Finite Group Databasebeta

← #35610355

Subgroups — #35610355

Order 21248.

3110 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128253C211yesmaximal, characteristic, complemented
2C22×C42×D83C211yesmaximal, characteristic
3#24915814C212yesmaximal, complemented
4#24915812C212yesmaximal, complemented
5#24915802C211yesmaximal, characteristic, complemented
6#24915800C212yesmaximal, complemented
7#24915770C214yesmaximal, complemented
8#24915751C211yesmaximal, characteristic
9#24915749C212yesmaximal
10#24915747C211yesmaximal, characteristic
11#24910001C212yesmaximal, complemented
12#24909997C214yesmaximal, complemented
13#24909993C212yesmaximal, complemented
14#24909942C212yesmaximal, complemented
15#24909865C211yesmaximal, characteristic, complemented
16#24909843C212yesmaximal
17C83×#2855C211yesmaximal, characteristic, complemented
18C23×C4×D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21#19128253—28no—
22C2×#14581791C2211yescharacteristic, complemented
23C2×#14581790C2211yescharacteristic, complemented
24C2×#14581782C2212yescomplemented
25C2×#14581772C2212yes—
26C2×#14581771C2211yescharacteristic
27C2×#14581770C2214yes—
28C2×#14581769C2212yes—
29C2×#14581768C2212yes—
30C2×Q8×Dic83C2211yescharacteristic, complemented
31C2×#14581757C2211yescharacteristic, complemented
32C2×#14581757C2212yescomplemented
33C2×#14581748C2212yes—
34C2×#14581748C2212yes—
35C22×C4×Dic83C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C2×C42×D83—28no—
39C2×C42×D83C2212yes—
40C2×C42×D83C2212yes—
41C2×C42×D83C2212yes—
42C2×C42×D83C2212yes—
43#19127607C2212yescomplemented
44#19127605C2214yescomplemented
45#19127599C2212yescomplemented
46#19127598C2214yescomplemented
47#19127598C2214yescomplemented
48#19127596C2214yescomplemented
49#19127588C2214yescomplemented
50#19127585C2214yescomplemented
51#19127584C2214yescomplemented
52#19127576C2212yes—
53#19127575C2214yes—
54#19127575C2214yes—
55#19127574C2212yes—
56#19127573C2212yes—
57#19127572C2214yes—
58#19127572C2214yes—
59#19127570C2212yescomplemented
60#19127565C2212yescomplemented
61#19127564C2212yes—
62#19127561C2211yescharacteristic
63#19127560C2214yes—
64#19127560C2214yes—
65#19127560C2214yes—
66#19127559C2212yes—
67#19127558C2212yes—
68#19127558C2212yes—
69#19127556C2212yes—
70#19127556C2212yes—
71C4⋊C4×Dic83C2212yescomplemented
72C4⋊C4×Dic83C2214yescomplemented
73#19127552C2212yescomplemented
74#19127552C2214yescomplemented
75#19127548C2214yes—
76#19127548C2214yes—
77C2×C22⋊Q8×C83C2211yescharacteristic
78C22×C42×C83C2211yescharacteristic
79#391×C83C2212yescomplemented
80#389×C83C2212yescomplemented
81#387×C83C2214yescomplemented
82#385×C83C2212yes—
83#381×C83C2212yes—
84#380×C83C2211yescharacteristic
85C24×D83C2311yescharacteristic
86C22×Dic166C2312yes—
87C22×Dic166C2311yescharacteristic
88C23×Dic83C2311yescharacteristic
89C23×Dic83C2311yescharacteristic
90C23×Dic83C2311yescharacteristic
91C22×C4×D83—24no—
92C22×C4×D83—24no—
93C22×C4×D83—24no—
94C22×C4×D83—28no—
95C22×C4×D83—28no—
96C22×C4×D83—24no—
97C22×C4×D83Q818yescomplemented
98C22×C4×D83C2312yes—
99C22×C4×D83C2312yes—
100C22×C4×D83C2312yes—
101C22×C4×D83C2312yes—
102C22×C4×D83C2312yes—
103C22×C4×D83C2312yes—
104#14581791—24no—
105#14581790—24no—
106#14581782—28no—
107#14581772—28no—
108#14581771—24no—
109#14581770—216no—
110#14581769—28no—
111#14581768—28no—
112Q8×Dic83—24no—
113#14581757—28no—
114#14581757—24no—
115#14581748—28no—
116#14581748—28no—
117C2×C4⋊Dic83C2312yes—
118C2×C4⋊Dic83C2314yes—
119C2×C4⋊Dic83C2311yescharacteristic
120C2×C4⋊Dic83C2312yes—
121C2×Dic83⋊C4C2314yes—
122C2×Dic83⋊C4C2314yes—
123C2×Dic83⋊C4C2314yes—
124C2×Dic83⋊C4C2314yes—
125C2×Dic83⋊C4C2312yes—
126C2×Dic83⋊C4C2312yes—
127C2×Dic83⋊C4C2312yes—
128C2×Dic83⋊C4C2312yes—
129C2×Dic83⋊C4C2312yes—
130C2×C22⋊Dic83C2312yes—
131C2×C22⋊Dic83C2312yes—
132C2×(C2×D83)⋊C4C2314yes—
133C2×(C2×D83)⋊C4C2314yes—
134C2×(C2×D83)⋊C4C2314yes—
135C2×(C2×D83)⋊C4C2314yes—
136C2×C4×Dic83—24no—
137C2×C4×Dic83—24no—
138C2×C4×Dic83D418yes—
139C2×C4×Dic83C2312yes—
140C2×C4×Dic83C2314yes—
141C2×C4×Dic83C2312yes—
142C2×C4×Dic83C2312yes—
143C2×C4×Dic83C2312yes—
144C2×C4×Dic83C2312yes—
145C2×C4×Dic83C2312yes—
146C2×C4×Dic83C2311yescharacteristic
147C2×C4×Dic83C2311yescharacteristic
148C2×C4×Dic83C2311yescharacteristic
149C2×C4×Dic83C2311yescharacteristic
150C42×D83—28no—
151C42×D83—28no—
152C42×D83—28no—
153C42×D83—28no—
154C83⋊#95C2314yes—
155C83⋊#95C2312yes—
156C83⋊#95C2314yes—
157C83⋊#95C2314yes—
158C83⋊#95C2314yes—
159C83⋊#95C2314yes—
160C83⋊#95C2314yes—
161C22×Q8×C83C2311yescharacteristic
162C23×C4×C83C2311yescharacteristic
163C23×C4×C83C2311yescharacteristic
164C23×C4×C83C2311yescharacteristic
165C22⋊Q8×C83—24no—
166C2×C4⋊C4×C83C2312yes—
167C2×C4⋊C4×C83C2314yes—
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2312yes—
170C2×C22⋊C4×C83C2312yes—
171C2×C22⋊C4×C83C2312yes—
172C2×C42×C83—24no—
173C2×C42×C83C2312yes—
174C2×C42×C83C2312yes—
175#95×C83C2314yes—
176#95×C83C2312yes—
177#95×C83C2314yes—
178#95×C83C2314yes—
179C23×D83—22no—
180C23×D83—22no—
181C23×D83—24no—
182C23×D83—24no—
183C23×D83C2×Q814yes—
184C23×D83C2412yes—
185C2×Dic166—22no—
186C2×Dic166—24no—
187C2×Dic166—24no—
188C2×Dic166—28no—
189C22×Dic83—22no—
190C22×Dic83—24no—
191C22×Dic83—24no—
192C22×Dic83C2×D414yes—
193C22×Dic83C2×D414yes—
194C22×Dic83C2×Q814yes—
195C22×Dic83#4114yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C22×Dic83C2414yes—
199C22×Dic83C2411yescharacteristic
200C22×Dic83C2412yes—
201C22×Dic83C2411yescharacteristic
202C22×Dic83C2411yescharacteristic
203C22×Dic83C2411yescharacteristic
204C2×C4×D83—232no—
205C2×C4×D83—232no—
206C2×C4×D83—24no—
207C2×C4×D83—24no—
208C2×C4×D83—24no—
209C2×C4×D83—24no—
210C2×C4×D83—24no—
211C2×C4×D83—24no—
212C2×C4×D83—232no—
213C2×C4×D83—24no—
214C2×C4×D83—24no—
215C2×C4×D83—24no—
216C2×C4×D83—24no—
217C2×C4×D83—24no—
218C2×C4×D83—24no—
219C2×C4×D83—24no—
220C2×C4×D83—24no—
221C2×C4×D83C2×Q818yes—
222C2×C4×D83C2×Q818yes—
223C2×C4×D83#4118yes—
224C2×C4×D83#4118yes—
225C4⋊Dic83—22no—
226C4⋊Dic83—24no—
227C4⋊Dic83—24no—
228C4⋊Dic83—28no—
229Dic83⋊C4—24no—
230Dic83⋊C4—28no—
231Dic83⋊C4—24no—
232Dic83⋊C4—24no—
233Dic83⋊C4—24no—
234Dic83⋊C4—24no—
235Dic83⋊C4—28no—
236Dic83⋊C4—28no—
237Dic83⋊C4—28no—
238C22⋊Dic83—24no—
239C22⋊Dic83—24no—
240(C2×D83)⋊C4—28no—
241(C2×D83)⋊C4—28no—
242(C2×D83)⋊C4—28no—
243(C2×D83)⋊C4—28no—
244C4×Dic83—24no—
245C4×Dic83—24no—
246C4×Dic83—24no—
247C4×Dic83—24no—
248C4×Dic83—24no—
249C4×Dic83—24no—
250C4×Dic83—28no—
251C4×Dic83C2×D414yes—
252C4×Dic83C2×D414yes—
253C4×Dic83C2×D414yes—
254C4×Dic83C2×D414yes—
255C24×C83C2411yescharacteristic
256C2×Q8×C83—22no—
257C2×Q8×C83—24no—
258C22×C4×C83—22no—
259C22×C4×C83—22no—
260C22×C4×C83—22no—
261C22×C4×C83—24no—
262C22×C4×C83—24no—
263C22×C4×C83C2×D414yes—
264C22×C4×C83C2×Q814yes—
265C22×C4×C83C2412yes—
266C22×C4×C83C2414yes—
267C22×C4×C83C2412yes—
268C22×C4×C83C2411yescharacteristic
269C22×C4×C83C2412yes—
270C22×C4×C83C2412yes—
271C22×C4×C83C2411yescharacteristic
272C4⋊C4×C83—24no—
273C4⋊C4×C83—22no—
274C4⋊C4×C83—28no—
275C4⋊C4×C83—24no—
276C22⋊C4×C83—24no—
277C22⋊C4×C83—24no—
278C42×C83—24no—
279C42×C83—24no—
280C23×C83—22no—
281C23×C83—22no—
282C23×C83C22×D412yes—
283C23×C83C22×Q812yes—
284C23×C83C2×#4112yes—
285C23×C83C2511yescharacteristic
286C22×D83—28no—
287C22×D83—28no—
288C22×D83—216no—
289C22×D83—28no—
290C22×D83—22no—
291C22×D83—22no—
292C22×D83—22no—
293C22×D83—22no—
294C22×D83—216no—
295C22×D83C22×Q814yes—
296C22×D83C2×#4114yes—
297C22×D83C2×#4114yes—
298Q8×C83—44no—
299C2×C4×C83—28no—
300C2×C4×C83—28no—
301C2×C4×C83—22no—
302C2×C4×C83—22no—
303C2×C4×C83—22no—
304C2×C4×C83—22no—
305C2×C4×C83—22no—
306C2×C4×C83—28no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—24no—
310C2×C4×C83—24no—
311C2×C4×C83—24no—
312C2×C4×C83—24no—
313C2×C4×C83—24no—
314C2×C4×C83C22×D412yes—
315C2×C4×C83C22×D412yes—
316C2×C4×C83C22×Q814yes—
317C2×C4×C83C2×#4114yes—
318C2×C4×C83C2×#4114yes—
319C2×Dic83—28no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—28no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—24no—
327C2×Dic83—24no—
328C2×Dic83—24no—
329C2×Dic83—24no—
330C2×Dic83—24no—
331C2×Dic83C22⋊Q8116yescomplemented
332C2×Dic83C22×D412yes—
333C2×Dic83C22×D412yes—
334C2×Dic83C22×D412yes—
335C2×Dic83C22×D412yes—
336C2×Dic83C22×Q812yes—
337C2×Dic83C22×Q812yes—
338C2×Dic83C2×#4114yes—
339C2×Dic83C2×#4112yes—
340C2×Dic83C2×#4112yes—
341C2×Dic83C2×#4114yes—
342C4×D83—216no—
343C4×D83—216no—
344C4×D83—216no—
345C4×D83—216no—
346C4×D83—216no—
347C4×D83—216no—
348Dic166—44no—
349Dic166—48no—
350C22×C83—22no—
351C22×C83—22no—
352C22×C83—24no—
353C22×C83—24no—
354C22×C83C2×C22⋊Q814yes—
355C22×C83C23×D411yescharacteristic
356C22×C83C23×Q811yescharacteristic
357C22×C83C22×#4111yescharacteristic
358C22×C83C22×#4112yes—
359C22×C83C22×#4112yes—
360C2×D83—232no—
361C2×D83—24no—
362C2×D83—24no—
363C2×D83—24no—
364C2×D83—24no—
365C2×D83—24no—
366C2×D83—24no—
367C2×D83#53318yescomplemented
368C4×C83—24no—
369C4×C83—22no—
370C4×C83—24no—
371C4×C83—42no—
372C4×C83—42no—
373C4×C83—44no—
374C4×C83#52514yes—
375Dic83—22no—
376Dic83—24no—
377Dic83—42no—
378Dic83—42no—
379Dic83—44no—
380Dic83C2×C22⋊Q814yes—
381Dic83C2×C22⋊Q814yes—
382Dic83#52514yes—
383#36625—831nomaximal, Sylow
384C2×C83—24no—
385C2×C83C22×C22⋊Q811yescharacteristic
386C2×C83C2×#52511yescharacteristic
387C2×C83C2×#52511yescharacteristic
388C2×C83C2×#53312yes—
389C2×C83#344412yes—
390D83—28no—
391C2×#533—831no—
392C23×C42—831no—
393#2857—832no—
394#2857—832no—
395#2855—831no—
396#2855—832no—
397#2855D8311yescharacteristic, complemented
398#2851—834no—
399#2848—832no—
400#2848—831no—
401#2848—831no—
402C4×C22⋊Q8—832no—
403C4×C22⋊Q8—832no—
404C4×C22⋊Q8—834no—
405#2296—832no—
406#2285—831no—
407#2280—832no—
408C83#3662511yescharacteristic, complemented, Sylow
409C24×C4—831no—
410C24×C4—831no—
411C24×C4—831no—
412#533—1668no—
413C2×C4⋊Q8—831no—
414C2×C4⋊Q8—831no—
415C2×#125—832no—
416C2×C22⋊Q8—832no—
417C2×C22⋊Q8—831no—
418C2×C22⋊Q8—834no—
419C2×C22⋊Q8—832no—
420C2×C22⋊Q8—832no—
421C2×C22⋊Q8C2×D8311yescharacteristic
422C2×C4×Q8—831no—
423C2×C4×Q8—831no—
424C2×C4×Q8—832no—
425C2×#117—832no—
426C2×#117—832no—
427C22×C42—831no—
428C22×C42—831no—
429C22×C42—831no—
430C22×C42—832no—
431C22×C42—832no—
432C22×C42—832no—
433C22×C42—832no—
434C22×C42—1668no—
435C22×C42C2×D8311yescharacteristic
436#391—832no—
437#391—834no—
438#391C2×D8312yescomplemented
439#389—834no—
440#389—832no—
441#389—834no—
442#389—834no—
443#389C2×D8312yescomplemented
444#387—834no—
445#387—834no—
446#387—834no—
447#387C2×D8314yescomplemented
448#385—832no—
449#385—834no—
450#385—834no—
451#385—832no—
452#385—832no—
453#385—834no—
454#385—834no—
455#385C2×D8312yes—
456#384—832no—
457#382—832no—
458#381—832no—
459#381C2×D8312yes—
460#380—831no—
461#380—832no—
462#380—832no—
463#380—832no—
464#380—834no—
465#380—834no—
466#380—834no—
467#380C2×D8311yescharacteristic
468#379—832no—
469#379—832no—
470C4×C4⋊C4—832no—
471C4×C4⋊C4—834no—
472C4×C4⋊C4—832no—
473C4×C4⋊C4—834no—
474C4×C22⋊C4—834no—
475C4×C22⋊C4—834no—
476C25—831no—
477C22×Q8—832no—
478C22×Q8—831no—
479C22×Q8C22×D8311yescharacteristic
480C23×C4—831no—
481C23×C4—831no—
482C23×C4—838no—
483C23×C4—832no—
484C23×C4—832no—
485C23×C4—832no—
486C23×C4—832no—
487C23×C4—831no—
488C23×C4—832no—
489C23×C4—832no—
490C23×C4—1664no—
491C23×C4—1668no—
492C23×C4—1668no—
493C23×C4—1664no—
494C23×C4—1664no—
495C23×C4—1664no—
496C23×C4C22×D8311yescharacteristic
497C23×C4C22×D8311yescharacteristic
498C23×C4C22×D8311yescharacteristic
499C4⋊Q8—1664no—
500C4⋊Q8—1664no—
501#125—1668no—
502C22⋊Q8—24no—
503C22⋊Q8—1668no—
504C22⋊Q8—16616no—
505C22⋊Q8—1668no—
506C22⋊Q8—1668no—
507C22⋊Q8—1664no—
508C4×Q8—1668no—
509C4×Q8—1664no—
510C4×Q8—1664no—
511#117—1668no—
512#117—1668no—
513C2×C4⋊C4—832no—
514C2×C4⋊C4—832no—
515C2×C4⋊C4—834no—
516C2×C4⋊C4—832no—
517C2×C4⋊C4—832no—
518C2×C4⋊C4—832no—
519C2×C4⋊C4—832no—
520C2×C4⋊C4—831no—
521C2×C4⋊C4—834no—
522C2×C4⋊C4—832no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—834no—
526C2×C4⋊C4C22×D8312yes—
527C2×C4⋊C4C22×D8311yescharacteristic
528C2×C4⋊C4C22×D8312yes—
529C2×C4⋊C4C22×D8314yes—
530C2×C22⋊C4—832no—
531C2×C22⋊C4—832no—
532C2×C22⋊C4—834no—
533C2×C22⋊C4—834no—
534C2×C22⋊C4—834no—
535C2×C22⋊C4—834no—
536C2×C22⋊C4C22×D8312yes—
537C2×C22⋊C4C22×D8312yes—
538C2×C42—24no—
539C2×C42—838no—
540C2×C42—831no—
541C2×C42—831no—
542C2×C42—831no—
543C2×C42—831no—
544C2×C42—832no—
545C2×C42—832no—
546C2×C42—834no—
547C2×C42—832no—
548C2×C42—832no—
549C2×C42—832no—
550C2×C42—832no—
551C2×C42—1668no—
552C2×C42—1668no—
553C2×C42—1668no—
554C2×C42—1668no—
555C2×C42—1664no—
556C2×C42—1664no—
557C2×C42C22×D8312yes—
558C2×C42C22×D8312yes—
559#95—834no—
560#95—834no—
561#95—834no—
562#95—832no—
563#95—834no—
564#95—834no—
565#95—834no—
566#95C22×D8314yes—
567#95C22×D8314yes—
568#95C22×D8314yes—
569#95C22×D8312yes—
570C24—832no—
571C24—834no—
572C24—1664no—
573C24—1664no—
574C24—1662no—
575C24—1662no—
576C24C23×D8311yescharacteristic
577C2×Q8—22no—
578C2×Q8—24no—
579C2×Q8—1664no—
580C2×Q8—1668no—
581C2×Q8—1662no—
582C2×Q8—1664no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—834no—
589C22×C4—834no—
590C22×C4—834no—
591C22×C4—831no—
592C22×C4—831no—
593C22×C4—831no—
594C22×C4—834no—
595C22×C4—831no—
596C22×C4—832no—
597C22×C4—838no—
598C22×C4—838no—
599C22×C4—838no—
600C22×C4—838no—
601C22×C4—834no—
602C22×C4—832no—
603C22×C4—832no—
604C22×C4—1664no—
605C22×C4—1664no—
606C22×C4—1664no—
607C22×C4—1664no—
608C22×C4—16632no—
609C22×C4—1664no—
610C22×C4—1664no—
611C22×C4—1664no—
612C22×C4—1664no—
613C22×C4—1664no—
614C22×C4—1664no—
615C22×C4—16632no—
616C22×C4—16632no—
617C22×C4—1664no—
618C22×C4—1664no—
619C22×C4—1662no—
620C22×C4—1664no—
621C22×C4—1664no—
622C22×C4—1664no—
623C22×C4—1664no—
624C22×C4D4×D8314yes—
625C22×C4Q8×D8314yes—
626C22×C4C23×D8314yes—
627C22×C4C23×D8312yes—
628C22×C4C23×D8312yes—
629C22×C4C23×D8311yescharacteristic
630C22×C4C23×D8312yes—
631C22×C4C23×D8312yes—
632C22×C4C23×D8311yescharacteristic
633C4⋊C4—24no—
634C4⋊C4—22no—
635C4⋊C4—24no—
636C4⋊C4—28no—
637C4⋊C4—1664no—
638C4⋊C4—1664no—
639C4⋊C4—1668no—
640C4⋊C4—1664no—
641C4⋊C4—1664no—
642C4⋊C4—1664no—
643C4⋊C4—1668no—
644C4⋊C4—1668no—
645C4⋊C4—1668no—
646C4⋊C4—1664no—
647C4⋊C4—1662no—
648C4⋊C4—1668no—
649C4⋊C4—1664no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—1668no—
653C22⋊C4—1668no—
654C22⋊C4—1668no—
655C22⋊C4—1668no—
656C22⋊C4—1664no—
657C22⋊C4—1664no—
658C42—24no—
659C42—24no—
660C42—834no—
661C42—834no—
662C42—834no—
663C42—834no—
664C42—1664no—
665C42—1664no—
666C42—1664no—
667C42—1664no—
668C42—1664no—
669C42—1664no—
670C42—1668no—
671C23—22no—
672C23—22no—
673C23—834no—
674C23—834no—
675C23—834no—
676C23—16616no—
677C23—1668no—
678C23—1668no—
679C23—16616no—
680C23—1668no—
681C23—1662no—
682C23—1662no—
683C23—1662no—
684C23—1662no—
685C23C2×D4×D8312yes—
686C23C2×Q8×D8312yes—
687C23#41×D8312yes—
688C23C24×D8311yescharacteristic
689Q8—44no—
690Q8—3328no—
691Q8—3324no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—8316no—
708C2×C4—832no—
709C2×C4—832no—
710C2×C4—832no—
711C2×C4—832no—
712C2×C4—832no—
713C2×C4—832no—
714C2×C4—832no—
715C2×C4—834no—
716C2×C4—832no—
717C2×C4—834no—
718C2×C4—16616no—
719C2×C4—16616no—
720C2×C4—16616no—
721C2×C4—16616no—
722C2×C4—16616no—
723C2×C4—1662no—
724C2×C4—1662no—
725C2×C4—1664no—
726C2×C4—1664no—
727C2×C4—1664no—
728C2×C4—1664no—
729C2×C4—1664no—
730C2×C4—1668no—
731C2×C4—1668no—
732C2×C4—1662no—
733C2×C4—1662no—
734C2×C4—1662no—
735C2×C4—16616no—
736C2×C4C2×D4×D8312yes—
737C2×C4C2×D4×D8312yes—
738C2×C4C2×Q8×D8314yes—
739C2×C4#41×D8314yes—
740C2×C4#41×D8314yes—
741C22—22no—
742C22—22no—
743C22—24no—
744C22—24no—
745C22—838no—
746C22—16632no—
747C22—1664no—
748C22—1664no—
749C22—1664no—
750C22—1664no—
751C22—1664no—
752C22—1664no—
753C22C22⋊Q8×D8314yes—
754C22C22×D4×D8311yescharacteristic
755C22C22×Q8×D8311yescharacteristic
756C22C2×#41×D8311yescharacteristic
757C22C2×#41×D8312yes—
758C22C2×#41×D8312yes—
759C4—24no—
760C4—24no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—44no—
765C4—3322no—
766C4—3322no—
767C4—3324no—
768C4—834no—
769C4—834no—
770C4—834no—
771C4—1662no—
772C4—1664no—
773C4#1912820914yes—
774C2—24no—
775C2—1668no—
776C2C2×C22⋊Q8×D8311yescharacteristic
777C2#525×D8311yescharacteristic
778C2C2×#1912820911yescharacteristic
779C2#533×D8312yes—
780C2#2492075712yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2855C2
prime radicalC24×D83C23
hypercenter#2855D83
hypocenterC83#36625
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2855

Complements

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

NH ≅ G/Ntype
1. C2×#19128253C2semidirect
3. #24915814C2semidirect
4. #24915812C2semidirect
5. #24915802C2semidirect
6. #24915800C2semidirect
7. #24915770C2semidirect
11. #24910001C2semidirect
12. #24909997C2semidirect
13. #24909993C2semidirect
14. #24909942C2semidirect
15. #24909865C2semidirect
17. C83×#2855C2semidirect
22. C2×#14581791C22semidirect
23. C2×#14581790C22semidirect
24. C2×#14581782C22semidirect
30. C2×Q8×Dic83C22semidirect
31. C2×#14581757C22semidirect
32. C2×#14581757C22semidirect
43. #19127607C22semidirect
44. #19127605C22semidirect
45. #19127599C22semidirect
46. #19127598C22semidirect
47. #19127598C22semidirect
48. #19127596C22semidirect
49. #19127588C22semidirect
50. #19127585C22semidirect
51. #19127584C22semidirect
59. #19127570C22semidirect
60. #19127565C22semidirect
71. C4⋊C4×Dic83C22semidirect
72. C4⋊C4×Dic83C22semidirect
73. #19127552C22semidirect
74. #19127552C22semidirect
79. #391×C83C22semidirect
80. #389×C83C22semidirect
81. #387×C83C22semidirect
97. C22×C4×D83Q8semidirect
331. C2×Dic83C22⋊Q8semidirect
367. C2×D83#533semidirect
397. #2855D83semidirect
408. C83#36625semidirect
438. #391C2×D83semidirect
443. #389C2×D83semidirect
447. #387C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282532
C22×C42×D832
#249158142
#249158122
#249158022
#249158002
#249157702
#249157512
#249157492
#249157472
#249100012
#249099972
#249099932
#249099422
#249098652
#249098432
C83×#28552
#3662583