Finite Group Databasebeta

← C83×#24428 #35252252

Subgroups — C83×#24428 #35252252

Order 21248.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C83C211yesmaximal, characteristic, complemented
2C2×#466×C83C211yesmaximal, characteristic, complemented
3C2×#449×C83C211yesmaximal, characteristic, complemented
4C2×#447×C83C211yesmaximal, characteristic, complemented
5C2×#416×C83C211yesmaximal, characteristic, complemented
6C83×#2414C211yesmaximal, characteristic, complemented
7C83×#2042C211yesmaximal, characteristic, complemented
8C83×#2036C211yesmaximal, characteristic, complemented
9C83×#2012C211yesmaximal, characteristic, complemented
10C83×#2000C211yesmaximal, characteristic, complemented
11C83×#1879C211yesmaximal, characteristic, complemented
12C83×#1875C211yesmaximal, characteristic, complemented
13C83×#1869C211yesmaximal, characteristic, complemented
14C83×#1862C211yesmaximal, characteristic, complemented
15C83×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic, complemented
19C22×D8×C83C2211yescharacteristic
20C22×D8×C83C2211yescharacteristic
21C23×C8×C83C2211yescharacteristic, complemented
22#546×C83—24no—
23#546×C83—24no—
24C2×#124×C83C2211yescharacteristic
25C2×#123×C83—21no—
26C2×C22⋊Q8×C83C2211yescharacteristic
27C2×#121×C83—21no—
28C2×#121×C83C2211yescharacteristic
29C2×#121×C83C2211yescharacteristic
30C2×#121×C83C2211yescharacteristic, complemented
31C2×#120×C83—21no—
32C2×C4×D4×C83C2211yescharacteristic
33C2×C4×D4×C83C2211yescharacteristic
34C2×#117×C83C2211yescharacteristic, complemented
35C22×C22⋊C4×C83—21no—
36#466×C83—24no—
37#449×C83—24no—
38#447×C83—24no—
39C2×#107×C83C2211yescharacteristic, complemented
40#416×C83—24no—
41C2×#103×C83C2211yescharacteristic, complemented
42C2×#103×C83C2211yescharacteristic, complemented
43C2×#103×C83C2211yescharacteristic, complemented
44C2×#102×C83C2211yescharacteristic
45C2×#102×C83C2211yescharacteristic
46C2×#102×C83C2211yescharacteristic
47C2×#102×C83C2211yescharacteristic
48C2×#102×C83C2211yescharacteristic
49C2×#102×C83C2211yescharacteristic
50C2×#102×C83C2211yescharacteristic, complemented
51C2×C22⋊C8×C83C2211yescharacteristic
52C2×C22⋊C8×C83C2211yescharacteristic
53C2×C22⋊C8×C83C2211yescharacteristic, complemented
54#394×C83—21no—
55#392×C83—21no—
56#390×C83—21no—
57#390×C83C2211yescharacteristic, complemented
58#389×C83C2211yescharacteristic, complemented
59#388×C83—21no—
60#380×C83C2211yescharacteristic
61#340×C83C2211yescharacteristic, complemented
62#340×C83C2211yescharacteristic, complemented
63#336×C83C2211yescharacteristic, complemented
64#336×C83C2211yescharacteristic, complemented
65C25×C83—21no—
66C2×#41×C83—22no—
67C2×#41×C83—22no—
68C2×#41×C83—22no—
69C2×#41×C83—41no—
70C2×#41×C83—41no—
71C2×#41×C83D414yescomplemented
72C22×Q8×C83C2311yescharacteristic
73C22×D4×C83—21no—
74C22×D4×C83—21no—
75C22×D4×C83—22no—
76C22×D4×C83—22no—
77C22×D4×C83—22no—
78C22×D4×C83—22no—
79C22×D4×C83—21no—
80C22×D4×C83—21no—
81C22×D4×C83—21no—
82C22×D4×C83—41no—
83C22×D4×C83—41no—
84C22×D4×C83D411yescharacteristic
85C22×D4×C83C2311yescharacteristic
86C22×D4×C83C2311yescharacteristic
87C22×D4×C83C2311yescharacteristic
88C23×C4×C83—21no—
89C23×C4×C83—21no—
90C23×C4×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C2×SD16×C83—22no—
93C2×SD16×C83—41no—
94C2×SD16×C83—41no—
95C2×D8×C83—22no—
96C2×D8×C83—22no—
97C2×D8×C83—22no—
98C2×D8×C83—22no—
99C2×D8×C83—22no—
100C2×D8×C83—41no—
101C22×C8×C83—22no—
102C22×C8×C83—22no—
103C22×C8×C83—41no—
104C22×C8×C83C2311yescharacteristic
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108#124×C83—22no—
109#124×C83—22no—
110#123×C83—28no—
111C22⋊Q8×C83—22no—
112C22⋊Q8×C83—22no—
113#121×C83—28no—
114#121×C83—22no—
115#121×C83—22no—
116#121×C83—22no—
117#121×C83—22no—
118#121×C83—41no—
119#121×C83D414yescomplemented
120#120×C83—28no—
121C4×D4×C83—22no—
122C4×D4×C83—22no—
123C4×D4×C83—22no—
124C4×D4×C83—22no—
125#117×C83—22no—
126#117×C83—41no—
127C2×C4⋊C4×C83—21no—
128C2×C4⋊C4×C83—21no—
129C2×C4⋊C4×C83D411yescharacteristic
130C2×C4⋊C4×C83C2311yescharacteristic
131C2×C4⋊C4×C83C2311yescharacteristic
132C2×C4⋊C4×C83C2311yescharacteristic
133C2×C4⋊C4×C83C2311yescharacteristic
134C2×C22⋊C4×C83—28no—
135C2×C22⋊C4×C83—21no—
136C2×C22⋊C4×C83—21no—
137C2×C22⋊C4×C83—21no—
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×C83D411yescharacteristic
147C2×C22⋊C4×C83D411yescharacteristic
148C2×C42×C83—21no—
149C2×C42×C83C2311yescharacteristic
150#107×C83—22no—
151#103×C83—22no—
152#103×C83—22no—
153#103×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—
166C24×C83—21no—
167C24×C83—24no—
168C24×C83—21no—
169C24×C83—21no—
170C24×C83—42no—
171C24×C83—42no—
172C24×C83—42no—
173C24×C83—42no—
174C24×C83—81no—
175C24×C83—81no—
176C24×C83C2×D411yescharacteristic
177C24×C83C2×D411yescharacteristic
178#41×C83—28no—
179#41×C83—44no—
180#41×C83—44no—
181#41×C83—44no—
182C2×Q8×C83—21no—
183C2×Q8×C83—21no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—21no—
187C2×Q8×C83C2×D412yes—
188C2×D4×C83—24no—
189C2×D4×C83—22no—
190C2×D4×C83—24no—
191C2×D4×C83—22no—
192C2×D4×C83—24no—
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—21no—
204C2×D4×C83—21no—
205C2×D4×C83—21no—
206C2×D4×C83—21no—
207C2×D4×C83—41no—
208C2×D4×C83—42no—
209C2×D4×C83—42no—
210C2×D4×C83—42no—
211C2×D4×C83—44no—
212C2×D4×C83—44no—
213C2×D4×C83—44no—
214C2×D4×C83—42no—
215C2×D4×C83—42no—
216C2×D4×C83—44no—
217C2×D4×C83—42no—
218C2×D4×C83—42no—
219C2×D4×C83—81no—
220C2×D4×C83—81no—
221C2×D4×C83—81no—
222C2×D4×C83—81no—
223C2×D4×C83—81no—
224C2×D4×C83C2×D412yes—
225C2×D4×C83C2×D412yes—
226C2×D4×C83C2×D412yes—
227C2×D4×C83#4112yes—
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—24no—
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—42no—
246C22×C4×C83—42no—
247C22×C4×C83—81no—
248C22×C4×C83—81no—
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D412yes—
254C22×C4×C83C2×D412yes—
255C22×C4×C83C2411yescharacteristic
256SD16×C83—44no—
257D8×C83—44no—
258D8×C83—44no—
259C2×C8×C83—21no—
260C2×C8×C83—21no—
261C2×C8×C83—21no—
262C2×C8×C83—21no—
263C2×C8×C83—21no—
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—44no—
271C2×C8×C83C2×D412yes—
272C4⋊C4×C83—24no—
273C4⋊C4×C83—22no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—21no—
280C4⋊C4×C83—81no—
281C4⋊C4×C83C2×D412yes—
282C4⋊C4×C83C2×D412yes—
283C22⋊C4×C83—24no—
284C22⋊C4×C83—24no—
285C22⋊C4×C83—24no—
286C22⋊C4×C83—24no—
287C22⋊C4×C83—22no—
288C22⋊C4×C83—22no—
289C22⋊C4×C83—24no—
290C22⋊C4×C83—42no—
291C22⋊C4×C83—42no—
292C22⋊C4×C83—42no—
293C22⋊C4×C83—42no—
294C22⋊C4×C83—81no—
295C22⋊C4×C83—81no—
296C42×C83—21no—
297C42×C83—21no—
298C42×C83—42no—
299C23×C83—21no—
300C23×C83—22no—
301C23×C83—21no—
302C23×C83—21no—
303C23×C83—22no—
304C23×C83—21no—
305C23×C83—21no—
306C23×C83—22no—
307C23×C83—21no—
308C23×C83—21no—
309C23×C83—21no—
310C23×C83—21no—
311C23×C83—21no—
312C23×C83—21no—
313C23×C83—21no—
314C23×C83—22no—
315C23×C83—48no—
316C23×C83—48no—
317C23×C83—41no—
318C23×C83—41no—
319C23×C83—41no—
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—41no—
334C23×C83—84no—
335C23×C83—84no—
336C23×C83—84no—
337C23×C83—84no—
338C23×C83—84no—
339C23×C83#12012yes—
340C23×C83#13512yes—
341C23×C83C22×D411yescharacteristic
342Q8×C83—22no—
343Q8×C83—22no—
344Q8×C83—41no—
345Q8×C83—41no—
346D4×C83—22no—
347D4×C83—22no—
348D4×C83—22no—
349D4×C83—22no—
350D4×C83—22no—
351D4×C83—44no—
352D4×C83—48no—
353D4×C83—48no—
354D4×C83—41no—
355D4×C83—41no—
356D4×C83—41no—
357D4×C83—41no—
358D4×C83—41no—
359D4×C83—41no—
360D4×C83—84no—
361D4×C83—84no—
362D4×C83—84no—
363D4×C83#12114yes—
364C2×C4×C83—21no—
365C2×C4×C83—21no—
366C2×C4×C83—22no—
367C2×C4×C83—22no—
368C2×C4×C83—22no—
369C2×C4×C83—22no—
370C2×C4×C83—21no—
371C2×C4×C83—21no—
372C2×C4×C83—22no—
373C2×C4×C83—22no—
374C2×C4×C83—21no—
375C2×C4×C83—22no—
376C2×C4×C83—21no—
377C2×C4×C83—21no—
378C2×C4×C83—21no—
379C2×C4×C83—21no—
380C2×C4×C83—21no—
381C2×C4×C83—21no—
382C2×C4×C83—48no—
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—41no—
397C2×C4×C83—41no—
398C2×C4×C83—41no—
399C2×C4×C83—84no—
400C2×C4×C83#12012yes—
401C2×C4×C83C22×D411yescharacteristic
402C2×C4×C83C22×D411yescharacteristic
403C2×C4×C83C22×D411yescharacteristic
404C2×C4×C83C2×#4111yescharacteristic
405C2×C4×C83H(5,𝔽2)11yescharacteristic
406C2×C4×C83H(5,𝔽2)11yescharacteristic
407C8×C83—22no—
408C8×C83—41no—
409C8×C83—41no—
410C8×C83—41no—
411C22×C83—22no—
412C22×C83—24no—
413C22×C83—22no—
414C22×C83—22no—
415C22×C83—22no—
416C22×C83—22no—
417C22×C83—22no—
418C22×C83—41no—
419C22×C83—42no—
420C22×C83—42no—
421C22×C83—41no—
422C22×C83—41no—
423C22×C83—41no—
424C22×C83—42no—
425C22×C83—41no—
426C22×C83—42no—
427C22×C83—41no—
428C22×C83—42no—
429C22×C83—41no—
430C22×C83—41no—
431C22×C83—42no—
432C22×C83—42no—
433C22×C83—42no—
434C22×C83—42no—
435C22×C83—816no—
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×C83—81no—
445C22×C83—81no—
446C22×C83—81no—
447C22×C83C2×#12011yescharacteristic
448C22×C83D4211yescharacteristic
449C22×C83#54611yescharacteristic
450C22×C83C2×#13511yescharacteristic
451C22×C83#57511yescharacteristic
452C22×C83#57611yescharacteristic
453C22×C83#57611yescharacteristic
454C4×C83—22no—
455C4×C83—41no—
456C4×C83—42no—
457C4×C83—41no—
458C4×C83—41no—
459C4×C83—42no—
460C4×C83—42no—
461C4×C83—81no—
462C4×C83—81no—
463C4×C83C2×#12111yescharacteristic
464C4×C83#53411yescharacteristic
465C4×C83D4211yescharacteristic
466C4×C83#54611yescharacteristic
467#24428C8311yesmaximal, characteristic, direct product factor, Sylow
468C2×C83—42no—
469C2×C83—42no—
470C2×C83—44no—
471C2×C83—82no—
472C2×C83—161no—
473C2×C83#241011yescharacteristic
474C2×C83#300211yescharacteristic
475C2×C83#300811yescharacteristic
476C2×C83#326811yescharacteristic
477C2×C83#328011yescharacteristic
478C2×C83#329711yescharacteristic
479C2×C83#331911yescharacteristic
480C2×#546C2×C8311yescharacteristic, complemented
481C2×#466C2×C8311yescharacteristic, complemented
482C2×#449C2×C8311yescharacteristic, complemented
483C2×#447C2×C8311yescharacteristic, complemented
484C2×#416C2×C8311yescharacteristic, complemented
485#2414C2×C8311yescharacteristic, complemented
486#2042C2×C8311yescharacteristic, complemented
487#2036C2×C8311yescharacteristic, complemented
488#2012C2×C8311yescharacteristic, complemented
489#2000C2×C8311yescharacteristic, complemented
490#1879C2×C8311yescharacteristic, complemented
491#1875C2×C8311yescharacteristic, complemented
492#1869C2×C8311yescharacteristic, complemented
493#1862C2×C8311yescharacteristic, complemented
494#1786C2×C8311yescharacteristic, complemented
495C83#2442811yescharacteristic, direct product factor, Sylow
496C22×#41C22×C8311yescharacteristic
497C23×D4C22×C8311yescharacteristic
498C22×SD16C22×C8311yescharacteristic, complemented
499C22×D8C22×C8311yescharacteristic
500C22×D8C22×C8311yescharacteristic
501C23×C8C22×C8311yescharacteristic, complemented
502#546—24no—
503#546—24no—
504C2×#124C22×C8311yescharacteristic
505C2×#123—21no—
506C2×C22⋊Q8C22×C8311yescharacteristic
507C2×#121—21no—
508C2×#121C22×C8311yescharacteristic
509C2×#121C22×C8311yescharacteristic
510C2×#121C22×C8311yescharacteristic, complemented
511C2×#120—21no—
512C2×C4×D4C22×C8311yescharacteristic
513C2×C4×D4C22×C8311yescharacteristic
514C2×#117C22×C8311yescharacteristic, complemented
515C22×C22⋊C4—21no—
516#466—24no—
517#449—24no—
518#447—24no—
519C2×#107C22×C8311yescharacteristic, complemented
520#416—24no—
521C2×#103C22×C8311yescharacteristic, complemented
522C2×#103C22×C8311yescharacteristic, complemented
523C2×#103C22×C8311yescharacteristic, complemented
524C2×#102C22×C8311yescharacteristic
525C2×#102C22×C8311yescharacteristic
526C2×#102C22×C8311yescharacteristic
527C2×#102C22×C8311yescharacteristic
528C2×#102C22×C8311yescharacteristic
529C2×#102C22×C8311yescharacteristic
530C2×#102C22×C8311yescharacteristic, complemented
531C2×C22⋊C8C22×C8311yescharacteristic
532C2×C22⋊C8C22×C8311yescharacteristic
533C2×C22⋊C8C22×C8311yescharacteristic, complemented
534#394—21no—
535#392—21no—
536#390—21no—
537#390C22×C8311yescharacteristic, complemented
538#389C22×C8311yescharacteristic, complemented
539#388—21no—
540#380C22×C8311yescharacteristic
541#340C22×C8311yescharacteristic, complemented
542#340C22×C8311yescharacteristic, complemented
543#336C22×C8311yescharacteristic, complemented
544#336C22×C8311yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C8314yescomplemented
552C22×Q8C23×C8311yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C8311yescharacteristic
565C22×D4C23×C8311yescharacteristic
566C22×D4C23×C8311yescharacteristic
567C22×D4C23×C8311yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C8311yescharacteristic
571C23×C4C23×C8311yescharacteristic
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C8311yescharacteristic
585C22×C8C23×C8311yescharacteristic
586C22×C8C23×C8311yescharacteristic
587C22×C8C23×C8311yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121D4×C8314yescomplemented
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C8311yescharacteristic
610C2×C4⋊C4C23×C8311yescharacteristic
611C2×C4⋊C4C23×C8311yescharacteristic
612C2×C4⋊C4C23×C8311yescharacteristic
613C2×C4⋊C4C23×C8311yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
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—
626C2×C22⋊C4D4×C8311yescharacteristic
627C2×C22⋊C4D4×C8311yescharacteristic
628C2×C42—21no—
629C2×C42C23×C8311yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102D4×C8314yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C8311yescharacteristic
657C24C2×D4×C8311yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C8312yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
673C2×D4—21no—
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—21no—
686C2×D4—21no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C8312yes—
705C2×D4C2×D4×C8312yes—
706C2×D4C2×D4×C8312yes—
707C2×D4#41×C8312yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
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—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C8311yescharacteristic
730C22×C4C2×D4×C8311yescharacteristic
731C22×C4C2×D4×C8311yescharacteristic
732C22×C4C2×D4×C8311yescharacteristic
733C22×C4C2×D4×C8312yes—
734C22×C4C2×D4×C8312yes—
735C22×C4C24×C8311yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739C2×C8—21no—
740C2×C8—21no—
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—44no—
751C2×C8C2×D4×C8312yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C8312yes—
762C4⋊C4C2×D4×C8312yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—48no—
796C23—48no—
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—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#120×C8312yes—
820C23#135×C8312yes—
821C23C22×D4×C8311yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C8314yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
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—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C8312yes—
881C2×C4C22×D4×C8311yescharacteristic
882C2×C4C22×D4×C8311yescharacteristic
883C2×C4C22×D4×C8311yescharacteristic
884C2×C4C2×#41×C8311yescharacteristic
885C2×C4H(5,𝔽2)×C8311yescharacteristic
886C2×C4H(5,𝔽2)×C8311yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—24no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C8311yescharacteristic
928C22D42×C8311yescharacteristic
929C22#546×C8311yescharacteristic
930C22C2×#135×C8311yescharacteristic
931C22#575×C8311yescharacteristic
932C22#576×C8311yescharacteristic
933C22#576×C8311yescharacteristic
934C4—22no—
935C4—42no—
936C4—41no—
937C4—42no—
938C4—41no—
939C4—41no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C8311yescharacteristic
944C4#534×C8311yescharacteristic
945C4D42×C8311yescharacteristic
946C4#546×C8311yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—161no—
952C2C83×#241011yescharacteristic
953C2C83×#300211yescharacteristic
954C2C83×#300811yescharacteristic
955C2C83×#326811yescharacteristic
956C2C83×#328011yescharacteristic
957C2C83×#329711yescharacteristic
958C2C83×#331911yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
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
1. C2×#546×C83C2semidirect
2. C2×#466×C83C2semidirect
3. C2×#449×C83C2semidirect
4. C2×#447×C83C2semidirect
5. C2×#416×C83C2semidirect
6. C83×#2414C2semidirect
7. C83×#2042C2semidirect
8. C83×#2036C2semidirect
9. C83×#2012C2semidirect
10. C83×#2000C2semidirect
11. C83×#1879C2semidirect
12. C83×#1875C2semidirect
13. C83×#1869C2semidirect
14. C83×#1862C2semidirect
15. C83×#1786C2semidirect
18. C22×SD16×C83C22semidirect
21. C23×C8×C83C22semidirect
30. C2×#121×C83C22semidirect
34. C2×#117×C83C22semidirect
39. C2×#107×C83C22semidirect
41. C2×#103×C83C22semidirect
42. C2×#103×C83C22semidirect
43. C2×#103×C83C22semidirect
50. C2×#102×C83C22semidirect
53. C2×C22⋊C8×C83C22semidirect
57. #390×C83C22semidirect
58. #389×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
63. #336×C83C22semidirect
64. #336×C83C22semidirect
71. C2×#41×C83D4semidirect
119. #121×C83D4semidirect
160. #102×C83D4semidirect
467. #24428C83direct (N × H)
480. C2×#546C2×C83semidirect
481. C2×#466C2×C83semidirect
482. C2×#449C2×C83semidirect
483. C2×#447C2×C83semidirect
484. C2×#416C2×C83semidirect
485. #2414C2×C83semidirect
486. #2042C2×C83semidirect
487. #2036C2×C83semidirect
488. #2012C2×C83semidirect
489. #2000C2×C83semidirect
490. #1879C2×C83semidirect
491. #1875C2×C83semidirect
492. #1869C2×C83semidirect
493. #1862C2×C83semidirect
494. #1786C2×C83semidirect
495. C83#24428direct (N × H)
498. C22×SD16C22×C83semidirect
501. C23×C8C22×C83semidirect
510. C2×#121C22×C83semidirect
514. C2×#117C22×C83semidirect
519. C2×#107C22×C83semidirect
521. C2×#103C22×C83semidirect
522. C2×#103C22×C83semidirect
523. C2×#103C22×C83semidirect
530. C2×#102C22×C83semidirect
533. C2×C22⋊C8C22×C83semidirect
537. #390C22×C83semidirect
538. #389C22×C83semidirect
541. #340C22×C83semidirect
542. #340C22×C83semidirect
543. #336C22×C83semidirect
544. #336C22×C83semidirect
551. C2×#41D4×C83semidirect
599. #121D4×C83semidirect
640. #102D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C832
C2×#466×C832
C2×#449×C832
C2×#447×C832
C2×#416×C832
C83×#24142
C83×#20422
C83×#20362
C83×#20122
C83×#20002
C83×#18792
C83×#18752
C83×#18692
C83×#18622
C83×#17862
#2442883