Finite Group Databasebeta

← C2×C83×#3306 #35288949

Subgroups — C2×C83×#3306 #35288949

Order 21248.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C83C211yesmaximal, characteristic, complemented
2C2×#546×C83C211yesmaximal, characteristic, complemented
3C83×#3306C2116yesmaximal, direct product factor
4C2×#489×C83C211yesmaximal, characteristic, complemented
5C2×#481×C83C211yesmaximal, characteristic, complemented
6C2×#483×C83C211yesmaximal, characteristic, complemented
7C2×#476×C83C211yesmaximal, characteristic, complemented
8C2×#469×C83C211yesmaximal, characteristic, complemented
9C2×#465×C83C211yesmaximal, characteristic, complemented
10C2×#463×C83C211yesmaximal, characteristic, complemented
11C2×#449×C83C211yesmaximal, characteristic, complemented
12C2×#447×C83C211yesmaximal, characteristic, complemented
13C2×#442×C83C211yesmaximal, characteristic, complemented
14C2×#435×C83C211yesmaximal, characteristic, complemented
15C2×#417×C83C211yesmaximal, characteristic, complemented
16C22×#102×C83C211yesmaximal, characteristic, complemented
17C22×#41×C83—21no—
18C22×#41×C83C2211yescharacteristic
19C23×D4×C83C2211yescharacteristic
20C22×SD16×C83C2211yescharacteristic, complemented
21C22×D8×C83C2211yescharacteristic
22C22×D8×C83C2211yescharacteristic
23C22×M16×C83C2211yescharacteristic, complemented
24C23×C8×C83C2211yescharacteristic
25#547×C83—24no—
26#547×C83C2218yescomplemented
27#546×C83—24no—
28#546×C83C2218yescomplemented
29C2×C4⋊Q8×C83C2211yescharacteristic, complemented
30C2×#124×C83C2211yescharacteristic
31C2×#123×C83—21no—
32C2×#123×C83—21no—
33C2×#123×C83—21no—
34C2×C22⋊Q8×C83—21no—
35C2×C22⋊Q8×C83C2211yescharacteristic
36C2×#121×C83—21no—
37C2×#121×C83C2211yescharacteristic
38C2×#121×C83C2211yescharacteristic
39C2×#121×C83C2211yescharacteristic, complemented
40C2×#120×C83—21no—
41C2×C4×D4×C83C2211yescharacteristic
42C2×C4×D4×C83C2211yescharacteristic
43C2×C4×D4×C83C2211yescharacteristic, complemented
44C22×C4⋊C4×C83C2211yescharacteristic
45C22×C4⋊C4×C83C2211yescharacteristic, complemented
46C22×C22⋊C4×C83—21no—
47#489×C83C2218yescomplemented
48#483×C83C2218yescomplemented
49#481×C83C2218yescomplemented
50#476×C83C2218yescomplemented
51#469×C83C2218yescomplemented
52#465×C83C2218yescomplemented
53#463×C83C2218yescomplemented
54#449×C83C2218yescomplemented
55#447×C83C2218yescomplemented
56#442×C83C2218yescomplemented
57#435×C83C2218yescomplemented
58C2×#106×C83C2211yescharacteristic, complemented
59C2×#106×C83C2211yescharacteristic, complemented
60C2×#106×C83C2211yescharacteristic, complemented
61C2×C4⋊C8×C83C2211yescharacteristic, complemented
62#417×C83C2218yescomplemented
63C2×#103×C83C2211yescharacteristic, complemented
64C2×#103×C83C2211yescharacteristic, complemented
65C2×#103×C83C2211yescharacteristic, complemented
66C2×#102×C83C2211yescharacteristic
67C2×#102×C83C2211yescharacteristic
68C2×#102×C83C2211yescharacteristic
69C2×#102×C83C2211yescharacteristic
70C2×#102×C83C2211yescharacteristic
71C2×#102×C83C2211yescharacteristic
72C2×#102×C83C2218yescomplemented
73C2×#102×C83C2211yescharacteristic, complemented
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×C22⋊C8×C83C2211yescharacteristic, complemented
76C2×#97×C83C2211yescharacteristic, complemented
77C25×C83—21no—
78C2×#41×C83—28no—
79C2×#41×C83—22no—
80C2×#41×C83—24no—
81C2×#41×C83—42no—
82C2×#41×C83—48no—
83C2×#41×C83C2314yes—
84C22×Q8×C83—21no—
85C22×Q8×C83C2311yescharacteristic
86C22×D4×C83—24no—
87C22×D4×C83—21no—
88C22×D4×C83—21no—
89C22×D4×C83—21no—
90C22×D4×C83—21no—
91C22×D4×C83—21no—
92C22×D4×C83—22no—
93C22×D4×C83—42no—
94C22×D4×C83D411yescharacteristic
95C22×D4×C83C2311yescharacteristic
96C22×D4×C83C2311yescharacteristic
97C22×D4×C83C2314yes—
98C22×D4×C83C2311yescharacteristic
99C23×C4×C83—21no—
100C23×C4×C83—21no—
101C23×C4×C83—21no—
102C23×C4×C83—21no—
103C23×C4×C83—21no—
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2311yescharacteristic
106C2×SD16×C83—42no—
107C2×SD16×C83C2314yescomplemented
108C2×D8×C83—24no—
109C2×D8×C83—42no—
110C2×D8×C83C2314yes—
111C2×D8×C83C2314yes—
112C2×M16×C83—42no—
113C2×M16×C83C2314yescomplemented
114C22×C8×C83—42no—
115C22×C8×C83C2311yescharacteristic
116C22×C8×C83C2311yescharacteristic
117C22×C8×C83C2311yescharacteristic
118C22×C8×C83C2311yescharacteristic
119C22×C8×C83C2314yes—
120C4⋊Q8×C83—22no—
121C4⋊Q8×C83C2314yescomplemented
122#124×C83—22no—
123#124×C83C2314yes—
124#123×C83—28no—
125#123×C83—28no—
126#123×C83—28no—
127C22⋊Q8×C83—22no—
128C22⋊Q8×C83—28no—
129C22⋊Q8×C83C2314yes—
130#121×C83—22no—
131#121×C83—22no—
132#121×C83—22no—
133#121×C83—28no—
134#121×C83C2314yes—
135#121×C83C2314yes—
136#121×C83C2314yescomplemented
137#120×C83—28no—
138C4×D4×C83—22no—
139C4×D4×C83—22no—
140C4×D4×C83D414yes—
141C4×D4×C83C2314yes—
142C4×D4×C83C2314yes—
143C4×D4×C83C2314yescomplemented
144C2×C4⋊C4×C83—21no—
145C2×C4⋊C4×C83—22no—
146C2×C4⋊C4×C83—21no—
147C2×C4⋊C4×C83—22no—
148C2×C4⋊C4×C83—21no—
149C2×C4⋊C4×C83—21no—
150C2×C4⋊C4×C83D411yescharacteristic
151C2×C4⋊C4×C83C2314yes—
152C2×C4⋊C4×C83C2311yescharacteristic
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2311yescharacteristic
156C2×C4⋊C4×C83C2314yescomplemented
157C2×C22⋊C4×C83—21no—
158C2×C22⋊C4×C83—21no—
159C2×C22⋊C4×C83—21no—
160C2×C22⋊C4×C83—21no—
161C2×C22⋊C4×C83—21no—
162C2×C22⋊C4×C83—21no—
163C2×C22⋊C4×C83—21no—
164C2×C22⋊C4×C83—21no—
165C2×C22⋊C4×C83—28no—
166C2×C22⋊C4×C83D411yescharacteristic
167C2×C22⋊C4×C83D411yescharacteristic
168C2×C42×C83C2311yescharacteristic
169#106×C83C2314yescomplemented
170#106×C83C2314yescomplemented
171#106×C83C2314yescomplemented
172C4⋊C8×C83C2314yescomplemented
173#103×C83C2314yescomplemented
174#103×C83C2314yescomplemented
175#103×C83C2314yescomplemented
176#102×C83C2314yes—
177#102×C83C2314yes—
178#102×C83C2314yes—
179#102×C83C2314yes—
180#102×C83C2314yes—
181#102×C83C2314yes—
182#102×C83C2314yescomplemented
183C22⋊C8×C83C2314yes—
184C22⋊C8×C83C2314yescomplemented
185#97×C83C2314yescomplemented
186C24×C83—21no—
187C24×C83—21no—
188C24×C83—21no—
189C24×C83—24no—
190C24×C83—44no—
191C24×C83—44no—
192C24×C83—82no—
193C24×C83C2×D411yescharacteristic
194C24×C83C2×D411yescharacteristic
195#41×C83—28no—
196#41×C83—44no—
197#41×C83—48no—
198#41×C83—432no—
199C2×Q8×C83—21no—
200C2×Q8×C83—24no—
201C2×Q8×C83—22no—
202C2×Q8×C83—22no—
203C2×Q8×C83—44no—
204C2×Q8×C83C2412yes—
205C2×D4×C83—24no—
206C2×D4×C83—28no—
207C2×D4×C83—24no—
208C2×D4×C83—24no—
209C2×D4×C83—24no—
210C2×D4×C83—24no—
211C2×D4×C83—21no—
212C2×D4×C83—21no—
213C2×D4×C83—24no—
214C2×D4×C83—21no—
215C2×D4×C83—22no—
216C2×D4×C83—22no—
217C2×D4×C83—22no—
218C2×D4×C83—22no—
219C2×D4×C83—22no—
220C2×D4×C83—44no—
221C2×D4×C83—48no—
222C2×D4×C83—44no—
223C2×D4×C83—44no—
224C2×D4×C83—44no—
225C2×D4×C83—44no—
226C2×D4×C83—82no—
227C2×D4×C83C2×D414yes—
228C2×D4×C83#4114yescomplemented
229C2×D4×C83C2412yes—
230C2×D4×C83C2412yes—
231C2×D4×C83C2412yes—
232C22×C4×C83—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—24no—
237C22×C4×C83—24no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—24no—
244C22×C4×C83—24no—
245C22×C4×C83—24no—
246C22×C4×C83—44no—
247C22×C4×C83—44no—
248C22×C4×C83—44no—
249C22×C4×C83—44no—
250C22×C4×C83—82no—
251C22×C4×C83C2×D412yes—
252C22×C4×C83C2×D412yes—
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2412yes—
258C22×C4×C83C2412yes—
259C22×C4×C83C2411yescharacteristic
260SD16×C83—44no—
261D8×C83—28no—
262D8×C83—44no—
263M16×C83—44no—
264C2×C8×C83—22no—
265C2×C8×C83—22no—
266C2×C8×C83—22no—
267C2×C8×C83—22no—
268C2×C8×C83—44no—
269C2×C8×C83C2412yes—
270C2×C8×C83C2412yes—
271C2×C8×C83C2412yes—
272C2×C8×C83C2412yes—
273C4⋊C4×C83—21no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—24no—
277C4⋊C4×C83—24no—
278C4⋊C4×C83—24no—
279C4⋊C4×C83—24no—
280C4⋊C4×C83—21no—
281C4⋊C4×C83C2×D414yes—
282C4⋊C4×C83C2412yes—
283C4⋊C4×C83C2412yes—
284C4⋊C4×C83C2412yes—
285C4⋊C4×C83C2412yes—
286C22⋊C4×C83—24no—
287C22⋊C4×C83—24no—
288C22⋊C4×C83—24no—
289C22⋊C4×C83—24no—
290C22⋊C4×C83—24no—
291C22⋊C4×C83—24no—
292C22⋊C4×C83—24no—
293C22⋊C4×C83—24no—
294C22⋊C4×C83C2×D414yes—
295C22⋊C4×C83C2×D414yes—
296C42×C83C2×D412yes—
297C42×C83C2412yes—
298C23×C83—22no—
299C23×C83—22no—
300C23×C83—22no—
301C23×C83—24no—
302C23×C83—22no—
303C23×C83—22no—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—48no—
308C23×C83—42no—
309C23×C83—42no—
310C23×C83—42no—
311C23×C83—42no—
312C23×C83—42no—
313C23×C83—48no—
314C23×C83—42no—
315C23×C83—42no—
316C23×C83—42no—
317C23×C83—84no—
318C23×C83—816no—
319C23×C83AGL(1,ℤ/8)14yes—
320C23×C83C22×D412yes—
321C23×C83C22×D412yes—
322C23×C83C22×D411yescharacteristic
323Q8×C83—22no—
324Q8×C83—22no—
325Q8×C83—48no—
326Q8×C83—42no—
327D4×C83—28no—
328D4×C83—24no—
329D4×C83—22no—
330D4×C83—22no—
331D4×C83—22no—
332D4×C83—22no—
333D4×C83—22no—
334D4×C83—48no—
335D4×C83—48no—
336D4×C83—48no—
337D4×C83—48no—
338D4×C83—42no—
339D4×C83—42no—
340D4×C83—84no—
341D4×C83C2×#4114yescomplemented
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—22no—
345C2×C4×C83—22no—
346C2×C4×C83—24no—
347C2×C4×C83—24no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—48no—
358C2×C4×C83—48no—
359C2×C4×C83—48no—
360C2×C4×C83—42no—
361C2×C4×C83—42no—
362C2×C4×C83—42no—
363C2×C4×C83—42no—
364C2×C4×C83—48no—
365C2×C4×C83—42no—
366C2×C4×C83—84no—
367C2×C4×C83C22×D412yes—
368C2×C4×C83C22×D412yes—
369C2×C4×C83C22×D412yes—
370C2×C4×C83C22×D412yes—
371C2×C4×C83C22×D411yescharacteristic
372C2×C4×C83C2×#4112yes—
373C2×C4×C83H(5,𝔽2)12yes—
374C2×C4×C83C2511yescharacteristic
375C8×C83—22no—
376C8×C83—22no—
377C8×C83—22no—
378C8×C83—22no—
379C22×C83—22no—
380C22×C83—28no—
381C22×C83—22no—
382C22×C83—22no—
383C22×C83—24no—
384C22×C83—22no—
385C22×C83—22no—
386C22×C83—44no—
387C22×C83—48no—
388C22×C83—42no—
389C22×C83—42no—
390C22×C83—42no—
391C22×C83—42no—
392C22×C83—42no—
393C22×C83—42no—
394C22×C83—42no—
395C22×C83—42no—
396C22×C83—816no—
397C22×C83—84no—
398C22×C83—84no—
399C22×C83#54612yes—
400C22×C83C2×AGL(1,ℤ/8)14yes—
401C22×C83C2×AGL(1,ℤ/8)12yes—
402C22×C83#57712yes—
403C22×C83C23×D411yescharacteristic
404C4×C83—22no—
405C4×C83—22no—
406C4×C83—22no—
407C4×C83—22no—
408C4×C83—42no—
409C4×C83—42no—
410C4×C83—42no—
411C4×C83—42no—
412C4×C83—42no—
413C4×C83#54612yes—
414C4×C83C22×#4111yescharacteristic
415C4×C83C2×H(5,𝔽2)11yescharacteristic
416C2×#3306C8311yesmaximal, characteristic, direct product factor, Sylow
417C2×C83—24no—
418C2×C83—42no—
419C2×C83—44no—
420C2×C83—82no—
421C2×C83—82no—
422C2×C83#330614yesdirect product factor
423C2×C83C2×#54611yescharacteristic
424C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
425C2×C83C2×#57711yescharacteristic
426C2×#547C2×C8311yescharacteristic, complemented
427C2×#546C2×C8311yescharacteristic, complemented
428#3306C2×C83116yesdirect product factor
429C2×#489C2×C8311yescharacteristic, complemented
430C2×#481C2×C8311yescharacteristic, complemented
431C2×#483C2×C8311yescharacteristic, complemented
432C2×#476C2×C8311yescharacteristic, complemented
433C2×#469C2×C8311yescharacteristic, complemented
434C2×#465C2×C8311yescharacteristic, complemented
435C2×#463C2×C8311yescharacteristic, complemented
436C2×#449C2×C8311yescharacteristic, complemented
437C2×#447C2×C8311yescharacteristic, complemented
438C2×#442C2×C8311yescharacteristic, complemented
439C2×#435C2×C8311yescharacteristic, complemented
440C2×#417C2×C8311yescharacteristic, complemented
441C22×#102C2×C8311yescharacteristic, complemented
442C83C2×#330611yescharacteristic, direct product factor, Sylow
443C22×#41—21no—
444C22×#41C22×C8311yescharacteristic
445C23×D4C22×C8311yescharacteristic
446C22×SD16C22×C8311yescharacteristic, complemented
447C22×D8C22×C8311yescharacteristic
448C22×D8C22×C8311yescharacteristic
449C22×M16C22×C8311yescharacteristic, complemented
450C23×C8C22×C8311yescharacteristic
451#547—24no—
452#547C22×C8318yescomplemented
453#546—24no—
454#546C22×C8318yescomplemented
455C2×C4⋊Q8C22×C8311yescharacteristic, complemented
456C2×#124C22×C8311yescharacteristic
457C2×#123—21no—
458C2×#123—21no—
459C2×#123—21no—
460C2×C22⋊Q8—21no—
461C2×C22⋊Q8C22×C8311yescharacteristic
462C2×#121—21no—
463C2×#121C22×C8311yescharacteristic
464C2×#121C22×C8311yescharacteristic
465C2×#121C22×C8311yescharacteristic, complemented
466C2×#120—21no—
467C2×C4×D4C22×C8311yescharacteristic
468C2×C4×D4C22×C8311yescharacteristic
469C2×C4×D4C22×C8311yescharacteristic, complemented
470C22×C4⋊C4C22×C8311yescharacteristic
471C22×C4⋊C4C22×C8311yescharacteristic, complemented
472C22×C22⋊C4—21no—
473#489C22×C8318yescomplemented
474#483C22×C8318yescomplemented
475#481C22×C8318yescomplemented
476#476C22×C8318yescomplemented
477#469C22×C8318yescomplemented
478#465C22×C8318yescomplemented
479#463C22×C8318yescomplemented
480#449C22×C8318yescomplemented
481#447C22×C8318yescomplemented
482#442C22×C8318yescomplemented
483#435C22×C8318yescomplemented
484C2×#106C22×C8311yescharacteristic, complemented
485C2×#106C22×C8311yescharacteristic, complemented
486C2×#106C22×C8311yescharacteristic, complemented
487C2×C4⋊C8C22×C8311yescharacteristic, complemented
488#417C22×C8318yescomplemented
489C2×#103C22×C8311yescharacteristic, complemented
490C2×#103C22×C8311yescharacteristic, complemented
491C2×#103C22×C8311yescharacteristic, complemented
492C2×#102C22×C8311yescharacteristic
493C2×#102C22×C8311yescharacteristic
494C2×#102C22×C8311yescharacteristic
495C2×#102C22×C8311yescharacteristic
496C2×#102C22×C8311yescharacteristic
497C2×#102C22×C8311yescharacteristic
498C2×#102C22×C8318yescomplemented
499C2×#102C22×C8311yescharacteristic, complemented
500C2×C22⋊C8C22×C8311yescharacteristic
501C2×C22⋊C8C22×C8311yescharacteristic, complemented
502C2×#97C22×C8311yescharacteristic, complemented
503C25—21no—
504C2×#41—28no—
505C2×#41—22no—
506C2×#41—24no—
507C2×#41—42no—
508C2×#41—48no—
509C2×#41C23×C8314yes—
510C22×Q8—21no—
511C22×Q8C23×C8311yescharacteristic
512C22×D4—24no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—42no—
520C22×D4D4×C8311yescharacteristic
521C22×D4C23×C8311yescharacteristic
522C22×D4C23×C8311yescharacteristic
523C22×D4C23×C8314yes—
524C22×D4C23×C8311yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C23×C8311yescharacteristic
531C23×C4C23×C8311yescharacteristic
532C2×SD16—42no—
533C2×SD16C23×C8314yescomplemented
534C2×D8—24no—
535C2×D8—42no—
536C2×D8C23×C8314yes—
537C2×D8C23×C8314yes—
538C2×M16—42no—
539C2×M16C23×C8314yescomplemented
540C22×C8—42no—
541C22×C8C23×C8311yescharacteristic
542C22×C8C23×C8311yescharacteristic
543C22×C8C23×C8311yescharacteristic
544C22×C8C23×C8311yescharacteristic
545C22×C8C23×C8314yes—
546C4⋊Q8—22no—
547C4⋊Q8C23×C8314yescomplemented
548#124—22no—
549#124C23×C8314yes—
550#123—28no—
551#123—28no—
552#123—28no—
553C22⋊Q8—22no—
554C22⋊Q8—28no—
555C22⋊Q8C23×C8314yes—
556#121—22no—
557#121—22no—
558#121—22no—
559#121—28no—
560#121C23×C8314yes—
561#121C23×C8314yes—
562#121C23×C8314yescomplemented
563#120—28no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4D4×C8314yes—
567C4×D4C23×C8314yes—
568C4×D4C23×C8314yes—
569C4×D4C23×C8314yescomplemented
570C2×C4⋊C4—21no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4D4×C8311yescharacteristic
577C2×C4⋊C4C23×C8311yescharacteristic
578C2×C4⋊C4C23×C8311yescharacteristic
579C2×C4⋊C4C23×C8314yes—
580C2×C4⋊C4C23×C8311yescharacteristic
581C2×C4⋊C4C23×C8311yescharacteristic
582C2×C4⋊C4C23×C8314yescomplemented
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—28no—
592C2×C22⋊C4D4×C8311yescharacteristic
593C2×C22⋊C4D4×C8311yescharacteristic
594C2×C42C23×C8311yescharacteristic
595#106C23×C8314yescomplemented
596#106C23×C8314yescomplemented
597#106C23×C8314yescomplemented
598C4⋊C8C23×C8314yescomplemented
599#103C23×C8314yescomplemented
600#103C23×C8314yescomplemented
601#103C23×C8314yescomplemented
602#102C23×C8314yes—
603#102C23×C8314yes—
604#102C23×C8314yes—
605#102C23×C8314yes—
606#102C23×C8314yes—
607#102C23×C8314yes—
608#102C23×C8314yescomplemented
609C22⋊C8C23×C8314yes—
610C22⋊C8C23×C8314yescomplemented
611#97C23×C8314yescomplemented
612C24—21no—
613C24—21no—
614C24—21no—
615C24—24no—
616C24—44no—
617C24—44no—
618C24—82no—
619C24C2×D4×C8311yescharacteristic
620C24C2×D4×C8311yescharacteristic
621#41—28no—
622#41—44no—
623#41—48no—
624#41—432no—
625C2×Q8—21no—
626C2×Q8—24no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—44no—
630C2×Q8C24×C8312yes—
631C2×D4—24no—
632C2×D4—28no—
633C2×D4—24no—
634C2×D4—24no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—24no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—82no—
653C2×D4C2×D4×C8314yes—
654C2×D4#41×C8314yescomplemented
655C2×D4C24×C8312yes—
656C2×D4C24×C8312yes—
657C2×D4C24×C8312yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—82no—
677C22×C4C2×D4×C8311yescharacteristic
678C22×C4C2×D4×C8311yescharacteristic
679C22×C4C2×D4×C8311yescharacteristic
680C22×C4C2×D4×C8311yescharacteristic
681C22×C4C2×D4×C8312yes—
682C22×C4C2×D4×C8312yes—
683C22×C4C24×C8312yes—
684C22×C4C24×C8312yes—
685C22×C4C24×C8311yescharacteristic
686SD16—44no—
687D8—28no—
688D8—44no—
689M16—44no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8—44no—
695C2×C8C24×C8312yes—
696C2×C8C24×C8312yes—
697C2×C8C24×C8312yes—
698C2×C8C24×C8312yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—21no—
707C4⋊C4C2×D4×C8314yes—
708C4⋊C4C24×C8312yes—
709C4⋊C4C24×C8312yes—
710C4⋊C4C24×C8312yes—
711C4⋊C4C24×C8312yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4C2×D4×C8314yes—
721C22⋊C4C2×D4×C8314yes—
722C42C2×D4×C8312yes—
723C42C24×C8312yes—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—48no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—48no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—84no—
744C23—816no—
745C23AGL(1,ℤ/8)×C8314yes—
746C23C22×D4×C8312yes—
747C23C22×D4×C8312yes—
748C23C22×D4×C8311yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—48no—
752Q8—42no—
753D4—28no—
754D4—24no—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—48no—
764D4—42no—
765D4—42no—
766D4—84no—
767D4C2×#41×C8314yescomplemented
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—48no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—48no—
791C2×C4—42no—
792C2×C4—84no—
793C2×C4C22×D4×C8312yes—
794C2×C4C22×D4×C8312yes—
795C2×C4C22×D4×C8312yes—
796C2×C4C22×D4×C8312yes—
797C2×C4C22×D4×C8311yescharacteristic
798C2×C4C2×#41×C8312yes—
799C2×C4H(5,𝔽2)×C8312yes—
800C2×C4C25×C8311yescharacteristic
801C8—22no—
802C8—22no—
803C8—22no—
804C8—22no—
805C22—28no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—24no—
812C22—44no—
813C22—48no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—84no—
824C22—84no—
825C22#546×C8312yes—
826C22C2×AGL(1,ℤ/8)×C8314yes—
827C22C2×AGL(1,ℤ/8)×C8312yes—
828C22#577×C8312yes—
829C22C23×D4×C8311yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4#546×C8312yes—
840C4C22×#41×C8311yescharacteristic
841C4C2×H(5,𝔽2)×C8311yescharacteristic
842C2—24no—
843C2—42no—
844C2—44no—
845C2—82no—
846C2—82no—
847C2C83×#330614yesdirect product factor
848C2C2×#546×C8311yescharacteristic
849C2C22×AGL(1,ℤ/8)×C8311yescharacteristic
850C2C2×#577×C8311yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC2×C4C25×C83
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C83C2semidirect
2. C2×#546×C83C2semidirect
3. C83×#3306C2direct (N × H)
4. C2×#489×C83C2semidirect
5. C2×#481×C83C2semidirect
6. C2×#483×C83C2semidirect
7. C2×#476×C83C2semidirect
8. C2×#469×C83C2semidirect
9. C2×#465×C83C2semidirect
10. C2×#463×C83C2semidirect
11. C2×#449×C83C2semidirect
12. C2×#447×C83C2semidirect
13. C2×#442×C83C2semidirect
14. C2×#435×C83C2semidirect
15. C2×#417×C83C2semidirect
16. C22×#102×C83C2semidirect
20. C22×SD16×C83C22semidirect
23. C22×M16×C83C22semidirect
26. #547×C83C22semidirect
28. #546×C83C22semidirect
29. C2×C4⋊Q8×C83C22semidirect
39. C2×#121×C83C22semidirect
43. C2×C4×D4×C83C22semidirect
45. C22×C4⋊C4×C83C22semidirect
47. #489×C83C22semidirect
48. #483×C83C22semidirect
49. #481×C83C22semidirect
50. #476×C83C22semidirect
51. #469×C83C22semidirect
52. #465×C83C22semidirect
53. #463×C83C22semidirect
54. #449×C83C22semidirect
55. #447×C83C22semidirect
56. #442×C83C22semidirect
57. #435×C83C22semidirect
58. C2×#106×C83C22semidirect
59. C2×#106×C83C22semidirect
60. C2×#106×C83C22semidirect
61. C2×C4⋊C8×C83C22semidirect
62. #417×C83C22semidirect
63. C2×#103×C83C22semidirect
64. C2×#103×C83C22semidirect
65. C2×#103×C83C22semidirect
72. C2×#102×C83C22semidirect
73. C2×#102×C83C22semidirect
75. C2×C22⋊C8×C83C22semidirect
76. C2×#97×C83C22semidirect
107. C2×SD16×C83C23semidirect
113. C2×M16×C83C23semidirect
121. C4⋊Q8×C83C23semidirect
136. #121×C83C23semidirect
143. C4×D4×C83C23semidirect
156. C2×C4⋊C4×C83C23semidirect
169. #106×C83C23semidirect
170. #106×C83C23semidirect
171. #106×C83C23semidirect
172. C4⋊C8×C83C23semidirect
173. #103×C83C23semidirect
174. #103×C83C23semidirect
175. #103×C83C23semidirect
182. #102×C83C23semidirect
184. C22⋊C8×C83C23semidirect
185. #97×C83C23semidirect
228. C2×D4×C83#41semidirect
341. D4×C83C2×#41semidirect
416. C2×#3306C83direct (N × H)
422. C2×C83#3306direct (N × H)
426. C2×#547C2×C83semidirect
427. C2×#546C2×C83semidirect
428. #3306C2×C83direct (N × H)
429. C2×#489C2×C83semidirect
430. C2×#481C2×C83semidirect
431. C2×#483C2×C83semidirect
432. C2×#476C2×C83semidirect
433. C2×#469C2×C83semidirect
434. C2×#465C2×C83semidirect
435. C2×#463C2×C83semidirect
436. C2×#449C2×C83semidirect
437. C2×#447C2×C83semidirect
438. C2×#442C2×C83semidirect
439. C2×#435C2×C83semidirect
440. C2×#417C2×C83semidirect
441. C22×#102C2×C83semidirect
442. C83C2×#3306direct (N × H)
446. C22×SD16C22×C83semidirect
449. C22×M16C22×C83semidirect
452. #547C22×C83semidirect
454. #546C22×C83semidirect
455. C2×C4⋊Q8C22×C83semidirect
465. C2×#121C22×C83semidirect
469. C2×C4×D4C22×C83semidirect
471. C22×C4⋊C4C22×C83semidirect
473. #489C22×C83semidirect
474. #483C22×C83semidirect
475. #481C22×C83semidirect
476. #476C22×C83semidirect
477. #469C22×C83semidirect
478. #465C22×C83semidirect
479. #463C22×C83semidirect
480. #449C22×C83semidirect
481. #447C22×C83semidirect
482. #442C22×C83semidirect
483. #435C22×C83semidirect
484. C2×#106C22×C83semidirect
485. C2×#106C22×C83semidirect
486. C2×#106C22×C83semidirect
487. C2×C4⋊C8C22×C83semidirect
488. #417C22×C83semidirect
489. C2×#103C22×C83semidirect
490. C2×#103C22×C83semidirect
491. C2×#103C22×C83semidirect
498. C2×#102C22×C83semidirect
499. C2×#102C22×C83semidirect
501. C2×C22⋊C8C22×C83semidirect
502. C2×#97C22×C83semidirect
533. C2×SD16C23×C83semidirect
539. C2×M16C23×C83semidirect
547. C4⋊Q8C23×C83semidirect
562. #121C23×C83semidirect
569. C4×D4C23×C83semidirect
582. C2×C4⋊C4C23×C83semidirect
595. #106C23×C83semidirect
596. #106C23×C83semidirect
597. #106C23×C83semidirect
598. C4⋊C8C23×C83semidirect
599. #103C23×C83semidirect
600. #103C23×C83semidirect
601. #103C23×C83semidirect
608. #102C23×C83semidirect
610. C22⋊C8C23×C83semidirect
611. #97C23×C83semidirect
654. C2×D4#41×C83semidirect
767. D4C2×#41×C83semidirect
847. C2C83×#3306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#547×C832
C2×#546×C832
C83×#33062
C2×#489×C832
C2×#481×C832
C2×#483×C832
C2×#476×C832
C2×#469×C832
C2×#465×C832
C2×#463×C832
C2×#449×C832
C2×#447×C832
C2×#442×C832
C2×#435×C832
C2×#417×C832
C22×#102×C832
C2×#330683