Finite Group Databasebeta

← C2×#24917093 #36271562

Subgroups — C2×#24917093 #36271562

Order 21248.

2898 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581825C211yesmaximal, characteristic, complemented
2C2×#19128212C211yesmaximal, characteristic
3C22×#14581771C211yesmaximal, characteristic, complemented
4#24917093C2116yesmaximal, direct product factor
5C2×#19127959C212yesmaximal, complemented
6C2×#19127947C212yesmaximal, complemented
7C2×#19127942C212yesmaximal, complemented
8C2×#19127930C212yesmaximal, complemented
9C2×#19127743C211yesmaximal, characteristic, complemented
10C2×#19127703C211yesmaximal, characteristic, complemented
11C2×#19127711C211yesmaximal, characteristic, complemented
12C23×M16×C83C211yesmaximal, characteristic, complemented
13C22×#13050590C2211yescharacteristic
14C23×Dic166C2211yescharacteristic
15C2×#14581825—28no—
16C2×#14581825C2218yescomplemented
17C22×Dic332C2212yescomplemented
18C22×#13050579C2212yescomplemented
19#19128212—24no—
20#19128212C2218yes—
21C2×#14581775—21no—
22C2×#14581771—24no—
23C2×#14581771—21no—
24C2×#14581771—21no—
25C2×#14581771C2212yes—
26C2×#14581771C2211yescharacteristic
27C2×#14581771C2212yes—
28C2×#14581771C2211yescharacteristic
29C2×#14581771C2218yescomplemented
30C2×#14581766C2211yescharacteristic
31C2×#14581766C2211yescharacteristic
32C2×#14581761—21no—
33C2×C4×C22⋊D83—21no—
34C2×C4×C22⋊D83—21no—
35C2×#14581751C2211yescharacteristic
36C22×C4⋊Dic83C2211yescharacteristic
37C22×Dic83⋊C4—21no—
38C22×C22⋊Dic83—21no—
39#19127959C22116yescomplemented
40#19127947C22116yescomplemented
41#19127942C22116yescomplemented
42#19127930C22116yescomplemented
43#19127743C2218yescomplemented
44C2×#14581726C2212yescomplemented
45C2×#14581724C2212yescomplemented
46#19127711C2218yescomplemented
47#19127703C2218yescomplemented
48C2×#14581717C2212yescomplemented
49C2×#14581717C2212yescomplemented
50C2×#14581717C2212yescomplemented
51C2×#14581714C2212yescomplemented
52C24×C4×C83C2211yescharacteristic
53C22×M16×C83—28no—
54C22×M16×C83C2211yescharacteristic
55C22×M16×C83C2212yes—
56C22×M16×C83C2211yescharacteristic
57C22×M16×C83C2218yescomplemented
58C23×C8×C83C2212yes—
59C2×#13050590—22no—
60C2×#13050590—24no—
61C2×#13050590—24no—
62C2×#13050590C2314yes—
63C22×Dic166—21no—
64C22×Dic166—22no—
65C22×Dic166—24no—
66C22×Dic166—24no—
67C22×Dic166C2312yes—
68C22×Dic166C2311yescharacteristic
69C22×Dic166C2314yes—
70C22×D332C2311yescharacteristic
71C22×C22⋊D83—21no—
72C22×C22⋊D83—21no—
73C22×C22⋊D83—21no—
74C23×Dic83—21no—
75C23×Dic83—21no—
76C22×C4×D83—21no—
77#14581825—232no—
78C2×Dic332—28no—
79C2×Dic332C2318yescomplemented
80C2×#13050579—28no—
81C2×#13050579C2318yescomplemented
82#14581775—28no—
83#14581771—24no—
84#14581771—24no—
85#14581771—28no—
86#14581771—28no—
87#14581771—22no—
88#14581771—22no—
89#14581771C2318yes—
90#14581771C2314yes—
91#14581771C2318yes—
92#14581771C2314yes—
93#14581766—22no—
94#14581766—22no—
95#14581766C2314yes—
96#14581766C2314yes—
97#14581761—28no—
98C4×C22⋊D83—28no—
99C4×C22⋊D83—28no—
100#14581751—22no—
101#14581751C2314yes—
102C2×C4⋊Dic83—21no—
103C2×C4⋊Dic83—22no—
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2314yes—
106C2×C4⋊Dic83C2311yescharacteristic
107C2×C4⋊Dic83C2311yescharacteristic
108C2×Dic83⋊C4—22no—
109C2×Dic83⋊C4—22no—
110C2×Dic83⋊C4—28no—
111C2×Dic83⋊C4—21no—
112C2×Dic83⋊C4—21no—
113C2×C22⋊Dic83—22no—
114C2×C22⋊Dic83—22no—
115C2×C22⋊Dic83—28no—
116C2×C22⋊Dic83—21no—
117C2×C22⋊Dic83—21no—
118C2×C22⋊Dic83—21no—
119C2×(C2×D83)⋊C4—21no—
120C2×(C2×D83)⋊C4—21no—
121C2×C4×Dic83—21no—
122#14581726C2318yescomplemented
123#14581724C2318yescomplemented
124#14581717C2318yescomplemented
125#14581717C2318yescomplemented
126#14581717C2318yescomplemented
127#14581714C2318yescomplemented
128C25×C83D411yescharacteristic
129C23×C4×C83—24no—
130C23×C4×C83—24no—
131C23×C4×C83D411yescharacteristic
132C23×C4×C83D411yescharacteristic
133C23×C4×C83D411yescharacteristic
134C23×C4×C83D414yes—
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2314yes—
138C23×C4×C83C2311yescharacteristic
139C2×M16×C83—24no—
140C2×M16×C83—232no—
141C2×M16×C83—28no—
142C2×M16×C83D418yescomplemented
143C2×M16×C83C2318yes—
144C2×M16×C83C2314yes—
145C2×M16×C83C2314yes—
146C22×C8×C83—28no—
147C22×C8×C83C2312yes—
148C22×C8×C83C2318yes—
149C22×C8×C83C2312yes—
150C23×D83—21no—
151#13050590—28no—
152#13050590—28no—
153#13050590—48no—
154C2×Dic166—24no—
155C2×Dic166—22no—
156C2×Dic166—28no—
157C2×Dic166—24no—
158C2×Dic166—28no—
159C2×Dic166—22no—
160C2×Dic166—24no—
161C2×Dic166—22no—
162C2×Dic166—21no—
163C2×Dic166—44no—
164C2×Dic166—48no—
165C2×Dic166C2414yes—
166C2×Dic166C2412yes—
167C2×D332—22no—
168C2×D332—22no—
169C2×D332—21no—
170C2×D332C2412yes—
171C2×C22⋊D83—24no—
172C2×C22⋊D83—24no—
173C2×C22⋊D83—24no—
174C2×C22⋊D83—44no—
175C2×C22⋊D83—44no—
176C2×C22⋊D83—44no—
177C22×Dic83—21no—
178C22×Dic83—24no—
179C22×Dic83—22no—
180C22×Dic83—24no—
181C22×Dic83—22no—
182C22×Dic83—21no—
183C22×Dic83—21no—
184C22×Dic83—44no—
185C22×Dic83—44no—
186C2×C4×D83—24no—
187C2×C4×D83—44no—
188Dic332—216no—
189#13050579—216no—
190C4⋊Dic83—21no—
191C4⋊Dic83—21no—
192C4⋊Dic83—24no—
193C4⋊Dic83—22no—
194C4⋊Dic83C2412yes—
195C4⋊Dic83C2412yes—
196C4⋊Dic83C2414yes—
197Dic83⋊C4—28no—
198Dic83⋊C4—28no—
199Dic83⋊C4—24no—
200Dic83⋊C4—24no—
201C22⋊Dic83—24no—
202C22⋊Dic83—24no—
203C22⋊Dic83—24no—
204C22⋊Dic83—28no—
205C22⋊Dic83—28no—
206(C2×D83)⋊C4—24no—
207(C2×D83)⋊C4—24no—
208C4×Dic83—24no—
209C24×C83—24no—
210C24×C83—24no—
211C24×C83—42no—
212C24×C83C2×D411yescharacteristic
213C24×C83C2×D414yes—
214C24×C83C2×D411yescharacteristic
215C24×C83C2×D411yescharacteristic
216C22×C4×C83—24no—
217C22×C4×C83—24no—
218C22×C4×C83—24no—
219C22×C4×C83—216no—
220C22×C4×C83—22no—
221C22×C4×C83—28no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—28no—
226C22×C4×C83C2×D414yes—
227C22×C4×C83C2×D412yes—
228C22×C4×C83C2×D412yes—
229C22×C4×C83C2×D414yes—
230C22×C4×C83C2×D414yes—
231C22×C4×C83C2×D414yes—
232C22×C4×C83C2×D411yescharacteristic
233C22×C4×C83C2×D411yescharacteristic
234C22×C4×C83C2×D411yescharacteristic
235C22×C4×C83C2×D412yes—
236C22×C4×C83#4114yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2411yescharacteristic
240C22×C4×C83C2412yes—
241M16×C83—28no—
242M16×C83—216no—
243M16×C83C2×D4116yescomplemented
244C2×C8×C83—24no—
245C2×C8×C83—216no—
246C2×C8×C83C2×D418yes—
247C2×C8×C83C2414yes—
248C2×C8×C83C2414yes—
249C23×C83—22no—
250C23×C83—22no—
251C23×C83—22no—
252C23×C83—22no—
253C23×C83—28no—
254C23×C83—22no—
255C23×C83—22no—
256C23×C83—28no—
257C23×C83—22no—
258C23×C83—44no—
259C23×C83—416no—
260C23×C83#12114yes—
261C23×C83#13714yescomplemented
262C23×C83C22×D412yes—
263C23×C83C22×D412yes—
264C23×C83C22×D412yes—
265C23×C83C22×D411yescharacteristic
266C22×D83—22no—
267C22×D83—42no—
268C22×D83—42no—
269C22×D83—42no—
270C2×C4×C83—28no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—24no—
274C2×C4×C83—24no—
275C2×C4×C83—28no—
276C2×C4×C83—28no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83#12114yes—
282C2×C4×C83#12118yes—
283C2×C4×C83C22×D412yes—
284C2×C4×C83C22×D414yes—
285C2×C4×C83C22×D412yes—
286C2×C4×C83C22×D412yes—
287C2×C4×C83C22×D412yes—
288C2×C4×C83C22×D411yescharacteristic
289C2×C4×C83C2×#4112yes—
290C2×C4×C83C2×#4114yes—
291C2×C4×C83C2511yescharacteristic
292C22⋊D83—48no—
293C22⋊D83—48no—
294C22⋊D83—48no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—24no—
298C2×Dic83—22no—
299C2×Dic83—24no—
300C2×Dic83—48no—
301C2×Dic83—42no—
302C2×Dic83—48no—
303C2×Dic83—44no—
304C2×Dic83—42no—
305C2×Dic83—44no—
306C2×Dic83—42no—
307D332—22no—
308D332—22no—
309D332—42no—
310C4×D83—48no—
311Dic166—24no—
312Dic166—22no—
313Dic166—24no—
314Dic166—22no—
315Dic166—44no—
316Dic166—48no—
317Dic166—42no—
318C8×C83—24no—
319C8×C83C22×D418yes—
320C22×C83—22no—
321C22×C83—28no—
322C22×C83—28no—
323C22×C83—22no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—22no—
329C22×C83—416no—
330C22×C83—44no—
331C22×C83C2×#12114yes—
332C22×C83C2×#12112yes—
333C22×C83C2×#13712yes—
334C22×C83C2×#13714yescomplemented
335C22×C83#57512yes—
336C22×C83C23×D411yescharacteristic
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—42no—
340C2×D83—84no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83C2×#12112yes—
344C4×C83C2×#12114yes—
345C4×C83C23×D411yescharacteristic
346C4×C83C22×#4111yescharacteristic
347Dic83—44no—
348Dic83—42no—
349Dic83—42no—
350Dic83—44no—
351Dic83—42no—
352C2×#3056—831nomaximal, Sylow
353C2×C83—24no—
354C2×C83—24no—
355C2×C83—42no—
356C2×C83#305614yescomplemented
357C2×C83C22×#12111yescharacteristic
358C2×C83C22×#13711yescharacteristic
359C2×C83C2×#57511yescharacteristic
360D83—82no—
361C22×#137—831no—
362C23×M16D8311yescharacteristic, complemented
363C2×#525—831no—
364C22×C22⋊Q8—831no—
365#3056—8316no—
366C2×#470—832no—
367C2×#468—832no—
368C2×#467—832no—
369C2×#465—832no—
370C2×#428—831no—
371C2×#417—831no—
372C2×#419—831no—
373C83C2×#305611yescharacteristic, complemented, Sylow
374C22×#41—831no—
375C23×Q8—831no—
376C24×C4C2×D8311yescharacteristic
377C2×#137—838no—
378C2×#137—1668no—
379C22×Q16—832no—
380C22×SD16—832no—
381C22×M16—28no—
382C22×M16C2×D8311yescharacteristic
383C22×M16C2×D8312yes—
384C22×M16C2×D8311yescharacteristic
385C22×M16C2×D8318yescomplemented
386C23×C8C2×D8312yes—
387#525—838no—
388#525—1664no—
389C2×#123—1661no—
390C2×C22⋊Q8—832no—
391C2×C22⋊Q8—832no—
392C2×C22⋊Q8—838no—
393C2×C22⋊Q8—831no—
394C2×C22⋊Q8—831no—
395C2×C22⋊Q8—1661no—
396C2×C22⋊Q8—1661no—
397C2×C22⋊Q8—1664no—
398C2×#121—831no—
399C2×#121—831no—
400C2×#120—1661no—
401C2×C4×D4—1661no—
402C2×C4×D4—1661no—
403C2×#117—831no—
404C22×C4⋊C4—831no—
405C22×C4⋊C4—1661no—
406C22×C22⋊C4—1661no—
407#470—8316no—
408#468—8316no—
409#467—8316no—
410#465—8316no—
411#428—838no—
412C2×#107—832no—
413C2×#106—832no—
414#419—838no—
415#417—838no—
416C2×#103—832no—
417C2×#103—832no—
418C2×#103—832no—
419C2×#102—832no—
420C25D33211yescharacteristic
421C2×#41—834no—
422C2×#41—1664no—
423C2×#41—1664no—
424C2×#41—1662no—
425C22×Q8—832no—
426C22×Q8—831no—
427C22×Q8—834no—
428C22×Q8—1664no—
429C22×Q8—1664no—
430C22×Q8—1662no—
431C22×Q8—1661no—
432C22×D4—831no—
433C22×D4—1661no—
434C22×D4—1661no—
435C22×D4—1661no—
436C23×C4—24no—
437C23×C4—24no—
438C23×C4—1661no—
439C23×C4—1661no—
440C23×C4—1661no—
441C23×C4D33211yescharacteristic
442C23×C4D33211yescharacteristic
443C23×C4D33211yescharacteristic
444C23×C4D33214yes—
445C23×C4C22×D8311yescharacteristic
446C23×C4C22×D8311yescharacteristic
447C23×C4C22×D8314yes—
448C23×C4C22×D8311yescharacteristic
449#137—16632no—
450C2×Q16—838no—
451C2×Q16—1668no—
452C2×SD16—838no—
453C2×SD16—1668no—
454C2×M16—24no—
455C2×M16—232no—
456C2×M16—28no—
457C2×M16C22⋊D8318yescomplemented
458C2×M16C22×D8314yes—
459C2×M16C22×D8318yes—
460C2×M16C22×D8314yes—
461C22×C8—28no—
462C22×C8C22×D8312yes—
463C22×C8C22×D8318yes—
464C22×C8C22×D8312yes—
465#123—1668no—
466C22⋊Q8—838no—
467C22⋊Q8—838no—
468C22⋊Q8—834no—
469C22⋊Q8—834no—
470C22⋊Q8—1668no—
471C22⋊Q8—1668no—
472C22⋊Q8—1664no—
473C22⋊Q8—1664no—
474C22⋊Q8—1662no—
475C22⋊Q8—1662no—
476#121—834no—
477#121—834no—
478#121—1662no—
479#121—1662no—
480#120—1668no—
481C4×D4—1668no—
482C4×D4—1668no—
483#117—834no—
484#117—1662no—
485C2×C4⋊C4—832no—
486C2×C4⋊C4—834no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—1662no—
490C2×C4⋊C4—1661no—
491C2×C4⋊C4—1668no—
492C2×C4⋊C4—1662no—
493C2×C4⋊C4—1662no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4—1661no—
496C2×C22⋊C4—1668no—
497C2×C22⋊C4—1662no—
498C2×C22⋊C4—1662no—
499C2×C22⋊C4—1661no—
500C2×C22⋊C4—1661no—
501C2×C22⋊C4—1661no—
502C2×C22⋊C4—1661no—
503C2×C22⋊C4—1661no—
504C2×C42—1661no—
505#107—838no—
506#106—838no—
507#103—838no—
508#103—838no—
509#103—838no—
510#102—838no—
511C24—24no—
512C24—24no—
513C24—42no—
514C24—1661no—
515C24C2×D33211yescharacteristic
516C24C2×D33214yes—
517C24C2×D33211yescharacteristic
518C24C2×D33211yescharacteristic
519#41—3328no—
520#41—1668no—
521#41—1668no—
522C2×Q8—3324no—
523C2×Q8—3328no—
524C2×Q8—834no—
525C2×Q8—832no—
526C2×Q8—1664no—
527C2×Q8—1662no—
528C2×Q8—1668no—
529C2×Q8—1664no—
530C2×Q8—1668no—
531C2×Q8—1662no—
532C2×Q8—1664no—
533C2×Q8—1662no—
534C2×Q8—1661no—
535C2×D4—3324no—
536C2×D4—3324no—
537C2×D4—3324no—
538C2×D4—832no—
539C2×D4—1664no—
540C2×D4—1664no—
541C2×D4—1664no—
542C2×D4—1662no—
543C2×D4—1661no—
544C2×D4—1662no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—216no—
549C22×C4—22no—
550C22×C4—28no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—28no—
555C22×C4—3324no—
556C22×C4—3324no—
557C22×C4—3324no—
558C22×C4—1664no—
559C22×C4—1664no—
560C22×C4—1661no—
561C22×C4—1661no—
562C22×C4—1662no—
563C22×C4—1661no—
564C22×C4—1662no—
565C22×C4—1664no—
566C22×C4C2×C22⋊D8314yes—
567C22×C4C2×D33214yes—
568C22×C4C2×D33214yes—
569C22×C4C2×D33214yes—
570C22×C4C2×D33212yes—
571C22×C4C2×D33212yes—
572C22×C4C2×D33211yescharacteristic
573C22×C4C2×D33211yescharacteristic
574C22×C4C2×D33212yes—
575C22×C4C2×D33211yescharacteristic
576C22×C4#1305059014yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8312yes—
579C22×C4C23×D8312yes—
580C22×C4C23×D8311yescharacteristic
581Q16—16616no—
582SD16—16616no—
583M16—28no—
584M16—216no—
585M16C2×C22⋊D83116yescomplemented
586C2×C8—24no—
587C2×C8—216no—
588C2×C8C2×C22⋊D8318yes—
589C2×C8C23×D8314yes—
590C2×C8C23×D8314yes—
591C4⋊C4—834no—
592C4⋊C4—832no—
593C4⋊C4—832no—
594C4⋊C4—1664no—
595C4⋊C4—1662no—
596C4⋊C4—1661no—
597C4⋊C4—1661no—
598C4⋊C4—1668no—
599C4⋊C4—1668no—
600C4⋊C4—1664no—
601C4⋊C4—1664no—
602C22⋊C4—1668no—
603C22⋊C4—1668no—
604C22⋊C4—1664no—
605C22⋊C4—1664no—
606C22⋊C4—1664no—
607C22⋊C4—1664no—
608C22⋊C4—1664no—
609C42—1664no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—28no—
615C23—22no—
616C23—22no—
617C23—28no—
618C23—22no—
619C23—44no—
620C23—416no—
621C23—3322no—
622C23—3322no—
623C23—3322no—
624C23—1662no—
625C23#1458176614yes—
626C23#1458182514yescomplemented
627C23C22×D33212yes—
628C23C22×D33212yes—
629C23C22×D33212yes—
630C23C22×D33211yescharacteristic
631Q8—3328no—
632Q8—3324no—
633Q8—3322no—
634Q8—1664no—
635Q8—1662no—
636Q8—1664no—
637Q8—1662no—
638D4—3328no—
639D4—3328no—
640D4—3328no—
641D4—3322no—
642D4—1662no—
643D4—1662no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—3328no—
656C2×C4—3322no—
657C2×C4—3328no—
658C2×C4—3324no—
659C2×C4—3322no—
660C2×C4—3324no—
661C2×C4—3322no—
662C2×C4—3328no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1664no—
666C2×C4—1662no—
667C2×C4—1664no—
668C2×C4#1458176614yes—
669C2×C4#1458176618yes—
670C2×C4C22×C22⋊D8312yes—
671C2×C4C22×C22⋊D8314yes—
672C2×C4C22×D33212yes—
673C2×C4C22×D33212yes—
674C2×C4C22×D33212yes—
675C2×C4C22×D33211yescharacteristic
676C2×C4C2×#1305059012yes—
677C2×C4C2×#1305059014yes—
678C2×C4C24×D8311yescharacteristic
679C8—24no—
680C8C22×C22⋊D8318yes—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—28no—
685C22—28no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—416no—
691C22—44no—
692C22—3322no—
693C22—3322no—
694C22—3322no—
695C22—6644no—
696C22C2×#1458176614yes—
697C22C2×#1458176612yes—
698C22C2×#1458182512yes—
699C22C2×#1458182514yescomplemented
700C22#1912850112yes—
701C22C23×D33211yescharacteristic
702C4—22no—
703C4—22no—
704C4—3322no—
705C4—3324no—
706C4—3322no—
707C4—3322no—
708C4—3324no—
709C4C2×#1458176614yes—
710C4C2×#1458176612yes—
711C4C23×C22⋊D8311yescharacteristic
712C4C22×#1305059011yescharacteristic
713C2—24no—
714C2—24no—
715C2—42no—
716C2—6642no—
717C2#2491709314yesdirect product factor
718C2C22×#1458176611yescharacteristic
719C2C22×#1458182511yescharacteristic
720C2C2×#1912850111yescharacteristic
subgroupG/H
centerC23C22×D332
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC23×M16×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128212C2
hypercenterC23×M16D83
hypocenterC83C2×#3056
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×M16

Complements

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

NH ≅ G/Ntype
1. C22×#14581825C2semidirect
3. C22×#14581771C2semidirect
4. #24917093C2direct (N × H)
5. C2×#19127959C2semidirect
6. C2×#19127947C2semidirect
7. C2×#19127942C2semidirect
8. C2×#19127930C2semidirect
9. C2×#19127743C2semidirect
10. C2×#19127703C2semidirect
11. C2×#19127711C2semidirect
12. C23×M16×C83C2semidirect
16. C2×#14581825C22semidirect
17. C22×Dic332C22semidirect
18. C22×#13050579C22semidirect
29. C2×#14581771C22semidirect
39. #19127959C22semidirect
40. #19127947C22semidirect
41. #19127942C22semidirect
42. #19127930C22semidirect
43. #19127743C22semidirect
44. C2×#14581726C22semidirect
45. C2×#14581724C22semidirect
46. #19127711C22semidirect
47. #19127703C22semidirect
48. C2×#14581717C22semidirect
49. C2×#14581717C22semidirect
50. C2×#14581717C22semidirect
51. C2×#14581714C22semidirect
57. C22×M16×C83C22semidirect
79. C2×Dic332C23semidirect
81. C2×#13050579C23semidirect
122. #14581726C23semidirect
123. #14581724C23semidirect
124. #14581717C23semidirect
125. #14581717C23semidirect
126. #14581717C23semidirect
127. #14581714C23semidirect
142. C2×M16×C83D4semidirect
243. M16×C83C2×D4semidirect
261. C23×C83#137semidirect
334. C22×C83C2×#137semidirect
356. C2×C83#3056semidirect
362. C23×M16D83semidirect
373. C83C2×#3056semidirect
385. C22×M16C2×D83semidirect
457. C2×M16C22⋊D83semidirect
585. M16C2×C22⋊D83semidirect
626. C23#14581825semidirect
699. C22C2×#14581825semidirect
717. C2#24917093direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145818252
C2×#191282122
C22×#145817712
#249170932
C2×#191279592
C2×#191279472
C2×#191279422
C2×#191279302
C2×#191277432
C2×#191277032
C2×#191277112
C23×M16×C832
C2×#305683