Finite Group Databasebeta

← C83×#14421 #35242245

Subgroups — C83×#14421 #35242245

Order 21248.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#124×C83C211yesmaximal, characteristic
2C2×#391×C83C211yesmaximal, characteristic, complemented
3C2×#388×C83C211yesmaximal, characteristic, complemented
4C2×#386×C83C211yesmaximal, characteristic
5C2×#385×C83C211yesmaximal, characteristic, complemented
6C83×#1446C211yesmaximal, characteristic, complemented
7C83×#1440C211yesmaximal, characteristic, complemented
8C83×#1439C211yesmaximal, characteristic, complemented
9C83×#1439C211yesmaximal, characteristic, complemented
10C83×#1439C211yesmaximal, characteristic, complemented
11C83×#1438C211yesmaximal, characteristic
12C83×#1437C211yesmaximal, characteristic, complemented
13C83×C4⋊#95C211yesmaximal, characteristic, complemented
14C83×#1434C211yesmaximal, characteristic, complemented
15C83×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C24×C4×C83C2211yescharacteristic
19C2×#124×C83—24no—
20C2×#124×C83—24no—
21C2×#124×C83C418yescomplemented
22C22×C4⋊C4×C83C2211yescharacteristic
23C22×C4⋊C4×C83C2211yescharacteristic
24C22×C4⋊C4×C83C2211yescharacteristic
25C22×C22⋊C4×C83C2211yescharacteristic
26C22×C22⋊C4×C83C2211yescharacteristic
27C22×C22⋊C4×C83C2211yescharacteristic
28C22×C22⋊C4×C83C2211yescharacteristic
29C22×C22⋊C4×C83C2211yescharacteristic
30C22×C22⋊C4×C83C2211yescharacteristic
31C22×C22⋊C4×C83C2211yescharacteristic
32C22×C22⋊C4×C83C2211yescharacteristic
33C22×C22⋊C4×C83C2211yescharacteristic
34C22×C22⋊C4×C83C2211yescharacteristic
35C22×C22⋊C4×C83C2211yescharacteristic
36C22×C42×C83C2211yescharacteristic
37C22×C42×C83C2211yescharacteristic
38#391×C83—24no—
39#388×C83—24no—
40#386×C83—24no—
41#385×C83—24no—
42C2×#95×C83C2211yescharacteristic
43C2×#95×C83C2211yescharacteristic
44C2×#95×C83C2211yescharacteristic
45C2×#95×C83C2211yescharacteristic
46C2×#95×C83C2211yescharacteristic
47C2×#95×C83C2211yescharacteristic
48C2×#95×C83C2211yescharacteristic
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C2×#95×C83C2211yescharacteristic
57C2×#95×C83C2211yescharacteristic
58C25×C83C2311yescharacteristic
59C25×C83C2311yescharacteristic
60C22×Q8×C83—22no—
61C22×Q8×C83—22no—
62C22×Q8×C83—22no—
63C22×Q8×C83—22no—
64C22×Q8×C83—41no—
65C22×Q8×C83—41no—
66C22×Q8×C83C2×C414yescomplemented
67C22×D4×C83—22no—
68C22×D4×C83—22no—
69C22×D4×C83—22no—
70C22×D4×C83—22no—
71C22×D4×C83—41no—
72C22×D4×C83—41no—
73C22×D4×C83C2×C414yes—
74C23×C4×C83—22no—
75C23×C4×C83—22no—
76C23×C4×C83—22no—
77C23×C4×C83—41no—
78C23×C4×C83—41no—
79C23×C4×C83—41no—
80C23×C4×C83—41no—
81C23×C4×C83C2311yescharacteristic
82C23×C4×C83C2311yescharacteristic
83C23×C4×C83C2311yescharacteristic
84C23×C4×C83C2311yescharacteristic
85C23×C4×C83C2311yescharacteristic
86C23×C4×C83C2311yescharacteristic
87C23×C4×C83C2311yescharacteristic
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C23×C4×C83C2311yescharacteristic
94#124×C83—232no—
95C2×C4⋊C4×C83—22no—
96C2×C4⋊C4×C83—22no—
97C2×C4⋊C4×C83—22no—
98C2×C4⋊C4×C83—22no—
99C2×C4⋊C4×C83—22no—
100C2×C4⋊C4×C83—22no—
101C2×C4⋊C4×C83—41no—
102C2×C4⋊C4×C83—41no—
103C2×C4⋊C4×C83—41no—
104C2×C22⋊C4×C83—22no—
105C2×C22⋊C4×C83—22no—
106C2×C22⋊C4×C83—22no—
107C2×C22⋊C4×C83—22no—
108C2×C22⋊C4×C83—22no—
109C2×C22⋊C4×C83—22no—
110C2×C22⋊C4×C83—22no—
111C2×C22⋊C4×C83—22no—
112C2×C22⋊C4×C83—22no—
113C2×C22⋊C4×C83—22no—
114C2×C22⋊C4×C83—22no—
115C2×C22⋊C4×C83—22no—
116C2×C22⋊C4×C83—22no—
117C2×C22⋊C4×C83—22no—
118C2×C22⋊C4×C83—22no—
119C2×C22⋊C4×C83—41no—
120C2×C22⋊C4×C83—41no—
121C2×C22⋊C4×C83—41no—
122C2×C22⋊C4×C83—41no—
123C2×C22⋊C4×C83—41no—
124C2×C22⋊C4×C83—41no—
125C2×C22⋊C4×C83—41no—
126C2×C22⋊C4×C83—41no—
127C2×C22⋊C4×C83—41no—
128C2×C22⋊C4×C83—41no—
129C2×C22⋊C4×C83—41no—
130C2×C22⋊C4×C83—41no—
131C2×C22⋊C4×C83C2×C414yes—
132C2×C22⋊C4×C83C2×C414yes—
133C2×C22⋊C4×C83C2×C414yescomplemented
134C2×C22⋊C4×C83C2×C414yescomplemented
135C2×C22⋊C4×C83D414yes—
136C2×C22⋊C4×C83D414yes—
137C2×C42×C83—22no—
138C2×C42×C83—22no—
139C2×C42×C83—22no—
140C2×C42×C83—22no—
141C2×C42×C83—41no—
142C2×C42×C83C2×C414yescomplemented
143#95×C83—22no—
144#95×C83—22no—
145#95×C83—22no—
146#95×C83—22no—
147#95×C83—22no—
148#95×C83—22no—
149#95×C83—22no—
150#95×C83—22no—
151#95×C83—22no—
152#95×C83—41no—
153#95×C83—41no—
154#95×C83—41no—
155#95×C83—41no—
156#95×C83—41no—
157#95×C83—41no—
158#95×C83D414yes—
159C24×C83—21no—
160C24×C83—21no—
161C24×C83—21no—
162C24×C83—21no—
163C24×C83—21no—
164C24×C83—21no—
165C24×C83—21no—
166C24×C83—21no—
167C24×C83—21no—
168C24×C83—21no—
169C24×C83—21no—
170C24×C83—21no—
171C24×C83—21no—
172C24×C83—21no—
173C24×C83—21no—
174C24×C83—21no—
175C24×C83—21no—
176C24×C83—21no—
177C24×C83—21no—
178C24×C83—21no—
179C24×C83—21no—
180C24×C83—21no—
181C24×C83—21no—
182C24×C83—21no—
183C24×C83—21no—
184C24×C83—21no—
185C24×C83C22×C412yes—
186C24×C83C22×C412yes—
187C24×C83C2×D412yes—
188C24×C83C2×D412yes—
189C24×C83C2411yescharacteristic
190C2×Q8×C83—28no—
191C2×Q8×C83—28no—
192C2×Q8×C83—44no—
193C2×Q8×C83—44no—
194C2×Q8×C83—44no—
195C2×Q8×C83—44no—
196C2×Q8×C83—44no—
197C2×D4×C83—28no—
198C2×D4×C83—28no—
199C2×D4×C83—44no—
200C2×D4×C83—44no—
201C2×D4×C83—44no—
202C2×D4×C83—44no—
203C2×D4×C83—44no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
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—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
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—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83—21no—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83—21no—
265C22×C4×C83—21no—
266C22×C4×C83—21no—
267C22×C4×C83—21no—
268C22×C4×C83—21no—
269C22×C4×C83—21no—
270C22×C4×C83—21no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83—21no—
276C22×C4×C83—21no—
277C22×C4×C83—21no—
278C22×C4×C83—21no—
279C22×C4×C83—21no—
280C22×C4×C83—44no—
281C22×C4×C83—44no—
282C22×C4×C83—44no—
283C22×C4×C83—44no—
284C22×C4×C83—44no—
285C22×C4×C83—44no—
286C22×C4×C83—44no—
287C22×C4×C83C22×C412yes—
288C22×C4×C83C22×C412yes—
289C22×C4×C83C22×C412yes—
290C22×C4×C83C22×C412yes—
291C22×C4×C83C22×C412yes—
292C22×C4×C83C2×D412yes—
293C22×C4×C83C2×D412yes—
294C22×C4×C83C2×D412yes—
295C22×C4×C83C2×D412yes—
296C22×C4×C83C2×D412yes—
297C22×C4×C83C2×D412yes—
298C22×C4×C83C2×D412yes—
299C22×C4×C83#4112yes—
300C22×C4×C83#4112yes—
301C22×C4×C83#4112yes—
302C4⋊C4×C83—44no—
303C4⋊C4×C83—44no—
304C4⋊C4×C83—44no—
305C22⋊C4×C83—28no—
306C22⋊C4×C83—28no—
307C22⋊C4×C83—28no—
308C22⋊C4×C83—44no—
309C22⋊C4×C83—44no—
310C22⋊C4×C83—44no—
311C22⋊C4×C83—44no—
312C22⋊C4×C83—44no—
313C22⋊C4×C83—44no—
314C22⋊C4×C83—44no—
315C22⋊C4×C83C22⋊C4116yescomplemented
316C42×C83—28no—
317C42×C83—44no—
318C23×C83—22no—
319C23×C83—22no—
320C23×C83—22no—
321C23×C83—22no—
322C23×C83—22no—
323C23×C83—22no—
324C23×C83—22no—
325C23×C83—22no—
326C23×C83—22no—
327C23×C83—22no—
328C23×C83—22no—
329C23×C83—22no—
330C23×C83—22no—
331C23×C83—22no—
332C23×C83—22no—
333C23×C83—22no—
334C23×C83—22no—
335C23×C83—22no—
336C23×C83—22no—
337C23×C83—22no—
338C23×C83—22no—
339C23×C83—22no—
340C23×C83—22no—
341C23×C83—22no—
342C23×C83—22no—
343C23×C83—41no—
344C23×C83—41no—
345C23×C83—41no—
346C23×C83—41no—
347C23×C83—41no—
348C23×C83—41no—
349C23×C83—41no—
350C23×C83—41no—
351C23×C83—41no—
352C23×C83—41no—
353C23×C83—41no—
354C23×C83—41no—
355C23×C83—41no—
356C23×C83—41no—
357C23×C83—41no—
358C23×C83—41no—
359C23×C83—41no—
360C23×C83—41no—
361C23×C83—41no—
362C23×C83—41no—
363C23×C83—41no—
364C23×C83—41no—
365C23×C83—41no—
366C23×C83—41no—
367C23×C83—41no—
368C23×C83—41no—
369C23×C83—41no—
370C23×C83—41no—
371C23×C83—41no—
372C23×C83—41no—
373C23×C83—41no—
374C23×C83—41no—
375C23×C83—41no—
376C23×C83—41no—
377C23×C83—41no—
378C23×C83—41no—
379C23×C83—41no—
380C23×C83—41no—
381C23×C83—41no—
382C23×C83—41no—
383C23×C83—41no—
384C23×C83—41no—
385C23×C83—41no—
386C23×C83—41no—
387C23×C83C2×C22⋊C414yes—
388C23×C83C23×C411yescharacteristic
389C23×C83C22×D411yescharacteristic
390C23×C83C22×D411yescharacteristic
391C23×C83C22×D411yescharacteristic
392C23×C83C2×#4111yescharacteristic
393C23×C83C2×#4111yescharacteristic
394C23×C83C2×#4111yescharacteristic
395C23×C83H(5,𝔽2)11yescharacteristic
396C23×C83H(5,𝔽2)11yescharacteristic
397C23×C83H(5,𝔽2)11yescharacteristic
398C23×C83H(5,𝔽2)11yescharacteristic
399C23×C83H(5,𝔽2)11yescharacteristic
400C23×C832−1+411yescharacteristic
401C23×C832−1+411yescharacteristic
402C23×C832−1+411yescharacteristic
403Q8×C83—416no—
404D4×C83—416no—
405C2×C4×C83—22no—
406C2×C4×C83—22no—
407C2×C4×C83—22no—
408C2×C4×C83—22no—
409C2×C4×C83—22no—
410C2×C4×C83—22no—
411C2×C4×C83—22no—
412C2×C4×C83—22no—
413C2×C4×C83—22no—
414C2×C4×C83—22no—
415C2×C4×C83—22no—
416C2×C4×C83—22no—
417C2×C4×C83—22no—
418C2×C4×C83—22no—
419C2×C4×C83—22no—
420C2×C4×C83—22no—
421C2×C4×C83—22no—
422C2×C4×C83—22no—
423C2×C4×C83—22no—
424C2×C4×C83—22no—
425C2×C4×C83—22no—
426C2×C4×C83—22no—
427C2×C4×C83—22no—
428C2×C4×C83—22no—
429C2×C4×C83—22no—
430C2×C4×C83—22no—
431C2×C4×C83—22no—
432C2×C4×C83—22no—
433C2×C4×C83—22no—
434C2×C4×C83—22no—
435C2×C4×C83—22no—
436C2×C4×C83—22no—
437C2×C4×C83—22no—
438C2×C4×C83—22no—
439C2×C4×C83—22no—
440C2×C4×C83—22no—
441C2×C4×C83—416no—
442C2×C4×C83—41no—
443C2×C4×C83—41no—
444C2×C4×C83—41no—
445C2×C4×C83—41no—
446C2×C4×C83—41no—
447C2×C4×C83—41no—
448C2×C4×C83—41no—
449C2×C4×C83—41no—
450C2×C4×C83—41no—
451C2×C4×C83—41no—
452C2×C4×C83—41no—
453C2×C4×C83—41no—
454C2×C4×C83—41no—
455C2×C4×C83—41no—
456C2×C4×C83—41no—
457C2×C4×C83—41no—
458C2×C4×C83—41no—
459C2×C4×C83—41no—
460C2×C4×C83—41no—
461C2×C4×C83—41no—
462C2×C4×C83—41no—
463C2×C4×C83—41no—
464C2×C4×C83—41no—
465C2×C4×C83—41no—
466C2×C4×C83—41no—
467C2×C4×C83—41no—
468C2×C4×C83—41no—
469C2×C4×C83—41no—
470C2×C4×C83—41no—
471C2×C4×C83—41no—
472C2×C4×C83—41no—
473C2×C4×C83—41no—
474C2×C4×C83—41no—
475C2×C4×C83—41no—
476C2×C4×C83—41no—
477C2×C4×C83—41no—
478C2×C4×C83—41no—
479C2×C4×C83—41no—
480C2×C4×C83—41no—
481C2×C4×C83—41no—
482C2×C4×C83—41no—
483C2×C4×C83—41no—
484C2×C4×C83—41no—
485C2×C4×C83—41no—
486C2×C4×C83—41no—
487C2×C4×C83—41no—
488C2×C4×C83—41no—
489C2×C4×C83—41no—
490C2×C4×C83—41no—
491C2×C4×C83—41no—
492C2×C4×C83—41no—
493C2×C4×C83—41no—
494C2×C4×C83C2×C22⋊C414yes—
495C2×C4×C83C2×C22⋊C414yes—
496C2×C4×C83C4×D414yes—
497C22×C83—24no—
498C22×C83—24no—
499C22×C83—24no—
500C22×C83—42no—
501C22×C83—42no—
502C22×C83—42no—
503C22×C83—42no—
504C22×C83—42no—
505C22×C83—42no—
506C22×C83—42no—
507C22×C83—42no—
508C22×C83—42no—
509C22×C83—42no—
510C22×C83—42no—
511C22×C83—42no—
512C22×C83—42no—
513C22×C83—42no—
514C22×C83—42no—
515C22×C83—42no—
516C22×C83—42no—
517C22×C83—42no—
518C22×C83—42no—
519C22×C83—81no—
520C22×C83—81no—
521C22×C83—81no—
522C22×C83—81no—
523C22×C83—81no—
524C22×C83—81no—
525C22×C83—81no—
526C22×C83—81no—
527C22×C83C22×C22⋊C411yescharacteristic
528C22×C83C2×C4×D411yescharacteristic
529C22×C83C4×#4111yescharacteristic
530C22×C83#51811yescharacteristic
531C22×C83#52011yescharacteristic
532C22×C83#52011yescharacteristic
533C22×C83#52011yescharacteristic
534C22×C83#53511yescharacteristic
535C22×C83#53511yescharacteristic
536C22×C83#53611yescharacteristic
537C22×C83#53611yescharacteristic
538C22×C83#53711yescharacteristic
539C22×C83#53711yescharacteristic
540C22×C83#53811yescharacteristic
541C22×C83#53811yescharacteristic
542C22×C83#54211yescharacteristic
543C22×C83#54211yescharacteristic
544C22×C83#54211yescharacteristic
545C22×C83#54211yescharacteristic
546C22×C83D4211yescharacteristic
547C22×C83D4211yescharacteristic
548C22×C83#54611yescharacteristic
549C22×C83#54611yescharacteristic
550C22×C83#54611yescharacteristic
551C22×C83#54611yescharacteristic
552C22×C83#54611yescharacteristic
553C22×C83#54711yescharacteristic
554C22×C83#54711yescharacteristic
555C22×C83#54811yescharacteristic
556C22×C83#55611yescharacteristic
557C22×C83#55911yescharacteristic
558C22×C83H(3,𝔽4)11yescharacteristic
559C22×C83#56211yescharacteristic
560C22×C83#56211yescharacteristic
561C22×C83#56311yescharacteristic
562C4×C83—24no—
563C4×C83—24no—
564C4×C83—24no—
565C4×C83—42no—
566C4×C83—42no—
567C4×C83—42no—
568C4×C83—42no—
569C4×C83—42no—
570C4×C83—42no—
571C4×C83—81no—
572C4×C83—81no—
573C4×C83—81no—
574C4×C83—81no—
575#14421C8311yesmaximal, characteristic, direct product factor, Sylow
576C2×C83—44no—
577C2×C83—82no—
578C2×C83#231111yescharacteristic
579C2×C83#232611yescharacteristic
580C2×C83#233711yescharacteristic
581C2×C83D4×C22⋊C411yescharacteristic
582C2×C83#233911yescharacteristic
583C2×C83#236711yescharacteristic
584C2×C83#237911yescharacteristic
585C2×C83#267011yescharacteristic
586C2×C83#267211yescharacteristic
587C2×C83#267411yescharacteristic
588C2×C83#267611yescharacteristic
589C2×C83#270011yescharacteristic
590C2×C83#271011yescharacteristic
591C2×C83#271211yescharacteristic
592C2×C83#271511yescharacteristic
593C22×#124C2×C8311yescharacteristic
594C2×#391C2×C8311yescharacteristic, complemented
595C2×#388C2×C8311yescharacteristic, complemented
596C2×#386C2×C8311yescharacteristic
597C2×#385C2×C8311yescharacteristic, complemented
598#1446C2×C8311yescharacteristic, complemented
599#1440C2×C8311yescharacteristic, complemented
600#1439C2×C8311yescharacteristic, complemented
601#1439C2×C8311yescharacteristic, complemented
602#1439C2×C8311yescharacteristic, complemented
603#1438C2×C8311yescharacteristic
604#1437C2×C8311yescharacteristic, complemented
605C4⋊#95C2×C8311yescharacteristic, complemented
606#1434C2×C8311yescharacteristic, complemented
607C22⋊#95C2×C8311yescharacteristic, complemented
608C83#1442111yescharacteristic, direct product factor, Sylow
609C23×Q8C22×C8311yescharacteristic
610C23×D4C22×C8311yescharacteristic
611C24×C4C22×C8311yescharacteristic
612C2×#124—24no—
613C2×#124—24no—
614C2×#124C4×C8318yescomplemented
615C22×C4⋊C4C22×C8311yescharacteristic
616C22×C4⋊C4C22×C8311yescharacteristic
617C22×C4⋊C4C22×C8311yescharacteristic
618C22×C22⋊C4C22×C8311yescharacteristic
619C22×C22⋊C4C22×C8311yescharacteristic
620C22×C22⋊C4C22×C8311yescharacteristic
621C22×C22⋊C4C22×C8311yescharacteristic
622C22×C22⋊C4C22×C8311yescharacteristic
623C22×C22⋊C4C22×C8311yescharacteristic
624C22×C22⋊C4C22×C8311yescharacteristic
625C22×C22⋊C4C22×C8311yescharacteristic
626C22×C22⋊C4C22×C8311yescharacteristic
627C22×C22⋊C4C22×C8311yescharacteristic
628C22×C22⋊C4C22×C8311yescharacteristic
629C22×C42C22×C8311yescharacteristic
630C22×C42C22×C8311yescharacteristic
631#391—24no—
632#388—24no—
633#386—24no—
634#385—24no—
635C2×#95C22×C8311yescharacteristic
636C2×#95C22×C8311yescharacteristic
637C2×#95C22×C8311yescharacteristic
638C2×#95C22×C8311yescharacteristic
639C2×#95C22×C8311yescharacteristic
640C2×#95C22×C8311yescharacteristic
641C2×#95C22×C8311yescharacteristic
642C2×#95C22×C8311yescharacteristic
643C2×#95C22×C8311yescharacteristic
644C2×#95C22×C8311yescharacteristic
645C2×#95C22×C8311yescharacteristic
646C2×#95C22×C8311yescharacteristic
647C2×#95C22×C8311yescharacteristic
648C2×#95C22×C8311yescharacteristic
649C2×#95C22×C8311yescharacteristic
650C2×#95C22×C8311yescharacteristic
651C25C23×C8311yescharacteristic
652C25C23×C8311yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—41no—
658C22×Q8—41no—
659C22×Q8C2×C4×C8314yescomplemented
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4C2×C4×C8314yes—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—41no—
671C23×C4—41no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4C23×C8311yescharacteristic
675C23×C4C23×C8311yescharacteristic
676C23×C4C23×C8311yescharacteristic
677C23×C4C23×C8311yescharacteristic
678C23×C4C23×C8311yescharacteristic
679C23×C4C23×C8311yescharacteristic
680C23×C4C23×C8311yescharacteristic
681C23×C4C23×C8311yescharacteristic
682C23×C4C23×C8311yescharacteristic
683C23×C4C23×C8311yescharacteristic
684C23×C4C23×C8311yescharacteristic
685C23×C4C23×C8311yescharacteristic
686C23×C4C23×C8311yescharacteristic
687#124—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—41no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4C2×C4×C8314yes—
725C2×C22⋊C4C2×C4×C8314yes—
726C2×C22⋊C4C2×C4×C8314yescomplemented
727C2×C22⋊C4C2×C4×C8314yescomplemented
728C2×C22⋊C4D4×C8314yes—
729C2×C22⋊C4D4×C8314yes—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—22no—
734C2×C42—41no—
735C2×C42C2×C4×C8314yescomplemented
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—41no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751#95D4×C8314yes—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24C22×C4×C8312yes—
779C24C22×C4×C8312yes—
780C24C2×D4×C8312yes—
781C24C2×D4×C8312yes—
782C24C24×C8311yescharacteristic
783C2×Q8—28no—
784C2×Q8—28no—
785C2×Q8—44no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4C22×C4×C8312yes—
881C22×C4C22×C4×C8312yes—
882C22×C4C22×C4×C8312yes—
883C22×C4C22×C4×C8312yes—
884C22×C4C22×C4×C8312yes—
885C22×C4C2×D4×C8312yes—
886C22×C4C2×D4×C8312yes—
887C22×C4C2×D4×C8312yes—
888C22×C4C2×D4×C8312yes—
889C22×C4C2×D4×C8312yes—
890C22×C4C2×D4×C8312yes—
891C22×C4C2×D4×C8312yes—
892C22×C4#41×C8312yes—
893C22×C4#41×C8312yes—
894C22×C4#41×C8312yes—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4C22⋊C4×C83116yescomplemented
909C42—28no—
910C42—44no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C2×C22⋊C4×C8314yes—
981C23C23×C4×C8311yescharacteristic
982C23C22×D4×C8311yescharacteristic
983C23C22×D4×C8311yescharacteristic
984C23C22×D4×C8311yescharacteristic
985C23C2×#41×C8311yescharacteristic
986C23C2×#41×C8311yescharacteristic
987C23C2×#41×C8311yescharacteristic
988C23H(5,𝔽2)×C8311yescharacteristic
989C23H(5,𝔽2)×C8311yescharacteristic
990C23H(5,𝔽2)×C8311yescharacteristic
991C23H(5,𝔽2)×C8311yescharacteristic
992C23H(5,𝔽2)×C8311yescharacteristic
993C232−1+4×C8311yescharacteristic
994C232−1+4×C8311yescharacteristic
995C232−1+4×C8311yescharacteristic
996Q8—416no—
997D4—416no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—416no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4C2×C22⋊C4×C8314yes—
1088C2×C4C2×C22⋊C4×C8314yes—
1089C2×C4C4×D4×C8314yes—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22C22×C22⋊C4×C8311yescharacteristic
1121C22C2×C4×D4×C8311yescharacteristic
1122C22C4×#41×C8311yescharacteristic
1123C22#518×C8311yescharacteristic
1124C22#520×C8311yescharacteristic
1125C22#520×C8311yescharacteristic
1126C22#520×C8311yescharacteristic
1127C22#535×C8311yescharacteristic
1128C22#535×C8311yescharacteristic
1129C22#536×C8311yescharacteristic
1130C22#536×C8311yescharacteristic
1131C22#537×C8311yescharacteristic
1132C22#537×C8311yescharacteristic
1133C22#538×C8311yescharacteristic
1134C22#538×C8311yescharacteristic
1135C22#542×C8311yescharacteristic
1136C22#542×C8311yescharacteristic
1137C22#542×C8311yescharacteristic
1138C22#542×C8311yescharacteristic
1139C22D42×C8311yescharacteristic
1140C22D42×C8311yescharacteristic
1141C22#546×C8311yescharacteristic
1142C22#546×C8311yescharacteristic
1143C22#546×C8311yescharacteristic
1144C22#546×C8311yescharacteristic
1145C22#546×C8311yescharacteristic
1146C22#547×C8311yescharacteristic
1147C22#547×C8311yescharacteristic
1148C22#548×C8311yescharacteristic
1149C22#556×C8311yescharacteristic
1150C22#559×C8311yescharacteristic
1151C22H(3,𝔽4)×C8311yescharacteristic
1152C22#562×C8311yescharacteristic
1153C22#562×C8311yescharacteristic
1154C22#563×C8311yescharacteristic
1155C4—24no—
1156C4—24no—
1157C4—24no—
1158C4—42no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C2—44no—
1169C2—82no—
1170C2C83×#231111yescharacteristic
1171C2C83×#232611yescharacteristic
1172C2C83×#233711yescharacteristic
1173C2D4×C22⋊C4×C8311yescharacteristic
1174C2C83×#233911yescharacteristic
1175C2C83×#236711yescharacteristic
1176C2C83×#237911yescharacteristic
1177C2C83×#267011yescharacteristic
1178C2C83×#267211yescharacteristic
1179C2C83×#267411yescharacteristic
1180C2C83×#267611yescharacteristic
1181C2C83×#270011yescharacteristic
1182C2C83×#271011yescharacteristic
1183C2C83×#271211yescharacteristic
1184C2C83×#271511yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutatorC23C23×C4×C83
Frattini, cosocleC24C24×C83
prime radicalC23×D4×C83C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#391×C83C2semidirect
3. C2×#388×C83C2semidirect
5. C2×#385×C83C2semidirect
6. C83×#1446C2semidirect
7. C83×#1440C2semidirect
8. C83×#1439C2semidirect
9. C83×#1439C2semidirect
10. C83×#1439C2semidirect
12. C83×#1437C2semidirect
13. C83×C4⋊#95C2semidirect
14. C83×#1434C2semidirect
15. C83×C22⋊#95C2semidirect
21. C2×#124×C83C4semidirect
66. C22×Q8×C83C2×C4semidirect
133. C2×C22⋊C4×C83C2×C4semidirect
134. C2×C22⋊C4×C83C2×C4semidirect
142. C2×C42×C83C2×C4semidirect
315. C22⋊C4×C83C22⋊C4semidirect
575. #14421C83direct (N × H)
594. C2×#391C2×C83semidirect
595. C2×#388C2×C83semidirect
597. C2×#385C2×C83semidirect
598. #1446C2×C83semidirect
599. #1440C2×C83semidirect
600. #1439C2×C83semidirect
601. #1439C2×C83semidirect
602. #1439C2×C83semidirect
604. #1437C2×C83semidirect
605. C4⋊#95C2×C83semidirect
606. #1434C2×C83semidirect
607. C22⋊#95C2×C83semidirect
608. C83#14421direct (N × H)
614. C2×#124C4×C83semidirect
659. C22×Q8C2×C4×C83semidirect
726. C2×C22⋊C4C2×C4×C83semidirect
727. C2×C22⋊C4C2×C4×C83semidirect
735. C2×C42C2×C4×C83semidirect
908. C22⋊C4C22⋊C4×C83semidirect

Maximal subgroups

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

subgroupindex
C22×#124×C832
C2×#391×C832
C2×#388×C832
C2×#386×C832
C2×#385×C832
C83×#14462
C83×#14402
C83×#14392
C83×#14382
C83×#14372
C83×C4⋊#952
C83×#14342
C83×C22⋊#952
#1442183