Finite Group Databasebeta

← #35327464

Subgroups — #35327464

Order 21248.

1586 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127595C211yesmaximal, characteristic
2C2×#19127568C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Dic83C211yesmaximal, characteristic
4#24905729C211yesmaximal, characteristic, complemented
5#24905719C211yesmaximal, characteristic, complemented
6#24905710C211yesmaximal, characteristic
7#24905708C211yesmaximal, characteristic
8#24905700C211yesmaximal, characteristic
9#24905697C211yesmaximal, characteristic, complemented
10#24905694C211yesmaximal, characteristic, complemented
11#24905689C211yesmaximal, characteristic, complemented
12#24905687C211yesmaximal, characteristic, complemented
13#24905686C211yesmaximal, characteristic
14#95×Dic83C211yesmaximal, characteristic, complemented
15C83×C22⋊#95C211yesmaximal, characteristic
16C22×C4⋊Dic83C2211yescharacteristic
17C22×Dic83⋊C4C2211yescharacteristic
18C22×C22⋊Dic83C2211yescharacteristic
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26#19127595C418yescomplemented
27#19127568—24no—
28C4×C22⋊Dic83—24no—
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2211yescharacteristic
34C2×C83⋊#95C2211yescharacteristic
35C2×C83⋊#95C2211yescharacteristic
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
47C24×C4×C83C2211yescharacteristic
48C22×C22⋊C4×C83C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C23×Dic83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C2×C4⋊Dic83—22no—
63C2×C4⋊Dic83—41no—
64C2×C4⋊Dic83—41no—
65C2×Dic83⋊C4—41no—
66C2×Dic83⋊C4—41no—
67C2×Dic83⋊C4C2×C414yescomplemented
68C2×C22⋊Dic83—22no—
69C2×C22⋊Dic83—22no—
70C2×C22⋊Dic83—22no—
71C2×C22⋊Dic83—22no—
72C2×C22⋊Dic83—22no—
73C2×C22⋊Dic83—22no—
74C2×C22⋊Dic83—22no—
75C2×C22⋊Dic83—22no—
76C2×C22⋊Dic83—22no—
77C2×C22⋊Dic83—41no—
78C2×C22⋊Dic83C2×C414yes—
79C2×C22⋊Dic83C2×C414yes—
80C2×C4×Dic83—22no—
81C2×C4×Dic83—22no—
82C2×C4×Dic83—22no—
83C2×C4×Dic83—22no—
84C2×C4×Dic83—22no—
85C2×C4×Dic83—22no—
86C2×C4×Dic83—22no—
87C2×C4×Dic83—22no—
88C2×C4×Dic83—41no—
89C2×C4×Dic83—41no—
90C2×C4×Dic83—41no—
91C2×C4×Dic83C2×C414yescomplemented
92C83⋊#95—22no—
93C83⋊#95—22no—
94C83⋊#95—22no—
95C83⋊#95—22no—
96C83⋊#95—22no—
97C83⋊#95—22no—
98C83⋊#95—22no—
99C83⋊#95—22no—
100C83⋊#95—22no—
101C83⋊#95—22no—
102C83⋊#95—22no—
103C83⋊#95—41no—
104C83⋊#95—41no—
105C83⋊#95—41no—
106C83⋊#95—41no—
107C83⋊#95C2×C414yescomplemented
108C83⋊#95C2×C414yescomplemented
109C83⋊#95D414yes—
110C25×C83C2311yescharacteristic
111C23×C4×C83—22no—
112C23×C4×C83—22no—
113C23×C4×C83—22no—
114C23×C4×C83—22no—
115C23×C4×C83—22no—
116C23×C4×C83—41no—
117C23×C4×C83—41no—
118C23×C4×C83C2311yescharacteristic
119C23×C4×C83C2311yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C2×C22⋊C4×C83—22no—
125C2×C22⋊C4×C83—22no—
126C2×C22⋊C4×C83—41no—
127C2×C22⋊C4×C83—41no—
128C2×C22⋊C4×C83—41no—
129C2×C22⋊C4×C83C2×C414yes—
130#95×C83—22no—
131#95×C83—22no—
132#95×C83—22no—
133#95×C83—41no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—21no—
139C22×Dic83—21no—
140C22×Dic83—21no—
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—21no—
147C22×Dic83—21no—
148C22×Dic83—21no—
149C22×Dic83—21no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154C22×Dic83—21no—
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×Dic83C22×C412yes—
182C22×Dic83C22×C412yes—
183C22×Dic83C22×C412yes—
184C22×Dic83C22×C412yes—
185C22×Dic83C2×D412yes—
186C22×Dic83C2×D412yes—
187C22×Dic83#4112yes—
188C22×Dic83#4112yes—
189C22×Dic83#4112yes—
190C4⋊Dic83—44no—
191Dic83⋊C4—44no—
192C22⋊Dic83—28no—
193C22⋊Dic83—28no—
194C22⋊Dic83—28no—
195C22⋊Dic83—44no—
196C4×Dic83—28no—
197C4×Dic83—44no—
198C4×Dic83—44no—
199C4×Dic83—44no—
200C24×C83—21no—
201C24×C83—21no—
202C24×C83—21no—
203C24×C83—21no—
204C24×C83—21no—
205C24×C83—21no—
206C24×C83—21no—
207C24×C83—21no—
208C24×C83—21no—
209C24×C83—21no—
210C24×C83—21no—
211C24×C83—21no—
212C24×C83C22×C412yes—
213C24×C83#4112yes—
214C24×C83#4112yes—
215C24×C83C2411yescharacteristic
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
220C22×C4×C83—28no—
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—44no—
253C22×C4×C83—44no—
254C22×C4×C83—44no—
255C22×C4×C83—44no—
256C22×C4×C83—44no—
257C22×C4×C83—44no—
258C22×C4×C83C22×C412yes—
259C22×C4×C83C22×C412yes—
260C22×C4×C83C2×D412yes—
261C22×C4×C83#4112yes—
262C22×C4×C83#4112yes—
263C22×C4×C83#4112yes—
264C22×C4×C83#4112yes—
265C22⋊C4×C83—44no—
266C22⋊C4×C83—44no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—22no—
279C23×C83—22no—
280C23×C83—22no—
281C23×C83—22no—
282C23×C83—22no—
283C23×C83—22no—
284C23×C83—22no—
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×C83—41no—
300C23×C83—41no—
301C23×C83#11714yes—
302C23×C83C23×C411yescharacteristic
303C23×C83C22×D411yescharacteristic
304C23×C83C2×#4111yescharacteristic
305C23×C83C2×#4111yescharacteristic
306C23×C83C2×#4111yescharacteristic
307C23×C83C2×#4111yescharacteristic
308C23×C83C2×#4111yescharacteristic
309C23×C83C2×#4111yescharacteristic
310C23×C83C2×#4111yescharacteristic
311C23×C83C2×#4111yescharacteristic
312C23×C83C2×#4111yescharacteristic
313C23×C83H(5,𝔽2)11yescharacteristic
314C23×C83H(5,𝔽2)11yescharacteristic
315C23×C83H(5,𝔽2)11yescharacteristic
316C23×C832−1+411yescharacteristic
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—416no—
336C2×C4×C83—41no—
337C2×C4×C83—41no—
338C2×C4×C83—41no—
339C2×C4×C83—41no—
340C2×C4×C83—41no—
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#12614yes—
360C2×Dic83—22no—
361C2×Dic83—22no—
362C2×Dic83—22no—
363C2×Dic83—22no—
364C2×Dic83—22no—
365C2×Dic83—22no—
366C2×Dic83—22no—
367C2×Dic83—22no—
368C2×Dic83—22no—
369C2×Dic83—22no—
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—41no—
385C2×Dic83—41no—
386C2×Dic83—41no—
387C2×Dic83—41no—
388C2×Dic83—41no—
389C2×Dic83—41no—
390C2×Dic83—41no—
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×Dic83C4×D414yes—
416C22×C83—24no—
417C22×C83—24no—
418C22×C83—24no—
419C22×C83—42no—
420C22×C83—42no—
421C22×C83—42no—
422C22×C83—42no—
423C22×C83—42no—
424C22×C83—42no—
425C22×C83—42no—
426C22×C83—42no—
427C22×C83—42no—
428C22×C83—42no—
429C22×C83—42no—
430C22×C83—42no—
431C22×C83C2×#11711yescharacteristic
432C22×C83C2×C4×D411yescharacteristic
433C22×C83C4×#4111yescharacteristic
434C22×C83C4×#4111yescharacteristic
435C22×C83C4×#4111yescharacteristic
436C22×C83#51811yescharacteristic
437C22×C83#52011yescharacteristic
438C22×C83#52511yescharacteristic
439C22×C83#52511yescharacteristic
440C22×C83C2×#12611yescharacteristic
441C22×C83#52911yescharacteristic
442C22×C83#52911yescharacteristic
443C22×C83#52911yescharacteristic
444C22×C83#52911yescharacteristic
445C22×C83#52911yescharacteristic
446C22×C83#53811yescharacteristic
447C22×C83#53811yescharacteristic
448C22×C83#54211yescharacteristic
449C22×C83#54211yescharacteristic
450C22×C83#54611yescharacteristic
451C22×C83#54611yescharacteristic
452C22×C83#54711yescharacteristic
453C22×C83#55011yescharacteristic
454C22×C83#55111yescharacteristic
455C22×C83#55111yescharacteristic
456C22×C83#55111yescharacteristic
457C22×C83#55111yescharacteristic
458C22×C83#55111yescharacteristic
459C22×C83#55211yescharacteristic
460C22×C83#55211yescharacteristic
461C22×C83#55211yescharacteristic
462C22×C83#55311yescharacteristic
463C22×C83#55311yescharacteristic
464C22×C83#55311yescharacteristic
465C22×C83#55511yescharacteristic
466C4×C83—24no—
467C4×C83—42no—
468C4×C83—42no—
469C4×C83—42no—
470C4×C83—42no—
471C4×C83—81no—
472Dic83—24no—
473Dic83—42no—
474Dic83—42no—
475Dic83—42no—
476Dic83—42no—
477Dic83—42no—
478Dic83—42no—
479Dic83—81no—
480#13990—831nomaximal, Sylow
481C2×C83—44no—
482C2×C83#229011yescharacteristic
483C2×C83C4×#12611yescharacteristic
484C2×C83#233711yescharacteristic
485C2×C83#234311yescharacteristic
486C2×C83#235311yescharacteristic
487C2×C83#235911yescharacteristic
488C2×C83#236311yescharacteristic
489C2×C83#246711yescharacteristic
490C2×C83#246811yescharacteristic
491C2×C83#247911yescharacteristic
492C2×C83#248011yescharacteristic
493C2×C83#249511yescharacteristic
494C2×C83#251511yescharacteristic
495C2×C83#257211yescharacteristic
496C2×C83#257811yescharacteristic
497C2×#388—831no—
498C2×#383—831no—
499C2×C4×C22⋊C4—831no—
500#1445—831no—
501#1442—831no—
502#1440—831no—
503#1439—831no—
504#1437—831no—
505#1436—831no—
506#1436—831no—
507#1434—831no—
508#1434—831no—
509C22⋊#95—831no—
510C22⋊#95D8311yescharacteristic
511C4×#95—831no—
512C83#1399011yescharacteristic, complemented, Sylow
513C24×C4C2×D8311yescharacteristic
514C22×C4⋊C4—831no—
515C22×C4⋊C4—831no—
516C22×C22⋊C4—831no—
517C22×C22⋊C4—831no—
518C22×C22⋊C4—831no—
519C22×C22⋊C4—831no—
520C22×C22⋊C4C2×D8311yescharacteristic
521C22×C22⋊C4C2×D8311yescharacteristic
522C22×C42—831no—
523C22×C42—831no—
524C22×C42—831no—
525C22×C42—831no—
526#388—838no—
527#383—1664no—
528C4×C22⋊C4—1664no—
529C2×#95—831no—
530C2×#95—831no—
531C2×#95—831no—
532C2×#95—831no—
533C2×#95—831no—
534C2×#95—831no—
535C2×#95—831no—
536C2×#95—831no—
537C2×#95—831no—
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×#95C2×D8311yescharacteristic
548C2×#95C2×D8311yescharacteristic
549C2×#95C2×D8311yescharacteristic
550C2×#95C2×D8311yescharacteristic
551C25C22×D8311yescharacteristic
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—41no—
558C23×C4—41no—
559C23×C4—831no—
560C23×C4—831no—
561C23×C4—831no—
562C23×C4—831no—
563C23×C4—831no—
564C23×C4—831no—
565C23×C4—831no—
566C23×C4—831no—
567C23×C4C22×D8311yescharacteristic
568C23×C4C22×D8311yescharacteristic
569C23×C4C22×D8311yescharacteristic
570C23×C4C22×D8311yescharacteristic
571C23×C4C22×D8311yescharacteristic
572C23×C4C22×D8311yescharacteristic
573C2×C4⋊C4—3321no—
574C2×C4⋊C4—3321no—
575C2×C4⋊C4—3321no—
576C2×C4⋊C4—3321no—
577C2×C4⋊C4—834no—
578C2×C4⋊C4—1662no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—3321no—
585C2×C22⋊C4—834no—
586C2×C22⋊C4—834no—
587C2×C22⋊C4—1662no—
588C2×C22⋊C4—1662no—
589C2×C22⋊C4—1662no—
590C2×C22⋊C4—1662no—
591C2×C22⋊C4—1662no—
592C2×C22⋊C4—1662no—
593C2×C22⋊C4—1662no—
594C2×C22⋊C4—1662no—
595C2×C22⋊C4—1662no—
596C2×C22⋊C4C4×D8314yes—
597C2×C42—3321no—
598C2×C42—3321no—
599C2×C42—3321no—
600C2×C42—834no—
601C2×C42—1662no—
602C2×C42—1662no—
603C2×C42—1662no—
604C2×C42—1662no—
605C2×C42—1662no—
606C2×C42—1662no—
607C2×C42—1662no—
608C2×C42—1662no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—41no—
613#95—3321no—
614#95—3321no—
615#95—3321no—
616#95—3321no—
617#95—834no—
618#95—834no—
619#95—834no—
620#95—1662no—
621#95—1662no—
622#95—1662no—
623#95—1662no—
624#95—1662no—
625#95—1662no—
626#95—1662no—
627#95—1662no—
628#95—1662no—
629#95—1662no—
630#95—1662no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C2×C4×D8312yes—
644C24#1305058912yes—
645C24#1305059112yes—
646C24C23×D8311yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—28no—
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—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—832no—
690C22×C4—832no—
691C22×C4—832no—
692C22×C4—832no—
693C22×C4—832no—
694C22×C4—832no—
695C22×C4—832no—
696C22×C4—832no—
697C22×C4—832no—
698C22×C4—1661no—
699C22×C4—1661no—
700C22×C4—1661no—
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×C4—1661no—
743C22×C4—1661no—
744C22×C4—1661no—
745C22×C4C2×C4×D8312yes—
746C22×C4C2×C4×D8312yes—
747C22×C4D4×D8312yes—
748C22×C4#1305058912yes—
749C22×C4#1305058912yes—
750C22×C4#1305059012yes—
751C22×C4#1305059012yes—
752C4⋊C4—3324no—
753C4⋊C4—3324no—
754C22⋊C4—44no—
755C22⋊C4—44no—
756C22⋊C4—3324no—
757C22⋊C4—1668no—
758C22⋊C4—1668no—
759C22⋊C4—1668no—
760C42—3324no—
761C42—3324no—
762C42—3324no—
763C42—1668no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#1458175014yes—
799C23C22×C4×D8311yescharacteristic
800C23C2×D4×D8311yescharacteristic
801C23#41×D8311yescharacteristic
802C23#41×D8311yescharacteristic
803C23#41×D8311yescharacteristic
804C23C2×#1305058911yescharacteristic
805C23C2×#1305058911yescharacteristic
806C23C2×#1305058911yescharacteristic
807C23C2×#1305059011yescharacteristic
808C23C2×#1305059011yescharacteristic
809C23C2×#1305059111yescharacteristic
810C23#1458183711yescharacteristic
811C23#1458183711yescharacteristic
812C23#1458183711yescharacteristic
813C23#1458183911yescharacteristic
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—416no—
833C2×C4—41no—
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—3321no—
857C2×C4—3321no—
858C2×C4—3321no—
859C2×C4—3321no—
860C2×C4—3321no—
861C2×C4—3321no—
862C2×C4—3321no—
863C2×C4—3321no—
864C2×C4—3321no—
865C2×C4—3321no—
866C2×C4—3321no—
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—834no—
888C2×C4—1662no—
889C2×C4—1662no—
890C2×C4—1662no—
891C2×C4—1662no—
892C2×C4—1662no—
893C2×C4—1662no—
894C2×C4—1662no—
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#1458178514yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#1458175011yescharacteristic
929C22C4×D4×D8311yescharacteristic
930C22C4×#1305058911yescharacteristic
931C22C4×#1305058911yescharacteristic
932C22C4×#1305059011yescharacteristic
933C22#1912817411yescharacteristic
934C22#1912818011yescharacteristic
935C22#1912820711yescharacteristic
936C22#1912821411yescharacteristic
937C22C2×#1458178511yescharacteristic
938C22#1912822811yescharacteristic
939C22#1912822911yescharacteristic
940C22#1912823111yescharacteristic
941C22#1912823311yescharacteristic
942C22#1912823711yescharacteristic
943C22#1912828311yescharacteristic
944C22#1912828611yescharacteristic
945C22#1912831811yescharacteristic
946C22#1912831911yescharacteristic
947C22#1912833811yescharacteristic
948C22#1912834111yescharacteristic
949C22#1912835611yescharacteristic
950C22#1912836911yescharacteristic
951C22#1912837711yescharacteristic
952C22#1912837711yescharacteristic
953C22#1912837811yescharacteristic
954C22#1912838011yescharacteristic
955C22#1912838211yescharacteristic
956C22#1912838811yescharacteristic
957C22#1912839011yescharacteristic
958C22#1912839311yescharacteristic
959C22#1912839611yescharacteristic
960C22#1912839911yescharacteristic
961C22#1912839911yescharacteristic
962C22#1912841511yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—81no—
969C4—3322no—
970C4—3322no—
971C4—3322no—
972C4—3322no—
973C4—3322no—
974C4—3322no—
975C4—6641no—
976C4—1664no—
977C2—44no—
978C2#2490989911yescharacteristic
979C2C4×#1458178511yescharacteristic
980C2#2491027211yescharacteristic
981C2#2491032111yescharacteristic
982C2#2491039911yescharacteristic
983C2#2491045611yescharacteristic
984C2#2491050411yescharacteristic
985C2#2491152111yescharacteristic
986C2#2491153611yescharacteristic
987C2#2491169311yescharacteristic
988C2#2491170811yescharacteristic
989C2#2491187011yescharacteristic
990C2#2491207811yescharacteristic
991C2#2491271411yescharacteristic
992C2#2491279611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×C22⋊#95C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC22⋊#95D83
hypocenterC83#13990
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#19127568C2semidirect
4. #24905729C2semidirect
5. #24905719C2semidirect
9. #24905697C2semidirect
10. #24905694C2semidirect
11. #24905689C2semidirect
12. #24905687C2semidirect
14. #95×Dic83C2semidirect
26. #19127595C4semidirect
67. C2×Dic83⋊C4C2×C4semidirect
91. C2×C4×Dic83C2×C4semidirect
107. C83⋊#95C2×C4semidirect
108. C83⋊#95C2×C4semidirect
512. C83#13990semidirect

Maximal subgroups

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

subgroupindex
C2×#191275952
C2×#191275682
C2×C4×C22⋊Dic832
#249057292
#249057192
#249057102
#249057082
#249057002
#249056972
#249056942
#249056892
#249056872
#249056862
#95×Dic832
C83×C22⋊#952
#1399083