Finite Group Databasebeta

← #35326501

Subgroups — #35326501

Order 21248.

1746 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×#19127559C211yesmaximal, characteristic
3C2×C4×Dic83⋊C4C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic83C211yesmaximal, characteristic
5#24905727C211yesmaximal, characteristic, complemented
6#24905726C211yesmaximal, characteristic, complemented
7#24905706C211yesmaximal, characteristic
8#24905706C211yesmaximal, characteristic
9#24905696C211yesmaximal, characteristic, complemented
10#24905694C211yesmaximal, characteristic, complemented
11#24905692C211yesmaximal, characteristic, complemented
12#24905689C211yesmaximal, characteristic, complemented
13#24905689C211yesmaximal, characteristic, complemented
14#24905685C211yesmaximal, characteristic
15C2×#388×C83C211yesmaximal, characteristic
16C24×Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2211yescharacteristic
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24C22×C22⋊Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26C22×C4×Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28#19127594—24no—
29#19127559—24no—
30C4×Dic83⋊C4—24no—
31C22⋊C4×Dic83C418yescomplemented
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×C83—24no—
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C23×Dic83—22no—
57C23×Dic83—22no—
58C23×Dic83—22no—
59C23×Dic83—22no—
60C23×Dic83—41no—
61C23×Dic83—41no—
62C23×Dic83C2×C414yes—
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—41no—
74C2×Dic83⋊C4—22no—
75C2×Dic83⋊C4—22no—
76C2×Dic83⋊C4—22no—
77C2×Dic83⋊C4—22no—
78C2×Dic83⋊C4—22no—
79C2×Dic83⋊C4—22no—
80C2×Dic83⋊C4—22no—
81C2×Dic83⋊C4—22no—
82C2×Dic83⋊C4—22no—
83C2×Dic83⋊C4—22no—
84C2×Dic83⋊C4—41no—
85C2×Dic83⋊C4—41no—
86C2×C22⋊Dic83—22no—
87C2×C22⋊Dic83—22no—
88C2×C22⋊Dic83—22no—
89C2×C22⋊Dic83—22no—
90C2×C22⋊Dic83—22no—
91C2×C22⋊Dic83—22no—
92C2×C22⋊Dic83—41no—
93C2×C22⋊Dic83—41no—
94C2×C22⋊Dic83C2×C414yes—
95C2×C4×Dic83—22no—
96C2×C4×Dic83—22no—
97C2×C4×Dic83—22no—
98C2×C4×Dic83—22no—
99C2×C4×Dic83—41no—
100C2×C4×Dic83—41no—
101C2×C4×Dic83—41no—
102C2×C4×Dic83C2×C414yes—
103C2×C4×Dic83C2×C414yes—
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—22no—
113C83⋊#95—41no—
114C83⋊#95—41no—
115C83⋊#95—41no—
116C83⋊#95—41no—
117C83⋊#95C2×C414yes—
118C83⋊#95C2×C414yes—
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—22no—
128C2×C4⋊C4×C83—22no—
129C2×C4⋊C4×C83—41no—
130C2×C22⋊C4×C83—22no—
131C2×C22⋊C4×C83—22no—
132C2×C22⋊C4×C83—22no—
133C2×C22⋊C4×C83—22no—
134C2×C22⋊C4×C83—41no—
135C2×C22⋊C4×C83—41no—
136C2×C22⋊C4×C83C2×C414yes—
137C2×C22⋊C4×C83D414yes—
138C2×C22⋊C4×C83Q814yes—
139C2×C42×C83—22no—
140C2×C42×C83—22no—
141C2×C42×C83—41no—
142#95×C83—22no—
143#95×C83—22no—
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—28no—
175C22×Dic83—28no—
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—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×Dic83C2×D412yes—
200C22×Dic83C2×D412yes—
201C22×Dic83#4112yes—
202C22×Dic83#4112yes—
203C22×Dic83#4112yes—
204C22×Dic83#4112yes—
205C22×Dic83#4112yes—
206C22×Dic83#4112yes—
207C4⋊Dic83—44no—
208Dic83⋊C4—28no—
209Dic83⋊C4—28no—
210Dic83⋊C4—44no—
211Dic83⋊C4—44no—
212C22⋊Dic83—28no—
213C22⋊Dic83—44no—
214C22⋊Dic83—44no—
215C4×Dic83—28no—
216C4×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×C83—21no—
265C22×C4×C83—21no—
266C22×C4×C83—21no—
267C22×C4×C83—21no—
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—44no—
278C22⋊C4×C83—44no—
279C22⋊C4×C83C4⋊C4116yescomplemented
280C42×C83—44no—
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×C83C2×#4111yescharacteristic
324C23×C83C2×#4111yescharacteristic
325C23×C83C2×#4111yescharacteristic
326C23×C83C2×#4111yescharacteristic
327C23×C83H(5,𝔽2)11yescharacteristic
328C23×C83H(5,𝔽2)11yescharacteristic
329C23×C83H(5,𝔽2)11yescharacteristic
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—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—41no—
353C2×C4×C83—41no—
354C2×C4×C83—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83—41no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—41no—
361C2×C4×C83—41no—
362C2×C4×C83—41no—
363C2×C4×C83—41no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83C2×C4⋊C414yes—
372C2×C4×C83C2×C4⋊C414yes—
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—22no—
392C2×Dic83—22no—
393C2×Dic83—22no—
394C2×Dic83—22no—
395C2×Dic83—22no—
396C2×Dic83—22no—
397C2×Dic83—22no—
398C2×Dic83—22no—
399C2×Dic83—22no—
400C2×Dic83—416no—
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#11714yes—
428C2×Dic83#11714yes—
429C2×Dic83C4×D414yes—
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×#11711yescharacteristic
447C22×C83C2×#11711yescharacteristic
448C22×C83C2×C4×D411yescharacteristic
449C22×C83C4×#4111yescharacteristic
450C22×C83#51811yescharacteristic
451C22×C83#52011yescharacteristic
452C22×C83#52511yescharacteristic
453C22×C83#52511yescharacteristic
454C22×C83#52911yescharacteristic
455C22×C83#52911yescharacteristic
456C22×C83#53211yescharacteristic
457C22×C83#53211yescharacteristic
458C22×C83#53311yescharacteristic
459C22×C83#53311yescharacteristic
460C22×C83#54011yescharacteristic
461C22×C83#54011yescharacteristic
462C22×C83#54211yescharacteristic
463C22×C83#54211yescharacteristic
464C22×C83D4211yescharacteristic
465C22×C83#54611yescharacteristic
466C22×C83#54611yescharacteristic
467C22×C83#54611yescharacteristic
468C22×C83#54611yescharacteristic
469C22×C83#54711yescharacteristic
470C22×C83D4×Q811yescharacteristic
471C22×C83#55111yescharacteristic
472C22×C83#55111yescharacteristic
473C22×C83#55311yescharacteristic
474C22×C83#55311yescharacteristic
475C22×C83#55411yescharacteristic
476C22×C83#55411yescharacteristic
477C22×C83#55411yescharacteristic
478C22×C83#55611yescharacteristic
479C22×C83#55611yescharacteristic
480C4×C83—24no—
481C4×C83—24no—
482C4×C83—42no—
483C4×C83—42no—
484C4×C83—81no—
485C4×C83—81no—
486Dic83—24no—
487Dic83—24no—
488Dic83—24no—
489Dic83—42no—
490Dic83—42no—
491Dic83—42no—
492Dic83—81no—
493Dic83—81no—
494#13891—831nomaximal, Sylow
495C2×C83—44no—
496C2×C83#228511yescharacteristic
497C2×C83#229011yescharacteristic
498C2×C83#231911yescharacteristic
499C2×C83#234211yescharacteristic
500C2×C83#234711yescharacteristic
501C2×C83D4×C4⋊C411yescharacteristic
502C2×C83#234911yescharacteristic
503C2×C83#246411yescharacteristic
504C2×C83#246411yescharacteristic
505C2×C83#246511yescharacteristic
506C2×C83#246511yescharacteristic
507C2×C83#252111yescharacteristic
508C2×C83#252111yescharacteristic
509C2×C83#252211yescharacteristic
510C2×C83#252211yescharacteristic
511C2×#388—831no—
512C2×#388D8311yescharacteristic
513C2×#380—831no—
514C2×C4×C4⋊C4—831no—
515C2×C4×C22⋊C4—831no—
516#1444—831no—
517#1444—831no—
518#1439—831no—
519#1439—831no—
520#1436—831no—
521#1436—831no—
522C4⋊#95—831no—
523#1434—831no—
524#1434—831no—
525C22⋊#95—831no—
526C83#1389111yescharacteristic, 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⋊C4C2×D8311yescharacteristic
534C22×C22⋊C4—831no—
535C22×C22⋊C4—831no—
536C22×C22⋊C4—831no—
537C22×C22⋊C4C2×D8311yescharacteristic
538C22×C22⋊C4C2×D8311yescharacteristic
539C22×C22⋊C4C2×D8311yescharacteristic
540C22×C42—831no—
541C22×C42—831no—
542C22×C42—831no—
543C22×C42C2×D8311yescharacteristic
544#388—24no—
545#388—1664no—
546#380—1664no—
547C4×C4⋊C4—1664no—
548C4×C22⋊C4—838no—
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—834no—
571C23×C4—831no—
572C23×C4—831no—
573C23×C4—831no—
574C23×C4—831no—
575C23×C4—831no—
576C23×C4—831no—
577C23×C4—831no—
578C23×C4—831no—
579C23×C4—1662no—
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—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—3321no—
593C2×C4⋊C4—3321no—
594C2×C4⋊C4—3321no—
595C2×C4⋊C4—1662no—
596C2×C4⋊C4—1662no—
597C2×C4⋊C4—1662no—
598C2×C4⋊C4—1662no—
599C2×C4⋊C4—1662no—
600C2×C4⋊C4—1662no—
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×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—41no—
612C2×C22⋊C4—41no—
613C2×C22⋊C4—3321no—
614C2×C22⋊C4—3321no—
615C2×C22⋊C4—834no—
616C2×C22⋊C4—1662no—
617C2×C22⋊C4—1662no—
618C2×C22⋊C4—1662no—
619C2×C22⋊C4—1662no—
620C2×C22⋊C4—1662no—
621C2×C22⋊C4—1662no—
622C2×C22⋊C4Dic16614yes—
623C2×C22⋊C4C4×D8314yes—
624C2×C22⋊C4C22⋊D8314yes—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—41no—
628C2×C42—3321no—
629C2×C42—3321no—
630C2×C42—3321no—
631C2×C42—834no—
632C2×C42—834no—
633C2×C42—1662no—
634C2×C42—1662no—
635C2×C42—1662no—
636C2×C42—1662no—
637#95—22no—
638#95—22no—
639#95—3321no—
640#95—3321no—
641#95—3321no—
642#95—3321no—
643#95—834no—
644#95—834no—
645#95—834no—
646#95—1662no—
647#95—1662no—
648#95—1662no—
649#95—1662no—
650#95—1662no—
651#95—1662no—
652#95—1662no—
653#95—1662no—
654#95—1662no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C4×D8312yes—
668C24C2×C22⋊D8312yes—
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—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—3324no—
706C22×C4—3324no—
707C22×C4—3324no—
708C22×C4—3324no—
709C22×C4—3324no—
710C22×C4—832no—
711C22×C4—832no—
712C22×C4—832no—
713C22×C4—832no—
714C22×C4—832no—
715C22×C4—832no—
716C22×C4—832no—
717C22×C4—832no—
718C22×C4—832no—
719C22×C4—832no—
720C22×C4—832no—
721C22×C4—832no—
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—1668no—
737C22×C4—1668no—
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×C4—1661no—
765C22×C4—1661no—
766C22×C4—1661no—
767C22×C4—1661no—
768C22×C4C2×C4×D8312yes—
769C22×C4C2×C4×D8312yes—
770C22×C4D4×D8312yes—
771C22×C4C2×C22⋊D8312yes—
772C22×C4C2×C22⋊D8312yes—
773C22×C4C2×Dic16612yes—
774C22×C4C2×Dic16612yes—
775C22×C4#1305058912yes—
776C4⋊C4—44no—
777C4⋊C4—3324no—
778C4⋊C4—3324no—
779C4⋊C4—3324no—
780C4⋊C4—1668no—
781C4⋊C4—1668no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—3324no—
785C22⋊C4—3324no—
786C22⋊C4—1668no—
787C22⋊C4Dic83⋊C4116yescomplemented
788C42—44no—
789C42—3324no—
790C42—3324no—
791C42—1668no—
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×Dic83⋊C414yes—
827C23C22×C4×D8311yescharacteristic
828C23C2×D4×D8311yescharacteristic
829C23C22×C22⋊D8311yescharacteristic
830C23C22×Dic16611yescharacteristic
831C23#41×D8311yescharacteristic
832C23#41×D8311yescharacteristic
833C23#41×D8311yescharacteristic
834C23#41×D8311yescharacteristic
835C23#41×D8311yescharacteristic
836C23#41×D8311yescharacteristic
837C23C2×#1305058911yescharacteristic
838C23#1458183711yescharacteristic
839C23#1458183711yescharacteristic
840C23#1458183811yescharacteristic
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—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—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—33216no—
909C2×C4—834no—
910C2×C4—834no—
911C2×C4—834no—
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×C4—1662no—
924C2×C4—1662no—
925C2×C4—1662no—
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×C4—1662no—
939C2×C4C2×Dic83⋊C414yes—
940C2×C4C2×Dic83⋊C414yes—
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×Dic83⋊C411yescharacteristic
957C22#117×D8311yescharacteristic
958C22#117×D8311yescharacteristic
959C22C4×D4×D8311yescharacteristic
960C22C4×#1305058911yescharacteristic
961C22#1912817311yescharacteristic
962C22#1912818011yescharacteristic
963C22#1912820911yescharacteristic
964C22#1912821111yescharacteristic
965C22#1912823011yescharacteristic
966C22#1912823411yescharacteristic
967C22#1912824711yescharacteristic
968C22#1912824711yescharacteristic
969C22#1912825411yescharacteristic
970C22#1912825411yescharacteristic
971C22#1912830111yescharacteristic
972C22#1912830311yescharacteristic
973C22#1912831511yescharacteristic
974C22#1912831711yescharacteristic
975C22D4×C22⋊D8311yescharacteristic
976C22#1912833911yescharacteristic
977C22#1912834311yescharacteristic
978C22#1912834511yescharacteristic
979C22#1912834811yescharacteristic
980C22#1912835011yescharacteristic
981C22D4×Dic16611yescharacteristic
982C22#1912837611yescharacteristic
983C22#1912838111yescharacteristic
984C22#1912839411yescharacteristic
985C22#1912839611yescharacteristic
986C22#1912840811yescharacteristic
987C22#1912841011yescharacteristic
988C22#1912841011yescharacteristic
989C22#1912841811yescharacteristic
990C22#1912842011yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—3322no—
998C4—3322no—
999C4—3322no—
1000C4—6641no—
1001C4—6641no—
1002C4—1664no—
1003C4—1664no—
1004C4—1664no—
1005C2—44no—
1006C2#2490986611yescharacteristic
1007C2#2490990511yescharacteristic
1008C2#2491010411yescharacteristic
1009C2#2491030711yescharacteristic
1010C2#2491035311yescharacteristic
1011C2D4×Dic83⋊C411yescharacteristic
1012C2#2491036811yescharacteristic
1013C2#2491146611yescharacteristic
1014C2#2491147411yescharacteristic
1015C2#2491148111yescharacteristic
1016C2#2491148911yescharacteristic
1017C2#2491216311yescharacteristic
1018C2#2491217111yescharacteristic
1019C2#2491217811yescharacteristic
1020C2#2491218611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#388×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83#13891
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic83⋊C4C2semidirect
5. #24905727C2semidirect
6. #24905726C2semidirect
9. #24905696C2semidirect
10. #24905694C2semidirect
11. #24905692C2semidirect
12. #24905689C2semidirect
13. #24905689C2semidirect
31. C22⋊C4×Dic83C4semidirect
279. C22⋊C4×C83C4⋊C4semidirect
526. C83#13891semidirect
787. 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×#191275592
C2×C4×Dic83⋊C42
C2×C22⋊C4×Dic832
#249057272
#249057262
#249057062
#249056962
#249056942
#249056922
#249056892
#249056852
C2×#388×C832
#1389183