#95—1662no—
469#342—834no—
470#342—832no—
471#342C2×D8312yescomplemented
472C25—831no—
473C25—831no—
474C22×D4—831no—
475C22×D4—831no—
476C22×D4—838no—
477C22×D4—831no—
478C22×D4—1662no—
479C22×D4—1662no—
480C22×D4—1664no—
481C22×D4C22×D8311yescharacteristic
482C23×C4—3324no—
483C23×C4—3324no—
484C23×C4—831no—
485C23×C4—831no—
486C23×C4—831no—
487C23×C4—831no—
488C23×C4—832no—
489C23×C4—832no—
490C23×C4—832no—
491C23×C4—831no—
492C23×C4—831no—
493C23×C4—831no—
494C23×C4—831no—
495C23×C4—831no—
496C23×C4—831no—
497C23×C4—831no—
498C23×C4—832no—
499C23×C4—1661no—
500C23×C4—1661no—
501C23×C4—1661no—
502C23×C4—1661no—
503C23×C4—1664no—
504C23×C4C4×D8311yescharacteristic, complemented
505C23×C4C22×D8311yescharacteristic
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—1662no—
509C4×D4—1662no—
510C4×D4—1662no—
511C4×D4—1662no—
512C4×D4—1662no—
513C4×D4—1662no—
514C4×D4—1662no—
515C4×D4—1662no—
516C4×D4—1662no—
517C4×D4—1662no—
518C4×D4—1662no—
519C4×D4—1662no—
520C4×D4—1662no—
521C4×D4—1662no—
522C2×C4⋊C4—831no—
523C2×C4⋊C4—831no—
524C2×C4⋊C4—831no—
525C2×C4⋊C4—1662no—
526C2×C4⋊C4—1662no—
527C2×C4⋊C4C4×D8311yescharacteristic, complemented
528C2×C22⋊C4—834no—
529C2×C22⋊C4—8316no—
530C2×C22⋊C4—831no—
531C2×C22⋊C4—831no—
532C2×C22⋊C4—831no—
533C2×C22⋊C4—831no—
534C2×C22⋊C4—831no—
535C2×C22⋊C4—831no—
536C2×C22⋊C4—1662no—
537C2×C22⋊C4—1662no—
538C2×C22⋊C4—1662no—
539C2×C22⋊C4—1662no—
540C2×C22⋊C4—1668no—
541C2×C22⋊C4—1664no—
542C2×C22⋊C4C4×D8311yescharacteristic, complemented
543C2×C22⋊C4C22×D8311yescharacteristic
544C2×C22⋊C4C22×D8314yes—
545C2×C42—22no—
546C2×C42—3328no—
547C2×C42—831no—
548C2×C42—831no—
549C2×C42—831no—
550C2×C42—1661no—
551C2×C42—1661no—
552C2×C42—1661no—
553C2×C42—1661no—
554C2×C42—1664no—
555C2×C42—1662no—
556C2×C42C4×D8311yescharacteristic, complemented
557#99—838no—
558#99—8316no—
559#99C4×D8318yesdirect product factor
560#95—22no—
561#95—1664no—
562#95—1662no—
563C24—3322no—
564C24—3322no—
565C24—3322no—
566C24—3322no—
567C24—834no—
568C24—831no—
569C24—832no—
570C24—834no—
571C24—831no—
572C24—834no—
573C24—831no—
574C24—832no—
575C24—1661no—
576C24—1661no—
577C24—1662no—
578C24C2×C4×D8311yescharacteristic
579C24C23×D8311yescharacteristic
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—834no—
583C2×D4—834no—
584C2×D4—834no—
585C2×D4—1662no—
586C2×D4—1662no—
587C2×D4—16616no—
588C2×D4—16616no—
589C2×D4—1662no—
590C2×D4—1662no—
591C2×D4—1662no—
592C2×D4—1662no—
593C2×D4C2×C4×D8314yes—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—3322no—
600C22×C4—3324no—
601C22×C4—3322no—
602C22×C4—3328no—
603C22×C4—3328no—
604C22×C4—3324no—
605C22×C4—3324no—
606C22×C4—3324no—
607C22×C4—3324no—
608C22×C4—3322no—
609C22×C4—3322no—
610C22×C4—3322no—
611C22×C4—3324no—
612C22×C4—3322no—
613C22×C4—3322no—
614C22×C4—3324no—
615C22×C4—3322no—
616C22×C4—3322no—
617C22×C4—831no—
618C22×C4—832no—
619C22×C4—832no—
620C22×C4—832no—
621C22×C4—832no—
622C22×C4—831no—
623C22×C4—831no—
624C22×C4—831no—
625C22×C4—831no—
626C22×C4—831no—
627C22×C4—832no—
628C22×C4—834no—
629C22×C4—831no—
630C22×C4—831no—
631C22×C4—832no—
632C22×C4—832no—
633C22×C4—831no—
634C22×C4—832no—
635C22×C4—1661no—
636C22×C4—1661no—
637C22×C4—1661no—
638C22×C4—1661no—
639C22×C4—16616no—
640C22×C4—1661no—
641C22×C4—1661no—
642C22×C4—1668no—
643C22×C4—1664no—
644C22×C4—1661no—
645C22×C4—1661no—
646C22×C4—1662no—
647C22×C4—1661no—
648C22×C4—1661no—
649C22×C4—1664no—
650C22×C4—1661no—
651C22×C4—1661no—
652C22×C4C2×C4×D8311yescharacteristic
653C22×C4C2×C4×D8311yescharacteristic
654C22×C4C2×C4×D8311yescharacteristic
655C22×C4C2×C4×D8311yescharacteristic
656C22×C4C2×C4×D8311yescharacteristic
657C22×C4D4×D8312yes—
658C22×C4D4×D8312yes—
659C4⋊C4—22no—
660C4⋊C4—1662no—
661C4⋊C4—1662no—
662C4⋊C4—1662no—
663C22⋊C4—22no—
664C22⋊C4—24no—
665C22⋊C4—22no—
666C22⋊C4—838no—
667C22⋊C4—1662no—
668C22⋊C4—1662no—
669C22⋊C4—1662no—
670C22⋊C4—16616no—
671C22⋊C4—1662no—
672C22⋊C4—1662no—
673C22⋊C4—1664no—
674C22⋊C4—1662no—
675C22⋊C4C2×C4×D8318yescomplemented
676C42—21no—
677C42—21no—
678C42—44no—
679C42—3324no—
680C42—3328no—
681C42—1661no—
682C42—1661no—
683C42—1661no—
684C42—1661no—
685C42—1661no—
686C42—1661no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—3321no—
694C23—3321no—
695C23—3322no—
696C23—3321no—
697C23—3322no—
698C23—3321no—
699C23—3322no—
700C23—3322no—
701C23—3322no—
702C23—3328no—
703C23—3322no—
704C23—3328no—
705C23—3328no—
706C23—3328no—
707C23—832no—
708C23—832no—
709C23—838no—
710C23—832no—
711C23—831no—
712C23—832no—
713C23—832no—
714C23—831no—
715C23—832no—
716C23—838no—
717C23—1664no—
718C23—1664no—
719C23—1664no—
720C23—1662no—
721C23—1664no—
722C23—1662no—
723C23—1661no—
724C23—1661no—
725C23C42×D8312yescomplemented
726C23C22×C4×D8311yescharacteristic
727C23C22×C4×D8312yes—
728C23C2×D4×D8312yes—
729C23#41×D8312yes—
730D4—28no—
731D4—1668no—
732D4—1668no—
733D4—1668no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—28no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—3322no—
750C2×C4—3322no—
751C2×C4—3322no—
752C2×C4—3322no—
753C2×C4—3322no—
754C2×C4—3322no—
755C2×C4—3322no—
756C2×C4—33232no—
757C2×C4—3322no—
758C2×C4—3322no—
759C2×C4—3322no—
760C2×C4—3324no—
761C2×C4—3324no—
762C2×C4—3322no—
763C2×C4—3322no—
764C2×C4—3322no—
765C2×C4—3321no—
766C2×C4—3321no—
767C2×C4—3322no—
768C2×C4—3321no—
769C2×C4—831no—
770C2×C4—834no—
771C2×C4—832no—
772C2×C4—831no—
773C2×C4—832no—
774C2×C4—1662no—
775C2×C4—1664no—
776C2×C4—1662no—
777C2×C4—1664no—
778C2×C4—1664no—
779C2×C4—1664no—
780C2×C4—1661no—
781C2×C4—1661no—
782C2×C4—1668no—
783C2×C4—1664no—
784C2×C4—1662no—
785C2×C4—1661no—
786C2×C4—1661no—
787C2×C4—1662no—
788C2×C4—1664no—
789C2×C4C42×D8312yescomplemented
790C2×C4C22⋊C4×D8311yescharacteristic
791C2×C4C22⋊C4×D8312yes—
792C2×C4C22⋊C4×D8311yescharacteristic
793C22—22no—
794C22—21no—
795C22—22no—
796C22—21no—
797C22—22no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—3322no—
805C22—3322no—
806C22—3328no—
807C22—3322no—
808C22—3322no—
809C22—3328no—
810C22—3328no—
811C22—3321no—
812C22—3321no—
813C22—832no—
814C22—832no—
815C22—832no—
816C22—832no—
817C22—834no—
818C22—16616no—
819C22—1664no—
820C22—1664no—
821C22—1662no—
822C22—1661no—
823C22—1662no—
824C22—1661no—
825C22—1662no—
826C22C2×C42×D8311yescharacteristic
827C22C2×C22⋊C4×D8311yescharacteristic
828C22#117×D8311yescharacteristic
829C22C4×D4×D8314yes—
830C4—21no—
831C4—22no—
832C4—22no—
833C4—48no—
834C4—41no—
835C4—41no—
836C4—3328no—
837C4—3321no—
838C4—3321no—
839C4—832no—
840C4—1661no—
841C4—1662no—
842C4—1662no—
843C4#99×D8312yesdirect product factor
844C2—24no—
845C2—21no—
846C2—21no—
847C2—42no—
848C2—3322no—
849C2—834no—
850C2—1662no—
851C2—1664no—
852C2C4×C22⋊C4×D8311yescharacteristic
853C2C2×#99×D8311yescharacteristic
854C2#410×D8311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D83
commutatorC22×C83C22×C42
FrattiniC24C23×D83
FittingC4×#99×C83C2
socleC22×C83C22×C22⋊C4
prime radicalC22×D4×D83C22
cosocleC24×C83C24
hypercenterC4×#99D83
hypocenterC83C2×C4×#99
LCSG ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. C4×C22⋊C4×D83C2semidirect
4. #99×Dic83C2semidirect
5. C4×#14581706C2semidirect
6. C4×#14581707C2semidirect
7. #24907250C2semidirect
8. #342×D83C2semidirect
9. C4×#99×C83C2semidirect
11. C23×C4×D83C4semidirect
13. C2×C4×D332C4semidirect
15. C2×#14581754C4semidirect
16. C2×C4×C22⋊D83C4semidirect
18. C2×(C22⋊D83)⋊C4C4semidirect
24. C2×C4⋊C4×D83C4semidirect
25. C2×C22⋊C4×D83C4semidirect
29. C2×C42×D83C4semidirect
32. #99×D83C4direct (N × H)
33. C22⋊C4×Dic83C22semidirect
35. C4×C22⋊Dic83C22semidirect
38. #19127468C22semidirect
39. #19127467C22semidirect
42. C4×C22⋊C4×C83C22semidirect
43. #342×C83C22semidirect
53. C23×Dic83C2×C4semidirect
69. C22×C4×D83C2×C4semidirect
70. C22×C4×D83C2×C4semidirect
89. C2×C4⋊Dic83C2×C4semidirect
90. C2×Dic83⋊C4C2×C4semidirect
91. C2×Dic83⋊C4C2×C4semidirect
94. C2×C22⋊Dic83C2×C4semidirect
100. C2×(C2×D83)⋊C4C2×C4semidirect
101. C2×(C2×D83)⋊C4C2×C4semidirect
107. C22⋊C4×D83C2×C4semidirect
110. C2×C4×Dic83C2×C4semidirect
111. C2×C4×Dic83C2×C4semidirect
112. C2×C4×Dic83C2×C4semidirect
118. #14581707C2×C4semidirect
119. #14581706C2×C4semidirect
123. C23×C4×C83C2×C4semidirect
127. C2×C4⋊C4×C83C2×C4semidirect
128. C2×C22⋊C4×C83C2×C4semidirect
132. C2×C42×C83C2×C4semidirect
133. #99×C83C2×C4semidirect
142. C23×D83C42semidirect
152. C2×D332C42semidirect
157. C2×C22⋊D83C42semidirect
203. C2×C4×D83C42semidirect
220. C22⋊Dic83C22×C4semidirect
255. C22⋊C4×C83C22×C4semidirect
265. C23×C83C2×C42semidirect
294. C22×D83C2×C42semidirect
318. C2×C4×C83C2×C42semidirect
339. C2×Dic83C2×C42semidirect
364. C4×D83#99direct (N × H)
408. C4×C83C2×#99semidirect
415. Dic83C2×#99semidirect
427. D83C4×#99direct (N × H)
435. C4×#99D83direct (N × H)
437. C83C2×C4×#99semidirect
467. C4×C22⋊C4C2×D83semidirect
471. #342C2×D83semidirect
504. C23×C4C4×D83semidirect
527. C2×C4⋊C4C4×D83semidirect
542. C2×C22⋊C4C4×D83semidirect
556. C2×C42C4×D83semidirect
559. #99C4×D83direct (N × H)
675. C22⋊C4C2×C4×D83semidirect
725. C23C42×D83semidirect
789. C2×C4C42×D83semidirect
843. C4#99×D83direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D832
C2×#99×D832
C4×C22⋊C4×D832
#99×Dic832
C4×#145817062
C4×#145817072
#249072502
#342×D832
C4×#99×C832
C2×C4×#9983