Finite Group Databasebeta

← C83×#22868 #35250692

Subgroups — C83×#22868 #35250692

Order 21248.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C83C211yesmaximal, characteristic
2C2×#442×C83C211yesmaximal, characteristic, complemented
3C2×#418×C83C211yesmaximal, characteristic, complemented
4C83×#2363C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
6C83×#1970C211yesmaximal, characteristic, complemented
7C83×#1936C211yesmaximal, characteristic, complemented
8C83×#1926C211yesmaximal, characteristic, complemented
9C83×#1895C211yesmaximal, characteristic, complemented
10C83×#1879C211yesmaximal, characteristic, complemented
11C83×#1879C211yesmaximal, characteristic, complemented
12C83×#1862C211yesmaximal, characteristic, complemented
13C83×#1854C211yesmaximal, characteristic, complemented
14C4×#102×C83C211yesmaximal, characteristic, complemented
15C83×#1753C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C22×D8×C83C2211yescharacteristic
18C22×D8×C83C2211yescharacteristic
19C22×M16×C83C2211yescharacteristic
20C2×#121×C83C2211yescharacteristic
21C2×C4×D4×C83C2211yescharacteristic
22C2×C4×D4×C83C2211yescharacteristic
23C2×C4×D4×C83C2211yescharacteristic, complemented
24C2×#117×C83C2211yescharacteristic
25C22×C22⋊C4×C83—21no—
26#447×C83C418yescomplemented
27#442×C83—24no—
28C2×#107×C83C2211yescharacteristic, complemented
29C2×#106×C83C2211yescharacteristic, complemented
30#418×C83—24no—
31C2×#102×C83C2211yescharacteristic
32C2×#102×C83C2211yescharacteristic
33C2×#102×C83C2211yescharacteristic
34C2×#102×C83C2211yescharacteristic
35C2×#102×C83C2211yescharacteristic
36C2×#102×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic, complemented
38C2×#102×C83C2211yescharacteristic, complemented
39C2×C22⋊C8×C83C2211yescharacteristic
40C2×#97×C83C2211yescharacteristic, complemented
41C2×C4×C8×C83C2211yescharacteristic, complemented
42#390×C83—21no—
43#390×C83C2211yescharacteristic
44#390×C83C2211yescharacteristic
45#390×C83C2211yescharacteristic, complemented
46#389×C83C2211yescharacteristic, complemented
47#388×C83—21no—
48#386×C83—21no—
49#386×C83—21no—
50#386×C83—21no—
51#380×C83C2211yescharacteristic
52#379×C83—21no—
53C4×C4⋊C4×C83C2211yescharacteristic, complemented
54C4×C22⋊C4×C83—21no—
55C4×C22⋊C4×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic, complemented
57#340×C83C2211yescharacteristic, complemented
58#340×C83C2211yescharacteristic, complemented
59#340×C83C2211yescharacteristic, complemented
60#336×C83C2211yescharacteristic, complemented
61#336×C83C2211yescharacteristic, complemented
62C25×C83—21no—
63C22×D4×C83—22no—
64C22×D4×C83—22no—
65C22×D4×C83—21no—
66C22×D4×C83—21no—
67C22×D4×C83—22no—
68C22×D4×C83—41no—
69C22×D4×C83—41no—
70C22×D4×C83C2×C414yescomplemented
71C22×D4×C83C2311yescharacteristic
72C22×D4×C83C2311yescharacteristic
73C22×D4×C83C2311yescharacteristic
74C23×C4×C83—21no—
75C23×C4×C83—21no—
76C23×C4×C83—21no—
77C23×C4×C83C2311yescharacteristic
78C2×D8×C83—22no—
79C2×D8×C83—22no—
80C2×D8×C83—41no—
81C2×D8×C83—41no—
82C2×D8×C83C2×C414yes—
83C2×D8×C83C2×C414yescomplemented
84C2×M16×C83—22no—
85C2×M16×C83—22no—
86C2×M16×C83—41no—
87C22×C8×C83C2311yescharacteristic
88C22×C8×C83C2311yescharacteristic
89C22×C8×C83C2311yescharacteristic
90C22×C8×C83C2311yescharacteristic
91#121×C83—22no—
92#121×C83C2×C414yescomplemented
93C4×D4×C83—22no—
94C4×D4×C83—22no—
95C4×D4×C83—22no—
96C4×D4×C83—41no—
97C4×D4×C83—41no—
98C4×D4×C83—41no—
99#117×C83—22no—
100#117×C83—41no—
101C2×C4⋊C4×C83—21no—
102C2×C4⋊C4×C83C2311yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C4⋊C4×C83C2311yescharacteristic
105C2×C4⋊C4×C83C2311yescharacteristic
106C2×C4⋊C4×C83C2311yescharacteristic
107C2×C22⋊C4×C83—21no—
108C2×C22⋊C4×C83—21no—
109C2×C22⋊C4×C83—21no—
110C2×C22⋊C4×C83—21no—
111C2×C22⋊C4×C83—21no—
112C2×C22⋊C4×C83—21no—
113C2×C22⋊C4×C83—21no—
114C2×C22⋊C4×C83—21no—
115C2×C22⋊C4×C83—21no—
116C2×C22⋊C4×C83—21no—
117C2×C22⋊C4×C83—21no—
118C2×C22⋊C4×C83—21no—
119C2×C22⋊C4×C83—44no—
120C2×C22⋊C4×C83D411yescharacteristic
121C2×C22⋊C4×C83D411yescharacteristic
122C2×C42×C83—21no—
123C2×C42×C83—21no—
124C2×C42×C83C2311yescharacteristic
125C2×C42×C83C2311yescharacteristic
126#107×C83—41no—
127#106×C83—22no—
128#102×C83—22no—
129#102×C83—22no—
130#102×C83—22no—
131#102×C83—22no—
132#102×C83—41no—
133#102×C83C2×C414yescomplemented
134#102×C83C2×C414yescomplemented
135#102×C83D414yescomplemented
136C22⋊C8×C83C2×C414yescomplemented
137#97×C83—22no—
138C4×C8×C83—41no—
139#95×C83—21no—
140#95×C83—21no—
141#95×C83—21no—
142#95×C83D411yescharacteristic
143#95×C83D411yescharacteristic
144C24×C83—21no—
145C24×C83—21no—
146C24×C83—21no—
147C24×C83—24no—
148C24×C83—42no—
149C24×C83—42no—
150C24×C83—42no—
151C24×C83—42no—
152C24×C83—81no—
153C24×C83—81no—
154C24×C83C2×D411yescharacteristic
155C2×D4×C83—28no—
156C2×D4×C83—24no—
157C2×D4×C83—24no—
158C2×D4×C83—21no—
159C2×D4×C83—21no—
160C2×D4×C83—21no—
161C2×D4×C83—21no—
162C2×D4×C83—21no—
163C2×D4×C83—21no—
164C2×D4×C83—21no—
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—44no—
172C2×D4×C83—44no—
173C2×D4×C83—44no—
174C2×D4×C83—42no—
175C2×D4×C83—42no—
176C2×D4×C83—81no—
177C2×D4×C83—81no—
178C2×D4×C83C22×C412yes—
179C2×D4×C83C22×C412yes—
180C2×D4×C83C22×C412yes—
181C2×D4×C83C2×D412yes—
182C2×D4×C83#4112yes—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—42no—
193C22×C4×C83—42no—
194C22×C4×C83—42no—
195C22×C4×C83—42no—
196C22×C4×C83—42no—
197C22×C4×C83—42no—
198C22×C4×C83—81no—
199C22×C4×C83—81no—
200C22×C4×C83—81no—
201C22×C4×C83C22×C412yes—
202C22×C4×C83C2×D411yescharacteristic
203C22×C4×C83C2×D411yescharacteristic
204C22×C4×C83C2×D411yescharacteristic
205C22×C4×C83C2×D411yescharacteristic
206C22×C4×C83C2×D411yescharacteristic
207C22×C4×C83#4112yes—
208C22×C4×C83C2411yescharacteristic
209D8×C83—28no—
210D8×C83—44no—
211M16×C83—44no—
212C2×C8×C83—21no—
213C2×C8×C83—21no—
214C2×C8×C83—21no—
215C2×C8×C83—21no—
216C2×C8×C83—21no—
217C2×C8×C83—21no—
218C2×C8×C83—21no—
219C2×C8×C83—21no—
220C2×C8×C83—21no—
221C2×C8×C83C22×C412yes—
222C2×C8×C83C22×C412yes—
223C2×C8×C83C2×D412yes—
224C4⋊C4×C83—21no—
225C4⋊C4×C83—21no—
226C4⋊C4×C83—21no—
227C4⋊C4×C83—21no—
228C4⋊C4×C83—21no—
229C4⋊C4×C83—21no—
230C4⋊C4×C83—21no—
231C4⋊C4×C83—21no—
232C4⋊C4×C83—81no—
233C4⋊C4×C83C22×C412yes—
234C4⋊C4×C83C2×D412yes—
235C22⋊C4×C83—24no—
236C22⋊C4×C83—22no—
237C22⋊C4×C83—41no—
238C22⋊C4×C83—42no—
239C22⋊C4×C83—42no—
240C22⋊C4×C83—42no—
241C22⋊C4×C83—42no—
242C22⋊C4×C83—42no—
243C22⋊C4×C83—42no—
244C22⋊C4×C83—42no—
245C22⋊C4×C83—42no—
246C22⋊C4×C83—81no—
247C22⋊C4×C83—81no—
248C22⋊C4×C83—81no—
249C42×C83—21no—
250C42×C83—21no—
251C42×C83—21no—
252C42×C83—21no—
253C42×C83—42no—
254C42×C83—81no—
255C23×C83—22no—
256C23×C83—21no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—21no—
260C23×C83—21no—
261C23×C83—21no—
262C23×C83—21no—
263C23×C83—21no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—48no—
267C23×C83—48no—
268C23×C83—41no—
269C23×C83—41no—
270C23×C83—41no—
271C23×C83—41no—
272C23×C83—41no—
273C23×C83—41no—
274C23×C83—41no—
275C23×C83—41no—
276C23×C83—41no—
277C23×C83—41no—
278C23×C83—41no—
279C23×C83—41no—
280C23×C83—41no—
281C23×C83—41no—
282C23×C83—41no—
283C23×C83—41no—
284C23×C83—84no—
285C23×C83—84no—
286C23×C83—84no—
287C23×C83—84no—
288C23×C83—84no—
289C23×C83C4×D412yes—
290C23×C83C22×D411yescharacteristic
291D4×C83—22no—
292D4×C83—22no—
293D4×C83—22no—
294D4×C83—22no—
295D4×C83—22no—
296D4×C83—22no—
297D4×C83—22no—
298D4×C83—48no—
299D4×C83—41no—
300D4×C83—41no—
301D4×C83—41no—
302D4×C83—41no—
303D4×C83—84no—
304D4×C83C4×D414yes—
305C2×C4×C83—21no—
306C2×C4×C83—21no—
307C2×C4×C83—21no—
308C2×C4×C83—21no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—21no—
315C2×C4×C83—21no—
316C2×C4×C83—22no—
317C2×C4×C83—21no—
318C2×C4×C83—21no—
319C2×C4×C83—21no—
320C2×C4×C83—21no—
321C2×C4×C83—21no—
322C2×C4×C83—21no—
323C2×C4×C83—21no—
324C2×C4×C83—41no—
325C2×C4×C83—41no—
326C2×C4×C83—41no—
327C2×C4×C83—41no—
328C2×C4×C83—41no—
329C2×C4×C83—41no—
330C2×C4×C83—41no—
331C2×C4×C83—41no—
332C2×C4×C83—41no—
333C2×C4×C83—41no—
334C2×C4×C83—41no—
335C2×C4×C83—41no—
336C2×C4×C83—41no—
337C2×C4×C83—84no—
338C2×C4×C83—84no—
339C2×C4×C83—84no—
340C2×C4×C83C4×D412yes—
341C2×C4×C83AGL(1,ℤ/8)12yes—
342C2×C4×C83C23×C411yescharacteristic
343C2×C4×C83C22×D411yescharacteristic
344C2×C4×C83C2×#4111yescharacteristic
345C2×C4×C83C2×#4111yescharacteristic
346C2×C4×C83H(5,𝔽2)11yescharacteristic
347C2×C4×C83H(5,𝔽2)11yescharacteristic
348C8×C83—22no—
349C8×C83—22no—
350C8×C83—22no—
351C8×C83—41no—
352C22×C83—22no—
353C22×C83—24no—
354C22×C83—22no—
355C22×C83—22no—
356C22×C83—42no—
357C22×C83—42no—
358C22×C83—41no—
359C22×C83—42no—
360C22×C83—42no—
361C22×C83—41no—
362C22×C83—42no—
363C22×C83—41no—
364C22×C83—41no—
365C22×C83—42no—
366C22×C83—42no—
367C22×C83—42no—
368C22×C83—42no—
369C22×C83—42no—
370C22×C83—42no—
371C22×C83—42no—
372C22×C83—816no—
373C22×C83—81no—
374C22×C83—81no—
375C22×C83—81no—
376C22×C83—81no—
377C22×C83—81no—
378C22×C83—81no—
379C22×C83—81no—
380C22×C83—81no—
381C22×C83C2×C4×D411yescharacteristic
382C22×C83D4211yescharacteristic
383C22×C83#54611yescharacteristic
384C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C83#57511yescharacteristic
386C22×C83#57611yescharacteristic
387C22×C83#57611yescharacteristic
388C4×C83—22no—
389C4×C83—22no—
390C4×C83—42no—
391C4×C83—41no—
392C4×C83—42no—
393C4×C83—41no—
394C4×C83—41no—
395C4×C83—81no—
396C4×C83—81no—
397C4×C83—81no—
398C4×C83C2×C4×D411yescharacteristic
399C4×C83#51811yescharacteristic
400C4×C83#54611yescharacteristic
401C4×C83#55111yescharacteristic
402#22868C8311yesmaximal, characteristic, direct product factor, Sylow
403C2×C83—42no—
404C2×C83—44no—
405C2×C83—82no—
406C2×C83—82no—
407C2×C83#235811yescharacteristic
408C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
409C2×C83#294811yescharacteristic
410C2×C83#327311yescharacteristic
411C2×C83#327411yescharacteristic
412C2×C83#331811yescharacteristic
413C2×C83#331911yescharacteristic
414C2×#447C2×C8311yescharacteristic
415C2×#442C2×C8311yescharacteristic, complemented
416C2×#418C2×C8311yescharacteristic, complemented
417#2363C2×C8311yescharacteristic, complemented
418D4×C22⋊C4C2×C8311yescharacteristic, complemented
419#1970C2×C8311yescharacteristic, complemented
420#1936C2×C8311yescharacteristic, complemented
421#1926C2×C8311yescharacteristic, complemented
422#1895C2×C8311yescharacteristic, complemented
423#1879C2×C8311yescharacteristic, complemented
424#1879C2×C8311yescharacteristic, complemented
425#1862C2×C8311yescharacteristic, complemented
426#1854C2×C8311yescharacteristic, complemented
427C4×#102C2×C8311yescharacteristic, complemented
428#1753C2×C8311yescharacteristic, complemented
429C83#2286811yescharacteristic, direct product factor, Sylow
430C23×D4C22×C8311yescharacteristic
431C22×D8C22×C8311yescharacteristic
432C22×D8C22×C8311yescharacteristic
433C22×M16C22×C8311yescharacteristic
434C2×#121C22×C8311yescharacteristic
435C2×C4×D4C22×C8311yescharacteristic
436C2×C4×D4C22×C8311yescharacteristic
437C2×C4×D4C22×C8311yescharacteristic, complemented
438C2×#117C22×C8311yescharacteristic
439C22×C22⋊C4—21no—
440#447C4×C8318yescomplemented
441#442—24no—
442C2×#107C22×C8311yescharacteristic, complemented
443C2×#106C22×C8311yescharacteristic, complemented
444#418—24no—
445C2×#102C22×C8311yescharacteristic
446C2×#102C22×C8311yescharacteristic
447C2×#102C22×C8311yescharacteristic
448C2×#102C22×C8311yescharacteristic
449C2×#102C22×C8311yescharacteristic
450C2×#102C22×C8311yescharacteristic
451C2×#102C22×C8311yescharacteristic, complemented
452C2×#102C22×C8311yescharacteristic, complemented
453C2×C22⋊C8C22×C8311yescharacteristic
454C2×#97C22×C8311yescharacteristic, complemented
455C2×C4×C8C22×C8311yescharacteristic, complemented
456#390—21no—
457#390C22×C8311yescharacteristic
458#390C22×C8311yescharacteristic
459#390C22×C8311yescharacteristic, complemented
460#389C22×C8311yescharacteristic, complemented
461#388—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#380C22×C8311yescharacteristic
466#379—21no—
467C4×C4⋊C4C22×C8311yescharacteristic, complemented
468C4×C22⋊C4—21no—
469C4×C22⋊C4C22×C8311yescharacteristic
470#340C22×C8311yescharacteristic, complemented
471#340C22×C8311yescharacteristic, complemented
472#340C22×C8311yescharacteristic, complemented
473#340C22×C8311yescharacteristic, complemented
474#336C22×C8311yescharacteristic, complemented
475#336C22×C8311yescharacteristic, complemented
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×C4×C8314yescomplemented
485C22×D4C23×C8311yescharacteristic
486C22×D4C23×C8311yescharacteristic
487C22×D4C23×C8311yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C8311yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×C4×C8314yes—
497C2×D8C2×C4×C8314yescomplemented
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C8311yescharacteristic
502C22×C8C23×C8311yescharacteristic
503C22×C8C23×C8311yescharacteristic
504C22×C8C23×C8311yescharacteristic
505#121—22no—
506#121C2×C4×C8314yescomplemented
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C8311yescharacteristic
517C2×C4⋊C4C23×C8311yescharacteristic
518C2×C4⋊C4C23×C8311yescharacteristic
519C2×C4⋊C4C23×C8311yescharacteristic
520C2×C4⋊C4C23×C8311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—44no—
534C2×C22⋊C4D4×C8311yescharacteristic
535C2×C22⋊C4D4×C8311yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C8311yescharacteristic
539C2×C42C23×C8311yescharacteristic
540#107—41no—
541#106—22no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—41no—
547#102C2×C4×C8314yescomplemented
548#102C2×C4×C8314yescomplemented
549#102D4×C8314yescomplemented
550C22⋊C8C2×C4×C8314yescomplemented
551#97—22no—
552C4×C8—41no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95D4×C8311yescharacteristic
557#95D4×C8311yescharacteristic
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C8311yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C8312yes—
593C2×D4C22×C4×C8312yes—
594C2×D4C22×C4×C8312yes—
595C2×D4C2×D4×C8312yes—
596C2×D4#41×C8312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C8312yes—
616C22×C4C2×D4×C8311yescharacteristic
617C22×C4C2×D4×C8311yescharacteristic
618C22×C4C2×D4×C8311yescharacteristic
619C22×C4C2×D4×C8311yescharacteristic
620C22×C4C2×D4×C8311yescharacteristic
621C22×C4#41×C8312yes—
622C22×C4C24×C8311yescharacteristic
623D8—28no—
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C22×C4×C8312yes—
636C2×C8C22×C4×C8312yes—
637C2×C8C2×D4×C8312yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C8312yes—
648C4⋊C4C2×D4×C8312yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C8312yes—
704C23C22×D4×C8311yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C8314yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C8312yes—
755C2×C4AGL(1,ℤ/8)×C8312yes—
756C2×C4C23×C4×C8311yescharacteristic
757C2×C4C22×D4×C8311yescharacteristic
758C2×C4C2×#41×C8311yescharacteristic
759C2×C4C2×#41×C8311yescharacteristic
760C2×C4H(5,𝔽2)×C8311yescharacteristic
761C2×C4H(5,𝔽2)×C8311yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C8311yescharacteristic
796C22D42×C8311yescharacteristic
797C22#546×C8311yescharacteristic
798C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
799C22#575×C8311yescharacteristic
800C22#576×C8311yescharacteristic
801C22#576×C8311yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—42no—
806C4—41no—
807C4—42no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C8311yescharacteristic
813C4#518×C8311yescharacteristic
814C4#546×C8311yescharacteristic
815C4#551×C8311yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2C83×#235811yescharacteristic
821C2C4×AGL(1,ℤ/8)×C8311yescharacteristic
822C2C83×#294811yescharacteristic
823C2C83×#327311yescharacteristic
824C2C83×#327411yescharacteristic
825C2C83×#331811yescharacteristic
826C2C83×#331911yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
prime radicalC2×#447×C83C2
LCSG ▷ C2×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
2. C2×#442×C83C2semidirect
3. C2×#418×C83C2semidirect
4. C83×#2363C2semidirect
5. D4×C22⋊C4×C83C2semidirect
6. C83×#1970C2semidirect
7. C83×#1936C2semidirect
8. C83×#1926C2semidirect
9. C83×#1895C2semidirect
10. C83×#1879C2semidirect
11. C83×#1879C2semidirect
12. C83×#1862C2semidirect
13. C83×#1854C2semidirect
14. C4×#102×C83C2semidirect
15. C83×#1753C2semidirect
23. C2×C4×D4×C83C22semidirect
26. #447×C83C4semidirect
28. C2×#107×C83C22semidirect
29. C2×#106×C83C22semidirect
37. C2×#102×C83C22semidirect
38. C2×#102×C83C22semidirect
40. C2×#97×C83C22semidirect
41. C2×C4×C8×C83C22semidirect
45. #390×C83C22semidirect
46. #389×C83C22semidirect
53. C4×C4⋊C4×C83C22semidirect
56. #340×C83C22semidirect
57. #340×C83C22semidirect
58. #340×C83C22semidirect
59. #340×C83C22semidirect
60. #336×C83C22semidirect
61. #336×C83C22semidirect
70. C22×D4×C83C2×C4semidirect
83. C2×D8×C83C2×C4semidirect
92. #121×C83C2×C4semidirect
133. #102×C83C2×C4semidirect
134. #102×C83C2×C4semidirect
135. #102×C83D4semidirect
136. C22⋊C8×C83C2×C4semidirect
402. #22868C83direct (N × H)
415. C2×#442C2×C83semidirect
416. C2×#418C2×C83semidirect
417. #2363C2×C83semidirect
418. D4×C22⋊C4C2×C83semidirect
419. #1970C2×C83semidirect
420. #1936C2×C83semidirect
421. #1926C2×C83semidirect
422. #1895C2×C83semidirect
423. #1879C2×C83semidirect
424. #1879C2×C83semidirect
425. #1862C2×C83semidirect
426. #1854C2×C83semidirect
427. C4×#102C2×C83semidirect
428. #1753C2×C83semidirect
429. C83#22868direct (N × H)
437. C2×C4×D4C22×C83semidirect
440. #447C4×C83semidirect
442. C2×#107C22×C83semidirect
443. C2×#106C22×C83semidirect
451. C2×#102C22×C83semidirect
452. C2×#102C22×C83semidirect
454. C2×#97C22×C83semidirect
455. C2×C4×C8C22×C83semidirect
459. #390C22×C83semidirect
460. #389C22×C83semidirect
467. C4×C4⋊C4C22×C83semidirect
470. #340C22×C83semidirect
471. #340C22×C83semidirect
472. #340C22×C83semidirect
473. #340C22×C83semidirect
474. #336C22×C83semidirect
475. #336C22×C83semidirect
484. C22×D4C2×C4×C83semidirect
497. C2×D8C2×C4×C83semidirect
506. #121C2×C4×C83semidirect
547. #102C2×C4×C83semidirect
548. #102C2×C4×C83semidirect
549. #102D4×C83semidirect
550. C22⋊C8C2×C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C832
C2×#442×C832
C2×#418×C832
C83×#23632
D4×C22⋊C4×C832
C83×#19702
C83×#19362
C83×#19262
C83×#18952
C83×#18792
C83×#18622
C83×#18542
C4×#102×C832
C83×#17532
#2286883