Finite Group Databasebeta

← C83×#16528 #35244352

Subgroups — C83×#16528 #35244352

Order 21248.

1330 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C83C211yesmaximal, characteristic
2C2×#397×C83C211yesmaximal, characteristic
3C2×#397×C83C211yesmaximal, characteristic
4C2×#389×C83C211yesmaximal, characteristic, complemented
5C83×#1445C211yesmaximal, characteristic, complemented
6C83×#1444C211yesmaximal, characteristic, complemented
7C83×#1444C211yesmaximal, characteristic, complemented
8C83×#1443C211yesmaximal, characteristic, complemented
9C83×#1442C211yesmaximal, characteristic, complemented
10C83×#1442C211yesmaximal, characteristic, complemented
11C83×#1440C211yesmaximal, characteristic
12C83×#1439C211yesmaximal, characteristic
13C83×#1439C211yesmaximal, characteristic
14C83×#1437C211yesmaximal, characteristic
15C83×#1436C211yesmaximal, characteristic, complemented
16C22×C4⋊C4×C83C2211yescharacteristic
17C22×C4⋊C4×C83C2211yescharacteristic
18C22×C4⋊C4×C83C2211yescharacteristic
19C22×C4⋊C4×C83C2211yescharacteristic
20C22×C4⋊C4×C83C2211yescharacteristic
21C22×C4⋊C4×C83C2211yescharacteristic
22C22×C4⋊C4×C83C2211yescharacteristic
23C22×C22⋊C4×C83C2211yescharacteristic
24C22×C22⋊C4×C83C2211yescharacteristic
25C22×C22⋊C4×C83C2211yescharacteristic
26C22×C22⋊C4×C83C2211yescharacteristic
27C22×C22⋊C4×C83C2211yescharacteristic
28C22×C22⋊C4×C83C2211yescharacteristic
29C22×C22⋊C4×C83C2211yescharacteristic
30C22×C42×C83C2211yescharacteristic
31#399×C83—24no—
32#397×C83—24no—
33#397×C83—24no—
34#389×C83—24no—
35C2×#95×C83C2211yescharacteristic
36C2×#95×C83C2211yescharacteristic
37C2×#95×C83C2211yescharacteristic
38C2×#95×C83C2211yescharacteristic
39C2×#95×C83C2211yescharacteristic
40C2×#95×C83C2211yescharacteristic
41C2×#95×C83C2211yescharacteristic
42C2×#95×C83C2211yescharacteristic
43C2×#95×C83C2211yescharacteristic
44C2×#95×C83C2211yescharacteristic
45C2×#95×C83C2211yescharacteristic
46C2×#95×C83C2211yescharacteristic
47C2×#95×C83C2211yescharacteristic
48C2×#95×C83C2211yescharacteristic
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C2×#95×C83C2211yescharacteristic
55C25×C83C2311yescharacteristic
56C23×C4×C83C2311yescharacteristic
57C23×C4×C83C2311yescharacteristic
58C23×C4×C83C2311yescharacteristic
59C23×C4×C83C2311yescharacteristic
60C23×C4×C83C2311yescharacteristic
61C23×C4×C83C2311yescharacteristic
62C23×C4×C83C2311yescharacteristic
63C23×C4×C83C2311yescharacteristic
64C23×C4×C83C2311yescharacteristic
65C23×C4×C83C2311yescharacteristic
66C23×C4×C83C2311yescharacteristic
67C23×C4×C83C2311yescharacteristic
68C23×C4×C83C2311yescharacteristic
69C23×C4×C83C2311yescharacteristic
70C2×C4⋊C4×C83—22no—
71C2×C4⋊C4×C83—22no—
72C2×C4⋊C4×C83—22no—
73C2×C4⋊C4×C83—22no—
74C2×C4⋊C4×C83—22no—
75C2×C4⋊C4×C83—22no—
76C2×C4⋊C4×C83—22no—
77C2×C4⋊C4×C83—22no—
78C2×C4⋊C4×C83—22no—
79C2×C4⋊C4×C83—22no—
80C2×C4⋊C4×C83—41no—
81C2×C4⋊C4×C83—41no—
82C2×C4⋊C4×C83—41no—
83C2×C4⋊C4×C83—41no—
84C2×C4⋊C4×C83—41no—
85C2×C4⋊C4×C83—41no—
86C2×C4⋊C4×C83—41no—
87C2×C4⋊C4×C83—41no—
88C2×C4⋊C4×C83—41no—
89C2×C4⋊C4×C83—41no—
90C2×C4⋊C4×C83D414yes—
91C2×C22⋊C4×C83—22no—
92C2×C22⋊C4×C83—22no—
93C2×C22⋊C4×C83—22no—
94C2×C22⋊C4×C83—22no—
95C2×C22⋊C4×C83—22no—
96C2×C22⋊C4×C83—22no—
97C2×C22⋊C4×C83—22no—
98C2×C22⋊C4×C83—22no—
99C2×C22⋊C4×C83—22no—
100C2×C22⋊C4×C83—22no—
101C2×C22⋊C4×C83—22no—
102C2×C22⋊C4×C83—22no—
103C2×C22⋊C4×C83—41no—
104C2×C22⋊C4×C83—41no—
105C2×C22⋊C4×C83—41no—
106C2×C22⋊C4×C83—41no—
107C2×C22⋊C4×C83—41no—
108C2×C22⋊C4×C83—41no—
109C2×C22⋊C4×C83—41no—
110C2×C22⋊C4×C83—41no—
111C2×C22⋊C4×C83D414yes—
112C2×C42×C83—22no—
113C2×C42×C83—41no—
114C2×C42×C83—41no—
115#95×C83—22no—
116#95×C83—22no—
117#95×C83—22no—
118#95×C83—22no—
119#95×C83—22no—
120#95×C83—22no—
121#95×C83—22no—
122#95×C83—22no—
123#95×C83—22no—
124#95×C83—22no—
125#95×C83—22no—
126#95×C83—22no—
127#95×C83—22no—
128#95×C83—22no—
129#95×C83—22no—
130#95×C83—22no—
131#95×C83—41no—
132#95×C83—41no—
133#95×C83—41no—
134#95×C83—41no—
135C24×C83—21no—
136C24×C83—21no—
137C24×C83—21no—
138C24×C83—21no—
139C24×C83—21no—
140C24×C83—21no—
141C24×C83—21no—
142C24×C83—21no—
143C24×C83—21no—
144C24×C83—21no—
145C24×C83—21no—
146C24×C83—21no—
147C24×C83—21no—
148C24×C83—21no—
149C24×C83C2×D412yes—
150C24×C83C2411yescharacteristic
151C22×C4×C83—21no—
152C22×C4×C83—21no—
153C22×C4×C83—21no—
154C22×C4×C83—21no—
155C22×C4×C83—21no—
156C22×C4×C83—21no—
157C22×C4×C83—21no—
158C22×C4×C83—21no—
159C22×C4×C83—21no—
160C22×C4×C83—21no—
161C22×C4×C83—21no—
162C22×C4×C83—21no—
163C22×C4×C83—21no—
164C22×C4×C83—21no—
165C22×C4×C83—21no—
166C22×C4×C83—21no—
167C22×C4×C83—21no—
168C22×C4×C83—21no—
169C22×C4×C83—21no—
170C22×C4×C83—21no—
171C22×C4×C83—21no—
172C22×C4×C83—21no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83—21no—
177C22×C4×C83—21no—
178C22×C4×C83—21no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—21no—
182C22×C4×C83—21no—
183C22×C4×C83—21no—
184C22×C4×C83—21no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
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—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—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83C2×D412yes—
240C22×C4×C83C2×D412yes—
241C22×C4×C83C2×D412yes—
242C22×C4×C83C2×D412yes—
243C22×C4×C83C2×D412yes—
244C22×C4×C83#4112yes—
245C22×C4×C83#4112yes—
246C22×C4×C83#4112yes—
247C22×C4×C83#4112yes—
248C22×C4×C83#4112yes—
249C4⋊C4×C83—28no—
250C4⋊C4×C83—44no—
251C4⋊C4×C83—44no—
252C4⋊C4×C83—44no—
253C4⋊C4×C83—44no—
254C4⋊C4×C83—44no—
255C4⋊C4×C83—44no—
256C22⋊C4×C83—44no—
257C22⋊C4×C83—44no—
258C22⋊C4×C83—44no—
259C22⋊C4×C83—44no—
260C22⋊C4×C83—44no—
261C22⋊C4×C83—44no—
262C22⋊C4×C83—44no—
263C42×C83—44no—
264C23×C83—22no—
265C23×C83—22no—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—41no—
272C23×C83—41no—
273C23×C83—41no—
274C23×C83—41no—
275C23×C83—41no—
276C23×C83—41no—
277C23×C83—41no—
278C23×C83—41no—
279C23×C83—41no—
280C23×C83—41no—
281C23×C83—41no—
282C23×C83—41no—
283C23×C83—41no—
284C23×C83—41no—
285C23×C83—41no—
286C23×C83—41no—
287C23×C83—41no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83—41no—
299C23×C83C22×D411yescharacteristic
300C23×C83C22×D411yescharacteristic
301C23×C83C2×#4111yescharacteristic
302C23×C83C2×#4111yescharacteristic
303C23×C83C2×#4111yescharacteristic
304C23×C83C2×#4111yescharacteristic
305C23×C83C2×#4111yescharacteristic
306C23×C83H(5,𝔽2)11yescharacteristic
307C23×C83H(5,𝔽2)11yescharacteristic
308C23×C83H(5,𝔽2)11yescharacteristic
309C23×C83H(5,𝔽2)11yescharacteristic
310C23×C832−1+411yescharacteristic
311C23×C832−1+411yescharacteristic
312C23×C832−1+411yescharacteristic
313C23×C832−1+411yescharacteristic
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—41no—
342C2×C4×C83—41no—
343C2×C4×C83—41no—
344C2×C4×C83—41no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×C4×C83—41no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—41no—
353C2×C4×C83—41no—
354C2×C4×C83—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83—41no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—41no—
361C2×C4×C83—41no—
362C2×C4×C83—41no—
363C2×C4×C83—41no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83—41no—
372C2×C4×C83—41no—
373C2×C4×C83—41no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
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—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—41no—
406C2×C4×C83—41no—
407C2×C4×C83—41no—
408C2×C4×C83—41no—
409C2×C4×C83—41no—
410C2×C4×C83—41no—
411C2×C4×C83#12314yes—
412C22×C83—42no—
413C22×C83—42no—
414C22×C83—42no—
415C22×C83—42no—
416C22×C83—42no—
417C22×C83—42no—
418C22×C83—42no—
419C22×C83—81no—
420C22×C83—81no—
421C22×C83—81no—
422C22×C83—81no—
423C22×C83—81no—
424C22×C83—81no—
425C22×C83—81no—
426C22×C83—81no—
427C22×C83C2×#12311yescharacteristic
428C22×C83#52911yescharacteristic
429C22×C83#53211yescharacteristic
430C22×C83#53411yescharacteristic
431C22×C83#53511yescharacteristic
432C22×C83#53611yescharacteristic
433C22×C83#53611yescharacteristic
434C22×C83#53911yescharacteristic
435C22×C83#53911yescharacteristic
436C22×C83#53911yescharacteristic
437C22×C83#53911yescharacteristic
438C22×C83#53911yescharacteristic
439C22×C83#53911yescharacteristic
440C22×C83#54011yescharacteristic
441C22×C83#54111yescharacteristic
442C22×C83#54211yescharacteristic
443C22×C83#54211yescharacteristic
444C22×C83#54211yescharacteristic
445C22×C83#54211yescharacteristic
446C22×C83D4211yescharacteristic
447C22×C83#54611yescharacteristic
448C22×C83#54711yescharacteristic
449C22×C83#54711yescharacteristic
450C22×C83#54711yescharacteristic
451C22×C83#54811yescharacteristic
452C22×C83#55011yescharacteristic
453C22×C83#55111yescharacteristic
454C22×C83#55211yescharacteristic
455C22×C83#55311yescharacteristic
456C22×C83#55611yescharacteristic
457C22×C83#55911yescharacteristic
458C22×C83#56011yescharacteristic
459C22×C83#56311yescharacteristic
460C22×C83#56311yescharacteristic
461C22×C83#56311yescharacteristic
462C4×C83—24no—
463C4×C83—42no—
464C4×C83—42no—
465C4×C83—42no—
466C4×C83—42no—
467C4×C83—42no—
468C4×C83—42no—
469C4×C83—42no—
470C4×C83—81no—
471C4×C83—81no—
472C4×C83—81no—
473C4×C83—81no—
474C4×C83—81no—
475C4×C83—81no—
476#16528C8311yesmaximal, characteristic, direct product factor, Sylow
477C2×C83—82no—
478C2×C83#242211yescharacteristic
479C2×C83#244811yescharacteristic
480C2×C83#255311yescharacteristic
481C2×C83#262311yescharacteristic
482C2×C83#265411yescharacteristic
483C2×C83#266311yescharacteristic
484C2×C83#267311yescharacteristic
485C2×C83#267411yescharacteristic
486C2×C83#268911yescharacteristic
487C2×C83#272111yescharacteristic
488C2×C83#272311yescharacteristic
489C2×C83#272411yescharacteristic
490C2×C83#277711yescharacteristic
491C2×C83#279611yescharacteristic
492C2×C83#283811yescharacteristic
493C2×#399C2×C8311yescharacteristic
494C2×#397C2×C8311yescharacteristic
495C2×#397C2×C8311yescharacteristic
496C2×#389C2×C8311yescharacteristic, complemented
497#1445C2×C8311yescharacteristic, complemented
498#1444C2×C8311yescharacteristic, complemented
499#1444C2×C8311yescharacteristic, complemented
500#1443C2×C8311yescharacteristic, complemented
501#1442C2×C8311yescharacteristic, complemented
502#1442C2×C8311yescharacteristic, complemented
503#1440C2×C8311yescharacteristic
504#1439C2×C8311yescharacteristic
505#1439C2×C8311yescharacteristic
506#1437C2×C8311yescharacteristic
507#1436C2×C8311yescharacteristic, complemented
508C83#1652811yescharacteristic, direct product factor, Sylow
509C22×C4⋊C4C22×C8311yescharacteristic
510C22×C4⋊C4C22×C8311yescharacteristic
511C22×C4⋊C4C22×C8311yescharacteristic
512C22×C4⋊C4C22×C8311yescharacteristic
513C22×C4⋊C4C22×C8311yescharacteristic
514C22×C4⋊C4C22×C8311yescharacteristic
515C22×C4⋊C4C22×C8311yescharacteristic
516C22×C22⋊C4C22×C8311yescharacteristic
517C22×C22⋊C4C22×C8311yescharacteristic
518C22×C22⋊C4C22×C8311yescharacteristic
519C22×C22⋊C4C22×C8311yescharacteristic
520C22×C22⋊C4C22×C8311yescharacteristic
521C22×C22⋊C4C22×C8311yescharacteristic
522C22×C22⋊C4C22×C8311yescharacteristic
523C22×C42C22×C8311yescharacteristic
524#399—24no—
525#397—24no—
526#397—24no—
527#389—24no—
528C2×#95C22×C8311yescharacteristic
529C2×#95C22×C8311yescharacteristic
530C2×#95C22×C8311yescharacteristic
531C2×#95C22×C8311yescharacteristic
532C2×#95C22×C8311yescharacteristic
533C2×#95C22×C8311yescharacteristic
534C2×#95C22×C8311yescharacteristic
535C2×#95C22×C8311yescharacteristic
536C2×#95C22×C8311yescharacteristic
537C2×#95C22×C8311yescharacteristic
538C2×#95C22×C8311yescharacteristic
539C2×#95C22×C8311yescharacteristic
540C2×#95C22×C8311yescharacteristic
541C2×#95C22×C8311yescharacteristic
542C2×#95C22×C8311yescharacteristic
543C2×#95C22×C8311yescharacteristic
544C2×#95C22×C8311yescharacteristic
545C2×#95C22×C8311yescharacteristic
546C2×#95C22×C8311yescharacteristic
547C2×#95C22×C8311yescharacteristic
548C25C23×C8311yescharacteristic
549C23×C4C23×C8311yescharacteristic
550C23×C4C23×C8311yescharacteristic
551C23×C4C23×C8311yescharacteristic
552C23×C4C23×C8311yescharacteristic
553C23×C4C23×C8311yescharacteristic
554C23×C4C23×C8311yescharacteristic
555C23×C4C23×C8311yescharacteristic
556C23×C4C23×C8311yescharacteristic
557C23×C4C23×C8311yescharacteristic
558C23×C4C23×C8311yescharacteristic
559C23×C4C23×C8311yescharacteristic
560C23×C4C23×C8311yescharacteristic
561C23×C4C23×C8311yescharacteristic
562C23×C4C23×C8311yescharacteristic
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4D4×C8314yes—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4D4×C8314yes—
605C2×C42—22no—
606C2×C42—41no—
607C2×C42—41no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—41no—
625#95—41no—
626#95—41no—
627#95—41no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24C2×D4×C8312yes—
643C24C24×C8311yescharacteristic
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
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—21no—
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×C4C2×D4×C8312yes—
733C22×C4C2×D4×C8312yes—
734C22×C4C2×D4×C8312yes—
735C22×C4C2×D4×C8312yes—
736C22×C4C2×D4×C8312yes—
737C22×C4#41×C8312yes—
738C22×C4#41×C8312yes—
739C22×C4#41×C8312yes—
740C22×C4#41×C8312yes—
741C22×C4#41×C8312yes—
742C4⋊C4—28no—
743C4⋊C4—44no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—44no—
747C4⋊C4—44no—
748C4⋊C4—44no—
749C22⋊C4—44no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—44no—
753C22⋊C4—44no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C42—44no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23C22×D4×C8311yescharacteristic
793C23C22×D4×C8311yescharacteristic
794C23C2×#41×C8311yescharacteristic
795C23C2×#41×C8311yescharacteristic
796C23C2×#41×C8311yescharacteristic
797C23C2×#41×C8311yescharacteristic
798C23C2×#41×C8311yescharacteristic
799C23H(5,𝔽2)×C8311yescharacteristic
800C23H(5,𝔽2)×C8311yescharacteristic
801C23H(5,𝔽2)×C8311yescharacteristic
802C23H(5,𝔽2)×C8311yescharacteristic
803C232−1+4×C8311yescharacteristic
804C232−1+4×C8311yescharacteristic
805C232−1+4×C8311yescharacteristic
806C232−1+4×C8311yescharacteristic
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
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—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—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4#123×C8314yes—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22C2×#123×C8311yescharacteristic
921C22#529×C8311yescharacteristic
922C22#532×C8311yescharacteristic
923C22#534×C8311yescharacteristic
924C22#535×C8311yescharacteristic
925C22#536×C8311yescharacteristic
926C22#536×C8311yescharacteristic
927C22#539×C8311yescharacteristic
928C22#539×C8311yescharacteristic
929C22#539×C8311yescharacteristic
930C22#539×C8311yescharacteristic
931C22#539×C8311yescharacteristic
932C22#539×C8311yescharacteristic
933C22#540×C8311yescharacteristic
934C22#541×C8311yescharacteristic
935C22#542×C8311yescharacteristic
936C22#542×C8311yescharacteristic
937C22#542×C8311yescharacteristic
938C22#542×C8311yescharacteristic
939C22D42×C8311yescharacteristic
940C22#546×C8311yescharacteristic
941C22#547×C8311yescharacteristic
942C22#547×C8311yescharacteristic
943C22#547×C8311yescharacteristic
944C22#548×C8311yescharacteristic
945C22#550×C8311yescharacteristic
946C22#551×C8311yescharacteristic
947C22#552×C8311yescharacteristic
948C22#553×C8311yescharacteristic
949C22#556×C8311yescharacteristic
950C22#559×C8311yescharacteristic
951C22#560×C8311yescharacteristic
952C22#563×C8311yescharacteristic
953C22#563×C8311yescharacteristic
954C22#563×C8311yescharacteristic
955C4—24no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—42no—
961C4—42no—
962C4—42no—
963C4—81no—
964C4—81no—
965C4—81no—
966C4—81no—
967C4—81no—
968C4—81no—
969C2—82no—
970C2C83×#242211yescharacteristic
971C2C83×#244811yescharacteristic
972C2C83×#255311yescharacteristic
973C2C83×#262311yescharacteristic
974C2C83×#265411yescharacteristic
975C2C83×#266311yescharacteristic
976C2C83×#267311yescharacteristic
977C2C83×#267411yescharacteristic
978C2C83×#268911yescharacteristic
979C2C83×#272111yescharacteristic
980C2C83×#272311yescharacteristic
981C2C83×#272411yescharacteristic
982C2C83×#277711yescharacteristic
983C2C83×#279611yescharacteristic
984C2C83×#283811yescharacteristic
subgroupG/H
center, socleC24×C83C24
commutator, Frattini, cosocleC24C24×C83
prime radicalC25×C83C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C83 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#389×C83C2semidirect
5. C83×#1445C2semidirect
6. C83×#1444C2semidirect
7. C83×#1444C2semidirect
8. C83×#1443C2semidirect
9. C83×#1442C2semidirect
10. C83×#1442C2semidirect
15. C83×#1436C2semidirect
476. #16528C83direct (N × H)
496. C2×#389C2×C83semidirect
497. #1445C2×C83semidirect
498. #1444C2×C83semidirect
499. #1444C2×C83semidirect
500. #1443C2×C83semidirect
501. #1442C2×C83semidirect
502. #1442C2×C83semidirect
507. #1436C2×C83semidirect
508. C83#16528direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#399×C832
C2×#397×C832
C2×#389×C832
C83×#14452
C83×#14442
C83×#14432
C83×#14422
C83×#14402
C83×#14392
C83×#14372
C83×#14362
#1652883