Finite Group Databasebeta

← #35328102

Subgroups — #35328102

Order 21248.

2366 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic83⋊C4C211yesmaximal, characteristic
2C2×#19127599C212yesmaximal, complemented
3C2×#19127576C211yesmaximal, characteristic
4C2×#19127576C211yesmaximal, characteristic
5C2×#19127574C211yesmaximal, characteristic
6#24905727C212yesmaximal, complemented
7#24905715C212yesmaximal, complemented
8#24905696C212yesmaximal, complemented
9#24905685C211yesmaximal, characteristic
10#24905685C211yesmaximal, characteristic
11C2×C4×C22⋊C4×C83C211yesmaximal, characteristic
12C24×Dic83C2211yescharacteristic
13C24×Dic83C2211yescharacteristic
14C22×C4⋊Dic83C2212yes—
15C22×C4⋊Dic83C2212yes—
16C22×Dic83⋊C4—28no—
17C22×Dic83⋊C4—24no—
18C22×Dic83⋊C4C2212yes—
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2212yes—
21C22×Dic83⋊C4C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24#19127599—28no—
25#19127576—24no—
26#19127576C418yescomplemented
27#19127574—24no—
28C2×C83⋊#95C2211yescharacteristic
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C2×C83⋊#95C2212yes—
36C24×C4×C83C2211yescharacteristic
37C22×C22⋊C4×C83C2211yescharacteristic
38C22×C22⋊C4×C83C2211yescharacteristic
39C22×C42×C83C2212yes—
40C4×C22⋊C4×C83—24no—
41C2×#95×C83C2212yes—
42C23×Dic83—24no—
43C23×Dic83—24no—
44C23×Dic83—24no—
45C23×Dic83—22no—
46C23×Dic83—22no—
47C23×Dic83—22no—
48C23×Dic83—22no—
49C23×Dic83—22no—
50C23×Dic83—42no—
51C23×Dic83C2×C414yes—
52C23×Dic83C2311yescharacteristic
53C23×Dic83C2311yescharacteristic
54C23×Dic83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2312yes—
57C23×Dic83C2312yes—
58C2×C4⋊Dic83—24no—
59C2×C4⋊Dic83—24no—
60C2×C4⋊Dic83—24no—
61C2×C4⋊Dic83—24no—
62C2×C4⋊Dic83—42no—
63C2×C4⋊Dic83C2×C418yescomplemented
64C2×Dic83⋊C4—232no—
65C2×Dic83⋊C4—24no—
66C2×Dic83⋊C4—24no—
67C2×Dic83⋊C4—24no—
68C2×Dic83⋊C4—24no—
69C2×Dic83⋊C4—24no—
70C2×Dic83⋊C4—22no—
71C2×Dic83⋊C4—22no—
72C2×Dic83⋊C4—24no—
73C2×Dic83⋊C4—42no—
74C2×Dic83⋊C4D418yes—
75C2×C22⋊Dic83—22no—
76C2×C22⋊Dic83—22no—
77C2×C22⋊Dic83—22no—
78C2×C22⋊Dic83—22no—
79C2×C22⋊Dic83—22no—
80C2×C22⋊Dic83C2×C414yes—
81C83⋊#95—24no—
82C83⋊#95—24no—
83C83⋊#95—24no—
84C83⋊#95—22no—
85C83⋊#95—22no—
86C83⋊#95—24no—
87C83⋊#95—42no—
88C83⋊#95C2×C418yescomplemented
89C25×C83C2311yescharacteristic
90C23×C4×C83—22no—
91C23×C4×C83—22no—
92C23×C4×C83—24no—
93C23×C4×C83—42no—
94C23×C4×C83D414yes—
95C23×C4×C83C2311yescharacteristic
96C23×C4×C83C2312yes—
97C23×C4×C83C2312yes—
98C23×C4×C83C2311yescharacteristic
99C2×C22⋊C4×C83—22no—
100C2×C22⋊C4×C83—22no—
101C2×C22⋊C4×C83C2×C414yes—
102C2×C22⋊C4×C83D414yes—
103C2×C22⋊C4×C83Q814yes—
104C2×C22⋊C4×C83Q814yes—
105C2×C42×C83—24no—
106C2×C42×C83—24no—
107C2×C42×C83—42no—
108#95×C83—24no—
109C22×Dic83—216no—
110C22×Dic83—28no—
111C22×Dic83—28no—
112C22×Dic83—28no—
113C22×Dic83—22no—
114C22×Dic83—22no—
115C22×Dic83—22no—
116C22×Dic83—22no—
117C22×Dic83—216no—
118C22×Dic83—28no—
119C22×Dic83—22no—
120C22×Dic83—22no—
121C22×Dic83—22no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—22no—
125C22×Dic83—22no—
126C22×Dic83—21no—
127C22×Dic83—21no—
128C22×Dic83—22no—
129C22×Dic83—22no—
130C22×Dic83—22no—
131C22×Dic83—22no—
132C22×Dic83—22no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—22no—
136C22×Dic83—21no—
137C22×Dic83—21no—
138C22×Dic83—22no—
139C22×Dic83—21no—
140C22×Dic83—21no—
141C22×Dic83—22no—
142C22×Dic83—22no—
143C22×Dic83—48no—
144C22×Dic83—48no—
145C22×Dic83—44no—
146C22×Dic83—44no—
147C22×Dic83C22×C412yes—
148C22×Dic83C22×C412yes—
149C22×Dic83C22×C414yes—
150C22×Dic83C2×D414yes—
151C22×Dic83C2×D414yes—
152C22×Dic83#4114yes—
153C4⋊Dic83—216no—
154C4⋊Dic83—48no—
155Dic83⋊C4—216no—
156Dic83⋊C4—216no—
157Dic83⋊C4—44no—
158Dic83⋊C4—44no—
159C22⋊Dic83—28no—
160C22⋊Dic83—44no—
161C24×C83—22no—
162C24×C83—22no—
163C24×C83—22no—
164C24×C83—22no—
165C24×C83C22×C412yes—
166C24×C83C2×D412yes—
167C24×C83C2×D412yes—
168C24×C83C2×Q812yes—
169C24×C83C2×Q812yes—
170C24×C83#4112yes—
171C24×C83#4112yes—
172C24×C83C2411yescharacteristic
173C22×C4×C83—21no—
174C22×C4×C83—22no—
175C22×C4×C83—21no—
176C22×C4×C83—22no—
177C22×C4×C83—22no—
178C22×C4×C83—22no—
179C22×C4×C83—22no—
180C22×C4×C83—28no—
181C22×C4×C83—21no—
182C22×C4×C83—22no—
183C22×C4×C83—22no—
184C22×C4×C83—22no—
185C22×C4×C83—22no—
186C22×C4×C83—21no—
187C22×C4×C83—22no—
188C22×C4×C83—22no—
189C22×C4×C83—22no—
190C22×C4×C83—22no—
191C22×C4×C83—28no—
192C22×C4×C83—44no—
193C22×C4×C83—48no—
194C22×C4×C83—48no—
195C22×C4×C83C22×C414yes—
196C22×C4×C83C2×D414yes—
197C22×C4×C83C2×D414yes—
198C22×C4×C83C2×D412yes—
199C22×C4×C83C2×D412yes—
200C22×C4×C83C2×Q814yes—
201C22×C4×C83C2×Q814yes—
202C22⋊C4×C83—28no—
203C22⋊C4×C83C4⋊C4116yescomplemented
204C42×C83—48no—
205C23×C83—24no—
206C23×C83—24no—
207C23×C83—22no—
208C23×C83—22no—
209C23×C83—24no—
210C23×C83—22no—
211C23×C83—22no—
212C23×C83—24no—
213C23×C83—24no—
214C23×C83—24no—
215C23×C83—24no—
216C23×C83—24no—
217C23×C83—24no—
218C23×C83—24no—
219C23×C83—24no—
220C23×C83—24no—
221C23×C83C2×C4⋊C414yes—
222C23×C83C4×D414yes—
223C23×C83C4×Q814yes—
224C23×C83#12114yes—
225C23×C83C22⋊Q814yes—
226C23×C83#12514yes—
227C23×C83C4⋊Q814yes—
228C23×C83C23×C411yescharacteristic
229C23×C83C22×D412yes—
230C23×C83C22×D411yescharacteristic
231C23×C83C22×D411yescharacteristic
232C23×C83C22×Q811yescharacteristic
233C23×C83C22×Q811yescharacteristic
234C23×C83C2×#4112yes—
235C23×C83C2×#4111yescharacteristic
236C23×C83C2×#4111yescharacteristic
237C23×C83H(5,𝔽2)12yes—
238C23×C832−1+412yes—
239C2×C4×C83—24no—
240C2×C4×C83—24no—
241C2×C4×C83—22no—
242C2×C4×C83—22no—
243C2×C4×C83—24no—
244C2×C4×C83—24no—
245C2×C4×C83—24no—
246C2×C4×C83—24no—
247C2×C4×C83—24no—
248C2×C4×C83—24no—
249C2×C4×C83—22no—
250C2×C4×C83—22no—
251C2×C4×C83—24no—
252C2×C4×C83—22no—
253C2×C4×C83—24no—
254C2×C4×C83—24no—
255C2×C4×C83—416no—
256C2×C4×C83—42no—
257C2×C4×C83—42no—
258C2×C4×C83—42no—
259C2×C4×C83—42no—
260C2×C4×C83—42no—
261C2×C4×C83—42no—
262C2×C4×C83C2×C4⋊C418yescomplemented
263C2×C4×C83#12014yes—
264C2×Dic83—232no—
265C2×Dic83—24no—
266C2×Dic83—24no—
267C2×Dic83—24no—
268C2×Dic83—24no—
269C2×Dic83—24no—
270C2×Dic83—24no—
271C2×Dic83—22no—
272C2×Dic83—22no—
273C2×Dic83—24no—
274C2×Dic83—24no—
275C2×Dic83—24no—
276C2×Dic83—24no—
277C2×Dic83—24no—
278C2×Dic83—416no—
279C2×Dic83—41no—
280C2×Dic83—42no—
281C2×Dic83—42no—
282C2×Dic83—41no—
283C2×Dic83—41no—
284C2×Dic83—42no—
285C2×Dic83—41no—
286C2×Dic83—42no—
287C2×Dic83—42no—
288C2×Dic83—42no—
289C2×Dic83—41no—
290C2×Dic83—41no—
291C2×Dic83—41no—
292C2×Dic83—41no—
293C2×Dic83—41no—
294C2×Dic83—41no—
295C2×Dic83—42no—
296C2×Dic83—42no—
297C2×Dic83—42no—
298C2×Dic83—42no—
299C2×Dic83C4×D418yes—
300C22×C83—24no—
301C22×C83—24no—
302C22×C83—28no—
303C22×C83—28no—
304C22×C83—24no—
305C22×C83—24no—
306C22×C83—24no—
307C22×C83—28no—
308C22×C83—28no—
309C22×C83—24no—
310C22×C83#38918yescomplemented
311C22×C83C22×C4⋊C411yescharacteristic
312C22×C83C2×C4×D412yes—
313C22×C83C2×C4×D411yescharacteristic
314C22×C83C2×C4×Q811yescharacteristic
315C22×C83#52012yes—
316C22×C83C2×#12011yescharacteristic
317C22×C83C2×#12111yescharacteristic
318C22×C83C2×C22⋊Q811yescharacteristic
319C22×C83#52512yes—
320C22×C83#52511yescharacteristic
321C22×C83C2×#12511yescharacteristic
322C22×C83C2×C4⋊Q811yescharacteristic
323C22×C83#53411yescharacteristic
324C22×C83#53611yescharacteristic
325C22×C83#53912yes—
326C22×C83D4212yes—
327C22×C83#54612yes—
328C22×C83#54712yes—
329C22×C83D4×Q812yes—
330C22×C83D4×Q812yes—
331C22×C83#55212yes—
332C22×C83#55412yes—
333C22×C83#55412yes—
334C4×C83—28no—
335C4×C83—24no—
336C4×C83—42no—
337C4×C83—44no—
338Dic83—28no—
339Dic83—42no—
340Dic83—44no—
341Dic83—42no—
342Dic83—81no—
343Dic83—81no—
344#14043—831nomaximal, Sylow
345C2×C83—28no—
346C2×C83C2×#38911yescharacteristic
347C2×C83C4×#12011yescharacteristic
348C2×C83#232211yescharacteristic
349C2×C83D4×C4⋊C412yes—
350C2×C83#236012yes—
351C2×C83#241011yescharacteristic
352C2×C83#241311yescharacteristic
353C2×C83#243411yescharacteristic
354C2×C83#244912yes—
355C2×C83#247312yes—
356C2×C83#258311yescharacteristic
357C23×C4⋊C4—831no—
358C2×#389—832no—
359C2×#385—831no—
360C2×#385—831no—
361C2×#385—831no—
362C2×C4×C22⋊C4D8311yescharacteristic
363#1444—832no—
364#1441—832no—
365#1436—832no—
366C22⋊#95—831no—
367C22⋊#95—831no—
368C83#1404311yescharacteristic, complemented, Sylow
369C24×C4—831no—
370C24×C4—831no—
371C24×C4C2×D8311yescharacteristic
372C22×C4⋊C4—831no—
373C22×C4⋊C4—832no—
374C22×C4⋊C4—832no—
375C22×C4⋊C4—832no—
376C22×C4⋊C4—832no—
377C22×C4⋊C4—831no—
378C22×C4⋊C4—1668no—
379C22×C4⋊C4—1664no—
380C22×C22⋊C4—831no—
381C22×C22⋊C4—831no—
382C22×C22⋊C4C2×D8311yescharacteristic
383C22×C22⋊C4C2×D8311yescharacteristic
384C22×C42C2×D8312yes—
385#389—1668no—
386#385—838no—
387#385—1664no—
388#385—1664no—
389C4×C22⋊C4—24no—
390C2×#95—832no—
391C2×#95—832no—
392C2×#95—832no—
393C2×#95—832no—
394C2×#95—832no—
395C2×#95—831no—
396C2×#95—832no—
397C2×#95—831no—
398C2×#95C2×D8312yes—
399C25C22×D8311yescharacteristic
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—42no—
404C23×C4—3322no—
405C23×C4—832no—
406C23×C4—834no—
407C23×C4—831no—
408C23×C4—831no—
409C23×C4—832no—
410C23×C4—831no—
411C23×C4—831no—
412C23×C4—1662no—
413C23×C4—1662no—
414C23×C4—1664no—
415C23×C4—1662no—
416C23×C4—1664no—
417C23×C4—1664no—
418C23×C4—1662no—
419C23×C4—1662no—
420C23×C4D33214yes—
421C23×C4C22×D8311yescharacteristic
422C23×C4C22×D8312yes—
423C23×C4C22×D8312yes—
424C23×C4C22×D8311yescharacteristic
425C2×C4⋊C4—3322no—
426C2×C4⋊C4—3322no—
427C2×C4⋊C4—838no—
428C2×C4⋊C4—838no—
429C2×C4⋊C4—1664no—
430C2×C4⋊C4—1664no—
431C2×C4⋊C4—1664no—
432C2×C4⋊C4—1662no—
433C2×C4⋊C4—1662no—
434C2×C4⋊C4—1664no—
435C2×C4⋊C4—1664no—
436C2×C4⋊C4—1664no—
437C2×C4⋊C4—1664no—
438C2×C4⋊C4—16632no—
439C2×C4⋊C4—1664no—
440C2×C4⋊C4—1664no—
441C2×C4⋊C4—1664no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—834no—
445C2×C22⋊C4—1662no—
446C2×C22⋊C4—1662no—
447C2×C22⋊C4—1662no—
448C2×C22⋊C4—1662no—
449C2×C22⋊C4—1662no—
450C2×C22⋊C4Dic16614yes—
451C2×C22⋊C4Dic16614yes—
452C2×C22⋊C4C4×D8314yes—
453C2×C22⋊C4C22⋊D8314yes—
454C2×C42—24no—
455C2×C42—24no—
456C2×C42—42no—
457#95—24no—
458#95—3322no—
459#95—838no—
460#95—1664no—
461#95—1664no—
462#95—1664no—
463#95—1664no—
464#95—1662no—
465#95—1662no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C2×C4×D8312yes—
471C24C2×C22⋊D8312yes—
472C24C2×D33212yes—
473C24C2×Dic16612yes—
474C24C2×Dic16612yes—
475C24#1305059012yes—
476C24#1305059012yes—
477C24C23×D8311yescharacteristic
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—44no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—3324no—
501C22×C4—3324no—
502C22×C4—3328no—
503C22×C4—3328no—
504C22×C4—834no—
505C22×C4—834no—
506C22×C4—834no—
507C22×C4—832no—
508C22×C4—832no—
509C22×C4—834no—
510C22×C4—1662no—
511C22×C4—1661no—
512C22×C4—1661no—
513C22×C4—1661no—
514C22×C4—1661no—
515C22×C4—1662no—
516C22×C4—1661no—
517C22×C4—1661no—
518C22×C4—1662no—
519C22×C4—1662no—
520C22×C4—1668no—
521C22×C4—1662no—
522C22×C4—1662no—
523C22×C4—1662no—
524C22×C4—1661no—
525C22×C4—1661no—
526C22×C4—1662no—
527C22×C4—1662no—
528C22×C4—1661no—
529C22×C4—1661no—
530C22×C4—1662no—
531C22×C4—1662no—
532C22×C4—1662no—
533C22×C4—1662no—
534C22×C4—1662no—
535C22×C4—16616no—
536C22×C4—1668no—
537C22×C4—16616no—
538C22×C4—1668no—
539C22×C4—1662no—
540C22×C4—1662no—
541C22×C4—1662no—
542C22×C4—1662no—
543C22×C4—1668no—
544C22×C4C2×C4×D8314yes—
545C22×C4D4×D8314yes—
546C22×C4C2×C22⋊D8314yes—
547C22×C4C2×D33212yes—
548C22×C4C2×D33212yes—
549C22×C4C2×Dic16614yes—
550C22×C4C2×Dic16614yes—
551C4⋊C4—3324no—
552C4⋊C4—3328no—
553C4⋊C4—3324no—
554C4⋊C4—16616no—
555C4⋊C4—16616no—
556C4⋊C4—16616no—
557C22⋊C4—28no—
558C22⋊C4—3324no—
559C22⋊C4—1668no—
560C22⋊C4Dic83⋊C4116yescomplemented
561C42—48no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—22no—
573C23—24no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23C2×Dic83⋊C414yes—
579C23C4×D33214yes—
580C23C4×Dic16614yes—
581C23#1458176614yes—
582C23#1458177114yes—
583C23#1458178414yes—
584C23#1458179214yes—
585C23C22×C4×D8311yescharacteristic
586C23C2×D4×D8312yes—
587C23C22×C22⋊D8311yescharacteristic
588C23C22×D33211yescharacteristic
589C23C22×Dic16611yescharacteristic
590C23C22×Dic16611yescharacteristic
591C23#41×D8312yes—
592C23C2×#1305059011yescharacteristic
593C23C2×#1305059011yescharacteristic
594C23#1458183712yes—
595C23#1458183912yes—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—416no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—33216no—
620C2×C4—3322no—
621C2×C4—3322no—
622C2×C4—3321no—
623C2×C4—3322no—
624C2×C4—3322no—
625C2×C4—3321no—
626C2×C4—3321no—
627C2×C4—3322no—
628C2×C4—3321no—
629C2×C4—3322no—
630C2×C4—3322no—
631C2×C4—3322no—
632C2×C4—3322no—
633C2×C4—3322no—
634C2×C4—3321no—
635C2×C4—3321no—
636C2×C4—3321no—
637C2×C4—3321no—
638C2×C4—3321no—
639C2×C4—3321no—
640C2×C4—838no—
641C2×C4—1664no—
642C2×C4—1664no—
643C2×C4—1664no—
644C2×C4—1662no—
645C2×C4—1662no—
646C2×C4—1664no—
647C2×C4—1664no—
648C2×C4—16632no—
649C2×C4—1664no—
650C2×C4—1664no—
651C2×C4—1664no—
652C2×C4—1664no—
653C2×C4—1664no—
654C2×C4—1664no—
655C2×C4C2×Dic83⋊C418yescomplemented
656C2×C4#1458176214yes—
657C22—24no—
658C22—24no—
659C22—28no—
660C22—24no—
661C22—28no—
662C22—24no—
663C22—28no—
664C22—24no—
665C22—24no—
666C22—28no—
667C22#1912759918yescomplemented
668C22C22×Dic83⋊C411yescharacteristic
669C22C4×D4×D8312yes—
670C22C2×C4×D33211yescharacteristic
671C22C2×C4×Dic16611yescharacteristic
672C22#1912818012yes—
673C22C2×#1458176211yescharacteristic
674C22C2×#1458176611yescharacteristic
675C22C2×#1458177111yescharacteristic
676C22#1912821012yes—
677C22#1912821311yescharacteristic
678C22C2×#1458178411yescharacteristic
679C22C2×#1458179211yescharacteristic
680C22#1912826311yescharacteristic
681C22#1912827711yescharacteristic
682C22#1912829312yes—
683C22D4×C22⋊D8312yes—
684C22#1912834112yes—
685C22#1912835012yes—
686C22D4×Dic16612yes—
687C22D4×Dic16612yes—
688C22#1912838412yes—
689C22#1912841012yes—
690C22#1912841012yes—
691C4—28no—
692C4—24no—
693C4—44no—
694C4—42no—
695C4—3322no—
696C4—3322no—
697C4—3324no—
698C4—6641no—
699C4—6641no—
700C4—1668no—
701C2—28no—
702C2C2×#1912759911yescharacteristic
703C2C4×#1458176211yescharacteristic
704C2#2491013411yescharacteristic
705C2D4×Dic83⋊C412yes—
706C2#2491046912yes—
707C2#2491083111yescharacteristic
708C2#2491086411yescharacteristic
709C2#2491110711yescharacteristic
710C2#2491126612yes—
711C2#2491160412yes—
712C2#2491283811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×C4×C22⋊C4D83
hypocenterC83#14043
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#19127599C2semidirect
6. #24905727C2semidirect
7. #24905715C2semidirect
8. #24905696C2semidirect
26. #19127576C4semidirect
63. C2×C4⋊Dic83C2×C4semidirect
88. C83⋊#95C2×C4semidirect
203. C22⋊C4×C83C4⋊C4semidirect
262. C2×C4×C83C2×C4⋊C4semidirect
310. C22×C83#389semidirect
368. C83#14043semidirect
560. C22⋊C4Dic83⋊C4semidirect
655. C2×C4C2×Dic83⋊C4semidirect
667. C22#19127599semidirect

Maximal subgroups

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

subgroupindex
C23×Dic83⋊C42
C2×#191275992
C2×#191275762
C2×#191275742
#249057272
#249057152
#249056962
#249056852
C2×C4×C22⋊C4×C832
#1404383