Finite Group Databasebeta

← C2×#24918859 #36277287

Subgroups — C2×#24918859 #36277287

Order 21248.

1930 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×#19128235C211yesmaximal, characteristic, complemented
2#24918859C2116yesmaximal, direct product factor
3C2×#19128008C211yesmaximal, characteristic, complemented
4C2×#19128005C211yesmaximal, characteristic, complemented
5C2×#19128001C211yesmaximal, characteristic, complemented
6C2×#19127998C211yesmaximal, characteristic, complemented
7C2×#19127957C211yesmaximal, characteristic, complemented
8C2×#19127952C211yesmaximal, characteristic
9C2×#19127949C211yesmaximal, characteristic, complemented
10C2×#19127945C211yesmaximal, characteristic, complemented
11C2×#19127923C211yesmaximal, characteristic, complemented
12C2×#19127920C211yesmaximal, characteristic, complemented
13C2×#19127916C211yesmaximal, characteristic, complemented
14C2×#19127913C211yesmaximal, characteristic, complemented
15C2×#19127725C211yesmaximal, characteristic, complemented
16C2×#529×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C22×#13050578C2211yescharacteristic
19C22×#13050577C2211yescharacteristic
20C22×#13050575C2211yescharacteristic
21C22×#13050574C2211yescharacteristic
22C22×#13050574C2211yescharacteristic
23#19128235—24no—
24#19128235C2218yescomplemented
25C2×#14581786—21no—
26C2×#14581784C2211yescharacteristic
27C2×#14581780C2211yescharacteristic
28C2×#14581775—21no—
29C2×#14581771C2211yescharacteristic
30C2×#14581766C2211yescharacteristic
31C2×C4×Dic166C2211yescharacteristic
32C2×C4×D332C2211yescharacteristic
33C2×C4×C22⋊D83—21no—
34C2×#14581749—21no—
35#19128008C2218yescomplemented
36#19128005C2218yescomplemented
37#19128001C2218yescomplemented
38#19127998C2218yescomplemented
39#19127957C2218yescomplemented
40#19127952C2218yes—
41#19127949C2218yescomplemented
42#19127945C2218yescomplemented
43#19127923C2218yescomplemented
44#19127920C2218yescomplemented
45#19127916C2218yescomplemented
46#19127913C2218yescomplemented
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51#19127725C2218yescomplemented
52C2×C4⋊(C83⋊C8)C2211yescharacteristic
53C2×C4⋊(C83⋊C8)C2211yescharacteristic
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×C4⋊(C83⋊C8)C2211yescharacteristic
56C2×#14581716C2211yescharacteristic
57C2×#14581716C2211yescharacteristic
58C2×#14581715C2211yescharacteristic
59C2×#14581715C2211yescharacteristic
60C2×#14581713C2211yescharacteristic
61C2×#14581713C2211yescharacteristic
62C2×#14581712C2211yescharacteristic
63C2×#14581712C2211yescharacteristic
64#529×C83—24no—
65#529×C83C2218yescomplemented
66C2×#126×C83—21no—
67C2×#125×C83C2211yescharacteristic
68C2×#124×C83C2211yescharacteristic
69C2×#123×C83—21no—
70C2×C22⋊Q8×C83C2211yescharacteristic
71C2×#121×C83C2211yescharacteristic
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×D4×C83—21no—
74C2×C4×D4×C83C2211yescharacteristic
75C2×#117×C83—21no—
76C22×C42×C83C2211yescharacteristic
77C22×Dic166C2311yescharacteristic
78C22×D332C2311yescharacteristic
79C22×C22⋊D83—21no—
80C22×C4×D83—21no—
81C2×#13050580—42no—
82C2×#13050580C2314yes—
83C2×#13050578—42no—
84C2×#13050578C2314yes—
85C2×#13050577—42no—
86C2×#13050577C2314yes—
87C2×#13050575—42no—
88C2×#13050575C2314yes—
89C2×#13050574—42no—
90C2×#13050574—42no—
91C2×#13050574C2314yes—
92C2×#13050574C2314yes—
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2311yescharacteristic
95C22×C83⋊C8C2311yescharacteristic
96C22×C83⋊C8C2311yescharacteristic
97#14581786—28no—
98#14581784—22no—
99#14581784C2314yes—
100#14581780—22no—
101#14581780C2314yes—
102#14581775—28no—
103#14581771—22no—
104#14581771C2314yes—
105#14581766—22no—
106#14581766C2314yes—
107C4×Dic166—22no—
108C4×Dic166C2314yes—
109C4×D332—22no—
110C4×D332C2314yes—
111C4×C22⋊D83—28no—
112#14581749—28no—
113C2×C4⋊Dic83C2311yescharacteristic
114C2×C4⋊Dic83C2311yescharacteristic
115C2×Dic83⋊C4—21no—
116C2×Dic83⋊C4—21no—
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#14581725C2314yes—
126#14581725C2314yes—
127#14581723C2314yes—
128#14581723C2314yes—
129C4⋊(C83⋊C8)C2314yes—
130C4⋊(C83⋊C8)C2314yes—
131C4⋊(C83⋊C8)C2314yes—
132C4⋊(C83⋊C8)C2314yes—
133#14581716C2314yes—
134#14581716C2314yes—
135#14581715C2314yes—
136#14581715C2314yes—
137#14581713C2314yes—
138#14581713C2314yes—
139#14581712C2314yes—
140#14581712C2314yes—
141C22×Q8×C83C2311yescharacteristic
142C22×D4×C83—21no—
143C22×D4×C83C2311yescharacteristic
144C23×C4×C83—21no—
145C23×C4×C83D411yescharacteristic
146C23×C4×C83D411yescharacteristic
147C23×C4×C83C2311yescharacteristic
148#126×C83—28no—
149#125×C83—22no—
150#125×C83C2314yes—
151#124×C83—22no—
152#124×C83C2314yes—
153#123×C83—28no—
154C22⋊Q8×C83—22no—
155C22⋊Q8×C83C2314yes—
156#121×C83—22no—
157#121×C83C2314yes—
158C4×Q8×C83—22no—
159C4×Q8×C83C2314yes—
160C4×D4×C83—28no—
161C4×D4×C83—22no—
162C4×D4×C83C2314yes—
163#117×C83—28no—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2311yescharacteristic
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×C83D411yescharacteristic
177C2×C42×C83D411yescharacteristic
178C2×C42×C83D414yes—
179C2×C42×C83C2311yescharacteristic
180C2×C42×C83C2311yescharacteristic
181C2×C42×C83C2314yes—
182C23×D83—21no—
183C2×Dic166—22no—
184C2×Dic166—22no—
185C2×Dic166—21no—
186C2×Dic166C2412yes—
187C2×D332—22no—
188C2×D332—22no—
189C2×D332—21no—
190C2×D332C2412yes—
191C2×C22⋊D83—24no—
192C2×C22⋊D83—44no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C2×C4×D83—24no—
197C2×C4×D83—44no—
198#13050580—44no—
199#13050578—44no—
200#13050577—44no—
201#13050575—44no—
202#13050574—44no—
203#13050574—44no—
204C2×C83⋊C8—22no—
205C2×C83⋊C8—22no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—22no—
208C2×C83⋊C8C2412yes—
209C2×C83⋊C8C2412yes—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C4⋊Dic83—21no—
213C4⋊Dic83—21no—
214C4⋊Dic83C2412yes—
215C4⋊Dic83C2412yes—
216Dic83⋊C4—24no—
217Dic83⋊C4—24no—
218Dic83⋊C4—24no—
219Dic83⋊C4—24no—
220C22⋊Dic83—24no—
221(C2×D83)⋊C4—24no—
222(C2×D83)⋊C4—24no—
223(C2×D83)⋊C4—24no—
224(C2×D83)⋊C4—24no—
225C4×Dic83—24no—
226C24×C83—21no—
227C24×C83C2×D411yescharacteristic
228C2×Q8×C83—21no—
229C2×Q8×C83—22no—
230C2×Q8×C83—22no—
231C2×Q8×C83C2412yes—
232C2×D4×C83—24no—
233C2×D4×C83—21no—
234C2×D4×C83—22no—
235C2×D4×C83—22no—
236C2×D4×C83—44no—
237C2×D4×C83C2412yes—
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—24no—
244C22×C4×C83—42no—
245C22×C4×C83—42no—
246C22×C4×C83—44no—
247C22×C4×C83C2×D412yes—
248C22×C4×C83C2×D411yescharacteristic
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2×D411yescharacteristic
251C22×C4×C83C2×D411yescharacteristic
252C22×C4×C83C2×D411yescharacteristic
253C22×C4×C83C2×D414yes—
254C22×C4×C83C2×D414yes—
255C22×C4×C83C2412yes—
256C22×C4×C83C2411yescharacteristic
257C4⋊C4×C83—24no—
258C4⋊C4×C83—24no—
259C4⋊C4×C83—24no—
260C4⋊C4×C83—24no—
261C4⋊C4×C83—21no—
262C4⋊C4×C83—21no—
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—
270C42×C83—24no—
271C42×C83C2×D412yes—
272C42×C83C2×D414yes—
273C42×C83C2×D414yes—
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—
293D4×C83—22no—
294D4×C83—22no—
295D4×C83—48no—
296D4×C83—42no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—22no—
302C2×C4×C83—24no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—44no—
309C2×C4×C83—44no—
310C2×C4×C83—48no—
311C2×C4×C83—42no—
312C2×C4×C83—42no—
313C2×C4×C83—42no—
314C2×C4×C83C22×D412yes—
315C2×C4×C83C22×D412yes—
316C2×C4×C83C22×D412yes—
317C2×C4×C83C22×D412yes—
318C2×C4×C83C22×D412yes—
319C2×C4×C83C22×D411yescharacteristic
320C2×C4×C83H(5,𝔽2)12yes—
321C2×C4×C832−1+412yes—
322C2×C4×C83C2511yescharacteristic
323C22⋊D83—48no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—42no—
328C2×Dic83—42no—
329C2×Dic83—42no—
330D332—22no—
331D332—22no—
332D332—42no—
333C4×D83—48no—
334Dic166—22no—
335Dic166—22no—
336Dic166—42no—
337C83⋊C8—22no—
338C83⋊C8—22no—
339C83⋊C8—22no—
340C83⋊C8—22no—
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#53712yes—
350C22×C83#57512yes—
351C22×C83#57512yes—
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#53712yes—
366C4×C83C2×H(5,𝔽2)11yescharacteristic
367C4×C83C2×2−1+411yescharacteristic
368Dic83—42no—
369Dic83—42no—
370Dic83—42no—
371C2×#3256—831nomaximal, Sylow
372C2×C83—42no—
373C2×C83—82no—
374C2×C83#325614yescomplemented
375C2×C83C2×#53711yescharacteristic
376C2×C83C2×#57511yescharacteristic
377C2×C83C2×#57511yescharacteristic
378D83—82no—
379C2×#529—831no—
380C2×#529D8311yescharacteristic, complemented
381#3256—8316no—
382C2×#479—831no—
383C2×#479—831no—
384C2×#478—831no—
385C2×#478—831no—
386C2×#470—831no—
387C2×#469—831no—
388C2×#468—831no—
389C2×#468—831no—
390C2×#464—831no—
391C2×#464—831no—
392C2×#463—831no—
393C2×#463—831no—
394C2×#423—831no—
395C83C2×#325611yescharacteristic, complemented, Sylow
396C22×Q16—831no—
397C22×SD16—831no—
398C22×SD16—831no—
399C22×D8—831no—
400C22×M16—831no—
401C22×M16—831no—
402#529—24no—
403#529—838no—
404#529—1664no—
405#529C2×D8318yescomplemented
406C2×#126—21no—
407C2×#126—1661no—
408C2×#125—831no—
409C2×#125C2×D8311yescharacteristic
410C2×#124—831no—
411C2×#124C2×D8311yescharacteristic
412C2×#123—21no—
413C2×#123—1661no—
414C2×C22⋊Q8—831no—
415C2×C22⋊Q8C2×D8311yescharacteristic
416C2×#121—831no—
417C2×#121C2×D8311yescharacteristic
418C2×C4×Q8—831no—
419C2×C4×Q8C2×D8311yescharacteristic
420C2×C4×D4—21no—
421C2×C4×D4—831no—
422C2×C4×D4—1661no—
423C2×C4×D4C2×D8311yescharacteristic
424C2×#117—21no—
425C2×#117—1661no—
426C22×C42C2×D8311yescharacteristic
427#479—838no—
428#479—838no—
429#478—838no—
430#478—838no—
431#470—838no—
432#469—838no—
433#468—838no—
434#468—838no—
435#464—838no—
436#464—838no—
437#463—838no—
438#463—838no—
439C2×#107—831no—
440C2×#107—831no—
441C2×#106—831no—
442C2×#106—831no—
443#423—838no—
444C2×C4⋊C8—831no—
445C2×C4⋊C8—831no—
446C2×C4⋊C8—831no—
447C2×C4⋊C8—831no—
448C2×#103—831no—
449C2×#103—831no—
450C2×#103—831no—
451C2×#103—831no—
452C2×#102—831no—
453C2×#102—831no—
454C2×#102—831no—
455C2×#102—831no—
456C22×Q8—831no—
457C22×Q8C22×D8311yescharacteristic
458C22×D4—21no—
459C22×D4—831no—
460C22×D4—1661no—
461C22×D4C22×D8311yescharacteristic
462C23×C4—21no—
463C23×C4—1661no—
464C23×C4C22⋊D8311yescharacteristic
465C23×C4C22⋊D8311yescharacteristic
466C23×C4C22×D8311yescharacteristic
467C2×Q16—3322no—
468C2×Q16—834no—
469C2×SD16—3322no—
470C2×SD16—3322no—
471C2×SD16—834no—
472C2×SD16—834no—
473C2×D8—3322no—
474C2×D8—834no—
475C2×M16—3322no—
476C2×M16—3322no—
477C2×M16—834no—
478C2×M16—834no—
479C22×C8—831no—
480C22×C8—831no—
481C22×C8—831no—
482C22×C8—831no—
483#126—28no—
484#126—1668no—
485#125—22no—
486#125—834no—
487#125—1662no—
488#125C22×D8314yes—
489#124—22no—
490#124—834no—
491#124—1662no—
492#124C22×D8314yes—
493#123—28no—
494#123—1668no—
495C22⋊Q8—22no—
496C22⋊Q8—834no—
497C22⋊Q8—1662no—
498C22⋊Q8C22×D8314yes—
499#121—22no—
500#121—834no—
501#121—1662no—
502#121C22×D8314yes—
503C4×Q8—22no—
504C4×Q8—834no—
505C4×Q8—1662no—
506C4×Q8C22×D8314yes—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—834no—
510C4×D4—1668no—
511C4×D4—1662no—
512C4×D4C22×D8314yes—
513#117—28no—
514#117—1668no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—831no—
520C2×C4⋊C4—831no—
521C2×C4⋊C4—1661no—
522C2×C4⋊C4—1661no—
523C2×C4⋊C4—1661no—
524C2×C4⋊C4—1661no—
525C2×C4⋊C4C22×D8311yescharacteristic
526C2×C4⋊C4C22×D8311yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1661no—
533C2×C22⋊C4—1661no—
534C2×C22⋊C4—1661no—
535C2×C22⋊C4—1661no—
536C2×C22⋊C4—1661no—
537C2×C42—21no—
538C2×C42—1661no—
539C2×C42C22⋊D8311yescharacteristic
540C2×C42C22⋊D8311yescharacteristic
541C2×C42C22⋊D8314yes—
542C2×C42C22×D8311yescharacteristic
543C2×C42C22×D8311yescharacteristic
544C2×C42C22×D8314yes—
545#107—834no—
546#107—834no—
547#106—834no—
548#106—834no—
549C4⋊C8—834no—
550C4⋊C8—834no—
551C4⋊C8—834no—
552C4⋊C8—834no—
553#103—834no—
554#103—834no—
555#103—834no—
556#103—834no—
557#102—834no—
558#102—834no—
559#102—834no—
560#102—834no—
561C24—21no—
562C24—1661no—
563C24C2×C22⋊D8311yescharacteristic
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—832no—
568C2×Q8—1662no—
569C2×Q8—1662no—
570C2×Q8—1661no—
571C2×Q8C23×D8312yes—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—44no—
577C2×D4—3324no—
578C2×D4—832no—
579C2×D4—1664no—
580C2×D4—1661no—
581C2×D4—1662no—
582C2×D4—1662no—
583C2×D4C23×D8312yes—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—24no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—3324no—
594C22×C4—1661no—
595C22×C4—1661no—
596C22×C4—1661no—
597C22×C4—1664no—
598C22×C4C2×C22⋊D8312yes—
599C22×C4C2×C22⋊D8311yescharacteristic
600C22×C4C2×C22⋊D8311yescharacteristic
601C22×C4C2×C22⋊D8311yescharacteristic
602C22×C4C2×C22⋊D8311yescharacteristic
603C22×C4C2×C22⋊D8311yescharacteristic
604C22×C4C2×C22⋊D8314yes—
605C22×C4C2×C22⋊D8314yes—
606C22×C4C23×D8312yes—
607C22×C4C23×D8311yescharacteristic
608Q16—3324no—
609SD16—3324no—
610SD16—3324no—
611D8—3324no—
612M16—3324no—
613M16—3324no—
614C2×C8—832no—
615C2×C8—832no—
616C2×C8—832no—
617C2×C8—832no—
618C2×C8—1662no—
619C2×C8—1662no—
620C2×C8—1662no—
621C2×C8—1662no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—832no—
629C4⋊C4—832no—
630C4⋊C4—1661no—
631C4⋊C4—1661no—
632C4⋊C4—1664no—
633C4⋊C4—1664no—
634C4⋊C4—1664no—
635C4⋊C4—1664no—
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—
648C42—24no—
649C42—1664no—
650C42C2×C22⋊D8314yes—
651C42C2×C22⋊D8312yes—
652C42C2×C22⋊D8312yes—
653C42C2×C22⋊D8314yes—
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—3322no—
673Q8—1662no—
674Q8—1662no—
675D4—22no—
676D4—22no—
677D4—48no—
678D4—42no—
679D4—3328no—
680D4—3322no—
681D4—1662no—
682D4—1662no—
683C2×C4—22no—
684C2×C4—22no—
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—44no—
695C2×C4—44no—
696C2×C4—48no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—3328no—
701C2×C4—3322no—
702C2×C4—3322no—
703C2×C4—3322no—
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#1458183812yes—
714C2×C4#1458183912yes—
715C2×C4C24×D8311yescharacteristic
716C8—1662no—
717C8—1662no—
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#1912827912yes—
733C22#1912849912yes—
734C22#1912849912yes—
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#1912827912yes—
748C4C2×#1458183811yescharacteristic
749C4C2×#1458183911yescharacteristic
750C2—42no—
751C2—82no—
752C2—6642no—
753C2#2491885914yesdirect product factor
754C2C2×#1912827911yescharacteristic
755C2C2×#1912849911yescharacteristic
756C2C2×#1912849911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#529×C83C2
socleC23×C83C22×D4
prime radicalC2×#19127952C2
hypercenterC2×#529D83
hypocenterC83C2×#3256
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#19128235C2semidirect
2. #24918859C2direct (N × H)
3. C2×#19128008C2semidirect
4. C2×#19128005C2semidirect
5. C2×#19128001C2semidirect
6. C2×#19127998C2semidirect
7. C2×#19127957C2semidirect
9. C2×#19127949C2semidirect
10. C2×#19127945C2semidirect
11. C2×#19127923C2semidirect
12. C2×#19127920C2semidirect
13. C2×#19127916C2semidirect
14. C2×#19127913C2semidirect
15. C2×#19127725C2semidirect
16. C2×#529×C83C2semidirect
24. #19128235C22semidirect
35. #19128008C22semidirect
36. #19128005C22semidirect
37. #19128001C22semidirect
38. #19127998C22semidirect
39. #19127957C22semidirect
41. #19127949C22semidirect
42. #19127945C22semidirect
43. #19127923C22semidirect
44. #19127920C22semidirect
45. #19127916C22semidirect
46. #19127913C22semidirect
51. #19127725C22semidirect
65. #529×C83C22semidirect
374. C2×C83#3256semidirect
380. C2×#529D83semidirect
395. C83C2×#3256semidirect
405. #529C2×D83semidirect
753. C2#24918859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282352
#249188592
C2×#191280082
C2×#191280052
C2×#191280012
C2×#191279982
C2×#191279572
C2×#191279522
C2×#191279492
C2×#191279452
C2×#191279232
C2×#191279202
C2×#191279162
C2×#191279132
C2×#191277252
C2×#529×C832
C2×#325683