Finite Group Databasebeta

← C83×#25168 #35252992

Subgroups — C83×#25168 #35252992

Order 21248.

1396 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C83C211yesmaximal, characteristic, complemented
2C2×#447×C83C211yesmaximal, characteristic, complemented
3C2×#447×C83C211yesmaximal, characteristic, complemented
4C2×#442×C83C211yesmaximal, characteristic, complemented
5C83×#2428C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
7C83×#2065C211yesmaximal, characteristic, complemented
8C83×#2034C211yesmaximal, characteristic, complemented
9C83×#2034C211yesmaximal, characteristic, complemented
10C83×#2011C211yesmaximal, characteristic, complemented
11C83×#1972C211yesmaximal, characteristic, complemented
12C83×#1924C211yesmaximal, characteristic, complemented
13C83×#1879C211yesmaximal, characteristic, complemented
14C83×#1879C211yesmaximal, characteristic, complemented
15C83×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C22×D8×C83C2211yescharacteristic
18C22×D8×C83C2211yescharacteristic
19C22×D8×C83C2211yescharacteristic
20C22×D8×C83C2211yescharacteristic
21C2×#127×C83C2211yescharacteristic, complemented
22C2×#121×C83—21no—
23C2×#121×C83C2211yescharacteristic
24C2×#121×C83C2211yescharacteristic
25C2×C4×D4×C83C2211yescharacteristic
26C2×C4×D4×C83C2211yescharacteristic
27C2×C4×D4×C83C2211yescharacteristic, complemented
28C22×C22⋊C4×C83—21no—
29#459×C83—24no—
30#447×C83—24no—
31#447×C83—24no—
32#442×C83—24no—
33C2×#106×C83C2211yescharacteristic, complemented
34C2×#106×C83C2211yescharacteristic, complemented
35C2×C4⋊C8×C83C2211yescharacteristic, complemented
36C2×#102×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic
38C2×#102×C83C2211yescharacteristic
39C2×#102×C83C2211yescharacteristic
40C2×#102×C83C2211yescharacteristic, complemented
41C2×#102×C83C2211yescharacteristic, complemented
42C2×#102×C83C2211yescharacteristic, complemented
43C2×#102×C83C2211yescharacteristic, complemented
44C2×C22⋊C8×C83C2211yescharacteristic
45C2×C22⋊C8×C83C2211yescharacteristic
46C2×#97×C83C2211yescharacteristic, complemented
47#394×C83—21no—
48#392×C83—21no—
49#390×C83C2211yescharacteristic
50#390×C83C2211yescharacteristic
51#390×C83C2211yescharacteristic, complemented
52#389×C83C2211yescharacteristic, complemented
53#386×C83—21no—
54#386×C83—21no—
55#386×C83—21no—
56#380×C83C2211yescharacteristic
57#379×C83—21no—
58C4×C22⋊C4×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic, complemented
60#340×C83C2211yescharacteristic, complemented
61#336×C83C2211yescharacteristic, complemented
62#336×C83C2211yescharacteristic, complemented
63C25×C83—21no—
64C22×D4×C83—22no—
65C22×D4×C83—22no—
66C22×D4×C83—22no—
67C22×D4×C83—22no—
68C22×D4×C83—21no—
69C22×D4×C83—21no—
70C22×D4×C83—21no—
71C22×D4×C83—21no—
72C22×D4×C83—21no—
73C22×D4×C83—41no—
74C22×D4×C83—41no—
75C22×D4×C83C2311yescharacteristic
76C22×D4×C83C2311yescharacteristic
77C22×D4×C83C2311yescharacteristic
78C22×D4×C83C2311yescharacteristic
79C23×C4×C83—21no—
80C23×C4×C83—21no—
81C23×C4×C83—21no—
82C23×C4×C83C2311yescharacteristic
83C2×D8×C83—22no—
84C2×D8×C83—22no—
85C2×D8×C83—22no—
86C2×D8×C83—22no—
87C2×D8×C83—22no—
88C2×D8×C83—22no—
89C2×D8×C83—22no—
90C2×D8×C83—22no—
91C2×D8×C83—22no—
92C2×D8×C83—41no—
93C2×D8×C83—41no—
94C2×D8×C83D414yescomplemented
95C22×C8×C83C2311yescharacteristic
96C22×C8×C83C2311yescharacteristic
97C22×C8×C83C2311yescharacteristic
98C22×C8×C83C2311yescharacteristic
99#127×C83—22no—
100#127×C83—41no—
101#121×C83—22no—
102#121×C83—22no—
103#121×C83—44no—
104#121×C83—41no—
105#121×C83—41no—
106C4×D4×C83—22no—
107C4×D4×C83—22no—
108C4×D4×C83—22no—
109C4×D4×C83—41no—
110C4×D4×C83—41no—
111C4×D4×C83—41no—
112C2×C4⋊C4×C83—21no—
113C2×C4⋊C4×C83C2311yescharacteristic
114C2×C4⋊C4×C83C2311yescharacteristic
115C2×C4⋊C4×C83C2311yescharacteristic
116C2×C4⋊C4×C83C2311yescharacteristic
117C2×C22⋊C4×C83—21no—
118C2×C22⋊C4×C83—21no—
119C2×C22⋊C4×C83—21no—
120C2×C22⋊C4×C83—21no—
121C2×C22⋊C4×C83—21no—
122C2×C22⋊C4×C83—21no—
123C2×C22⋊C4×C83—21no—
124C2×C22⋊C4×C83—21no—
125C2×C22⋊C4×C83—21no—
126C2×C22⋊C4×C83—21no—
127C2×C22⋊C4×C83—21no—
128C2×C22⋊C4×C83—21no—
129C2×C22⋊C4×C83—44no—
130C2×C22⋊C4×C83D411yescharacteristic
131C2×C22⋊C4×C83D411yescharacteristic
132C2×C42×C83C2311yescharacteristic
133C2×C42×C83C2311yescharacteristic
134#106×C83—22no—
135#106×C83—41no—
136C4⋊C8×C83—22no—
137#102×C83—22no—
138#102×C83—22no—
139#102×C83—22no—
140#102×C83—22no—
141#102×C83—22no—
142#102×C83—22no—
143#102×C83—41no—
144#102×C83D414yescomplemented
145C22⋊C8×C83—22no—
146C22⋊C8×C83—22no—
147#97×C83—22no—
148#95×C83—21no—
149#95×C83—21no—
150#95×C83D411yescharacteristic
151#95×C83D411yescharacteristic
152C24×C83—21no—
153C24×C83—24no—
154C24×C83—21no—
155C24×C83—21no—
156C24×C83—21no—
157C24×C83—42no—
158C24×C83—42no—
159C24×C83—42no—
160C24×C83—42no—
161C24×C83—81no—
162C24×C83—81no—
163C24×C83C2×D411yescharacteristic
164C2×D4×C83—24no—
165C2×D4×C83—21no—
166C2×D4×C83—21no—
167C2×D4×C83—21no—
168C2×D4×C83—21no—
169C2×D4×C83—21no—
170C2×D4×C83—21no—
171C2×D4×C83—21no—
172C2×D4×C83—21no—
173C2×D4×C83—21no—
174C2×D4×C83—21no—
175C2×D4×C83—21no—
176C2×D4×C83—21no—
177C2×D4×C83—21no—
178C2×D4×C83—21no—
179C2×D4×C83—21no—
180C2×D4×C83—21no—
181C2×D4×C83—21no—
182C2×D4×C83—21no—
183C2×D4×C83—21no—
184C2×D4×C83—42no—
185C2×D4×C83—42no—
186C2×D4×C83—42no—
187C2×D4×C83—42no—
188C2×D4×C83—42no—
189C2×D4×C83—42no—
190C2×D4×C83—44no—
191C2×D4×C83—44no—
192C2×D4×C83—44no—
193C2×D4×C83—44no—
194C2×D4×C83—42no—
195C2×D4×C83—42no—
196C2×D4×C83—42no—
197C2×D4×C83—42no—
198C2×D4×C83—81no—
199C2×D4×C83—81no—
200C2×D4×C83—81no—
201C2×D4×C83—81no—
202C2×D4×C83C2×D412yes—
203C2×D4×C83C2×D412yes—
204C2×D4×C83C2×D412yes—
205C2×D4×C83#4112yes—
206C2×D4×C83#4112yes—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83—42no—
218C22×C4×C83—42no—
219C22×C4×C83—42no—
220C22×C4×C83—42no—
221C22×C4×C83—42no—
222C22×C4×C83—42no—
223C22×C4×C83—81no—
224C22×C4×C83—81no—
225C22×C4×C83—81no—
226C22×C4×C83C2×D411yescharacteristic
227C22×C4×C83C2×D411yescharacteristic
228C22×C4×C83C2×D411yescharacteristic
229C22×C4×C83C2×D411yescharacteristic
230C22×C4×C83C2×D411yescharacteristic
231C22×C4×C83C2411yescharacteristic
232D8×C83—28no—
233D8×C83—44no—
234D8×C83—44no—
235D8×C83—44no—
236C2×C8×C83—21no—
237C2×C8×C83—21no—
238C2×C8×C83—21no—
239C2×C8×C83—21no—
240C2×C8×C83—21no—
241C2×C8×C83—21no—
242C2×C8×C83—21no—
243C2×C8×C83—21no—
244C2×C8×C83—21no—
245C2×C8×C83—21no—
246C2×C8×C83C2×D412yes—
247C2×C8×C83C2×D412yes—
248C4⋊C4×C83—21no—
249C4⋊C4×C83—21no—
250C4⋊C4×C83—21no—
251C4⋊C4×C83—21no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83—42no—
256C4⋊C4×C83C2×D412yes—
257C22⋊C4×C83—22no—
258C22⋊C4×C83—22no—
259C22⋊C4×C83—42no—
260C22⋊C4×C83—42no—
261C22⋊C4×C83—42no—
262C22⋊C4×C83—42no—
263C22⋊C4×C83—42no—
264C22⋊C4×C83—42no—
265C22⋊C4×C83—42no—
266C22⋊C4×C83—42no—
267C22⋊C4×C83—42no—
268C22⋊C4×C83—81no—
269C22⋊C4×C83—81no—
270C22⋊C4×C83—81no—
271C42×C83—21no—
272C42×C83—21no—
273C42×C83—21no—
274C42×C83—21no—
275C23×C83—21no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—22no—
279C23×C83—21no—
280C23×C83—21no—
281C23×C83—21no—
282C23×C83—21no—
283C23×C83—21no—
284C23×C83—22no—
285C23×C83—22no—
286C23×C83—48no—
287C23×C83—48no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83—41no—
299C23×C83—41no—
300C23×C83—41no—
301C23×C83—41no—
302C23×C83—41no—
303C23×C83—41no—
304C23×C83—41no—
305C23×C83—41no—
306C23×C83—41no—
307C23×C83—41no—
308C23×C83—41no—
309C23×C83—41no—
310C23×C83—41no—
311C23×C83—84no—
312C23×C83—84no—
313C23×C83—84no—
314C23×C83—84no—
315C23×C83—84no—
316C23×C83AGL(1,ℤ/8)12yes—
317C23×C83C22×D411yescharacteristic
318D4×C83—22no—
319D4×C83—22no—
320D4×C83—22no—
321D4×C83—22no—
322D4×C83—22no—
323D4×C83—22no—
324D4×C83—22no—
325D4×C83—48no—
326D4×C83—41no—
327D4×C83—41no—
328D4×C83—41no—
329D4×C83—41no—
330D4×C83—41no—
331D4×C83—41no—
332D4×C83—41no—
333D4×C83—41no—
334D4×C83—84no—
335D4×C83—84no—
336D4×C83—84no—
337D4×C83—84no—
338D4×C83#12114yescomplemented
339C2×C4×C83—21no—
340C2×C4×C83—21no—
341C2×C4×C83—21no—
342C2×C4×C83—21no—
343C2×C4×C83—21no—
344C2×C4×C83—21no—
345C2×C4×C83—22no—
346C2×C4×C83—21no—
347C2×C4×C83—21no—
348C2×C4×C83—21no—
349C2×C4×C83—21no—
350C2×C4×C83—21no—
351C2×C4×C83—21no—
352C2×C4×C83—21no—
353C2×C4×C83—21no—
354C2×C4×C83—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83—41no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—41no—
361C2×C4×C83—41no—
362C2×C4×C83—41no—
363C2×C4×C83—41no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
369C2×C4×C83—84no—
370C2×C4×C83—84no—
371C2×C4×C83—84no—
372C2×C4×C83AGL(1,ℤ/8)12yes—
373C2×C4×C83C22×D411yescharacteristic
374C2×C4×C83C22×D411yescharacteristic
375C2×C4×C83C2×#4111yescharacteristic
376C2×C4×C83C2×#4111yescharacteristic
377C2×C4×C83H(5,𝔽2)11yescharacteristic
378C2×C4×C83H(5,𝔽2)11yescharacteristic
379C8×C83—22no—
380C8×C83—22no—
381C8×C83—41no—
382C8×C83—41no—
383C22×C83—22no—
384C22×C83—24no—
385C22×C83—22no—
386C22×C83—22no—
387C22×C83—42no—
388C22×C83—41no—
389C22×C83—42no—
390C22×C83—41no—
391C22×C83—42no—
392C22×C83—41no—
393C22×C83—42no—
394C22×C83—42no—
395C22×C83—42no—
396C22×C83—41no—
397C22×C83—42no—
398C22×C83—42no—
399C22×C83—42no—
400C22×C83—42no—
401C22×C83—42no—
402C22×C83—42no—
403C22×C83—816no—
404C22×C83—81no—
405C22×C83—81no—
406C22×C83—81no—
407C22×C83—81no—
408C22×C83—81no—
409C22×C83—81no—
410C22×C83—81no—
411C22×C83—81no—
412C22×C83—81no—
413C22×C83—81no—
414C22×C83—81no—
415C22×C83—81no—
416C22×C83—81no—
417C22×C83—81no—
418C22×C83—81no—
419C22×C83#52511yescharacteristic
420C22×C83D4211yescharacteristic
421C22×C83D4211yescharacteristic
422C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C83#57611yescharacteristic
425C22×C83#57611yescharacteristic
426C4×C83—22no—
427C4×C83—41no—
428C4×C83—41no—
429C4×C83—41no—
430C4×C83—42no—
431C4×C83—41no—
432C4×C83—81no—
433C4×C83—81no—
434C4×C83—81no—
435C4×C83C2×#12111yescharacteristic
436C4×C83#53811yescharacteristic
437C4×C83#54611yescharacteristic
438C4×C83#54611yescharacteristic
439#25168C8311yesmaximal, characteristic, direct product factor, Sylow
440C2×C83—42no—
441C2×C83—44no—
442C2×C83—82no—
443C2×C83—82no—
444C2×C83—161no—
445C2×C83#242411yescharacteristic
446C2×C83#310911yescharacteristic
447C2×C83#312211yescharacteristic
448C2×C83#326411yescharacteristic
449C2×C83#326411yescharacteristic
450C2×C83#326411yescharacteristic
451C2×C83#327411yescharacteristic
452C2×#459C2×C8311yescharacteristic, complemented
453C2×#447C2×C8311yescharacteristic, complemented
454C2×#447C2×C8311yescharacteristic, complemented
455C2×#442C2×C8311yescharacteristic, complemented
456#2428C2×C8311yescharacteristic, complemented
457D4×C22⋊C4C2×C8311yescharacteristic, complemented
458#2065C2×C8311yescharacteristic, complemented
459#2034C2×C8311yescharacteristic, complemented
460#2034C2×C8311yescharacteristic, complemented
461#2011C2×C8311yescharacteristic, complemented
462#1972C2×C8311yescharacteristic, complemented
463#1924C2×C8311yescharacteristic, complemented
464#1879C2×C8311yescharacteristic, complemented
465#1879C2×C8311yescharacteristic, complemented
466#1864C2×C8311yescharacteristic, complemented
467C83#2516811yescharacteristic, direct product factor, Sylow
468C23×D4C22×C8311yescharacteristic
469C22×D8C22×C8311yescharacteristic
470C22×D8C22×C8311yescharacteristic
471C22×D8C22×C8311yescharacteristic
472C22×D8C22×C8311yescharacteristic
473C2×#127C22×C8311yescharacteristic, complemented
474C2×#121—21no—
475C2×#121C22×C8311yescharacteristic
476C2×#121C22×C8311yescharacteristic
477C2×C4×D4C22×C8311yescharacteristic
478C2×C4×D4C22×C8311yescharacteristic
479C2×C4×D4C22×C8311yescharacteristic, complemented
480C22×C22⋊C4—21no—
481#459—24no—
482#447—24no—
483#447—24no—
484#442—24no—
485C2×#106C22×C8311yescharacteristic, complemented
486C2×#106C22×C8311yescharacteristic, complemented
487C2×C4⋊C8C22×C8311yescharacteristic, complemented
488C2×#102C22×C8311yescharacteristic
489C2×#102C22×C8311yescharacteristic
490C2×#102C22×C8311yescharacteristic
491C2×#102C22×C8311yescharacteristic
492C2×#102C22×C8311yescharacteristic, complemented
493C2×#102C22×C8311yescharacteristic, complemented
494C2×#102C22×C8311yescharacteristic, complemented
495C2×#102C22×C8311yescharacteristic, complemented
496C2×C22⋊C8C22×C8311yescharacteristic
497C2×C22⋊C8C22×C8311yescharacteristic
498C2×#97C22×C8311yescharacteristic, complemented
499#394—21no—
500#392—21no—
501#390C22×C8311yescharacteristic
502#390C22×C8311yescharacteristic
503#390C22×C8311yescharacteristic, complemented
504#389C22×C8311yescharacteristic, complemented
505#386—21no—
506#386—21no—
507#386—21no—
508#380C22×C8311yescharacteristic
509#379—21no—
510C4×C22⋊C4C22×C8311yescharacteristic
511#340C22×C8311yescharacteristic, complemented
512#340C22×C8311yescharacteristic, complemented
513#336C22×C8311yescharacteristic, complemented
514#336C22×C8311yescharacteristic, complemented
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C23×C8311yescharacteristic
528C22×D4C23×C8311yescharacteristic
529C22×D4C23×C8311yescharacteristic
530C22×D4C23×C8311yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C23×C8311yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8D4×C8314yescomplemented
547C22×C8C23×C8311yescharacteristic
548C22×C8C23×C8311yescharacteristic
549C22×C8C23×C8311yescharacteristic
550C22×C8C23×C8311yescharacteristic
551#127—22no—
552#127—41no—
553#121—22no—
554#121—22no—
555#121—44no—
556#121—41no—
557#121—41no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4C23×C8311yescharacteristic
566C2×C4⋊C4C23×C8311yescharacteristic
567C2×C4⋊C4C23×C8311yescharacteristic
568C2×C4⋊C4C23×C8311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—44no—
582C2×C22⋊C4D4×C8311yescharacteristic
583C2×C22⋊C4D4×C8311yescharacteristic
584C2×C42C23×C8311yescharacteristic
585C2×C42C23×C8311yescharacteristic
586#106—22no—
587#106—41no—
588C4⋊C8—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102D4×C8314yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599#97—22no—
600#95—21no—
601#95—21no—
602#95D4×C8311yescharacteristic
603#95D4×C8311yescharacteristic
604C24—21no—
605C24—24no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C8311yescharacteristic
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4C2×D4×C8312yes—
655C2×D4C2×D4×C8312yes—
656C2×D4C2×D4×C8312yes—
657C2×D4#41×C8312yes—
658C2×D4#41×C8312yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—81no—
678C22×C4C2×D4×C8311yescharacteristic
679C22×C4C2×D4×C8311yescharacteristic
680C22×C4C2×D4×C8311yescharacteristic
681C22×C4C2×D4×C8311yescharacteristic
682C22×C4C2×D4×C8311yescharacteristic
683C22×C4C24×C8311yescharacteristic
684D8—28no—
685D8—44no—
686D8—44no—
687D8—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8C2×D4×C8312yes—
699C2×C8C2×D4×C8312yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4C2×D4×C8312yes—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C22⋊C4—81no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—22no—
738C23—48no—
739C23—48no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23AGL(1,ℤ/8)×C8312yes—
769C23C22×D4×C8311yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4#121×C8314yescomplemented
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4—84no—
824C2×C4AGL(1,ℤ/8)×C8312yes—
825C2×C4C22×D4×C8311yescharacteristic
826C2×C4C22×D4×C8311yescharacteristic
827C2×C4C2×#41×C8311yescharacteristic
828C2×C4C2×#41×C8311yescharacteristic
829C2×C4H(5,𝔽2)×C8311yescharacteristic
830C2×C4H(5,𝔽2)×C8311yescharacteristic
831C8—22no—
832C8—22no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—24no—
837C22—22no—
838C22—22no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—816no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22#525×C8311yescharacteristic
872C22D42×C8311yescharacteristic
873C22D42×C8311yescharacteristic
874C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
875C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
876C22#576×C8311yescharacteristic
877C22#576×C8311yescharacteristic
878C4—22no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—42no—
883C4—41no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4C2×#121×C8311yescharacteristic
888C4#538×C8311yescharacteristic
889C4#546×C8311yescharacteristic
890C4#546×C8311yescharacteristic
891C2—42no—
892C2—44no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2C83×#242411yescharacteristic
897C2C83×#310911yescharacteristic
898C2C83×#312211yescharacteristic
899C2C83×#326411yescharacteristic
900C2C83×#326411yescharacteristic
901C2C83×#326411yescharacteristic
902C2C83×#327411yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C4×C22⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C83C2semidirect
2. C2×#447×C83C2semidirect
3. C2×#447×C83C2semidirect
4. C2×#442×C83C2semidirect
5. C83×#2428C2semidirect
6. D4×C22⋊C4×C83C2semidirect
7. C83×#2065C2semidirect
8. C83×#2034C2semidirect
9. C83×#2034C2semidirect
10. C83×#2011C2semidirect
11. C83×#1972C2semidirect
12. C83×#1924C2semidirect
13. C83×#1879C2semidirect
14. C83×#1879C2semidirect
15. C83×#1864C2semidirect
21. C2×#127×C83C22semidirect
27. C2×C4×D4×C83C22semidirect
33. C2×#106×C83C22semidirect
34. C2×#106×C83C22semidirect
35. C2×C4⋊C8×C83C22semidirect
40. C2×#102×C83C22semidirect
41. C2×#102×C83C22semidirect
42. C2×#102×C83C22semidirect
43. C2×#102×C83C22semidirect
46. C2×#97×C83C22semidirect
51. #390×C83C22semidirect
52. #389×C83C22semidirect
59. #340×C83C22semidirect
60. #340×C83C22semidirect
61. #336×C83C22semidirect
62. #336×C83C22semidirect
94. C2×D8×C83D4semidirect
144. #102×C83D4semidirect
338. D4×C83#121semidirect
439. #25168C83direct (N × H)
452. C2×#459C2×C83semidirect
453. C2×#447C2×C83semidirect
454. C2×#447C2×C83semidirect
455. C2×#442C2×C83semidirect
456. #2428C2×C83semidirect
457. D4×C22⋊C4C2×C83semidirect
458. #2065C2×C83semidirect
459. #2034C2×C83semidirect
460. #2034C2×C83semidirect
461. #2011C2×C83semidirect
462. #1972C2×C83semidirect
463. #1924C2×C83semidirect
464. #1879C2×C83semidirect
465. #1879C2×C83semidirect
466. #1864C2×C83semidirect
467. C83#25168direct (N × H)
473. C2×#127C22×C83semidirect
479. C2×C4×D4C22×C83semidirect
485. C2×#106C22×C83semidirect
486. C2×#106C22×C83semidirect
487. C2×C4⋊C8C22×C83semidirect
492. C2×#102C22×C83semidirect
493. C2×#102C22×C83semidirect
494. C2×#102C22×C83semidirect
495. C2×#102C22×C83semidirect
498. C2×#97C22×C83semidirect
503. #390C22×C83semidirect
504. #389C22×C83semidirect
511. #340C22×C83semidirect
512. #340C22×C83semidirect
513. #336C22×C83semidirect
514. #336C22×C83semidirect
546. C2×D8D4×C83semidirect
596. #102D4×C83semidirect
790. D4#121×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C832
C2×#447×C832
C2×#442×C832
C83×#24282
D4×C22⋊C4×C832
C83×#20652
C83×#20342
C83×#20112
C83×#19722
C83×#19242
C83×#18792
C83×#18642
#2516883