Finite Group Databasebeta

← #35409747

Subgroups — #35409747

Order 21248.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128212C211yesmaximal, characteristic
2#24909846C211yesmaximal, characteristic, complemented
3#24908448C212yesmaximal, complemented
4#24908299C212yesmaximal, complemented
5#24907916C214yesmaximal, complemented
6C4×#14581706C214yesmaximal, complemented
7C2×C4×C22⋊C4×C83C211yesmaximal, characteristic, complemented
8C22×#13050590C411yescharacteristic, complemented
9#19128212—21no—
10#19128212—21no—
11#19128212—21no—
12#19128212—21no—
13#19128212—21no—
14#19128212—21no—
15#19128212—21no—
16#19128212—21no—
17C2×#14581775C412yescomplemented
18C2×#14581771C411yescharacteristic, complemented
19C2×#14581771C2211yescharacteristic
20C2×#14581766C411yescharacteristic, complemented
21C2×#14581766C2211yescharacteristic
22C2×#14581761C2212yes—
23C2×C4×C22⋊D83C412yescomplemented
24C2×C4×C22⋊D83C2212yes—
25C2×#14581751—21no—
26C2×#14581751C411yescharacteristic, complemented
27C2×#14581706C2218yes—
28#19127564—21no—
29#19127561—21no—
30#19127561C2212yes—
31#19127557C2212yes—
32C4×C22⋊Dic83—21no—
33C4×C22⋊Dic83C2212yes—
34#19127467C2218yes—
35C24×C4×C83C2211yescharacteristic
36C22×C22⋊C4×C83C2212yes—
37C22×C42×C83—21no—
38C4×C22⋊C4×C83—21no—
39C4×C22⋊C4×C83—21no—
40C4×C22⋊C4×C83C2212yes—
41C4×C22⋊C4×C83C2212yes—
42C2×#95×C83—21no—
43C2×#13050590—21no—
44C2×#13050590—21no—
45C2×#13050590—21no—
46C2×#13050590—21no—
47C2×#13050590—44no—
48C22×Dic166C2×C411yescharacteristic, complemented
49C22×D332C2×C411yescharacteristic, complemented
50C22×C22⋊D83C2×C412yes—
51C22×C22⋊D83C2×C412yes—
52C22×C22⋊D83C2312yes—
53C22×C4×D83C2×C412yescomplemented
54#14581775—22no—
55#14581775—22no—
56#14581775—22no—
57#14581775—22no—
58#14581771—21no—
59#14581771—21no—
60#14581771—21no—
61#14581771—21no—
62#14581771—21no—
63#14581771—21no—
64#14581771—21no—
65#14581771—21no—
66#14581766—21no—
67#14581766—21no—
68#14581766—21no—
69#14581766—21no—
70#14581766—21no—
71#14581766—21no—
72#14581766—21no—
73#14581766—21no—
74#14581761—22no—
75#14581761—22no—
76#14581761—22no—
77#14581761—22no—
78C4×C22⋊D83—22no—
79C4×C22⋊D83—22no—
80C4×C22⋊D83—22no—
81C4×C22⋊D83—22no—
82C4×C22⋊D83—22no—
83C4×C22⋊D83—22no—
84C4×C22⋊D83—22no—
85C4×C22⋊D83—22no—
86#14581751—21no—
87#14581751—21no—
88#14581751—21no—
89#14581751—21no—
90#14581751—44no—
91C2×C4⋊Dic83—22no—
92C2×C4⋊Dic83C2×C411yescharacteristic, complemented
93C2×C4⋊Dic83C2×C411yescharacteristic, complemented
94C2×Dic83⋊C4C2×C412yescomplemented
95C2×Dic83⋊C4C2×C412yescomplemented
96C2×C22⋊Dic83—22no—
97C2×C22⋊Dic83—22no—
98C2×C22⋊Dic83C2×C412yes—
99C2×C22⋊Dic83C2×C412yes—
100C2×C22⋊Dic83C2314yes—
101C2×C22⋊Dic83C2312yes—
102C2×(C2×D83)⋊C4C2×C412yescomplemented
103C2×(C2×D83)⋊C4C2×C412yescomplemented
104C2×C4×Dic83—22no—
105C2×C4×Dic83C2×C412yescomplemented
106#14581706—216no—
107C83⋊#95—22no—
108C83⋊#95—22no—
109C25×C83C2311yescharacteristic
110C23×C4×C83—22no—
111C23×C4×C83—44no—
112C23×C4×C83C2×C411yescharacteristic
113C23×C4×C83C2×C411yescharacteristic
114C23×C4×C83C2×C411yescharacteristic
115C23×C4×C83C2×C411yescharacteristic
116C23×C4×C83D411yescharacteristic
117C23×C4×C83D411yescharacteristic
118C23×C4×C83D411yescharacteristic
119C23×C4×C83D411yescharacteristic
120C23×C4×C83D411yescharacteristic
121C23×C4×C83D411yescharacteristic
122C23×C4×C83D411yescharacteristic
123C23×C4×C83D411yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C2×C22⋊C4×C83—22no—
127C2×C22⋊C4×C83—28no—
128C2×C22⋊C4×C83C2314yes—
129C2×C42×C83—22no—
130C2×C42×C83—22no—
131C2×C42×C83—44no—
132#95×C83—22no—
133#95×C83—22no—
134C23×D83C22×C412yes—
135#13050590—44no—
136#13050590—44no—
137#13050590—44no—
138#13050590—44no—
139C2×Dic166—21no—
140C2×Dic166—21no—
141C2×Dic166—42no—
142C2×D332—21no—
143C2×D332—21no—
144C2×D332—42no—
145C2×C22⋊D83—22no—
146C2×C22⋊D83—22no—
147C2×C22⋊D83—22no—
148C2×C22⋊D83—22no—
149C2×C22⋊D83—22no—
150C2×C22⋊D83—22no—
151C2×C22⋊D83—28no—
152C2×C22⋊D83—44no—
153C2×C22⋊D83—44no—
154C22×Dic83—24no—
155C22×Dic83C22×C412yes—
156C22×Dic83C22×C412yes—
157C22×Dic83C22×C412yes—
158C2×C4×D83—22no—
159C2×C4×D83—22no—
160C2×C4×D83—44no—
161C4⋊Dic83—21no—
162C4⋊Dic83—21no—
163C4⋊Dic83—21no—
164C4⋊Dic83—21no—
165C4⋊Dic83—44no—
166Dic83⋊C4—22no—
167Dic83⋊C4—22no—
168Dic83⋊C4—22no—
169Dic83⋊C4—22no—
170C22⋊Dic83—22no—
171C22⋊Dic83—22no—
172C22⋊Dic83—22no—
173C22⋊Dic83—22no—
174C22⋊Dic83—22no—
175C22⋊Dic83—22no—
176C22⋊Dic83—28no—
177C22⋊Dic83—44no—
178C22⋊Dic83—44no—
179(C2×D83)⋊C4—22no—
180(C2×D83)⋊C4—22no—
181(C2×D83)⋊C4—22no—
182(C2×D83)⋊C4—22no—
183C4×Dic83—22no—
184C4×Dic83—22no—
185C4×Dic83—44no—
186C24×C83—24no—
187C24×C83—42no—
188C24×C83—42no—
189C24×C83C22×C411yescharacteristic
190C24×C83C22×C411yescharacteristic
191C24×C83C2×D411yescharacteristic
192C24×C83C2×D411yescharacteristic
193C24×C83C2×D411yescharacteristic
194C24×C83C2×D411yescharacteristic
195C24×C83C2411yescharacteristic
196C22×C4×C83—24no—
197C22×C4×C83—24no—
198C22×C4×C83—24no—
199C22×C4×C83—28no—
200C22×C4×C83—24no—
201C22×C4×C83—42no—
202C22×C4×C83—42no—
203C22×C4×C83—42no—
204C22×C4×C83—42no—
205C22×C4×C83—42no—
206C22×C4×C83—42no—
207C22×C4×C83—42no—
208C22×C4×C83—42no—
209C22×C4×C83—42no—
210C22×C4×C83—42no—
211C22×C4×C83—42no—
212C22×C4×C83—44no—
213C22×C4×C83—44no—
214C22×C4×C83C22⋊C411yescharacteristic
215C22×C4×C83C22⋊C411yescharacteristic
216C22×C4×C83C22⋊C411yescharacteristic
217C22×C4×C83C22⋊C411yescharacteristic
218C22×C4×C83C22⋊C411yescharacteristic
219C22×C4×C83C22⋊C411yescharacteristic
220C22×C4×C83C22⋊C411yescharacteristic
221C22×C4×C83C22⋊C411yescharacteristic
222C22×C4×C83C22⋊C411yescharacteristic
223C22×C4×C83C22⋊C411yescharacteristic
224C22×C4×C83C22⋊C411yescharacteristic
225C22×C4×C83C22⋊C411yescharacteristic
226C22×C4×C83C22⋊C411yescharacteristic
227C22×C4×C83C22⋊C411yescharacteristic
228C22×C4×C83C22⋊C411yescharacteristic
229C22×C4×C83C22⋊C411yescharacteristic
230C22×C4×C83C22×C411yescharacteristic
231C22×C4×C83C22×C411yescharacteristic
232C22×C4×C83C22×C411yescharacteristic
233C22×C4×C83C22×C411yescharacteristic
234C22×C4×C83C2×D411yescharacteristic
235C22×C4×C83C2×D411yescharacteristic
236C22×C4×C83C2×D411yescharacteristic
237C22×C4×C83C2×D411yescharacteristic
238C22×C4×C83C2×D411yescharacteristic
239C22×C4×C83C2×D411yescharacteristic
240C22×C4×C83C2×D411yescharacteristic
241C22×C4×C83C2×D411yescharacteristic
242C22⋊C4×C83—28no—
243C22⋊C4×C83—24no—
244C22⋊C4×C83#4118yescomplemented
245C42×C83—44no—
246C42×C83—44no—
247C23×C83—22no—
248C23×C83—22no—
249C23×C83—22no—
250C23×C83—22no—
251C23×C83—22no—
252C23×C83—22no—
253C23×C83—22no—
254C23×C83—22no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—41no—
260C23×C83—41no—
261C23×C83—41no—
262C23×C83—41no—
263C23×C83—41no—
264C23×C83—41no—
265C23×C83—41no—
266C23×C83—41no—
267C23×C83—416no—
268C23×C83C2×C22⋊C411yescharacteristic
269C23×C83C2×C22⋊C411yescharacteristic
270C23×C83C2×C22⋊C411yescharacteristic
271C23×C83C2×C22⋊C411yescharacteristic
272C23×C83C23×C411yescharacteristic
273C23×C83C22×D411yescharacteristic
274C23×C83C22×D411yescharacteristic
275C23×C83C2×#4114yes—
276C22×D83—22no—
277C22×D83—24no—
278C22×D83—42no—
279C22×D83—42no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—22no—
295C2×C4×C83—28no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83—41no—
299C2×C4×C83—41no—
300C2×C4×C83—41no—
301C2×C4×C83—41no—
302C2×C4×C83—41no—
303C2×C4×C83—41no—
304C2×C4×C83—41no—
305C2×C4×C83—41no—
306C2×C4×C83—41no—
307C2×C4×C83—41no—
308C2×C4×C83—44no—
309C2×C4×C83—416no—
310C2×C4×C83—44no—
311C2×C4×C83#9914yescomplemented
312C2×C4×C83C2×C22⋊C411yescharacteristic
313C2×C4×C83C2×C22⋊C411yescharacteristic
314C2×C4×C83C2×C22⋊C411yescharacteristic
315C2×C4×C83C2×C22⋊C411yescharacteristic
316C2×C4×C83C2×C22⋊C411yescharacteristic
317C2×C4×C83C2×C22⋊C411yescharacteristic
318C2×C4×C83C2×C22⋊C411yescharacteristic
319C2×C4×C83C2×C22⋊C411yescharacteristic
320C22⋊D83—44no—
321C22⋊D83—44no—
322C22⋊D83—44no—
323C22⋊D83—44no—
324C22⋊D83—44no—
325C22⋊D83—44no—
326C2×Dic83—22no—
327C2×Dic83—22no—
328C2×Dic83—22no—
329C2×Dic83—24no—
330C2×Dic83—42no—
331C2×Dic83—42no—
332C2×Dic83—44no—
333C2×Dic83—44no—
334C2×Dic83—44no—
335D332—42no—
336D332—42no—
337C4×D83—44no—
338C4×D83—44no—
339Dic166—42no—
340Dic166—42no—
341C22×C83—28no—
342C22×C83—21no—
343C22×C83—21no—
344C22×C83—21no—
345C22×C83—21no—
346C22×C83—21no—
347C22×C83—21no—
348C22×C83—21no—
349C22×C83—21no—
350C22×C83—21no—
351C22×C83—21no—
352C22×C83—21no—
353C22×C83—21no—
354C22×C83—21no—
355C22×C83—21no—
356C22×C83—21no—
357C22×C83—21no—
358C22×C83—44no—
359C22×C83—44no—
360C22×C83—44no—
361C22×C83—44no—
362C22×C83—44no—
363C22×C83—44no—
364C22×C83C2×#9912yes—
365C22×C83#41012yes—
366C22×C83C22×C22⋊C411yescharacteristic
367C22×C83C4×#4112yes—
368C22×C83#52512yes—
369C22×C83#53212yes—
370C2×D83—42no—
371C2×D83—42no—
372C2×D83—42no—
373C2×D83—84no—
374C4×C83—21no—
375C4×C83—21no—
376C4×C83—21no—
377C4×C83—21no—
378C4×C83—21no—
379C4×C83—21no—
380C4×C83—48no—
381C4×C83C2×#9912yes—
382C4×C83C2×#9912yes—
383Dic83—42no—
384Dic83—42no—
385Dic83—42no—
386Dic83—84no—
387#21420—831nomaximal, Sylow
388C2×C83—22no—
389C2×C83—22no—
390C2×C83—22no—
391C2×C83—22no—
392C2×C83—22no—
393C2×C83—41no—
394C2×C83—41no—
395C2×C83#229711yescharacteristic
396C2×C83C22×#9911yescharacteristic
397C2×C83C2×#41011yescharacteristic
398D83—82no—
399C2×#525—831no—
400#2280—831no—
401C2×C4×C22⋊C4D8311yescharacteristic, complemented
402#1996—832no—
403#1964—832no—
404#1898—834no—
405C4×#99—834no—
406C83#2142011yescharacteristic, complemented, Sylow
407C22×#41—831no—
408C24×C4C2×D8311yescharacteristic
409#525—1661no—
410#525—1661no—
411#525—1661no—
412#525—1661no—
413#525—1661no—
414#525—1661no—
415#525—1661no—
416#525—1661no—
417C2×#123—832no—
418C2×C22⋊Q8—831no—
419C2×C22⋊Q8—831no—
420C2×#121—831no—
421C2×#121—831no—
422C2×#120—832no—
423C2×C4×D4—832no—
424C2×C4×D4—832no—
425C2×#117—831no—
426C2×#117—1661no—
427C22×C22⋊C4C2×D8312yes—
428C22×C42—21no—
429C2×#99—838no—
430#381—1661no—
431#380—832no—
432#380—1661no—
433#379—832no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—832no—
437C4×C22⋊C4—1661no—
438C4×C22⋊C4C2×D8312yes—
439C4×C22⋊C4C2×D8312yes—
440C2×#95—21no—
441#342—838no—
442C25C22×D8311yescharacteristic
443C2×#41—3324no—
444C2×#41—1661no—
445C2×#41—1661no—
446C2×#41—1661no—
447C2×#41—1661no—
448C22×Q8—831no—
449C22×D4—832no—
450C22×D4—832no—
451C22×D4—832no—
452C22×D4—831no—
453C23×C4—22no—
454C23×C4—44no—
455C23×C4—832no—
456C23×C4C4×D8311yescharacteristic
457C23×C4C4×D8311yescharacteristic
458C23×C4C4×D8311yescharacteristic
459C23×C4C4×D8311yescharacteristic
460C23×C4D33211yescharacteristic
461C23×C4D33211yescharacteristic
462C23×C4D33211yescharacteristic
463C23×C4D33211yescharacteristic
464C23×C4C22⋊D8311yescharacteristic
465C23×C4C22⋊D8311yescharacteristic
466C23×C4C22⋊D8311yescharacteristic
467C23×C4C22⋊D8311yescharacteristic
468C23×C4C22×D8311yescharacteristic
469C23×C4C22×D8311yescharacteristic
470#123—1662no—
471#123—1662no—
472#123—1662no—
473#123—1662no—
474C22⋊Q8—1661no—
475C22⋊Q8—1661no—
476C22⋊Q8—1661no—
477C22⋊Q8—1661no—
478C22⋊Q8—1661no—
479C22⋊Q8—1661no—
480C22⋊Q8—1661no—
481C22⋊Q8—1661no—
482#121—1661no—
483#121—1661no—
484#121—1661no—
485#121—1661no—
486#121—1661no—
487#121—1661no—
488#121—1661no—
489#121—1661no—
490#120—1662no—
491#120—1662no—
492#120—1662no—
493#120—1662no—
494C4×D4—1662no—
495C4×D4—1662no—
496C4×D4—1662no—
497C4×D4—1662no—
498C4×D4—1662no—
499C4×D4—1662no—
500C4×D4—1662no—
501C4×D4—1662no—
502#117—3324no—
503#117—1661no—
504#117—1661no—
505#117—1661no—
506#117—1661no—
507C2×C4⋊C4—831no—
508C2×C4⋊C4—831no—
509C2×C4⋊C4—832no—
510C2×C4⋊C4—832no—
511C2×C4⋊C4—1662no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—832no—
515C2×C22⋊C4—832no—
516C2×C22⋊C4—832no—
517C2×C22⋊C4—832no—
518C2×C22⋊C4—832no—
519C2×C22⋊C4—834no—
520C2×C22⋊C4—1662no—
521C2×C22⋊C4—1662no—
522C2×C22⋊C4C22×D8314yes—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—44no—
526C2×C42—832no—
527C2×C42—1662no—
528#99—16616no—
529#95—22no—
530#95—22no—
531#95—1662no—
532#95—1662no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24—832no—
537C24C2×C4×D8311yescharacteristic
538C24C2×C4×D8311yescharacteristic
539C24C2×C22⋊D8311yescharacteristic
540C24C2×C22⋊D8311yescharacteristic
541C24C2×D33211yescharacteristic
542C24C2×D33211yescharacteristic
543C24C23×D8311yescharacteristic
544#41—3324no—
545#41—3324no—
546#41—3324no—
547#41—3324no—
548C2×Q8—3322no—
549C2×Q8—1661no—
550C2×Q8—1661no—
551C2×D4—3322no—
552C2×D4—3324no—
553C2×D4—3324no—
554C2×D4—1662no—
555C2×D4—1662no—
556C2×D4—1668no—
557C2×D4—1662no—
558C2×D4—1662no—
559C2×D4—1662no—
560C2×D4—1662no—
561C2×D4—1661no—
562C2×D4—1661no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—3324no—
582C22×C4—832no—
583C22×C4—832no—
584C22×C4—832no—
585C22×C4—1664no—
586C22×C4—1662no—
587C22×C4—1662no—
588C22×C4(C2×D83)⋊C411yescharacteristic
589C22×C4(C2×D83)⋊C411yescharacteristic
590C22×C4(C2×D83)⋊C411yescharacteristic
591C22×C4(C2×D83)⋊C411yescharacteristic
592C22×C4(C2×D83)⋊C411yescharacteristic
593C22×C4(C2×D83)⋊C411yescharacteristic
594C22×C4(C2×D83)⋊C411yescharacteristic
595C22×C4(C2×D83)⋊C411yescharacteristic
596C22×C4(C2×D83)⋊C411yescharacteristic
597C22×C4(C2×D83)⋊C411yescharacteristic
598C22×C4(C2×D83)⋊C411yescharacteristic
599C22×C4(C2×D83)⋊C411yescharacteristic
600C22×C4(C2×D83)⋊C411yescharacteristic
601C22×C4(C2×D83)⋊C411yescharacteristic
602C22×C4(C2×D83)⋊C411yescharacteristic
603C22×C4(C2×D83)⋊C411yescharacteristic
604C22×C4C2×C4×D8311yescharacteristic
605C22×C4C2×C4×D8311yescharacteristic
606C22×C4C2×C4×D8311yescharacteristic
607C22×C4C2×C4×D8311yescharacteristic
608C22×C4C2×C22⋊D8311yescharacteristic
609C22×C4C2×C22⋊D8311yescharacteristic
610C22×C4C2×C22⋊D8311yescharacteristic
611C22×C4C2×C22⋊D8311yescharacteristic
612C22×C4C2×D33211yescharacteristic
613C22×C4C2×D33211yescharacteristic
614C22×C4C2×D33211yescharacteristic
615C22×C4C2×D33211yescharacteristic
616C4⋊C4—3324no—
617C4⋊C4—1661no—
618C4⋊C4—1661no—
619C4⋊C4—1661no—
620C4⋊C4—1661no—
621C4⋊C4—1662no—
622C4⋊C4—1662no—
623C4⋊C4—1662no—
624C4⋊C4—1662no—
625C22⋊C4—28no—
626C22⋊C4—24no—
627C22⋊C4—3324no—
628C22⋊C4—3324no—
629C22⋊C4—1668no—
630C22⋊C4—1662no—
631C22⋊C4—1662no—
632C22⋊C4—1662no—
633C22⋊C4—1662no—
634C22⋊C4—1662no—
635C22⋊C4—1662no—
636C22⋊C4—1662no—
637C22⋊C4—1662no—
638C22⋊C4—1662no—
639C22⋊C4—1662no—
640C22⋊C4#1305059018yescomplemented
641C42—44no—
642C42—44no—
643C42—3324no—
644C42—1662no—
645C42—1662no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—3322no—
668C23—3322no—
669C23—1662no—
670C23—1664no—
671C23C2×(C2×D83)⋊C411yescharacteristic
672C23C2×(C2×D83)⋊C411yescharacteristic
673C23C2×(C2×D83)⋊C411yescharacteristic
674C23C2×(C2×D83)⋊C411yescharacteristic
675C23C22×C4×D8311yescharacteristic
676C23C22×C22⋊D8311yescharacteristic
677C23C22×D33211yescharacteristic
678C23C2×#1305059014yes—
679Q8—3322no—
680Q8—3322no—
681D4—3322no—
682D4—3324no—
683D4—3324no—
684D4—3324no—
685D4—3324no—
686D4—3324no—
687D4—3324no—
688D4—3322no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—44no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—3324no—
721C2×C4—3324no—
722C2×C4—3322no—
723C2×C4—3322no—
724C2×C4—3324no—
725C2×C4—3324no—
726C2×C4—3324no—
727C2×C4—1662no—
728C2×C4—1662no—
729C2×C4—1662no—
730C2×C4—1664no—
731C2×C4#1458170614yescomplemented
732C2×C4C2×(C2×D83)⋊C411yescharacteristic
733C2×C4C2×(C2×D83)⋊C411yescharacteristic
734C2×C4C2×(C2×D83)⋊C411yescharacteristic
735C2×C4C2×(C2×D83)⋊C411yescharacteristic
736C2×C4C2×(C2×D83)⋊C411yescharacteristic
737C2×C4C2×(C2×D83)⋊C411yescharacteristic
738C2×C4C2×(C2×D83)⋊C411yescharacteristic
739C2×C4C2×(C2×D83)⋊C411yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—3322no—
764C22—3322no—
765C22—3322no—
766C22—6644no—
767C22C2×#1458170612yes—
768C22#1912767412yes—
769C22C22×(C2×D83)⋊C411yescharacteristic
770C22C4×#1305059012yes—
771C22#1912821212yes—
772C22#1912825112yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—3322no—
781C4—3322no—
782C4—3322no—
783C4—6644no—
784C4C2×#1458170612yes—
785C4C2×#1458170612yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—6642no—
794C2#2490995311yescharacteristic
795C2C22×#1458170611yescharacteristic
796C2C2×#1912767411yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D83)⋊C4
commutatorC23×C83C23×C4
FrattiniC24C23×D83
FittingC2×C4×C22⋊C4×C83C2
socleC22×C83C22×C22⋊C4
prime radicalC2×#19128212C2
cosocleC24×C83C24
hypercenterC2×C4×C22⋊C4D83
hypocenterC83#21420
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #24909846C2semidirect
3. #24908448C2semidirect
4. #24908299C2semidirect
5. #24907916C2semidirect
6. C4×#14581706C2semidirect
7. C2×C4×C22⋊C4×C83C2semidirect
8. C22×#13050590C4semidirect
17. C2×#14581775C4semidirect
18. C2×#14581771C4semidirect
20. C2×#14581766C4semidirect
23. C2×C4×C22⋊D83C4semidirect
26. C2×#14581751C4semidirect
48. C22×Dic166C2×C4semidirect
49. C22×D332C2×C4semidirect
53. C22×C4×D83C2×C4semidirect
92. C2×C4⋊Dic83C2×C4semidirect
93. C2×C4⋊Dic83C2×C4semidirect
94. C2×Dic83⋊C4C2×C4semidirect
95. C2×Dic83⋊C4C2×C4semidirect
102. C2×(C2×D83)⋊C4C2×C4semidirect
103. C2×(C2×D83)⋊C4C2×C4semidirect
105. C2×C4×Dic83C2×C4semidirect
244. C22⋊C4×C83#41semidirect
311. C2×C4×C83#99semidirect
401. C2×C4×C22⋊C4D83semidirect
406. C83#21420semidirect
640. C22⋊C4#13050590semidirect
731. C2×C4#14581706semidirect

Maximal subgroups

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

subgroupindex
C2×#191282122
#249098462
#249084482
#249082992
#249079162
C4×#145817062
C2×C4×C22⋊C4×C832
#2142083