Finite Group Databasebeta

← #35327503

Subgroups — #35327503

Order 21248.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127591C212yesmaximal
2C2×#19127558C211yesmaximal, characteristic
3C2×#19127558C211yesmaximal, characteristic
4C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
6#24905722C212yesmaximal, complemented
7#24905711C212yesmaximal
8#24905693C211yesmaximal, characteristic, complemented
9#24905692C211yesmaximal, characteristic, complemented
10#24905689C212yesmaximal, complemented
11C2×#389×C83C211yesmaximal, characteristic, complemented
12C23×C4×D83C2211yescharacteristic
13C22×C4⋊Dic83C2211yescharacteristic
14C22×C4⋊Dic83C2211yescharacteristic
15C22×(C2×D83)⋊C4C2211yescharacteristic
16C22×(C2×D83)⋊C4C2212yes—
17C22×(C2×D83)⋊C4C2212yes—
18C22×(C2×D83)⋊C4C2211yescharacteristic
19C22×C4×Dic83C2212yes—
20C22×C4×Dic83C2211yescharacteristic
21#19127591—28no—
22#19127558—24no—
23#19127558C418yescomplemented
24C4⋊C4×Dic83—24no—
25C4×(C2×D83)⋊C4—24no—
26C2×C83⋊#95C2212yes—
27C2×C83⋊#95C2212yes—
28C2×C83⋊#95C2212yes—
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2212yes—
31C2×C83⋊#95C2211yescharacteristic
32C2×C83⋊#95C2212yes—
33C2×C83⋊#95C2212yes—
34C2×C83⋊#95C2212yes—
35C22×C4⋊C4×C83C2212yes—
36C22×C4⋊C4×C83C2211yescharacteristic
37C22×C4⋊C4×C83C2211yescharacteristic
38C22×C42×C83C2211yescharacteristic
39#389×C83—24no—
40C2×#95×C83C2212yes—
41C24×D83C2311yescharacteristic
42C23×Dic83C2312yes—
43C23×Dic83C2312yes—
44C23×Dic83C2311yescharacteristic
45C23×Dic83C2311yescharacteristic
46C23×Dic83C2311yescharacteristic
47C22×C4×D83—22no—
48C22×C4×D83—22no—
49C22×C4×D83—22no—
50C22×C4×D83—22no—
51C22×C4×D83—22no—
52C22×C4×D83—22no—
53C22×C4×D83C2×C414yes—
54C2×C4⋊Dic83—22no—
55C2×C4⋊Dic83—22no—
56C2×C4⋊Dic83—22no—
57C2×C4⋊Dic83—22no—
58C2×C4⋊Dic83—22no—
59C2×C4⋊Dic83C2×C414yes—
60C2×(C2×D83)⋊C4—24no—
61C2×(C2×D83)⋊C4—22no—
62C2×(C2×D83)⋊C4—24no—
63C2×(C2×D83)⋊C4—22no—
64C2×(C2×D83)⋊C4—22no—
65C2×(C2×D83)⋊C4—22no—
66C2×(C2×D83)⋊C4—24no—
67C2×(C2×D83)⋊C4—24no—
68C2×(C2×D83)⋊C4—22no—
69C2×(C2×D83)⋊C4—42no—
70C2×(C2×D83)⋊C4C2×C418yes—
71C2×(C2×D83)⋊C4D414yes—
72C2×C4×Dic83—24no—
73C2×C4×Dic83—24no—
74C2×C4×Dic83—24no—
75C2×C4×Dic83—22no—
76C2×C4×Dic83—22no—
77C2×C4×Dic83D414yes—
78C83⋊#95—24no—
79C83⋊#95—24no—
80C83⋊#95—22no—
81C83⋊#95—22no—
82C83⋊#95—24no—
83C83⋊#95—24no—
84C83⋊#95—24no—
85C83⋊#95—42no—
86C83⋊#95C2×C418yes—
87C23×C4×C83C2312yes—
88C23×C4×C83C2311yescharacteristic
89C23×C4×C83C2312yes—
90C23×C4×C83C2311yescharacteristic
91C23×C4×C83C2311yescharacteristic
92C2×C4⋊C4×C83—22no—
93C2×C4⋊C4×C83—22no—
94C2×C4⋊C4×C83—22no—
95C2×C4⋊C4×C83—22no—
96C2×C4⋊C4×C83—24no—
97C2×C4⋊C4×C83—24no—
98C2×C4⋊C4×C83—42no—
99C2×C4⋊C4×C83C2×C414yes—
100C2×C4⋊C4×C83D414yes—
101C2×C42×C83—22no—
102C2×C42×C83—22no—
103C2×C42×C83—22no—
104#95×C83—24no—
105C23×D83—21no—
106C23×D83—21no—
107C23×D83—21no—
108C23×D83—21no—
109C23×D83—21no—
110C23×D83—21no—
111C23×D83—21no—
112C23×D83—21no—
113C23×D83—21no—
114C23×D83—21no—
115C23×D83—21no—
116C23×D83—21no—
117C23×D83C22×C412yes—
118C23×D83C2×D412yes—
119C23×D83#4112yes—
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—22no—
127C22×Dic83—22no—
128C22×Dic83—21no—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—22no—
133C22×Dic83—22no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83—22no—
137C22×Dic83—21no—
138C22×Dic83—21no—
139C22×Dic83—22no—
140C22×Dic83—21no—
141C22×Dic83—21no—
142C22×Dic83—22no—
143C22×Dic83—22no—
144C22×Dic83—22no—
145C22×Dic83—22no—
146C22×Dic83—22no—
147C22×Dic83—22no—
148C22×Dic83—22no—
149C22×Dic83C22×C412yes—
150C22×Dic83C22×C414yes—
151C22×Dic83C2×D412yes—
152C22×Dic83C2×D412yes—
153C22×Dic83C2×D412yes—
154C22×Dic83#4112yes—
155C2×C4×D83—28no—
156C2×C4×D83—28no—
157C2×C4×D83—28no—
158C2×C4×D83—44no—
159C2×C4×D83—44no—
160C2×C4×D83—44no—
161C2×C4×D83—44no—
162C4⋊Dic83—28no—
163C4⋊Dic83—44no—
164(C2×D83)⋊C4—28no—
165(C2×D83)⋊C4—216no—
166(C2×D83)⋊C4—28no—
167(C2×D83)⋊C4—48no—
168C4×Dic83—28no—
169C4×Dic83—48no—
170C24×C83C2411yescharacteristic
171C22×C4×C83—21no—
172C22×C4×C83—22no—
173C22×C4×C83—21no—
174C22×C4×C83—21no—
175C22×C4×C83—21no—
176C22×C4×C83—22no—
177C22×C4×C83—22no—
178C22×C4×C83—22no—
179C22×C4×C83—21no—
180C22×C4×C83—21no—
181C22×C4×C83—22no—
182C22×C4×C83—22no—
183C22×C4×C83—22no—
184C22×C4×C83—22no—
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—22no—
189C22×C4×C83—22no—
190C22×C4×C83—22no—
191C22×C4×C83—21no—
192C22×C4×C83—22no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83C22×C414yes—
196C22×C4×C83C22×C412yes—
197C22×C4×C83C2×D412yes—
198C22×C4×C83C2×D412yes—
199C22×C4×C83C2×D414yes—
200C22×C4×C83C2×D412yes—
201C22×C4×C83#4112yes—
202C22×C4×C83#4112yes—
203C22×C4×C83#4112yes—
204C22×C4×C83#4112yes—
205C22×C4×C83#4112yes—
206C4⋊C4×C83—28no—
207C4⋊C4×C83—28no—
208C4⋊C4×C83—48no—
209C42×C83—44no—
210C23×C83C23×C411yescharacteristic
211C23×C83C22×D411yescharacteristic
212C23×C83C22×D411yescharacteristic
213C23×C83C22×D411yescharacteristic
214C23×C83C2×#4111yescharacteristic
215C23×C83C2×#4111yescharacteristic
216C23×C83C2×#4111yescharacteristic
217C23×C83C2×#4111yescharacteristic
218C23×C83C2×#4111yescharacteristic
219C23×C83C2×#4111yescharacteristic
220C23×C83C2×#4111yescharacteristic
221C23×C83H(5,𝔽2)11yescharacteristic
222C23×C832−1+411yescharacteristic
223C23×C832−1+411yescharacteristic
224C23×C832−1+411yescharacteristic
225C22×D83—22no—
226C22×D83—22no—
227C22×D83—22no—
228C22×D83—22no—
229C22×D83—22no—
230C22×D83—22no—
231C22×D83—22no—
232C22×D83—22no—
233C22×D83—22no—
234C22×D83—22no—
235C22×D83—22no—
236C22×D83—22no—
237C22×D83—22no—
238C22×D83—22no—
239C22×D83—22no—
240C22×D83—22no—
241C22×D83—22no—
242C22×D83—22no—
243C22×D83—41no—
244C22×D83—41no—
245C22×D83—41no—
246C22×D83—41no—
247C22×D83—41no—
248C22×D83—41no—
249C22×D83—41no—
250C22×D83—41no—
251C22×D83—41no—
252C22×D83—41no—
253C22×D83—41no—
254C22×D83—41no—
255C22×D83—41no—
256C22×D83—41no—
257C22×D83—41no—
258C22×D83—41no—
259C22×D83C4×D414yes—
260C2×C4×C83—24no—
261C2×C4×C83—24no—
262C2×C4×C83—24no—
263C2×C4×C83—24no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—24no—
268C2×C4×C83—24no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—41no—
273C2×C4×C83—41no—
274C2×C4×C83—42no—
275C2×C4×C83—41no—
276C2×C4×C83—41no—
277C2×C4×C83—42no—
278C2×C4×C83—42no—
279C2×C4×C83—41no—
280C2×C4×C83—42no—
281C2×C4×C83—42no—
282C2×C4×C83—42no—
283C2×C4×C83—41no—
284C2×C4×C83—41no—
285C2×C4×C83—42no—
286C2×C4×C83—41no—
287C2×C4×C83—42no—
288C2×C4×C83#11714yes—
289C2×C4×C83C4×D414yes—
290C2×C4×C83C4×D414yes—
291C2×C4×C83#12114yes—
292C2×C4×C83#12314yes—
293C2×C4×C83#12414yes—
294C2×C4×C83#12614yes—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—24no—
303C2×Dic83—24no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—24no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—42no—
311C2×Dic83—41no—
312C2×Dic83—41no—
313C2×Dic83—42no—
314C2×Dic83—41no—
315C2×Dic83—41no—
316C2×Dic83—42no—
317C2×Dic83—42no—
318C2×Dic83—41no—
319C2×Dic83—41no—
320C2×Dic83—41no—
321C2×Dic83—41no—
322C2×Dic83—42no—
323C2×Dic83—42no—
324C2×Dic83—42no—
325C2×Dic83—42no—
326C2×Dic83—42no—
327C2×Dic83—42no—
328C2×Dic83—42no—
329C2×Dic83#12114yes—
330C4×D83—416no—
331C22×C83C2×#11711yescharacteristic
332C22×C83C2×C4×D411yescharacteristic
333C22×C83C2×C4×D411yescharacteristic
334C22×C83C2×C4×D411yescharacteristic
335C22×C83C4×#4111yescharacteristic
336C22×C83#51911yescharacteristic
337C22×C83#52011yescharacteristic
338C22×C83C2×#12111yescharacteristic
339C22×C83C2×#12111yescharacteristic
340C22×C83C2×#12311yescharacteristic
341C22×C83#52511yescharacteristic
342C22×C83C2×#12411yescharacteristic
343C22×C83C2×#12611yescharacteristic
344C22×C83#52911yescharacteristic
345C22×C83#53211yescharacteristic
346C22×C83#53611yescharacteristic
347C22×C83#53711yescharacteristic
348C22×C83#54111yescharacteristic
349C22×C83#54211yescharacteristic
350C22×C83D4211yescharacteristic
351C22×C83#54711yescharacteristic
352C22×C83#54711yescharacteristic
353C22×C83#54711yescharacteristic
354C22×C83#54711yescharacteristic
355C22×C83#54811yescharacteristic
356C22×C83#54811yescharacteristic
357C22×C83#55211yescharacteristic
358C22×C83#55211yescharacteristic
359C22×C83#55211yescharacteristic
360C22×C83#55211yescharacteristic
361C22×C83#55211yescharacteristic
362C22×C83#55311yescharacteristic
363C22×C83#55511yescharacteristic
364C22×C83#55511yescharacteristic
365C22×C83#55611yescharacteristic
366C2×D83—24no—
367C2×D83—24no—
368C2×D83—24no—
369C2×D83—42no—
370C2×D83—42no—
371C2×D83—42no—
372C2×D83—42no—
373C2×D83—42no—
374C2×D83—42no—
375C2×D83—42no—
376C2×D83—42no—
377C2×D83—42no—
378C2×D83—42no—
379C2×D83—42no—
380C2×D83—42no—
381C4×C83—44no—
382C4×C83—42no—
383C4×C83—44no—
384C4×C83—42no—
385C4×C83#38818yescomplemented
386Dic83—24no—
387Dic83—42no—
388Dic83—42no—
389Dic83—44no—
390Dic83—82no—
391#13994—831nomaximal, Sylow
392C2×C83C2×#38811yescharacteristic
393C2×C83C4×#12111yescharacteristic
394C2×C83#232311yescharacteristic
395C2×C83#234411yescharacteristic
396C2×C83#234611yescharacteristic
397C2×C83#236111yescharacteristic
398C2×C83#236211yescharacteristic
399C2×C83#248511yescharacteristic
400C2×C83#248611yescharacteristic
401C2×C83#248911yescharacteristic
402C2×C83#249111yescharacteristic
403C2×C83#249511yescharacteristic
404C2×C83#249611yescharacteristic
405C2×C83#253611yescharacteristic
406C2×C83#253711yescharacteristic
407D83—44no—
408C2×#389D8311yescharacteristic, complemented
409C2×#388—832no—
410C2×#380—831no—
411C2×#380—831no—
412C2×C4×C4⋊C4—831no—
413C2×C4×C22⋊C4—831no—
414#1442—832no—
415#1440—832no—
416C4⋊#95—831no—
417C4⋊#95—831no—
418#1434—832no—
419C83#1399411yescharacteristic, complemented, Sylow
420C24×C4—831no—
421C22×C4⋊C4—831no—
422C22×C4⋊C4—831no—
423C22×C4⋊C4C2×D8312yes—
424C22×C4⋊C4C2×D8311yescharacteristic
425C22×C4⋊C4C2×D8311yescharacteristic
426C22×C22⋊C4—832no—
427C22×C22⋊C4—832no—
428C22×C22⋊C4—831no—
429C22×C22⋊C4—831no—
430C22×C42—831no—
431C22×C42—832no—
432C22×C42C2×D8311yescharacteristic
433#389—24no—
434#388—1668no—
435#380—838no—
436#380—1664no—
437C4×C4⋊C4—1664no—
438C4×C22⋊C4—1664no—
439C2×#95—832no—
440C2×#95—832no—
441C2×#95—831no—
442C2×#95—832no—
443C2×#95—832no—
444C2×#95—832no—
445C2×#95—832no—
446C2×#95—832no—
447C2×#95—831no—
448C2×#95C2×D8312yes—
449C25—831no—
450C23×C4—831no—
451C23×C4—832no—
452C23×C4—831no—
453C23×C4—831no—
454C23×C4—834no—
455C23×C4—832no—
456C23×C4—1662no—
457C23×C4—1662no—
458C23×C4—1662no—
459C23×C4—1662no—
460C23×C4—1662no—
461C23×C4—1662no—
462C23×C4C22×D8312yes—
463C23×C4C22×D8311yescharacteristic
464C23×C4C22×D8312yes—
465C23×C4C22×D8311yescharacteristic
466C23×C4C22×D8311yescharacteristic
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—1662no—
476C2×C4⋊C4—1662no—
477C2×C4⋊C4—1662no—
478C2×C4⋊C4—1662no—
479C2×C4⋊C4—1662no—
480C2×C4⋊C4C4×D8314yes—
481C2×C4⋊C4C22⋊D8314yes—
482C2×C22⋊C4—3322no—
483C2×C22⋊C4—838no—
484C2×C22⋊C4—834no—
485C2×C22⋊C4—1664no—
486C2×C22⋊C4—1664no—
487C2×C22⋊C4—1662no—
488C2×C22⋊C4—1662no—
489C2×C22⋊C4—1662no—
490C2×C22⋊C4—1664no—
491C2×C22⋊C4—1664no—
492C2×C22⋊C4—1662no—
493C2×C22⋊C4—1662no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—834no—
498C2×C42—1664no—
499C2×C42—1664no—
500C2×C42—1664no—
501C2×C42—1662no—
502C2×C42—1662no—
503#95—24no—
504#95—3322no—
505#95—838no—
506#95—1662no—
507#95—1662no—
508#95—1664no—
509#95—1664no—
510#95—1664no—
511#95—1664no—
512#95—1664no—
513C24—832no—
514C24—832no—
515C24—832no—
516C24—1661no—
517C24—1661no—
518C24—1661no—
519C24—1661no—
520C24—1661no—
521C24—1661no—
522C24—1661no—
523C24—1661no—
524C24—1661no—
525C24—1661no—
526C24—1661no—
527C24—1661no—
528C24C23×D8311yescharacteristic
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—3324no—
554C22×C4—3324no—
555C22×C4—3324no—
556C22×C4—3324no—
557C22×C4—832no—
558C22×C4—832no—
559C22×C4—832no—
560C22×C4—832no—
561C22×C4—834no—
562C22×C4—832no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1661no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1661no—
574C22×C4—1662no—
575C22×C4—1661no—
576C22×C4—1662no—
577C22×C4—1661no—
578C22×C4—1661no—
579C22×C4—1661no—
580C22×C4—1662no—
581C22×C4—1661no—
582C22×C4—1661no—
583C22×C4—1662no—
584C22×C4—1661no—
585C22×C4—1661no—
586C22×C4—1661no—
587C22×C4—1661no—
588C22×C4—1668no—
589C22×C4—1668no—
590C22×C4—1668no—
591C22×C4—1661no—
592C22×C4—1661no—
593C22×C4—1661no—
594C22×C4—1661no—
595C22×C4C2×C4×D8314yes—
596C22×C4C2×C4×D8312yes—
597C22×C4D4×D8312yes—
598C22×C4D4×D8312yes—
599C22×C4C2×C22⋊D8314yes—
600C22×C4C2×C22⋊D8312yes—
601C22×C4#1305058912yes—
602C22×C4#1305059012yes—
603C22×C4#1305059112yes—
604C22×C4#1305059112yes—
605C22×C4#1305059112yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—48no—
609C4⋊C4—3324no—
610C4⋊C4—1668no—
611C22⋊C4—3328no—
612C22⋊C4—1668no—
613C22⋊C4—16616no—
614C22⋊C4—1668no—
615C42—44no—
616C42—3328no—
617C42—1668no—
618C23—3321no—
619C23—3321no—
620C23—3321no—
621C23—3321no—
622C23—3321no—
623C23—3321no—
624C23—3321no—
625C23—3321no—
626C23—3321no—
627C23—3321no—
628C23—3321no—
629C23—3321no—
630C23—3321no—
631C23—3321no—
632C23—3321no—
633C23—3321no—
634C23—834no—
635C23—1662no—
636C23—1662no—
637C23—1662no—
638C23—1662no—
639C23—1662no—
640C23—1662no—
641C23—1662no—
642C23—1662no—
643C23—1662no—
644C23—1662no—
645C23—1662no—
646C23—1662no—
647C23—1662no—
648C23—1662no—
649C23—1662no—
650C23—1662no—
651C23—1662no—
652C23—1662no—
653C23C22×C4×D8311yescharacteristic
654C23C2×D4×D8311yescharacteristic
655C23C2×D4×D8311yescharacteristic
656C23C22×C22⋊D8311yescharacteristic
657C23#41×D8311yescharacteristic
658C23#41×D8311yescharacteristic
659C23C2×#1305058911yescharacteristic
660C23C2×#1305059011yescharacteristic
661C23C2×#1305059111yescharacteristic
662C23C2×#1305059111yescharacteristic
663C23C2×#1305059111yescharacteristic
664C23#1458183711yescharacteristic
665C23#1458183911yescharacteristic
666C23#1458183911yescharacteristic
667C23#1458184011yescharacteristic
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—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—3321no—
697C2×C4—3321no—
698C2×C4—3321no—
699C2×C4—3321no—
700C2×C4—3322no—
701C2×C4—3321no—
702C2×C4—3321no—
703C2×C4—3322no—
704C2×C4—3321no—
705C2×C4—3321no—
706C2×C4—3322no—
707C2×C4—3322no—
708C2×C4—33216no—
709C2×C4—3322no—
710C2×C4—3322no—
711C2×C4—3322no—
712C2×C4—3322no—
713C2×C4—3322no—
714C2×C4—3322no—
715C2×C4—3322no—
716C2×C4—834no—
717C2×C4—1662no—
718C2×C4—1664no—
719C2×C4—1662no—
720C2×C4—1664no—
721C2×C4—1662no—
722C2×C4—1664no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4—1662no—
730C2×C4—1662no—
731C2×C4—1662no—
732C2×C4#1458175014yes—
733C2×C4C4×C22⋊D8314yes—
734C2×C4#1458175414yes—
735C2×C4#1458176414yes—
736C2×C4#1458177714yes—
737C2×C4#1458178114yes—
738C2×C4#1458178714yes—
739C22—3322no—
740C22—3322no—
741C22—3322no—
742C22—3322no—
743C22—3322no—
744C22—3322no—
745C22—3322no—
746C22—3322no—
747C22—3322no—
748C22—3322no—
749C22—3322no—
750C22—3322no—
751C22—1664no—
752C22—1664no—
753C22—1664no—
754C22C2×#1458175011yescharacteristic
755C22C4×D4×D8311yescharacteristic
756C22C2×C4×C22⋊D8311yescharacteristic
757C22C2×#1458175411yescharacteristic
758C22C4×#1305059111yescharacteristic
759C22#1912817711yescharacteristic
760C22#1912818011yescharacteristic
761C22#121×D8311yescharacteristic
762C22C2×#1458176411yescharacteristic
763C22C2×#1458177711yescharacteristic
764C22#1912821411yescharacteristic
765C22C2×#1458178111yescharacteristic
766C22C2×#1458178711yescharacteristic
767C22#1912823611yescharacteristic
768C22#1912825211yescharacteristic
769C22#1912827411yescharacteristic
770C22#1912828011yescharacteristic
771C22#1912831411yescharacteristic
772C22#1912832511yescharacteristic
773C22D4×C22⋊D8311yescharacteristic
774C22#1912835011yescharacteristic
775C22#1912835111yescharacteristic
776C22#1912835411yescharacteristic
777C22#1912835611yescharacteristic
778C22#1912835811yescharacteristic
779C22#1912836211yescharacteristic
780C22#1912838511yescharacteristic
781C22#1912838911yescharacteristic
782C22#1912838911yescharacteristic
783C22#1912839211yescharacteristic
784C22#1912839311yescharacteristic
785C22#1912840111yescharacteristic
786C22#1912841511yescharacteristic
787C22#1912841711yescharacteristic
788C22#1912842411yescharacteristic
789C4—44no—
790C4—42no—
791C4—44no—
792C4—42no—
793C4—3322no—
794C4—3324no—
795C4—3322no—
796C4—6642no—
797C4—1664no—
798C4#1912759118yescomplemented
799C2—3324no—
800C2C2×#1912759111yescharacteristic
801C2#2490997111yescharacteristic
802C2#2491014311yescharacteristic
803C2#2491033111yescharacteristic
804C2#2491034711yescharacteristic
805C2#2491047511yescharacteristic
806C2#2491048611yescharacteristic
807C2#2491176311yescharacteristic
808C2#2491176911yescharacteristic
809C2#2491180711yescharacteristic
810C2#2491182911yescharacteristic
811C2#2491187211yescharacteristic
812C2#2491188311yescharacteristic
813C2#2491237011yescharacteristic
814C2#2491237711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#389×C83C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#389D83
hypocenterC83#13994
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic83C2semidirect
6. #24905722C2semidirect
8. #24905693C2semidirect
9. #24905692C2semidirect
10. #24905689C2semidirect
11. C2×#389×C83C2semidirect
23. #19127558C4semidirect
385. C4×C83#388semidirect
408. C2×#389D83semidirect
419. C83#13994semidirect
798. C4#19127591semidirect

Maximal subgroups

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

subgroupindex
C2×#191275912
C2×#191275582
C2×C4⋊C4×Dic832
C2×C4×(C2×D83)⋊C42
#249057222
#249057112
#249056932
#249056922
#249056892
C2×#389×C832
#1399483