Finite Group Databasebeta

← C2×#24920210 #36284147

Subgroups — C2×#24920210 #36284147

Order 21248.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128411C211yesmaximal, characteristic, complemented
2#24920210C2116yesmaximal, direct product factor
3C2×#19128065C211yesmaximal, characteristic, complemented
4C2×#19128060C211yesmaximal, characteristic, complemented
5C2×#19128055C211yesmaximal, characteristic, complemented
6C2×#19128008C211yesmaximal, characteristic, complemented
7C2×#19128001C211yesmaximal, characteristic, complemented
8C2×#19127981C211yesmaximal, characteristic, complemented
9C2×#19127913C211yesmaximal, characteristic, complemented
10C2×#19127913C211yesmaximal, characteristic, complemented
11C2×#19127893C211yesmaximal, characteristic
12C2×#19127832C211yesmaximal, characteristic, complemented
13C2×#19127811C211yesmaximal, characteristic, complemented
14C2×#19127799C211yesmaximal, characteristic, complemented
15C2×C4×#13050575C211yesmaximal, characteristic, complemented
16C2×#559×C83C211yesmaximal, characteristic, complemented
17C22×#13050577C2211yescharacteristic
18C22×#13050575C2211yescharacteristic
19C22×#13050575C2211yescharacteristic
20#19128411—24no—
21#19128411C2218yescomplemented
22C2×#14581792C2211yescharacteristic
23C2×#14581784C2211yescharacteristic
24C2×#14581784C2211yescharacteristic
25C2×#14581770—21no—
26C2×#14581770—21no—
27C2×#14581768—21no—
28C2×C4×D332C2211yescharacteristic
29C2×C4×D332C2211yescharacteristic
30C2×C4×D332C2211yescharacteristic
31C2×C4⋊C4×D83—21no—
32#19128065C2218yescomplemented
33#19128060C2218yescomplemented
34#19128055C2218yescomplemented
35#19128008C2218yescomplemented
36#19128001C2218yescomplemented
37#19127981C2218yescomplemented
38#19127913C2218yescomplemented
39#19127913C2218yescomplemented
40#19127893C2218yes—
41#19127832C2218yescomplemented
42#19127811C2218yescomplemented
43#19127799C2218yescomplemented
44C4×#13050575C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49C2×C4⋊(C83⋊C8)C2211yescharacteristic
50C2×C4⋊(C83⋊C8)C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581716C2211yescharacteristic
54C2×#14581713C2211yescharacteristic
55C2×#14581713C2211yescharacteristic
56C2×#14581713C2211yescharacteristic
57C2×#14581713C2211yescharacteristic
58C2×#14581713C2211yescharacteristic
59C2×#14581713C2211yescharacteristic
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×Dic166—21no—
78C22×D332C2311yescharacteristic
79C22×C4×D83—21no—
80C22×C4×D83—21no—
81C22×C4×D83—21no—
82C2×#13050577—24no—
83C2×#13050577C2314yes—
84C2×#13050575—24no—
85C2×#13050575—24no—
86C2×#13050575C2314yes—
87C2×#13050575C2314yes—
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90C22×C83⋊C8C2311yescharacteristic
91C22×C83⋊C8C2311yescharacteristic
92#14581792—22no—
93#14581792C2314yes—
94#14581784—22no—
95#14581784—22no—
96#14581784C2314yes—
97#14581784C2314yes—
98#14581770—28no—
99#14581770—28no—
100#14581768—28no—
101C4×D332—22no—
102C4×D332—22no—
103C4×D332—22no—
104C4×D332C2314yes—
105C4×D332C2314yes—
106C4×D332C2314yes—
107C2×C4⋊Dic83—21no—
108C2×C4⋊Dic83C2311yescharacteristic
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2311yescharacteristic
111C2×Dic83⋊C4—21no—
112C2×Dic83⋊C4—21no—
113C2×Dic83⋊C4—21no—
114C2×Dic83⋊C4—21no—
115C4⋊C4×D83—28no—
116C2×(C2×D83)⋊C4—21no—
117C2×(C2×D83)⋊C4—21no—
118C2×(C2×D83)⋊C4—21no—
119#14581725C2314yes—
120#14581725C2314yes—
121#14581723C2314yes—
122C4⋊(C83⋊C8)C2314yes—
123C4⋊(C83⋊C8)C2314yes—
124C4⋊(C83⋊C8)C2314yes—
125#14581716C2314yes—
126#14581716C2314yes—
127#14581716C2314yes—
128#14581713C2314yes—
129#14581713C2314yes—
130#14581713C2314yes—
131#14581713C2314yes—
132#14581713C2314yes—
133#14581713C2314yes—
134#14581712C2314yes—
135#14581703C2314yes—
136#14581703C2314yes—
137C4×C83⋊C8C2314yes—
138C22×Q8×C83D411yescharacteristic
139C22×Q8×C83C2311yescharacteristic
140C22×D4×C83—21no—
141C22×D4×C83—21no—
142C22×D4×C83C2311yescharacteristic
143C22×D4×C83C2311yescharacteristic
144C23×C4×C83—21no—
145C23×C4×C83—21no—
146#127×C83—22no—
147#127×C83C2314yes—
148#124×C83—28no—
149#124×C83—22no—
150#124×C83—22no—
151#124×C83C2314yes—
152#124×C83C2314yes—
153#123×C83—28no—
154#123×C83—28no—
155C4×Q8×C83—22no—
156C4×Q8×C83D414yes—
157C4×Q8×C83C2314yes—
158C4×Q8×C83C2314yes—
159C4×D4×C83—28no—
160C4×D4×C83—22no—
161C4×D4×C83—22no—
162C4×D4×C83C2314yes—
163C4×D4×C83C2314yes—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83D411yescharacteristic
166C2×C4⋊C4×C83D411yescharacteristic
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C22⋊C4×C83—21no—
170C2×C22⋊C4×C83—21no—
171C2×C22⋊C4×C83—21no—
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83—21no—
175C2×C42×C83—21no—
176C2×C42×C83C2311yescharacteristic
177C2×C42×C83C2311yescharacteristic
178C2×C42×C83C2311yescharacteristic
179C23×D83—21no—
180C2×Dic166—24no—
181C2×Dic166—82no—
182C2×D332—21no—
183C2×D332—22no—
184C2×D332#4114yes—
185C2×D332C2412yes—
186C22×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189C2×C4×D83—24no—
190C2×C4×D83—24no—
191C2×C4×D83—24no—
192C2×C4×D83—44no—
193C2×C4×D83—82no—
194C2×C4×D83—82no—
195#13050577—28no—
196#13050575—28no—
197#13050575—28no—
198C2×C83⋊C8—22no—
199C2×C83⋊C8—22no—
200C2×C83⋊C8—22no—
201C2×C83⋊C8—22no—
202C2×C83⋊C8C2412yes—
203C2×C83⋊C8C2412yes—
204C2×C83⋊C8C2412yes—
205C2×C83⋊C8C2412yes—
206C4⋊Dic83—24no—
207C4⋊Dic83—21no—
208C4⋊Dic83—21no—
209C4⋊Dic83—21no—
210C4⋊Dic83C2412yes—
211C4⋊Dic83C2412yes—
212C4⋊Dic83C2412yes—
213Dic83⋊C4—24no—
214Dic83⋊C4—24no—
215Dic83⋊C4—24no—
216Dic83⋊C4—24no—
217(C2×D83)⋊C4—24no—
218(C2×D83)⋊C4—24no—
219(C2×D83)⋊C4—24no—
220C24×C83—21no—
221C24×C83—21no—
222C2×Q8×C83—21no—
223C2×Q8×C83—22no—
224C2×Q8×C83—22no—
225C2×Q8×C83—42no—
226C2×Q8×C83C2×D414yes—
227C2×Q8×C83C2412yes—
228C2×D4×C83—21no—
229C2×D4×C83—21no—
230C2×D4×C83—24no—
231C2×D4×C83—24no—
232C2×D4×C83—22no—
233C2×D4×C83—22no—
234C2×D4×C83—22no—
235C2×D4×C83—22no—
236C2×D4×C83—44no—
237C2×D4×C83—82no—
238C2×D4×C83C2412yes—
239C2×D4×C83C2412yes—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—24no—
243C22×C4×C83—24no—
244C22×C4×C83—82no—
245C22×C4×C83—82no—
246C22×C4×C83C2×D411yescharacteristic
247C22×C4×C83C2×D411yescharacteristic
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2411yescharacteristic
253C4⋊C4×C83—24no—
254C4⋊C4×C83—21no—
255C4⋊C4×C83C2×D414yes—
256C4⋊C4×C83C2×D414yes—
257C4⋊C4×C83C2×D414yes—
258C4⋊C4×C83C2412yes—
259C22⋊C4×C83—24no—
260C22⋊C4×C83—24no—
261C22⋊C4×C83—24no—
262C22⋊C4×C83—24no—
263C22⋊C4×C83—24no—
264C22⋊C4×C83—24no—
265C42×C83—24no—
266C42×C83C2×D412yes—
267C42×C83C2×D412yes—
268C42×C83C2×D412yes—
269C42×C83C2412yes—
270C42×C83C2412yes—
271C42×C83C2412yes—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—42no—
275C23×C83—42no—
276C23×C83—42no—
277C23×C83—42no—
278C23×C83—42no—
279C23×C83—42no—
280C23×C83C22×D411yescharacteristic
281C22×D83—24no—
282C22×D83—22no—
283C22×D83—42no—
284C22×D83—42no—
285Q8×C83—22no—
286Q8×C83—22no—
287Q8×C83—44no—
288Q8×C83—42no—
289D4×C83—22no—
290D4×C83—22no—
291D4×C83—22no—
292D4×C83—22no—
293D4×C83—48no—
294D4×C83—42no—
295D4×C83—42no—
296D4×C83—84no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—42no—
306C2×C4×C83—42no—
307C2×C4×C83—84no—
308C2×C4×C83—84no—
309C2×C4×C83C22×D412yes—
310C2×C4×C83C22×D412yes—
311C2×C4×C83C22×D412yes—
312C2×C4×C83C22×D412yes—
313C2×C4×C83C22×D412yes—
314C2×C4×C83C22×D412yes—
315C2×C4×C83C22×D411yescharacteristic
316C2×C4×C83C2×#4112yes—
317C2×C4×C832−1+412yes—
318C2×C4×C83C2511yescharacteristic
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—42no—
323C2×Dic83—42no—
324C2×Dic83—42no—
325D332—24no—
326D332—22no—
327D332C2×#4114yes—
328C4×D83—48no—
329C4×D83—84no—
330C4×D83—84no—
331Dic166—84no—
332C83⋊C8—22no—
333C83⋊C8—22no—
334C83⋊C8—22no—
335C83⋊C8—22no—
336C22×C83—42no—
337C22×C83—42no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83—84no—
343C22×C83—84no—
344C22×C83#54812yes—
345C22×C83#57512yes—
346C22×C83#57612yes—
347C22×C83C23×D411yescharacteristic
348C2×D83—24no—
349C2×D83—48no—
350C2×D83—42no—
351C2×D83—42no—
352C4×C83—22no—
353C4×C83—22no—
354C4×C83—22no—
355C4×C83—22no—
356C4×C83—22no—
357C4×C83—22no—
358C4×C83—42no—
359C4×C83—42no—
360C4×C83#54812yes—
361C4×C83C22×#4111yescharacteristic
362C4×C83C2×2−1+411yescharacteristic
363Dic83—42no—
364Dic83—42no—
365Dic83—42no—
366C2×#3370—831nomaximal, Sylow
367C2×C83—82no—
368C2×C83—82no—
369C2×C83#337014yescomplemented
370C2×C83C2×#54811yescharacteristic
371C2×C83C2×#57511yescharacteristic
372C2×C83C2×#57611yescharacteristic
373D83—44no—
374C2×#559D8311yescharacteristic, complemented
375C2×#554—831no—
376#3370—8316no—
377C2×#490—831no—
378C2×#489—831no—
379C2×#488—831no—
380C2×#479—831no—
381C2×#478—831no—
382C2×#474—831no—
383C2×#463—831no—
384C2×#463—831no—
385C2×#459—831no—
386C2×#446—831no—
387C2×#442—831no—
388C2×#440—831no—
389C2×C4×D8—831no—
390C83C2×#337011yescharacteristic, complemented, Sylow
391C22×SD16—831no—
392C22×D8—831no—
393C22×D8—831no—
394#559—24no—
395#559C2×D8318yescomplemented
396#554—838no—
397#554—1664no—
398C2×C4⋊Q8—831no—
399C2×#127C2×D8311yescharacteristic
400C2×#125—831no—
401C2×#125—831no—
402C2×#124—21no—
403C2×#124C2×D8311yescharacteristic
404C2×#124C2×D8311yescharacteristic
405C2×#123—21no—
406C2×#123—21no—
407C2×C22⋊Q8—1661no—
408C2×C22⋊Q8—1661no—
409C2×C22⋊Q8—1661no—
410C2×C4×Q8C2×D8311yescharacteristic
411C2×C4×Q8C2×D8311yescharacteristic
412C2×C4×D4—21no—
413C2×C4×D4—831no—
414C2×C4×D4—831no—
415C2×C4×D4—831no—
416C2×C4×D4C2×D8311yescharacteristic
417C2×C4×D4C2×D8311yescharacteristic
418C22×C4⋊C4—1661no—
419#490—838no—
420#489—838no—
421#488—838no—
422#479—838no—
423#478—838no—
424#474—838no—
425#463—838no—
426#463—838no—
427#459—838no—
428#446—838no—
429#442—838no—
430#440—838no—
431C4×D8—838no—
432C2×#107—831no—
433C2×#107—831no—
434C2×#106—831no—
435C2×C4⋊C8—831no—
436C2×C4⋊C8—831no—
437C2×C4⋊C8—831no—
438C2×#103—831no—
439C2×#103—831no—
440C2×#103—831no—
441C2×#102—831no—
442C2×#102—831no—
443C2×#102—831no—
444C2×#102—831no—
445C2×#102—831no—
446C2×#102—831no—
447C2×#102—831no—
448C2×#97—831no—
449C2×#97—831no—
450C2×C4×C8—831no—
451C22×Q8—1661no—
452C22×Q8C22⋊D8311yescharacteristic
453C22×Q8C22×D8311yescharacteristic
454C22×D4—21no—
455C22×D4—21no—
456C22×D4—831no—
457C22×D4C22×D8311yescharacteristic
458C22×D4C22×D8311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—1661no—
462C23×C4—1661no—
463C23×C4—1661no—
464C2×SD16—834no—
465C2×SD16—1664no—
466C2×D8—834no—
467C2×D8—834no—
468C2×D8—1664no—
469C2×D8—1664no—
470C22×C8—831no—
471C22×C8—831no—
472C22×C8—831no—
473C22×C8—831no—
474C4⋊Q8—834no—
475C4⋊Q8—1662no—
476#127—22no—
477#127C22×D8314yes—
478#125—834no—
479#125—834no—
480#125—1662no—
481#125—1662no—
482#124—28no—
483#124—22no—
484#124—22no—
485#124C22×D8314yes—
486#124C22×D8314yes—
487#123—28no—
488#123—28no—
489C22⋊Q8—1668no—
490C22⋊Q8—1668no—
491C22⋊Q8—1668no—
492C4×Q8—22no—
493C4×Q8C22⋊D8314yes—
494C4×Q8C22×D8314yes—
495C4×Q8C22×D8314yes—
496C4×D4—28no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—834no—
500C4×D4—834no—
501C4×D4—834no—
502C4×D4—1662no—
503C4×D4—1662no—
504C4×D4—1662no—
505C4×D4C22×D8314yes—
506C4×D4C22×D8314yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—831no—
510C2×C4⋊C4—831no—
511C2×C4⋊C4—1661no—
512C2×C4⋊C4—1661no—
513C2×C4⋊C4—1661no—
514C2×C4⋊C4—1661no—
515C2×C4⋊C4—1661no—
516C2×C4⋊C4—1668no—
517C2×C4⋊C4C22⋊D8311yescharacteristic
518C2×C4⋊C4C22⋊D8311yescharacteristic
519C2×C4⋊C4C22⋊D8311yescharacteristic
520C2×C4⋊C4C22×D8311yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1661no—
528C2×C22⋊C4—1661no—
529C2×C22⋊C4—1661no—
530C2×C42—21no—
531C2×C42C22×D8311yescharacteristic
532C2×C42C22×D8311yescharacteristic
533C2×C42C22×D8311yescharacteristic
534#107—834no—
535#107—834no—
536#106—834no—
537C4⋊C8—834no—
538C4⋊C8—834no—
539C4⋊C8—834no—
540#103—834no—
541#103—834no—
542#103—834no—
543#102—834no—
544#102—834no—
545#102—834no—
546#102—834no—
547#102—834no—
548#102—834no—
549#102—834no—
550#97—834no—
551#97—834no—
552C4×C8—834no—
553C24—21no—
554C24—21no—
555C24—1661no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—42no—
560C2×Q8—6642no—
561C2×Q8—1664no—
562C2×Q8C2×C22⋊D8314yes—
563C2×Q8C23×D8312yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C2×D4—82no—
574C2×D4—834no—
575C2×D4—832no—
576C2×D4—1661no—
577C2×D4—1662no—
578C2×D4C23×D8312yes—
579C2×D4C23×D8312yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—3324no—
587C22×C4—6642no—
588C22×C4—6642no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1664no—
593C22×C4—1664no—
594C22×C4—1664no—
595C22×C4C2×C22⋊D8311yescharacteristic
596C22×C4C2×C22⋊D8311yescharacteristic
597C22×C4C2×C22⋊D8311yescharacteristic
598C22×C4C2×C22⋊D8311yescharacteristic
599C22×C4C2×C22⋊D8311yescharacteristic
600C22×C4C2×C22⋊D8311yescharacteristic
601C22×C4C23×D8311yescharacteristic
602SD16—1668no—
603D8—1668no—
604D8—1668no—
605C2×C8—832no—
606C2×C8—832no—
607C2×C8—832no—
608C2×C8—832no—
609C2×C8—1662no—
610C2×C8—1662no—
611C2×C8—1662no—
612C2×C8—1662no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—832no—
616C4⋊C4—832no—
617C4⋊C4—832no—
618C4⋊C4—1661no—
619C4⋊C4—1661no—
620C4⋊C4—1661no—
621C4⋊C4—1664no—
622C4⋊C4—1664no—
623C4⋊C4—1664no—
624C4⋊C4—1664no—
625C4⋊C4—1664no—
626C4⋊C4C2×C22⋊D8314yes—
627C4⋊C4C2×C22⋊D8314yes—
628C4⋊C4C2×C22⋊D8314yes—
629C4⋊C4C23×D8312yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—1664no—
637C22⋊C4—1664no—
638C22⋊C4—1664no—
639C42—24no—
640C42C2×C22⋊D8312yes—
641C42C2×C22⋊D8312yes—
642C42C2×C22⋊D8312yes—
643C42C23×D8312yes—
644C42C23×D8312yes—
645C42C23×D8312yes—
646C23—22no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—3322no—
655C23—3322no—
656C23—1664no—
657C23—1662no—
658C23C22×C22⋊D8311yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—44no—
662Q8—42no—
663Q8—6644no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—42no—
670D4—42no—
671D4—84no—
672D4—834no—
673D4—1664no—
674D4—1662no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—84no—
686C2×C4—84no—
687C2×C4—3328no—
688C2×C4—3322no—
689C2×C4—3322no—
690C2×C4—3322no—
691C2×C4—6644no—
692C2×C4—6644no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4C22×C22⋊D8312yes—
697C2×C4C22×C22⋊D8312yes—
698C2×C4C22×C22⋊D8312yes—
699C2×C4C22×C22⋊D8312yes—
700C2×C4C22×C22⋊D8312yes—
701C2×C4C22×C22⋊D8312yes—
702C2×C4C22×C22⋊D8311yescharacteristic
703C2×C4#41×D8312yes—
704C2×C4#1458183912yes—
705C2×C4C24×D8311yescharacteristic
706C8—1662no—
707C8—1662no—
708C8—1662no—
709C8—1662no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—84no—
718C22—3322no—
719C22—3322no—
720C22—3328no—
721C22—1664no—
722C22#1912835812yes—
723C22#1912849912yes—
724C22#1912850412yes—
725C22C23×C22⋊D8311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—3322no—
735C4—3322no—
736C4—3322no—
737C4#1912835812yes—
738C4C2×#41×D8311yescharacteristic
739C4C2×#1458183911yescharacteristic
740C2—82no—
741C2—82no—
742C2—3324no—
743C2#2492021014yesdirect product factor
744C2C2×#1912835811yescharacteristic
745C2C2×#1912849911yescharacteristic
746C2C2×#1912850411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#559×C83C2
socleC23×C83C22×D4
prime radicalC2×#19127893C2
hypercenterC2×#559D83
hypocenterC83C2×#3370
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×#19128411C2semidirect
2. #24920210C2direct (N × H)
3. C2×#19128065C2semidirect
4. C2×#19128060C2semidirect
5. C2×#19128055C2semidirect
6. C2×#19128008C2semidirect
7. C2×#19128001C2semidirect
8. C2×#19127981C2semidirect
9. C2×#19127913C2semidirect
10. C2×#19127913C2semidirect
12. C2×#19127832C2semidirect
13. C2×#19127811C2semidirect
14. C2×#19127799C2semidirect
15. C2×C4×#13050575C2semidirect
16. C2×#559×C83C2semidirect
21. #19128411C22semidirect
32. #19128065C22semidirect
33. #19128060C22semidirect
34. #19128055C22semidirect
35. #19128008C22semidirect
36. #19128001C22semidirect
37. #19127981C22semidirect
38. #19127913C22semidirect
39. #19127913C22semidirect
41. #19127832C22semidirect
42. #19127811C22semidirect
43. #19127799C22semidirect
44. C4×#13050575C22semidirect
65. #559×C83C22semidirect
369. C2×C83#3370semidirect
374. C2×#559D83semidirect
390. C83C2×#3370semidirect
395. #559C2×D83semidirect
743. C2#24920210direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284112
#249202102
C2×#191280652
C2×#191280602
C2×#191280552
C2×#191280082
C2×#191280012
C2×#191279812
C2×#191279132
C2×#191278932
C2×#191278322
C2×#191278112
C2×#191277992
C2×C4×#130505752
C2×#559×C832
C2×#337083