Finite Group Databasebeta

← #35333367

Subgroups — #35333367

Order 21248.

1550 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127594C211yesmaximal, characteristic
2C2×#19127576C211yesmaximal, characteristic
3#24905726C211yesmaximal, characteristic, complemented
4#24905719C211yesmaximal, characteristic, complemented
5#24905719C211yesmaximal, characteristic, complemented
6#24905715C211yesmaximal, characteristic, complemented
7#24905706C211yesmaximal, characteristic
8#24905706C211yesmaximal, characteristic
9#24905696C211yesmaximal, characteristic, complemented
10#24905693C211yesmaximal, characteristic, complemented
11#24905692C211yesmaximal, characteristic, complemented
12#24905689C211yesmaximal, characteristic, complemented
13#24905685C211yesmaximal, characteristic
14#24905685C211yesmaximal, characteristic
15C2×#388×C83C211yesmaximal, characteristic
16C24×Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24C22×C22⋊Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26#19127594C418yescomplemented
27#19127576—24no—
28C2×C83⋊#95C2211yescharacteristic
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
46C22×C4⋊C4×C83C2211yescharacteristic
47C22×C22⋊C4×C83C2211yescharacteristic
48C22×C22⋊C4×C83C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C22×C42×C83C2211yescharacteristic
51#388×C83—24no—
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C23×Dic83—22no—
55C23×Dic83—22no—
56C23×Dic83—22no—
57C23×Dic83—41no—
58C23×Dic83—41no—
59C23×Dic83—41no—
60C23×Dic83—41no—
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2311yescharacteristic
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2311yescharacteristic
67C23×Dic83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C2×C4⋊Dic83—22no—
70C2×C4⋊Dic83—22no—
71C2×C4⋊Dic83—22no—
72C2×C4⋊Dic83—22no—
73C2×C4⋊Dic83—41no—
74C2×C4⋊Dic83—41no—
75C2×C4⋊Dic83—41no—
76C2×C4⋊Dic83—41no—
77C2×C4⋊Dic83C2×C414yescomplemented
78C2×Dic83⋊C4—22no—
79C2×Dic83⋊C4—41no—
80C2×Dic83⋊C4—41no—
81C2×Dic83⋊C4—41no—
82C2×Dic83⋊C4—41no—
83C2×Dic83⋊C4—41no—
84C2×C22⋊Dic83—22no—
85C2×C22⋊Dic83—41no—
86C2×C22⋊Dic83—41no—
87C2×C22⋊Dic83—41no—
88C2×C22⋊Dic83—41no—
89C2×C22⋊Dic83—41no—
90C2×C22⋊Dic83—41no—
91C2×C22⋊Dic83C2×C414yes—
92C2×C22⋊Dic83C2×C414yes—
93C2×C4×Dic83—41no—
94C2×C4×Dic83—41no—
95C2×C4×Dic83C2×C414yescomplemented
96C83⋊#95—22no—
97C83⋊#95—22no—
98C83⋊#95—22no—
99C83⋊#95—22no—
100C83⋊#95—22no—
101C83⋊#95—41no—
102C83⋊#95—41no—
103C83⋊#95—41no—
104C83⋊#95—41no—
105C83⋊#95—41no—
106C83⋊#95—41no—
107C83⋊#95—41no—
108C83⋊#95—41no—
109C83⋊#95—41no—
110C83⋊#95—41no—
111C83⋊#95—41no—
112C83⋊#95C2×C414yescomplemented
113C83⋊#95C2×C414yescomplemented
114C25×C83C2311yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C23×C4×C83C2311yescharacteristic
118C23×C4×C83C2311yescharacteristic
119C23×C4×C83C2311yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C2×C4⋊C4×C83—22no—
122C2×C4⋊C4×C83—22no—
123C2×C4⋊C4×C83—41no—
124C2×C22⋊C4×C83—22no—
125C2×C22⋊C4×C83—22no—
126C2×C22⋊C4×C83—22no—
127C2×C22⋊C4×C83—22no—
128C2×C22⋊C4×C83—41no—
129C2×C22⋊C4×C83—41no—
130C2×C22⋊C4×C83C2×C414yes—
131C2×C22⋊C4×C83D414yes—
132C2×C22⋊C4×C83Q814yes—
133C2×C42×C83—22no—
134C2×C42×C83—22no—
135C2×C42×C83—41no—
136#95×C83—22no—
137#95×C83—22no—
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×Dic83—21no—
182C22×Dic83—21no—
183C22×Dic83—21no—
184C22×Dic83—21no—
185C22×Dic83—21no—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—44no—
189C22×Dic83—44no—
190C22×Dic83—44no—
191C22×Dic83—44no—
192C22×Dic83—44no—
193C22×Dic83—44no—
194C22×Dic83—44no—
195C22×Dic83C22×C412yes—
196C22×Dic83C22×C412yes—
197C22×Dic83C22×C412yes—
198C22×Dic83C22×C412yes—
199C22×Dic83#4112yes—
200C22×Dic83#4112yes—
201C4⋊Dic83—44no—
202C4⋊Dic83—44no—
203C4⋊Dic83—44no—
204Dic83⋊C4—44no—
205Dic83⋊C4—44no—
206C22⋊Dic83—44no—
207C22⋊Dic83—44no—
208C22⋊Dic83—44no—
209C4×Dic83—44no—
210C24×C83—21no—
211C24×C83—21no—
212C24×C83—21no—
213C24×C83—21no—
214C24×C83—21no—
215C24×C83—21no—
216C24×C83—21no—
217C24×C83—21no—
218C24×C83—21no—
219C24×C83—21no—
220C24×C83—21no—
221C24×C83—21no—
222C24×C83C22×C412yes—
223C24×C83C2×D412yes—
224C24×C83C2×Q812yes—
225C24×C83C2411yescharacteristic
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×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83C22×C412yes—
261C22×C4×C83C22×C412yes—
262C22×C4×C83C2×D412yes—
263C22×C4×C83C2×D412yes—
264C22×C4×C83C2×Q812yes—
265C22×C4×C83C2×Q812yes—
266C22×C4×C83#4112yes—
267C22×C4×C83#4112yes—
268C4⋊C4×C83—44no—
269C22⋊C4×C83—44no—
270C22⋊C4×C83—44no—
271C22⋊C4×C83C4⋊C4116yescomplemented
272C42×C83—44no—
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—22no—
286C23×C83—22no—
287C23×C83—22no—
288C23×C83—22no—
289C23×C83—22no—
290C23×C83—22no—
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—41no—
302C23×C83—41no—
303C23×C83—41no—
304C23×C83—41no—
305C23×C83—41no—
306C23×C83—41no—
307C23×C83C2×C4⋊C414yes—
308C23×C83C23×C411yescharacteristic
309C23×C83C22×D411yescharacteristic
310C23×C83C22×Q811yescharacteristic
311C23×C83C2×#4111yescharacteristic
312C23×C83C2×#4111yescharacteristic
313C23×C83C2×#4111yescharacteristic
314C23×C83C2×#4111yescharacteristic
315C23×C83H(5,𝔽2)11yescharacteristic
316C23×C83H(5,𝔽2)11yescharacteristic
317C23×C83H(5,𝔽2)11yescharacteristic
318C23×C83H(5,𝔽2)11yescharacteristic
319C23×C83H(5,𝔽2)11yescharacteristic
320C23×C83H(5,𝔽2)11yescharacteristic
321C23×C832−1+411yescharacteristic
322C23×C832−1+411yescharacteristic
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×C83C2×C4⋊C414yes—
364C2×C4×C83C2×C4⋊C414yes—
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—416no—
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×Dic83—41no—
416C2×Dic83—41no—
417C2×Dic83—41no—
418C2×Dic83—41no—
419C2×Dic83—41no—
420C2×Dic83—41no—
421C2×Dic83—41no—
422C22×C83—24no—
423C22×C83—24no—
424C22×C83—24no—
425C22×C83—42no—
426C22×C83—42no—
427C22×C83—42no—
428C22×C83—42no—
429C22×C83—42no—
430C22×C83—42no—
431C22×C83—42no—
432C22×C83—42no—
433C22×C83—42no—
434C22×C83—42no—
435C22×C83—42no—
436C22×C83—42no—
437C22×C83C22×C4⋊C411yescharacteristic
438C22×C83C4×#4111yescharacteristic
439C22×C83C4×#4111yescharacteristic
440C22×C83#51811yescharacteristic
441C22×C83#51811yescharacteristic
442C22×C83#52011yescharacteristic
443C22×C83#52011yescharacteristic
444C22×C83#53511yescharacteristic
445C22×C83#53611yescharacteristic
446C22×C83#53811yescharacteristic
447C22×C83#53811yescharacteristic
448C22×C83#53811yescharacteristic
449C22×C83#53911yescharacteristic
450C22×C83#54011yescharacteristic
451C22×C83#54211yescharacteristic
452C22×C83#54211yescharacteristic
453C22×C83#54211yescharacteristic
454C22×C83#54411yescharacteristic
455C22×C83#54411yescharacteristic
456C22×C83#54611yescharacteristic
457C22×C83#54611yescharacteristic
458C22×C83#54611yescharacteristic
459C22×C83#54611yescharacteristic
460C22×C83#55111yescharacteristic
461C22×C83#55211yescharacteristic
462C22×C83#55311yescharacteristic
463C22×C83#55411yescharacteristic
464C22×C83#55411yescharacteristic
465C22×C83#55411yescharacteristic
466C22×C83#55411yescharacteristic
467C22×C83#55611yescharacteristic
468C22×C83#56011yescharacteristic
469C22×C83#56011yescharacteristic
470C22×C83#56211yescharacteristic
471C22×C83#56211yescharacteristic
472C4×C83—24no—
473C4×C83—24no—
474C4×C83—42no—
475C4×C83—42no—
476C4×C83—81no—
477C4×C83—81no—
478Dic83—42no—
479Dic83—42no—
480Dic83—42no—
481Dic83—42no—
482Dic83—42no—
483Dic83—42no—
484Dic83—81no—
485Dic83—81no—
486#14488—831nomaximal, Sylow
487C2×C83—44no—
488C2×C83#231711yescharacteristic
489C2×C83#233511yescharacteristic
490C2×C83#233711yescharacteristic
491C2×C83#234911yescharacteristic
492C2×C83#234911yescharacteristic
493C2×C83#237311yescharacteristic
494C2×C83#237711yescharacteristic
495C2×C83#268511yescharacteristic
496C2×C83#268711yescharacteristic
497C2×C83#270011yescharacteristic
498C2×C83#270311yescharacteristic
499C2×C83#274211yescharacteristic
500C2×C83#276811yescharacteristic
501C2×C83#278811yescharacteristic
502C2×C83#279011yescharacteristic
503C2×#388—831no—
504C2×#388D8311yescharacteristic
505C2×#385—831no—
506#1444—831no—
507#1442—831no—
508#1442—831no—
509#1441—831no—
510#1439—831no—
511#1439—831no—
512#1436—831no—
513C4⋊#95—831no—
514C4⋊#95—831no—
515#1434—831no—
516C22⋊#95—831no—
517C22⋊#95—831no—
518C83#1448811yescharacteristic, complemented, Sylow
519C24×C4—831no—
520C22×C4⋊C4—831no—
521C22×C4⋊C4—831no—
522C22×C4⋊C4—831no—
523C22×C4⋊C4—831no—
524C22×C4⋊C4—831no—
525C22×C4⋊C4C2×D8311yescharacteristic
526C22×C22⋊C4—831no—
527C22×C22⋊C4—831no—
528C22×C22⋊C4—831no—
529C22×C22⋊C4C2×D8311yescharacteristic
530C22×C22⋊C4C2×D8311yescharacteristic
531C22×C22⋊C4C2×D8311yescharacteristic
532C22×C42—831no—
533C22×C42C2×D8311yescharacteristic
534#388—24no—
535#388—838no—
536#385—1664no—
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×#95—831no—
548C2×#95—831no—
549C2×#95—831no—
550C2×#95—831no—
551C2×#95—831no—
552C2×#95—831no—
553C2×#95—831no—
554C2×#95—831no—
555C2×#95C2×D8311yescharacteristic
556C2×#95C2×D8311yescharacteristic
557C25C22×D8311yescharacteristic
558C23×C4—3321no—
559C23×C4—3321no—
560C23×C4—3321no—
561C23×C4—3321no—
562C23×C4—831no—
563C23×C4—831no—
564C23×C4—831no—
565C23×C4—831no—
566C23×C4—831no—
567C23×C4—831no—
568C23×C4—831no—
569C23×C4—831no—
570C23×C4—1662no—
571C23×C4—1662no—
572C23×C4—1662no—
573C23×C4C22×D8311yescharacteristic
574C23×C4C22×D8311yescharacteristic
575C23×C4C22×D8311yescharacteristic
576C23×C4C22×D8311yescharacteristic
577C23×C4C22×D8311yescharacteristic
578C23×C4C22×D8311yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—3321no—
583C2×C4⋊C4—3321no—
584C2×C4⋊C4—3321no—
585C2×C4⋊C4—3321no—
586C2×C4⋊C4—3321no—
587C2×C4⋊C4—3321no—
588C2×C4⋊C4—3321no—
589C2×C4⋊C4—3321no—
590C2×C4⋊C4—3321no—
591C2×C4⋊C4—834no—
592C2×C4⋊C4—1662no—
593C2×C4⋊C4—1662no—
594C2×C4⋊C4—1662no—
595C2×C4⋊C4—1662no—
596C2×C4⋊C4—1662no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—3321no—
604C2×C22⋊C4—3321no—
605C2×C22⋊C4—3321no—
606C2×C22⋊C4—3321no—
607C2×C22⋊C4—3321no—
608C2×C22⋊C4—3321no—
609C2×C22⋊C4—834no—
610C2×C22⋊C4—834no—
611C2×C22⋊C4—1662no—
612C2×C22⋊C4Dic16614yes—
613C2×C22⋊C4C4×D8314yes—
614C2×C22⋊C4C22⋊D8314yes—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—3321no—
619C2×C42—3321no—
620C2×C42—834no—
621#95—22no—
622#95—22no—
623#95—3321no—
624#95—3321no—
625#95—3321no—
626#95—3321no—
627#95—3321no—
628#95—3321no—
629#95—3321no—
630#95—3321no—
631#95—3321no—
632#95—3321no—
633#95—3321no—
634#95—834no—
635#95—834no—
636#95—1662no—
637#95—1662no—
638#95—1662no—
639#95—1662no—
640#95—1662no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C2×C4×D8312yes—
654C24C2×C22⋊D8312yes—
655C24C2×Dic16612yes—
656C24C23×D8311yescharacteristic
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—3324no—
692C22×C4—3324no—
693C22×C4—3324no—
694C22×C4—3324no—
695C22×C4—3324no—
696C22×C4—3324no—
697C22×C4—3324no—
698C22×C4—832no—
699C22×C4—832no—
700C22×C4—832no—
701C22×C4—832no—
702C22×C4—832no—
703C22×C4—832no—
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×C4—1661no—
746C22×C4—1661no—
747C22×C4—1661no—
748C22×C4—1661no—
749C22×C4—1661no—
750C22×C4—1661no—
751C22×C4—1661no—
752C22×C4—1661no—
753C22×C4—1661no—
754C22×C4C2×C4×D8312yes—
755C22×C4C2×C4×D8312yes—
756C22×C4C2×C22⋊D8312yes—
757C22×C4C2×C22⋊D8312yes—
758C22×C4C2×Dic16612yes—
759C22×C4C2×Dic16612yes—
760C22×C4#1305058912yes—
761C22×C4#1305058912yes—
762C4⋊C4—44no—
763C4⋊C4—3324no—
764C4⋊C4—3324no—
765C4⋊C4—3324no—
766C4⋊C4—3324no—
767C4⋊C4—3324no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—3324no—
771C22⋊C4—3324no—
772C22⋊C4—3324no—
773C22⋊C4Dic83⋊C4116yescomplemented
774C42—44no—
775C42—3324no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×Dic83⋊C414yes—
811C23C22×C4×D8311yescharacteristic
812C23C22×C22⋊D8311yescharacteristic
813C23C22×Dic16611yescharacteristic
814C23#41×D8311yescharacteristic
815C23#41×D8311yescharacteristic
816C23C2×#1305058911yescharacteristic
817C23C2×#1305058911yescharacteristic
818C23#1458183711yescharacteristic
819C23#1458183711yescharacteristic
820C23#1458183811yescharacteristic
821C23#1458183811yescharacteristic
822C23#1458183811yescharacteristic
823C23#1458183811yescharacteristic
824C23#1458183911yescharacteristic
825C23#1458183911yescharacteristic
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—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—33216no—
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—3321no—
895C2×C4—3321no—
896C2×C4—3321no—
897C2×C4—3321no—
898C2×C4—3321no—
899C2×C4—3321no—
900C2×C4—3321no—
901C2×C4—3321no—
902C2×C4—3321no—
903C2×C4—3321no—
904C2×C4—3321no—
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—1662no—
917C2×C4—1662no—
918C2×C4—1662no—
919C2×C4—1662no—
920C2×C4—1662no—
921C2×C4—1662no—
922C2×C4—1662no—
923C2×C4C2×Dic83⋊C414yes—
924C2×C4C2×Dic83⋊C414yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×Dic83⋊C411yescharacteristic
941C22C4×#1305058911yescharacteristic
942C22C4×#1305058911yescharacteristic
943C22#1912817311yescharacteristic
944C22#1912817311yescharacteristic
945C22#1912818111yescharacteristic
946C22#1912818111yescharacteristic
947C22#1912826511yescharacteristic
948C22#1912827211yescharacteristic
949C22#1912828811yescharacteristic
950C22#1912829011yescharacteristic
951C22#1912829011yescharacteristic
952C22#1912829511yescharacteristic
953C22#1912830411yescharacteristic
954C22#1912831511yescharacteristic
955C22#1912831911yescharacteristic
956C22#1912832011yescharacteristic
957C22#1912832911yescharacteristic
958C22#1912832911yescharacteristic
959C22#1912833911yescharacteristic
960C22#1912833911yescharacteristic
961C22#1912834511yescharacteristic
962C22#1912834511yescharacteristic
963C22#1912837611yescharacteristic
964C22#1912838811yescharacteristic
965C22#1912840311yescharacteristic
966C22#1912840811yescharacteristic
967C22#1912840811yescharacteristic
968C22#1912841011yescharacteristic
969C22#1912841011yescharacteristic
970C22#1912842011yescharacteristic
971C22#1912843911yescharacteristic
972C22#1912844211yescharacteristic
973C22#1912844511yescharacteristic
974C22#1912844811yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—81no—
980C4—81no—
981C4—3322no—
982C4—3322no—
983C4—3322no—
984C4—3322no—
985C4—3322no—
986C4—3322no—
987C4—6641no—
988C4—6641no—
989C2—44no—
990C2#2491008311yescharacteristic
991C2#2491026011yescharacteristic
992C2#2491027011yescharacteristic
993C2#2491036811yescharacteristic
994C2#2491036811yescharacteristic
995C2#2491059011yescharacteristic
996C2#2491061611yescharacteristic
997C2#2491384811yescharacteristic
998C2#2491387811yescharacteristic
999C2#2491405511yescharacteristic
1000C2#2491410211yescharacteristic
1001C2#2491458911yescharacteristic
1002C2#2491494711yescharacteristic
1003C2#2491520611yescharacteristic
1004C2#2491523311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#388×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83#14488
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. #24905726C2semidirect
4. #24905719C2semidirect
5. #24905719C2semidirect
6. #24905715C2semidirect
9. #24905696C2semidirect
10. #24905693C2semidirect
11. #24905692C2semidirect
12. #24905689C2semidirect
26. #19127594C4semidirect
77. C2×C4⋊Dic83C2×C4semidirect
95. C2×C4×Dic83C2×C4semidirect
112. C83⋊#95C2×C4semidirect
113. C83⋊#95C2×C4semidirect
271. C22⋊C4×C83C4⋊C4semidirect
518. C83#14488semidirect
773. C22⋊C4Dic83⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#191275942
C2×#191275762
#249057262
#249057192
#249057152
#249057062
#249056962
#249056932
#249056922
#249056892
#249056852
C2×#388×C832
#1448883