Finite Group Databasebeta

← #35325809

Subgroups — #35325809

Order 21248.

2398 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581748C211yesmaximal, characteristic
2C2×#19127562C211yesmaximal, characteristic
3C2×C22⋊C4×Dic83C211yesmaximal, characteristic
4C22×C83⋊#95C211yesmaximal, characteristic
5#24905698C212yesmaximal, complemented
6#24905696C212yesmaximal, complemented
7#24905687C212yesmaximal, complemented
8#24905686C211yesmaximal, characteristic
9#24905685C211yesmaximal, characteristic
10C4×C83⋊#95C212yesmaximal, complemented
11C2×C4×C22⋊C4×C83C211yesmaximal, characteristic
12C24×Dic83C2211yescharacteristic
13C24×Dic83C2211yescharacteristic
14C2×#14581748—24no—
15C2×#14581748—24no—
16C2×#14581748C418yescomplemented
17C22×Dic83⋊C4C2212yes—
18C22×C22⋊Dic83C2211yescharacteristic
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C4×Dic83C2212yes—
21C22×C4×Dic83C2212yes—
22#19127562C418yescomplemented
23C22⋊C4×Dic83—24no—
24C2×C83⋊#95C418yescomplemented
25C2×C83⋊#95C2212yes—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2212yes—
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2211yescharacteristic
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—22no—
44C23×Dic83—22no—
45C23×Dic83—22no—
46C23×Dic83—22no—
47C23×Dic83—22no—
48C23×Dic83—22no—
49C23×Dic83—42no—
50C23×Dic83C2×C414yes—
51C23×Dic83C2×C414yes—
52C23×Dic83C2×C414yes—
53C23×Dic83C2×C414yes—
54C23×Dic83C2312yes—
55C23×Dic83C2312yes—
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60#14581748—232no—
61C2×Dic83⋊C4—24no—
62C2×Dic83⋊C4—24no—
63C2×Dic83⋊C4C2×C418yescomplemented
64C2×C22⋊Dic83—22no—
65C2×C22⋊Dic83—22no—
66C2×C22⋊Dic83—22no—
67C2×C22⋊Dic83—22no—
68C2×C22⋊Dic83C2×C414yes—
69C2×C22⋊Dic83C2×C414yes—
70C2×C4×Dic83—24no—
71C2×C4×Dic83—24no—
72C2×C4×Dic83—24no—
73C2×C4×Dic83—24no—
74C2×C4×Dic83—42no—
75C2×C4×Dic83C2×C418yescomplemented
76C83⋊#95—24no—
77C83⋊#95—24no—
78C83⋊#95—24no—
79C83⋊#95—42no—
80C83⋊#95—42no—
81C83⋊#95C2×C414yes—
82C83⋊#95C2×C414yes—
83C83⋊#95C2×C414yes—
84C83⋊#95C2×C414yes—
85C83⋊#95C2×C418yescomplemented
86C83⋊#95C2×C418yescomplemented
87C25×C83C2311yescharacteristic
88C23×C4×C83—22no—
89C23×C4×C83—22no—
90C23×C4×C83—24no—
91C23×C4×C83—42no—
92C23×C4×C83C2×C414yes—
93C23×C4×C83C2312yes—
94C23×C4×C83C2311yescharacteristic
95C23×C4×C83C2312yes—
96C23×C4×C83C2311yescharacteristic
97C2×C22⋊C4×C83—22no—
98C2×C22⋊C4×C83—22no—
99C2×C22⋊C4×C83C2×C414yes—
100C2×C22⋊C4×C83C2×C414yes—
101C2×C22⋊C4×C83D414yes—
102C2×C22⋊C4×C83D414yes—
103C2×C42×C83—24no—
104C2×C42×C83—24no—
105C2×C42×C83—42no—
106#95×C83—24no—
107C22×Dic83—28no—
108C22×Dic83—28no—
109C22×Dic83—28no—
110C22×Dic83—28no—
111C22×Dic83—28no—
112C22×Dic83—28no—
113C22×Dic83—21no—
114C22×Dic83—21no—
115C22×Dic83—21no—
116C22×Dic83—21no—
117C22×Dic83—21no—
118C22×Dic83—21no—
119C22×Dic83—21no—
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—22no—
124C22×Dic83—28no—
125C22×Dic83—21no—
126C22×Dic83—22no—
127C22×Dic83—22no—
128C22×Dic83—22no—
129C22×Dic83—22no—
130C22×Dic83—21no—
131C22×Dic83—22no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—22no—
136C22×Dic83—22no—
137C22×Dic83—22no—
138C22×Dic83—22no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83—28no—
142C22×Dic83—44no—
143C22×Dic83—48no—
144C22×Dic83—48no—
145C22×Dic83C42116yescomplemented
146C22×Dic83C22×C412yes—
147C22×Dic83C22×C414yes—
148C22×Dic83C22×C414yes—
149C22×Dic83C22×C412yes—
150C22×Dic83C22×C412yes—
151C22×Dic83C22×C412yes—
152C22×Dic83C22×C412yes—
153C22×Dic83C22×C412yes—
154C22×Dic83C22×C412yes—
155C22×Dic83C22×C412yes—
156C22×Dic83#4114yes—
157Dic83⋊C4—216no—
158C22⋊Dic83—28no—
159C22⋊Dic83—28no—
160C4×Dic83—216no—
161C4×Dic83—48no—
162C24×C83—22no—
163C24×C83—22no—
164C24×C83—22no—
165C24×C83—22no—
166C24×C83C22×C412yes—
167C24×C83C22×C412yes—
168C24×C83C22×C412yes—
169C24×C83C2×D412yes—
170C24×C83C2×D412yes—
171C24×C83#4112yes—
172C24×C83#4112yes—
173C24×C83C2411yescharacteristic
174C22×C4×C83—21no—
175C22×C4×C83—22no—
176C22×C4×C83—21no—
177C22×C4×C83—22no—
178C22×C4×C83—22no—
179C22×C4×C83—22no—
180C22×C4×C83—22no—
181C22×C4×C83—28no—
182C22×C4×C83—21no—
183C22×C4×C83—22no—
184C22×C4×C83—22no—
185C22×C4×C83—22no—
186C22×C4×C83—22no—
187C22×C4×C83—21no—
188C22×C4×C83—22no—
189C22×C4×C83—22no—
190C22×C4×C83—22no—
191C22×C4×C83—22no—
192C22×C4×C83—28no—
193C22×C4×C83—44no—
194C22×C4×C83—48no—
195C22×C4×C83—48no—
196C22×C4×C83C22×C414yes—
197C22×C4×C83C22×C412yes—
198C22×C4×C83C22×C414yes—
199C22×C4×C83C22×C412yes—
200C22×C4×C83C2×D414yes—
201C22×C4×C83C2×D414yes—
202C22×C4×C83#4114yes—
203C22⋊C4×C83—28no—
204C22⋊C4×C83C22⋊C4116yes—
205C42×C83—48no—
206C23×C83—22no—
207C23×C83—22no—
208C23×C83—24no—
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×C83—24no—
222C23×C83C2×C4214yes—
223C23×C83C2×C22⋊C414yes—
224C23×C83#11714yes—
225C23×C83C4×D414yes—
226C23×C83C4×D414yes—
227C23×C83C4×D414yes—
228C23×C83C4×D414yes—
229C23×C83C23×C411yescharacteristic
230C23×C83C23×C411yescharacteristic
231C23×C83C23×C411yescharacteristic
232C23×C83C22×D411yescharacteristic
233C23×C83C22×D411yescharacteristic
234C23×C83C2×#4112yes—
235C23×C83C2×#4112yes—
236C23×C83C2×#4111yescharacteristic
237C23×C83C2×#4111yescharacteristic
238C23×C83H(5,𝔽2)12yes—
239C23×C832−1+412yes—
240C2×C4×C83—22no—
241C2×C4×C83—24no—
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—24no—
250C2×C4×C83—22no—
251C2×C4×C83—24no—
252C2×C4×C83—22no—
253C2×C4×C83—24no—
254C2×C4×C83—22no—
255C2×C4×C83—24no—
256C2×C4×C83—416no—
257C2×C4×C83—42no—
258C2×C4×C83—42no—
259C2×C4×C83—42no—
260C2×C4×C83—42no—
261C2×C4×C83—42no—
262C2×C4×C83—42no—
263C2×C4×C83C2×C22⋊C418yes—
264C2×C4×C83#11714yescomplemented
265C2×Dic83—22no—
266C2×Dic83—22no—
267C2×Dic83—22no—
268C2×Dic83—22no—
269C2×Dic83—22no—
270C2×Dic83—22no—
271C2×Dic83—22no—
272C2×Dic83—22no—
273C2×Dic83—22no—
274C2×Dic83—22no—
275C2×Dic83—22no—
276C2×Dic83—22no—
277C2×Dic83—22no—
278C2×Dic83—22no—
279C2×Dic83—24no—
280C2×Dic83—24no—
281C2×Dic83—232no—
282C2×Dic83—24no—
283C2×Dic83—22no—
284C2×Dic83—24no—
285C2×Dic83—22no—
286C2×Dic83—24no—
287C2×Dic83—24no—
288C2×Dic83—22no—
289C2×Dic83—24no—
290C2×Dic83—24no—
291C2×Dic83—416no—
292C2×Dic83—42no—
293C2×Dic83—42no—
294C2×Dic83—42no—
295C2×Dic83—42no—
296C2×Dic83—42no—
297C2×Dic83—42no—
298C2×Dic83—42no—
299C2×Dic83—42no—
300C2×Dic83—42no—
301C2×Dic83—42no—
302C2×Dic83C2×C4214yes—
303C2×Dic83C2×C4214yes—
304C2×Dic83#11714yescomplemented
305C22×C83—28no—
306C22×C83—24no—
307C22×C83—24no—
308C22×C83—28no—
309C22×C83—24no—
310C22×C83—24no—
311C22×C83—28no—
312C22×C83—28no—
313C22×C83—24no—
314C22×C83—24no—
315C22×C83C4×C22⋊C418yes—
316C22×C83C22×C4211yescharacteristic
317C22×C83C22×C22⋊C411yescharacteristic
318C22×C83C2×#11711yescharacteristic
319C22×C83C2×#11711yescharacteristic
320C22×C83C2×#11711yescharacteristic
321C22×C83C2×C4×D411yescharacteristic
322C22×C83C2×C4×D411yescharacteristic
323C22×C83C2×C4×D411yescharacteristic
324C22×C83C2×C4×D411yescharacteristic
325C22×C83C4×#4112yes—
326C22×C83C4×#4112yes—
327C22×C83#51811yescharacteristic
328C22×C83#51911yescharacteristic
329C22×C83#52012yes—
330C22×C83#52012yes—
331C22×C83#54612yes—
332C22×C83#54612yes—
333C22×C83#54712yes—
334C22×C83#54712yes—
335C22×C83#55112yes—
336C22×C83#55112yes—
337C22×C83#55212yes—
338C22×C83#55212yes—
339C4×C83—28no—
340C4×C83—24no—
341C4×C83—42no—
342C4×C83—44no—
343Dic83—24no—
344Dic83—24no—
345Dic83—24no—
346Dic83—44no—
347Dic83—42no—
348Dic83—44no—
349#13799—831nomaximal, Sylow
350C2×C83—28no—
351C2×C83C2×C4×C22⋊C411yescharacteristic
352C2×C83C4×#11711yescharacteristic
353C2×C83#227411yescharacteristic
354C2×C83#233912yes—
355C2×C83#234211yescharacteristic
356C2×C83#234211yescharacteristic
357C2×C83#234312yes—
358C2×C83#234411yescharacteristic
359C2×C83#234411yescharacteristic
360C2×C83#235912yes—
361C2×C83#235912yes—
362C22×#117—831no—
363C2×#381—831no—
364C2×C4×C22⋊C4—831no—
365C2×C4×C22⋊C4D8311yescharacteristic
366C22×#95—831no—
367#1436—832no—
368#1436—832no—
369#1434—832no—
370C22⋊#95—831no—
371C22⋊#95—831no—
372C4×#95—832no—
373C83#1379911yescharacteristic, complemented, Sylow
374C24×C4—831no—
375C24×C4—831no—
376C24×C4C2×D8311yescharacteristic
377C2×#117—838no—
378C2×#117—1664no—
379C2×#117—1664no—
380C22×C4⋊C4—832no—
381C22×C22⋊C4—831no—
382C22×C22⋊C4—831no—
383C22×C22⋊C4C2×D8311yescharacteristic
384C22×C22⋊C4C2×D8311yescharacteristic
385C22×C42—832no—
386C22×C42—832no—
387C22×C42C2×D8312yes—
388#381—838no—
389C4×C22⋊C4—24no—
390C4×C22⋊C4—1664no—
391C2×#95—832no—
392C2×#95—832no—
393C2×#95—838no—
394C2×#95—831no—
395C2×#95—832no—
396C2×#95—831no—
397C2×#95—831no—
398C2×#95—831no—
399C2×#95—832no—
400C2×#95—832no—
401C2×#95—832no—
402C2×#95—832no—
403C2×#95C2×D8312yes—
404C25C22×D8311yescharacteristic
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—42no—
409C23×C4—3322no—
410C23×C4—834no—
411C23×C4—834no—
412C23×C4—834no—
413C23×C4—834no—
414C23×C4—831no—
415C23×C4—831no—
416C23×C4—831no—
417C23×C4—832no—
418C23×C4—832no—
419C23×C4—831no—
420C23×C4—1664no—
421C23×C4—1662no—
422C23×C4—1662no—
423C23×C4—1662no—
424C23×C4—1662no—
425C23×C4—1662no—
426C23×C4—1662no—
427C23×C4C4×D8314yes—
428C23×C4C22×D8312yes—
429C23×C4C22×D8311yescharacteristic
430C23×C4C22×D8312yes—
431C23×C4C22×D8311yescharacteristic
432#117—16632no—
433C2×C4⋊C4—838no—
434C2×C4⋊C4—1664no—
435C2×C4⋊C4—1664no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—834no—
439C2×C22⋊C4—834no—
440C2×C22⋊C4—1662no—
441C2×C22⋊C4—1662no—
442C2×C22⋊C4—1662no—
443C2×C22⋊C4—1662no—
444C2×C22⋊C4C4×D8314yes—
445C2×C22⋊C4C4×D8314yes—
446C2×C22⋊C4D33214yes—
447C2×C22⋊C4C22⋊D8314yes—
448C2×C42—24no—
449C2×C42—24no—
450C2×C42—42no—
451C2×C42—3322no—
452C2×C42—838no—
453C2×C42—1664no—
454C2×C42—1664no—
455C2×C42—1664no—
456C2×C42—1664no—
457#95—24no—
458#95—3322no—
459#95—3322no—
460#95—834no—
461#95—834no—
462#95—834no—
463#95—834no—
464#95—838no—
465#95—838no—
466#95—1664no—
467#95—1664no—
468#95—1664no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24C2×C4×D8312yes—
474C24C2×C4×D8312yes—
475C24C2×C4×D8312yes—
476C24C2×C22⋊D8312yes—
477C24C2×D33212yes—
478C24#1305059012yes—
479C24#1305059012yes—
480C24C23×D8311yescharacteristic
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—44no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—3328no—
504C22×C4—3328no—
505C22×C4—3324no—
506C22×C4—832no—
507C22×C4—832no—
508C22×C4—832no—
509C22×C4—832no—
510C22×C4—832no—
511C22×C4—832no—
512C22×C4—832no—
513C22×C4—834no—
514C22×C4—8316no—
515C22×C4—834no—
516C22×C4—832no—
517C22×C4—834no—
518C22×C4—1668no—
519C22×C4—1662no—
520C22×C4—1661no—
521C22×C4—1662no—
522C22×C4—1662no—
523C22×C4—1662no—
524C22×C4—1662no—
525C22×C4—1662no—
526C22×C4—1662no—
527C22×C4—1662no—
528C22×C4—1662no—
529C22×C4—1661no—
530C22×C4—1662no—
531C22×C4—1662no—
532C22×C4—1662no—
533C22×C4—1662no—
534C22×C4—1662no—
535C22×C4—1668no—
536C22×C4—1661no—
537C22×C4—1661no—
538C22×C4—1661no—
539C22×C4—1661no—
540C22×C4—1661no—
541C22×C4—1661no—
542C22×C4—1661no—
543C22×C4—1661no—
544C22×C4—1661no—
545C22×C4—1661no—
546C22×C4—1662no—
547C22×C4—1668no—
548C22×C4—1668no—
549C22×C4—1668no—
550C22×C4—1668no—
551C22×C4—1668no—
552C22×C4—1668no—
553C22×C4C2×C4×D8314yes—
554C22×C4C2×C4×D8312yes—
555C22×C4C2×C4×D8314yes—
556C22×C4C2×C4×D8312yes—
557C22×C4C2×C22⋊D8314yes—
558C22×C4C2×D33214yes—
559C22×C4#1305058914yes—
560C4⋊C4—16616no—
561C22⋊C4—28no—
562C22⋊C4—1668no—
563C22⋊C4—1668no—
564C22⋊C4(C2×D83)⋊C4116yes—
565C42—48no—
566C42—3328no—
567C42—16616no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—22no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23C42×D8314yes—
585C23C2×(C2×D83)⋊C414yes—
586C23#1458174914yes—
587C23C4×C22⋊D8314yes—
588C23C4×C22⋊D8314yes—
589C23C4×D33214yes—
590C23C4×D33214yes—
591C23C22×C4×D8311yescharacteristic
592C23C22×C4×D8311yescharacteristic
593C23C22×C4×D8311yescharacteristic
594C23C22×C22⋊D8311yescharacteristic
595C23C22×D33211yescharacteristic
596C23#41×D8312yes—
597C23C2×#1305058912yes—
598C23C2×#1305059011yescharacteristic
599C23C2×#1305059011yescharacteristic
600C23#1458183712yes—
601C23#1458183912yes—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—24no—
618C2×C4—416no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—3322no—
626C2×C4—3322no—
627C2×C4—3322no—
628C2×C4—3322no—
629C2×C4—3322no—
630C2×C4—3322no—
631C2×C4—3322no—
632C2×C4—3322no—
633C2×C4—3322no—
634C2×C4—3322no—
635C2×C4—33216no—
636C2×C4—834no—
637C2×C4—834no—
638C2×C4—834no—
639C2×C4—1664no—
640C2×C4—1662no—
641C2×C4—1664no—
642C2×C4—1662no—
643C2×C4—1664no—
644C2×C4—1664no—
645C2×C4—1662no—
646C2×C4—1664no—
647C2×C4—1664no—
648C2×C4—1664no—
649C2×C4—1664no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—16632no—
665C2×C4C2×(C2×D83)⋊C418yes—
666C2×C4#1458174814yescomplemented
667C22—28no—
668C22—28no—
669C22—28no—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—28no—
674C22—24no—
675C22—24no—
676C22—24no—
677C22C4×(C2×D83)⋊C418yes—
678C22C2×C42×D8311yescharacteristic
679C22C22×(C2×D83)⋊C411yescharacteristic
680C22#117×D8311yescharacteristic
681C22C2×#1458174811yescharacteristic
682C22C2×#1458174911yescharacteristic
683C22C2×C4×C22⋊D8311yescharacteristic
684C22C2×C4×C22⋊D8311yescharacteristic
685C22C2×C4×D33211yescharacteristic
686C22C2×C4×D33211yescharacteristic
687C22C4×#1305058912yes—
688C22C4×#1305058912yes—
689C22#1912817411yescharacteristic
690C22#1912817811yescharacteristic
691C22#1912818012yes—
692C22#1912818012yes—
693C22#1912834512yes—
694C22#1912834612yes—
695C22#1912835012yes—
696C22#1912835512yes—
697C22#1912837712yes—
698C22#1912838012yes—
699C22#1912838412yes—
700C22#1912839112yes—
701C4—28no—
702C4—24no—
703C4—44no—
704C4—42no—
705C4—3324no—
706C4—3324no—
707C4—3322no—
708C4—1664no—
709C4—1664no—
710C4—1664no—
711C2—28no—
712C2C2×C4×(C2×D83)⋊C411yescharacteristic
713C2C4×#1458174811yescharacteristic
714C2#2490981811yescharacteristic
715C2#2491028812yes—
716C2#2491030811yescharacteristic
717C2#2491031511yescharacteristic
718C2#2491031712yes—
719C2#2491033011yescharacteristic
720C2#2491033311yescharacteristic
721C2#2491044912yes—
722C2#2491045712yes—
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×C4×C22⋊C4D83
hypocenterC83#13799
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #24905698C2semidirect
6. #24905696C2semidirect
7. #24905687C2semidirect
10. C4×C83⋊#95C2semidirect
16. C2×#14581748C4semidirect
22. #19127562C4semidirect
24. C2×C83⋊#95C4semidirect
63. C2×Dic83⋊C4C2×C4semidirect
75. C2×C4×Dic83C2×C4semidirect
85. C83⋊#95C2×C4semidirect
86. C83⋊#95C2×C4semidirect
145. C22×Dic83C42semidirect
264. C2×C4×C83#117semidirect
304. C2×Dic83#117semidirect
373. C83#13799semidirect
666. C2×C4#14581748semidirect

Maximal subgroups

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

subgroupindex
C22×#145817482
C2×#191275622
C2×C22⋊C4×Dic832
C22×C83⋊#952
#249056982
#249056962
#249056872
#249056862
#249056852
C4×C83⋊#952
C2×C4×C22⋊C4×C832
#1379983