Finite Group Databasebeta

← C2×C83×#3296 #35288938

Subgroups — C2×C83×#3296 #35288938

Order 21248.

2286 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C83C211yesmaximal, characteristic, complemented
2C2×#546×C83C211yesmaximal, characteristic
3C83×#3296C2116yesmaximal, direct product factor
4C2×#488×C83C211yesmaximal, characteristic, complemented
5C2×#482×C83C211yesmaximal, characteristic, complemented
6C2×#483×C83C211yesmaximal, characteristic, complemented
7C2×#478×C83C211yesmaximal, characteristic, complemented
8C2×#467×C83C211yesmaximal, characteristic, complemented
9C2×#465×C83C211yesmaximal, characteristic, complemented
10C2×#464×C83C211yesmaximal, characteristic, complemented
11C2×#452×C83C211yesmaximal, characteristic, complemented
12C2×#450×C83C211yesmaximal, characteristic, complemented
13C2×C4×SD16×C83C211yesmaximal, characteristic, complemented
14C2×C8×D4×C83C211yesmaximal, characteristic, complemented
15C2×#416×C83C211yesmaximal, characteristic, complemented
16C22×#102×C83C211yesmaximal, characteristic, complemented
17C22×#41×C83C2211yescharacteristic
18C23×D4×C83C2211yescharacteristic
19C22×Q16×C83C2211yescharacteristic, complemented
20C22×SD16×C83C2211yescharacteristic
21C22×SD16×C83C2211yescharacteristic
22C23×C8×C83C2211yescharacteristic
23C23×C8×C83C2211yescharacteristic, complemented
24#552×C83—24no—
25#552×C83C2218yescomplemented
26#546×C83—24no—
27#546×C83C2218yes—
28C2×#126×C83—21no—
29C2×#125×C83—21no—
30C2×#125×C83C2211yescharacteristic, complemented
31C2×#124×C83C2211yescharacteristic
32C2×#123×C83—21no—
33C2×#123×C83—21no—
34C2×C22⋊Q8×C83C2211yescharacteristic
35C2×C22⋊Q8×C83C2211yescharacteristic
36C2×C22⋊Q8×C83C2211yescharacteristic, complemented
37C2×#121×C83—21no—
38C2×#121×C83C2211yescharacteristic
39C2×#120×C83—21no—
40C2×C4×Q8×C83C2211yescharacteristic, complemented
41C2×C4×D4×C83C2211yescharacteristic
42C2×C4×D4×C83C2211yescharacteristic
43C2×#117×C83—21no—
44C2×#117×C83C2211yescharacteristic, complemented
45C22×C4⋊C4×C83C2211yescharacteristic
46C22×C22⋊C4×C83—21no—
47#488×C83C2218yescomplemented
48#483×C83C2218yescomplemented
49#482×C83C2218yescomplemented
50#478×C83C2218yescomplemented
51#467×C83C2218yescomplemented
52#465×C83C2218yescomplemented
53#464×C83C2218yescomplemented
54#452×C83C2218yescomplemented
55#450×C83C2218yescomplemented
56C4×SD16×C83C2218yescomplemented
57C8×D4×C83C2218yescomplemented
58C2×#107×C83C2211yescharacteristic, complemented
59C2×#106×C83C2211yescharacteristic, complemented
60C2×#106×C83C2211yescharacteristic, complemented
61C2×C4⋊C8×C83C2211yescharacteristic, complemented
62#416×C83C2218yescomplemented
63C2×#103×C83C2211yescharacteristic, complemented
64C2×#103×C83C2211yescharacteristic, complemented
65C2×#103×C83C2211yescharacteristic, complemented
66C2×#103×C83C2211yescharacteristic, complemented
67C2×#102×C83C2211yescharacteristic
68C2×#102×C83C2211yescharacteristic
69C2×#102×C83C2211yescharacteristic
70C2×#102×C83C2211yescharacteristic
71C2×#102×C83C2211yescharacteristic
72C2×#102×C83C2211yescharacteristic
73C2×#102×C83C2218yescomplemented
74C2×C22⋊C8×C83C2211yescharacteristic
75C2×C22⋊C8×C83C2211yescharacteristic, complemented
76C2×C4×C8×C83C2211yescharacteristic, complemented
77C25×C83—21no—
78C2×#41×C83—22no—
79C2×#41×C83—24no—
80C2×#41×C83—42no—
81C2×#41×C83C2314yes—
82C22×Q8×C83C2311yescharacteristic
83C22×Q8×C83C2311yescharacteristic
84C22×D4×C83—24no—
85C22×D4×C83—21no—
86C22×D4×C83—21no—
87C22×D4×C83—21no—
88C22×D4×C83—22no—
89C22×D4×C83—42no—
90C22×D4×C83D411yescharacteristic
91C22×D4×C83C2311yescharacteristic
92C22×D4×C83C2314yes—
93C22×D4×C83C2311yescharacteristic
94C23×C4×C83—21no—
95C23×C4×C83—21no—
96C23×C4×C83—21no—
97C23×C4×C83C2311yescharacteristic
98C23×C4×C83C2311yescharacteristic
99C2×Q16×C83—42no—
100C2×Q16×C83C2314yescomplemented
101C2×SD16×C83—24no—
102C2×SD16×C83—42no—
103C2×SD16×C83C2314yes—
104C2×SD16×C83C2314yes—
105C22×C8×C83—42no—
106C22×C8×C83—42no—
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109C22×C8×C83C2311yescharacteristic
110C22×C8×C83C2311yescharacteristic
111C22×C8×C83C2314yes—
112C22×C8×C83C2314yescomplemented
113#126×C83—28no—
114#125×C83—28no—
115#125×C83—22no—
116#125×C83C2314yescomplemented
117#124×C83—22no—
118#124×C83C2314yes—
119#123×C83—28no—
120#123×C83—28no—
121C22⋊Q8×C83—22no—
122C22⋊Q8×C83—22no—
123C22⋊Q8×C83—22no—
124C22⋊Q8×C83C2314yes—
125C22⋊Q8×C83C2314yes—
126C22⋊Q8×C83C2314yescomplemented
127#121×C83—22no—
128#121×C83—28no—
129#121×C83C2314yes—
130#120×C83—28no—
131C4×Q8×C83—22no—
132C4×Q8×C83C2314yescomplemented
133C4×D4×C83—22no—
134C4×D4×C83D414yes—
135C4×D4×C83C2314yes—
136C4×D4×C83C2314yes—
137#117×C83—22no—
138#117×C83—28no—
139#117×C83C2314yescomplemented
140C2×C4⋊C4×C83—21no—
141C2×C4⋊C4×C83—22no—
142C2×C4⋊C4×C83—21no—
143C2×C4⋊C4×C83—21no—
144C2×C4⋊C4×C83—21no—
145C2×C4⋊C4×C83—21no—
146C2×C4⋊C4×C83—21no—
147C2×C4⋊C4×C83—21no—
148C2×C4⋊C4×C83D411yescharacteristic
149C2×C4⋊C4×C83C2314yes—
150C2×C4⋊C4×C83C2311yescharacteristic
151C2×C4⋊C4×C83C2311yescharacteristic
152C2×C4⋊C4×C83C2311yescharacteristic
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C22⋊C4×C83—21no—
155C2×C22⋊C4×C83—21no—
156C2×C22⋊C4×C83—21no—
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—28no—
163C2×C22⋊C4×C83D411yescharacteristic
164C2×C22⋊C4×C83D411yescharacteristic
165C2×C42×C83—21no—
166C2×C42×C83—21no—
167C2×C42×C83C2311yescharacteristic
168#107×C83C2314yescomplemented
169#106×C83C2314yescomplemented
170#106×C83C2314yescomplemented
171C4⋊C8×C83C2314yescomplemented
172#103×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—
182C22⋊C8×C83C2314yes—
183C22⋊C8×C83C2314yescomplemented
184C4×C8×C83C2314yescomplemented
185C24×C83—21no—
186C24×C83—21no—
187C24×C83—24no—
188C24×C83—44no—
189C24×C83—44no—
190C24×C83—82no—
191C24×C83C2×D411yescharacteristic
192C24×C83C2×D411yescharacteristic
193#41×C83—28no—
194#41×C83—44no—
195#41×C83—48no—
196C2×Q8×C83—21no—
197C2×Q8×C83—21no—
198C2×Q8×C83—22no—
199C2×Q8×C83—22no—
200C2×Q8×C83—22no—
201C2×Q8×C83—22no—
202C2×Q8×C83C2412yes—
203C2×Q8×C83C2412yes—
204C2×D4×C83—24no—
205C2×D4×C83—28no—
206C2×D4×C83—24no—
207C2×D4×C83—24no—
208C2×D4×C83—21no—
209C2×D4×C83—24no—
210C2×D4×C83—21no—
211C2×D4×C83—22no—
212C2×D4×C83—22no—
213C2×D4×C83—22no—
214C2×D4×C83—44no—
215C2×D4×C83—48no—
216C2×D4×C83—44no—
217C2×D4×C83—44no—
218C2×D4×C83—82no—
219C2×D4×C83C2×D414yes—
220C2×D4×C83#4114yes—
221C2×D4×C83C2412yes—
222C2×D4×C83C2412yes—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—24no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—24no—
235C22×C4×C83—24no—
236C22×C4×C83—44no—
237C22×C4×C83—44no—
238C22×C4×C83—82no—
239C22×C4×C83C2×D412yes—
240C22×C4×C83C2×D412yes—
241C22×C4×C83C2×D411yescharacteristic
242C22×C4×C83C2×D411yescharacteristic
243C22×C4×C83C2×D411yescharacteristic
244C22×C4×C83C2×D411yescharacteristic
245C22×C4×C83C2412yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2411yescharacteristic
248Q16×C83—44no—
249SD16×C83—28no—
250SD16×C83—44no—
251C2×C8×C83—22no—
252C2×C8×C83—22no—
253C2×C8×C83—22no—
254C2×C8×C83—22no—
255C2×C8×C83—44no—
256C2×C8×C83—44no—
257C2×C8×C83C2412yes—
258C2×C8×C83C2412yes—
259C2×C8×C83C2412yes—
260C2×C8×C83C2412yes—
261C4⋊C4×C83—21no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83—24no—
264C4⋊C4×C83—24no—
265C4⋊C4×C83—24no—
266C4⋊C4×C83—24no—
267C4⋊C4×C83—24no—
268C4⋊C4×C83—24no—
269C4⋊C4×C83—24no—
270C4⋊C4×C83—21no—
271C4⋊C4×C83—21no—
272C4⋊C4×C83C2×D414yes—
273C4⋊C4×C83C2412yes—
274C4⋊C4×C83C2412yes—
275C4⋊C4×C83C2412yes—
276C4⋊C4×C83C2412yes—
277C22⋊C4×C83—24no—
278C22⋊C4×C83—24no—
279C22⋊C4×C83—24no—
280C22⋊C4×C83—24no—
281C22⋊C4×C83—24no—
282C22⋊C4×C83—24no—
283C22⋊C4×C83—24no—
284C22⋊C4×C83—24no—
285C22⋊C4×C83C2×D414yes—
286C22⋊C4×C83C2×D414yes—
287C42×C83—24no—
288C42×C83—24no—
289C42×C83C2×D412yes—
290C42×C83C2412yes—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—24no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—22no—
299C23×C83—48no—
300C23×C83—42no—
301C23×C83—42no—
302C23×C83—42no—
303C23×C83—48no—
304C23×C83—42no—
305C23×C83—42no—
306C23×C83—84no—
307C23×C83—816no—
308C23×C83#13514yes—
309C23×C83C22×D412yes—
310C23×C83C22×D412yes—
311C23×C83C22×D411yescharacteristic
312Q8×C83—22no—
313Q8×C83—22no—
314Q8×C83—22no—
315Q8×C83—22no—
316Q8×C83—42no—
317Q8×C83—42no—
318D4×C83—28no—
319D4×C83—24no—
320D4×C83—22no—
321D4×C83—22no—
322D4×C83—22no—
323D4×C83—48no—
324D4×C83—48no—
325D4×C83—42no—
326D4×C83—84no—
327D4×C83C2×#4114yes—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—24no—
333C2×C4×C83—24no—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—22no—
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—48no—
345C2×C4×C83—42no—
346C2×C4×C83—42no—
347C2×C4×C83—48no—
348C2×C4×C83—42no—
349C2×C4×C83—42no—
350C2×C4×C83—42no—
351C2×C4×C83—42no—
352C2×C4×C83—84no—
353C2×C4×C83C22×D412yes—
354C2×C4×C83C22×D412yes—
355C2×C4×C83C22×D412yes—
356C2×C4×C83C22×D412yes—
357C2×C4×C83C22×D411yescharacteristic
358C2×C4×C83C2×#4112yes—
359C2×C4×C83H(5,𝔽2)12yes—
360C2×C4×C83C2511yescharacteristic
361C8×C83—22no—
362C8×C83—22no—
363C8×C83—22no—
364C8×C83—22no—
365C22×C83—22no—
366C22×C83—28no—
367C22×C83—22no—
368C22×C83—22no—
369C22×C83—24no—
370C22×C83—22no—
371C22×C83—22no—
372C22×C83—44no—
373C22×C83—48no—
374C22×C83—42no—
375C22×C83—42no—
376C22×C83—42no—
377C22×C83—42no—
378C22×C83—42no—
379C22×C83—816no—
380C22×C83—84no—
381C22×C83#54612yes—
382C22×C83C2×#13514yes—
383C22×C83C2×#13512yes—
384C22×C83#57712yes—
385C22×C83C23×D411yescharacteristic
386C4×C83—22no—
387C4×C83—22no—
388C4×C83—22no—
389C4×C83—22no—
390C4×C83—42no—
391C4×C83—42no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83—42no—
395C4×C83—42no—
396C4×C83#54612yes—
397C4×C83C22×#4111yescharacteristic
398C4×C83C2×H(5,𝔽2)11yescharacteristic
399C2×#3296C8311yesmaximal, characteristic, direct product factor, Sylow
400C2×C83—24no—
401C2×C83—42no—
402C2×C83—44no—
403C2×C83—82no—
404C2×C83#329614yesdirect product factor
405C2×C83C2×#54611yescharacteristic
406C2×C83C22×#13511yescharacteristic
407C2×C83C2×#57711yescharacteristic
408C2×#552C2×C8311yescharacteristic, complemented
409C2×#546C2×C8311yescharacteristic
410#3296C2×C83116yesdirect product factor
411C2×#488C2×C8311yescharacteristic, complemented
412C2×#482C2×C8311yescharacteristic, complemented
413C2×#483C2×C8311yescharacteristic, complemented
414C2×#478C2×C8311yescharacteristic, complemented
415C2×#467C2×C8311yescharacteristic, complemented
416C2×#465C2×C8311yescharacteristic, complemented
417C2×#464C2×C8311yescharacteristic, complemented
418C2×#452C2×C8311yescharacteristic, complemented
419C2×#450C2×C8311yescharacteristic, complemented
420C2×C4×SD16C2×C8311yescharacteristic, complemented
421C2×C8×D4C2×C8311yescharacteristic, complemented
422C2×#416C2×C8311yescharacteristic, complemented
423C22×#102C2×C8311yescharacteristic, complemented
424C83C2×#329611yescharacteristic, direct product factor, Sylow
425C22×#41C22×C8311yescharacteristic
426C23×D4C22×C8311yescharacteristic
427C22×Q16C22×C8311yescharacteristic, complemented
428C22×SD16C22×C8311yescharacteristic
429C22×SD16C22×C8311yescharacteristic
430C23×C8C22×C8311yescharacteristic
431C23×C8C22×C8311yescharacteristic, complemented
432#552—24no—
433#552C22×C8318yescomplemented
434#546—24no—
435#546C22×C8318yes—
436C2×#126—21no—
437C2×#125—21no—
438C2×#125C22×C8311yescharacteristic, complemented
439C2×#124C22×C8311yescharacteristic
440C2×#123—21no—
441C2×#123—21no—
442C2×C22⋊Q8C22×C8311yescharacteristic
443C2×C22⋊Q8C22×C8311yescharacteristic
444C2×C22⋊Q8C22×C8311yescharacteristic, complemented
445C2×#121—21no—
446C2×#121C22×C8311yescharacteristic
447C2×#120—21no—
448C2×C4×Q8C22×C8311yescharacteristic, complemented
449C2×C4×D4C22×C8311yescharacteristic
450C2×C4×D4C22×C8311yescharacteristic
451C2×#117—21no—
452C2×#117C22×C8311yescharacteristic, complemented
453C22×C4⋊C4C22×C8311yescharacteristic
454C22×C22⋊C4—21no—
455#488C22×C8318yescomplemented
456#483C22×C8318yescomplemented
457#482C22×C8318yescomplemented
458#478C22×C8318yescomplemented
459#467C22×C8318yescomplemented
460#465C22×C8318yescomplemented
461#464C22×C8318yescomplemented
462#452C22×C8318yescomplemented
463#450C22×C8318yescomplemented
464C4×SD16C22×C8318yescomplemented
465C8×D4C22×C8318yescomplemented
466C2×#107C22×C8311yescharacteristic, complemented
467C2×#106C22×C8311yescharacteristic, complemented
468C2×#106C22×C8311yescharacteristic, complemented
469C2×C4⋊C8C22×C8311yescharacteristic, complemented
470#416C22×C8318yescomplemented
471C2×#103C22×C8311yescharacteristic, complemented
472C2×#103C22×C8311yescharacteristic, complemented
473C2×#103C22×C8311yescharacteristic, complemented
474C2×#103C22×C8311yescharacteristic, complemented
475C2×#102C22×C8311yescharacteristic
476C2×#102C22×C8311yescharacteristic
477C2×#102C22×C8311yescharacteristic
478C2×#102C22×C8311yescharacteristic
479C2×#102C22×C8311yescharacteristic
480C2×#102C22×C8311yescharacteristic
481C2×#102C22×C8318yescomplemented
482C2×C22⋊C8C22×C8311yescharacteristic
483C2×C22⋊C8C22×C8311yescharacteristic, complemented
484C2×C4×C8C22×C8311yescharacteristic, complemented
485C25—21no—
486C2×#41—22no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41C23×C8314yes—
490C22×Q8C23×C8311yescharacteristic
491C22×Q8C23×C8311yescharacteristic
492C22×D4—24no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—42no—
498C22×D4D4×C8311yescharacteristic
499C22×D4C23×C8311yescharacteristic
500C22×D4C23×C8314yes—
501C22×D4C23×C8311yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C23×C8311yescharacteristic
506C23×C4C23×C8311yescharacteristic
507C2×Q16—42no—
508C2×Q16C23×C8314yescomplemented
509C2×SD16—24no—
510C2×SD16—42no—
511C2×SD16C23×C8314yes—
512C2×SD16C23×C8314yes—
513C22×C8—42no—
514C22×C8—42no—
515C22×C8C23×C8311yescharacteristic
516C22×C8C23×C8311yescharacteristic
517C22×C8C23×C8311yescharacteristic
518C22×C8C23×C8311yescharacteristic
519C22×C8C23×C8314yes—
520C22×C8C23×C8314yescomplemented
521#126—28no—
522#125—28no—
523#125—22no—
524#125C23×C8314yescomplemented
525#124—22no—
526#124C23×C8314yes—
527#123—28no—
528#123—28no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8C23×C8314yes—
533C22⋊Q8C23×C8314yes—
534C22⋊Q8C23×C8314yescomplemented
535#121—22no—
536#121—28no—
537#121C23×C8314yes—
538#120—28no—
539C4×Q8—22no—
540C4×Q8C23×C8314yescomplemented
541C4×D4—22no—
542C4×D4D4×C8314yes—
543C4×D4C23×C8314yes—
544C4×D4C23×C8314yes—
545#117—22no—
546#117—28no—
547#117C23×C8314yescomplemented
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4D4×C8311yescharacteristic
557C2×C4⋊C4C23×C8311yescharacteristic
558C2×C4⋊C4C23×C8311yescharacteristic
559C2×C4⋊C4C23×C8314yes—
560C2×C4⋊C4C23×C8311yescharacteristic
561C2×C4⋊C4C23×C8311yescharacteristic
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—28no—
571C2×C22⋊C4D4×C8311yescharacteristic
572C2×C22⋊C4D4×C8311yescharacteristic
573C2×C42—21no—
574C2×C42—21no—
575C2×C42C23×C8311yescharacteristic
576#107C23×C8314yescomplemented
577#106C23×C8314yescomplemented
578#106C23×C8314yescomplemented
579C4⋊C8C23×C8314yescomplemented
580#103C23×C8314yescomplemented
581#103C23×C8314yescomplemented
582#103C23×C8314yescomplemented
583#103C23×C8314yescomplemented
584#102C23×C8314yes—
585#102C23×C8314yes—
586#102C23×C8314yes—
587#102C23×C8314yes—
588#102C23×C8314yes—
589#102C23×C8314yes—
590C22⋊C8C23×C8314yes—
591C22⋊C8C23×C8314yescomplemented
592C4×C8C23×C8314yescomplemented
593C24—21no—
594C24—21no—
595C24—24no—
596C24—44no—
597C24—44no—
598C24—82no—
599C24C2×D4×C8311yescharacteristic
600C24C2×D4×C8311yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8C24×C8312yes—
611C2×Q8C24×C8312yes—
612C2×D4—24no—
613C2×D4—28no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—21no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—48no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—82no—
627C2×D4C2×D4×C8314yes—
628C2×D4#41×C8314yes—
629C2×D4C24×C8312yes—
630C2×D4C24×C8312yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—24no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—82no—
647C22×C4C2×D4×C8311yescharacteristic
648C22×C4C2×D4×C8311yescharacteristic
649C22×C4C2×D4×C8311yescharacteristic
650C22×C4C2×D4×C8311yescharacteristic
651C22×C4C2×D4×C8312yes—
652C22×C4C2×D4×C8312yes—
653C22×C4C24×C8312yes—
654C22×C4C24×C8312yes—
655C22×C4C24×C8311yescharacteristic
656Q16—44no—
657SD16—28no—
658SD16—44no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—44no—
665C2×C8C24×C8312yes—
666C2×C8C24×C8312yes—
667C2×C8C24×C8312yes—
668C2×C8C24×C8312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4C2×D4×C8314yes—
681C4⋊C4C24×C8312yes—
682C4⋊C4C24×C8312yes—
683C4⋊C4C24×C8312yes—
684C4⋊C4C24×C8312yes—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4C2×D4×C8314yes—
694C22⋊C4C2×D4×C8314yes—
695C42—24no—
696C42—24no—
697C42C2×D4×C8312yes—
698C42C24×C8312yes—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—48no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—48no—
712C23—42no—
713C23—42no—
714C23—84no—
715C23—816no—
716C23#135×C8314yes—
717C23C22×D4×C8312yes—
718C23C22×D4×C8312yes—
719C23C22×D4×C8311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—22no—
724Q8—42no—
725Q8—42no—
726D4—28no—
727D4—24no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—48no—
732D4—48no—
733D4—42no—
734D4—84no—
735D4C2×#41×C8314yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—48no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—84no—
761C2×C4C22×D4×C8312yes—
762C2×C4C22×D4×C8312yes—
763C2×C4C22×D4×C8312yes—
764C2×C4C22×D4×C8312yes—
765C2×C4C22×D4×C8311yescharacteristic
766C2×C4C2×#41×C8312yes—
767C2×C4H(5,𝔽2)×C8312yes—
768C2×C4C25×C8311yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8—22no—
773C22—28no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—24no—
780C22—44no—
781C22—48no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—816no—
788C22—84no—
789C22#546×C8312yes—
790C22C2×#135×C8314yes—
791C22C2×#135×C8312yes—
792C22#577×C8312yes—
793C22C23×D4×C8311yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4#546×C8312yes—
805C4C22×#41×C8311yescharacteristic
806C4C2×H(5,𝔽2)×C8311yescharacteristic
807C2—24no—
808C2—42no—
809C2—44no—
810C2—82no—
811C2C83×#329614yesdirect product factor
812C2C2×#546×C8311yescharacteristic
813C2C22×#135×C8311yescharacteristic
814C2C2×#577×C8311yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC2×C4C25×C83
prime radicalC2×#546×C83C2
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×#552×C83C2semidirect
3. C83×#3296C2direct (N × H)
4. C2×#488×C83C2semidirect
5. C2×#482×C83C2semidirect
6. C2×#483×C83C2semidirect
7. C2×#478×C83C2semidirect
8. C2×#467×C83C2semidirect
9. C2×#465×C83C2semidirect
10. C2×#464×C83C2semidirect
11. C2×#452×C83C2semidirect
12. C2×#450×C83C2semidirect
13. C2×C4×SD16×C83C2semidirect
14. C2×C8×D4×C83C2semidirect
15. C2×#416×C83C2semidirect
16. C22×#102×C83C2semidirect
19. C22×Q16×C83C22semidirect
23. C23×C8×C83C22semidirect
25. #552×C83C22semidirect
30. C2×#125×C83C22semidirect
36. C2×C22⋊Q8×C83C22semidirect
40. C2×C4×Q8×C83C22semidirect
44. C2×#117×C83C22semidirect
47. #488×C83C22semidirect
48. #483×C83C22semidirect
49. #482×C83C22semidirect
50. #478×C83C22semidirect
51. #467×C83C22semidirect
52. #465×C83C22semidirect
53. #464×C83C22semidirect
54. #452×C83C22semidirect
55. #450×C83C22semidirect
56. C4×SD16×C83C22semidirect
57. C8×D4×C83C22semidirect
58. C2×#107×C83C22semidirect
59. C2×#106×C83C22semidirect
60. C2×#106×C83C22semidirect
61. C2×C4⋊C8×C83C22semidirect
62. #416×C83C22semidirect
63. C2×#103×C83C22semidirect
64. C2×#103×C83C22semidirect
65. C2×#103×C83C22semidirect
66. C2×#103×C83C22semidirect
73. C2×#102×C83C22semidirect
75. C2×C22⋊C8×C83C22semidirect
76. C2×C4×C8×C83C22semidirect
100. C2×Q16×C83C23semidirect
112. C22×C8×C83C23semidirect
116. #125×C83C23semidirect
126. C22⋊Q8×C83C23semidirect
132. C4×Q8×C83C23semidirect
139. #117×C83C23semidirect
168. #107×C83C23semidirect
169. #106×C83C23semidirect
170. #106×C83C23semidirect
171. C4⋊C8×C83C23semidirect
172. #103×C83C23semidirect
173. #103×C83C23semidirect
174. #103×C83C23semidirect
175. #103×C83C23semidirect
183. C22⋊C8×C83C23semidirect
184. C4×C8×C83C23semidirect
399. C2×#3296C83direct (N × H)
404. C2×C83#3296direct (N × H)
408. C2×#552C2×C83semidirect
410. #3296C2×C83direct (N × H)
411. C2×#488C2×C83semidirect
412. C2×#482C2×C83semidirect
413. C2×#483C2×C83semidirect
414. C2×#478C2×C83semidirect
415. C2×#467C2×C83semidirect
416. C2×#465C2×C83semidirect
417. C2×#464C2×C83semidirect
418. C2×#452C2×C83semidirect
419. C2×#450C2×C83semidirect
420. C2×C4×SD16C2×C83semidirect
421. C2×C8×D4C2×C83semidirect
422. C2×#416C2×C83semidirect
423. C22×#102C2×C83semidirect
424. C83C2×#3296direct (N × H)
427. C22×Q16C22×C83semidirect
431. C23×C8C22×C83semidirect
433. #552C22×C83semidirect
438. C2×#125C22×C83semidirect
444. C2×C22⋊Q8C22×C83semidirect
448. C2×C4×Q8C22×C83semidirect
452. C2×#117C22×C83semidirect
455. #488C22×C83semidirect
456. #483C22×C83semidirect
457. #482C22×C83semidirect
458. #478C22×C83semidirect
459. #467C22×C83semidirect
460. #465C22×C83semidirect
461. #464C22×C83semidirect
462. #452C22×C83semidirect
463. #450C22×C83semidirect
464. C4×SD16C22×C83semidirect
465. C8×D4C22×C83semidirect
466. C2×#107C22×C83semidirect
467. C2×#106C22×C83semidirect
468. C2×#106C22×C83semidirect
469. C2×C4⋊C8C22×C83semidirect
470. #416C22×C83semidirect
471. C2×#103C22×C83semidirect
472. C2×#103C22×C83semidirect
473. C2×#103C22×C83semidirect
474. C2×#103C22×C83semidirect
481. C2×#102C22×C83semidirect
483. C2×C22⋊C8C22×C83semidirect
484. C2×C4×C8C22×C83semidirect
508. C2×Q16C23×C83semidirect
520. C22×C8C23×C83semidirect
524. #125C23×C83semidirect
534. C22⋊Q8C23×C83semidirect
540. C4×Q8C23×C83semidirect
547. #117C23×C83semidirect
576. #107C23×C83semidirect
577. #106C23×C83semidirect
578. #106C23×C83semidirect
579. C4⋊C8C23×C83semidirect
580. #103C23×C83semidirect
581. #103C23×C83semidirect
582. #103C23×C83semidirect
583. #103C23×C83semidirect
591. C22⋊C8C23×C83semidirect
592. C4×C8C23×C83semidirect
811. C2C83×#3296direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#552×C832
C2×#546×C832
C83×#32962
C2×#488×C832
C2×#482×C832
C2×#483×C832
C2×#478×C832
C2×#467×C832
C2×#465×C832
C2×#464×C832
C2×#452×C832
C2×#450×C832
C2×C4×SD16×C832
C2×C8×D4×C832
C2×#416×C832
C22×#102×C832
C2×#329683