Finite Group Databasebeta

← C83×#24388 #35252212

Subgroups — C83×#24388 #35252212

Order 21248.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C83C211yesmaximal, characteristic, complemented
2C2×#469×C83C211yesmaximal, characteristic, complemented
3C2×#468×C83C211yesmaximal, characteristic, complemented
4C2×#449×C83C211yesmaximal, characteristic, complemented
5C2×#407×C83C211yesmaximal, characteristic, complemented
6C83×#2847C211yesmaximal, characteristic, complemented
7C83×#2035C211yesmaximal, characteristic, complemented
8C83×#2033C211yesmaximal, characteristic, complemented
9C83×#2000C211yesmaximal, characteristic, complemented
10C83×#1999C211yesmaximal, characteristic, complemented
11C83×#1895C211yesmaximal, characteristic, complemented
12C83×#1894C211yesmaximal, characteristic, complemented
13C83×#1875C211yesmaximal, characteristic, complemented
14C83×#1854C211yesmaximal, characteristic, complemented
15C83×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C24×C4×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic, complemented
19C22×D8×C83C2211yescharacteristic, complemented
20C22×M16×C83C2211yescharacteristic
21C22×M16×C83C2211yescharacteristic
22#525×C83—24no—
23#525×C83—24no—
24C2×#123×C83—21no—
25C2×C22⋊Q8×C83C2211yescharacteristic
26C2×C22⋊Q8×C83C2211yescharacteristic
27C2×#121×C83C2211yescharacteristic
28C2×#121×C83C2211yescharacteristic
29C2×#121×C83C2211yescharacteristic
30C2×#121×C83C2211yescharacteristic
31C2×#121×C83C2211yescharacteristic
32C2×#120×C83—21no—
33C2×#120×C83—21no—
34C2×C4×D4×C83—21no—
35C2×C4×D4×C83—21no—
36C2×#117×C83C2211yescharacteristic
37#469×C83—24no—
38#468×C83—24no—
39#449×C83—24no—
40C2×#107×C83C2211yescharacteristic, complemented
41C2×#106×C83C2211yescharacteristic, complemented
42C2×#103×C83C2211yescharacteristic, complemented
43C2×#103×C83C2211yescharacteristic, complemented
44C2×#103×C83C2211yescharacteristic, complemented
45C2×#102×C83C2211yescharacteristic, complemented
46C2×#102×C83C2211yescharacteristic, complemented
47C2×#102×C83C2211yescharacteristic, complemented
48C2×#102×C83C2211yescharacteristic, complemented
49C2×#102×C83C2211yescharacteristic, complemented
50#407×C83—24no—
51C2×C22⋊C8×C83C2211yescharacteristic
52C2×C22⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic
54C2×C22⋊C8×C83C2211yescharacteristic
55#386×C83—21no—
56#386×C83—21no—
57#386×C83—21no—
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic
60#380×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic, complemented
62#340×C83C2211yescharacteristic, complemented
63#340×C83C2211yescharacteristic, complemented
64#340×C83C2211yescharacteristic, complemented
65C25×C83D411yescharacteristic
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—22no—
70C2×#41×C83—41no—
71C2×#41×C83—41no—
72C22×Q8×C83C2311yescharacteristic
73C22×D4×C83—21no—
74C22×D4×C83—21no—
75C22×D4×C83—21no—
76C22×D4×C83—21no—
77C22×D4×C83—21no—
78C22×D4×C83—21no—
79C22×D4×C83C2311yescharacteristic
80C22×D4×C83C2311yescharacteristic
81C23×C4×C83—21no—
82C23×C4×C83—22no—
83C23×C4×C83—22no—
84C23×C4×C83—22no—
85C23×C4×C83—22no—
86C23×C4×C83—41no—
87C23×C4×C83—41no—
88C23×C4×C83D411yescharacteristic
89C23×C4×C83D411yescharacteristic
90C23×C4×C83D411yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C23×C4×C83C2311yescharacteristic
94C2×SD16×C83—22no—
95C2×SD16×C83—22no—
96C2×SD16×C83—41no—
97C2×D8×C83—22no—
98C2×D8×C83—22no—
99C2×D8×C83—41no—
100C2×M16×C83—22no—
101C2×M16×C83—22no—
102C2×M16×C83—22no—
103C2×M16×C83—22no—
104C2×M16×C83—41no—
105C2×M16×C83—41no—
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109C22×C8×C83C2311yescharacteristic
110#123×C83—28no—
111C22⋊Q8×C83—22no—
112C22⋊Q8×C83—22no—
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83D414yescomplemented
115#121×C83—22no—
116#121×C83—22no—
117#121×C83—22no—
118#121×C83—22no—
119#121×C83—22no—
120#121×C83—22no—
121#121×C83—22no—
122#121×C83—41no—
123#121×C83—41no—
124#121×C83D414yescomplemented
125#120×C83—28no—
126#120×C83—44no—
127C4×D4×C83—28no—
128C4×D4×C83—28no—
129#117×C83—22no—
130#117×C83—22no—
131C2×C4⋊C4×C83—21no—
132C2×C4⋊C4×C83—21no—
133C2×C4⋊C4×C83C2311yescharacteristic
134C2×C4⋊C4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83C2311yescharacteristic
137C2×C4⋊C4×C83C2311yescharacteristic
138C2×C22⋊C4×C83—21no—
139C2×C22⋊C4×C83—21no—
140C2×C22⋊C4×C83—21no—
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×C83—21no—
148C2×C22⋊C4×C83—21no—
149C2×C42×C83—21no—
150#107×C83—22no—
151#106×C83—22no—
152#103×C83—22no—
153#103×C83—22no—
154#103×C83—41no—
155#102×C83—22no—
156#102×C83—22no—
157#102×C83—22no—
158#102×C83—22no—
159#102×C83—41no—
160C22⋊C8×C83—22no—
161C22⋊C8×C83—22no—
162C22⋊C8×C83—22no—
163C22⋊C8×C83D414yescomplemented
164#95×C83—21no—
165#95×C83—21no—
166#95×C83—21no—
167C24×C83—22no—
168C24×C83—22no—
169C24×C83—22no—
170C24×C83—21no—
171C24×C83—21no—
172C24×C83—41no—
173C24×C83—41no—
174C24×C83—41no—
175C24×C83—41no—
176C24×C83C2×D411yescharacteristic
177C24×C83C2×D411yescharacteristic
178C24×C83C2×D411yescharacteristic
179#41×C83—44no—
180#41×C83—44no—
181#41×C83—44no—
182#41×C83—44no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—21no—
187C2×Q8×C83—21no—
188C2×Q8×C83C2×D412yes—
189C2×D4×C83—24no—
190C2×D4×C83—24no—
191C2×D4×C83—24no—
192C2×D4×C83—21no—
193C2×D4×C83—21no—
194C2×D4×C83—21no—
195C2×D4×C83—21no—
196C2×D4×C83—21no—
197C2×D4×C83—21no—
198C2×D4×C83—21no—
199C2×D4×C83—21no—
200C2×D4×C83—21no—
201C2×D4×C83—21no—
202C2×D4×C83—21no—
203C2×D4×C83—42no—
204C2×D4×C83—42no—
205C2×D4×C83—42no—
206C2×D4×C83—42no—
207C2×D4×C83—42no—
208C2×D4×C83—42no—
209C2×D4×C83—42no—
210C2×D4×C83—42no—
211C2×D4×C83—42no—
212C2×D4×C83—42no—
213C2×D4×C83—42no—
214C2×D4×C83—42no—
215C2×D4×C83—42no—
216C2×D4×C83—42no—
217C2×D4×C83—42no—
218C2×D4×C83C2×D412yes—
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—24no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
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—41no—
247C22×C4×C83—41no—
248C22×C4×C83—41no—
249C22×C4×C83—44no—
250C22×C4×C83—44no—
251C22×C4×C83—44no—
252C22×C4×C83—44no—
253C22×C4×C83—42no—
254C22×C4×C83—42no—
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2×D412yes—
258C22×C4×C83C2×D412yes—
259C22×C4×C83C2×D411yescharacteristic
260C22×C4×C83C2×D412yes—
261C22×C4×C83#4112yes—
262C22×C4×C83C2411yescharacteristic
263SD16×C83—44no—
264D8×C83—44no—
265M16×C83—44no—
266M16×C83—44no—
267C2×C8×C83—21no—
268C2×C8×C83—21no—
269C2×C8×C83—21no—
270C2×C8×C83—21no—
271C2×C8×C83—21no—
272C2×C8×C83—21no—
273C2×C8×C83—21no—
274C2×C8×C83—21no—
275C2×C8×C83—21no—
276C2×C8×C83—21no—
277C2×C8×C83C2×D412yes—
278C2×C8×C83C2×D412yes—
279C4⋊C4×C83—24no—
280C4⋊C4×C83—24no—
281C4⋊C4×C83—21no—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—21no—
284C4⋊C4×C83—21no—
285C4⋊C4×C83—21no—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—21no—
288C4⋊C4×C83—21no—
289C4⋊C4×C83C2×D412yes—
290C4⋊C4×C83C2×D412yes—
291C22⋊C4×C83—24no—
292C22⋊C4×C83—24no—
293C22⋊C4×C83—24no—
294C22⋊C4×C83—24no—
295C22⋊C4×C83—24no—
296C22⋊C4×C83—42no—
297C22⋊C4×C83—42no—
298C22⋊C4×C83—42no—
299C22⋊C4×C83—42no—
300C22⋊C4×C83—42no—
301C22⋊C4×C83—42no—
302C42×C83—24no—
303C23×C83—21no—
304C23×C83—21no—
305C23×C83—21no—
306C23×C83—21no—
307C23×C83—21no—
308C23×C83—21no—
309C23×C83—21no—
310C23×C83—21no—
311C23×C83—21no—
312C23×C83—21no—
313C23×C83—21no—
314C23×C83—21no—
315C23×C83—21no—
316C23×C83—21no—
317C23×C83—21no—
318C23×C83—21no—
319C23×C83—21no—
320C23×C83—21no—
321C23×C83—22no—
322C23×C83—44no—
323C23×C83—44no—
324C23×C83—44no—
325C23×C83—44no—
326C23×C83—44no—
327C23×C83—44no—
328C23×C83—44no—
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#12012yes—
343C23×C83#12112yes—
344C23×C83AGL(1,ℤ/8)12yes—
345C23×C83C22×D411yescharacteristic
346Q8×C83—22no—
347Q8×C83—22no—
348Q8×C83—41no—
349Q8×C83—41no—
350D4×C83—22no—
351D4×C83—22no—
352D4×C83—48no—
353D4×C83—48no—
354D4×C83—48no—
355D4×C83—41no—
356D4×C83—41no—
357D4×C83—41no—
358D4×C83—41no—
359D4×C83—41no—
360D4×C83—41no—
361D4×C83—84no—
362D4×C83—84no—
363D4×C83—84no—
364C2×C4×C83—21no—
365C2×C4×C83—21no—
366C2×C4×C83—21no—
367C2×C4×C83—21no—
368C2×C4×C83—22no—
369C2×C4×C83—22no—
370C2×C4×C83—22no—
371C2×C4×C83—22no—
372C2×C4×C83—22no—
373C2×C4×C83—22no—
374C2×C4×C83—22no—
375C2×C4×C83—22no—
376C2×C4×C83—22no—
377C2×C4×C83—22no—
378C2×C4×C83—21no—
379C2×C4×C83—22no—
380C2×C4×C83—21no—
381C2×C4×C83—21no—
382C2×C4×C83—44no—
383C2×C4×C83—44no—
384C2×C4×C83—44no—
385C2×C4×C83—48no—
386C2×C4×C83—41no—
387C2×C4×C83—41no—
388C2×C4×C83—41no—
389C2×C4×C83—41no—
390C2×C4×C83—41no—
391C2×C4×C83—41no—
392C2×C4×C83—41no—
393C2×C4×C83—41no—
394C2×C4×C83—41no—
395C2×C4×C83—41no—
396C2×C4×C83—41no—
397C2×C4×C83—41no—
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#12012yes—
406C2×C4×C83#12112yes—
407C2×C4×C83C22×D411yescharacteristic
408C2×C4×C83C22×D411yescharacteristic
409C2×C4×C83C22×D411yescharacteristic
410C2×C4×C83C2×#4111yescharacteristic
411C2×C4×C83H(5,𝔽2)11yescharacteristic
412C2×C4×C83H(5,𝔽2)11yescharacteristic
413C8×C83—22no—
414C8×C83—22no—
415C8×C83—41no—
416C8×C83—41no—
417C22×C83—22no—
418C22×C83—22no—
419C22×C83—22no—
420C22×C83—22no—
421C22×C83—22no—
422C22×C83—22no—
423C22×C83—22no—
424C22×C83—22no—
425C22×C83—22no—
426C22×C83—416no—
427C22×C83—41no—
428C22×C83—41no—
429C22×C83—41no—
430C22×C83—41no—
431C22×C83—41no—
432C22×C83—41no—
433C22×C83—41no—
434C22×C83—41no—
435C22×C83—41no—
436C22×C83—41no—
437C22×C83—41no—
438C22×C83—41no—
439C22×C83—42no—
440C22×C83—42no—
441C22×C83—42no—
442C22×C83—81no—
443C22×C83—81no—
444C22×C83—81no—
445C22×C83—81no—
446C22×C83—81no—
447C22×C83—81no—
448C22×C83—81no—
449C22×C83—81no—
450C22×C83—81no—
451C22×C83—81no—
452C22×C83—81no—
453C22×C83C2×#12011yescharacteristic
454C22×C83C2×#12111yescharacteristic
455C22×C83#53411yescharacteristic
456C22×C83C2×AGL(1,ℤ/8)11yescharacteristic
457C22×C83#57511yescharacteristic
458C22×C83#57511yescharacteristic
459C22×C83#57511yescharacteristic
460C4×C83—22no—
461C4×C83—22no—
462C4×C83—41no—
463C4×C83—42no—
464C4×C83—42no—
465C4×C83—42no—
466C4×C83—81no—
467C4×C83—81no—
468C4×C83—81no—
469C4×C83D4211yescharacteristic
470C4×C83D4211yescharacteristic
471C4×C83#54611yescharacteristic
472C4×C83#54611yescharacteristic
473#24388C8311yesmaximal, characteristic, direct product factor, Sylow
474C2×C83—42no—
475C2×C83—42no—
476C2×C83—42no—
477C2×C83—82no—
478C2×C83—161no—
479C2×C83#241011yescharacteristic
480C2×C83#300511yescharacteristic
481C2×C83#300611yescharacteristic
482C2×C83#305411yescharacteristic
483C2×C83#305511yescharacteristic
484C2×C83#319411yescharacteristic
485C2×C83#319711yescharacteristic
486C2×#525C2×C8311yescharacteristic, complemented
487C2×#469C2×C8311yescharacteristic, complemented
488C2×#468C2×C8311yescharacteristic, complemented
489C2×#449C2×C8311yescharacteristic, complemented
490C2×#407C2×C8311yescharacteristic, complemented
491#2847C2×C8311yescharacteristic, complemented
492#2035C2×C8311yescharacteristic, complemented
493#2033C2×C8311yescharacteristic, complemented
494#2000C2×C8311yescharacteristic, complemented
495#1999C2×C8311yescharacteristic, complemented
496#1895C2×C8311yescharacteristic, complemented
497#1894C2×C8311yescharacteristic, complemented
498#1875C2×C8311yescharacteristic, complemented
499#1854C2×C8311yescharacteristic, complemented
500#1788C2×C8311yescharacteristic, complemented
501C83#2438811yescharacteristic, direct product factor, Sylow
502C22×#41C22×C8311yescharacteristic
503C24×C4C22×C8311yescharacteristic
504C22×SD16C22×C8311yescharacteristic, complemented
505C22×D8C22×C8311yescharacteristic, complemented
506C22×M16C22×C8311yescharacteristic
507C22×M16C22×C8311yescharacteristic
508#525—24no—
509#525—24no—
510C2×#123—21no—
511C2×C22⋊Q8C22×C8311yescharacteristic
512C2×C22⋊Q8C22×C8311yescharacteristic
513C2×#121C22×C8311yescharacteristic
514C2×#121C22×C8311yescharacteristic
515C2×#121C22×C8311yescharacteristic
516C2×#121C22×C8311yescharacteristic
517C2×#121C22×C8311yescharacteristic
518C2×#120—21no—
519C2×#120—21no—
520C2×C4×D4—21no—
521C2×C4×D4—21no—
522C2×#117C22×C8311yescharacteristic
523#469—24no—
524#468—24no—
525#449—24no—
526C2×#107C22×C8311yescharacteristic, complemented
527C2×#106C22×C8311yescharacteristic, complemented
528C2×#103C22×C8311yescharacteristic, complemented
529C2×#103C22×C8311yescharacteristic, complemented
530C2×#103C22×C8311yescharacteristic, complemented
531C2×#102C22×C8311yescharacteristic, complemented
532C2×#102C22×C8311yescharacteristic, complemented
533C2×#102C22×C8311yescharacteristic, complemented
534C2×#102C22×C8311yescharacteristic, complemented
535C2×#102C22×C8311yescharacteristic, complemented
536#407—24no—
537C2×C22⋊C8C22×C8311yescharacteristic
538C2×C22⋊C8C22×C8311yescharacteristic
539C2×C22⋊C8C22×C8311yescharacteristic
540C2×C22⋊C8C22×C8311yescharacteristic
541#386—21no—
542#386—21no—
543#386—21no—
544#380C22×C8311yescharacteristic
545#380C22×C8311yescharacteristic
546#380C22×C8311yescharacteristic
547#340C22×C8311yescharacteristic, complemented
548#340C22×C8311yescharacteristic, complemented
549#340C22×C8311yescharacteristic, complemented
550#340C22×C8311yescharacteristic, complemented
551C25D4×C8311yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—41no—
557C2×#41—41no—
558C22×Q8C23×C8311yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4C23×C8311yescharacteristic
566C22×D4C23×C8311yescharacteristic
567C23×C4—21no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4D4×C8311yescharacteristic
575C23×C4D4×C8311yescharacteristic
576C23×C4D4×C8311yescharacteristic
577C23×C4C23×C8311yescharacteristic
578C23×C4C23×C8311yescharacteristic
579C23×C4C23×C8311yescharacteristic
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—41no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—22no—
589C2×M16—22no—
590C2×M16—41no—
591C2×M16—41no—
592C22×C8C23×C8311yescharacteristic
593C22×C8C23×C8311yescharacteristic
594C22×C8C23×C8311yescharacteristic
595C22×C8C23×C8311yescharacteristic
596#123—28no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8D4×C8314yescomplemented
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—41no—
609#121—41no—
610#121D4×C8314yescomplemented
611#120—28no—
612#120—44no—
613C4×D4—28no—
614C4×D4—28no—
615#117—22no—
616#117—22no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4C23×C8311yescharacteristic
620C2×C4⋊C4C23×C8311yescharacteristic
621C2×C4⋊C4C23×C8311yescharacteristic
622C2×C4⋊C4C23×C8311yescharacteristic
623C2×C4⋊C4C23×C8311yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C42—21no—
636#107—22no—
637#106—22no—
638#103—22no—
639#103—22no—
640#103—41no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102—41no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—22no—
649C22⋊C8D4×C8314yescomplemented
650#95—21no—
651#95—21no—
652#95—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24—41no—
662C24C2×D4×C8311yescharacteristic
663C24C2×D4×C8311yescharacteristic
664C24C2×D4×C8311yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C8312yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C8312yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C8311yescharacteristic
742C22×C4C2×D4×C8311yescharacteristic
743C22×C4C2×D4×C8312yes—
744C22×C4C2×D4×C8312yes—
745C22×C4C2×D4×C8311yescharacteristic
746C22×C4C2×D4×C8312yes—
747C22×C4#41×C8312yes—
748C22×C4C24×C8311yescharacteristic
749SD16—44no—
750D8—44no—
751M16—44no—
752M16—44no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8C2×D4×C8312yes—
764C2×C8C2×D4×C8312yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C8312yes—
776C4⋊C4C2×D4×C8312yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—22no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23#120×C8312yes—
829C23#121×C8312yes—
830C23AGL(1,ℤ/8)×C8312yes—
831C23C22×D4×C8311yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4#120×C8312yes—
892C2×C4#121×C8312yes—
893C2×C4C22×D4×C8311yescharacteristic
894C2×C4C22×D4×C8311yescharacteristic
895C2×C4C22×D4×C8311yescharacteristic
896C2×C4C2×#41×C8311yescharacteristic
897C2×C4H(5,𝔽2)×C8311yescharacteristic
898C2×C4H(5,𝔽2)×C8311yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—416no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22C2×#120×C8311yescharacteristic
940C22C2×#121×C8311yescharacteristic
941C22#534×C8311yescharacteristic
942C22C2×AGL(1,ℤ/8)×C8311yescharacteristic
943C22#575×C8311yescharacteristic
944C22#575×C8311yescharacteristic
945C22#575×C8311yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C8311yescharacteristic
956C4D42×C8311yescharacteristic
957C4#546×C8311yescharacteristic
958C4#546×C8311yescharacteristic
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C83×#241011yescharacteristic
965C2C83×#300511yescharacteristic
966C2C83×#300611yescharacteristic
967C2C83×#305411yescharacteristic
968C2C83×#305511yescharacteristic
969C2C83×#319411yescharacteristic
970C2C83×#319711yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C24×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#525×C83C2semidirect
2. C2×#469×C83C2semidirect
3. C2×#468×C83C2semidirect
4. C2×#449×C83C2semidirect
5. C2×#407×C83C2semidirect
6. C83×#2847C2semidirect
7. C83×#2035C2semidirect
8. C83×#2033C2semidirect
9. C83×#2000C2semidirect
10. C83×#1999C2semidirect
11. C83×#1895C2semidirect
12. C83×#1894C2semidirect
13. C83×#1875C2semidirect
14. C83×#1854C2semidirect
15. C83×#1788C2semidirect
18. C22×SD16×C83C22semidirect
19. C22×D8×C83C22semidirect
40. C2×#107×C83C22semidirect
41. C2×#106×C83C22semidirect
42. C2×#103×C83C22semidirect
43. C2×#103×C83C22semidirect
44. C2×#103×C83C22semidirect
45. C2×#102×C83C22semidirect
46. C2×#102×C83C22semidirect
47. C2×#102×C83C22semidirect
48. C2×#102×C83C22semidirect
49. C2×#102×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
63. #340×C83C22semidirect
64. #340×C83C22semidirect
114. C22⋊Q8×C83D4semidirect
124. #121×C83D4semidirect
163. C22⋊C8×C83D4semidirect
473. #24388C83direct (N × H)
486. C2×#525C2×C83semidirect
487. C2×#469C2×C83semidirect
488. C2×#468C2×C83semidirect
489. C2×#449C2×C83semidirect
490. C2×#407C2×C83semidirect
491. #2847C2×C83semidirect
492. #2035C2×C83semidirect
493. #2033C2×C83semidirect
494. #2000C2×C83semidirect
495. #1999C2×C83semidirect
496. #1895C2×C83semidirect
497. #1894C2×C83semidirect
498. #1875C2×C83semidirect
499. #1854C2×C83semidirect
500. #1788C2×C83semidirect
501. C83#24388direct (N × H)
504. C22×SD16C22×C83semidirect
505. C22×D8C22×C83semidirect
526. C2×#107C22×C83semidirect
527. C2×#106C22×C83semidirect
528. C2×#103C22×C83semidirect
529. C2×#103C22×C83semidirect
530. C2×#103C22×C83semidirect
531. C2×#102C22×C83semidirect
532. C2×#102C22×C83semidirect
533. C2×#102C22×C83semidirect
534. C2×#102C22×C83semidirect
535. C2×#102C22×C83semidirect
547. #340C22×C83semidirect
548. #340C22×C83semidirect
549. #340C22×C83semidirect
550. #340C22×C83semidirect
600. C22⋊Q8D4×C83semidirect
610. #121D4×C83semidirect
649. C22⋊C8D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C832
C2×#469×C832
C2×#468×C832
C2×#449×C832
C2×#407×C832
C83×#28472
C83×#20352
C83×#20332
C83×#20002
C83×#19992
C83×#18952
C83×#18942
C83×#18752
C83×#18542
C83×#17882
#2438883