Finite Group Databasebeta

← #35327949

Subgroups — #35327949

Order 21248.

1594 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127593C211yesmaximal, characteristic
2C2×#19127593C211yesmaximal, characteristic
3C2×#19127591C211yesmaximal, characteristic
4C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
5C2×C4×C4⋊Dic83C211yesmaximal, characteristic, complemented
6#24905728C211yesmaximal, characteristic, complemented
7#24905723C211yesmaximal, characteristic, complemented
8#24905709C211yesmaximal, characteristic
9#24905709C211yesmaximal, characteristic
10#24905701C211yesmaximal, characteristic
11#24905699C211yesmaximal, characteristic
12#24905697C211yesmaximal, characteristic, complemented
13#24905697C211yesmaximal, characteristic, complemented
14#24905687C211yesmaximal, characteristic, complemented
15C83×#1436C211yesmaximal, characteristic, complemented
16C22×C4⋊Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×(C2×D83)⋊C4C2211yescharacteristic
21C22×(C2×D83)⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2211yescharacteristic
23C22×(C2×D83)⋊C4C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30C22×C4×Dic83C2211yescharacteristic
31#19127593—24no—
32#19127593C418yescomplemented
33#19127591—24no—
34C4⋊C4×Dic83—24no—
35C4×C4⋊Dic83—24no—
36C2×C83⋊#95C2211yescharacteristic
37C2×C83⋊#95C2211yescharacteristic
38C2×C83⋊#95C2211yescharacteristic
39C2×C83⋊#95C2211yescharacteristic
40C2×C83⋊#95C2211yescharacteristic
41C2×C83⋊#95C2211yescharacteristic
42C2×C83⋊#95C2211yescharacteristic
43C2×C83⋊#95C2211yescharacteristic
44C2×C83⋊#95C2211yescharacteristic
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2211yescharacteristic
49C22×C4⋊C4×C83C2211yescharacteristic
50C22×C42×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C24×D83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83—22no—
67C2×C4⋊Dic83—22no—
68C2×C4⋊Dic83—22no—
69C2×C4⋊Dic83—22no—
70C2×C4⋊Dic83—22no—
71C2×C4⋊Dic83—22no—
72C2×C4⋊Dic83—22no—
73C2×C4⋊Dic83—22no—
74C2×C4⋊Dic83—41no—
75C2×C4⋊Dic83C2×C414yes—
76C2×(C2×D83)⋊C4—22no—
77C2×(C2×D83)⋊C4—22no—
78C2×(C2×D83)⋊C4—22no—
79C2×(C2×D83)⋊C4—22no—
80C2×(C2×D83)⋊C4—22no—
81C2×(C2×D83)⋊C4—22no—
82C2×(C2×D83)⋊C4—22no—
83C2×(C2×D83)⋊C4—22no—
84C2×(C2×D83)⋊C4—22no—
85C2×(C2×D83)⋊C4—22no—
86C2×(C2×D83)⋊C4—22no—
87C2×(C2×D83)⋊C4—22no—
88C2×(C2×D83)⋊C4—22no—
89C2×(C2×D83)⋊C4—22no—
90C2×(C2×D83)⋊C4—41no—
91C2×(C2×D83)⋊C4—41no—
92C2×(C2×D83)⋊C4—41no—
93C2×(C2×D83)⋊C4—41no—
94C2×(C2×D83)⋊C4C2×C414yes—
95C2×(C2×D83)⋊C4C2×C414yes—
96C2×(C2×D83)⋊C4C2×C414yes—
97C2×C4×Dic83—22no—
98C2×C4×Dic83—22no—
99C2×C4×Dic83—22no—
100C2×C4×Dic83—22no—
101C2×C4×Dic83—22no—
102C2×C4×Dic83—22no—
103C2×C4×Dic83—22no—
104C2×C4×Dic83—22no—
105C2×C4×Dic83—41no—
106C2×C4×Dic83—41no—
107C2×C4×Dic83—41no—
108C2×C4×Dic83C2×C414yes—
109C83⋊#95—22no—
110C83⋊#95—22no—
111C83⋊#95—22no—
112C83⋊#95—22no—
113C83⋊#95—22no—
114C83⋊#95—22no—
115C83⋊#95—22no—
116C83⋊#95—41no—
117C83⋊#95—41no—
118C83⋊#95—41no—
119C83⋊#95—41no—
120C83⋊#95C2×C414yes—
121C83⋊#95D414yes—
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C2×C4⋊C4×C83—22no—
130C2×C4⋊C4×C83—22no—
131C2×C4⋊C4×C83D414yes—
132C2×C42×C83—22no—
133C2×C42×C83—22no—
134C2×C42×C83—22no—
135#95×C83—22no—
136#95×C83—22no—
137#95×C83—22no—
138#95×C83—22no—
139#95×C83C2×C414yes—
140C23×D83—21no—
141C23×D83—21no—
142C23×D83—21no—
143C23×D83—21no—
144C23×D83—21no—
145C23×D83—21no—
146C23×D83—21no—
147C23×D83—21no—
148C23×D83—21no—
149C23×D83—21no—
150C23×D83—21no—
151C23×D83—21no—
152C23×D83—21no—
153C23×D83—21no—
154C23×D83C22×C412yes—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83—21no—
159C22×Dic83—21no—
160C22×Dic83—21no—
161C22×Dic83—21no—
162C22×Dic83—21no—
163C22×Dic83—21no—
164C22×Dic83—21no—
165C22×Dic83—21no—
166C22×Dic83—21no—
167C22×Dic83—21no—
168C22×Dic83—21no—
169C22×Dic83—21no—
170C22×Dic83—21no—
171C22×Dic83—21no—
172C22×Dic83—21no—
173C22×Dic83—21no—
174C22×Dic83—21no—
175C22×Dic83—21no—
176C22×Dic83—21no—
177C22×Dic83—21no—
178C22×Dic83—21no—
179C22×Dic83—21no—
180C22×Dic83—21no—
181C22×Dic83—21no—
182C22×Dic83—21no—
183C22×Dic83—21no—
184C22×Dic83—21no—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83C22×C412yes—
197C22×Dic83C22×C412yes—
198C22×Dic83C22×C412yes—
199C22×Dic83C2×D412yes—
200C22×Dic83C2×D412yes—
201C22×Dic83#4112yes—
202C22×Dic83#4112yes—
203C22×Dic83#4112yes—
204C4⋊Dic83—28no—
205C4⋊Dic83—28no—
206C4⋊Dic83—28no—
207C4⋊Dic83—44no—
208(C2×D83)⋊C4—28no—
209(C2×D83)⋊C4—28no—
210(C2×D83)⋊C4—28no—
211(C2×D83)⋊C4—44no—
212(C2×D83)⋊C4—44no—
213(C2×D83)⋊C4—44no—
214(C2×D83)⋊C4—44no—
215C4×Dic83—28no—
216C4×Dic83—44no—
217C4×Dic83—44no—
218C4×Dic83—44no—
219C24×C83C2411yescharacteristic
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×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×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83C22×C412yes—
258C22×C4×C83C22×C412yes—
259C22×C4×C83C22×C412yes—
260C22×C4×C83C2×D412yes—
261C22×C4×C83C2×D412yes—
262C22×C4×C83C2×D412yes—
263C22×C4×C83C2×D412yes—
264C22×C4×C83#4112yes—
265C22×C4×C83#4112yes—
266C22×C4×C83#4112yes—
267C22×C4×C83#4112yes—
268C22×C4×C83#4112yes—
269C4⋊C4×C83—28no—
270C42×C83—28no—
271C23×C83C23×C411yescharacteristic
272C23×C83C22×D411yescharacteristic
273C23×C83C22×D411yescharacteristic
274C23×C83C2×#4111yescharacteristic
275C23×C83C2×#4111yescharacteristic
276C23×C83C2×#4111yescharacteristic
277C23×C83C2×#4111yescharacteristic
278C23×C83C2×#4111yescharacteristic
279C23×C83C2×#4111yescharacteristic
280C23×C83C2×#4111yescharacteristic
281C23×C83C2×#4111yescharacteristic
282C23×C83H(5,𝔽2)11yescharacteristic
283C23×C83H(5,𝔽2)11yescharacteristic
284C23×C832−1+411yescharacteristic
285C23×C832−1+411yescharacteristic
286C22×D83—22no—
287C22×D83—22no—
288C22×D83—22no—
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—22no—
292C22×D83—22no—
293C22×D83—41no—
294C22×D83—41no—
295C22×D83—41no—
296C22×D83—41no—
297C22×D83—41no—
298C22×D83—41no—
299C22×D83—41no—
300C22×D83—41no—
301C22×D83—41no—
302C22×D83—41no—
303C22×D83—41no—
304C22×D83—41no—
305C22×D83—41no—
306C22×D83—41no—
307C22×D83—41no—
308C22×D83—41no—
309C22×D83—41no—
310C22×D83—41no—
311C22×D83—41no—
312C22×D83—41no—
313C22×D83—41no—
314C22×D83—41no—
315C22×D83—41no—
316C22×D83—41no—
317C22×D83—41no—
318C22×D83—41no—
319C22×D83—41no—
320C22×D83—41no—
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—22no—
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—22no—
345C2×C4×C83—22no—
346C2×C4×C83—22no—
347C2×C4×C83—22no—
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#11714yes—
368C2×C4×C83C4×D414yes—
369C2×C4×C83#12314yes—
370C2×Dic83—22no—
371C2×Dic83—22no—
372C2×Dic83—22no—
373C2×Dic83—22no—
374C2×Dic83—22no—
375C2×Dic83—22no—
376C2×Dic83—22no—
377C2×Dic83—22no—
378C2×Dic83—22no—
379C2×Dic83—22no—
380C2×Dic83—22no—
381C2×Dic83—22no—
382C2×Dic83—22no—
383C2×Dic83—22no—
384C2×Dic83—22no—
385C2×Dic83—22no—
386C2×Dic83—22no—
387C2×Dic83—22no—
388C2×Dic83—22no—
389C2×Dic83—22no—
390C2×Dic83—22no—
391C2×Dic83—41no—
392C2×Dic83—41no—
393C2×Dic83—41no—
394C2×Dic83—41no—
395C2×Dic83—41no—
396C2×Dic83—41no—
397C2×Dic83—41no—
398C2×Dic83—41no—
399C2×Dic83—41no—
400C2×Dic83—41no—
401C2×Dic83—41no—
402C2×Dic83—41no—
403C2×Dic83—41no—
404C2×Dic83—41no—
405C2×Dic83—41no—
406C2×Dic83—41no—
407C2×Dic83—41no—
408C2×Dic83—41no—
409C2×Dic83—41no—
410C2×Dic83—41no—
411C2×Dic83—41no—
412C2×Dic83—41no—
413C2×Dic83—41no—
414C2×Dic83—41no—
415C2×Dic83—41no—
416C2×Dic83—41no—
417C2×Dic83—41no—
418C2×Dic83C4×D414yes—
419C22×C83C2×#11711yescharacteristic
420C22×C83C2×C4×D411yescharacteristic
421C22×C83C2×C4×D411yescharacteristic
422C22×C83C4×#4111yescharacteristic
423C22×C83C4×#4111yescharacteristic
424C22×C83#52011yescharacteristic
425C22×C83#52011yescharacteristic
426C22×C83C2×#12311yescharacteristic
427C22×C83#52511yescharacteristic
428C22×C83#52511yescharacteristic
429C22×C83#52511yescharacteristic
430C22×C83#52911yescharacteristic
431C22×C83#52911yescharacteristic
432C22×C83#52911yescharacteristic
433C22×C83#52911yescharacteristic
434C22×C83#53811yescharacteristic
435C22×C83#53911yescharacteristic
436C22×C83#54111yescharacteristic
437C22×C83#54211yescharacteristic
438C22×C83D4211yescharacteristic
439C22×C83#54611yescharacteristic
440C22×C83#54711yescharacteristic
441C22×C83#54711yescharacteristic
442C22×C83#54811yescharacteristic
443C22×C83#54811yescharacteristic
444C22×C83#55011yescharacteristic
445C22×C83#55311yescharacteristic
446C22×C83#55311yescharacteristic
447C22×C83#55311yescharacteristic
448C22×C83#55511yescharacteristic
449C22×C83#55611yescharacteristic
450C22×C83#55611yescharacteristic
451C22×C83#55611yescharacteristic
452C22×C83#55611yescharacteristic
453C22×C83#55911yescharacteristic
454C2×D83—42no—
455C2×D83—42no—
456C2×D83—42no—
457C2×D83—42no—
458C2×D83—42no—
459C2×D83—42no—
460C2×D83—42no—
461C2×D83—81no—
462C2×D83—81no—
463C2×D83—81no—
464C2×D83—81no—
465C2×D83—81no—
466C2×D83—81no—
467C2×D83—81no—
468C2×D83—81no—
469C4×C83—24no—
470C4×C83—24no—
471C4×C83—24no—
472C4×C83—42no—
473C4×C83—42no—
474C4×C83—42no—
475C4×C83—81no—
476Dic83—24no—
477Dic83—42no—
478Dic83—42no—
479Dic83—42no—
480Dic83—42no—
481Dic83—42no—
482Dic83—81no—
483#14031—831nomaximal, Sylow
484C2×C83#229011yescharacteristic
485C2×C83C4×#12311yescharacteristic
486C2×C83#233411yescharacteristic
487C2×C83#234711yescharacteristic
488C2×C83#235411yescharacteristic
489C2×C83#236111yescharacteristic
490C2×C83#236711yescharacteristic
491C2×C83#244311yescharacteristic
492C2×C83#244811yescharacteristic
493C2×C83#245611yescharacteristic
494C2×C83#246911yescharacteristic
495C2×C83#246911yescharacteristic
496C2×C83#247411yescharacteristic
497C2×C83#259311yescharacteristic
498C2×C83#259411yescharacteristic
499D83—82no—
500C2×#388—831no—
501C2×#388—831no—
502C2×#388—831no—
503C2×C4×C4⋊C4—831no—
504C2×C4×C4⋊C4—831no—
505#1444—831no—
506#1443—831no—
507#1439—831no—
508#1439—831no—
509#1437—831no—
510#1437—831no—
511#1436—831no—
512#1436—831no—
513#1436D8311yescharacteristic, complemented
514#1434—831no—
515C83#1403111yescharacteristic, complemented, Sylow
516C22×C4⋊C4—831no—
517C22×C4⋊C4—831no—
518C22×C4⋊C4—831no—
519C22×C4⋊C4—831no—
520C22×C4⋊C4C2×D8311yescharacteristic
521C22×C22⋊C4—831no—
522C22×C22⋊C4—831no—
523C22×C22⋊C4—831no—
524C22×C22⋊C4—831no—
525C22×C22⋊C4—831no—
526C22×C22⋊C4—831no—
527C22×C22⋊C4—831no—
528C22×C42—831no—
529C22×C42—831no—
530C22×C42—831no—
531C22×C42—831no—
532C22×C42C2×D8311yescharacteristic
533#388—838no—
534#388—1664no—
535#388—1664no—
536C4×C4⋊C4—1664no—
537C4×C4⋊C4—1664no—
538C2×#95—831no—
539C2×#95—831no—
540C2×#95—831no—
541C2×#95—831no—
542C2×#95—831no—
543C2×#95—831no—
544C2×#95—831no—
545C2×#95—831no—
546C2×#95—831no—
547C2×#95—831no—
548C2×#95—831no—
549C2×#95—831no—
550C2×#95—831no—
551C2×#95C2×D8311yescharacteristic
552C2×#95C2×D8311yescharacteristic
553C2×#95C2×D8311yescharacteristic
554C2×#95C2×D8311yescharacteristic
555C2×#95C2×D8311yescharacteristic
556C25—831no—
557C23×C4—831no—
558C23×C4—831no—
559C23×C4—831no—
560C23×C4—831no—
561C23×C4—831no—
562C23×C4—831no—
563C23×C4—831no—
564C23×C4C22×D8311yescharacteristic
565C23×C4C22×D8311yescharacteristic
566C23×C4C22×D8311yescharacteristic
567C23×C4C22×D8311yescharacteristic
568C23×C4C22×D8311yescharacteristic
569C23×C4C22×D8311yescharacteristic
570C23×C4C22×D8311yescharacteristic
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—3321no—
574C2×C4⋊C4—834no—
575C2×C4⋊C4—1662no—
576C2×C4⋊C4—1662no—
577C2×C4⋊C4—1662no—
578C2×C4⋊C4—1662no—
579C2×C4⋊C4—1662no—
580C2×C4⋊C4—1662no—
581C2×C4⋊C4—1662no—
582C2×C4⋊C4—1662no—
583C2×C4⋊C4—1662no—
584C2×C4⋊C4—1662no—
585C2×C4⋊C4D33214yes—
586C2×C22⋊C4—3321no—
587C2×C22⋊C4—3321no—
588C2×C22⋊C4—3321no—
589C2×C22⋊C4—3321no—
590C2×C22⋊C4—834no—
591C2×C22⋊C4—834no—
592C2×C22⋊C4—834no—
593C2×C22⋊C4—1662no—
594C2×C22⋊C4—1662no—
595C2×C22⋊C4—1662no—
596C2×C22⋊C4—1662no—
597C2×C22⋊C4—1662no—
598C2×C22⋊C4—1662no—
599C2×C22⋊C4—1662no—
600C2×C22⋊C4—1662no—
601C2×C22⋊C4—1662no—
602C2×C22⋊C4—1662no—
603C2×C22⋊C4—1662no—
604C2×C22⋊C4—1662no—
605C2×C22⋊C4—1662no—
606C2×C22⋊C4—1662no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—3321no—
611C2×C42—3321no—
612C2×C42—3321no—
613C2×C42—834no—
614C2×C42—1662no—
615C2×C42—1662no—
616C2×C42—1662no—
617C2×C42—1662no—
618C2×C42—1662no—
619C2×C42—1662no—
620C2×C42—1662no—
621C2×C42—1662no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—3321no—
627#95—3321no—
628#95—3321no—
629#95—3321no—
630#95—834no—
631#95—834no—
632#95—1662no—
633#95—1662no—
634#95—1662no—
635#95—1662no—
636#95—1662no—
637#95—1662no—
638#95—1662no—
639#95C4×D8314yes—
640C24—832no—
641C24—1661no—
642C24—1661no—
643C24—1661no—
644C24—1661no—
645C24—1661no—
646C24—1661no—
647C24—1661no—
648C24—1661no—
649C24—1661no—
650C24—1661no—
651C24—1661no—
652C24—1661no—
653C24—1661no—
654C24—1661no—
655C24C23×D8311yescharacteristic
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—832no—
694C22×C4—832no—
695C22×C4—832no—
696C22×C4—832no—
697C22×C4—832no—
698C22×C4—832no—
699C22×C4—832no—
700C22×C4—832no—
701C22×C4—1661no—
702C22×C4—1661no—
703C22×C4—1661no—
704C22×C4—1661no—
705C22×C4—1661no—
706C22×C4—1661no—
707C22×C4—1661no—
708C22×C4—1661no—
709C22×C4—1661no—
710C22×C4—1661no—
711C22×C4—1661no—
712C22×C4—1661no—
713C22×C4—1661no—
714C22×C4—1661no—
715C22×C4—1661no—
716C22×C4—1661no—
717C22×C4—1661no—
718C22×C4—1661no—
719C22×C4—1661no—
720C22×C4—1661no—
721C22×C4—1661no—
722C22×C4—1661no—
723C22×C4—1661no—
724C22×C4—1661no—
725C22×C4—1661no—
726C22×C4—1661no—
727C22×C4—1661no—
728C22×C4—1661no—
729C22×C4—1661no—
730C22×C4—1661no—
731C22×C4—1661no—
732C22×C4—1661no—
733C22×C4—1661no—
734C22×C4—1661no—
735C22×C4—1661no—
736C22×C4—1661no—
737C22×C4—1661no—
738C22×C4—1661no—
739C22×C4—1661no—
740C22×C4—1661no—
741C22×C4—1661no—
742C22×C4C2×C4×D8312yes—
743C22×C4C2×C4×D8312yes—
744C22×C4C2×C4×D8312yes—
745C22×C4D4×D8312yes—
746C22×C4C2×D33212yes—
747C22×C4C2×D33212yes—
748C22×C4C2×D33212yes—
749C22×C4#1305058912yes—
750C22×C4#1305058912yes—
751C22×C4#1305058912yes—
752C22×C4#1305059012yes—
753C22×C4#1305059112yes—
754C4⋊C4—28no—
755C4⋊C4—3324no—
756C4⋊C4—1668no—
757C4⋊C4—1668no—
758C4⋊C4—1668no—
759C22⋊C4—3324no—
760C22⋊C4—3324no—
761C22⋊C4—3324no—
762C22⋊C4—3324no—
763C22⋊C4—1668no—
764C22⋊C4—1668no—
765C22⋊C4—1668no—
766C42—28no—
767C42—3324no—
768C42—3324no—
769C42—3324no—
770C42—1668no—
771C23—3321no—
772C23—3321no—
773C23—3321no—
774C23—3321no—
775C23—3321no—
776C23—3321no—
777C23—3321no—
778C23—3321no—
779C23—3321no—
780C23—3321no—
781C23—3321no—
782C23—3321no—
783C23—3321no—
784C23—3321no—
785C23—3321no—
786C23—3321no—
787C23—3321no—
788C23—3321no—
789C23—3321no—
790C23—3321no—
791C23—3321no—
792C23—3321no—
793C23—3321no—
794C23—3321no—
795C23—3321no—
796C23—3321no—
797C23—3321no—
798C23—3321no—
799C23—1662no—
800C23—1662no—
801C23—1662no—
802C23—1662no—
803C23—1662no—
804C23—1662no—
805C23—1662no—
806C23C22×C4×D8311yescharacteristic
807C23C2×D4×D8311yescharacteristic
808C23C22×D33211yescharacteristic
809C23#41×D8311yescharacteristic
810C23#41×D8311yescharacteristic
811C23#41×D8311yescharacteristic
812C23C2×#1305058911yescharacteristic
813C23C2×#1305058911yescharacteristic
814C23C2×#1305058911yescharacteristic
815C23C2×#1305059011yescharacteristic
816C23C2×#1305059111yescharacteristic
817C23#1458183811yescharacteristic
818C23#1458183811yescharacteristic
819C23#1458183911yescharacteristic
820C23#1458184011yescharacteristic
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—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
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—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—3321no—
868C2×C4—3321no—
869C2×C4—3321no—
870C2×C4—3321no—
871C2×C4—3321no—
872C2×C4—3321no—
873C2×C4—3321no—
874C2×C4—3321no—
875C2×C4—3321no—
876C2×C4—3321no—
877C2×C4—3321no—
878C2×C4—3321no—
879C2×C4—3321no—
880C2×C4—3321no—
881C2×C4—3321no—
882C2×C4—3321no—
883C2×C4—3321no—
884C2×C4—3321no—
885C2×C4—3321no—
886C2×C4—3321no—
887C2×C4—3321no—
888C2×C4—3321no—
889C2×C4—3321no—
890C2×C4—3321no—
891C2×C4—3321no—
892C2×C4—3321no—
893C2×C4—3321no—
894C2×C4—834no—
895C2×C4—1662no—
896C2×C4—1662no—
897C2×C4—1662no—
898C2×C4—1662no—
899C2×C4—1662no—
900C2×C4—1662no—
901C2×C4—1662no—
902C2×C4—1662no—
903C2×C4—1662no—
904C2×C4—1662no—
905C2×C4—1662no—
906C2×C4—1662no—
907C2×C4—1662no—
908C2×C4—1662no—
909C2×C4—1662no—
910C2×C4—1662no—
911C2×C4—1662no—
912C2×C4—1662no—
913C2×C4—1662no—
914C2×C4—1662no—
915C2×C4—1662no—
916C2×C4#1458175014yes—
917C2×C4C4×D33214yes—
918C2×C4#1458177614yes—
919C22—3322no—
920C22—3322no—
921C22—3322no—
922C22—3322no—
923C22—3322no—
924C22—3322no—
925C22—3322no—
926C22—6641no—
927C22—6641no—
928C22—6641no—
929C22—6641no—
930C22—6641no—
931C22—6641no—
932C22—6641no—
933C22—6641no—
934C22C2×#1458175011yescharacteristic
935C22C4×D4×D8311yescharacteristic
936C22C2×C4×D33211yescharacteristic
937C22C4×#1305058911yescharacteristic
938C22C4×#1305058911yescharacteristic
939C22#1912818111yescharacteristic
940C22#1912818311yescharacteristic
941C22C2×#1458177611yescharacteristic
942C22#1912820711yescharacteristic
943C22#1912821311yescharacteristic
944C22#1912821411yescharacteristic
945C22#1912822811yescharacteristic
946C22#1912823111yescharacteristic
947C22#1912823111yescharacteristic
948C22#1912823711yescharacteristic
949C22#1912829011yescharacteristic
950C22#1912829511yescharacteristic
951C22#1912831011yescharacteristic
952C22#1912832411yescharacteristic
953C22D4×D33211yescharacteristic
954C22#1912834311yescharacteristic
955C22#1912835211yescharacteristic
956C22#1912835511yescharacteristic
957C22#1912835711yescharacteristic
958C22#1912836311yescharacteristic
959C22#1912837311yescharacteristic
960C22#1912839511yescharacteristic
961C22#1912840311yescharacteristic
962C22#1912840411yescharacteristic
963C22#1912841611yescharacteristic
964C22#1912841811yescharacteristic
965C22#1912842211yescharacteristic
966C22#1912842411yescharacteristic
967C22#1912842511yescharacteristic
968C22#1912843311yescharacteristic
969C4—24no—
970C4—24no—
971C4—24no—
972C4—42no—
973C4—42no—
974C4—42no—
975C4—81no—
976C4—3322no—
977C4—3322no—
978C4—3322no—
979C4—3322no—
980C4—3322no—
981C4—6641no—
982C4—1664no—
983C2—6642no—
984C2#2490989911yescharacteristic
985C2C4×#1458177611yescharacteristic
986C2#2491024311yescharacteristic
987C2#2491035511yescharacteristic
988C2#2491041011yescharacteristic
989C2#2491048111yescharacteristic
990C2#2491053711yescharacteristic
991C2#2491119611yescharacteristic
992C2#2491125911yescharacteristic
993C2#2491135311yescharacteristic
994C2#2491154211yescharacteristic
995C2#2491155111yescharacteristic
996C2#2491161611yescharacteristic
997C2#2491296111yescharacteristic
998C2#2491296611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1436C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenter#1436D83
hypocenterC83#14031
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic83C2semidirect
5. C2×C4×C4⋊Dic83C2semidirect
6. #24905728C2semidirect
7. #24905723C2semidirect
12. #24905697C2semidirect
13. #24905697C2semidirect
14. #24905687C2semidirect
15. C83×#1436C2semidirect
32. #19127593C4semidirect
513. #1436D83semidirect
515. C83#14031semidirect

Maximal subgroups

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

subgroupindex
C2×#191275932
C2×#191275912
C2×C4⋊C4×Dic832
C2×C4×C4⋊Dic832
#249057282
#249057232
#249057092
#249057012
#249056992
#249056972
#249056872
C83×#14362
#1403183