Finite Group Databasebeta

← #35325971

Subgroups — #35325971

Order 21248.

2666 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D83C211yesmaximal, characteristic
2C2×#19127601C212yesmaximal
3C2×C4×Dic83⋊C4C212yesmaximal, complemented
4C2×#19127548C211yesmaximal, characteristic, complemented
5#24905701C212yesmaximal, complemented
6#24905700C212yesmaximal, complemented
7Dic83⋊#95C211yesmaximal, characteristic, complemented
8#24905686C211yesmaximal, characteristic, complemented
9(C2×D83)⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic83C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
12C23×C22⋊D83C2211yescharacteristic
13C23×C4×D83C2211yescharacteristic
14C2×C4×C22⋊D83—28no—
15C2×C4×C22⋊D83C418yescomplemented
16C22×Dic83⋊C4C2212yes—
17C22×Dic83⋊C4C2211yescharacteristic
18C22×C22⋊Dic83C2211yescharacteristic
19C22×C22⋊Dic83C2212yes—
20C22×(C2×D83)⋊C4C2211yescharacteristic
21C22×(C2×D83)⋊C4C2212yes—
22C22×(C2×D83)⋊C4C2212yes—
23C22×C4×Dic83C2212yes—
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2212yes—
26#19127601C4116yescomplemented
27C4×Dic83⋊C4—28no—
28#19127548—24no—
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2212yes—
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C24×C4×C83C2211yescharacteristic
36C22×C22⋊C4×C83C2212yes—
37C22×C42×C83C2212yes—
38C4×C22⋊C4×C83—24no—
39C2×#95×C83C2211yescharacteristic
40C2×#95×C83C2211yescharacteristic
41C24×D83C2311yescharacteristic
42C22×C22⋊D83—24no—
43C22×C22⋊D83—22no—
44C22×C22⋊D83—22no—
45C22×C22⋊D83C2×C418yes—
46C22×C22⋊D83C2×C414yes—
47C23×Dic83C2312yes—
48C23×Dic83C2312yes—
49C23×Dic83C2311yescharacteristic
50C23×Dic83C2311yescharacteristic
51C23×Dic83C2311yescharacteristic
52C22×C4×D83—24no—
53C22×C4×D83—22no—
54C22×C4×D83—22no—
55C22×C4×D83—42no—
56C22×C4×D83C2×C414yes—
57C4×C22⋊D83—232no—
58C2×Dic83⋊C4—24no—
59C2×Dic83⋊C4—24no—
60C2×Dic83⋊C4C2×C414yes—
61C2×Dic83⋊C4C2×C418yescomplemented
62C2×Dic83⋊C4D418yes—
63C2×C22⋊Dic83—24no—
64C2×C22⋊Dic83—42no—
65C2×C22⋊Dic83—42no—
66C2×C22⋊Dic83C2×C414yes—
67C2×C22⋊Dic83C2×C418yescomplemented
68C2×(C2×D83)⋊C4—24no—
69C2×(C2×D83)⋊C4—24no—
70C2×(C2×D83)⋊C4—24no—
71C2×(C2×D83)⋊C4—42no—
72C2×(C2×D83)⋊C4—42no—
73C2×(C2×D83)⋊C4C2×C414yes—
74C2×(C2×D83)⋊C4C2×C418yescomplemented
75C2×(C2×D83)⋊C4C2×C418yescomplemented
76C2×C4×Dic83—24no—
77C2×C4×Dic83—24no—
78C2×C4×Dic83—24no—
79C2×C4×Dic83—24no—
80C2×C4×Dic83—24no—
81C2×C4×Dic83—42no—
82C2×C4×Dic83C2×C414yes—
83C2×C4×Dic83C2×C418yescomplemented
84C83⋊#95—24no—
85C83⋊#95—24no—
86C83⋊#95—22no—
87C83⋊#95—22no—
88C83⋊#95—24no—
89C83⋊#95—42no—
90C25×C83C2311yescharacteristic
91C23×C4×C83—24no—
92C23×C4×C83—22no—
93C23×C4×C83—22no—
94C23×C4×C83—42no—
95C23×C4×C83C2×C414yes—
96C23×C4×C83C2312yes—
97C23×C4×C83C2311yescharacteristic
98C23×C4×C83C2312yes—
99C23×C4×C83C2311yescharacteristic
100C2×C22⋊C4×C83—24no—
101C2×C22⋊C4×C83—24no—
102C2×C22⋊C4×C83C2×C418yescomplemented
103C2×C42×C83—24no—
104C2×C42×C83—24no—
105C2×C42×C83—42no—
106#95×C83—22no—
107#95×C83D414yescomplemented
108C23×D83—22no—
109C23×D83—21no—
110C23×D83—21no—
111C23×D83—21no—
112C23×D83—21no—
113C23×D83—22no—
114C23×D83—22no—
115C23×D83—21no—
116C23×D83—21no—
117C23×D83C22×C412yes—
118C23×D83C22×C414yes—
119C2×C22⋊D83—28no—
120C2×C22⋊D83—28no—
121C2×C22⋊D83—216no—
122C2×C22⋊D83—216no—
123C2×C22⋊D83C42116yescomplemented
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—22no—
127C22×Dic83—22no—
128C22×Dic83—22no—
129C22×Dic83—22no—
130C22×Dic83—22no—
131C22×Dic83—22no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—22no—
135C22×Dic83—22no—
136C22×Dic83—22no—
137C22×Dic83—21no—
138C22×Dic83—22no—
139C22×Dic83—22no—
140C22×Dic83—22no—
141C22×Dic83—22no—
142C22×Dic83—21no—
143C22×Dic83C22×C412yes—
144C22×Dic83C22×C414yes—
145C22×Dic83C22×C414yes—
146C22×Dic83C22×C412yes—
147C22×Dic83C22×C412yes—
148C22×Dic83C22×C414yes—
149C22×Dic83C2×D414yes—
150C22×Dic83C2×D414yes—
151C22×Dic83#4112yes—
152C22×Dic83#4112yes—
153C2×C4×D83—28no—
154C2×C4×D83—28no—
155C2×C4×D83—44no—
156C2×C4×D83—48no—
157C2×C4×D83—48no—
158Dic83⋊C4—216no—
159Dic83⋊C4C22⋊C4116yescomplemented
160C22⋊Dic83—28no—
161C22⋊Dic83—48no—
162(C2×D83)⋊C4—28no—
163(C2×D83)⋊C4—216no—
164(C2×D83)⋊C4—48no—
165C4×Dic83—28no—
166C4×Dic83—216no—
167C4×Dic83—48no—
168C24×C83—22no—
169C24×C83—21no—
170C24×C83—21no—
171C24×C83—21no—
172C24×C83—22no—
173C24×C83—21no—
174C24×C83—22no—
175C24×C83—21no—
176C24×C83—21no—
177C24×C83C22×C414yes—
178C24×C83C22×C412yes—
179C24×C83C2411yescharacteristic
180C22×C4×C83—22no—
181C22×C4×C83—21no—
182C22×C4×C83—22no—
183C22×C4×C83—21no—
184C22×C4×C83—22no—
185C22×C4×C83—22no—
186C22×C4×C83—22no—
187C22×C4×C83—22no—
188C22×C4×C83—22no—
189C22×C4×C83—22no—
190C22×C4×C83—22no—
191C22×C4×C83—22no—
192C22×C4×C83—22no—
193C22×C4×C83—22no—
194C22×C4×C83—22no—
195C22×C4×C83—28no—
196C22×C4×C83—28no—
197C22×C4×C83—44no—
198C22×C4×C83—48no—
199C22×C4×C83—48no—
200C22×C4×C83C22×C414yes—
201C22×C4×C83C22×C412yes—
202C22×C4×C83C22×C412yes—
203C22×C4×C83C22×C414yes—
204C22×C4×C83C2×D414yes—
205C22×C4×C83C2×D412yes—
206C22×C4×C83C2×D414yes—
207C22×C4×C83#4112yes—
208C22×C4×C83#4114yes—
209C22⋊C4×C83—216no—
210C42×C83—48no—
211C23×C83—22no—
212C23×C83—22no—
213C23×C83—24no—
214C23×C83—22no—
215C23×C83—24no—
216C23×C83—24no—
217C23×C83—22no—
218C23×C83—24no—
219C23×C83—22no—
220C23×C83—24no—
221C23×C83—24no—
222C23×C83—22no—
223C23×C83—42no—
224C23×C83—42no—
225C23×C83—41no—
226C23×C83—42no—
227C23×C83—41no—
228C23×C83—42no—
229C23×C83—42no—
230C23×C83—41no—
231C23×C83—41no—
232C23×C83—42no—
233C23×C83C2×C4214yes—
234C23×C83C23×C411yescharacteristic
235C23×C83C23×C412yes—
236C23×C83C22×D412yes—
237C23×C83C22×D411yescharacteristic
238C23×C83C2×#4111yescharacteristic
239C23×C83C2×#4111yescharacteristic
240C23×C83C2×#4111yescharacteristic
241C23×C83C2×#4112yes—
242C23×C83H(5,𝔽2)12yes—
243C23×C83H(5,𝔽2)11yescharacteristic
244C23×C832−1+411yescharacteristic
245C22×D83—22no—
246C22×D83—22no—
247C22×D83—24no—
248C22×D83—22no—
249C22×D83—24no—
250C22×D83—24no—
251C22×D83—22no—
252C22×D83—24no—
253C22×D83—24no—
254C22×D83—22no—
255C22×D83—24no—
256C22×D83—22no—
257C22×D83—42no—
258C22×D83—42no—
259C22×D83—41no—
260C22×D83—42no—
261C22×D83—41no—
262C22×D83—42no—
263C22×D83—42no—
264C22×D83—41no—
265C22×D83—41no—
266C22×D83—42no—
267C22×D83C2×C4214yes—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—24no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—24no—
274C2×C4×C83—24no—
275C2×C4×C83—24no—
276C2×C4×C83—24no—
277C2×C4×C83—24no—
278C2×C4×C83—24no—
279C2×C4×C83—24no—
280C2×C4×C83—24no—
281C2×C4×C83—24no—
282C2×C4×C83—24no—
283C2×C4×C83—24no—
284C2×C4×C83—24no—
285C2×C4×C83—416no—
286C2×C4×C83—42no—
287C2×C4×C83—42no—
288C2×C4×C83—42no—
289C2×C4×C83—42no—
290C2×C4×C83C2×C22⋊C414yes—
291C2×C4×C83C4×D414yes—
292C2×C4×C83C4×D418yescomplemented
293C22⋊D83—232no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—24no—
297C2×Dic83—24no—
298C2×Dic83—22no—
299C2×Dic83—24no—
300C2×Dic83—24no—
301C2×Dic83—24no—
302C2×Dic83—22no—
303C2×Dic83—24no—
304C2×Dic83—24no—
305C2×Dic83—24no—
306C2×Dic83—22no—
307C2×Dic83—42no—
308C2×Dic83—42no—
309C2×Dic83—42no—
310C2×Dic83—42no—
311C2×Dic83—42no—
312C2×Dic83—42no—
313C2×Dic83—42no—
314C2×Dic83—42no—
315C2×Dic83—42no—
316C2×Dic83—42no—
317C2×Dic83C2×C4214yes—
318C2×Dic83C2×C22⋊C414yes—
319C2×Dic83C2×C22⋊C414yes—
320C2×Dic83#11714yes—
321C2×Dic83C4×D418yes—
322C2×Dic83C4×D418yes—
323C4×D83—416no—
324C22×C83—24no—
325C22×C83—24no—
326C22×C83—24no—
327C22×C83—42no—
328C22×C83—42no—
329C22×C83—42no—
330C22×C83—42no—
331C22×C83—44no—
332C22×C83—44no—
333C22×C83—44no—
334C22×C83—44no—
335C22×C83C22×C4211yescharacteristic
336C22×C83C22×C22⋊C411yescharacteristic
337C22×C83C2×#11711yescharacteristic
338C22×C83C2×C4×D412yes—
339C22×C83C2×C4×D412yes—
340C22×C83C2×C4×D411yescharacteristic
341C22×C83C2×C4×D412yes—
342C22×C83C4×#4111yescharacteristic
343C22×C83C4×#4112yes—
344C22×C83#51812yes—
345C22×C83#51811yescharacteristic
346C22×C83#52012yes—
347C22×C83#52011yescharacteristic
348C22×C83D4212yes—
349C22×C83#54612yes—
350C22×C83#54711yescharacteristic
351C22×C83#54812yes—
352C22×C83#55011yescharacteristic
353C22×C83#55012yes—
354C22×C83#55312yes—
355C22×C83#55511yescharacteristic
356C22×C83#55611yescharacteristic
357C22×C83#55912yes—
358C2×D83—24no—
359C2×D83—24no—
360C2×D83—24no—
361C2×D83—42no—
362C2×D83—42no—
363C2×D83—42no—
364C2×D83—42no—
365C2×D83—44no—
366C2×D83—44no—
367C2×D83—44no—
368C2×D83—44no—
369C4×C83—24no—
370C4×C83—24no—
371C4×C83—28no—
372C4×C83—44no—
373Dic83—24no—
374Dic83—42no—
375Dic83—44no—
376Dic83—44no—
377Dic83C4×C22⋊C418yescomplemented
378#13820—831nomaximal, Sylow
379C2×C83—44no—
380C2×C83C2×C4×C22⋊C411yescharacteristic
381C2×C83C42×D411yescharacteristic
382C2×C83#227511yescharacteristic
383C2×C83D4×C22⋊C411yescharacteristic
384C2×C83#234111yescharacteristic
385C2×C83#235411yescharacteristic
386C2×C83#235711yescharacteristic
387C2×C83#236112yes—
388C2×C83#236312yes—
389C2×C83#236612yes—
390C2×C83#236712yes—
391D83—44no—
392C22×C4×D4—831no—
393C2×#390—832no—
394C2×C4×C4⋊C4—832no—
395C2×C4×C22⋊C4—831no—
396C2×C4×C22⋊C4D8311yescharacteristic, complemented
397#1437—832no—
398#1437—832no—
399C4⋊#95—831no—
400C22⋊#95—831no—
401C22⋊#95—831no—
402C4×#95—831no—
403C83#1382011yescharacteristic, complemented, Sylow
404C23×D4—831no—
405C24×C4—831no—
406C24×C4C2×D8311yescharacteristic
407C2×C4×D4—838no—
408C2×C4×D4—1668no—
409C22×C4⋊C4—831no—
410C22×C4⋊C4—832no—
411C22×C22⋊C4—832no—
412C22×C22⋊C4—832no—
413C22×C22⋊C4—831no—
414C22×C22⋊C4—831no—
415C22×C22⋊C4—832no—
416C22×C22⋊C4C2×D8312yes—
417C22×C42—832no—
418C22×C42—831no—
419C22×C42—832no—
420C22×C42C2×D8312yes—
421#390—8316no—
422C4×C4⋊C4—1668no—
423C4×C22⋊C4—24no—
424C4×C22⋊C4—1664no—
425C2×#95—832no—
426C2×#95—831no—
427C2×#95—832no—
428C2×#95—831no—
429C2×#95—832no—
430C2×#95—832no—
431C2×#95C2×D8311yescharacteristic
432C2×#95C2×D8311yescharacteristic
433C25—831no—
434C25C22×D8311yescharacteristic
435C22×D4—834no—
436C22×D4—838no—
437C22×D4—1664no—
438C22×D4—1662no—
439C22×D4—1662no—
440C23×C4—24no—
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—42no—
444C23×C4—3322no—
445C23×C4—834no—
446C23×C4—831no—
447C23×C4—831no—
448C23×C4—832no—
449C23×C4—832no—
450C23×C4—831no—
451C23×C4—1664no—
452C23×C4—1662no—
453C23×C4—1662no—
454C23×C4C4×D8314yes—
455C23×C4C22×D8312yes—
456C23×C4C22×D8311yescharacteristic
457C23×C4C22×D8312yes—
458C23×C4C22×D8311yescharacteristic
459C4×D4—16632no—
460C2×C4⋊C4—834no—
461C2×C4⋊C4—838no—
462C2×C4⋊C4—838no—
463C2×C4⋊C4—1664no—
464C2×C4⋊C4—1664no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—3322no—
468C2×C22⋊C4—3322no—
469C2×C22⋊C4—3322no—
470C2×C22⋊C4—3322no—
471C2×C22⋊C4—838no—
472C2×C22⋊C4—838no—
473C2×C22⋊C4—834no—
474C2×C22⋊C4—834no—
475C2×C22⋊C4—838no—
476C2×C22⋊C4—1664no—
477C2×C22⋊C4—1664no—
478C2×C22⋊C4—1664no—
479C2×C22⋊C4—1664no—
480C2×C22⋊C4C4×D8318yescomplemented
481C2×C42—24no—
482C2×C42—24no—
483C2×C42—42no—
484C2×C42—3322no—
485C2×C42—834no—
486C2×C42—838no—
487C2×C42—1664no—
488C2×C42—1664no—
489C2×C42—1664no—
490C2×C42—1664no—
491C2×C42—1664no—
492#95—22no—
493#95—3322no—
494#95—1664no—
495#95—1664no—
496#95—1662no—
497#95—1662no—
498#95—1664no—
499#95C22⋊D8314yescomplemented
500C24—22no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—22no—
505C24—21no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—834no—
510C24—832no—
511C24—1662no—
512C24—1661no—
513C24—1661no—
514C24—1661no—
515C24—1662no—
516C24—1661no—
517C24—1662no—
518C24—1661no—
519C24—1661no—
520C24C2×C4×D8314yes—
521C24C2×C4×D8312yes—
522C24C23×D8311yescharacteristic
523C2×D4—8316no—
524C2×D4—1668no—
525C2×D4—1668no—
526C2×D4—16616no—
527C2×D4—16616no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—3328no—
549C22×C4—3328no—
550C22×C4—3324no—
551C22×C4—832no—
552C22×C4—834no—
553C22×C4—834no—
554C22×C4—832no—
555C22×C4—832no—
556C22×C4—832no—
557C22×C4—834no—
558C22×C4—832no—
559C22×C4—834no—
560C22×C4—834no—
561C22×C4—1668no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4—1661no—
575C22×C4—1662no—
576C22×C4—1662no—
577C22×C4—1661no—
578C22×C4—1668no—
579C22×C4—1661no—
580C22×C4—1661no—
581C22×C4—1662no—
582C22×C4C2×C4×D8314yes—
583C22×C4C2×C4×D8312yes—
584C22×C4C2×C4×D8312yes—
585C22×C4C2×C4×D8314yes—
586C22×C4D4×D8314yes—
587C22×C4C2×C22⋊D8312yes—
588C22×C4C2×C22⋊D8314yes—
589C22×C4#1305059012yes—
590C22×C4#1305059014yes—
591C4⋊C4—8316no—
592C4⋊C4—16616no—
593C22⋊C4—216no—
594C22⋊C4—3328no—
595C22⋊C4—3328no—
596C22⋊C4—1668no—
597C22⋊C4—1668no—
598C22⋊C4—16616no—
599C42—48no—
600C42—3328no—
601C42—1668no—
602C42—16616no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—3322no—
626C23—3322no—
627C23—3321no—
628C23—3322no—
629C23—3321no—
630C23—3322no—
631C23—3322no—
632C23—3321no—
633C23—3321no—
634C23—3322no—
635C23—834no—
636C23—1662no—
637C23—1662no—
638C23—1664no—
639C23—1664no—
640C23—1664no—
641C23—1662no—
642C23—1662no—
643C23—1664no—
644C23—1664no—
645C23—1662no—
646C23—1664no—
647C23—1662no—
648C23C42×D8314yes—
649C23C22×C4×D8311yescharacteristic
650C23C22×C4×D8312yes—
651C23C2×D4×D8312yes—
652C23C22×C22⋊D8311yescharacteristic
653C23#41×D8311yescharacteristic
654C23#41×D8311yescharacteristic
655C23C2×#1305059011yescharacteristic
656C23C2×#1305059012yes—
657C23#1458183712yes—
658C23#1458183811yescharacteristic
659C23#1458183911yescharacteristic
660D4—16632no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—416no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—33216no—
684C2×C4—3322no—
685C2×C4—3322no—
686C2×C4—3322no—
687C2×C4—3322no—
688C2×C4—3322no—
689C2×C4—3322no—
690C2×C4—3322no—
691C2×C4—3322no—
692C2×C4—3322no—
693C2×C4—3322no—
694C2×C4—834no—
695C2×C4—834no—
696C2×C4—834no—
697C2×C4—838no—
698C2×C4—838no—
699C2×C4—834no—
700C2×C4—1662no—
701C2×C4—1664no—
702C2×C4—1664no—
703C2×C4—1664no—
704C2×C4—1664no—
705C2×C4—1662no—
706C2×C4—1664no—
707C2×C4—1664no—
708C2×C4—1662no—
709C2×C4—1664no—
710C2×C4—1664no—
711C2×C4—1662no—
712C2×C4—1662no—
713C2×C4C22⋊C4×D8314yes—
714C2×C4C4×C22⋊D8314yes—
715C2×C4C4×C22⋊D8318yescomplemented
716C22—24no—
717C22—24no—
718C22—24no—
719C22—42no—
720C22—42no—
721C22—44no—
722C22—44no—
723C22—44no—
724C22—44no—
725C22—42no—
726C22—42no—
727C22—3322no—
728C22—3322no—
729C22—3324no—
730C22—3324no—
731C22—3324no—
732C22—3324no—
733C22—3322no—
734C22—3322no—
735C22—1664no—
736C22—1664no—
737C22—1664no—
738C22C2×C42×D8311yescharacteristic
739C22C2×C22⋊C4×D8311yescharacteristic
740C22#117×D8311yescharacteristic
741C22C4×D4×D8312yes—
742C22C4×D4×D8312yes—
743C22C2×C4×C22⋊D8311yescharacteristic
744C22C2×C4×C22⋊D8312yes—
745C22C4×#1305059011yescharacteristic
746C22C4×#1305059012yes—
747C22#1912817312yes—
748C22#1912817411yescharacteristic
749C22#1912818012yes—
750C22#1912818111yescharacteristic
751C22D4×C22⋊D8312yes—
752C22#1912834112yes—
753C22#1912835011yescharacteristic
754C22#1912836012yes—
755C22#1912837011yescharacteristic
756C22#1912837212yes—
757C22#1912840012yes—
758C22#1912841411yescharacteristic
759C22#1912841911yescharacteristic
760C22#1912843412yes—
761C4—28no—
762C4—24no—
763C4—24no—
764C4—44no—
765C4—3324no—
766C4—3324no—
767C4—3322no—
768C4—838no—
769C4—1664no—
770C2—44no—
771C2—3324no—
772C2C4×C22⋊C4×D8311yescharacteristic
773C2C42×C22⋊D8311yescharacteristic
774C2#2490982211yescharacteristic
775C2C22⋊C4×C22⋊D8311yescharacteristic
776C2#2491030311yescharacteristic
777C2#2491041311yescharacteristic
778C2#2491043711yescharacteristic
779C2#2491048012yes—
780C2#2491050212yes—
781C2#2491052512yes—
782C2#2491053512yes—
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC2×C4×C22⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×C4×C22⋊C4D83
hypocenterC83#13820
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic83⋊C4C2semidirect
4. C2×#19127548C2semidirect
5. #24905701C2semidirect
6. #24905700C2semidirect
7. Dic83⋊#95C2semidirect
8. #24905686C2semidirect
9. (C2×D83)⋊#95C2semidirect
10. #95×Dic83C2semidirect
11. C2×C4×C22⋊C4×C83C2semidirect
15. C2×C4×C22⋊D83C4semidirect
26. #19127601C4semidirect
61. C2×Dic83⋊C4C2×C4semidirect
67. C2×C22⋊Dic83C2×C4semidirect
74. C2×(C2×D83)⋊C4C2×C4semidirect
75. C2×(C2×D83)⋊C4C2×C4semidirect
83. C2×C4×Dic83C2×C4semidirect
102. C2×C22⋊C4×C83C2×C4semidirect
107. #95×C83D4semidirect
123. C2×C22⋊D83C42semidirect
159. Dic83⋊C4C22⋊C4semidirect
292. C2×C4×C83C4×D4semidirect
377. Dic83C4×C22⋊C4semidirect
396. C2×C4×C22⋊C4D83semidirect
403. C83#13820semidirect
480. C2×C22⋊C4C4×D83semidirect
499. #95C22⋊D83semidirect
715. C2×C4C4×C22⋊D83semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D832
C2×#191276012
C2×C4×Dic83⋊C42
C2×#191275482
#249057012
#249057002
Dic83⋊#952
#249056862
(C2×D83)⋊#952
#95×Dic832
C2×C4×C22⋊C4×C832
#1382083