Finite Group Databasebeta

← #35332376

Subgroups — #35332376

Order 21248.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127600C211yesmaximal, characteristic, complemented
2C2×#19127594C211yesmaximal, characteristic
3C2×#19127576C211yesmaximal, characteristic
4C2×#19127576C211yesmaximal, characteristic
5C2×#19127576C211yesmaximal, characteristic
6C2×#19127571C211yesmaximal, characteristic, complemented
7#24905728C211yesmaximal, characteristic, complemented
8#24905728C211yesmaximal, characteristic, complemented
9#24905720C211yesmaximal, characteristic, complemented
10#24905716C211yesmaximal, characteristic, complemented
11#24905708C211yesmaximal, characteristic
12#24905708C211yesmaximal, characteristic
13#24905697C211yesmaximal, characteristic, complemented
14#24905690C211yesmaximal, characteristic, complemented
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×C4⋊Dic83C2211yescharacteristic
25C22×C4⋊Dic83C2211yescharacteristic
26C22×C22⋊Dic83C2211yescharacteristic
27C22×C22⋊Dic83C2211yescharacteristic
28C22×C22⋊Dic83C2211yescharacteristic
29C22×C4×Dic83C2211yescharacteristic
30#19127600—24no—
31#19127594—24no—
32#19127576—24no—
33#19127576—24no—
34#19127576—24no—
35#19127571—24no—
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
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C22×C4⋊C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C22⋊C4×C83C2211yescharacteristic
53C22×C22⋊C4×C83C2211yescharacteristic
54C22×C42×C83C2211yescharacteristic
55#388×C83C418yescomplemented
56C2×#95×C83C2211yescharacteristic
57C2×#95×C83C2211yescharacteristic
58C23×Dic83—22no—
59C23×Dic83—22no—
60C23×Dic83—22no—
61C23×Dic83—41no—
62C23×Dic83—41no—
63C23×Dic83—41no—
64C23×Dic83—41no—
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2311yescharacteristic
67C23×Dic83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
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—22no—
83C2×C4⋊Dic83—22no—
84C2×C4⋊Dic83—22no—
85C2×C4⋊Dic83—22no—
86C2×C4⋊Dic83—22no—
87C2×C4⋊Dic83—41no—
88C2×C4⋊Dic83—41no—
89C2×C4⋊Dic83—41no—
90C2×C4⋊Dic83—41no—
91C2×C4⋊Dic83—41no—
92C2×C4⋊Dic83—41no—
93C2×C4⋊Dic83—41no—
94C2×C4⋊Dic83—41no—
95C2×C4⋊Dic83—41no—
96C2×C4⋊Dic83—41no—
97C2×C4⋊Dic83—41no—
98C2×C4⋊Dic83—41no—
99C2×C4⋊Dic83D414yes—
100C2×C22⋊Dic83—22no—
101C2×C22⋊Dic83—22no—
102C2×C22⋊Dic83—22no—
103C2×C22⋊Dic83—22no—
104C2×C22⋊Dic83—22no—
105C2×C22⋊Dic83—41no—
106C2×C22⋊Dic83—41no—
107C2×C22⋊Dic83—41no—
108C2×C22⋊Dic83—41no—
109C2×C4×Dic83—22no—
110C2×C4×Dic83—22no—
111C2×C4×Dic83—41no—
112C83⋊#95—22no—
113C83⋊#95—22no—
114C83⋊#95—22no—
115C83⋊#95—22no—
116C83⋊#95—22no—
117C83⋊#95—22no—
118C83⋊#95—22no—
119C83⋊#95—22no—
120C83⋊#95—22no—
121C83⋊#95—22no—
122C83⋊#95—41no—
123C83⋊#95—41no—
124C83⋊#95—41no—
125C83⋊#95D414yes—
126C25×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C2×C4⋊C4×C83—22no—
134C2×C4⋊C4×C83—22no—
135C2×C4⋊C4×C83C2×C414yescomplemented
136C2×C22⋊C4×C83—22no—
137C2×C22⋊C4×C83—22no—
138C2×C22⋊C4×C83—22no—
139C2×C22⋊C4×C83—22no—
140C2×C22⋊C4×C83C2×C414yes—
141C2×C22⋊C4×C83C2×C414yes—
142C2×C22⋊C4×C83C2×C414yes—
143C2×C22⋊C4×C83D414yes—
144C2×C22⋊C4×C83Q814yes—
145C2×C42×C83—22no—
146C2×C42×C83—22no—
147C2×C42×C83C2×C414yescomplemented
148#95×C83C2×C414yescomplemented
149#95×C83C2×C414yescomplemented
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—21no—
197C22×Dic83—21no—
198C22×Dic83—21no—
199C22×Dic83—21no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C22×Dic83—44no—
203C22×Dic83—44no—
204C22×Dic83—44no—
205C22×Dic83—44no—
206C22×Dic83—44no—
207C22×Dic83—44no—
208C22×Dic83—44no—
209C22×Dic83C2×D412yes—
210C22×Dic83C2×D412yes—
211C22×Dic83C2×D412yes—
212C22×Dic83C2×D412yes—
213C4⋊Dic83—44no—
214C4⋊Dic83—44no—
215C4⋊Dic83—44no—
216C4⋊Dic83—44no—
217C4⋊Dic83—44no—
218C4⋊Dic83—44no—
219C4⋊Dic83—44no—
220C4⋊Dic83—44no—
221C4⋊Dic83—44no—
222C22⋊Dic83—44no—
223C22⋊Dic83—44no—
224C22⋊Dic83—44no—
225C4×Dic83—44no—
226C24×C83—21no—
227C24×C83—21no—
228C24×C83—21no—
229C24×C83—21no—
230C24×C83—21no—
231C24×C83—21no—
232C24×C83—21no—
233C24×C83—21no—
234C24×C83—21no—
235C24×C83—21no—
236C24×C83—21no—
237C24×C83—21no—
238C24×C83C22×C412yes—
239C24×C83C2×D412yes—
240C24×C83C2×Q812yes—
241C24×C83C2411yescharacteristic
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×C83—21no—
269C22×C4×C83—21no—
270C22×C4×C83C22×C412yes—
271C22×C4×C83C22×C412yes—
272C22×C4×C83C22×C412yes—
273C22×C4×C83C22×C412yes—
274C22×C4×C83C22×C412yes—
275C22×C4×C83C22×C412yes—
276C22×C4×C83C2×D412yes—
277C22×C4×C83C2×D412yes—
278C22×C4×C83C2×D412yes—
279C22×C4×C83C2×D412yes—
280C22×C4×C83C2×Q812yes—
281C22×C4×C83C2×Q812yes—
282C22×C4×C83#4112yes—
283C22×C4×C83#4112yes—
284C4⋊C4×C83—28no—
285C22⋊C4×C83—28no—
286C22⋊C4×C83—28no—
287C22⋊C4×C83C4⋊C4116yescomplemented
288C42×C83—28no—
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—22no—
300C23×C83—22no—
301C23×C83—22no—
302C23×C83—22no—
303C23×C83—22no—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
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×C83—41no—
316C23×C83—41no—
317C23×C83—41no—
318C23×C83—41no—
319C23×C83—41no—
320C23×C83—41no—
321C23×C83—41no—
322C23×C83—41no—
323C23×C83C2×C4⋊C414yes—
324C23×C83C23×C411yescharacteristic
325C23×C83C22×D411yescharacteristic
326C23×C83C22×D411yescharacteristic
327C23×C83C22×D411yescharacteristic
328C23×C83C22×Q811yescharacteristic
329C23×C83C2×#4111yescharacteristic
330C23×C83C2×#4111yescharacteristic
331C23×C83H(5,𝔽2)11yescharacteristic
332C23×C83H(5,𝔽2)11yescharacteristic
333C23×C83H(5,𝔽2)11yescharacteristic
334C23×C83H(5,𝔽2)11yescharacteristic
335C23×C832−1+411yescharacteristic
336C23×C832−1+411yescharacteristic
337C23×C832−1+411yescharacteristic
338C23×C832−1+411yescharacteristic
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—22no—
359C2×C4×C83—22no—
360C2×C4×C83—22no—
361C2×C4×C83—22no—
362C2×C4×C83—22no—
363C2×C4×C83—22no—
364C2×C4×C83—22no—
365C2×C4×C83—22no—
366C2×C4×C83—22no—
367C2×C4×C83—22no—
368C2×C4×C83—22no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83—41no—
372C2×C4×C83—41no—
373C2×C4×C83—41no—
374C2×C4×C83—41no—
375C2×C4×C83—41no—
376C2×C4×C83—41no—
377C2×C4×C83C2×C4⋊C414yes—
378C2×C4×C83C2×C4⋊C414yes—
379C2×C4×C83C4×D414yes—
380C2×C4×C83C4×D414yes—
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—416no—
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—
430C2×Dic83—41no—
431C2×Dic83—41no—
432C2×Dic83—41no—
433C2×Dic83—41no—
434C2×Dic83—41no—
435C2×Dic83—41no—
436C2×Dic83—41no—
437C2×Dic83—41no—
438C22×C83—24no—
439C22×C83—24no—
440C22×C83—24no—
441C22×C83—42no—
442C22×C83—42no—
443C22×C83—42no—
444C22×C83—42no—
445C22×C83—42no—
446C22×C83—42no—
447C22×C83—42no—
448C22×C83—42no—
449C22×C83—42no—
450C22×C83—42no—
451C22×C83—42no—
452C22×C83—42no—
453C22×C83C22×C4⋊C411yescharacteristic
454C22×C83C2×C4×D411yescharacteristic
455C22×C83C2×C4×D411yescharacteristic
456C22×C83#52011yescharacteristic
457C22×C83#52011yescharacteristic
458C22×C83#52011yescharacteristic
459C22×C83#52011yescharacteristic
460C22×C83#53411yescharacteristic
461C22×C83#53511yescharacteristic
462C22×C83#53511yescharacteristic
463C22×C83#53611yescharacteristic
464C22×C83#53611yescharacteristic
465C22×C83#53611yescharacteristic
466C22×C83#53911yescharacteristic
467C22×C83#53911yescharacteristic
468C22×C83#54211yescharacteristic
469C22×C83#54211yescharacteristic
470C22×C83#54411yescharacteristic
471C22×C83#54411yescharacteristic
472C22×C83D4211yescharacteristic
473C22×C83D4211yescharacteristic
474C22×C83D4211yescharacteristic
475C22×C83#54711yescharacteristic
476C22×C83#54711yescharacteristic
477C22×C83#54711yescharacteristic
478C22×C83#54811yescharacteristic
479C22×C83D4×Q811yescharacteristic
480C22×C83D4×Q811yescharacteristic
481C22×C83#55311yescharacteristic
482C22×C83#55411yescharacteristic
483C22×C83#55411yescharacteristic
484C22×C83#56011yescharacteristic
485C22×C83#56311yescharacteristic
486C22×C83#56311yescharacteristic
487C22×C83#56311yescharacteristic
488C4×C83—24no—
489C4×C83—24no—
490C4×C83—24no—
491C4×C83—24no—
492C4×C83—42no—
493C4×C83—42no—
494Dic83—42no—
495Dic83—42no—
496Dic83—42no—
497Dic83—42no—
498Dic83—81no—
499Dic83—81no—
500Dic83—81no—
501Dic83—81no—
502#14405—831nomaximal, Sylow
503C2×C83—44no—
504C2×C83#231711yescharacteristic
505C2×C83#232211yescharacteristic
506C2×C83#232611yescharacteristic
507C2×C83D4×C4⋊C411yescharacteristic
508C2×C83D4×C4⋊C411yescharacteristic
509C2×C83#236111yescharacteristic
510C2×C83#238311yescharacteristic
511C2×C83#266911yescharacteristic
512C2×C83#267411yescharacteristic
513C2×C83#267711yescharacteristic
514C2×C83#268011yescharacteristic
515C2×C83#271811yescharacteristic
516C2×C83#272011yescharacteristic
517C2×C83#272911yescharacteristic
518C2×C83#279011yescharacteristic
519C2×#389—831no—
520C2×#388—831no—
521C2×#388D8311yescharacteristic
522C2×#385—831no—
523C2×#385—831no—
524C2×#385—831no—
525C2×#384—831no—
526#1444—831no—
527#1444—831no—
528#1442—831no—
529#1441—831no—
530#1439—831no—
531#1439—831no—
532#1436—831no—
533#1434—831no—
534C83#1440511yescharacteristic, complemented, Sylow
535C24×C4—831no—
536C22×C4⋊C4—831no—
537C22×C4⋊C4—831no—
538C22×C4⋊C4—831no—
539C22×C4⋊C4—831no—
540C22×C4⋊C4—831no—
541C22×C4⋊C4—831no—
542C22×C4⋊C4—831no—
543C22×C4⋊C4—831no—
544C22×C4⋊C4—831no—
545C22×C4⋊C4C2×D8311yescharacteristic
546C22×C22⋊C4—831no—
547C22×C22⋊C4—831no—
548C22×C22⋊C4—831no—
549C22×C22⋊C4C2×D8311yescharacteristic
550C22×C22⋊C4C2×D8311yescharacteristic
551C22×C22⋊C4C2×D8311yescharacteristic
552C22×C42—831no—
553C22×C42C2×D8311yescharacteristic
554#389—1664no—
555#388—1664no—
556#388Dic8318yescomplemented
557#385—1664no—
558#385—1664no—
559#385—1664no—
560#384—1664no—
561C2×#95—831no—
562C2×#95—831no—
563C2×#95—831no—
564C2×#95—831no—
565C2×#95—831no—
566C2×#95—831no—
567C2×#95—831no—
568C2×#95—831no—
569C2×#95—831no—
570C2×#95—831no—
571C2×#95—831no—
572C2×#95—831no—
573C2×#95—831no—
574C2×#95—831no—
575C2×#95C2×D8311yescharacteristic
576C2×#95C2×D8311yescharacteristic
577C25C22×D8311yescharacteristic
578C23×C4—3321no—
579C23×C4—3321no—
580C23×C4—3321no—
581C23×C4—3321no—
582C23×C4—831no—
583C23×C4—831no—
584C23×C4—831no—
585C23×C4—831no—
586C23×C4—831no—
587C23×C4—831no—
588C23×C4—831no—
589C23×C4—831no—
590C23×C4—1662no—
591C23×C4—1662no—
592C23×C4—1662no—
593C23×C4C22×D8311yescharacteristic
594C23×C4C22×D8311yescharacteristic
595C23×C4C22×D8311yescharacteristic
596C23×C4C22×D8311yescharacteristic
597C23×C4C22×D8311yescharacteristic
598C23×C4C22×D8311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—3321no—
602C2×C4⋊C4—3321no—
603C2×C4⋊C4—3321no—
604C2×C4⋊C4—3321no—
605C2×C4⋊C4—3321no—
606C2×C4⋊C4—3321no—
607C2×C4⋊C4—3321no—
608C2×C4⋊C4—3321no—
609C2×C4⋊C4—3321no—
610C2×C4⋊C4—3321no—
611C2×C4⋊C4—3321no—
612C2×C4⋊C4—3321no—
613C2×C4⋊C4—834no—
614C2×C4⋊C4—1662no—
615C2×C4⋊C4—1662no—
616C2×C4⋊C4—1662no—
617C2×C4⋊C4—1662no—
618C2×C4⋊C4—1662no—
619C2×C4⋊C4—1662no—
620C2×C4⋊C4—1662no—
621C2×C4⋊C4—1662no—
622C2×C4⋊C4—1662no—
623C2×C4⋊C4—1662no—
624C2×C4⋊C4—1662no—
625C2×C4⋊C4—1662no—
626C2×C4⋊C4—1662no—
627C2×C4⋊C4—1662no—
628C2×C4⋊C4C2×Dic8314yescomplemented
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—3321no—
634C2×C22⋊C4—3321no—
635C2×C22⋊C4—3321no—
636C2×C22⋊C4—3321no—
637C2×C22⋊C4—1662no—
638C2×C22⋊C4—1662no—
639C2×C22⋊C4—1662no—
640C2×C22⋊C4—1662no—
641C2×C22⋊C4—1662no—
642C2×C22⋊C4Dic16614yes—
643C2×C22⋊C4D33214yes—
644C2×C22⋊C4C2×Dic8314yes—
645C2×C22⋊C4C2×Dic8314yes—
646C2×C22⋊C4C2×Dic8314yes—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—3321no—
650C2×C42—1662no—
651C2×C42—1662no—
652C2×C42C2×Dic8314yescomplemented
653#95—3321no—
654#95—3321no—
655#95—3321no—
656#95—834no—
657#95—1662no—
658#95—1662no—
659#95—1662no—
660#95—1662no—
661#95—1662no—
662#95—1662no—
663#95—1662no—
664#95—1662no—
665#95—1662no—
666#95—1662no—
667#95C2×Dic8314yescomplemented
668#95C2×Dic8314yescomplemented
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×Dic8312yes—
682C24C2×D33212yes—
683C24C2×Dic16612yes—
684C24C23×D8311yescharacteristic
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—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—3324no—
714C22×C4—3324no—
715C22×C4—3324no—
716C22×C4—3324no—
717C22×C4—3324no—
718C22×C4—3324no—
719C22×C4—3324no—
720C22×C4—832no—
721C22×C4—832no—
722C22×C4—832no—
723C22×C4—832no—
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×C4—1661no—
769C22×C4—1661no—
770C22×C4—1661no—
771C22×C4—1661no—
772C22×C4—1661no—
773C22×C4—1661no—
774C22×C4—1661no—
775C22×C4—1661no—
776C22×C4C22×Dic8312yes—
777C22×C4C22×Dic8312yes—
778C22×C4C22×Dic8312yes—
779C22×C4C22×Dic8312yes—
780C22×C4C22×Dic8312yes—
781C22×C4C22×Dic8312yes—
782C22×C4D4×D8312yes—
783C22×C4D4×D8312yes—
784C22×C4C2×D33212yes—
785C22×C4C2×D33212yes—
786C22×C4C2×Dic16612yes—
787C22×C4C2×Dic16612yes—
788C22×C4#1305058912yes—
789C22×C4#1305058912yes—
790C4⋊C4—28no—
791C4⋊C4—3324no—
792C4⋊C4—3324no—
793C4⋊C4—3324no—
794C4⋊C4—3324no—
795C4⋊C4—3324no—
796C4⋊C4—3324no—
797C4⋊C4—3324no—
798C4⋊C4—3324no—
799C4⋊C4—3324no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—3324no—
803C22⋊C4—3324no—
804C22⋊C4—3324no—
805C22⋊C4C4⋊Dic83116yescomplemented
806C42—28no—
807C42—3324no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊Dic8314yes—
843C23C23×Dic8311yescharacteristic
844C23C2×D4×D8311yescharacteristic
845C23C2×D4×D8311yescharacteristic
846C23C22×D33211yescharacteristic
847C23C22×Dic16611yescharacteristic
848C23C2×#1305058911yescharacteristic
849C23C2×#1305058911yescharacteristic
850C23#1458183811yescharacteristic
851C23#1458183811yescharacteristic
852C23#1458183811yescharacteristic
853C23#1458183811yescharacteristic
854C23#1458183911yescharacteristic
855C23#1458183911yescharacteristic
856C23#1458183911yescharacteristic
857C23#1458183911yescharacteristic
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—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—33216no—
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—3321no—
927C2×C4—3321no—
928C2×C4—3321no—
929C2×C4—3321no—
930C2×C4—3321no—
931C2×C4—3321no—
932C2×C4—3321no—
933C2×C4—3321no—
934C2×C4—3321no—
935C2×C4—3321no—
936C2×C4—3321no—
937C2×C4—3321no—
938C2×C4—3321no—
939C2×C4—3321no—
940C2×C4—3321no—
941C2×C4—1662no—
942C2×C4—1662no—
943C2×C4—1662no—
944C2×C4—1662no—
945C2×C4—1662no—
946C2×C4—1662no—
947C2×C4—1662no—
948C2×C4—1662no—
949C2×C4—1662no—
950C2×C4—1662no—
951C2×C4—1662no—
952C2×C4—1662no—
953C2×C4C2×C4⋊Dic8314yes—
954C2×C4C2×C4⋊Dic8314yes—
955C2×C4D4×Dic8314yes—
956C2×C4D4×Dic8314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊Dic8311yescharacteristic
973C22C2×D4×Dic8311yescharacteristic
974C22C2×D4×Dic8311yescharacteristic
975C22#1912818411yescharacteristic
976C22#1912818411yescharacteristic
977C22#1912818411yescharacteristic
978C22#1912818411yescharacteristic
979C22#1912826211yescharacteristic
980C22#1912826911yescharacteristic
981C22#1912827011yescharacteristic
982C22#1912827111yescharacteristic
983C22#1912827311yescharacteristic
984C22#1912827711yescharacteristic
985C22#1912829511yescharacteristic
986C22#1912829511yescharacteristic
987C22#1912832011yescharacteristic
988C22#1912832011yescharacteristic
989C22#1912832911yescharacteristic
990C22#1912832911yescharacteristic
991C22#1912833511yescharacteristic
992C22D4×D33211yescharacteristic
993C22D4×D33211yescharacteristic
994C22#1912835111yescharacteristic
995C22#1912835511yescharacteristic
996C22#1912835511yescharacteristic
997C22#1912835711yescharacteristic
998C22D4×Dic16611yescharacteristic
999C22D4×Dic16611yescharacteristic
1000C22#1912840311yescharacteristic
1001C22#1912840811yescharacteristic
1002C22#1912840811yescharacteristic
1003C22#1912844211yescharacteristic
1004C22#1912845311yescharacteristic
1005C22#1912845311yescharacteristic
1006C22#1912845311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—3322no—
1014C4—3322no—
1015C4—3322no—
1016C4—3322no—
1017C4—6641no—
1018C4—6641no—
1019C4—6641no—
1020C4—6641no—
1021C2—44no—
1022C2#2491008611yescharacteristic
1023C2#2491013511yescharacteristic
1024C2#2491017611yescharacteristic
1025C2D4×C4⋊Dic8311yescharacteristic
1026C2D4×C4⋊Dic8311yescharacteristic
1027C2#2491048311yescharacteristic
1028C2#2491065511yescharacteristic
1029C2#2491367811yescharacteristic
1030C2#2491374211yescharacteristic
1031C2#2491377511yescharacteristic
1032C2#2491380111yescharacteristic
1033C2#2491431111yescharacteristic
1034C2#2491434011yescharacteristic
1035C2#2491444611yescharacteristic
1036C2#2491523311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#388×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83#14405
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#19127600C2semidirect
6. C2×#19127571C2semidirect
7. #24905728C2semidirect
8. #24905728C2semidirect
9. #24905720C2semidirect
10. #24905716C2semidirect
13. #24905697C2semidirect
14. #24905690C2semidirect
55. #388×C83C4semidirect
135. C2×C4⋊C4×C83C2×C4semidirect
147. C2×C42×C83C2×C4semidirect
148. #95×C83C2×C4semidirect
149. #95×C83C2×C4semidirect
287. C22⋊C4×C83C4⋊C4semidirect
534. C83#14405semidirect
556. #388Dic83semidirect
628. C2×C4⋊C4C2×Dic83semidirect
652. C2×C42C2×Dic83semidirect
667. #95C2×Dic83semidirect
668. #95C2×Dic83semidirect
805. C22⋊C4C4⋊Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191276002
C2×#191275942
C2×#191275762
C2×#191275712
#249057282
#249057202
#249057162
#249057082
#249056972
#249056902
C2×#388×C832
#1440583