Finite Group Databasebeta

← C2×#24918140 #36274282

Subgroups — C2×#24918140 #36274282

Order 21248.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128306C211yesmaximal, characteristic, complemented
2#24918140C2116yesmaximal, direct product factor
3C2×#19128107C211yesmaximal, characteristic, complemented
4C2×#19128091C211yesmaximal, characteristic, complemented
5C2×#19128055C211yesmaximal, characteristic, complemented
6C2×#19128049C211yesmaximal, characteristic, complemented
7C2×#19127952C211yesmaximal, characteristic, complemented
8C2×#19127949C211yesmaximal, characteristic, complemented
9C2×#19127935C211yesmaximal, characteristic, complemented
10C2×#19127932C211yesmaximal, characteristic, complemented
11C2×#19127811C211yesmaximal, characteristic, complemented
12C2×#19127799C211yesmaximal, characteristic, complemented
13C2×C4×#13050577C211yesmaximal, characteristic, complemented
14C2×C4×#13050575C211yesmaximal, characteristic, complemented
15C2×#19127657C211yesmaximal, characteristic, complemented
16C2×#542×C83C211yesmaximal, characteristic, complemented
17C22×#13050577C2211yescharacteristic
18C22×#13050577C2211yescharacteristic
19C22×#13050575C2211yescharacteristic
20C22×#13050575C2211yescharacteristic
21C22×#13050574C2211yescharacteristic
22C23×C83⋊C8C2211yescharacteristic
23#19128306—24no—
24#19128306C2218yescomplemented
25C2×#14581789C2211yescharacteristic
26C2×#14581784C2211yescharacteristic
27C2×#14581777—21no—
28C2×#14581777—21no—
29C2×#14581766C2211yescharacteristic
30C2×#14581766C2211yescharacteristic
31C2×#14581765—21no—
32C2×#14581765—21no—
33C2×C4×D332C2211yescharacteristic
34C2×C4×D332C2211yescharacteristic
35#19128107C2218yescomplemented
36#19128091C2218yescomplemented
37#19128055C2218yescomplemented
38#19128049C2218yescomplemented
39#19127952C2218yescomplemented
40#19127949C2218yescomplemented
41#19127935C2218yescomplemented
42#19127932C2218yescomplemented
43#19127811C2218yescomplemented
44#19127799C2218yescomplemented
45C4×#13050577C2218yescomplemented
46C4×#13050575C2218yescomplemented
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581713C2211yescharacteristic
54C2×#14581713C2211yescharacteristic
55C2×#14581712C2211yescharacteristic
56C2×#14581712C2211yescharacteristic
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×D332—21no—
78C22×D332—21no—
79C22×D332C2311yescharacteristic
80C22×D332C2311yescharacteristic
81C22×C22⋊D83—21no—
82C22×C22⋊D83—21no—
83C22×C4×D83—21no—
84C22×C4×D83—21no—
85C2×#13050577—24no—
86C2×#13050577—24no—
87C2×#13050577C2314yes—
88C2×#13050577C2314yes—
89C2×#13050575—24no—
90C2×#13050575—24no—
91C2×#13050575C2314yes—
92C2×#13050575C2314yes—
93C2×#13050574—24no—
94C2×#13050574C2314yes—
95C22×C83⋊C8—24no—
96C22×C83⋊C8C2311yescharacteristic
97C22×C83⋊C8C2311yescharacteristic
98C22×C83⋊C8C2314yes—
99C22×C83⋊C8C2311yescharacteristic
100C22×C83⋊C8C2311yescharacteristic
101#14581789—22no—
102#14581789C2314yes—
103#14581784—22no—
104#14581784C2314yes—
105#14581777—28no—
106#14581777—28no—
107#14581766—22no—
108#14581766—22no—
109#14581766C2314yes—
110#14581766C2314yes—
111#14581765—28no—
112#14581765—28no—
113C4×D332—22no—
114C4×D332—22no—
115C4×D332C2314yes—
116C4×D332C2314yes—
117C2×C4⋊Dic83C2311yescharacteristic
118C2×C4⋊Dic83C2311yescharacteristic
119C2×Dic83⋊C4—21no—
120C2×Dic83⋊C4—21no—
121C2×(C2×D83)⋊C4—21no—
122C2×(C2×D83)⋊C4—21no—
123C2×(C2×D83)⋊C4—21no—
124C2×(C2×D83)⋊C4—21no—
125#14581725C2314yes—
126#14581725C2314yes—
127#14581723C2314yes—
128#14581723C2314yes—
129#14581716C2314yes—
130#14581716C2314yes—
131#14581713C2314yes—
132#14581713C2314yes—
133#14581712C2314yes—
134#14581712C2314yes—
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—
183C23×D83—21no—
184C2×D332—22no—
185C2×D332—22no—
186C2×D332—22no—
187C2×D332—22no—
188C2×D332—21no—
189C2×D332—21no—
190C2×D332—24no—
191C2×D332—24no—
192C2×D332—82no—
193C2×D332—82no—
194C2×D332C2412yes—
195C2×D332C2412yes—
196C2×C22⋊D83—24no—
197C2×C22⋊D83—24no—
198C2×C22⋊D83—82no—
199C2×C22⋊D83—82no—
200C22×Dic83—21no—
201C22×Dic83—21no—
202C2×C4×D83—24no—
203C2×C4×D83—24no—
204C2×C4×D83—82no—
205C2×C4×D83—82no—
206#13050577—28no—
207#13050577—28no—
208#13050575—28no—
209#13050575—28no—
210#13050574—28no—
211C2×C83⋊C8—22no—
212C2×C83⋊C8—22no—
213C2×C83⋊C8—28no—
214C2×C83⋊C8#4114yes—
215C2×C83⋊C8#4114yes—
216C2×C83⋊C8C2412yes—
217C2×C83⋊C8C2412yes—
218C2×C83⋊C8C2412yes—
219C2×C83⋊C8C2412yes—
220C4⋊Dic83—21no—
221C4⋊Dic83—21no—
222C4⋊Dic83C2412yes—
223C4⋊Dic83C2412yes—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226(C2×D83)⋊C4—24no—
227(C2×D83)⋊C4—24no—
228(C2×D83)⋊C4—24no—
229(C2×D83)⋊C4—24no—
230C24×C83—21no—
231C24×C83C2×D411yescharacteristic
232C2×Q8×C83—21no—
233C2×Q8×C83—24no—
234C2×Q8×C83—22no—
235C2×Q8×C83—22no—
236C2×Q8×C83—82no—
237C2×Q8×C83C2412yes—
238C2×D4×C83—24no—
239C2×D4×C83—21no—
240C2×D4×C83—22no—
241C2×D4×C83—22no—
242C2×D4×C83—82no—
243C2×D4×C83C2412yes—
244C22×C4×C83—22no—
245C22×C4×C83—22no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—24no—
250C22×C4×C83—82no—
251C22×C4×C83C2×D412yes—
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D411yescharacteristic
254C22×C4×C83C2×D411yescharacteristic
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2412yes—
258C22×C4×C83C2411yescharacteristic
259C4⋊C4×C83—24no—
260C4⋊C4×C83—24no—
261C4⋊C4×C83—24no—
262C4⋊C4×C83—21no—
263C4⋊C4×C83—21no—
264C4⋊C4×C83C2×D414yes—
265C4⋊C4×C83C2×D414yes—
266C4⋊C4×C83C2412yes—
267C4⋊C4×C83C2412yes—
268C22⋊C4×C83—24no—
269C22⋊C4×C83—24no—
270C22⋊C4×C83—24no—
271C22⋊C4×C83—24no—
272C22⋊C4×C83—24no—
273C22⋊C4×C83C2×D414yes—
274C22⋊C4×C83C2×D414yes—
275C42×C83—24no—
276C42×C83C2×D412yes—
277C42×C83C2×D412yes—
278C42×C83C2412yes—
279C42×C83C2412yes—
280C23×C83—22no—
281C23×C83—22no—
282C23×C83—22no—
283C23×C83—22no—
284C23×C83—42no—
285C23×C83—42no—
286C23×C83—42no—
287C23×C83C22×D412yes—
288C23×C83C22×D411yescharacteristic
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—42no—
292C22×D83—42no—
293C22×D83—42no—
294C22×D83—42no—
295C22×D83—42no—
296C22×D83—42no—
297Q8×C83—22no—
298Q8×C83—22no—
299Q8×C83—42no—
300Q8×C83—84no—
301D4×C83—22no—
302D4×C83—22no—
303D4×C83—42no—
304D4×C83—84no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—24no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—42no—
317C2×C4×C83—42no—
318C2×C4×C83—42no—
319C2×C4×C83—84no—
320C2×C4×C83C22×D412yes—
321C2×C4×C83C22×D412yes—
322C2×C4×C83C22×D412yes—
323C2×C4×C83C22×D412yes—
324C2×C4×C83C22×D412yes—
325C2×C4×C83C22×D411yescharacteristic
326C2×C4×C83C2×#4112yes—
327C2×C4×C83C2×#4112yes—
328C2×C4×C83C2511yescharacteristic
329C22⋊D83—84no—
330C22⋊D83—84no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—42no—
334C2×Dic83—42no—
335D332—22no—
336D332—22no—
337D332—22no—
338D332—22no—
339D332—42no—
340D332—42no—
341D332—84no—
342D332—84no—
343C4×D83—84no—
344C4×D83—84no—
345C83⋊C8—22no—
346C83⋊C8—22no—
347C83⋊C8C2×#4114yes—
348C83⋊C8C2×#4114yes—
349C22×C83—22no—
350C22×C83—22no—
351C22×C83—22no—
352C22×C83—44no—
353C22×C83—42no—
354C22×C83—42no—
355C22×C83—42no—
356C22×C83—84no—
357C22×C83#53212yes—
358C22×C83#57612yes—
359C22×C83#57712yes—
360C22×C83C23×D411yescharacteristic
361C2×D83—42no—
362C2×D83—42no—
363C2×D83—42no—
364C2×D83—42no—
365C2×D83—42no—
366C2×D83—42no—
367C2×D83—84no—
368C2×D83—84no—
369C4×C83—22no—
370C4×C83—22no—
371C4×C83—22no—
372C4×C83—22no—
373C4×C83—22no—
374C4×C83—42no—
375C4×C83—42no—
376C4×C83—42no—
377C4×C83#53212yes—
378C4×C83C22×#4111yescharacteristic
379C4×C83C22×#4111yescharacteristic
380Dic83—42no—
381Dic83—42no—
382C2×#3179—831nomaximal, Sylow
383C2×C83—42no—
384C2×C83—82no—
385C2×C83#317914yescomplemented
386C2×C83C2×#53211yescharacteristic
387C2×C83C2×#57611yescharacteristic
388C2×C83C2×#57711yescharacteristic
389D83—82no—
390D83—82no—
391C2×#542D8311yescharacteristic, complemented
392C2×#540—831no—
393#3179—8316no—
394C2×#501—831no—
395C2×#496—831no—
396C2×#488—831no—
397C2×#486—831no—
398C2×#469—831no—
399C2×#468—831no—
400C2×#466—831no—
401C2×#465—831no—
402C2×#442—831no—
403C2×#440—831no—
404C2×C4×SD16—831no—
405C2×C4×D8—831no—
406C2×#405—831no—
407C83C2×#317911yescharacteristic, complemented, Sylow
408C22×SD16—831no—
409C22×SD16—831no—
410C22×D8—831no—
411C22×D8—831no—
412C22×M16—831no—
413C23×C8—831no—
414#542—24no—
415#542C2×D8318yescomplemented
416#540—838no—
417#540—1664no—
418C2×C4⋊Q8C2×D8311yescharacteristic
419C2×#127—831no—
420C2×#126—21no—
421C2×#125—831no—
422C2×#124—21no—
423C2×#124C2×D8311yescharacteristic
424C2×#123—21no—
425C2×#123—1661no—
426C2×#123—1661no—
427C2×C22⋊Q8—21no—
428C2×C22⋊Q8C2×D8311yescharacteristic
429C2×#121—831no—
430C2×#121—831no—
431C2×#121—1661no—
432C2×#121—1661no—
433C2×#121C2×D8311yescharacteristic
434C2×C4×Q8C2×D8311yescharacteristic
435C2×C4×D4—831no—
436C2×C4×D4—831no—
437C2×C4×D4C2×D8311yescharacteristic
438C2×#117C2×D8311yescharacteristic
439#501—838no—
440#496—838no—
441#488—838no—
442#486—838no—
443#469—838no—
444#468—838no—
445#466—838no—
446#465—838no—
447#442—838no—
448#440—838no—
449C4×SD16—838no—
450C4×D8—838no—
451C2×#107—831no—
452C2×#107—831no—
453C2×#106—831no—
454C2×#106—831no—
455C2×#103—831no—
456C2×#103—831no—
457C2×#102—831no—
458C2×#102—831no—
459C2×#102—831no—
460C2×#102—831no—
461C2×#102—831no—
462C2×#102—831no—
463#405—838no—
464C2×#97—831no—
465C2×#97—831no—
466C2×C4×C8—831no—
467C2×C4×C8—831no—
468C22×Q8—21no—
469C22×Q8C22×D8311yescharacteristic
470C22×D4—21no—
471C22×D4—831no—
472C22×D4—831no—
473C22×D4—1661no—
474C22×D4—1661no—
475C22×D4—1661no—
476C22×D4—1661no—
477C22×D4C22×D8311yescharacteristic
478C23×C4—21no—
479C23×C4—1661no—
480C23×C4—1661no—
481C23×C4C22×D8311yescharacteristic
482C2×SD16—834no—
483C2×SD16—834no—
484C2×SD16—1664no—
485C2×SD16—1664no—
486C2×D8—834no—
487C2×D8—834no—
488C2×D8—1664no—
489C2×D8—1664no—
490C2×M16—834no—
491C2×M16—1664no—
492C22×C8—831no—
493C22×C8—831no—
494C22×C8—831no—
495C22×C8—834no—
496C22×C8—831no—
497C22×C8—1664no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D8314yes—
500#127—834no—
501#127—1662no—
502#126—28no—
503#125—834no—
504#125—1662no—
505#124—28no—
506#124—22no—
507#124C22×D8314yes—
508#123—28no—
509#123—1668no—
510#123—1668no—
511C22⋊Q8—22no—
512C22⋊Q8—28no—
513C22⋊Q8C22×D8314yes—
514#121—22no—
515#121—834no—
516#121—834no—
517#121—1662no—
518#121—1662no—
519#121—1668no—
520#121—1668no—
521#121C22×D8314yes—
522C4×Q8—22no—
523C4×Q8C22×D8314yes—
524C4×D4—22no—
525C4×D4—834no—
526C4×D4—834no—
527C4×D4—1662no—
528C4×D4—1662no—
529C4×D4C22×D8314yes—
530#117C22⋊D8314yes—
531#117C22×D8314yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—831no—
536C2×C4⋊C4—831no—
537C2×C4⋊C4—1661no—
538C2×C4⋊C4—1661no—
539C2×C4⋊C4C22⋊D8311yescharacteristic
540C2×C4⋊C4C22⋊D8311yescharacteristic
541C2×C4⋊C4C22×D8311yescharacteristic
542C2×C4⋊C4C22×D8311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—1661no—
549C2×C22⋊C4—1661no—
550C2×C22⋊C4—1661no—
551C2×C22⋊C4—1661no—
552C2×C22⋊C4C22⋊D8311yescharacteristic
553C2×C22⋊C4C22⋊D8311yescharacteristic
554C2×C42—21no—
555C2×C42C22×D8311yescharacteristic
556C2×C42C22×D8311yescharacteristic
557#107—834no—
558#107—834no—
559#106—834no—
560#106—834no—
561#103—834no—
562#103—834no—
563#102—834no—
564#102—834no—
565#102—834no—
566#102—834no—
567#102—834no—
568#102—834no—
569#97—834no—
570#97—834no—
571C4×C8—834no—
572C4×C8—834no—
573C24—21no—
574C24—1661no—
575C24—1661no—
576C24C2×C22⋊D8311yescharacteristic
577C2×Q8—21no—
578C2×Q8—24no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—82no—
582C2×Q8C23×D8312yes—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—82no—
588C2×D4—832no—
589C2×D4—832no—
590C2×D4—6642no—
591C2×D4—6642no—
592C2×D4—6642no—
593C2×D4—6642no—
594C2×D4—1664no—
595C2×D4—1664no—
596C2×D4—1661no—
597C2×D4—1661no—
598C2×D4—1664no—
599C2×D4—1664no—
600C2×D4—1662no—
601C2×D4—1662no—
602C2×D4—1662no—
603C2×D4—1662no—
604C2×D4C23×D8312yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—6642no—
613C22×C4—6642no—
614C22×C4—1661no—
615C22×C4—1661no—
616C22×C4—1664no—
617C22×C4—1664no—
618C22×C4C2×C22⋊D8312yes—
619C22×C4C2×C22⋊D8311yescharacteristic
620C22×C4C2×C22⋊D8311yescharacteristic
621C22×C4C2×C22⋊D8311yescharacteristic
622C22×C4C2×C22⋊D8311yescharacteristic
623C22×C4C2×C22⋊D8311yescharacteristic
624C22×C4C23×D8312yes—
625C22×C4C23×D8311yescharacteristic
626SD16—1668no—
627SD16—1668no—
628D8—1668no—
629D8—1668no—
630M16—1668no—
631C2×C8—834no—
632C2×C8—834no—
633C2×C8—832no—
634C2×C8—832no—
635C2×C8—832no—
636C2×C8—832no—
637C2×C8—1668no—
638C2×C8—1662no—
639C2×C8—1662no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—832no—
646C4⋊C4—832no—
647C4⋊C4—1661no—
648C4⋊C4—1661no—
649C4⋊C4—1664no—
650C4⋊C4—1664no—
651C4⋊C4C2×C22⋊D8314yes—
652C4⋊C4C2×C22⋊D8314yes—
653C4⋊C4C23×D8312yes—
654C4⋊C4C23×D8312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1664no—
661C22⋊C4—1664no—
662C22⋊C4—1664no—
663C22⋊C4—1664no—
664C22⋊C4C2×C22⋊D8314yes—
665C22⋊C4C2×C22⋊D8314yes—
666C42—24no—
667C42C2×C22⋊D8312yes—
668C42C2×C22⋊D8312yes—
669C42C23×D8312yes—
670C42C23×D8312yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—3322no—
679C23—3322no—
680C23—3322no—
681C23—3322no—
682C23—3322no—
683C23—3322no—
684C23—1662no—
685C23—1662no—
686C23C22×C22⋊D8312yes—
687C23C22×C22⋊D8311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—84no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—3322no—
697D4—3322no—
698D4—6644no—
699D4—6644no—
700D4—6644no—
701D4—6644no—
702D4—1662no—
703D4—1662no—
704D4—1662no—
705D4—1662no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—3322no—
722C2×C4—3322no—
723C2×C4—6644no—
724C2×C4—6644no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4C22×C22⋊D8312yes—
728C2×C4C22×C22⋊D8312yes—
729C2×C4C22×C22⋊D8312yes—
730C2×C4C22×C22⋊D8312yes—
731C2×C4C22×C22⋊D8312yes—
732C2×C4C22×C22⋊D8311yescharacteristic
733C2×C4#41×D8312yes—
734C2×C4#41×D8312yes—
735C2×C4C24×D8311yescharacteristic
736C8—834no—
737C8—834no—
738C8—1662no—
739C8—1662no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—3322no—
749C22—3322no—
750C22—3322no—
751C22—3322no—
752C22—3322no—
753C22—3322no—
754C22—6644no—
755C22—6644no—
756C22#1912824712yes—
757C22#1912850412yes—
758C22#1912850912yes—
759C22C23×C22⋊D8311yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—3322no—
769C4—3322no—
770C4#1912824712yes—
771C4C2×#41×D8311yescharacteristic
772C4C2×#41×D8311yescharacteristic
773C2—42no—
774C2—82no—
775C2—6642no—
776C2—6642no—
777C2#2491814014yesdirect product factor
778C2C2×#1912824711yescharacteristic
779C2C2×#1912850411yescharacteristic
780C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#542×C83C2
socleC23×C83C22×D4
hypercenterC2×#542D83
hypocenterC83C2×#3179
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×#19128306C2semidirect
2. #24918140C2direct (N × H)
3. C2×#19128107C2semidirect
4. C2×#19128091C2semidirect
5. C2×#19128055C2semidirect
6. C2×#19128049C2semidirect
7. C2×#19127952C2semidirect
8. C2×#19127949C2semidirect
9. C2×#19127935C2semidirect
10. C2×#19127932C2semidirect
11. C2×#19127811C2semidirect
12. C2×#19127799C2semidirect
13. C2×C4×#13050577C2semidirect
14. C2×C4×#13050575C2semidirect
15. C2×#19127657C2semidirect
16. C2×#542×C83C2semidirect
24. #19128306C22semidirect
35. #19128107C22semidirect
36. #19128091C22semidirect
37. #19128055C22semidirect
38. #19128049C22semidirect
39. #19127952C22semidirect
40. #19127949C22semidirect
41. #19127935C22semidirect
42. #19127932C22semidirect
43. #19127811C22semidirect
44. #19127799C22semidirect
45. C4×#13050577C22semidirect
46. C4×#13050575C22semidirect
59. #19127657C22semidirect
65. #542×C83C22semidirect
385. C2×C83#3179semidirect
391. C2×#542D83semidirect
407. C83C2×#3179semidirect
415. #542C2×D83semidirect
777. C2#24918140direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283062
#249181402
C2×#191281072
C2×#191280912
C2×#191280552
C2×#191280492
C2×#191279522
C2×#191279492
C2×#191279352
C2×#191279322
C2×#191278112
C2×#191277992
C2×C4×#130505772
C2×C4×#130505752
C2×#191276572
C2×#542×C832
C2×#317983