Finite Group Databasebeta

← C83×#24394 #35252218

Subgroups — C83×#24394 #35252218

Order 21248.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C83C211yesmaximal, characteristic
2C2×#468×C83C211yesmaximal, characteristic, complemented
3C2×#465×C83C211yesmaximal, characteristic, complemented
4C2×#450×C83C211yesmaximal, characteristic, complemented
5C2×#408×C83C211yesmaximal, characteristic, complemented
6C83×#2616C211yesmaximal, characteristic, complemented
7C83×#2034C211yesmaximal, characteristic, complemented
8C83×#2033C211yesmaximal, characteristic, complemented
9C83×#2000C211yesmaximal, characteristic, complemented
10C83×#2000C211yesmaximal, characteristic, complemented
11C83×#1895C211yesmaximal, characteristic, complemented
12C83×#1893C211yesmaximal, characteristic, complemented
13C83×#1873C211yesmaximal, characteristic, complemented
14C83×#1854C211yesmaximal, characteristic, complemented
15C83×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C83C2211yescharacteristic
17C23×D4×C83C2211yescharacteristic
18C22×SD16×C83C2211yescharacteristic
19C22×SD16×C83C2211yescharacteristic
20C22×M16×C83C2211yescharacteristic, complemented
21C23×C8×C83C2211yescharacteristic, complemented
22#535×C83—24no—
23#535×C83—24no—
24C2×#127×C83—21no—
25C2×#124×C83—21no—
26C2×C22⋊Q8×C83C2211yescharacteristic
27C2×C22⋊Q8×C83C2211yescharacteristic, complemented
28C2×C22⋊Q8×C83C2211yescharacteristic, complemented
29C2×#121×C83C2211yescharacteristic
30C2×#121×C83C2211yescharacteristic
31C2×#121×C83C2211yescharacteristic
32C2×#121×C83C2211yescharacteristic
33C2×#120×C83—21no—
34C2×#120×C83—21no—
35C2×#117×C83C2211yescharacteristic
36#468×C83—24no—
37#465×C83—24no—
38#450×C83—24no—
39C2×#107×C83C2211yescharacteristic, complemented
40C2×#106×C83C2211yescharacteristic, complemented
41C2×#103×C83C2211yescharacteristic, complemented
42C2×#103×C83C2211yescharacteristic, complemented
43C2×#102×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, complemented
53C2×C22⋊C8×C83C2211yescharacteristic, complemented
54#395×C83—21no—
55#394×C83—21no—
56#394×C83—21no—
57#394×C83—21no—
58#380×C83C2211yescharacteristic
59#380×C83C2211yescharacteristic, complemented
60#380×C83C2211yescharacteristic, complemented
61#340×C83C2211yescharacteristic, complemented
62#340×C83C2211yescharacteristic, complemented
63#340×C83C2211yescharacteristic, complemented
64#340×C83C2211yescharacteristic, complemented
65C25×C83—21no—
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×C83D411yescharacteristic
73C22×Q8×C83C2311yescharacteristic
74C22×D4×C83—21no—
75C22×D4×C83—21no—
76C22×D4×C83—21no—
77C22×D4×C83—21no—
78C22×D4×C83—22no—
79C22×D4×C83—22no—
80C22×D4×C83—21no—
81C22×D4×C83—22no—
82C22×D4×C83—22no—
83C22×D4×C83—41no—
84C22×D4×C83—41no—
85C22×D4×C83D411yescharacteristic
86C22×D4×C83D411yescharacteristic
87C22×D4×C83D411yescharacteristic
88C22×D4×C83C2311yescharacteristic
89C22×D4×C83C2311yescharacteristic
90C23×C4×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C23×C4×C83C2311yescharacteristic
93C2×SD16×C83—22no—
94C2×SD16×C83—22no—
95C2×SD16×C83—22no—
96C2×SD16×C83—22no—
97C2×SD16×C83—41no—
98C2×SD16×C83—41no—
99C2×M16×C83—22no—
100C2×M16×C83—22no—
101C2×M16×C83—41no—
102C22×C8×C83—22no—
103C22×C8×C83—22no—
104C22×C8×C83—41no—
105C22×C8×C83C2311yescharacteristic
106C22×C8×C83C2311yescharacteristic
107C22×C8×C83C2311yescharacteristic
108C22×C8×C83C2311yescharacteristic
109#127×C83—28no—
110#124×C83—28no—
111C22⋊Q8×C83—22no—
112C22⋊Q8×C83—22no—
113C22⋊Q8×C83—22no—
114C22⋊Q8×C83—22no—
115C22⋊Q8×C83—41no—
116C22⋊Q8×C83—41no—
117#121×C83—22no—
118#121×C83—22no—
119#121×C83—22no—
120#121×C83—22no—
121#121×C83—22no—
122#121×C83—22no—
123#121×C83D414yes—
124#121×C83D414yes—
125#120×C83—28no—
126#120×C83—28no—
127#117×C83—22no—
128#117×C83—22no—
129C2×C4⋊C4×C83—21no—
130C2×C4⋊C4×C83—21no—
131C2×C4⋊C4×C83—21no—
132C2×C4⋊C4×C83C2311yescharacteristic
133C2×C4⋊C4×C83C2311yescharacteristic
134C2×C4⋊C4×C83C2311yescharacteristic
135C2×C4⋊C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83C2311yescharacteristic
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×C83—21no—
147C2×C22⋊C4×C83—21no—
148C2×C42×C83—21no—
149#107×C83—22no—
150#106×C83—22no—
151#103×C83—22no—
152#103×C83—22no—
153#102×C83—22no—
154#102×C83—22no—
155#102×C83—22no—
156#102×C83—22no—
157#102×C83—41no—
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—24no—
167C24×C83—21no—
168C24×C83—21no—
169C24×C83—42no—
170C24×C83—42no—
171C24×C83—81no—
172C24×C83—81no—
173C24×C83—81no—
174C24×C83—81no—
175C24×C83C2×D411yescharacteristic
176C24×C83C2×D411yescharacteristic
177C24×C83C2×D411yescharacteristic
178#41×C83—44no—
179#41×C83—44no—
180#41×C83—44no—
181#41×C83—44no—
182C2×Q8×C83—22no—
183C2×Q8×C83—22no—
184C2×Q8×C83—21no—
185C2×Q8×C83—21no—
186C2×Q8×C83—21no—
187C2×Q8×C83—21no—
188C2×Q8×C83—21no—
189C2×Q8×C83—21no—
190C2×Q8×C83—41no—
191C2×D4×C83—24no—
192C2×D4×C83—22no—
193C2×D4×C83—22no—
194C2×D4×C83—22no—
195C2×D4×C83—22no—
196C2×D4×C83—24no—
197C2×D4×C83—24no—
198C2×D4×C83—24no—
199C2×D4×C83—24no—
200C2×D4×C83—22no—
201C2×D4×C83—22no—
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—44no—
213C2×D4×C83—44no—
214C2×D4×C83—44no—
215C2×D4×C83—44no—
216C2×D4×C83—41no—
217C2×D4×C83—41no—
218C2×D4×C83—41no—
219C2×D4×C83—42no—
220C2×D4×C83—42no—
221C2×D4×C83—81no—
222C2×D4×C83—81no—
223C2×D4×C83—81no—
224C2×D4×C83—81no—
225C2×D4×C83—81no—
226C2×D4×C83—81no—
227C2×D4×C83—81no—
228C2×D4×C83—81no—
229C2×D4×C83C2×D412yes—
230C2×D4×C83C2×D412yes—
231C22×C4×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
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—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D412yes—
254C22×C4×C83C2×D412yes—
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D412yes—
257C22×C4×C83#4112yes—
258C22×C4×C83C2411yescharacteristic
259SD16×C83—44no—
260SD16×C83—44no—
261M16×C83—44no—
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—21no—
271C2×C8×C83—21no—
272C2×C8×C83—44no—
273C2×C8×C83C2×D412yes—
274C2×C8×C83C2×D412yes—
275C4⋊C4×C83—21no—
276C4⋊C4×C83—21no—
277C4⋊C4×C83—21no—
278C4⋊C4×C83—21no—
279C4⋊C4×C83—21no—
280C4⋊C4×C83—21no—
281C4⋊C4×C83—21no—
282C4⋊C4×C83—21no—
283C4⋊C4×C83—42no—
284C4⋊C4×C83—42no—
285C4⋊C4×C83—42no—
286C4⋊C4×C83C2×D412yes—
287C4⋊C4×C83C2×D412yes—
288C22⋊C4×C83—24no—
289C22⋊C4×C83—24no—
290C22⋊C4×C83—24no—
291C22⋊C4×C83—24no—
292C22⋊C4×C83—24no—
293C22⋊C4×C83—42no—
294C22⋊C4×C83—42no—
295C22⋊C4×C83—42no—
296C22⋊C4×C83—81no—
297C22⋊C4×C83—81no—
298C22⋊C4×C83—81no—
299C42×C83—24no—
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—22no—
313C23×C83—22no—
314C23×C83—21no—
315C23×C83—21no—
316C23×C83—21no—
317C23×C83—21no—
318C23×C83—21no—
319C23×C83—21no—
320C23×C83—21no—
321C23×C83—48no—
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—84no—
340C23×C83#12012yes—
341C23×C83#12112yes—
342C23×C83C22×D411yescharacteristic
343Q8×C83—44no—
344Q8×C83—41no—
345Q8×C83—41no—
346Q8×C83—41no—
347Q8×C83—41no—
348D4×C83—22no—
349D4×C83—22no—
350D4×C83—22no—
351D4×C83—22no—
352D4×C83—44no—
353D4×C83—44no—
354D4×C83—48no—
355D4×C83—44no—
356D4×C83—41no—
357D4×C83—41no—
358D4×C83—41no—
359D4×C83—41no—
360D4×C83—84no—
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—21no—
380C2×C4×C83—21no—
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—41no—
397C2×C4×C83—41no—
398C2×C4×C83—41no—
399C2×C4×C83—41no—
400C2×C4×C83—41no—
401C2×C4×C83#12012yes—
402C2×C4×C83#12112yes—
403C2×C4×C83C22×D411yescharacteristic
404C2×C4×C83C22×D411yescharacteristic
405C2×C4×C83C22×D411yescharacteristic
406C2×C4×C83C2×#4111yescharacteristic
407C2×C4×C83H(5,𝔽2)11yescharacteristic
408C2×C4×C83H(5,𝔽2)11yescharacteristic
409C8×C83—22no—
410C8×C83—22no—
411C8×C83—41no—
412C8×C83—41no—
413C22×C83—22no—
414C22×C83—22no—
415C22×C83—22no—
416C22×C83—22no—
417C22×C83—22no—
418C22×C83—22no—
419C22×C83—41no—
420C22×C83—41no—
421C22×C83—41no—
422C22×C83—41no—
423C22×C83—41no—
424C22×C83—41no—
425C22×C83—41no—
426C22×C83—41no—
427C22×C83—41no—
428C22×C83—42no—
429C22×C83—42no—
430C22×C83—41no—
431C22×C83—41no—
432C22×C83—41no—
433C22×C83—42no—
434C22×C83—42no—
435C22×C83—41no—
436C22×C83—42no—
437C22×C83—42no—
438C22×C83—41no—
439C22×C83—41no—
440C22×C83—816no—
441C22×C83—81no—
442C22×C83—81no—
443C22×C83—81no—
444C22×C83—81no—
445C22×C83—81no—
446C22×C83—81no—
447C22×C83—81no—
448C22×C83—81no—
449C22×C83C2×#12011yescharacteristic
450C22×C83C2×#12111yescharacteristic
451C22×C83#53411yescharacteristic
452C22×C83#57611yescharacteristic
453C22×C83#57711yescharacteristic
454C22×C83#57711yescharacteristic
455C22×C83#57711yescharacteristic
456C4×C83—22no—
457C4×C83—22no—
458C4×C83—41no—
459C4×C83—42no—
460C4×C83—42no—
461C4×C83—81no—
462C4×C83—81no—
463C4×C83—81no—
464C4×C83—81no—
465C4×C83D4211yescharacteristic
466C4×C83D4211yescharacteristic
467C4×C83#54611yescharacteristic
468C4×C83#54611yescharacteristic
469#24394C8311yesmaximal, characteristic, direct product factor, Sylow
470C2×C83—42no—
471C2×C83—42no—
472C2×C83—81no—
473C2×C83—82no—
474C2×C83—82no—
475C2×C83#241011yescharacteristic
476C2×C83#300911yescharacteristic
477C2×C83#301211yescharacteristic
478C2×C83#305711yescharacteristic
479C2×C83#306211yescharacteristic
480C2×C83#319811yescharacteristic
481C2×C83#320011yescharacteristic
482C2×#535C2×C8311yescharacteristic
483C2×#468C2×C8311yescharacteristic, complemented
484C2×#465C2×C8311yescharacteristic, complemented
485C2×#450C2×C8311yescharacteristic, complemented
486C2×#408C2×C8311yescharacteristic, complemented
487#2616C2×C8311yescharacteristic, complemented
488#2034C2×C8311yescharacteristic, complemented
489#2033C2×C8311yescharacteristic, complemented
490#2000C2×C8311yescharacteristic, complemented
491#2000C2×C8311yescharacteristic, complemented
492#1895C2×C8311yescharacteristic, complemented
493#1893C2×C8311yescharacteristic, complemented
494#1873C2×C8311yescharacteristic, complemented
495#1854C2×C8311yescharacteristic, complemented
496#1786C2×C8311yescharacteristic, complemented
497C83#2439411yescharacteristic, direct product factor, Sylow
498C22×#41C22×C8311yescharacteristic
499C23×D4C22×C8311yescharacteristic
500C22×SD16C22×C8311yescharacteristic
501C22×SD16C22×C8311yescharacteristic
502C22×M16C22×C8311yescharacteristic, complemented
503C23×C8C22×C8311yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127—21no—
507C2×#124—21no—
508C2×C22⋊Q8C22×C8311yescharacteristic
509C2×C22⋊Q8C22×C8311yescharacteristic, complemented
510C2×C22⋊Q8C22×C8311yescharacteristic, complemented
511C2×#121C22×C8311yescharacteristic
512C2×#121C22×C8311yescharacteristic
513C2×#121C22×C8311yescharacteristic
514C2×#121C22×C8311yescharacteristic
515C2×#120—21no—
516C2×#120—21no—
517C2×#117C22×C8311yescharacteristic
518#468—24no—
519#465—24no—
520#450—24no—
521C2×#107C22×C8311yescharacteristic, complemented
522C2×#106C22×C8311yescharacteristic, complemented
523C2×#103C22×C8311yescharacteristic, complemented
524C2×#103C22×C8311yescharacteristic, complemented
525C2×#102C22×C8311yescharacteristic
526C2×#102C22×C8311yescharacteristic
527C2×#102C22×C8311yescharacteristic
528C2×#102C22×C8311yescharacteristic
529C2×#102C22×C8311yescharacteristic
530C2×#102C22×C8311yescharacteristic
531#408—24no—
532C2×C22⋊C8C22×C8311yescharacteristic
533C2×C22⋊C8C22×C8311yescharacteristic
534C2×C22⋊C8C22×C8311yescharacteristic, complemented
535C2×C22⋊C8C22×C8311yescharacteristic, complemented
536#395—21no—
537#394—21no—
538#394—21no—
539#394—21no—
540#380C22×C8311yescharacteristic
541#380C22×C8311yescharacteristic, complemented
542#380C22×C8311yescharacteristic, complemented
543#340C22×C8311yescharacteristic, complemented
544#340C22×C8311yescharacteristic, complemented
545#340C22×C8311yescharacteristic, complemented
546#340C22×C8311yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
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—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C8311yescharacteristic
568C22×D4D4×C8311yescharacteristic
569C22×D4D4×C8311yescharacteristic
570C22×D4C23×C8311yescharacteristic
571C22×D4C23×C8311yescharacteristic
572C23×C4C23×C8311yescharacteristic
573C23×C4C23×C8311yescharacteristic
574C23×C4C23×C8311yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C8311yescharacteristic
588C22×C8C23×C8311yescharacteristic
589C22×C8C23×C8311yescharacteristic
590C22×C8C23×C8311yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C8314yes—
606#121D4×C8314yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C8311yescharacteristic
615C2×C4⋊C4C23×C8311yescharacteristic
616C2×C4⋊C4C23×C8311yescharacteristic
617C2×C4⋊C4C23×C8311yescharacteristic
618C2×C4⋊C4C23×C8311yescharacteristic
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⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C8314yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C8311yescharacteristic
658C24C2×D4×C8311yescharacteristic
659C24C2×D4×C8311yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C8312yes—
712C2×D4C2×D4×C8312yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
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—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C8311yescharacteristic
734C22×C4C2×D4×C8311yescharacteristic
735C22×C4C2×D4×C8312yes—
736C22×C4C2×D4×C8312yes—
737C22×C4C2×D4×C8311yescharacteristic
738C22×C4C2×D4×C8312yes—
739C22×C4#41×C8312yes—
740C22×C4C24×C8311yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C8312yes—
756C2×C8C2×D4×C8312yes—
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⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C8312yes—
769C4⋊C4C2×D4×C8312yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C8312yes—
823C23#121×C8312yes—
824C23C22×D4×C8311yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
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—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C8312yes—
884C2×C4#121×C8312yes—
885C2×C4C22×D4×C8311yescharacteristic
886C2×C4C22×D4×C8311yescharacteristic
887C2×C4C22×D4×C8311yescharacteristic
888C2×C4C2×#41×C8311yescharacteristic
889C2×C4H(5,𝔽2)×C8311yescharacteristic
890C2×C4H(5,𝔽2)×C8311yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C8311yescharacteristic
932C22C2×#121×C8311yescharacteristic
933C22#534×C8311yescharacteristic
934C22#576×C8311yescharacteristic
935C22#577×C8311yescharacteristic
936C22#577×C8311yescharacteristic
937C22#577×C8311yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C8311yescharacteristic
948C4D42×C8311yescharacteristic
949C4#546×C8311yescharacteristic
950C4#546×C8311yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2C83×#241011yescharacteristic
957C2C83×#300911yescharacteristic
958C2C83×#301211yescharacteristic
959C2C83×#305711yescharacteristic
960C2C83×#306211yescharacteristic
961C2C83×#319811yescharacteristic
962C2C83×#320011yescharacteristic
subgroupG/H
center, socleC23×C83C22×D4
commutator, Frattini, cosocleC22×C4C24×C83
prime radicalC2×#535×C83C2
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
2. C2×#468×C83C2semidirect
3. C2×#465×C83C2semidirect
4. C2×#450×C83C2semidirect
5. C2×#408×C83C2semidirect
6. C83×#2616C2semidirect
7. C83×#2034C2semidirect
8. C83×#2033C2semidirect
9. C83×#2000C2semidirect
10. C83×#2000C2semidirect
11. C83×#1895C2semidirect
12. C83×#1893C2semidirect
13. C83×#1873C2semidirect
14. C83×#1854C2semidirect
15. C83×#1786C2semidirect
20. C22×M16×C83C22semidirect
21. C23×C8×C83C22semidirect
27. C2×C22⋊Q8×C83C22semidirect
28. C2×C22⋊Q8×C83C22semidirect
39. C2×#107×C83C22semidirect
40. C2×#106×C83C22semidirect
41. C2×#103×C83C22semidirect
42. C2×#103×C83C22semidirect
52. C2×C22⋊C8×C83C22semidirect
53. C2×C22⋊C8×C83C22semidirect
59. #380×C83C22semidirect
60. #380×C83C22semidirect
61. #340×C83C22semidirect
62. #340×C83C22semidirect
63. #340×C83C22semidirect
64. #340×C83C22semidirect
162. C22⋊C8×C83D4semidirect
469. #24394C83direct (N × H)
483. C2×#468C2×C83semidirect
484. C2×#465C2×C83semidirect
485. C2×#450C2×C83semidirect
486. C2×#408C2×C83semidirect
487. #2616C2×C83semidirect
488. #2034C2×C83semidirect
489. #2033C2×C83semidirect
490. #2000C2×C83semidirect
491. #2000C2×C83semidirect
492. #1895C2×C83semidirect
493. #1893C2×C83semidirect
494. #1873C2×C83semidirect
495. #1854C2×C83semidirect
496. #1786C2×C83semidirect
497. C83#24394direct (N × H)
502. C22×M16C22×C83semidirect
503. C23×C8C22×C83semidirect
509. C2×C22⋊Q8C22×C83semidirect
510. C2×C22⋊Q8C22×C83semidirect
521. C2×#107C22×C83semidirect
522. C2×#106C22×C83semidirect
523. C2×#103C22×C83semidirect
524. C2×#103C22×C83semidirect
534. C2×C22⋊C8C22×C83semidirect
535. C2×C22⋊C8C22×C83semidirect
541. #380C22×C83semidirect
542. #380C22×C83semidirect
543. #340C22×C83semidirect
544. #340C22×C83semidirect
545. #340C22×C83semidirect
546. #340C22×C83semidirect
644. C22⋊C8D4×C83semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C832
C2×#468×C832
C2×#465×C832
C2×#450×C832
C2×#408×C832
C83×#26162
C83×#20342
C83×#20332
C83×#20002
C83×#18952
C83×#18932
C83×#18732
C83×#18542
C83×#17862
#2439483