Finite Group Databasebeta

← #35332349

Subgroups — #35332349

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×#19127594C211yesmaximal, characteristic
3C2×#19127574C211yesmaximal, characteristic
4C2×#19127566C211yesmaximal, characteristic, complemented
5#24905726C211yesmaximal, characteristic, complemented
6#24905726C211yesmaximal, characteristic, complemented
7#24905719C211yesmaximal, characteristic, complemented
8#24905715C211yesmaximal, characteristic, complemented
9#24905706C211yesmaximal, characteristic
10#24905706C211yesmaximal, characteristic
11#24905694C211yesmaximal, characteristic, complemented
12#24905692C211yesmaximal, characteristic, complemented
13Dic83⋊#95C211yesmaximal, characteristic, complemented
14#24905686C211yesmaximal, characteristic
15C2×#385×C83C211yesmaximal, characteristic
16C22×C4⋊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×C22⋊Dic83C2211yescharacteristic
26C22×C4×Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28#19127594—24no—
29#19127594C418yescomplemented
30#19127574—24no—
31#19127566—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
48C24×C4×C83C2211yescharacteristic
49C22×C4⋊C4×C83C2211yescharacteristic
50C22×C4⋊C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C22⋊C4×C83C2211yescharacteristic
53#385×C83—24no—
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83—41no—
67C2×C4⋊Dic83—41no—
68C2×C4⋊Dic83—41no—
69C2×C4⋊Dic83C2×C414yescomplemented
70C2×Dic83⋊C4—22no—
71C2×Dic83⋊C4—22no—
72C2×Dic83⋊C4—22no—
73C2×Dic83⋊C4—22no—
74C2×Dic83⋊C4—22no—
75C2×Dic83⋊C4—41no—
76C2×Dic83⋊C4—41no—
77C2×Dic83⋊C4—41no—
78C2×Dic83⋊C4—41no—
79C2×Dic83⋊C4—41no—
80C2×Dic83⋊C4—41no—
81C2×Dic83⋊C4—41no—
82C2×C22⋊Dic83—22no—
83C2×C22⋊Dic83—22no—
84C2×C22⋊Dic83—22no—
85C2×C22⋊Dic83—22no—
86C2×C22⋊Dic83—22no—
87C2×C22⋊Dic83—22no—
88C2×C22⋊Dic83—41no—
89C2×C22⋊Dic83—41no—
90C2×C22⋊Dic83—41no—
91C2×C22⋊Dic83—41no—
92C2×C22⋊Dic83C2×C414yes—
93C2×C22⋊Dic83C2×C414yes—
94C2×C4×Dic83—22no—
95C2×C4×Dic83—22no—
96C2×C4×Dic83—22no—
97C2×C4×Dic83—22no—
98C2×C4×Dic83—41no—
99C2×C4×Dic83C2×C414yescomplemented
100C83⋊#95—22no—
101C83⋊#95—22no—
102C83⋊#95—22no—
103C83⋊#95—22no—
104C83⋊#95—22no—
105C83⋊#95—22no—
106C83⋊#95—41no—
107C83⋊#95—41no—
108C83⋊#95—41no—
109C83⋊#95—41no—
110C83⋊#95—41no—
111C83⋊#95—41no—
112C83⋊#95—41no—
113C83⋊#95C2×C414yescomplemented
114C83⋊#95C2×C414yescomplemented
115C83⋊#95D414yes—
116C25×C83C2311yescharacteristic
117C23×C4×C83—22no—
118C23×C4×C83—22no—
119C23×C4×C83—22no—
120C23×C4×C83—41no—
121C23×C4×C83—41no—
122C23×C4×C83—41no—
123C23×C4×C83—41no—
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C2×C4⋊C4×C83—22no—
131C2×C4⋊C4×C83—22no—
132C2×C4⋊C4×C83—22no—
133C2×C4⋊C4×C83—22no—
134C2×C4⋊C4×C83—41no—
135C2×C4⋊C4×C83—41no—
136C2×C22⋊C4×C83—22no—
137C2×C22⋊C4×C83—41no—
138C2×C22⋊C4×C83—41no—
139C2×C22⋊C4×C83C2×C414yes—
140C2×C22⋊C4×C83D414yes—
141C2×C22⋊C4×C83Q814yes—
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—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×Dic83C22×C412yes—
193C22×Dic83C22×C412yes—
194C22×Dic83C22×C412yes—
195C22×Dic83C22×C412yes—
196C22×Dic83C2×D412yes—
197C22×Dic83C2×D412yes—
198C22×Dic83#4112yes—
199C22×Dic83#4112yes—
200C4⋊Dic83—44no—
201C4⋊Dic83—44no—
202Dic83⋊C4—44no—
203Dic83⋊C4—44no—
204Dic83⋊C4—44no—
205Dic83⋊C4—44no—
206C22⋊Dic83—28no—
207C22⋊Dic83—44no—
208C22⋊Dic83—44no—
209C22⋊Dic83—44no—
210C4×Dic83—28no—
211C4×Dic83—44no—
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×C83—21no—
223C24×C83—21no—
224C24×C83C22×C412yes—
225C24×C83C2×D412yes—
226C24×C83C2×Q812yes—
227C24×C83C2411yescharacteristic
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×C83—21no—
261C22×C4×C83—21no—
262C22×C4×C83—44no—
263C22×C4×C83—44no—
264C22×C4×C83—44no—
265C22×C4×C83—44no—
266C22×C4×C83—44no—
267C22×C4×C83—44no—
268C22×C4×C83—44no—
269C22×C4×C83C22×C412yes—
270C22×C4×C83C22×C412yes—
271C22×C4×C83C2×D412yes—
272C22×C4×C83C2×D412yes—
273C22×C4×C83C2×D412yes—
274C22×C4×C83C2×Q812yes—
275C22×C4×C83C2×Q812yes—
276C22×C4×C83#4112yes—
277C4⋊C4×C83—44no—
278C4⋊C4×C83—44no—
279C22⋊C4×C83—44no—
280C22⋊C4×C83C4⋊C4116yescomplemented
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—416no—
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×C83—41no—
372C2×C4×C83C2×C4⋊C414yes—
373C2×C4×C83C2×C4⋊C414yes—
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—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×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×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—42no—
483C4×C83—42no—
484C4×C83—81no—
485C4×C83—81no—
486Dic83—24no—
487Dic83—42no—
488Dic83—42no—
489Dic83—42no—
490Dic83—42no—
491Dic83—42no—
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×#388—831no—
513C2×#385—831no—
514C2×#385D8311yescharacteristic
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×C4C2×D8311yescharacteristic
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⋊C4C2×D8311yescharacteristic
535C22×C4⋊C4C2×D8311yescharacteristic
536C22×C22⋊C4—831no—
537C22×C22⋊C4—831no—
538C22×C22⋊C4—831no—
539C22×C22⋊C4—831no—
540C22×C22⋊C4C2×D8311yescharacteristic
541C22×C22⋊C4C2×D8311yescharacteristic
542C22×C42—831no—
543C22×C42—831no—
544#388—838no—
545#388—1664no—
546#385—24no—
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—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—41no—
575C23×C4—831no—
576C23×C4—831no—
577C23×C4—831no—
578C23×C4—831no—
579C23×C4—831no—
580C23×C4—831no—
581C23×C4—831no—
582C23×C4—831no—
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—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
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—3321no—
602C2×C4⋊C4—3321no—
603C2×C4⋊C4—3321no—
604C2×C4⋊C4—3321no—
605C2×C4⋊C4—834no—
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⋊C4—1662no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—41no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—3321no—
617C2×C22⋊C4—3321no—
618C2×C22⋊C4—3321no—
619C2×C22⋊C4—3321no—
620C2×C22⋊C4—834no—
621C2×C22⋊C4—834no—
622C2×C22⋊C4—1662no—
623C2×C22⋊C4—1662no—
624C2×C22⋊C4—1662no—
625C2×C22⋊C4—1662no—
626C2×C22⋊C4—1662no—
627C2×C22⋊C4—1662no—
628C2×C22⋊C4Dic16614yes—
629C2×C22⋊C4C4×D8314yes—
630C2×C22⋊C4C22⋊D8314yes—
631C2×C42—3321no—
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—3321no—
644#95—3321no—
645#95—3321no—
646#95—834no—
647#95—834no—
648#95—834no—
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—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
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—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×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—44no—
778C4⋊C4—3324no—
779C4⋊C4—3324no—
780C4⋊C4—3324no—
781C4⋊C4—3324no—
782C4⋊C4—3324no—
783C4⋊C4—3324no—
784C22⋊C4—44no—
785C22⋊C4—3324no—
786C22⋊C4—3324no—
787C22⋊C4—3324no—
788C22⋊C4—1668no—
789C22⋊C4Dic83⋊C4116yescomplemented
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
833C23C2×#1305058911yescharacteristic
834C23#1458183711yescharacteristic
835C23#1458183711yescharacteristic
836C23#1458183711yescharacteristic
837C23#1458183711yescharacteristic
838C23#1458183811yescharacteristic
839C23#1458183911yescharacteristic
840C23#1458184011yescharacteristic
841C23#1458184011yescharacteristic
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—416no—
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—41no—
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—834no—
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
957C22C4×D4×D8311yescharacteristic
958C22C4×#1305058911yescharacteristic
959C22#1912817311yescharacteristic
960C22#1912818011yescharacteristic
961C22#1912818211yescharacteristic
962C22#1912818211yescharacteristic
963C22#1912826611yescharacteristic
964C22#1912826811yescharacteristic
965C22#1912827511yescharacteristic
966C22#1912828111yescharacteristic
967C22#1912828611yescharacteristic
968C22#1912829411yescharacteristic
969C22#1912830311yescharacteristic
970C22#1912831111yescharacteristic
971C22#1912832111yescharacteristic
972C22#1912832111yescharacteristic
973C22#1912833211yescharacteristic
974C22#1912833211yescharacteristic
975C22D4×C22⋊D8311yescharacteristic
976C22#1912833811yescharacteristic
977C22#1912833911yescharacteristic
978C22#1912834511yescharacteristic
979C22#1912835011yescharacteristic
980C22#1912835311yescharacteristic
981C22D4×Dic16611yescharacteristic
982C22#1912837911yescharacteristic
983C22#1912838511yescharacteristic
984C22#1912840811yescharacteristic
985C22#1912841011yescharacteristic
986C22#1912841011yescharacteristic
987C22#1912844411yescharacteristic
988C22#1912844711yescharacteristic
989C22#1912844811yescharacteristic
990C22#1912845211yescharacteristic
991C4—24no—
992C4—24no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C4—3322no—
998C4—3322no—
999C4—3322no—
1000C4—3322no—
1001C4—3322no—
1002C4—6641no—
1003C4—6641no—
1004C4—1664no—
1005C2—44no—
1006C2#2491008711yescharacteristic
1007C2#2491015511yescharacteristic
1008C2#2491023311yescharacteristic
1009C2D4×Dic83⋊C411yescharacteristic
1010C2#2491036811yescharacteristic
1011C2#2491045811yescharacteristic
1012C2#2491063611yescharacteristic
1013C2#2491368511yescharacteristic
1014C2#2491371011yescharacteristic
1015C2#2491403311yescharacteristic
1016C2#2491412511yescharacteristic
1017C2#2491414511yescharacteristic
1018C2#2491434411yescharacteristic
1019C2#2491487711yescharacteristic
1020C2#2491494011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#385×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#385D83
hypocenterC83#14403
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#19127566C2semidirect
5. #24905726C2semidirect
6. #24905726C2semidirect
7. #24905719C2semidirect
8. #24905715C2semidirect
11. #24905694C2semidirect
12. #24905692C2semidirect
13. Dic83⋊#95C2semidirect
29. #19127594C4semidirect
69. C2×C4⋊Dic83C2×C4semidirect
99. C2×C4×Dic83C2×C4semidirect
113. C83⋊#95C2×C4semidirect
114. C83⋊#95C2×C4semidirect
280. C22⋊C4×C83C4⋊C4semidirect
526. C83#14403semidirect
789. 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×#191275742
C2×#191275662
#249057262
#249057192
#249057152
#249057062
#249056942
#249056922
Dic83⋊#952
#249056862
C2×#385×C832
#1440383