Finite Group Databasebeta

← #35332346

Subgroups — #35332346

Order 21248.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127594C211yesmaximal, characteristic
2C2×#19127576C211yesmaximal, characteristic
3C2×#19127576C211yesmaximal, characteristic
4C2×#19127567C211yesmaximal, characteristic, complemented
5#24905728C211yesmaximal, characteristic, complemented
6#24905728C211yesmaximal, characteristic, complemented
7#24905720C211yesmaximal, characteristic, complemented
8#24905716C211yesmaximal, characteristic, complemented
9#24905708C211yesmaximal, characteristic
10#24905708C211yesmaximal, characteristic
11#24905697C211yesmaximal, characteristic, complemented
12#24905693C211yesmaximal, characteristic, complemented
13#24905692C211yesmaximal, characteristic, complemented
14#24905685C211yesmaximal, characteristic
15C2×#388×C83C211yesmaximal, characteristic
16C24×Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21C22×C4⋊Dic83C2211yescharacteristic
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C22⋊Dic83C2211yescharacteristic
25C22×C22⋊Dic83C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28#19127594—24no—
29#19127576—24no—
30#19127576—24no—
31#19127567—24no—
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
47C2×C83⋊#95C2211yescharacteristic
48C22×C4⋊C4×C83C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C22×C22⋊C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C42×C83C2211yescharacteristic
53#388×C83C418yescomplemented
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C23×Dic83—22no—
57C23×Dic83—22no—
58C23×Dic83—22no—
59C23×Dic83—41no—
60C23×Dic83—41no—
61C23×Dic83—41no—
62C23×Dic83—41no—
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2311yescharacteristic
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2311yescharacteristic
67C23×Dic83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C2×C4⋊Dic83—22no—
72C2×C4⋊Dic83—22no—
73C2×C4⋊Dic83—22no—
74C2×C4⋊Dic83—22no—
75C2×C4⋊Dic83—22no—
76C2×C4⋊Dic83—22no—
77C2×C4⋊Dic83—22no—
78C2×C4⋊Dic83—22no—
79C2×C4⋊Dic83—22no—
80C2×C4⋊Dic83—22no—
81C2×C4⋊Dic83—22no—
82C2×C4⋊Dic83—41no—
83C2×C4⋊Dic83—41no—
84C2×C4⋊Dic83—41no—
85C2×C4⋊Dic83—41no—
86C2×C4⋊Dic83—41no—
87C2×C4⋊Dic83—41no—
88C2×C4⋊Dic83—41no—
89C2×C4⋊Dic83—41no—
90C2×C4⋊Dic83—41no—
91C2×C4⋊Dic83—41no—
92C2×C22⋊Dic83—22no—
93C2×C22⋊Dic83—22no—
94C2×C22⋊Dic83—22no—
95C2×C22⋊Dic83—22no—
96C2×C22⋊Dic83—22no—
97C2×C22⋊Dic83—41no—
98C2×C22⋊Dic83—41no—
99C2×C22⋊Dic83—41no—
100C2×C22⋊Dic83—41no—
101C2×C4×Dic83—22no—
102C2×C4×Dic83—22no—
103C2×C4×Dic83—41no—
104C83⋊#95—22no—
105C83⋊#95—22no—
106C83⋊#95—22no—
107C83⋊#95—22no—
108C83⋊#95—22no—
109C83⋊#95—22no—
110C83⋊#95—22no—
111C83⋊#95—22no—
112C83⋊#95—41no—
113C83⋊#95—41no—
114C83⋊#95—41no—
115C83⋊#95—41no—
116C83⋊#95—41no—
117C83⋊#95—41no—
118C83⋊#95—41no—
119C83⋊#95D414yes—
120C25×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C2×C4⋊C4×C83—41no—
128C2×C4⋊C4×C83—41no—
129C2×C4⋊C4×C83C2×C414yescomplemented
130C2×C22⋊C4×C83—22no—
131C2×C22⋊C4×C83—22no—
132C2×C22⋊C4×C83—41no—
133C2×C22⋊C4×C83—41no—
134C2×C22⋊C4×C83C2×C414yes—
135C2×C22⋊C4×C83C2×C414yes—
136C2×C22⋊C4×C83C2×C414yes—
137C2×C22⋊C4×C83D414yes—
138C2×C22⋊C4×C83Q814yes—
139C2×C42×C83—22no—
140C2×C42×C83—22no—
141C2×C42×C83C2×C414yescomplemented
142#95×C83C2×C414yescomplemented
143#95×C83C2×C414yescomplemented
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—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—44no—
197C22×Dic83—44no—
198C22×Dic83—44no—
199C22×Dic83—44no—
200C22×Dic83—44no—
201C22×Dic83—44no—
202C22×Dic83—44no—
203C22×Dic83C2×D412yes—
204C22×Dic83C2×D412yes—
205C22×Dic83#4112yes—
206C22×Dic83#4112yes—
207C4⋊Dic83—44no—
208C4⋊Dic83—44no—
209C4⋊Dic83—44no—
210C4⋊Dic83—44no—
211C4⋊Dic83—44no—
212C4⋊Dic83—44no—
213C4⋊Dic83—44no—
214C22⋊Dic83—44no—
215C22⋊Dic83—44no—
216C22⋊Dic83—44no—
217C4×Dic83—44no—
218C24×C83—21no—
219C24×C83—21no—
220C24×C83—21no—
221C24×C83—21no—
222C24×C83—21no—
223C24×C83—21no—
224C24×C83—21no—
225C24×C83—21no—
226C24×C83—21no—
227C24×C83—21no—
228C24×C83—21no—
229C24×C83—21no—
230C24×C83C22×C412yes—
231C24×C83C2×D412yes—
232C24×C83C2×Q812yes—
233C24×C83C2411yescharacteristic
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×C83—21no—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83C22×C412yes—
265C22×C4×C83C22×C412yes—
266C22×C4×C83C22×C412yes—
267C22×C4×C83C22×C412yes—
268C22×C4×C83C22×C412yes—
269C22×C4×C83C22×C412yes—
270C22×C4×C83C2×D412yes—
271C22×C4×C83C2×D412yes—
272C22×C4×C83C2×D412yes—
273C22×C4×C83C2×Q812yes—
274C22×C4×C83C2×Q812yes—
275C22×C4×C83#4112yes—
276C4⋊C4×C83—44no—
277C22⋊C4×C83—28no—
278C22⋊C4×C83—44no—
279C22⋊C4×C83C4⋊C4116yescomplemented
280C42×C83—28no—
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—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—22no—
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×C83—41no—
308C23×C83—41no—
309C23×C83—41no—
310C23×C83—41no—
311C23×C83—41no—
312C23×C83—41no—
313C23×C83—41no—
314C23×C83—41no—
315C23×C83C2×C4⋊C414yes—
316C23×C83C23×C411yescharacteristic
317C23×C83C22×D411yescharacteristic
318C23×C83C22×D411yescharacteristic
319C23×C83C22×Q811yescharacteristic
320C23×C83C2×#4111yescharacteristic
321C23×C83C2×#4111yescharacteristic
322C23×C83C2×#4111yescharacteristic
323C23×C83H(5,𝔽2)11yescharacteristic
324C23×C83H(5,𝔽2)11yescharacteristic
325C23×C83H(5,𝔽2)11yescharacteristic
326C23×C83H(5,𝔽2)11yescharacteristic
327C23×C83H(5,𝔽2)11yescharacteristic
328C23×C832−1+411yescharacteristic
329C23×C832−1+411yescharacteristic
330C23×C832−1+411yescharacteristic
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—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
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×C83C2×C4⋊C414yes—
371C2×C4×C83C2×C4⋊C414yes—
372C2×C4×C83C4×D414yes—
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—416no—
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—
422C2×Dic83—41no—
423C2×Dic83—41no—
424C2×Dic83—41no—
425C2×Dic83—41no—
426C2×Dic83—41no—
427C2×Dic83—41no—
428C2×Dic83—41no—
429C2×Dic83—41no—
430C22×C83—24no—
431C22×C83—24no—
432C22×C83—24no—
433C22×C83—42no—
434C22×C83—42no—
435C22×C83—42no—
436C22×C83—42no—
437C22×C83—42no—
438C22×C83—42no—
439C22×C83—42no—
440C22×C83—42no—
441C22×C83—42no—
442C22×C83—42no—
443C22×C83—42no—
444C22×C83—42no—
445C22×C83C22×C4⋊C411yescharacteristic
446C22×C83C2×C4×D411yescharacteristic
447C22×C83C4×#4111yescharacteristic
448C22×C83#51811yescharacteristic
449C22×C83#52011yescharacteristic
450C22×C83#52011yescharacteristic
451C22×C83#52011yescharacteristic
452C22×C83#53511yescharacteristic
453C22×C83#53511yescharacteristic
454C22×C83#53611yescharacteristic
455C22×C83#53711yescharacteristic
456C22×C83#53811yescharacteristic
457C22×C83#53911yescharacteristic
458C22×C83#54011yescharacteristic
459C22×C83#54111yescharacteristic
460C22×C83#54211yescharacteristic
461C22×C83#54211yescharacteristic
462C22×C83#54411yescharacteristic
463C22×C83#54411yescharacteristic
464C22×C83D4211yescharacteristic
465C22×C83#54611yescharacteristic
466C22×C83#54611yescharacteristic
467C22×C83#54611yescharacteristic
468C22×C83#54711yescharacteristic
469C22×C83#54711yescharacteristic
470C22×C83D4×Q811yescharacteristic
471C22×C83#55111yescharacteristic
472C22×C83#55211yescharacteristic
473C22×C83#55411yescharacteristic
474C22×C83#55411yescharacteristic
475C22×C83#55411yescharacteristic
476C22×C83H(3,𝔽4)11yescharacteristic
477C22×C83#56211yescharacteristic
478C22×C83#56211yescharacteristic
479C22×C83#56311yescharacteristic
480C4×C83—24no—
481C4×C83—24no—
482C4×C83—24no—
483C4×C83—42no—
484C4×C83—42no—
485C4×C83—42no—
486Dic83—42no—
487Dic83—42no—
488Dic83—42no—
489Dic83—42no—
490Dic83—81no—
491Dic83—81no—
492Dic83—81no—
493Dic83—81no—
494#14403—831nomaximal, Sylow
495C2×C83—44no—
496C2×C83#231711yescharacteristic
497C2×C83#232411yescharacteristic
498C2×C83#233411yescharacteristic
499C2×C83D4×C4⋊C411yescharacteristic
500C2×C83#234911yescharacteristic
501C2×C83#235911yescharacteristic
502C2×C83#237911yescharacteristic
503C2×C83#267011yescharacteristic
504C2×C83#267211yescharacteristic
505C2×C83#269811yescharacteristic
506C2×C83#270411yescharacteristic
507C2×C83#270611yescharacteristic
508C2×C83#272011yescharacteristic
509C2×C83#276311yescharacteristic
510C2×C83#276811yescharacteristic
511C2×#388—831no—
512C2×#388D8311yescharacteristic
513C2×#385—831no—
514C2×#385—831no—
515C2×#382—831no—
516#1444—831no—
517#1444—831no—
518#1442—831no—
519#1441—831no—
520#1439—831no—
521#1439—831no—
522#1436—831no—
523C4⋊#95—831no—
524C4⋊#95—831no—
525C22⋊#95—831no—
526C83#1440311yescharacteristic, complemented, Sylow
527C24×C4—831no—
528C22×C4⋊C4—831no—
529C22×C4⋊C4—831no—
530C22×C4⋊C4—831no—
531C22×C4⋊C4—831no—
532C22×C4⋊C4—831no—
533C22×C4⋊C4—831no—
534C22×C4⋊C4—831no—
535C22×C4⋊C4C2×D8311yescharacteristic
536C22×C22⋊C4—831no—
537C22×C22⋊C4—831no—
538C22×C22⋊C4—831no—
539C22×C22⋊C4C2×D8311yescharacteristic
540C22×C22⋊C4C2×D8311yescharacteristic
541C22×C22⋊C4C2×D8311yescharacteristic
542C22×C42—831no—
543C22×C42C2×D8311yescharacteristic
544#388—1664no—
545#388Dic8318yescomplemented
546#385—1664no—
547#385—1664no—
548#382—1664no—
549C2×#95—831no—
550C2×#95—831no—
551C2×#95—831no—
552C2×#95—831no—
553C2×#95—831no—
554C2×#95—831no—
555C2×#95—831no—
556C2×#95—831no—
557C2×#95—831no—
558C2×#95—831no—
559C2×#95—831no—
560C2×#95—831no—
561C2×#95—831no—
562C2×#95—831no—
563C2×#95—831no—
564C2×#95—831no—
565C2×#95C2×D8311yescharacteristic
566C2×#95C2×D8311yescharacteristic
567C25C22×D8311yescharacteristic
568C23×C4—3321no—
569C23×C4—3321no—
570C23×C4—3321no—
571C23×C4—3321no—
572C23×C4—831no—
573C23×C4—831no—
574C23×C4—831no—
575C23×C4—831no—
576C23×C4—831no—
577C23×C4—831no—
578C23×C4—831no—
579C23×C4—831no—
580C23×C4—1662no—
581C23×C4—1662no—
582C23×C4—1662no—
583C23×C4C22×D8311yescharacteristic
584C23×C4C22×D8311yescharacteristic
585C23×C4C22×D8311yescharacteristic
586C23×C4C22×D8311yescharacteristic
587C23×C4C22×D8311yescharacteristic
588C23×C4C22×D8311yescharacteristic
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—3321no—
592C2×C4⋊C4—3321no—
593C2×C4⋊C4—3321no—
594C2×C4⋊C4—3321no—
595C2×C4⋊C4—3321no—
596C2×C4⋊C4—3321no—
597C2×C4⋊C4—3321no—
598C2×C4⋊C4—3321no—
599C2×C4⋊C4—3321no—
600C2×C4⋊C4—3321no—
601C2×C4⋊C4—1662no—
602C2×C4⋊C4—1662no—
603C2×C4⋊C4—1662no—
604C2×C4⋊C4—1662no—
605C2×C4⋊C4—1662no—
606C2×C4⋊C4—1662no—
607C2×C4⋊C4—1662no—
608C2×C4⋊C4—1662no—
609C2×C4⋊C4—1662no—
610C2×C4⋊C4—1662no—
611C2×C4⋊C4—1662no—
612C2×C4⋊C4C2×Dic8314yescomplemented
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—3321no—
618C2×C22⋊C4—3321no—
619C2×C22⋊C4—3321no—
620C2×C22⋊C4—3321no—
621C2×C22⋊C4—1662no—
622C2×C22⋊C4—1662no—
623C2×C22⋊C4—1662no—
624C2×C22⋊C4—1662no—
625C2×C22⋊C4—1662no—
626C2×C22⋊C4Dic16614yes—
627C2×C22⋊C4D33214yes—
628C2×C22⋊C4C2×Dic8314yes—
629C2×C22⋊C4C2×Dic8314yes—
630C2×C22⋊C4C2×Dic8314yes—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—3321no—
634C2×C42—1662no—
635C2×C42—1662no—
636C2×C42C2×Dic8314yescomplemented
637#95—3321no—
638#95—3321no—
639#95—3321no—
640#95—3321no—
641#95—3321no—
642#95—3321no—
643#95—3321no—
644#95—834no—
645#95—1662no—
646#95—1662no—
647#95—1662no—
648#95—1662no—
649#95—1662no—
650#95—1662no—
651#95—1662no—
652#95—1662no—
653#95C2×Dic8314yescomplemented
654#95C2×Dic8314yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×Dic8312yes—
668C24C2×D33212yes—
669C24C2×Dic16612yes—
670C24C23×D8311yescharacteristic
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—3324no—
702C22×C4—3324no—
703C22×C4—3324no—
704C22×C4—3324no—
705C22×C4—3324no—
706C22×C4—3324no—
707C22×C4—3324no—
708C22×C4—832no—
709C22×C4—832no—
710C22×C4—832no—
711C22×C4—832no—
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×C4—1661no—
755C22×C4—1661no—
756C22×C4—1661no—
757C22×C4—1661no—
758C22×C4—1661no—
759C22×C4—1661no—
760C22×C4—1661no—
761C22×C4—1661no—
762C22×C4—1661no—
763C22×C4—1661no—
764C22×C4C22×Dic8312yes—
765C22×C4C22×Dic8312yes—
766C22×C4C22×Dic8312yes—
767C22×C4C22×Dic8312yes—
768C22×C4C22×Dic8312yes—
769C22×C4C22×Dic8312yes—
770C22×C4D4×D8312yes—
771C22×C4C2×D33212yes—
772C22×C4C2×D33212yes—
773C22×C4C2×Dic16612yes—
774C22×C4C2×Dic16612yes—
775C22×C4#1305058912yes—
776C4⋊C4—44no—
777C4⋊C4—3324no—
778C4⋊C4—3324no—
779C4⋊C4—3324no—
780C4⋊C4—3324no—
781C4⋊C4—3324no—
782C4⋊C4—3324no—
783C4⋊C4—3324no—
784C22⋊C4—28no—
785C22⋊C4—44no—
786C22⋊C4—3324no—
787C22⋊C4—3324no—
788C22⋊C4—3324no—
789C22⋊C4C4⋊Dic83116yescomplemented
790C42—28no—
791C42—3324no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4⋊Dic8314yes—
827C23C23×Dic8311yescharacteristic
828C23C2×D4×D8311yescharacteristic
829C23C22×D33211yescharacteristic
830C23C22×Dic16611yescharacteristic
831C23#41×D8311yescharacteristic
832C23#41×D8311yescharacteristic
833C23C2×#1305058911yescharacteristic
834C23#1458183711yescharacteristic
835C23#1458183711yescharacteristic
836C23#1458183811yescharacteristic
837C23#1458183811yescharacteristic
838C23#1458183811yescharacteristic
839C23#1458183911yescharacteristic
840C23#1458183911yescharacteristic
841C23#1458183911yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
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—33216no—
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—3321no—
906C2×C4—3321no—
907C2×C4—3321no—
908C2×C4—3321no—
909C2×C4—3321no—
910C2×C4—3321no—
911C2×C4—3321no—
912C2×C4—3321no—
913C2×C4—3321no—
914C2×C4—3321no—
915C2×C4—3321no—
916C2×C4—3321no—
917C2×C4—3321no—
918C2×C4—3321no—
919C2×C4—3321no—
920C2×C4—3321no—
921C2×C4—3321no—
922C2×C4—3321no—
923C2×C4—3321no—
924C2×C4—3321no—
925C2×C4—3321no—
926C2×C4—1662no—
927C2×C4—1662no—
928C2×C4—1662no—
929C2×C4—1662no—
930C2×C4—1662no—
931C2×C4—1662no—
932C2×C4—1662no—
933C2×C4—1662no—
934C2×C4—1662no—
935C2×C4—1662no—
936C2×C4—1662no—
937C2×C4—1662no—
938C2×C4C2×C4⋊Dic8314yes—
939C2×C4C2×C4⋊Dic8314yes—
940C2×C4D4×Dic8314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4⋊Dic8311yescharacteristic
957C22C2×D4×Dic8311yescharacteristic
958C22#41×Dic8311yescharacteristic
959C22#1912817611yescharacteristic
960C22#1912818411yescharacteristic
961C22#1912818411yescharacteristic
962C22#1912818411yescharacteristic
963C22#1912826711yescharacteristic
964C22#1912827011yescharacteristic
965C22#1912827711yescharacteristic
966C22#1912828011yescharacteristic
967C22#1912829011yescharacteristic
968C22#1912829211yescharacteristic
969C22#1912830411yescharacteristic
970C22#1912830811yescharacteristic
971C22#1912831711yescharacteristic
972C22#1912831811yescharacteristic
973C22#1912832911yescharacteristic
974C22#1912832911yescharacteristic
975C22D4×D33211yescharacteristic
976C22#1912834311yescharacteristic
977C22#1912834611yescharacteristic
978C22#1912834611yescharacteristic
979C22#1912834911yescharacteristic
980C22#1912835511yescharacteristic
981C22D4×Dic16611yescharacteristic
982C22#1912837411yescharacteristic
983C22#1912838811yescharacteristic
984C22#1912840811yescharacteristic
985C22#1912841011yescharacteristic
986C22#1912841011yescharacteristic
987C22#1912844311yescharacteristic
988C22#1912844511yescharacteristic
989C22#1912844511yescharacteristic
990C22#1912845111yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—3322no—
998C4—3322no—
999C4—3322no—
1000C4—3322no—
1001C4—6641no—
1002C4—6641no—
1003C4—6641no—
1004C4—6641no—
1005C2—44no—
1006C2#2491008611yescharacteristic
1007C2#2491015811yescharacteristic
1008C2#2491024211yescharacteristic
1009C2D4×C4⋊Dic8311yescharacteristic
1010C2#2491037311yescharacteristic
1011C2#2491045911yescharacteristic
1012C2#2491063711yescharacteristic
1013C2#2491368711yescharacteristic
1014C2#2491371211yescharacteristic
1015C2#2491403511yescharacteristic
1016C2#2491412211yescharacteristic
1017C2#2491414911yescharacteristic
1018C2#2491434711yescharacteristic
1019C2#2491487911yescharacteristic
1020C2#2491494711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#388×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83#14403
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#19127567C2semidirect
5. #24905728C2semidirect
6. #24905728C2semidirect
7. #24905720C2semidirect
8. #24905716C2semidirect
11. #24905697C2semidirect
12. #24905693C2semidirect
13. #24905692C2semidirect
53. #388×C83C4semidirect
129. C2×C4⋊C4×C83C2×C4semidirect
141. C2×C42×C83C2×C4semidirect
142. #95×C83C2×C4semidirect
143. #95×C83C2×C4semidirect
279. C22⋊C4×C83C4⋊C4semidirect
526. C83#14403semidirect
545. #388Dic83semidirect
612. C2×C4⋊C4C2×Dic83semidirect
636. C2×C42C2×Dic83semidirect
653. #95C2×Dic83semidirect
654. #95C2×Dic83semidirect
789. C22⋊C4C4⋊Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275942
C2×#191275762
C2×#191275672
#249057282
#249057202
#249057162
#249057082
#249056972
#249056932
#249056922
#249056852
C2×#388×C832
#1440383