Finite Group Databasebeta

← C83×#22677 #35250501

Subgroups — C83×#22677 #35250501

Order 21248.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#440×C83C211yesmaximal, characteristic
2C2×#440×C83C211yesmaximal, characteristic
3C2×C4×SD16×C83C211yesmaximal, characteristic
4C83×#2351C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C83C211yesmaximal, characteristic
6C83×#1943C211yesmaximal, characteristic, complemented
7C83×#1942C211yesmaximal, characteristic, complemented
8C83×#1865C211yesmaximal, characteristic, complemented
9C83×#1864C211yesmaximal, characteristic
10C83×#1863C211yesmaximal, characteristic, complemented
11C83×#1862C211yesmaximal, characteristic
12C83×#1847C211yesmaximal, characteristic, complemented
13C83×#1804C211yesmaximal, characteristic
14C83×#1803C211yesmaximal, characteristic, complemented
15C83×#1771C211yesmaximal, characteristic, complemented
16C22×SD16×C83C2211yescharacteristic
17C2×C4×Q8×C83C2211yescharacteristic
18C2×C4×Q8×C83C2211yescharacteristic
19C2×C4×Q8×C83C2211yescharacteristic
20C2×C4×D4×C83C2211yescharacteristic
21C2×C4×D4×C83C2211yescharacteristic
22C2×C4×D4×C83C2211yescharacteristic
23C22×C4⋊C4×C83—21no—
24#440×C83—24no—
25#440×C83C418yescomplemented
26C4×SD16×C83—24no—
27C2×#107×C83C2211yescharacteristic
28C2×#107×C83C2211yescharacteristic
29C2×#107×C83C2211yescharacteristic
30C2×#106×C83C2211yescharacteristic
31C2×#106×C83C2211yescharacteristic
32C2×C4⋊C8×C83C2211yescharacteristic
33C2×#103×C83C2211yescharacteristic
34C2×#103×C83C2211yescharacteristic
35C2×#103×C83C2211yescharacteristic
36C2×#102×C83C2211yescharacteristic
37C2×#102×C83C2211yescharacteristic
38C2×#102×C83C2211yescharacteristic
39C2×#97×C83C2211yescharacteristic
40C2×#97×C83C2211yescharacteristic
41C2×C4×C8×C83C2211yescharacteristic
42#389×C83—21no—
43#389×C83—21no—
44#389×C83C2211yescharacteristic
45#389×C83C2211yescharacteristic
46#389×C83C2211yescharacteristic
47#389×C83C2211yescharacteristic
48#385×C83—21no—
49#385×C83—21no—
50#384×C83C2211yescharacteristic
51#382×C83—21no—
52#382×C83C2211yescharacteristic
53#380×C83—21no—
54C4×C4⋊C4×C83—21no—
55C4×C4⋊C4×C83C2211yescharacteristic
56#340×C83C2211yescharacteristic
57#340×C83C2211yescharacteristic
58#340×C83C2211yescharacteristic
59#340×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62C22×Q8×C83C2311yescharacteristic
63C22×D4×C83C2311yescharacteristic
64C23×C4×C83—21no—
65C23×C4×C83—21no—
66C23×C4×C83—21no—
67C2×SD16×C83C2×C414yes—
68C2×SD16×C83D414yes—
69C2×SD16×C83Q814yes—
70C22×C8×C83C2311yescharacteristic
71C22×C8×C83C2311yescharacteristic
72C22×C8×C83C2311yescharacteristic
73C22×C8×C83C2311yescharacteristic
74C4×Q8×C83—22no—
75C4×Q8×C83—22no—
76C4×Q8×C83—22no—
77C4×Q8×C83—41no—
78C4×Q8×C83—41no—
79C4×Q8×C83C2×C414yescomplemented
80C4×D4×C83—22no—
81C4×D4×C83—22no—
82C4×D4×C83—22no—
83C4×D4×C83—41no—
84C4×D4×C83—41no—
85C4×D4×C83C2×C414yes—
86C2×C4⋊C4×C83—21no—
87C2×C4⋊C4×C83—21no—
88C2×C4⋊C4×C83—21no—
89C2×C4⋊C4×C83—21no—
90C2×C4⋊C4×C83—21no—
91C2×C4⋊C4×C83—21no—
92C2×C4⋊C4×C83—21no—
93C2×C4⋊C4×C83—21no—
94C2×C4⋊C4×C83—21no—
95C2×C4⋊C4×C83—44no—
96C2×C4⋊C4×C83D411yescharacteristic
97C2×C4⋊C4×C83D411yescharacteristic
98C2×C4⋊C4×C83C2311yescharacteristic
99C2×C4⋊C4×C83C2311yescharacteristic
100C2×C4⋊C4×C83C2311yescharacteristic
101C2×C4⋊C4×C83C2311yescharacteristic
102C2×C4⋊C4×C83C2311yescharacteristic
103C2×C4⋊C4×C83C2311yescharacteristic
104C2×C22⋊C4×C83—21no—
105C2×C22⋊C4×C83—21no—
106C2×C22⋊C4×C83—21no—
107C2×C42×C83—21no—
108C2×C42×C83—21no—
109C2×C42×C83—21no—
110C2×C42×C83C2311yescharacteristic
111C2×C42×C83C2311yescharacteristic
112C2×C42×C83C2311yescharacteristic
113#107×C83—22no—
114#107×C83—41no—
115#107×C83C2×C414yescomplemented
116#106×C83—22no—
117#106×C83—41no—
118C4⋊C8×C83—22no—
119#103×C83—22no—
120#103×C83—22no—
121#103×C83C2×C414yescomplemented
122#102×C83—22no—
123#102×C83—22no—
124#102×C83C2×C414yes—
125#97×C83—22no—
126#97×C83C2×C414yescomplemented
127C4×C8×C83—22no—
128#95×C83—21no—
129#95×C83—21no—
130#95×C83—21no—
131#95×C83—21no—
132#95×C83—21no—
133#95×C83—21no—
134#95×C83D411yescharacteristic
135#95×C83D411yescharacteristic
136C24×C83—21no—
137C2×Q8×C83—21no—
138C2×Q8×C83—21no—
139C2×Q8×C83—21no—
140C2×Q8×C83C22×C412yes—
141C2×Q8×C83C2×D412yes—
142C2×Q8×C83C2×Q812yes—
143C2×D4×C83—21no—
144C2×D4×C83—21no—
145C2×D4×C83—21no—
146C2×D4×C83C22×C412yes—
147C2×D4×C83C2×D412yes—
148C2×D4×C83C2×Q812yes—
149C22×C4×C83—21no—
150C22×C4×C83—21no—
151C22×C4×C83—21no—
152C22×C4×C83—24no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—42no—
158C22×C4×C83—42no—
159C22×C4×C83—42no—
160C22×C4×C83—42no—
161C22×C4×C83—42no—
162C22×C4×C83—42no—
163C22×C4×C83—81no—
164C22×C4×C83—81no—
165C22×C4×C83C2×D411yescharacteristic
166C22×C4×C83C2×D411yescharacteristic
167C22×C4×C83C2×D411yescharacteristic
168C22×C4×C83C2×D411yescharacteristic
169C22×C4×C83C2×D411yescharacteristic
170C22×C4×C83C2×D411yescharacteristic
171C22×C4×C83C2411yescharacteristic
172SD16×C83C4⋊C4116yescomplemented
173C2×C8×C83—21no—
174C2×C8×C83—21no—
175C2×C8×C83—21no—
176C2×C8×C83—21no—
177C2×C8×C83—21no—
178C2×C8×C83—21no—
179C2×C8×C83—21no—
180C2×C8×C83—21no—
181C2×C8×C83C22×C412yes—
182C2×C8×C83C22×C412yes—
183C2×C8×C83C2×D412yes—
184C2×C8×C83C2×Q812yes—
185C4⋊C4×C83—24no—
186C4⋊C4×C83—22no—
187C4⋊C4×C83—21no—
188C4⋊C4×C83—21no—
189C4⋊C4×C83—21no—
190C4⋊C4×C83—21no—
191C4⋊C4×C83—21no—
192C4⋊C4×C83—21no—
193C4⋊C4×C83—21no—
194C4⋊C4×C83—21no—
195C4⋊C4×C83—21no—
196C4⋊C4×C83—21no—
197C4⋊C4×C83—41no—
198C4⋊C4×C83—42no—
199C4⋊C4×C83—42no—
200C4⋊C4×C83—42no—
201C4⋊C4×C83—42no—
202C4⋊C4×C83—42no—
203C4⋊C4×C83—42no—
204C4⋊C4×C83—42no—
205C4⋊C4×C83—81no—
206C4⋊C4×C83C22×C412yes—
207C4⋊C4×C83C22×C412yes—
208C22⋊C4×C83—24no—
209C22⋊C4×C83—42no—
210C22⋊C4×C83—42no—
211C42×C83—24no—
212C42×C83—21no—
213C42×C83—21no—
214C42×C83—21no—
215C42×C83—21no—
216C42×C83—42no—
217C42×C83—42no—
218C42×C83C22×C412yes—
219C42×C83#4112yes—
220C23×C83—22no—
221C23×C83—22no—
222C23×C83—22no—
223C23×C83—41no—
224C23×C83—41no—
225C23×C83—41no—
226C23×C83—41no—
227C23×C83C22×D411yescharacteristic
228Q8×C83—22no—
229Q8×C83—22no—
230Q8×C83—22no—
231Q8×C83C2×C4⋊C414yescomplemented
232D4×C83—22no—
233D4×C83—22no—
234D4×C83—22no—
235D4×C83C2×C4⋊C414yes—
236C2×C4×C83—22no—
237C2×C4×C83—21no—
238C2×C4×C83—22no—
239C2×C4×C83—22no—
240C2×C4×C83—21no—
241C2×C4×C83—21no—
242C2×C4×C83—21no—
243C2×C4×C83—21no—
244C2×C4×C83—21no—
245C2×C4×C83—22no—
246C2×C4×C83—22no—
247C2×C4×C83—21no—
248C2×C4×C83—21no—
249C2×C4×C83—21no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—48no—
257C2×C4×C83—41no—
258C2×C4×C83—41no—
259C2×C4×C83—41no—
260C2×C4×C83—41no—
261C2×C4×C83—41no—
262C2×C4×C83—41no—
263C2×C4×C83—41no—
264C2×C4×C83—41no—
265C2×C4×C83—41no—
266C2×C4×C83—41no—
267C2×C4×C83—41no—
268C2×C4×C83—41no—
269C2×C4×C83—41no—
270C2×C4×C83—41no—
271C2×C4×C83—41no—
272C2×C4×C83—41no—
273C2×C4×C83—84no—
274C2×C4×C83—84no—
275C2×C4×C83C4×D412yes—
276C2×C4×C83C4×D412yes—
277C2×C4×C83AGL(1,ℤ/8)12yes—
278C2×C4×C83C23×C411yescharacteristic
279C2×C4×C83C22×D411yescharacteristic
280C2×C4×C83C22×Q811yescharacteristic
281C2×C4×C83C2×#4111yescharacteristic
282C2×C4×C83H(5,𝔽2)11yescharacteristic
283C2×C4×C832−1+411yescharacteristic
284C8×C83—22no—
285C8×C83—41no—
286C8×C83—41no—
287C8×C83C2×C4⋊C414yescomplemented
288C22×C83—24no—
289C22×C83—42no—
290C22×C83—42no—
291C22×C83—42no—
292C22×C83—42no—
293C22×C83—42no—
294C22×C83—42no—
295C22×C83C2×C4×D411yescharacteristic
296C22×C83D4211yescharacteristic
297C22×C83D4×Q811yescharacteristic
298C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
299C22×C83#57511yescharacteristic
300C22×C83#57711yescharacteristic
301C22×C83#57811yescharacteristic
302C4×C83—24no—
303C4×C83—22no—
304C4×C83—22no—
305C4×C83—22no—
306C4×C83—42no—
307C4×C83—42no—
308C4×C83—41no—
309C4×C83—41no—
310C4×C83—41no—
311C4×C83—81no—
312C4×C83—81no—
313C4×C83—81no—
314C4×C83—81no—
315C4×C83C22×C4⋊C411yescharacteristic
316C4×C83#52011yescharacteristic
317C4×C83#54711yescharacteristic
318C4×C83#55411yescharacteristic
319#22677C8311yesmaximal, characteristic, direct product factor, Sylow
320C2×C83—44no—
321C2×C83D4×C4⋊C411yescharacteristic
322C2×C83C4×AGL(1,ℤ/8)11yescharacteristic
323C2×C83#294711yescharacteristic
324C2×C83#326511yescharacteristic
325C2×C83#326911yescharacteristic
326C2×C83#338611yescharacteristic
327C2×C83#338811yescharacteristic
328C2×#440C2×C8311yescharacteristic
329C2×#440C2×C8311yescharacteristic
330C2×C4×SD16C2×C8311yescharacteristic
331#2351C2×C8311yescharacteristic, complemented
332D4×C4⋊C4C2×C8311yescharacteristic
333#1943C2×C8311yescharacteristic, complemented
334#1942C2×C8311yescharacteristic, complemented
335#1865C2×C8311yescharacteristic, complemented
336#1864C2×C8311yescharacteristic
337#1863C2×C8311yescharacteristic, complemented
338#1862C2×C8311yescharacteristic
339#1847C2×C8311yescharacteristic, complemented
340#1804C2×C8311yescharacteristic
341#1803C2×C8311yescharacteristic, complemented
342#1771C2×C8311yescharacteristic, complemented
343C83#2267711yescharacteristic, direct product factor, Sylow
344C22×SD16C22×C8311yescharacteristic
345C2×C4×Q8C22×C8311yescharacteristic
346C2×C4×Q8C22×C8311yescharacteristic
347C2×C4×Q8C22×C8311yescharacteristic
348C2×C4×D4C22×C8311yescharacteristic
349C2×C4×D4C22×C8311yescharacteristic
350C2×C4×D4C22×C8311yescharacteristic
351C22×C4⋊C4—21no—
352#440—24no—
353#440C4×C8318yescomplemented
354C4×SD16—24no—
355C2×#107C22×C8311yescharacteristic
356C2×#107C22×C8311yescharacteristic
357C2×#107C22×C8311yescharacteristic
358C2×#106C22×C8311yescharacteristic
359C2×#106C22×C8311yescharacteristic
360C2×C4⋊C8C22×C8311yescharacteristic
361C2×#103C22×C8311yescharacteristic
362C2×#103C22×C8311yescharacteristic
363C2×#103C22×C8311yescharacteristic
364C2×#102C22×C8311yescharacteristic
365C2×#102C22×C8311yescharacteristic
366C2×#102C22×C8311yescharacteristic
367C2×#97C22×C8311yescharacteristic
368C2×#97C22×C8311yescharacteristic
369C2×C4×C8C22×C8311yescharacteristic
370#389—21no—
371#389—21no—
372#389C22×C8311yescharacteristic
373#389C22×C8311yescharacteristic
374#389C22×C8311yescharacteristic
375#389C22×C8311yescharacteristic
376#385—21no—
377#385—21no—
378#384C22×C8311yescharacteristic
379#382—21no—
380#382C22×C8311yescharacteristic
381#380—21no—
382C4×C4⋊C4—21no—
383C4×C4⋊C4C22×C8311yescharacteristic
384#340C22×C8311yescharacteristic
385#340C22×C8311yescharacteristic
386#340C22×C8311yescharacteristic
387#340C22×C8311yescharacteristic
388#336C22×C8311yescharacteristic
389#336C22×C8311yescharacteristic
390C22×Q8C23×C8311yescharacteristic
391C22×D4C23×C8311yescharacteristic
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—21no—
395C2×SD16C2×C4×C8314yes—
396C2×SD16D4×C8314yes—
397C2×SD16Q8×C8314yes—
398C22×C8C23×C8311yescharacteristic
399C22×C8C23×C8311yescharacteristic
400C22×C8C23×C8311yescharacteristic
401C22×C8C23×C8311yescharacteristic
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—22no—
405C4×Q8—41no—
406C4×Q8—41no—
407C4×Q8C2×C4×C8314yescomplemented
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—41no—
412C4×D4—41no—
413C4×D4C2×C4×C8314yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—44no—
424C2×C4⋊C4D4×C8311yescharacteristic
425C2×C4⋊C4D4×C8311yescharacteristic
426C2×C4⋊C4C23×C8311yescharacteristic
427C2×C4⋊C4C23×C8311yescharacteristic
428C2×C4⋊C4C23×C8311yescharacteristic
429C2×C4⋊C4C23×C8311yescharacteristic
430C2×C4⋊C4C23×C8311yescharacteristic
431C2×C4⋊C4C23×C8311yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42C23×C8311yescharacteristic
439C2×C42C23×C8311yescharacteristic
440C2×C42C23×C8311yescharacteristic
441#107—22no—
442#107—41no—
443#107C2×C4×C8314yescomplemented
444#106—22no—
445#106—41no—
446C4⋊C8—22no—
447#103—22no—
448#103—22no—
449#103C2×C4×C8314yescomplemented
450#102—22no—
451#102—22no—
452#102C2×C4×C8314yes—
453#97—22no—
454#97C2×C4×C8314yescomplemented
455C4×C8—22no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95D4×C8311yescharacteristic
463#95D4×C8311yescharacteristic
464C24—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8C22×C4×C8312yes—
469C2×Q8C2×D4×C8312yes—
470C2×Q8C2×Q8×C8312yes—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4C22×C4×C8312yes—
475C2×D4C2×D4×C8312yes—
476C2×D4C2×Q8×C8312yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—81no—
492C22×C4—81no—
493C22×C4C2×D4×C8311yescharacteristic
494C22×C4C2×D4×C8311yescharacteristic
495C22×C4C2×D4×C8311yescharacteristic
496C22×C4C2×D4×C8311yescharacteristic
497C22×C4C2×D4×C8311yescharacteristic
498C22×C4C2×D4×C8311yescharacteristic
499C22×C4C24×C8311yescharacteristic
500SD16C4⋊C4×C83116yescomplemented
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8C22×C4×C8312yes—
510C2×C8C22×C4×C8312yes—
511C2×C8C2×D4×C8312yes—
512C2×C8C2×Q8×C8312yes—
513C4⋊C4—24no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—41no—
526C4⋊C4—42no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4C22×C4×C8312yes—
535C4⋊C4C22×C4×C8312yes—
536C22⋊C4—24no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C42—24no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—42no—
545C42—42no—
546C42C22×C4×C8312yes—
547C42#41×C8312yes—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C22×D4×C8311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—22no—
559Q8C2×C4⋊C4×C8314yescomplemented
560D4—22no—
561D4—22no—
562D4—22no—
563D4C2×C4⋊C4×C8314yes—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—48no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—84no—
602C2×C4—84no—
603C2×C4C4×D4×C8312yes—
604C2×C4C4×D4×C8312yes—
605C2×C4AGL(1,ℤ/8)×C8312yes—
606C2×C4C23×C4×C8311yescharacteristic
607C2×C4C22×D4×C8311yescharacteristic
608C2×C4C22×Q8×C8311yescharacteristic
609C2×C4C2×#41×C8311yescharacteristic
610C2×C4H(5,𝔽2)×C8311yescharacteristic
611C2×C42−1+4×C8311yescharacteristic
612C8—22no—
613C8—41no—
614C8—41no—
615C8C2×C4⋊C4×C8314yescomplemented
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×C4×D4×C8311yescharacteristic
624C22D42×C8311yescharacteristic
625C22D4×Q8×C8311yescharacteristic
626C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
627C22#575×C8311yescharacteristic
628C22#577×C8311yescharacteristic
629C22#578×C8311yescharacteristic
630C4—24no—
631C4—22no—
632C4—22no—
633C4—22no—
634C4—42no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—81no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4C22×C4⋊C4×C8311yescharacteristic
644C4#520×C8311yescharacteristic
645C4#547×C8311yescharacteristic
646C4#554×C8311yescharacteristic
647C2—44no—
648C2D4×C4⋊C4×C8311yescharacteristic
649C2C4×AGL(1,ℤ/8)×C8311yescharacteristic
650C2C83×#294711yescharacteristic
651C2C83×#326511yescharacteristic
652C2C83×#326911yescharacteristic
653C2C83×#338611yescharacteristic
654C2C83×#338811yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutatorC2×C4C23×C4×C83
Frattini, cosocleC22×C4C24×C83
prime radicalC22×D4×C83C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C4×C4⋊C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C83×#2351C2semidirect
6. C83×#1943C2semidirect
7. C83×#1942C2semidirect
8. C83×#1865C2semidirect
10. C83×#1863C2semidirect
12. C83×#1847C2semidirect
14. C83×#1803C2semidirect
15. C83×#1771C2semidirect
25. #440×C83C4semidirect
79. C4×Q8×C83C2×C4semidirect
115. #107×C83C2×C4semidirect
121. #103×C83C2×C4semidirect
126. #97×C83C2×C4semidirect
172. SD16×C83C4⋊C4semidirect
231. Q8×C83C2×C4⋊C4semidirect
287. C8×C83C2×C4⋊C4semidirect
319. #22677C83direct (N × H)
331. #2351C2×C83semidirect
333. #1943C2×C83semidirect
334. #1942C2×C83semidirect
335. #1865C2×C83semidirect
337. #1863C2×C83semidirect
339. #1847C2×C83semidirect
341. #1803C2×C83semidirect
342. #1771C2×C83semidirect
343. C83#22677direct (N × H)
353. #440C4×C83semidirect
407. C4×Q8C2×C4×C83semidirect
443. #107C2×C4×C83semidirect
449. #103C2×C4×C83semidirect
454. #97C2×C4×C83semidirect
500. SD16C4⋊C4×C83semidirect
559. Q8C2×C4⋊C4×C83semidirect
615. C8C2×C4⋊C4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#440×C832
C2×C4×SD16×C832
C83×#23512
D4×C4⋊C4×C832
C83×#19432
C83×#19422
C83×#18652
C83×#18642
C83×#18632
C83×#18622
C83×#18472
C83×#18042
C83×#18032
C83×#17712
#2267783