Finite Group Databasebeta

← C83×#14760 #35242584

Subgroups — C83×#14760 #35242584

Order 21248.

2414 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C83C211yesmaximal, characteristic, complemented
2C2×#392×C83C211yesmaximal, characteristic
3C2×#390×C83C211yesmaximal, characteristic, complemented
4C2×#388×C83C211yesmaximal, characteristic, complemented
5C2×#386×C83C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
7C83×#1441C211yesmaximal, characteristic, complemented
8C83×#1440C211yesmaximal, characteristic, complemented
9C83×#1439C211yesmaximal, characteristic, complemented
10C83×#1439C211yesmaximal, characteristic, complemented
11C83×#1438C211yesmaximal, characteristic, complemented
12C83×#1438C211yesmaximal, characteristic, complemented
13C83×#1438C211yesmaximal, characteristic, complemented
14C83×#1437C211yesmaximal, characteristic, complemented
15C83×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C23×D4×C83C2211yescharacteristic
19C24×C4×C83C2211yescharacteristic
20C2×#123×C83—24no—
21C2×#123×C83—24no—
22C2×#123×C83—24no—
23C22×C4⋊C4×C83C2211yescharacteristic
24C22×C4⋊C4×C83C2211yescharacteristic
25C22×C4⋊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×C22⋊C4×C83C2211yescharacteristic
37C22×C22⋊C4×C83C2211yescharacteristic
38C22×C22⋊C4×C83C2211yescharacteristic
39C22×C22⋊C4×C83C2211yescharacteristic
40C22×C42×C83C2211yescharacteristic
41C22×C42×C83C2211yescharacteristic
42#392×C83—24no—
43#390×C83—24no—
44#388×C83—24no—
45#386×C83—24no—
46C4×C22⋊C4×C83—24no—
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
58C2×#95×C83C2211yescharacteristic
59C25×C83C2311yescharacteristic
60C25×C83C2311yescharacteristic
61C25×C83C2311yescharacteristic
62C22×D4×C83—22no—
63C22×D4×C83—22no—
64C22×D4×C83—22no—
65C22×D4×C83—22no—
66C22×D4×C83—22no—
67C22×D4×C83—22no—
68C22×D4×C83—22no—
69C22×D4×C83—22no—
70C22×D4×C83—22no—
71C22×D4×C83—22no—
72C22×D4×C83—22no—
73C22×D4×C83—22no—
74C22×D4×C83—22no—
75C22×D4×C83—22no—
76C22×D4×C83—22no—
77C22×D4×C83—41no—
78C22×D4×C83—41no—
79C22×D4×C83—41no—
80C22×D4×C83—41no—
81C22×D4×C83—41no—
82C22×D4×C83—41no—
83C23×C4×C83—22no—
84C23×C4×C83—22no—
85C23×C4×C83—22no—
86C23×C4×C83—22no—
87C23×C4×C83—41no—
88C23×C4×C83—41no—
89C23×C4×C83D414yescomplemented
90C23×C4×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C23×C4×C83C2311yescharacteristic
94C23×C4×C83C2311yescharacteristic
95C23×C4×C83C2311yescharacteristic
96C23×C4×C83C2311yescharacteristic
97C23×C4×C83C2311yescharacteristic
98C23×C4×C83C2311yescharacteristic
99C23×C4×C83C2311yescharacteristic
100C23×C4×C83C2311yescharacteristic
101C23×C4×C83C2311yescharacteristic
102#123×C83—232no—
103C2×C4⋊C4×C83—22no—
104C2×C4⋊C4×C83—22no—
105C2×C4⋊C4×C83—22no—
106C2×C4⋊C4×C83—22no—
107C2×C4⋊C4×C83—22no—
108C2×C4⋊C4×C83—22no—
109C2×C4⋊C4×C83—22no—
110C2×C4⋊C4×C83—41no—
111C2×C4⋊C4×C83D414yescomplemented
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—22no—
120C2×C22⋊C4×C83—22no—
121C2×C22⋊C4×C83—22no—
122C2×C22⋊C4×C83—22no—
123C2×C22⋊C4×C83—22no—
124C2×C22⋊C4×C83—22no—
125C2×C22⋊C4×C83—22no—
126C2×C22⋊C4×C83—22no—
127C2×C22⋊C4×C83—22no—
128C2×C22⋊C4×C83—22no—
129C2×C22⋊C4×C83—22no—
130C2×C22⋊C4×C83—22no—
131C2×C22⋊C4×C83—22no—
132C2×C22⋊C4×C83—22no—
133C2×C22⋊C4×C83—22no—
134C2×C22⋊C4×C83—22no—
135C2×C22⋊C4×C83—22no—
136C2×C22⋊C4×C83—22no—
137C2×C22⋊C4×C83—22no—
138C2×C22⋊C4×C83—22no—
139C2×C22⋊C4×C83—22no—
140C2×C22⋊C4×C83—22no—
141C2×C22⋊C4×C83—22no—
142C2×C22⋊C4×C83—41no—
143C2×C22⋊C4×C83—41no—
144C2×C22⋊C4×C83—41no—
145C2×C22⋊C4×C83—41no—
146C2×C22⋊C4×C83—41no—
147C2×C22⋊C4×C83—41no—
148C2×C22⋊C4×C83—41no—
149C2×C22⋊C4×C83—41no—
150C2×C22⋊C4×C83—41no—
151C2×C22⋊C4×C83—41no—
152C2×C22⋊C4×C83D414yes—
153C2×C22⋊C4×C83D414yescomplemented
154C2×C42×C83—22no—
155C2×C42×C83—22no—
156C2×C42×C83—22no—
157C2×C42×C83—22no—
158C2×C42×C83—41no—
159C2×C42×C83—41no—
160#95×C83—22no—
161#95×C83—22no—
162#95×C83—22no—
163#95×C83—22no—
164#95×C83—22no—
165#95×C83—22no—
166#95×C83—22no—
167#95×C83—22no—
168#95×C83—22no—
169#95×C83—41no—
170#95×C83—41no—
171#95×C83—41no—
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×C83—21no—
186C24×C83—21no—
187C24×C83—21no—
188C24×C83—21no—
189C24×C83—21no—
190C24×C83—21no—
191C24×C83—21no—
192C24×C83—21no—
193C24×C83—21no—
194C24×C83—21no—
195C24×C83—21no—
196C24×C83—21no—
197C24×C83—21no—
198C24×C83—21no—
199C24×C83—21no—
200C24×C83—21no—
201C24×C83—21no—
202C24×C83—21no—
203C24×C83—21no—
204C24×C83—21no—
205C24×C83—21no—
206C24×C83—21no—
207C24×C83—21no—
208C24×C83—21no—
209C24×C83—21no—
210C24×C83—21no—
211C24×C83—21no—
212C24×C83C2×D412yes—
213C24×C83C2×D412yes—
214C24×C83C2×D412yes—
215C24×C83#4112yes—
216C24×C83#4112yes—
217C24×C83C2411yescharacteristic
218C2×D4×C83—28no—
219C2×D4×C83—28no—
220C2×D4×C83—28no—
221C2×D4×C83—44no—
222C2×D4×C83—44no—
223C2×D4×C83—44no—
224C2×D4×C83—44no—
225C2×D4×C83—44no—
226C2×D4×C83—44no—
227C2×D4×C83—44no—
228C2×D4×C83—44no—
229C2×D4×C83—44no—
230C2×D4×C83—44no—
231C2×D4×C83—44no—
232C2×D4×C83—44no—
233C2×D4×C83—44no—
234C2×D4×C83—44no—
235C2×D4×C83—44no—
236C2×D4×C83—44no—
237C2×D4×C83—44no—
238C2×D4×C83—44no—
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—28no—
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—21no—
281C22×C4×C83—21no—
282C22×C4×C83—21no—
283C22×C4×C83—21no—
284C22×C4×C83—21no—
285C22×C4×C83—21no—
286C22×C4×C83—21no—
287C22×C4×C83—21no—
288C22×C4×C83—21no—
289C22×C4×C83—21no—
290C22×C4×C83—21no—
291C22×C4×C83—21no—
292C22×C4×C83—21no—
293C22×C4×C83—21no—
294C22×C4×C83—21no—
295C22×C4×C83—21no—
296C22×C4×C83—28no—
297C22×C4×C83—21no—
298C22×C4×C83—21no—
299C22×C4×C83—21no—
300C22×C4×C83—21no—
301C22×C4×C83—21no—
302C22×C4×C83—21no—
303C22×C4×C83—21no—
304C22×C4×C83—21no—
305C22×C4×C83—21no—
306C22×C4×C83—21no—
307C22×C4×C83—21no—
308C22×C4×C83—21no—
309C22×C4×C83—21no—
310C22×C4×C83—21no—
311C22×C4×C83—44no—
312C22×C4×C83—44no—
313C22×C4×C83—44no—
314C22×C4×C83—44no—
315C22×C4×C83—44no—
316C22×C4×C83C2×D412yes—
317C22×C4×C83C2×D412yes—
318C22×C4×C83C2×D412yes—
319C22×C4×C83C2×D412yes—
320C22×C4×C83C2×D412yes—
321C22×C4×C83C2×D412yes—
322C22×C4×C83C2×D412yes—
323C22×C4×C83C2×D412yes—
324C22×C4×C83C2×D412yes—
325C22×C4×C83#4112yes—
326C22×C4×C83#4112yes—
327C22×C4×C83#4112yes—
328C22×C4×C83#4112yes—
329C22×C4×C83#4112yes—
330C4⋊C4×C83—28no—
331C4⋊C4×C83—28no—
332C4⋊C4×C83—44no—
333C22⋊C4×C83—28no—
334C22⋊C4×C83—28no—
335C22⋊C4×C83—28no—
336C22⋊C4×C83—28no—
337C22⋊C4×C83—28no—
338C22⋊C4×C83—28no—
339C22⋊C4×C83—44no—
340C22⋊C4×C83—44no—
341C22⋊C4×C83—44no—
342C22⋊C4×C83—44no—
343C22⋊C4×C83—44no—
344C22⋊C4×C83—44no—
345C22⋊C4×C83—44no—
346C22⋊C4×C83—44no—
347C42×C83—44no—
348C42×C83—44no—
349C23×C83—22no—
350C23×C83—22no—
351C23×C83—22no—
352C23×C83—22no—
353C23×C83—22no—
354C23×C83—22no—
355C23×C83—22no—
356C23×C83—22no—
357C23×C83—22no—
358C23×C83—22no—
359C23×C83—22no—
360C23×C83—22no—
361C23×C83—22no—
362C23×C83—22no—
363C23×C83—22no—
364C23×C83—22no—
365C23×C83—22no—
366C23×C83—22no—
367C23×C83—22no—
368C23×C83—22no—
369C23×C83—22no—
370C23×C83—22no—
371C23×C83—22no—
372C23×C83—22no—
373C23×C83—22no—
374C23×C83—22no—
375C23×C83—22no—
376C23×C83—22no—
377C23×C83—22no—
378C23×C83—22no—
379C23×C83—22no—
380C23×C83—22no—
381C23×C83—41no—
382C23×C83—41no—
383C23×C83—41no—
384C23×C83—41no—
385C23×C83—41no—
386C23×C83—41no—
387C23×C83—41no—
388C23×C83—41no—
389C23×C83—41no—
390C23×C83—41no—
391C23×C83—41no—
392C23×C83—41no—
393C23×C83—41no—
394C23×C83—41no—
395C23×C83—41no—
396C23×C83—41no—
397C23×C83—41no—
398C23×C83—41no—
399C23×C83—41no—
400C23×C83—41no—
401C23×C83—41no—
402C23×C83—41no—
403C23×C83—41no—
404C23×C83—41no—
405C23×C83—41no—
406C23×C83—41no—
407C23×C83—41no—
408C23×C83—41no—
409C23×C83—41no—
410C23×C83—41no—
411C23×C83—41no—
412C23×C83—41no—
413C23×C83—41no—
414C23×C83—41no—
415C23×C83—41no—
416C23×C83—41no—
417C23×C83—41no—
418C23×C83—41no—
419C23×C83—41no—
420C23×C83—41no—
421C23×C83—41no—
422C23×C83—41no—
423C23×C83—41no—
424C23×C83—41no—
425C23×C83—41no—
426C23×C83—41no—
427C23×C83—41no—
428C23×C83—41no—
429C23×C83—41no—
430C23×C83—41no—
431C23×C83—41no—
432C23×C83—41no—
433C23×C83—41no—
434C23×C83—41no—
435C23×C83—41no—
436C23×C83—41no—
437C23×C83—41no—
438C23×C83—41no—
439C23×C83—41no—
440C23×C83—41no—
441C23×C83—41no—
442C23×C83—41no—
443C23×C83—41no—
444C23×C83—41no—
445C23×C83—41no—
446C23×C83—41no—
447C23×C83—41no—
448C23×C83—41no—
449C23×C83—41no—
450C23×C83—41no—
451C23×C83—41no—
452C23×C83—41no—
453C23×C83#12114yes—
454C23×C83C22×D411yescharacteristic
455C23×C83C22×D411yescharacteristic
456C23×C83C22×D411yescharacteristic
457C23×C83C22×D411yescharacteristic
458C23×C83C2×#4111yescharacteristic
459C23×C83C2×#4111yescharacteristic
460C23×C83C2×#4111yescharacteristic
461C23×C83C2×#4111yescharacteristic
462C23×C83C2×#4111yescharacteristic
463C23×C83C2×#4111yescharacteristic
464C23×C83C2×#4111yescharacteristic
465C23×C83H(5,𝔽2)11yescharacteristic
466C23×C83H(5,𝔽2)11yescharacteristic
467C23×C83H(5,𝔽2)11yescharacteristic
468C23×C83H(5,𝔽2)11yescharacteristic
469D4×C83—416no—
470D4×C83—416no—
471D4×C83—416no—
472C2×C4×C83—22no—
473C2×C4×C83—22no—
474C2×C4×C83—22no—
475C2×C4×C83—22no—
476C2×C4×C83—22no—
477C2×C4×C83—22no—
478C2×C4×C83—22no—
479C2×C4×C83—22no—
480C2×C4×C83—22no—
481C2×C4×C83—22no—
482C2×C4×C83—22no—
483C2×C4×C83—22no—
484C2×C4×C83—22no—
485C2×C4×C83—22no—
486C2×C4×C83—22no—
487C2×C4×C83—22no—
488C2×C4×C83—22no—
489C2×C4×C83—22no—
490C2×C4×C83—22no—
491C2×C4×C83—22no—
492C2×C4×C83—22no—
493C2×C4×C83—22no—
494C2×C4×C83—22no—
495C2×C4×C83—22no—
496C2×C4×C83—22no—
497C2×C4×C83—22no—
498C2×C4×C83—22no—
499C2×C4×C83—22no—
500C2×C4×C83—22no—
501C2×C4×C83—22no—
502C2×C4×C83—22no—
503C2×C4×C83—22no—
504C2×C4×C83—22no—
505C2×C4×C83—22no—
506C2×C4×C83—22no—
507C2×C4×C83—22no—
508C2×C4×C83—416no—
509C2×C4×C83—41no—
510C2×C4×C83—41no—
511C2×C4×C83—41no—
512C2×C4×C83—41no—
513C2×C4×C83—41no—
514C2×C4×C83—41no—
515C2×C4×C83—41no—
516C2×C4×C83—41no—
517C2×C4×C83—41no—
518C2×C4×C83—41no—
519C2×C4×C83—41no—
520C2×C4×C83—41no—
521C2×C4×C83—41no—
522C2×C4×C83—41no—
523C2×C4×C83—41no—
524C2×C4×C83—41no—
525C2×C4×C83—41no—
526C2×C4×C83—41no—
527C2×C4×C83—41no—
528C2×C4×C83—41no—
529C2×C4×C83—41no—
530C2×C4×C83—41no—
531C2×C4×C83—41no—
532C2×C4×C83—41no—
533C2×C4×C83—41no—
534C2×C4×C83—41no—
535C2×C4×C83—41no—
536C2×C4×C83—41no—
537C2×C4×C83—41no—
538C2×C4×C83—41no—
539C2×C4×C83—41no—
540C2×C4×C83—41no—
541C2×C4×C83—41no—
542C2×C4×C83—41no—
543C2×C4×C83—41no—
544C2×C4×C83—41no—
545C2×C4×C83—41no—
546C2×C4×C83—41no—
547C2×C4×C83—41no—
548C2×C4×C83—41no—
549C2×C4×C83—41no—
550C2×C4×C83—41no—
551C2×C4×C83—41no—
552C2×C4×C83—41no—
553C2×C4×C83—41no—
554C2×C4×C83—41no—
555C2×C4×C83#12014yes—
556C2×C4×C83#12314yescomplemented
557C22×C83—24no—
558C22×C83—24no—
559C22×C83—24no—
560C22×C83—42no—
561C22×C83—42no—
562C22×C83—42no—
563C22×C83—42no—
564C22×C83—42no—
565C22×C83—42no—
566C22×C83—42no—
567C22×C83—42no—
568C22×C83—42no—
569C22×C83—42no—
570C22×C83—42no—
571C22×C83—42no—
572C22×C83—42no—
573C22×C83—42no—
574C22×C83—42no—
575C22×C83—42no—
576C22×C83—42no—
577C22×C83—42no—
578C22×C83—42no—
579C22×C83—42no—
580C22×C83—42no—
581C22×C83—42no—
582C22×C83—42no—
583C22×C83—42no—
584C22×C83—42no—
585C22×C83—42no—
586C22×C83—81no—
587C22×C83—81no—
588C22×C83—81no—
589C22×C83—81no—
590C22×C83—81no—
591C22×C83—81no—
592C22×C83—81no—
593C22×C83—81no—
594C22×C83—81no—
595C22×C83—81no—
596C22×C83—81no—
597C22×C83—81no—
598C22×C83—81no—
599C22×C83—81no—
600C22×C83—81no—
601C22×C83—81no—
602C22×C83C2×#12011yescharacteristic
603C22×C83C2×#12111yescharacteristic
604C22×C83C2×#12311yescharacteristic
605C22×C83#52511yescharacteristic
606C22×C83#52511yescharacteristic
607C22×C83#52511yescharacteristic
608C22×C83#52511yescharacteristic
609C22×C83#52911yescharacteristic
610C22×C83#52911yescharacteristic
611C22×C83#53211yescharacteristic
612C22×C83#53211yescharacteristic
613C22×C83#53211yescharacteristic
614C22×C83#53211yescharacteristic
615C22×C83#53411yescharacteristic
616C22×C83#53511yescharacteristic
617C22×C83#53811yescharacteristic
618C22×C83#53811yescharacteristic
619C22×C83#54011yescharacteristic
620C22×C83#54011yescharacteristic
621C22×C83D4211yescharacteristic
622C22×C83D4211yescharacteristic
623C22×C83#54611yescharacteristic
624C22×C83#54611yescharacteristic
625C22×C83#54611yescharacteristic
626C22×C83#54611yescharacteristic
627C22×C83#54611yescharacteristic
628C22×C83#54611yescharacteristic
629C22×C83#55011yescharacteristic
630C22×C83#55011yescharacteristic
631C22×C83#55111yescharacteristic
632C22×C83#55111yescharacteristic
633C22×C83#55111yescharacteristic
634C22×C83#55311yescharacteristic
635C22×C83#55311yescharacteristic
636C22×C83#55911yescharacteristic
637C4×C83—24no—
638C4×C83—24no—
639C4×C83—42no—
640C4×C83—42no—
641C4×C83—42no—
642C4×C83—42no—
643C4×C83—42no—
644C4×C83—42no—
645C4×C83—42no—
646C4×C83—42no—
647C4×C83—81no—
648C4×C83—81no—
649#14760C8311yesmaximal, characteristic, direct product factor, Sylow
650C2×C83—44no—
651C2×C83—82no—
652C2×C83—82no—
653C2×C83#238811yescharacteristic
654C2×C83#241011yescharacteristic
655C2×C83#241111yescharacteristic
656C2×C83#241811yescharacteristic
657C2×C83#243111yescharacteristic
658C2×C83#244511yescharacteristic
659C2×C83#245611yescharacteristic
660C2×C83#245711yescharacteristic
661C2×C83#246411yescharacteristic
662C2×C83#247111yescharacteristic
663C2×C83#255411yescharacteristic
664C2×C83#255711yescharacteristic
665C2×C83#260211yescharacteristic
666C2×C83#266111yescharacteristic
667C2×C83#285411yescharacteristic
668C22×#123C2×C8311yescharacteristic, complemented
669C2×#392C2×C8311yescharacteristic
670C2×#390C2×C8311yescharacteristic, complemented
671C2×#388C2×C8311yescharacteristic, complemented
672C2×#386C2×C8311yescharacteristic, complemented
673C2×C4×C22⋊C4C2×C8311yescharacteristic, complemented
674#1441C2×C8311yescharacteristic, complemented
675#1440C2×C8311yescharacteristic, complemented
676#1439C2×C8311yescharacteristic, complemented
677#1439C2×C8311yescharacteristic, complemented
678#1438C2×C8311yescharacteristic, complemented
679#1438C2×C8311yescharacteristic, complemented
680#1438C2×C8311yescharacteristic, complemented
681#1437C2×C8311yescharacteristic, complemented
682#1436C2×C8311yescharacteristic, complemented
683C83#1476011yescharacteristic, direct product factor, Sylow
684C23×D4C22×C8311yescharacteristic
685C23×D4C22×C8311yescharacteristic
686C23×D4C22×C8311yescharacteristic
687C24×C4C22×C8311yescharacteristic
688C2×#123—24no—
689C2×#123—24no—
690C2×#123—24no—
691C22×C4⋊C4C22×C8311yescharacteristic
692C22×C4⋊C4C22×C8311yescharacteristic
693C22×C4⋊C4C22×C8311yescharacteristic
694C22×C22⋊C4C22×C8311yescharacteristic
695C22×C22⋊C4C22×C8311yescharacteristic
696C22×C22⋊C4C22×C8311yescharacteristic
697C22×C22⋊C4C22×C8311yescharacteristic
698C22×C22⋊C4C22×C8311yescharacteristic
699C22×C22⋊C4C22×C8311yescharacteristic
700C22×C22⋊C4C22×C8311yescharacteristic
701C22×C22⋊C4C22×C8311yescharacteristic
702C22×C22⋊C4C22×C8311yescharacteristic
703C22×C22⋊C4C22×C8311yescharacteristic
704C22×C22⋊C4C22×C8311yescharacteristic
705C22×C22⋊C4C22×C8311yescharacteristic
706C22×C22⋊C4C22×C8311yescharacteristic
707C22×C22⋊C4C22×C8311yescharacteristic
708C22×C42C22×C8311yescharacteristic
709C22×C42C22×C8311yescharacteristic
710#392—24no—
711#390—24no—
712#388—24no—
713#386—24no—
714C4×C22⋊C4—24no—
715C2×#95C22×C8311yescharacteristic
716C2×#95C22×C8311yescharacteristic
717C2×#95C22×C8311yescharacteristic
718C2×#95C22×C8311yescharacteristic
719C2×#95C22×C8311yescharacteristic
720C2×#95C22×C8311yescharacteristic
721C2×#95C22×C8311yescharacteristic
722C2×#95C22×C8311yescharacteristic
723C2×#95C22×C8311yescharacteristic
724C2×#95C22×C8311yescharacteristic
725C2×#95C22×C8311yescharacteristic
726C2×#95C22×C8311yescharacteristic
727C25C23×C8311yescharacteristic
728C25C23×C8311yescharacteristic
729C25C23×C8311yescharacteristic
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4—41no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—22no—
755C23×C4—41no—
756C23×C4—41no—
757C23×C4D4×C8314yescomplemented
758C23×C4C23×C8311yescharacteristic
759C23×C4C23×C8311yescharacteristic
760C23×C4C23×C8311yescharacteristic
761C23×C4C23×C8311yescharacteristic
762C23×C4C23×C8311yescharacteristic
763C23×C4C23×C8311yescharacteristic
764C23×C4C23×C8311yescharacteristic
765C23×C4C23×C8311yescharacteristic
766C23×C4C23×C8311yescharacteristic
767C23×C4C23×C8311yescharacteristic
768C23×C4C23×C8311yescharacteristic
769C23×C4C23×C8311yescharacteristic
770#123—232no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—22no—
777C2×C4⋊C4—22no—
778C2×C4⋊C4—41no—
779C2×C4⋊C4D4×C8314yescomplemented
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4D4×C8314yes—
821C2×C22⋊C4D4×C8314yescomplemented
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—22no—
826C2×C42—41no—
827C2×C42—41no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—41no—
838#95—41no—
839#95—41no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24C2×D4×C8312yes—
881C24C2×D4×C8312yes—
882C24C2×D4×C8312yes—
883C24#41×C8312yes—
884C24#41×C8312yes—
885C24C24×C8311yescharacteristic
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—28no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—28no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4C2×D4×C8312yes—
985C22×C4C2×D4×C8312yes—
986C22×C4C2×D4×C8312yes—
987C22×C4C2×D4×C8312yes—
988C22×C4C2×D4×C8312yes—
989C22×C4C2×D4×C8312yes—
990C22×C4C2×D4×C8312yes—
991C22×C4C2×D4×C8312yes—
992C22×C4C2×D4×C8312yes—
993C22×C4#41×C8312yes—
994C22×C4#41×C8312yes—
995C22×C4#41×C8312yes—
996C22×C4#41×C8312yes—
997C22×C4#41×C8312yes—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—44no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C42—44no—
1016C42—44no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23#121×C8314yes—
1122C23C22×D4×C8311yescharacteristic
1123C23C22×D4×C8311yescharacteristic
1124C23C22×D4×C8311yescharacteristic
1125C23C22×D4×C8311yescharacteristic
1126C23C2×#41×C8311yescharacteristic
1127C23C2×#41×C8311yescharacteristic
1128C23C2×#41×C8311yescharacteristic
1129C23C2×#41×C8311yescharacteristic
1130C23C2×#41×C8311yescharacteristic
1131C23C2×#41×C8311yescharacteristic
1132C23C2×#41×C8311yescharacteristic
1133C23H(5,𝔽2)×C8311yescharacteristic
1134C23H(5,𝔽2)×C8311yescharacteristic
1135C23H(5,𝔽2)×C8311yescharacteristic
1136C23H(5,𝔽2)×C8311yescharacteristic
1137D4—416no—
1138D4—416no—
1139D4—416no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—416no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4#120×C8314yes—
1224C2×C4#123×C8314yescomplemented
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×#120×C8311yescharacteristic
1271C22C2×#121×C8311yescharacteristic
1272C22C2×#123×C8311yescharacteristic
1273C22#525×C8311yescharacteristic
1274C22#525×C8311yescharacteristic
1275C22#525×C8311yescharacteristic
1276C22#525×C8311yescharacteristic
1277C22#529×C8311yescharacteristic
1278C22#529×C8311yescharacteristic
1279C22#532×C8311yescharacteristic
1280C22#532×C8311yescharacteristic
1281C22#532×C8311yescharacteristic
1282C22#532×C8311yescharacteristic
1283C22#534×C8311yescharacteristic
1284C22#535×C8311yescharacteristic
1285C22#538×C8311yescharacteristic
1286C22#538×C8311yescharacteristic
1287C22#540×C8311yescharacteristic
1288C22#540×C8311yescharacteristic
1289C22D42×C8311yescharacteristic
1290C22D42×C8311yescharacteristic
1291C22#546×C8311yescharacteristic
1292C22#546×C8311yescharacteristic
1293C22#546×C8311yescharacteristic
1294C22#546×C8311yescharacteristic
1295C22#546×C8311yescharacteristic
1296C22#546×C8311yescharacteristic
1297C22#550×C8311yescharacteristic
1298C22#550×C8311yescharacteristic
1299C22#551×C8311yescharacteristic
1300C22#551×C8311yescharacteristic
1301C22#551×C8311yescharacteristic
1302C22#553×C8311yescharacteristic
1303C22#553×C8311yescharacteristic
1304C22#559×C8311yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—81no—
1316C4—81no—
1317C2—44no—
1318C2—82no—
1319C2—82no—
1320C2C83×#238811yescharacteristic
1321C2C83×#241011yescharacteristic
1322C2C83×#241111yescharacteristic
1323C2C83×#241811yescharacteristic
1324C2C83×#243111yescharacteristic
1325C2C83×#244511yescharacteristic
1326C2C83×#245611yescharacteristic
1327C2C83×#245711yescharacteristic
1328C2C83×#246411yescharacteristic
1329C2C83×#247111yescharacteristic
1330C2C83×#255411yescharacteristic
1331C2C83×#255711yescharacteristic
1332C2C83×#260211yescharacteristic
1333C2C83×#266111yescharacteristic
1334C2C83×#285411yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutator, Frattini, cosocleC24C24×C83
prime radicalC2×#392×C83C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C83C2semidirect
3. C2×#390×C83C2semidirect
4. C2×#388×C83C2semidirect
5. C2×#386×C83C2semidirect
6. C2×C4×C22⋊C4×C83C2semidirect
7. C83×#1441C2semidirect
8. C83×#1440C2semidirect
9. C83×#1439C2semidirect
10. C83×#1439C2semidirect
11. C83×#1438C2semidirect
12. C83×#1438C2semidirect
13. C83×#1438C2semidirect
14. C83×#1437C2semidirect
15. C83×#1436C2semidirect
89. C23×C4×C83D4semidirect
111. C2×C4⋊C4×C83D4semidirect
153. C2×C22⋊C4×C83D4semidirect
556. C2×C4×C83#123semidirect
649. #14760C83direct (N × H)
668. C22×#123C2×C83semidirect
670. C2×#390C2×C83semidirect
671. C2×#388C2×C83semidirect
672. C2×#386C2×C83semidirect
673. C2×C4×C22⋊C4C2×C83semidirect
674. #1441C2×C83semidirect
675. #1440C2×C83semidirect
676. #1439C2×C83semidirect
677. #1439C2×C83semidirect
678. #1438C2×C83semidirect
679. #1438C2×C83semidirect
680. #1438C2×C83semidirect
681. #1437C2×C83semidirect
682. #1436C2×C83semidirect
683. C83#14760direct (N × H)
757. C23×C4D4×C83semidirect
779. C2×C4⋊C4D4×C83semidirect
821. C2×C22⋊C4D4×C83semidirect
1224. C2×C4#123×C83semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C832
C2×#392×C832
C2×#390×C832
C2×#388×C832
C2×#386×C832
C2×C4×C22⋊C4×C832
C83×#14412
C83×#14402
C83×#14392
C83×#14382
C83×#14372
C83×#14362
#1476083