Finite Group Databasebeta

← C2×#24920547 #36285430

Subgroups — C2×#24920547 #36285430

Order 21248.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128436C211yesmaximal, characteristic, complemented
2#24920547C2116yesmaximal, direct product factor
3C2×#19128091C211yesmaximal, characteristic, complemented
4C2×#19128088C211yesmaximal, characteristic, complemented
5C2×#19128083C211yesmaximal, characteristic, complemented
6C2×#19127923C211yesmaximal, characteristic, complemented
7C2×#19127920C211yesmaximal, characteristic, complemented
8C2×#19127916C211yesmaximal, characteristic, complemented
9C2×#19127913C211yesmaximal, characteristic, complemented
10C2×#19127896C211yesmaximal, characteristic, complemented
11C2×#19127893C211yesmaximal, characteristic, complemented
12C2×#19127832C211yesmaximal, characteristic, complemented
13C2×#19127801C211yesmaximal, characteristic, complemented
14C2×#19127799C211yesmaximal, characteristic, complemented
15C2×C4×#13050575C211yesmaximal, characteristic, complemented
16C2×#559×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C22×#13050578C2211yescharacteristic
19C22×#13050578C2211yescharacteristic
20C22×#13050577C2211yescharacteristic
21C22×#13050577C2211yescharacteristic
22C22×#13050575C2211yescharacteristic
23C22×#13050575C2211yescharacteristic
24C22×#13050575C2211yescharacteristic
25C22×#13050575C2211yescharacteristic
26#19128436—24no—
27#19128436C2218yescomplemented
28C2×#14581789C2211yescharacteristic
29C2×#14581781—21no—
30C2×#14581780C2211yescharacteristic
31C2×#14581780C2211yescharacteristic
32C2×#14581777—21no—
33C2×#14581777—21no—
34C2×C4×Dic166C2211yescharacteristic
35C2×C4×D332C2211yescharacteristic
36C2×C4×D332C2211yescharacteristic
37C2×#14581754—21no—
38#19128091C2218yescomplemented
39#19128088C2218yescomplemented
40#19128083C2218yescomplemented
41#19127923C2218yescomplemented
42#19127920C2218yescomplemented
43#19127916C2218yescomplemented
44#19127913C2218yescomplemented
45#19127896C2218yescomplemented
46#19127893C2218yescomplemented
47#19127832C2218yescomplemented
48#19127801C2218yescomplemented
49#19127799C2218yescomplemented
50C4×#13050575C2218yescomplemented
51C2×#14581725C2211yescharacteristic
52C2×C4⋊(C83⋊C8)C2211yescharacteristic
53C2×C4⋊(C83⋊C8)C2211yescharacteristic
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×#14581716C2211yescharacteristic
56C2×#14581715C2211yescharacteristic
57C2×#14581713C2211yescharacteristic
58C2×#14581713C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×#14581703C2211yescharacteristic
62C2×#14581703C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#559×C83—24no—
65#559×C83C2218yescomplemented
66C2×#127×C83C2211yescharacteristic
67C2×#124×C83—21no—
68C2×#124×C83C2211yescharacteristic
69C2×#124×C83C2211yescharacteristic
70C2×#123×C83—21no—
71C2×#123×C83—21no—
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×Q8×C83C2211yescharacteristic
74C2×C4×D4×C83—21no—
75C2×C4×D4×C83C2211yescharacteristic
76C2×C4×D4×C83C2211yescharacteristic
77C22×Dic166C2311yescharacteristic
78C22×D332—21no—
79C22×D332—21no—
80C22×D332C2311yescharacteristic
81C22×D332C2311yescharacteristic
82C22×C4×D83—21no—
83C22×C4×D83—21no—
84C2×#13050580—42no—
85C2×#13050580C2314yes—
86C2×#13050578—24no—
87C2×#13050578—42no—
88C2×#13050578C2314yes—
89C2×#13050578C2314yes—
90C2×#13050577—24no—
91C2×#13050577—42no—
92C2×#13050577C2314yes—
93C2×#13050577C2314yes—
94C2×#13050575—24no—
95C2×#13050575—42no—
96C2×#13050575—42no—
97C2×#13050575—42no—
98C2×#13050575C2314yes—
99C2×#13050575C2314yes—
100C2×#13050575C2314yes—
101C2×#13050575C2314yes—
102C22×C83⋊C8C2311yescharacteristic
103C22×C83⋊C8C2311yescharacteristic
104C22×C83⋊C8C2311yescharacteristic
105C22×C83⋊C8C2311yescharacteristic
106#14581789—22no—
107#14581789C2314yes—
108#14581781—28no—
109#14581780—22no—
110#14581780—22no—
111#14581780C2314yes—
112#14581780C2314yes—
113#14581777—28no—
114#14581777—28no—
115C4×Dic166—22no—
116C4×Dic166C2314yes—
117C4×D332—22no—
118C4×D332—22no—
119C4×D332C2314yes—
120C4×D332C2314yes—
121#14581754—28no—
122C2×C4⋊Dic83C2311yescharacteristic
123C2×Dic83⋊C4—21no—
124C2×(C2×D83)⋊C4—21no—
125C2×(C2×D83)⋊C4—21no—
126C2×(C2×D83)⋊C4—21no—
127C2×(C2×D83)⋊C4—21no—
128C2×(C2×D83)⋊C4—21no—
129C2×(C2×D83)⋊C4—21no—
130C2×C4×Dic83—21no—
131#14581725C2314yes—
132C4⋊(C83⋊C8)C2314yes—
133C4⋊(C83⋊C8)C2314yes—
134C4⋊(C83⋊C8)C2314yes—
135#14581716C2314yes—
136#14581715C2314yes—
137#14581713C2314yes—
138#14581713C2314yes—
139#14581712C2314yes—
140#14581712C2314yes—
141#14581703C2314yes—
142#14581703C2314yes—
143C4×C83⋊C8C2314yes—
144C22×Q8×C83D411yescharacteristic
145C22×Q8×C83C2311yescharacteristic
146C22×D4×C83—21no—
147C22×D4×C83—21no—
148C22×D4×C83C2311yescharacteristic
149C22×D4×C83C2311yescharacteristic
150C23×C4×C83—21no—
151C23×C4×C83—21no—
152#127×C83—22no—
153#127×C83C2314yes—
154#124×C83—28no—
155#124×C83—22no—
156#124×C83—22no—
157#124×C83C2314yes—
158#124×C83C2314yes—
159#123×C83—28no—
160#123×C83—28no—
161C4×Q8×C83—22no—
162C4×Q8×C83D414yes—
163C4×Q8×C83C2314yes—
164C4×Q8×C83C2314yes—
165C4×D4×C83—28no—
166C4×D4×C83—22no—
167C4×D4×C83—22no—
168C4×D4×C83C2314yes—
169C4×D4×C83C2314yes—
170C2×C4⋊C4×C83—21no—
171C2×C4⋊C4×C83D411yescharacteristic
172C2×C4⋊C4×C83D411yescharacteristic
173C2×C4⋊C4×C83D411yescharacteristic
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83—21no—
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83—21no—
179C2×C22⋊C4×C83—21no—
180C2×C22⋊C4×C83—21no—
181C2×C42×C83—21no—
182C2×C42×C83C2311yescharacteristic
183C2×C42×C83C2311yescharacteristic
184C2×C42×C83C2311yescharacteristic
185C23×D83—21no—
186C23×D83—21no—
187C2×Dic166—22no—
188C2×Dic166—22no—
189C2×Dic166—21no—
190C2×Dic166C2412yes—
191C2×D332—22no—
192C2×D332—22no—
193C2×D332—22no—
194C2×D332—22no—
195C2×D332—21no—
196C2×D332—21no—
197C2×D332—24no—
198C2×D332—24no—
199C2×D332—44no—
200C2×D332—82no—
201C2×D332C2412yes—
202C2×D332C2412yes—
203C22×Dic83—21no—
204C22×Dic83—21no—
205C2×C4×D83—24no—
206C2×C4×D83—24no—
207C2×C4×D83—82no—
208C2×C4×D83—82no—
209#13050580—44no—
210#13050578—28no—
211#13050578—44no—
212#13050577—28no—
213#13050577—44no—
214#13050575—28no—
215#13050575—44no—
216#13050575—44no—
217#13050575—44no—
218C2×C83⋊C8—22no—
219C2×C83⋊C8—22no—
220C2×C83⋊C8—22no—
221C2×C83⋊C8#4114yes—
222C2×C83⋊C8C2412yes—
223C2×C83⋊C8C2412yes—
224C2×C83⋊C8C2412yes—
225C2×C83⋊C8C2412yes—
226C4⋊Dic83—21no—
227C4⋊Dic83C2412yes—
228Dic83⋊C4—24no—
229(C2×D83)⋊C4—24no—
230(C2×D83)⋊C4—24no—
231(C2×D83)⋊C4—24no—
232(C2×D83)⋊C4—24no—
233(C2×D83)⋊C4—24no—
234(C2×D83)⋊C4—24no—
235C4×Dic83—24no—
236C24×C83—21no—
237C24×C83—21no—
238C2×Q8×C83—21no—
239C2×Q8×C83—22no—
240C2×Q8×C83—22no—
241C2×Q8×C83—42no—
242C2×Q8×C83C2×D414yes—
243C2×Q8×C83C2412yes—
244C2×D4×C83—21no—
245C2×D4×C83—21no—
246C2×D4×C83—24no—
247C2×D4×C83—24no—
248C2×D4×C83—22no—
249C2×D4×C83—22no—
250C2×D4×C83—22no—
251C2×D4×C83—22no—
252C2×D4×C83—44no—
253C2×D4×C83—82no—
254C2×D4×C83C2412yes—
255C2×D4×C83C2412yes—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—24no—
259C22×C4×C83—24no—
260C22×C4×C83—82no—
261C22×C4×C83—82no—
262C22×C4×C83C2×D411yescharacteristic
263C22×C4×C83C2×D411yescharacteristic
264C22×C4×C83C2×D411yescharacteristic
265C22×C4×C83C2×D411yescharacteristic
266C22×C4×C83C2×D411yescharacteristic
267C22×C4×C83C2×D411yescharacteristic
268C22×C4×C83C2411yescharacteristic
269C4⋊C4×C83—24no—
270C4⋊C4×C83—21no—
271C4⋊C4×C83C2×D414yes—
272C4⋊C4×C83C2×D414yes—
273C4⋊C4×C83C2×D414yes—
274C4⋊C4×C83C2412yes—
275C22⋊C4×C83—24no—
276C22⋊C4×C83—24no—
277C22⋊C4×C83—24no—
278C22⋊C4×C83—24no—
279C22⋊C4×C83—24no—
280C22⋊C4×C83—24no—
281C42×C83—24no—
282C42×C83C2×D412yes—
283C42×C83C2×D412yes—
284C42×C83C2×D412yes—
285C42×C83C2412yes—
286C42×C83C2412yes—
287C42×C83C2412yes—
288C23×C83—22no—
289C23×C83—22no—
290C23×C83—42no—
291C23×C83—42no—
292C23×C83—42no—
293C23×C83—42no—
294C23×C83—42no—
295C23×C83—42no—
296C23×C83C22×D411yescharacteristic
297C22×D83—22no—
298C22×D83—22no—
299C22×D83—42no—
300C22×D83—42no—
301C22×D83—42no—
302C22×D83—42no—
303C22×D83—42no—
304C22×D83—42no—
305Q8×C83—22no—
306Q8×C83—22no—
307Q8×C83—44no—
308Q8×C83—42no—
309D4×C83—22no—
310D4×C83—22no—
311D4×C83—22no—
312D4×C83—22no—
313D4×C83—48no—
314D4×C83—42no—
315D4×C83—42no—
316D4×C83—84no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—42no—
326C2×C4×C83—42no—
327C2×C4×C83—84no—
328C2×C4×C83—84no—
329C2×C4×C83C22×D412yes—
330C2×C4×C83C22×D412yes—
331C2×C4×C83C22×D412yes—
332C2×C4×C83C22×D412yes—
333C2×C4×C83C22×D412yes—
334C2×C4×C83C22×D412yes—
335C2×C4×C83C22×D411yescharacteristic
336C2×C4×C83C2×#4112yes—
337C2×C4×C83H(5,𝔽2)12yes—
338C2×C4×C83C2511yescharacteristic
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—42no—
342C2×Dic83—42no—
343D332—22no—
344D332—22no—
345D332—22no—
346D332—22no—
347D332—48no—
348D332—42no—
349D332—42no—
350D332—84no—
351C4×D83—84no—
352C4×D83—84no—
353Dic166—22no—
354Dic166—22no—
355Dic166—42no—
356C83⋊C8—22no—
357C83⋊C8—22no—
358C83⋊C8—22no—
359C83⋊C8C2×#4114yes—
360C22×C83—42no—
361C22×C83—42no—
362C22×C83—42no—
363C22×C83—42no—
364C22×C83—42no—
365C22×C83—42no—
366C22×C83—84no—
367C22×C83—84no—
368C22×C83#55012yes—
369C22×C83#57512yes—
370C22×C83#57612yes—
371C22×C83C23×D411yescharacteristic
372C2×D83—42no—
373C2×D83—42no—
374C2×D83—42no—
375C2×D83—42no—
376C2×D83—42no—
377C2×D83—42no—
378C2×D83—84no—
379C2×D83—84no—
380C4×C83—22no—
381C4×C83—22no—
382C4×C83—22no—
383C4×C83—22no—
384C4×C83—22no—
385C4×C83—22no—
386C4×C83—42no—
387C4×C83—42no—
388C4×C83#55012yes—
389C4×C83C22×#4111yescharacteristic
390C4×C83C2×H(5,𝔽2)11yescharacteristic
391Dic83—42no—
392Dic83—42no—
393C2×#3403—831nomaximal, Sylow
394C2×C83—82no—
395C2×C83—82no—
396C2×C83#340314yescomplemented
397C2×C83C2×#55011yescharacteristic
398C2×C83C2×#57511yescharacteristic
399C2×C83C2×#57611yescharacteristic
400D83—82no—
401D83—82no—
402C2×#559—831no—
403C2×#559D8311yescharacteristic, complemented
404#3403—8316no—
405C2×#496—831no—
406C2×#496—831no—
407C2×#495—831no—
408C2×#464—831no—
409C2×#464—831no—
410C2×#463—831no—
411C2×#463—831no—
412C2×#459—831no—
413C2×#459—831no—
414C2×#446—831no—
415C2×#440—831no—
416C2×#440—831no—
417C2×C4×D8—831no—
418C83C2×#340311yescharacteristic, complemented, Sylow
419C22×Q16—831no—
420C22×SD16—831no—
421C22×SD16—831no—
422C22×SD16—831no—
423C22×SD16—831no—
424C22×D8—831no—
425C22×D8—831no—
426C22×D8—831no—
427C22×D8—831no—
428#559—24no—
429#559—838no—
430#559—1664no—
431#559C2×D8318yescomplemented
432C2×#127—831no—
433C2×#127C2×D8311yescharacteristic
434C2×#124—21no—
435C2×#124—831no—
436C2×#124—831no—
437C2×#124—1661no—
438C2×#124C2×D8311yescharacteristic
439C2×#124C2×D8311yescharacteristic
440C2×#123—21no—
441C2×#123—21no—
442C2×#123—1661no—
443C2×#123—1661no—
444C2×C4×Q8—831no—
445C2×C4×Q8C2×D8311yescharacteristic
446C2×C4×Q8C2×D8311yescharacteristic
447C2×C4×D4—21no—
448C2×C4×D4—831no—
449C2×C4×D4—831no—
450C2×C4×D4—1661no—
451C2×C4×D4C2×D8311yescharacteristic
452C2×C4×D4C2×D8311yescharacteristic
453#496—838no—
454#496—838no—
455#495—838no—
456#464—838no—
457#464—838no—
458#463—838no—
459#463—838no—
460#459—838no—
461#459—838no—
462#446—838no—
463#440—838no—
464#440—838no—
465C4×D8—838no—
466C2×#107—831no—
467C2×C4⋊C8—831no—
468C2×C4⋊C8—831no—
469C2×C4⋊C8—831no—
470C2×#103—831no—
471C2×#103—831no—
472C2×#102—831no—
473C2×#102—831no—
474C2×#102—831no—
475C2×#102—831no—
476C2×#97—831no—
477C2×#97—831no—
478C2×C4×C8—831no—
479C22×Q8—831no—
480C22×Q8C22⋊D8311yescharacteristic
481C22×Q8C22×D8311yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—831no—
485C22×D4—831no—
486C22×D4—1661no—
487C22×D4—1661no—
488C22×D4C22×D8311yescharacteristic
489C22×D4C22×D8311yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—1661no—
493C23×C4—1661no—
494C2×Q16—3322no—
495C2×Q16—834no—
496C2×SD16—3322no—
497C2×SD16—3322no—
498C2×SD16—834no—
499C2×SD16—834no—
500C2×SD16—834no—
501C2×SD16—834no—
502C2×SD16—1664no—
503C2×SD16—1664no—
504C2×D8—3322no—
505C2×D8—3322no—
506C2×D8—3322no—
507C2×D8—834no—
508C2×D8—834no—
509C2×D8—834no—
510C2×D8—834no—
511C2×D8—1664no—
512C22×C8—831no—
513C22×C8—831no—
514C22×C8—831no—
515C22×C8—831no—
516#127—22no—
517#127—834no—
518#127—1662no—
519#127C22×D8314yes—
520#124—28no—
521#124—22no—
522#124—22no—
523#124—834no—
524#124—834no—
525#124—1668no—
526#124—1662no—
527#124—1662no—
528#124C22×D8314yes—
529#124C22×D8314yes—
530#123—28no—
531#123—28no—
532#123—1668no—
533#123—1668no—
534C4×Q8—22no—
535C4×Q8—834no—
536C4×Q8—1662no—
537C4×Q8C22⋊D8314yes—
538C4×Q8C22×D8314yes—
539C4×Q8C22×D8314yes—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—834no—
544C4×D4—834no—
545C4×D4—1668no—
546C4×D4—1662no—
547C4×D4—1662no—
548C4×D4C22×D8314yes—
549C4×D4C22×D8314yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—831no—
552C2×C4⋊C4—1661no—
553C2×C4⋊C4C22⋊D8311yescharacteristic
554C2×C4⋊C4C22⋊D8311yescharacteristic
555C2×C4⋊C4C22⋊D8311yescharacteristic
556C2×C4⋊C4C22×D8311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—1661no—
564C2×C22⋊C4—1661no—
565C2×C22⋊C4—1661no—
566C2×C22⋊C4—1661no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4—1661no—
569C2×C42—21no—
570C2×C42—1661no—
571C2×C42C22×D8311yescharacteristic
572C2×C42C22×D8311yescharacteristic
573C2×C42C22×D8311yescharacteristic
574#107—834no—
575C4⋊C8—834no—
576C4⋊C8—834no—
577C4⋊C8—834no—
578#103—834no—
579#103—834no—
580#102—834no—
581#102—834no—
582#102—834no—
583#102—834no—
584#97—834no—
585#97—834no—
586C4×C8—834no—
587C24—21no—
588C24—21no—
589C24—1661no—
590C24—1661no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—42no—
595C2×Q8—832no—
596C2×Q8—1662no—
597C2×Q8—1662no—
598C2×Q8—1661no—
599C2×Q8C2×C22⋊D8314yes—
600C2×Q8C23×D8312yes—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—24no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—44no—
610C2×D4—82no—
611C2×D4—3324no—
612C2×D4—832no—
613C2×D4—832no—
614C2×D4—6642no—
615C2×D4—1664no—
616C2×D4—1661no—
617C2×D4—1661no—
618C2×D4—1664no—
619C2×D4—1662no—
620C2×D4—1662no—
621C2×D4—1662no—
622C2×D4—1662no—
623C2×D4C23×D8312yes—
624C2×D4C23×D8312yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—82no—
630C22×C4—82no—
631C22×C4—6642no—
632C22×C4—6642no—
633C22×C4—1661no—
634C22×C4—1661no—
635C22×C4—1664no—
636C22×C4—1664no—
637C22×C4C2×C22⋊D8311yescharacteristic
638C22×C4C2×C22⋊D8311yescharacteristic
639C22×C4C2×C22⋊D8311yescharacteristic
640C22×C4C2×C22⋊D8311yescharacteristic
641C22×C4C2×C22⋊D8311yescharacteristic
642C22×C4C2×C22⋊D8311yescharacteristic
643C22×C4C23×D8311yescharacteristic
644Q16—3324no—
645SD16—3324no—
646SD16—3324no—
647SD16—1668no—
648SD16—1668no—
649D8—3324no—
650D8—3324no—
651D8—3324no—
652D8—1668no—
653C2×C8—834no—
654C2×C8—832no—
655C2×C8—832no—
656C2×C8—832no—
657C2×C8—832no—
658C2×C8—1662no—
659C2×C8—1662no—
660C2×C8—1662no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—832no—
664C4⋊C4—1661no—
665C4⋊C4—1664no—
666C4⋊C4C2×C22⋊D8314yes—
667C4⋊C4C2×C22⋊D8314yes—
668C4⋊C4C2×C22⋊D8314yes—
669C4⋊C4C23×D8312yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—1664no—
677C22⋊C4—1664no—
678C22⋊C4—1664no—
679C22⋊C4—1664no—
680C22⋊C4—1664no—
681C22⋊C4—1664no—
682C42—24no—
683C42—1664no—
684C42C2×C22⋊D8312yes—
685C42C2×C22⋊D8312yes—
686C42C2×C22⋊D8312yes—
687C42C23×D8312yes—
688C42C23×D8312yes—
689C42C23×D8312yes—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—3322no—
699C23—3322no—
700C23—3322no—
701C23—3322no—
702C23—3322no—
703C23—3322no—
704C23—1662no—
705C23—1662no—
706C23C22×C22⋊D8311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—3322no—
712Q8—1662no—
713Q8—1662no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—3328no—
723D4—3322no—
724D4—3322no—
725D4—6644no—
726D4—1662no—
727D4—1662no—
728D4—1662no—
729D4—1662no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—3322no—
743C2×C4—3322no—
744C2×C4—6644no—
745C2×C4—6644no—
746C2×C4—1662no—
747C2×C4—1662no—
748C2×C4C22×C22⋊D8312yes—
749C2×C4C22×C22⋊D8312yes—
750C2×C4C22×C22⋊D8312yes—
751C2×C4C22×C22⋊D8312yes—
752C2×C4C22×C22⋊D8312yes—
753C2×C4C22×C22⋊D8312yes—
754C2×C4C22×C22⋊D8311yescharacteristic
755C2×C4#41×D8312yes—
756C2×C4#1458183812yes—
757C2×C4C24×D8311yescharacteristic
758C8—834no—
759C8—1662no—
760C8—1662no—
761C8—1662no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—3322no—
771C22—3322no—
772C22—3322no—
773C22—3322no—
774C22—3322no—
775C22—3322no—
776C22—6644no—
777C22—6644no—
778C22#1912837012yes—
779C22#1912849912yes—
780C22#1912850412yes—
781C22C23×C22⋊D8311yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—3322no—
791C4—3322no—
792C4#1912837012yes—
793C4C2×#41×D8311yescharacteristic
794C4C2×#1458183811yescharacteristic
795C2—82no—
796C2—82no—
797C2—6642no—
798C2—6642no—
799C2#2492054714yesdirect product factor
800C2C2×#1912837011yescharacteristic
801C2C2×#1912849911yescharacteristic
802C2C2×#1912850411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#559×C83C2
socleC23×C83C22×D4
hypercenterC2×#559D83
hypocenterC83C2×#3403
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#19128436C2semidirect
2. #24920547C2direct (N × H)
3. C2×#19128091C2semidirect
4. C2×#19128088C2semidirect
5. C2×#19128083C2semidirect
6. C2×#19127923C2semidirect
7. C2×#19127920C2semidirect
8. C2×#19127916C2semidirect
9. C2×#19127913C2semidirect
10. C2×#19127896C2semidirect
11. C2×#19127893C2semidirect
12. C2×#19127832C2semidirect
13. C2×#19127801C2semidirect
14. C2×#19127799C2semidirect
15. C2×C4×#13050575C2semidirect
16. C2×#559×C83C2semidirect
27. #19128436C22semidirect
38. #19128091C22semidirect
39. #19128088C22semidirect
40. #19128083C22semidirect
41. #19127923C22semidirect
42. #19127920C22semidirect
43. #19127916C22semidirect
44. #19127913C22semidirect
45. #19127896C22semidirect
46. #19127893C22semidirect
47. #19127832C22semidirect
48. #19127801C22semidirect
49. #19127799C22semidirect
50. C4×#13050575C22semidirect
65. #559×C83C22semidirect
396. C2×C83#3403semidirect
403. C2×#559D83semidirect
418. C83C2×#3403semidirect
431. #559C2×D83semidirect
799. C2#24920547direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284362
#249205472
C2×#191280912
C2×#191280882
C2×#191280832
C2×#191279232
C2×#191279202
C2×#191279162
C2×#191279132
C2×#191278962
C2×#191278932
C2×#191278322
C2×#191278012
C2×#191277992
C2×C4×#130505752
C2×#559×C832
C2×#340383