Finite Group Databasebeta

← C83×#24397 #35252221

Subgroups — C83×#24397 #35252221

Order 21248.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C83C211yesmaximal, characteristic, complemented
2C2×#469×C83C211yesmaximal, characteristic, complemented
3C2×#465×C83C211yesmaximal, characteristic, complemented
4C2×#449×C83C211yesmaximal, characteristic, complemented
5C2×#408×C83C211yesmaximal, characteristic, complemented
6C83×#2615C211yesmaximal, characteristic, complemented
7C83×#2035C211yesmaximal, characteristic, complemented
8C83×#2034C211yesmaximal, characteristic, complemented
9C83×#2000C211yesmaximal, characteristic, complemented
10C83×#1999C211yesmaximal, characteristic, complemented
11C83×#1894C211yesmaximal, characteristic, complemented
12C83×#1893C211yesmaximal, characteristic, complemented
13C83×#1874C211yesmaximal, characteristic, complemented
14C83×#1853C211yesmaximal, characteristic, complemented
15C83×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C22×#41×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic
19C22×D8×C83C2211yescharacteristic
20C22×M16×C83C2211yescharacteristic
21C23×C8×C83C2211yescharacteristic
22#537×C83—24no—
23#537×C83—24no—
24C2×C22⋊Q8×C83—21no—
25C2×C22⋊Q8×C83C2211yescharacteristic
26C2×C22⋊Q8×C83C2211yescharacteristic
27C2×#121×C83—21no—
28C2×#121×C83—21no—
29C2×#121×C83—21no—
30C2×#121×C83C2211yescharacteristic
31C2×#121×C83C2211yescharacteristic
32C2×#121×C83C2211yescharacteristic
33C2×#121×C83C2211yescharacteristic
34C2×#121×C83C2211yescharacteristic
35C22×C4⋊C4×C83C2211yescharacteristic
36#469×C83—24no—
37#465×C83—24no—
38#449×C83—24no—
39C2×#106×C83C2211yescharacteristic
40C2×#106×C83C2211yescharacteristic
41C2×#103×C83C2211yescharacteristic
42C2×#103×C83C2211yescharacteristic
43C2×#103×C83C2211yescharacteristic
44C2×#102×C83C2211yescharacteristic
45C2×#102×C83C2211yescharacteristic
46C2×#102×C83C2211yescharacteristic
47C2×#102×C83C2211yescharacteristic
48C2×#102×C83C2211yescharacteristic
49#408×C83—24no—
50C2×C22⋊C8×C83C2211yescharacteristic
51C2×C22⋊C8×C83C2211yescharacteristic
52C2×C22⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic
54#393×C83—21no—
55#392×C83—21no—
56#392×C83—21no—
57#392×C83—21no—
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic
60#380×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic
62#340×C83C2211yescharacteristic
63#340×C83C2211yescharacteristic
64#340×C83C2211yescharacteristic
65C2×#41×C83—22no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—22no—
70C2×#41×C83—22no—
71C2×#41×C83—22no—
72C2×#41×C83—22no—
73C2×#41×C83—41no—
74C2×#41×C83—41no—
75C2×#41×C83—41no—
76C2×#41×C83—41no—
77C22×Q8×C83D411yescharacteristic
78C22×Q8×C83C2311yescharacteristic
79C22×D4×C83—21no—
80C22×D4×C83—21no—
81C22×D4×C83—21no—
82C22×D4×C83—21no—
83C22×D4×C83—21no—
84C22×D4×C83—21no—
85C22×D4×C83D411yescharacteristic
86C22×D4×C83D411yescharacteristic
87C22×D4×C83D411yescharacteristic
88C22×D4×C83C2311yescharacteristic
89C22×D4×C83C2311yescharacteristic
90C23×C4×C83—21no—
91C23×C4×C83—21no—
92C23×C4×C83C2311yescharacteristic
93C23×C4×C83C2311yescharacteristic
94C23×C4×C83C2311yescharacteristic
95C2×SD16×C83—22no—
96C2×SD16×C83—22no—
97C2×SD16×C83—41no—
98C2×D8×C83—22no—
99C2×D8×C83—22no—
100C2×D8×C83—41no—
101C2×M16×C83—22no—
102C2×M16×C83—22no—
103C2×M16×C83—41no—
104C22×C8×C83—22no—
105C22×C8×C83—22no—
106C22×C8×C83—41no—
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109C22×C8×C83C2311yescharacteristic
110C22×C8×C83C2311yescharacteristic
111C22⋊Q8×C83—28no—
112C22⋊Q8×C83—22no—
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83—22no—
115C22⋊Q8×C83D414yescomplemented
116#121×C83—28no—
117#121×C83—28no—
118#121×C83—28no—
119#121×C83—22no—
120#121×C83—22no—
121#121×C83—22no—
122#121×C83—22no—
123#121×C83—22no—
124#121×C83—22no—
125#121×C83—22no—
126#121×C83—41no—
127#121×C83—41no—
128#121×C83D414yescomplemented
129C2×C4⋊C4×C83—21no—
130C2×C4⋊C4×C83—21no—
131C2×C4⋊C4×C83—21no—
132C2×C4⋊C4×C83—22no—
133C2×C4⋊C4×C83—22no—
134C2×C4⋊C4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83C2311yescharacteristic
137C2×C4⋊C4×C83C2311yescharacteristic
138C2×C4⋊C4×C83C2311yescharacteristic
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—
149#106×C83—22no—
150#106×C83—22no—
151#103×C83—22no—
152#103×C83—22no—
153#103×C83—41no—
154#102×C83—22no—
155#102×C83—22no—
156#102×C83—22no—
157#102×C83—22no—
158#102×C83—41no—
159C22⋊C8×C83—22no—
160C22⋊C8×C83—22no—
161C22⋊C8×C83—22no—
162C22⋊C8×C83D414yescomplemented
163#95×C83—21no—
164#95×C83—21no—
165#95×C83—21no—
166C24×C83—21no—
167C24×C83—21no—
168C24×C83C2×D411yescharacteristic
169C24×C83C2×D411yescharacteristic
170C24×C83C2×D411yescharacteristic
171#41×C83—44no—
172#41×C83—44no—
173#41×C83—44no—
174#41×C83—44no—
175#41×C83—44no—
176#41×C83—44no—
177#41×C83—44no—
178#41×C83—44no—
179C2×Q8×C83—22no—
180C2×Q8×C83—22no—
181C2×Q8×C83—21no—
182C2×Q8×C83—21no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—41no—
187C2×Q8×C83C2×D412yes—
188C2×D4×C83—24no—
189C2×D4×C83—22no—
190C2×D4×C83—22no—
191C2×D4×C83—22no—
192C2×D4×C83—22no—
193C2×D4×C83—24no—
194C2×D4×C83—24no—
195C2×D4×C83—22no—
196C2×D4×C83—22no—
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—21no—
204C2×D4×C83—21no—
205C2×D4×C83—21no—
206C2×D4×C83—21no—
207C2×D4×C83—21no—
208C2×D4×C83—41no—
209C2×D4×C83—41no—
210C2×D4×C83—41no—
211C2×D4×C83—42no—
212C2×D4×C83—42no—
213C2×D4×C83—42no—
214C2×D4×C83—42no—
215C2×D4×C83—42no—
216C2×D4×C83—81no—
217C2×D4×C83—81no—
218C2×D4×C83—81no—
219C2×D4×C83—81no—
220C2×D4×C83—81no—
221C2×D4×C83—81no—
222C2×D4×C83—81no—
223C2×D4×C83—81no—
224C2×D4×C83—81no—
225C2×D4×C83—81no—
226C2×D4×C83C2×D412yes—
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—24no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—24no—
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—42no—
250C22×C4×C83—42no—
251C22×C4×C83—81no—
252C22×C4×C83—81no—
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D412yes—
256C22×C4×C83C2×D412yes—
257C22×C4×C83C2×D411yescharacteristic
258C22×C4×C83C2×D412yes—
259C22×C4×C83#4112yes—
260C22×C4×C83C2411yescharacteristic
261SD16×C83—44no—
262D8×C83—44no—
263M16×C83—44no—
264C2×C8×C83—21no—
265C2×C8×C83—21no—
266C2×C8×C83—21no—
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—44no—
275C2×C8×C83C2×D412yes—
276C2×C8×C83C2×D412yes—
277C4⋊C4×C83—24no—
278C4⋊C4×C83—24no—
279C4⋊C4×C83—24no—
280C4⋊C4×C83—21no—
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×C83C2×D412yes—
289C4⋊C4×C83C2×D412yes—
290C22⋊C4×C83—24no—
291C22⋊C4×C83—24no—
292C22⋊C4×C83—24no—
293C22⋊C4×C83—24no—
294C22⋊C4×C83—42no—
295C22⋊C4×C83—42no—
296C22⋊C4×C83—42no—
297C22⋊C4×C83—81no—
298C22⋊C4×C83—81no—
299C22⋊C4×C83—81no—
300C23×C83—21no—
301C23×C83—21no—
302C23×C83—21no—
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—22no—
314C23×C83—21no—
315C23×C83—21no—
316C23×C83—21no—
317C23×C83—21no—
318C23×C83—21no—
319C23×C83—21no—
320C23×C83—41no—
321C23×C83—41no—
322C23×C83—41no—
323C23×C83—41no—
324C23×C83—41no—
325C23×C83—41no—
326C23×C83—41no—
327C23×C83—41no—
328C23×C83—41no—
329C23×C83—41no—
330C23×C83—41no—
331C23×C83—41no—
332C23×C83—41no—
333C23×C83#12012yes—
334C23×C83#12112yes—
335C23×C83C22×D411yescharacteristic
336Q8×C83—22no—
337Q8×C83—22no—
338Q8×C83—44no—
339Q8×C83—41no—
340Q8×C83—41no—
341D4×C83—22no—
342D4×C83—22no—
343D4×C83—44no—
344D4×C83—44no—
345D4×C83—44no—
346D4×C83—48no—
347D4×C83—41no—
348D4×C83—41no—
349D4×C83—41no—
350D4×C83—41no—
351D4×C83—41no—
352D4×C83—41no—
353D4×C83—84no—
354D4×C83—84no—
355D4×C83—84no—
356D4×C83—84no—
357D4×C83—84no—
358C2×C4×C83—21no—
359C2×C4×C83—21no—
360C2×C4×C83—21no—
361C2×C4×C83—21no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—22no—
367C2×C4×C83—22no—
368C2×C4×C83—22no—
369C2×C4×C83—22no—
370C2×C4×C83—22no—
371C2×C4×C83—22no—
372C2×C4×C83—22no—
373C2×C4×C83—21no—
374C2×C4×C83—21no—
375C2×C4×C83—21no—
376C2×C4×C83—48no—
377C2×C4×C83—41no—
378C2×C4×C83—41no—
379C2×C4×C83—41no—
380C2×C4×C83—41no—
381C2×C4×C83—41no—
382C2×C4×C83—41no—
383C2×C4×C83—41no—
384C2×C4×C83—41no—
385C2×C4×C83—41no—
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—84no—
397C2×C4×C83#12012yes—
398C2×C4×C83#12112yes—
399C2×C4×C83C22×D411yescharacteristic
400C2×C4×C83C22×D411yescharacteristic
401C2×C4×C83C22×D411yescharacteristic
402C2×C4×C83C2×#4111yescharacteristic
403C2×C4×C83H(5,𝔽2)11yescharacteristic
404C2×C4×C83H(5,𝔽2)11yescharacteristic
405C8×C83—22no—
406C8×C83—22no—
407C8×C83—41no—
408C8×C83—41no—
409C22×C83—22no—
410C22×C83—22no—
411C22×C83—22no—
412C22×C83—22no—
413C22×C83—22no—
414C22×C83—22no—
415C22×C83—41no—
416C22×C83—41no—
417C22×C83—41no—
418C22×C83—41no—
419C22×C83—41no—
420C22×C83—41no—
421C22×C83—41no—
422C22×C83—41no—
423C22×C83—42no—
424C22×C83—41no—
425C22×C83—41no—
426C22×C83—41no—
427C22×C83—41no—
428C22×C83—42no—
429C22×C83—41no—
430C22×C83—42no—
431C22×C83—41no—
432C22×C83—41no—
433C22×C83—81no—
434C22×C83—81no—
435C22×C83—81no—
436C22×C83—81no—
437C22×C83—81no—
438C22×C83—81no—
439C22×C83—81no—
440C22×C83—81no—
441C22×C83—81no—
442C22×C83—81no—
443C22×C83—81no—
444C22×C83C2×#12011yescharacteristic
445C22×C83C2×#12111yescharacteristic
446C22×C83#53411yescharacteristic
447C22×C83#57611yescharacteristic
448C22×C83#57711yescharacteristic
449C22×C83#57711yescharacteristic
450C22×C83#57711yescharacteristic
451C4×C83—22no—
452C4×C83—22no—
453C4×C83—41no—
454C4×C83—42no—
455C4×C83—42no—
456C4×C83—42no—
457C4×C83—81no—
458C4×C83—81no—
459C4×C83—81no—
460C4×C83D4211yescharacteristic
461C4×C83D4211yescharacteristic
462C4×C83#54611yescharacteristic
463C4×C83#54611yescharacteristic
464#24397C8311yesmaximal, characteristic, direct product factor, Sylow
465C2×C83—42no—
466C2×C83—42no—
467C2×C83—81no—
468C2×C83—82no—
469C2×C83—161no—
470C2×C83#241011yescharacteristic
471C2×C83#301011yescharacteristic
472C2×C83#301211yescharacteristic
473C2×C83#306011yescharacteristic
474C2×C83#306211yescharacteristic
475C2×C83#319811yescharacteristic
476C2×C83#320411yescharacteristic
477C2×#537C2×C8311yescharacteristic, complemented
478C2×#469C2×C8311yescharacteristic, complemented
479C2×#465C2×C8311yescharacteristic, complemented
480C2×#449C2×C8311yescharacteristic, complemented
481C2×#408C2×C8311yescharacteristic, complemented
482#2615C2×C8311yescharacteristic, complemented
483#2035C2×C8311yescharacteristic, complemented
484#2034C2×C8311yescharacteristic, complemented
485#2000C2×C8311yescharacteristic, complemented
486#1999C2×C8311yescharacteristic, complemented
487#1894C2×C8311yescharacteristic, complemented
488#1893C2×C8311yescharacteristic, complemented
489#1874C2×C8311yescharacteristic, complemented
490#1853C2×C8311yescharacteristic, complemented
491#1788C2×C8311yescharacteristic, complemented
492C83#2439711yescharacteristic, direct product factor, Sylow
493C22×#41C22×C8311yescharacteristic
494C22×#41C22×C8311yescharacteristic
495C22×SD16C22×C8311yescharacteristic
496C22×D8C22×C8311yescharacteristic
497C22×M16C22×C8311yescharacteristic
498C23×C8C22×C8311yescharacteristic
499#537—24no—
500#537—24no—
501C2×C22⋊Q8—21no—
502C2×C22⋊Q8C22×C8311yescharacteristic
503C2×C22⋊Q8C22×C8311yescharacteristic
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—21no—
507C2×#121C22×C8311yescharacteristic
508C2×#121C22×C8311yescharacteristic
509C2×#121C22×C8311yescharacteristic
510C2×#121C22×C8311yescharacteristic
511C2×#121C22×C8311yescharacteristic
512C22×C4⋊C4C22×C8311yescharacteristic
513#469—24no—
514#465—24no—
515#449—24no—
516C2×#106C22×C8311yescharacteristic
517C2×#106C22×C8311yescharacteristic
518C2×#103C22×C8311yescharacteristic
519C2×#103C22×C8311yescharacteristic
520C2×#103C22×C8311yescharacteristic
521C2×#102C22×C8311yescharacteristic
522C2×#102C22×C8311yescharacteristic
523C2×#102C22×C8311yescharacteristic
524C2×#102C22×C8311yescharacteristic
525C2×#102C22×C8311yescharacteristic
526#408—24no—
527C2×C22⋊C8C22×C8311yescharacteristic
528C2×C22⋊C8C22×C8311yescharacteristic
529C2×C22⋊C8C22×C8311yescharacteristic
530C2×C22⋊C8C22×C8311yescharacteristic
531#393—21no—
532#392—21no—
533#392—21no—
534#392—21no—
535#380C22×C8311yescharacteristic
536#380C22×C8311yescharacteristic
537#380C22×C8311yescharacteristic
538#340C22×C8311yescharacteristic
539#340C22×C8311yescharacteristic
540#340C22×C8311yescharacteristic
541#340C22×C8311yescharacteristic
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C8311yescharacteristic
555C22×Q8C23×C8311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4D4×C8311yescharacteristic
563C22×D4D4×C8311yescharacteristic
564C22×D4D4×C8311yescharacteristic
565C22×D4C23×C8311yescharacteristic
566C22×D4C23×C8311yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C8311yescharacteristic
570C23×C4C23×C8311yescharacteristic
571C23×C4C23×C8311yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C8311yescharacteristic
585C22×C8C23×C8311yescharacteristic
586C22×C8C23×C8311yescharacteristic
587C22×C8C23×C8311yescharacteristic
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C8314yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121D4×C8314yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4C23×C8311yescharacteristic
612C2×C4⋊C4C23×C8311yescharacteristic
613C2×C4⋊C4C23×C8311yescharacteristic
614C2×C4⋊C4C23×C8311yescharacteristic
615C2×C4⋊C4C23×C8311yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626#106—22no—
627#106—22no—
628#103—22no—
629#103—22no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8D4×C8314yescomplemented
640#95—21no—
641#95—21no—
642#95—21no—
643C24—21no—
644C24—21no—
645C24C2×D4×C8311yescharacteristic
646C24C2×D4×C8311yescharacteristic
647C24C2×D4×C8311yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C8312yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C8312yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C8311yescharacteristic
731C22×C4C2×D4×C8311yescharacteristic
732C22×C4C2×D4×C8312yes—
733C22×C4C2×D4×C8312yes—
734C22×C4C2×D4×C8311yescharacteristic
735C22×C4C2×D4×C8312yes—
736C22×C4#41×C8312yes—
737C22×C4C24×C8311yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8C2×D4×C8312yes—
753C2×C8C2×D4×C8312yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C8312yes—
766C4⋊C4C2×D4×C8312yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23#120×C8312yes—
811C23#121×C8312yes—
812C23C22×D4×C8311yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4#120×C8312yes—
875C2×C4#121×C8312yes—
876C2×C4C22×D4×C8311yescharacteristic
877C2×C4C22×D4×C8311yescharacteristic
878C2×C4C22×D4×C8311yescharacteristic
879C2×C4C2×#41×C8311yescharacteristic
880C2×C4H(5,𝔽2)×C8311yescharacteristic
881C2×C4H(5,𝔽2)×C8311yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×#120×C8311yescharacteristic
922C22C2×#121×C8311yescharacteristic
923C22#534×C8311yescharacteristic
924C22#576×C8311yescharacteristic
925C22#577×C8311yescharacteristic
926C22#577×C8311yescharacteristic
927C22#577×C8311yescharacteristic
928C4—22no—
929C4—22no—
930C4—41no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C8311yescharacteristic
938C4D42×C8311yescharacteristic
939C4#546×C8311yescharacteristic
940C4#546×C8311yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C83×#241011yescharacteristic
947C2C83×#301011yescharacteristic
948C2C83×#301211yescharacteristic
949C2C83×#306011yescharacteristic
950C2C83×#306211yescharacteristic
951C2C83×#319811yescharacteristic
952C2C83×#320411yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C83 ◁ C22×#41×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#537×C83C2semidirect
2. C2×#469×C83C2semidirect
3. C2×#465×C83C2semidirect
4. C2×#449×C83C2semidirect
5. C2×#408×C83C2semidirect
6. C83×#2615C2semidirect
7. C83×#2035C2semidirect
8. C83×#2034C2semidirect
9. C83×#2000C2semidirect
10. C83×#1999C2semidirect
11. C83×#1894C2semidirect
12. C83×#1893C2semidirect
13. C83×#1874C2semidirect
14. C83×#1853C2semidirect
15. C83×#1788C2semidirect
115. C22⋊Q8×C83D4semidirect
128. #121×C83D4semidirect
162. C22⋊C8×C83D4semidirect
464. #24397C83direct (N × H)
477. C2×#537C2×C83semidirect
478. C2×#469C2×C83semidirect
479. C2×#465C2×C83semidirect
480. C2×#449C2×C83semidirect
481. C2×#408C2×C83semidirect
482. #2615C2×C83semidirect
483. #2035C2×C83semidirect
484. #2034C2×C83semidirect
485. #2000C2×C83semidirect
486. #1999C2×C83semidirect
487. #1894C2×C83semidirect
488. #1893C2×C83semidirect
489. #1874C2×C83semidirect
490. #1853C2×C83semidirect
491. #1788C2×C83semidirect
492. C83#24397direct (N × H)
592. C22⋊Q8D4×C83semidirect
605. #121D4×C83semidirect
639. C22⋊C8D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C832
C2×#469×C832
C2×#465×C832
C2×#449×C832
C2×#408×C832
C83×#26152
C83×#20352
C83×#20342
C83×#20002
C83×#19992
C83×#18942
C83×#18932
C83×#18742
C83×#18532
C83×#17882
#2439783