Finite Group Databasebeta

← C2×#24918074 #36274196

Subgroups — C2×#24918074 #36274196

Order 21248.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128322C211yesmaximal, characteristic, complemented
2#24918074C2116yesmaximal, direct product factor
3C2×#19128097C211yesmaximal, characteristic, complemented
4C2×#19128083C211yesmaximal, characteristic, complemented
5C2×#19128063C211yesmaximal, characteristic, complemented
6C2×#19128060C211yesmaximal, characteristic, complemented
7C2×#19127957C211yesmaximal, characteristic, complemented
8C2×#19127952C211yesmaximal, characteristic
9C2×#19127932C211yesmaximal, characteristic, complemented
10C2×#19127928C211yesmaximal, characteristic, complemented
11C2×#19127811C211yesmaximal, characteristic, complemented
12C2×#19127806C211yesmaximal, characteristic, complemented
13C2×C4×#13050577C211yesmaximal, characteristic, complemented
14C2×C4×#13050578C211yesmaximal, characteristic, complemented
15C2×#19127657C211yesmaximal, characteristic, complemented
16C2×#542×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C22×#13050578C2211yescharacteristic
19C22×#13050577C2211yescharacteristic
20C22×#13050575C2211yescharacteristic
21C22×#13050574C2211yescharacteristic
22C23×C83⋊C8C2211yescharacteristic
23#19128322—24no—
24#19128322C2218yescomplemented
25C2×#14581792C2211yescharacteristic
26C2×#14581787—21no—
27C2×#14581780C2211yescharacteristic
28C2×#14581778—21no—
29C2×#14581774—21no—
30C2×#14581771C2211yescharacteristic
31C2×#14581770—21no—
32C2×#14581766C2211yescharacteristic
33C2×C4×Dic166C2211yescharacteristic
34C2×C4×D332C2211yescharacteristic
35#19128097C2218yescomplemented
36#19128083C2218yescomplemented
37#19128063C2218yescomplemented
38#19128060C2218yescomplemented
39#19127957C2218yescomplemented
40#19127952C2218yes—
41#19127932C2218yescomplemented
42#19127928C2218yescomplemented
43#19127811C2218yescomplemented
44#19127806C2218yescomplemented
45C4×#13050577C2218yescomplemented
46C4×#13050578C2218yescomplemented
47C2×#14581723C2211yescharacteristic
48C2×#14581723C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581715C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581713C2211yescharacteristic
56C2×#14581713C2211yescharacteristic
57C2×#14581712C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59#19127657C2218yescomplemented
60C2×#14581703C2211yescharacteristic
61C2×#14581703C2211yescharacteristic
62C2×C4×C83⋊C8C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#542×C83—24no—
65#542×C83C2218yescomplemented
66C2×C4⋊Q8×C83C2211yescharacteristic
67C2×#126×C83—21no—
68C2×#124×C83—21no—
69C2×#124×C83C2211yescharacteristic
70C2×#123×C83—21no—
71C2×C22⋊Q8×C83—21no—
72C2×C22⋊Q8×C83C2211yescharacteristic
73C2×#121×C83C2211yescharacteristic
74C2×C4×Q8×C83C2211yescharacteristic
75C2×C4×D4×C83C2211yescharacteristic
76C2×#117×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C22×D332C2311yescharacteristic
80C22×C22⋊D83—21no—
81C22×C4×D83—21no—
82C2×#13050580—24no—
83C2×#13050580C2314yes—
84C2×#13050578—24no—
85C2×#13050578C2314yes—
86C2×#13050577—24no—
87C2×#13050577C2314yes—
88C2×#13050575—24no—
89C2×#13050575C2314yes—
90C2×#13050574—24no—
91C2×#13050574C2314yes—
92C22×C83⋊C8—24no—
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2311yescharacteristic
95C22×C83⋊C8C2314yes—
96C22×C83⋊C8C2311yescharacteristic
97C22×C83⋊C8C2311yescharacteristic
98#14581792—22no—
99#14581792C2314yes—
100#14581787—28no—
101#14581780—22no—
102#14581780C2314yes—
103#14581778—28no—
104#14581774—28no—
105#14581771—22no—
106#14581771C2314yes—
107#14581770—28no—
108#14581766—22no—
109#14581766C2314yes—
110C4×Dic166—22no—
111C4×Dic166C2314yes—
112C4×D332—22no—
113C4×D332C2314yes—
114C2×C4⋊Dic83—21no—
115C2×C4⋊Dic83C2311yescharacteristic
116C2×C4⋊Dic83C2311yescharacteristic
117C2×Dic83⋊C4—21no—
118C2×Dic83⋊C4—21no—
119C2×C22⋊Dic83—21no—
120C2×(C2×D83)⋊C4—21no—
121C2×(C2×D83)⋊C4—21no—
122C2×(C2×D83)⋊C4—21no—
123C2×(C2×D83)⋊C4—21no—
124C2×C4×Dic83—21no—
125#14581723C2314yes—
126#14581723C2314yes—
127#14581723C2314yes—
128#14581723C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131#14581715C2314yes—
132#14581715C2314yes—
133#14581713C2314yes—
134#14581713C2314yes—
135#14581712C2314yes—
136#14581712C2314yes—
137#14581703C2314yes—
138#14581703C2314yes—
139C4×C83⋊C8C2314yes—
140C4×C83⋊C8C2314yes—
141C22×Q8×C83—21no—
142C22×Q8×C83C2311yescharacteristic
143C22×D4×C83—21no—
144C22×D4×C83C2311yescharacteristic
145C23×C4×C83—21no—
146C23×C4×C83C2311yescharacteristic
147C4⋊Q8×C83—22no—
148C4⋊Q8×C83C2314yes—
149#126×C83—28no—
150#124×C83—28no—
151#124×C83—22no—
152#124×C83C2314yes—
153#123×C83—28no—
154C22⋊Q8×C83—22no—
155C22⋊Q8×C83—28no—
156C22⋊Q8×C83C2314yes—
157#121×C83—22no—
158#121×C83C2314yes—
159C4×Q8×C83—22no—
160C4×Q8×C83C2314yes—
161C4×D4×C83—22no—
162C4×D4×C83C2314yes—
163#117×C83D414yes—
164#117×C83C2314yes—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83D411yescharacteristic
169C2×C4⋊C4×C83D411yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C22⋊C4×C83—21no—
173C2×C22⋊C4×C83—21no—
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83—21no—
177C2×C22⋊C4×C83D411yescharacteristic
178C2×C22⋊C4×C83D411yescharacteristic
179C2×C42×C83—21no—
180C2×C42×C83C2311yescharacteristic
181C2×C42×C83C2311yescharacteristic
182C23×D83—21no—
183C2×Dic166—22no—
184C2×Dic166—22no—
185C2×Dic166—21no—
186C2×Dic166—24no—
187C2×Dic166—82no—
188C2×Dic166C2412yes—
189C2×D332—22no—
190C2×D332—22no—
191C2×D332—21no—
192C2×D332C2412yes—
193C2×C22⋊D83—24no—
194C2×C22⋊D83—82no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C2×C4×D83—24no—
199C2×C4×D83—82no—
200#13050580—28no—
201#13050578—28no—
202#13050577—28no—
203#13050575—28no—
204#13050574—28no—
205C2×C83⋊C8—22no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—28no—
208C2×C83⋊C8#4114yes—
209C2×C83⋊C8#4114yes—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C2×C83⋊C8C2412yes—
213C2×C83⋊C8C2412yes—
214C4⋊Dic83—21no—
215C4⋊Dic83—21no—
216C4⋊Dic83—24no—
217C4⋊Dic83C2412yes—
218C4⋊Dic83C2412yes—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221C22⋊Dic83—24no—
222(C2×D83)⋊C4—24no—
223(C2×D83)⋊C4—24no—
224(C2×D83)⋊C4—24no—
225(C2×D83)⋊C4—24no—
226C4×Dic83—24no—
227C24×C83—21no—
228C24×C83C2×D411yescharacteristic
229C2×Q8×C83—21no—
230C2×Q8×C83—24no—
231C2×Q8×C83—22no—
232C2×Q8×C83—22no—
233C2×Q8×C83—82no—
234C2×Q8×C83C2412yes—
235C2×D4×C83—24no—
236C2×D4×C83—21no—
237C2×D4×C83—22no—
238C2×D4×C83—22no—
239C2×D4×C83—82no—
240C2×D4×C83C2412yes—
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—24no—
247C22×C4×C83—82no—
248C22×C4×C83C2×D412yes—
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2412yes—
255C22×C4×C83C2411yescharacteristic
256C4⋊C4×C83—24no—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—24no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83C2×D414yes—
262C4⋊C4×C83C2×D414yes—
263C4⋊C4×C83C2412yes—
264C4⋊C4×C83C2412yes—
265C22⋊C4×C83—24no—
266C22⋊C4×C83—24no—
267C22⋊C4×C83—24no—
268C22⋊C4×C83—24no—
269C22⋊C4×C83—24no—
270C22⋊C4×C83C2×D414yes—
271C22⋊C4×C83C2×D414yes—
272C42×C83—24no—
273C42×C83C2×D412yes—
274C42×C83C2×D412yes—
275C42×C83C2412yes—
276C42×C83C2412yes—
277C23×C83—22no—
278C23×C83—22no—
279C23×C83—22no—
280C23×C83—22no—
281C23×C83—42no—
282C23×C83—42no—
283C23×C83—42no—
284C23×C83C22×D412yes—
285C23×C83C22×D411yescharacteristic
286C22×D83—22no—
287C22×D83—42no—
288C22×D83—42no—
289C22×D83—42no—
290Q8×C83—22no—
291Q8×C83—22no—
292Q8×C83—42no—
293Q8×C83—84no—
294D4×C83—22no—
295D4×C83—22no—
296D4×C83—42no—
297D4×C83—84no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—24no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—42no—
310C2×C4×C83—42no—
311C2×C4×C83—42no—
312C2×C4×C83—84no—
313C2×C4×C83C22×D412yes—
314C2×C4×C83C22×D412yes—
315C2×C4×C83C22×D412yes—
316C2×C4×C83C22×D412yes—
317C2×C4×C83C22×D412yes—
318C2×C4×C83C22×D411yescharacteristic
319C2×C4×C83C2×#4112yes—
320C2×C4×C83C2×#4112yes—
321C2×C4×C83C2511yescharacteristic
322C22⋊D83—84no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—42no—
327C2×Dic83—42no—
328C2×Dic83—42no—
329D332—22no—
330D332—22no—
331D332—42no—
332C4×D83—84no—
333Dic166—22no—
334Dic166—22no—
335Dic166—42no—
336Dic166—84no—
337C83⋊C8—22no—
338C83⋊C8—22no—
339C83⋊C8C2×#4114yes—
340C83⋊C8C2×#4114yes—
341C22×C83—22no—
342C22×C83—22no—
343C22×C83—22no—
344C22×C83—44no—
345C22×C83—42no—
346C22×C83—42no—
347C22×C83—42no—
348C22×C83—84no—
349C22×C83#53212yes—
350C22×C83#57712yes—
351C22×C83#57712yes—
352C22×C83C23×D411yescharacteristic
353C2×D83—42no—
354C2×D83—42no—
355C2×D83—42no—
356C2×D83—84no—
357C4×C83—22no—
358C4×C83—22no—
359C4×C83—22no—
360C4×C83—22no—
361C4×C83—22no—
362C4×C83—42no—
363C4×C83—42no—
364C4×C83—42no—
365C4×C83#53212yes—
366C4×C83C22×#4111yescharacteristic
367C4×C83C22×#4111yescharacteristic
368Dic83—42no—
369Dic83—42no—
370Dic83—42no—
371C2×#3173—831nomaximal, Sylow
372C2×C83—42no—
373C2×C83—82no—
374C2×C83#317314yescomplemented
375C2×C83C2×#53211yescharacteristic
376C2×C83C2×#57711yescharacteristic
377C2×C83C2×#57711yescharacteristic
378D83—82no—
379C2×#542—831no—
380C2×#542D8311yescharacteristic, complemented
381#3173—8316no—
382C2×#498—831no—
383C2×#495—831no—
384C2×#489—831no—
385C2×#489—831no—
386C2×#470—831no—
387C2×#469—831no—
388C2×#465—831no—
389C2×#465—831no—
390C2×#442—831no—
391C2×#441—831no—
392C2×C4×SD16—831no—
393C2×C4×SD16—831no—
394C2×#405—831no—
395C83C2×#317311yescharacteristic, complemented, Sylow
396C22×Q16—831no—
397C22×SD16—831no—
398C22×SD16—831no—
399C22×D8—831no—
400C22×M16—831no—
401C23×C8—831no—
402#542—24no—
403#542—838no—
404#542—1664no—
405#542C2×D8318yescomplemented
406C2×C4⋊Q8—831no—
407C2×C4⋊Q8C2×D8311yescharacteristic
408C2×#126—21no—
409C2×#126—1661no—
410C2×#124—21no—
411C2×#124—831no—
412C2×#124—1661no—
413C2×#124C2×D8311yescharacteristic
414C2×#123—21no—
415C2×#123—1661no—
416C2×C22⋊Q8—21no—
417C2×C22⋊Q8—831no—
418C2×C22⋊Q8—1661no—
419C2×C22⋊Q8C2×D8311yescharacteristic
420C2×#121—831no—
421C2×#121C2×D8311yescharacteristic
422C2×C4×Q8—831no—
423C2×C4×Q8C2×D8311yescharacteristic
424C2×C4×D4—831no—
425C2×C4×D4C2×D8311yescharacteristic
426C2×#117C2×D8311yescharacteristic
427#498—838no—
428#495—838no—
429#489—838no—
430#489—838no—
431#470—838no—
432#469—838no—
433#465—838no—
434#465—838no—
435#442—838no—
436#441—838no—
437C4×SD16—838no—
438C4×SD16—838no—
439C2×#106—831no—
440C2×#106—831no—
441C2×#106—831no—
442C2×#106—831no—
443C2×#103—831no—
444C2×#103—831no—
445C2×#103—831no—
446C2×#103—831no—
447C2×#102—831no—
448C2×#102—831no—
449C2×#102—831no—
450C2×#102—831no—
451#405—838no—
452C2×#97—831no—
453C2×#97—831no—
454C2×C4×C8—831no—
455C2×C4×C8—831no—
456C22×Q8—21no—
457C22×Q8—831no—
458C22×Q8—1661no—
459C22×Q8C22×D8311yescharacteristic
460C22×D4—21no—
461C22×D4—831no—
462C22×D4—1661no—
463C22×D4C22×D8311yescharacteristic
464C23×C4—21no—
465C23×C4—1661no—
466C23×C4C22×D8311yescharacteristic
467C2×Q16—834no—
468C2×Q16—1664no—
469C2×SD16—834no—
470C2×SD16—834no—
471C2×SD16—1664no—
472C2×SD16—1664no—
473C2×D8—834no—
474C2×D8—1664no—
475C2×M16—834no—
476C2×M16—1664no—
477C22×C8—831no—
478C22×C8—831no—
479C22×C8—831no—
480C22×C8—834no—
481C22×C8—831no—
482C22×C8—1664no—
483C4⋊Q8—22no—
484C4⋊Q8—834no—
485C4⋊Q8—1662no—
486C4⋊Q8C22×D8314yes—
487#126—28no—
488#126—1668no—
489#124—28no—
490#124—22no—
491#124—834no—
492#124—1668no—
493#124—1662no—
494#124C22×D8314yes—
495#123—28no—
496#123—1668no—
497C22⋊Q8—22no—
498C22⋊Q8—28no—
499C22⋊Q8—834no—
500C22⋊Q8—1662no—
501C22⋊Q8—1668no—
502C22⋊Q8C22×D8314yes—
503#121—22no—
504#121—834no—
505#121—1662no—
506#121C22×D8314yes—
507C4×Q8—22no—
508C4×Q8—834no—
509C4×Q8—1662no—
510C4×Q8C22×D8314yes—
511C4×D4—22no—
512C4×D4—834no—
513C4×D4—1662no—
514C4×D4C22×D8314yes—
515#117C22⋊D8314yes—
516#117C22×D8314yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—831no—
521C2×C4⋊C4—831no—
522C2×C4⋊C4—1661no—
523C2×C4⋊C4—1661no—
524C2×C4⋊C4—1661no—
525C2×C4⋊C4C22⋊D8311yescharacteristic
526C2×C4⋊C4C22⋊D8311yescharacteristic
527C2×C4⋊C4C22×D8311yescharacteristic
528C2×C4⋊C4C22×D8311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—1661no—
535C2×C22⋊C4—1661no—
536C2×C22⋊C4—1661no—
537C2×C22⋊C4—1661no—
538C2×C22⋊C4—1661no—
539C2×C22⋊C4C22⋊D8311yescharacteristic
540C2×C22⋊C4C22⋊D8311yescharacteristic
541C2×C42—21no—
542C2×C42—1661no—
543C2×C42C22×D8311yescharacteristic
544C2×C42C22×D8311yescharacteristic
545#106—834no—
546#106—834no—
547#106—834no—
548#106—834no—
549#103—834no—
550#103—834no—
551#103—834no—
552#103—834no—
553#102—834no—
554#102—834no—
555#102—834no—
556#102—834no—
557#97—834no—
558#97—834no—
559C4×C8—834no—
560C4×C8—834no—
561C24—21no—
562C24—1661no—
563C24C2×C22⋊D8311yescharacteristic
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—832no—
570C2×Q8—6642no—
571C2×Q8—1662no—
572C2×Q8—1662no—
573C2×Q8—1661no—
574C2×Q8—1664no—
575C2×Q8C23×D8312yes—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—82no—
581C2×D4—832no—
582C2×D4—6642no—
583C2×D4—1664no—
584C2×D4—1661no—
585C2×D4—1662no—
586C2×D4—1662no—
587C2×D4C23×D8312yes—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—82no—
595C22×C4—6642no—
596C22×C4—1661no—
597C22×C4—1661no—
598C22×C4—1661no—
599C22×C4—1664no—
600C22×C4C2×C22⋊D8312yes—
601C22×C4C2×C22⋊D8311yescharacteristic
602C22×C4C2×C22⋊D8311yescharacteristic
603C22×C4C2×C22⋊D8311yescharacteristic
604C22×C4C2×C22⋊D8311yescharacteristic
605C22×C4C2×C22⋊D8311yescharacteristic
606C22×C4C23×D8312yes—
607C22×C4C23×D8311yescharacteristic
608Q16—1668no—
609SD16—1668no—
610SD16—1668no—
611D8—1668no—
612M16—1668no—
613C2×C8—834no—
614C2×C8—834no—
615C2×C8—832no—
616C2×C8—832no—
617C2×C8—832no—
618C2×C8—832no—
619C2×C8—1668no—
620C2×C8—1662no—
621C2×C8—1662no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—832no—
628C4⋊C4—832no—
629C4⋊C4—1661no—
630C4⋊C4—1661no—
631C4⋊C4—1664no—
632C4⋊C4—1664no—
633C4⋊C4—1664no—
634C4⋊C4C2×C22⋊D8314yes—
635C4⋊C4C2×C22⋊D8314yes—
636C4⋊C4C23×D8312yes—
637C4⋊C4C23×D8312yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—1664no—
644C22⋊C4—1664no—
645C22⋊C4—1664no—
646C22⋊C4—1664no—
647C22⋊C4—1664no—
648C22⋊C4C2×C22⋊D8314yes—
649C22⋊C4C2×C22⋊D8314yes—
650C42—24no—
651C42—1664no—
652C42C2×C22⋊D8312yes—
653C42C2×C22⋊D8312yes—
654C42C23×D8312yes—
655C42C23×D8312yes—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—3322no—
664C23—3322no—
665C23—3322no—
666C23—1662no—
667C23C22×C22⋊D8312yes—
668C23C22×C22⋊D8311yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—42no—
672Q8—84no—
673Q8—3322no—
674Q8—6644no—
675Q8—1662no—
676Q8—1662no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—84no—
681D4—3322no—
682D4—6644no—
683D4—1662no—
684D4—1662no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—84no—
700C2×C4—3322no—
701C2×C4—3322no—
702C2×C4—3322no—
703C2×C4—6644no—
704C2×C4—1662no—
705C2×C4—1662no—
706C2×C4—1662no—
707C2×C4C22×C22⋊D8312yes—
708C2×C4C22×C22⋊D8312yes—
709C2×C4C22×C22⋊D8312yes—
710C2×C4C22×C22⋊D8312yes—
711C2×C4C22×C22⋊D8312yes—
712C2×C4C22×C22⋊D8311yescharacteristic
713C2×C4#41×D8312yes—
714C2×C4#41×D8312yes—
715C2×C4C24×D8311yescharacteristic
716C8—834no—
717C8—834no—
718C8—1662no—
719C8—1662no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—3322no—
729C22—3322no—
730C22—3322no—
731C22—6644no—
732C22#1912824712yes—
733C22#1912850912yes—
734C22#1912851212yes—
735C22C23×C22⋊D8311yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—3322no—
745C4—3322no—
746C4—3322no—
747C4#1912824712yes—
748C4C2×#41×D8311yescharacteristic
749C4C2×#41×D8311yescharacteristic
750C2—42no—
751C2—82no—
752C2—6642no—
753C2#2491807414yesdirect product factor
754C2C2×#1912824711yescharacteristic
755C2C2×#1912850911yescharacteristic
756C2C2×#1912851211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#542×C83C2
socleC23×C83C22×D4
prime radicalC2×#19127952C2
hypercenterC2×#542D83
hypocenterC83C2×#3173
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#19128322C2semidirect
2. #24918074C2direct (N × H)
3. C2×#19128097C2semidirect
4. C2×#19128083C2semidirect
5. C2×#19128063C2semidirect
6. C2×#19128060C2semidirect
7. C2×#19127957C2semidirect
9. C2×#19127932C2semidirect
10. C2×#19127928C2semidirect
11. C2×#19127811C2semidirect
12. C2×#19127806C2semidirect
13. C2×C4×#13050577C2semidirect
14. C2×C4×#13050578C2semidirect
15. C2×#19127657C2semidirect
16. C2×#542×C83C2semidirect
24. #19128322C22semidirect
35. #19128097C22semidirect
36. #19128083C22semidirect
37. #19128063C22semidirect
38. #19128060C22semidirect
39. #19127957C22semidirect
41. #19127932C22semidirect
42. #19127928C22semidirect
43. #19127811C22semidirect
44. #19127806C22semidirect
45. C4×#13050577C22semidirect
46. C4×#13050578C22semidirect
59. #19127657C22semidirect
65. #542×C83C22semidirect
374. C2×C83#3173semidirect
380. C2×#542D83semidirect
395. C83C2×#3173semidirect
405. #542C2×D83semidirect
753. C2#24918074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283222
#249180742
C2×#191280972
C2×#191280832
C2×#191280632
C2×#191280602
C2×#191279572
C2×#191279522
C2×#191279322
C2×#191279282
C2×#191278112
C2×#191278062
C2×C4×#130505772
C2×C4×#130505782
C2×#191276572
C2×#542×C832
C2×#317383