Finite Group Databasebeta

← C83×#24432 #35252256

Subgroups — C83×#24432 #35252256

Order 21248.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C83C211yesmaximal, characteristic
2C2×#465×C83C211yesmaximal, characteristic, complemented
3C2×#450×C83C211yesmaximal, characteristic, complemented
4C2×#450×C83C211yesmaximal, characteristic, complemented
5C22×#102×C83C211yesmaximal, characteristic, complemented
6C83×#2417C211yesmaximal, characteristic, complemented
7C83×#2041C211yesmaximal, characteristic, complemented
8C83×#2034C211yesmaximal, characteristic, complemented
9C83×#2014C211yesmaximal, characteristic, complemented
10C83×#2000C211yesmaximal, characteristic, complemented
11C83×#1877C211yesmaximal, characteristic, complemented
12C83×#1874C211yesmaximal, characteristic, complemented
13C83×#1869C211yesmaximal, characteristic, complemented
14C83×#1864C211yesmaximal, characteristic, complemented
15C83×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C83—21no—
17C23×D4×C83C2211yescharacteristic
18C23×D4×C83C2211yescharacteristic
19C22×SD16×C83C2211yescharacteristic
20C22×SD16×C83C2211yescharacteristic, complemented
21C22×SD16×C83C2211yescharacteristic, complemented
22C23×C8×C83C2211yescharacteristic, complemented
23D42×C83—24no—
24D42×C83—24no—
25C2×#127×C83C2211yescharacteristic
26C2×C22⋊Q8×C83C2211yescharacteristic, complemented
27C2×C22⋊Q8×C83C2211yescharacteristic, complemented
28C2×#121×C83—21no—
29C2×#121×C83C2211yescharacteristic
30C2×#121×C83C2211yescharacteristic
31C2×#120×C83—21no—
32C2×#120×C83—21no—
33C2×C4×D4×C83C2211yescharacteristic
34C2×C4×D4×C83C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic, complemented
36#465×C83—24no—
37#450×C83—24no—
38#450×C83—24no—
39C2×#106×C83C2211yescharacteristic, complemented
40C2×#103×C83C2211yescharacteristic, complemented
41C2×#102×C83—24no—
42C2×#102×C83C2211yescharacteristic
43C2×#102×C83C2211yescharacteristic
44C2×#102×C83C2211yescharacteristic
45C2×#102×C83C2211yescharacteristic, complemented
46C2×#102×C83C2211yescharacteristic, complemented
47C2×#102×C83C2211yescharacteristic, complemented
48C2×#102×C83C2211yescharacteristic, complemented
49C2×#102×C83C2211yescharacteristic, complemented
50C2×#102×C83C2211yescharacteristic, complemented
51C2×C22⋊C8×C83C2211yescharacteristic, complemented
52C2×C22⋊C8×C83C2211yescharacteristic, complemented
53C2×C22⋊C8×C83C2211yescharacteristic, complemented
54#398×C83—21no—
55#396×C83—21no—
56#391×C83C2211yescharacteristic, complemented
57#389×C83C2211yescharacteristic, complemented
58#386×C83—21no—
59#380×C83—21no—
60#380×C83C2211yescharacteristic, complemented
61#340×C83C2211yescharacteristic, complemented
62#340×C83C2211yescharacteristic, complemented
63#336×C83C2211yescharacteristic, complemented
64#336×C83C2211yescharacteristic, complemented
65C25×C83—21no—
66C25×C83—21no—
67C22×Q8×C83C2311yescharacteristic
68C22×D4×C83—22no—
69C22×D4×C83—22no—
70C22×D4×C83—28no—
71C22×D4×C83—21no—
72C22×D4×C83—21no—
73C22×D4×C83—22no—
74C22×D4×C83—22no—
75C22×D4×C83—22no—
76C22×D4×C83—22no—
77C22×D4×C83—21no—
78C22×D4×C83—21no—
79C22×D4×C83—21no—
80C22×D4×C83—22no—
81C22×D4×C83—21no—
82C22×D4×C83—41no—
83C22×D4×C83—41no—
84C22×D4×C83—41no—
85C22×D4×C83—41no—
86C22×D4×C83—44no—
87C22×D4×C83—44no—
88C22×D4×C83D411yescharacteristic
89C22×D4×C83D414yes—
90C22×D4×C83C2311yescharacteristic
91C22×D4×C83C2311yescharacteristic
92C22×D4×C83C2311yescharacteristic
93C23×C4×C83—21no—
94C23×C4×C83—21no—
95C23×C4×C83C2311yescharacteristic
96C23×C4×C83C2311yescharacteristic
97C2×SD16×C83—22no—
98C2×SD16×C83—22no—
99C2×SD16×C83—22no—
100C2×SD16×C83—22no—
101C2×SD16×C83—22no—
102C2×SD16×C83—22no—
103C2×SD16×C83—41no—
104C2×SD16×C83—41no—
105C2×SD16×C83—41no—
106C22×C8×C83—22no—
107C22×C8×C83—22no—
108C22×C8×C83—41no—
109C22×C8×C83C2311yescharacteristic
110C22×C8×C83C2311yescharacteristic
111C22×C8×C83C2311yescharacteristic
112C22×C8×C83C2311yescharacteristic
113#127×C83—22no—
114#127×C83—22no—
115C22⋊Q8×C83—22no—
116C22⋊Q8×C83—22no—
117C22⋊Q8×C83—22no—
118C22⋊Q8×C83—41no—
119#121×C83—28no—
120#121×C83—22no—
121#121×C83—22no—
122#121×C83—22no—
123#121×C83D414yes—
124#120×C83—28no—
125#120×C83—28no—
126C4×D4×C83—22no—
127C4×D4×C83—22no—
128C4×D4×C83—22no—
129C4×D4×C83—22no—
130C2×C4⋊C4×C83—22no—
131C2×C4⋊C4×C83—21no—
132C2×C4⋊C4×C83—21no—
133C2×C4⋊C4×C83—21no—
134C2×C4⋊C4×C83—21no—
135C2×C4⋊C4×C83—41no—
136C2×C4⋊C4×C83D411yescharacteristic
137C2×C4⋊C4×C83C2311yescharacteristic
138C2×C4⋊C4×C83C2311yescharacteristic
139C2×C4⋊C4×C83C2311yescharacteristic
140C2×C4⋊C4×C83C2311yescharacteristic
141C2×C22⋊C4×C83—21no—
142C2×C22⋊C4×C83—21no—
143C2×C22⋊C4×C83—21no—
144C2×C22⋊C4×C83—21no—
145C2×C22⋊C4×C83—21no—
146C2×C22⋊C4×C83—21no—
147C2×C22⋊C4×C83D411yescharacteristic
148C2×C22⋊C4×C83D411yescharacteristic
149C2×C42×C83C2311yescharacteristic
150#106×C83—22no—
151#103×C83—22no—
152#102×C83—22no—
153#102×C83—22no—
154#102×C83—22no—
155#102×C83—22no—
156#102×C83—22no—
157#102×C83—22no—
158#102×C83—22no—
159#102×C83—41no—
160#102×C83D414yescomplemented
161C22⋊C8×C83—22no—
162C22⋊C8×C83—22no—
163C22⋊C8×C83—41no—
164#95×C83—21no—
165#95×C83—21no—
166#95×C83—21no—
167#95×C83—21no—
168C24×C83—21no—
169C24×C83—24no—
170C24×C83—21no—
171C24×C83—21no—
172C24×C83—24no—
173C24×C83—42no—
174C24×C83—42no—
175C24×C83—42no—
176C24×C83—42no—
177C24×C83—42no—
178C24×C83—42no—
179C24×C83—42no—
180C24×C83—42no—
181C24×C83—81no—
182C24×C83—81no—
183C24×C83—81no—
184C24×C83—81no—
185C24×C83C2×D411yescharacteristic
186C24×C83C2×D411yescharacteristic
187C2×Q8×C83—21no—
188C2×Q8×C83—21no—
189C2×Q8×C83—21no—
190C2×Q8×C83—21no—
191C2×Q8×C83—21no—
192C2×Q8×C83—21no—
193C2×D4×C83—22no—
194C2×D4×C83—22no—
195C2×D4×C83—28no—
196C2×D4×C83—24no—
197C2×D4×C83—24no—
198C2×D4×C83—24no—
199C2×D4×C83—24no—
200C2×D4×C83—24no—
201C2×D4×C83—24no—
202C2×D4×C83—21no—
203C2×D4×C83—21no—
204C2×D4×C83—21no—
205C2×D4×C83—21no—
206C2×D4×C83—21no—
207C2×D4×C83—21no—
208C2×D4×C83—21no—
209C2×D4×C83—21no—
210C2×D4×C83—21no—
211C2×D4×C83—21no—
212C2×D4×C83—21no—
213C2×D4×C83—21no—
214C2×D4×C83—21no—
215C2×D4×C83—44no—
216C2×D4×C83—44no—
217C2×D4×C83—44no—
218C2×D4×C83—42no—
219C2×D4×C83—42no—
220C2×D4×C83—42no—
221C2×D4×C83—42no—
222C2×D4×C83—42no—
223C2×D4×C83—44no—
224C2×D4×C83—44no—
225C2×D4×C83—432no—
226C2×D4×C83—44no—
227C2×D4×C83—42no—
228C2×D4×C83—42no—
229C2×D4×C83—42no—
230C2×D4×C83—42no—
231C2×D4×C83—44no—
232C2×D4×C83—42no—
233C2×D4×C83—81no—
234C2×D4×C83—81no—
235C2×D4×C83SD1614yescomplemented
236C2×D4×C83C2×D412yes—
237C2×D4×C83C2×D412yes—
238C2×D4×C83C2×D412yes—
239C2×D4×C83C2×D412yes—
240C2×D4×C83#4112yes—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—24no—
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—42no—
258C22×C4×C83—42no—
259C22×C4×C83—42no—
260C22×C4×C83—42no—
261C22×C4×C83—81no—
262C22×C4×C83C2×D411yescharacteristic
263C22×C4×C83C2×D411yescharacteristic
264C22×C4×C83C2×D411yescharacteristic
265C22×C4×C83C2×D412yes—
266C22×C4×C83C2×D412yes—
267C22×C4×C83C2×D411yescharacteristic
268C22×C4×C83C2411yescharacteristic
269SD16×C83—44no—
270SD16×C83—44no—
271SD16×C83—44no—
272C2×C8×C83—21no—
273C2×C8×C83—21no—
274C2×C8×C83—21no—
275C2×C8×C83—21no—
276C2×C8×C83—21no—
277C2×C8×C83—21no—
278C2×C8×C83—21no—
279C2×C8×C83—21no—
280C2×C8×C83—21no—
281C2×C8×C83—21no—
282C2×C8×C83—21no—
283C2×C8×C83—44no—
284C2×C8×C83C2×D412yescomplemented
285C4⋊C4×C83—22no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—21no—
288C4⋊C4×C83—21no—
289C4⋊C4×C83—21no—
290C4⋊C4×C83—21no—
291C4⋊C4×C83—21no—
292C4⋊C4×C83—42no—
293C4⋊C4×C83—42no—
294C4⋊C4×C83—42no—
295C4⋊C4×C83—81no—
296C4⋊C4×C83C2×D412yes—
297C4⋊C4×C83C2×D412yescomplemented
298C22⋊C4×C83—24no—
299C22⋊C4×C83—24no—
300C22⋊C4×C83—22no—
301C22⋊C4×C83—24no—
302C22⋊C4×C83—22no—
303C22⋊C4×C83—42no—
304C22⋊C4×C83—42no—
305C22⋊C4×C83—81no—
306C42×C83—21no—
307C42×C83—21no—
308C23×C83—21no—
309C23×C83—21no—
310C23×C83—21no—
311C23×C83—21no—
312C23×C83—21no—
313C23×C83—22no—
314C23×C83—21no—
315C23×C83—22no—
316C23×C83—21no—
317C23×C83—22no—
318C23×C83—21no—
319C23×C83—21no—
320C23×C83—21no—
321C23×C83—22no—
322C23×C83—22no—
323C23×C83—48no—
324C23×C83—48no—
325C23×C83—48no—
326C23×C83—41no—
327C23×C83—41no—
328C23×C83—41no—
329C23×C83—41no—
330C23×C83—41no—
331C23×C83—41no—
332C23×C83—41no—
333C23×C83—41no—
334C23×C83—41no—
335C23×C83—41no—
336C23×C83—41no—
337C23×C83—41no—
338C23×C83—41no—
339C23×C83—41no—
340C23×C83—41no—
341C23×C83—41no—
342C23×C83—48no—
343C23×C83—84no—
344C23×C83—84no—
345C23×C83—84no—
346C23×C83—84no—
347C23×C83—84no—
348C23×C83—84no—
349C23×C83—84no—
350C23×C83—84no—
351C23×C83—84no—
352C23×C83—84no—
353C23×C83#12012yes—
354C23×C83C2×SD1612yes—
355C23×C83C2×SD1612yes—
356C23×C83AGL(1,ℤ/8)12yes—
357C23×C83C22×D411yescharacteristic
358Q8×C83—41no—
359Q8×C83—41no—
360Q8×C83—41no—
361Q8×C83—41no—
362D4×C83—28no—
363D4×C83—22no—
364D4×C83—22no—
365D4×C83—22no—
366D4×C83—22no—
367D4×C83—22no—
368D4×C83—22no—
369D4×C83—22no—
370D4×C83—48no—
371D4×C83—48no—
372D4×C83—48no—
373D4×C83—48no—
374D4×C83—48no—
375D4×C83—41no—
376D4×C83—41no—
377D4×C83—41no—
378D4×C83—41no—
379D4×C83—84no—
380D4×C83#12114yes—
381C2×C4×C83—21no—
382C2×C4×C83—21no—
383C2×C4×C83—21no—
384C2×C4×C83—21no—
385C2×C4×C83—22no—
386C2×C4×C83—22no—
387C2×C4×C83—22no—
388C2×C4×C83—22no—
389C2×C4×C83—21no—
390C2×C4×C83—21no—
391C2×C4×C83—22no—
392C2×C4×C83—22no—
393C2×C4×C83—21no—
394C2×C4×C83—21no—
395C2×C4×C83—21no—
396C2×C4×C83—21no—
397C2×C4×C83—48no—
398C2×C4×C83—41no—
399C2×C4×C83—41no—
400C2×C4×C83—41no—
401C2×C4×C83—41no—
402C2×C4×C83—41no—
403C2×C4×C83—41no—
404C2×C4×C83—41no—
405C2×C4×C83—41no—
406C2×C4×C83—41no—
407C2×C4×C83—41no—
408C2×C4×C83—41no—
409C2×C4×C83—41no—
410C2×C4×C83—41no—
411C2×C4×C83—41no—
412C2×C4×C83—41no—
413C2×C4×C83—41no—
414C2×C4×C83—41no—
415C2×C4×C83—84no—
416C2×C4×C83#12012yes—
417C2×C4×C83C2×SD1612yes—
418C2×C4×C83C22×D411yescharacteristic
419C2×C4×C83C22×D411yescharacteristic
420C2×C4×C83C22×D411yescharacteristic
421C2×C4×C83C2×#4111yescharacteristic
422C2×C4×C83H(5,𝔽2)11yescharacteristic
423C2×C4×C83H(5,𝔽2)11yescharacteristic
424C8×C83—22no—
425C8×C83—41no—
426C8×C83—41no—
427C8×C83—41no—
428C22×C83—22no—
429C22×C83—22no—
430C22×C83—22no—
431C22×C83—22no—
432C22×C83—22no—
433C22×C83—22no—
434C22×C83—24no—
435C22×C83—22no—
436C22×C83—22no—
437C22×C83—22no—
438C22×C83—41no—
439C22×C83—42no—
440C22×C83—41no—
441C22×C83—42no—
442C22×C83—41no—
443C22×C83—42no—
444C22×C83—42no—
445C22×C83—42no—
446C22×C83—41no—
447C22×C83—42no—
448C22×C83—42no—
449C22×C83—42no—
450C22×C83—42no—
451C22×C83—42no—
452C22×C83—42no—
453C22×C83—42no—
454C22×C83—816no—
455C22×C83—816no—
456C22×C83—81no—
457C22×C83—81no—
458C22×C83—81no—
459C22×C83—81no—
460C22×C83—81no—
461C22×C83—81no—
462C22×C83—81no—
463C22×C83—81no—
464C22×C83#45014yescomplemented
465C22×C83C2×#12011yescharacteristic
466C22×C83D4211yescharacteristic
467C22×C83#54611yescharacteristic
468C22×C83C22×SD1611yescharacteristic
469C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C83#57611yescharacteristic
471C22×C83#57711yescharacteristic
472C4×C83—22no—
473C4×C83—22no—
474C4×C83—41no—
475C4×C83—42no—
476C4×C83—42no—
477C4×C83—41no—
478C4×C83—81no—
479C4×C83—81no—
480C4×C83—81no—
481C4×C83C2×#12111yescharacteristic
482C4×C83#53411yescharacteristic
483C4×C83D4211yescharacteristic
484C4×C83#54611yescharacteristic
485#24432C8311yesmaximal, characteristic, direct product factor, Sylow
486C2×C83—24no—
487C2×C83—42no—
488C2×C83—44no—
489C2×C83—82no—
490C2×C83—82no—
491C2×C83#241011yescharacteristic
492C2×C83C2×#45011yescharacteristic
493C2×C83#301211yescharacteristic
494C2×C83#326411yescharacteristic
495C2×C83D4×SD1611yescharacteristic
496C2×C83#329511yescharacteristic
497C2×C83#331011yescharacteristic
498C2×D42C2×C8311yescharacteristic
499C2×#465C2×C8311yescharacteristic, complemented
500C2×#450C2×C8311yescharacteristic, complemented
501C2×#450C2×C8311yescharacteristic, complemented
502C22×#102C2×C8311yescharacteristic, complemented
503#2417C2×C8311yescharacteristic, complemented
504#2041C2×C8311yescharacteristic, complemented
505#2034C2×C8311yescharacteristic, complemented
506#2014C2×C8311yescharacteristic, complemented
507#2000C2×C8311yescharacteristic, complemented
508#1877C2×C8311yescharacteristic, complemented
509#1874C2×C8311yescharacteristic, complemented
510#1869C2×C8311yescharacteristic, complemented
511#1864C2×C8311yescharacteristic, complemented
512#1786C2×C8311yescharacteristic, complemented
513C83#2443211yescharacteristic, direct product factor, Sylow
514C23×D4—21no—
515C23×D4C22×C8311yescharacteristic
516C23×D4C22×C8311yescharacteristic
517C22×SD16C22×C8311yescharacteristic
518C22×SD16C22×C8311yescharacteristic, complemented
519C22×SD16C22×C8311yescharacteristic, complemented
520C23×C8C22×C8311yescharacteristic, complemented
521D42—24no—
522D42—24no—
523C2×#127C22×C8311yescharacteristic
524C2×C22⋊Q8C22×C8311yescharacteristic, complemented
525C2×C22⋊Q8C22×C8311yescharacteristic, complemented
526C2×#121—21no—
527C2×#121C22×C8311yescharacteristic
528C2×#121C22×C8311yescharacteristic
529C2×#120—21no—
530C2×#120—21no—
531C2×C4×D4C22×C8311yescharacteristic
532C2×C4×D4C22×C8311yescharacteristic
533C22×C4⋊C4C22×C8311yescharacteristic, complemented
534#465—24no—
535#450—24no—
536#450—24no—
537C2×#106C22×C8311yescharacteristic, complemented
538C2×#103C22×C8311yescharacteristic, complemented
539C2×#102—24no—
540C2×#102C22×C8311yescharacteristic
541C2×#102C22×C8311yescharacteristic
542C2×#102C22×C8311yescharacteristic
543C2×#102C22×C8311yescharacteristic, complemented
544C2×#102C22×C8311yescharacteristic, complemented
545C2×#102C22×C8311yescharacteristic, complemented
546C2×#102C22×C8311yescharacteristic, complemented
547C2×#102C22×C8311yescharacteristic, complemented
548C2×#102C22×C8311yescharacteristic, complemented
549C2×C22⋊C8C22×C8311yescharacteristic, complemented
550C2×C22⋊C8C22×C8311yescharacteristic, complemented
551C2×C22⋊C8C22×C8311yescharacteristic, complemented
552#398—21no—
553#396—21no—
554#391C22×C8311yescharacteristic, complemented
555#389C22×C8311yescharacteristic, complemented
556#386—21no—
557#380—21no—
558#380C22×C8311yescharacteristic, complemented
559#340C22×C8311yescharacteristic, complemented
560#340C22×C8311yescharacteristic, complemented
561#336C22×C8311yescharacteristic, complemented
562#336C22×C8311yescharacteristic, complemented
563C25—21no—
564C25—21no—
565C22×Q8C23×C8311yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C8311yescharacteristic
587C22×D4D4×C8314yes—
588C22×D4C23×C8311yescharacteristic
589C22×D4C23×C8311yescharacteristic
590C22×D4C23×C8311yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C8311yescharacteristic
594C23×C4C23×C8311yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C8311yescharacteristic
608C22×C8C23×C8311yescharacteristic
609C22×C8C23×C8311yescharacteristic
610C22×C8C23×C8311yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C8314yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C8311yescharacteristic
635C2×C4⋊C4C23×C8311yescharacteristic
636C2×C4⋊C4C23×C8311yescharacteristic
637C2×C4⋊C4C23×C8311yescharacteristic
638C2×C4⋊C4C23×C8311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C8311yescharacteristic
646C2×C22⋊C4D4×C8311yescharacteristic
647C2×C42C23×C8311yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C8314yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C8311yescharacteristic
684C24C2×D4×C8311yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C8314yescomplemented
734C2×D4C2×D4×C8312yes—
735C2×D4C2×D4×C8312yes—
736C2×D4C2×D4×C8312yes—
737C2×D4C2×D4×C8312yes—
738C2×D4#41×C8312yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C8311yescharacteristic
761C22×C4C2×D4×C8311yescharacteristic
762C22×C4C2×D4×C8311yescharacteristic
763C22×C4C2×D4×C8312yes—
764C22×C4C2×D4×C8312yes—
765C22×C4C2×D4×C8311yescharacteristic
766C22×C4C24×C8311yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C8312yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C8312yes—
795C4⋊C4C2×D4×C8312yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C8312yes—
852C23C2×SD16×C8312yes—
853C23C2×SD16×C8312yes—
854C23AGL(1,ℤ/8)×C8312yes—
855C23C22×D4×C8311yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C8314yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C8312yes—
915C2×C4C2×SD16×C8312yes—
916C2×C4C22×D4×C8311yescharacteristic
917C2×C4C22×D4×C8311yescharacteristic
918C2×C4C22×D4×C8311yescharacteristic
919C2×C4C2×#41×C8311yescharacteristic
920C2×C4H(5,𝔽2)×C8311yescharacteristic
921C2×C4H(5,𝔽2)×C8311yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—24no—
935C22—22no—
936C22—42no—
937C22—42no—
938C22—41no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—41no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#450×C8314yescomplemented
963C22C2×#120×C8311yescharacteristic
964C22D42×C8311yescharacteristic
965C22#546×C8311yescharacteristic
966C22C22×SD16×C8311yescharacteristic
967C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
968C22#576×C8311yescharacteristic
969C22#577×C8311yescharacteristic
970C4—22no—
971C4—22no—
972C4—41no—
973C4—42no—
974C4—42no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C8311yescharacteristic
980C4#534×C8311yescharacteristic
981C4D42×C8311yescharacteristic
982C4#546×C8311yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C83×#241011yescharacteristic
989C2C2×#450×C8311yescharacteristic
990C2C83×#301211yescharacteristic
991C2C83×#326411yescharacteristic
992C2D4×SD16×C8311yescharacteristic
993C2C83×#329511yescharacteristic
994C2C83×#331011yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×D42×C83C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C2×C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#465×C83C2semidirect
3. C2×#450×C83C2semidirect
4. C2×#450×C83C2semidirect
5. C22×#102×C83C2semidirect
6. C83×#2417C2semidirect
7. C83×#2041C2semidirect
8. C83×#2034C2semidirect
9. C83×#2014C2semidirect
10. C83×#2000C2semidirect
11. C83×#1877C2semidirect
12. C83×#1874C2semidirect
13. C83×#1869C2semidirect
14. C83×#1864C2semidirect
15. C83×#1786C2semidirect
20. C22×SD16×C83C22semidirect
21. C22×SD16×C83C22semidirect
22. C23×C8×C83C22semidirect
26. C2×C22⋊Q8×C83C22semidirect
27. C2×C22⋊Q8×C83C22semidirect
35. C22×C4⋊C4×C83C22semidirect
39. C2×#106×C83C22semidirect
40. C2×#103×C83C22semidirect
45. C2×#102×C83C22semidirect
46. C2×#102×C83C22semidirect
47. C2×#102×C83C22semidirect
48. C2×#102×C83C22semidirect
49. C2×#102×C83C22semidirect
50. C2×#102×C83C22semidirect
51. C2×C22⋊C8×C83C22semidirect
52. C2×C22⋊C8×C83C22semidirect
53. C2×C22⋊C8×C83C22semidirect
56. #391×C83C22semidirect
57. #389×C83C22semidirect
60. #380×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
63. #336×C83C22semidirect
64. #336×C83C22semidirect
160. #102×C83D4semidirect
235. C2×D4×C83SD16semidirect
284. C2×C8×C83C2×D4semidirect
297. C4⋊C4×C83C2×D4semidirect
464. C22×C83#450semidirect
485. #24432C83direct (N × H)
499. C2×#465C2×C83semidirect
500. C2×#450C2×C83semidirect
501. C2×#450C2×C83semidirect
502. C22×#102C2×C83semidirect
503. #2417C2×C83semidirect
504. #2041C2×C83semidirect
505. #2034C2×C83semidirect
506. #2014C2×C83semidirect
507. #2000C2×C83semidirect
508. #1877C2×C83semidirect
509. #1874C2×C83semidirect
510. #1869C2×C83semidirect
511. #1864C2×C83semidirect
512. #1786C2×C83semidirect
513. C83#24432direct (N × H)
518. C22×SD16C22×C83semidirect
519. C22×SD16C22×C83semidirect
520. C23×C8C22×C83semidirect
524. C2×C22⋊Q8C22×C83semidirect
525. C2×C22⋊Q8C22×C83semidirect
533. C22×C4⋊C4C22×C83semidirect
537. C2×#106C22×C83semidirect
538. C2×#103C22×C83semidirect
543. C2×#102C22×C83semidirect
544. C2×#102C22×C83semidirect
545. C2×#102C22×C83semidirect
546. C2×#102C22×C83semidirect
547. C2×#102C22×C83semidirect
548. C2×#102C22×C83semidirect
549. C2×C22⋊C8C22×C83semidirect
550. C2×C22⋊C8C22×C83semidirect
551. C2×C22⋊C8C22×C83semidirect
554. #391C22×C83semidirect
555. #389C22×C83semidirect
558. #380C22×C83semidirect
559. #340C22×C83semidirect
560. #340C22×C83semidirect
561. #336C22×C83semidirect
562. #336C22×C83semidirect
658. #102D4×C83semidirect
733. C2×D4SD16×C83semidirect
782. C2×C8C2×D4×C83semidirect
795. C4⋊C4C2×D4×C83semidirect
962. C22#450×C83semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C832
C2×#465×C832
C2×#450×C832
C22×#102×C832
C83×#24172
C83×#20412
C83×#20342
C83×#20142
C83×#20002
C83×#18772
C83×#18742
C83×#18692
C83×#18642
C83×#17862
#2443283