Finite Group Databasebeta

← #760305

Subgroups — #760305

Order 512.

3176 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic
2C2×C4×#123C211yesmaximal, characteristic
3C22×#389C211yesmaximal, characteristic, complemented
4C2×#2283C211yesmaximal, characteristic, complemented
5#16678C212yesmaximal, complemented
6#16676C212yesmaximal, complemented
7#15221C212yesmaximal, complemented
8#15220C212yesmaximal, complemented
9#14919C212yesmaximal, complemented
10#14912C212yesmaximal
11#14910C212yesmaximal, complemented
12#14908C212yesmaximal, complemented
13#14130C211yesmaximal, characteristic, complemented
14#14046C212yesmaximal, complemented
15#14043C212yesmaximal, complemented
16#14019C212yesmaximal
17#13974C212yesmaximal, complemented
18#13924C211yesmaximal, characteristic, complemented
19#13872C211yesmaximal, characteristic
20C22×#123C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25C23×C42C2211yescharacteristic
26#2487—28no—
27C2×#400C2212yes—
28C2×#399C2212yes—
29C4×#123—28no—
30C2×#389—28no—
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2214yes—
38C2×#388C2211yescharacteristic
39C2×#388C2211yescharacteristic
40C2×#388C2214yes—
41C2×#387C2211yescharacteristic
42C2×#387C2211yescharacteristic
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2211yescharacteristic
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2211yescharacteristic
49#2283—28no—
50C2×#383C2212yes—
51C2×#382C2212yes—
52C2×#381C2212yes—
53C2×#381C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C2×#376C2212yes—
66C22×#95C2212yes—
67#1445C2212yes—
68#1445C2212yes—
69#1445C2214yes—
70#1444C2214yes—
71#1444C2212yes—
72#1443C2214yes—
73#1443C2214yes—
74#1442C2212yes—
75#1442C2214yes—
76#1442C2214yes—
77#1442C2214yes—
78#1441C2212yes—
79#1441C2214yes—
80#1441C2214yes—
81#1440C2214yes—
82#1439C2212yes—
83#1439C2214yes—
84#1439C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87C4⋊#95C2212yes—
88C4⋊#95C2212yes—
89C4⋊#95C2212yes—
90C4⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C22⋊#95C2212yes—
94C22⋊#95C2212yes—
95C23×D4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C2×#123—24no—
103C2×#123—24no—
104C2×#123—24no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—28no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—28no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—48no—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C42—24no—
143C22×C42—24no—
144C22×C42D418yes—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2314yes—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#400—28no—
154#399—28no—
155#389—28no—
156#389—28no—
157#389—28no—
158#389—28no—
159#389—28no—
160#389—28no—
161#389—48no—
162#388—24no—
163#388—24no—
164#388—48no—
165#387—24no—
166#387—24no—
167#386—28no—
168#386—24no—
169#386—28no—
170#385—24no—
171#385—28no—
172#385—28no—
173#383—28no—
174#382—28no—
175#381—24no—
176#381—28no—
177#380—24no—
178#380—28no—
179#380—28no—
180#380D418yes—
181C4×C4⋊C4—28no—
182C4×C4⋊C4—24no—
183C4×C4⋊C4—24no—
184C4×C22⋊C4—24no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—24no—
188#376—28no—
189C2×#95—28no—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C25C2411yescharacteristic
220C25C2411yescharacteristic
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4#4114yes—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—28no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—44no—
252C23×C4—42no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4C2×D414yes—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4C2×D414yes—
259C23×C4#4114yes—
260C23×C4C2411yescharacteristic
261C23×C4C2414yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2414yes—
265C23×C4C2411yescharacteristic
266C23×C4C2414yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2414yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277#123—232no—
278C4×D4—416no—
279C2×C4⋊C4—232no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—432no—
319C2×C4⋊C4—416no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4C2×D418yes—
323C2×C4⋊C4#4118yes—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C2×D418yes—
357C2×C22⋊C4#4114yes—
358C2×C42—232no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—28no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—28no—
375C2×C42—24no—
376C2×C42—44no—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380C2×C42C2×D414yes—
381#95—28no—
382#95—28no—
383#95—24no—
384#95—28no—
385#95—22no—
386#95—22no—
387#95—28no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—28no—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—22no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95C2×D418yes—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24C22×D412yes—
425C24C22×D412yes—
426C24C2×#4112yes—
427C24C2×#4112yes—
428C24C2×#4112yes—
429C24C2×#4112yes—
430C242−1+412yes—
431C242−1+412yes—
432C24C2511yescharacteristic
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—44no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—216no—
448C22×C4—216no—
449C22×C4—216no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—24no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—416no—
535C22×C4—416no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—88no—
551C22×C4—88no—
552C22×C4#121116yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D418yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4118yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4114yes—
569C22×C4H(5,𝔽2)14yes—
570C22×C42−1+414yes—
571C4⋊C4—216no—
572C4⋊C4—28no—
573C4⋊C4—28no—
574C4⋊C4—216no—
575C4⋊C4—216no—
576C4⋊C4—416no—
577C4⋊C4—44no—
578C4⋊C4—416no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—416no—
584C4⋊C4—48no—
585C4⋊C4—88no—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—28no—
589C22⋊C4—216no—
590C22⋊C4—416no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—48no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—88no—
598C42—28no—
599C42—28no—
600C42—28no—
601C42—28no—
602C42—416no—
603C42—44no—
604C42—44no—
605C42—44no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—42no—
634C23—41no—
635C23—42no—
636C23—41no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23C2×#12114yes—
646C23#52514yes—
647C23#53614yes—
648C23#54714yes—
649C23#54814yes—
650C23#55214yes—
651C23#55614yes—
652C23C23×D411yescharacteristic
653C23C23×D411yescharacteristic
654C23C22×#4111yescharacteristic
655C23C22×#4112yes—
656C23C22×#4111yescharacteristic
657C23C22×#4111yescharacteristic
658C23C2×H(5,𝔽2)12yes—
659C23C2×2−1+412yes—
660C23C2×2−1+411yescharacteristic
661C23C2×2−1+411yescharacteristic
662C23#58512yes—
663D4—416no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—232no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—28no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—28no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—28no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—24no—
695C2×C4—416no—
696C2×C4—432no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—44no—
700C2×C4—416no—
701C2×C4—44no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
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—44no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—44no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—816no—
761C2×C4—88no—
762C2×C4C2×#12114yes—
763C2×C4C2×#12114yes—
764C2×C4#52514yes—
765C2×C4#53514yes—
766C2×C4#53614yes—
767C2×C4#54718yes—
768C2×C4#55218yes—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—24no—
775C22—24no—
776C22—28no—
777C22—28no—
778C22—24no—
779C22—42no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—82no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—82no—
789C22—81no—
790C22#241518yes—
791C22C22×#12111yescharacteristic
792C22C2×#52511yescharacteristic
793C22C2×#52511yescharacteristic
794C22C2×#53511yescharacteristic
795C22C2×#53611yescharacteristic
796C22C2×#53611yescharacteristic
797C22#344911yescharacteristic
798C22C2×#54711yescharacteristic
799C22C2×#54712yes—
800C22C2×#54811yescharacteristic
801C22C2×#55212yes—
802C22C2×#55211yescharacteristic
803C22C2×#55611yescharacteristic
804C22#348112yes—
805C22#348112yes—
806C22#348812yes—
807C22#349412yes—
808C22#351512yes—
809C22#351512yes—
810C22#351612yes—
811C22#351612yes—
812C22#355212yes—
813C22#355212yes—
814C4—24no—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—48no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—48no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—84no—
828C4—84no—
829C4—81no—
830C4#241318yes—
831C2—28no—
832C2—82no—
833C2C2×#241511yescharacteristic
834C2C2×#241311yescharacteristic
835C2#3496311yescharacteristic
836C2#3513811yescharacteristic
837C2#3524511yescharacteristic
838C2#3525211yescharacteristic
839C2#3761711yescharacteristic
840C2#5906212yes—
841C2#5907612yes—
842C2#5924012yes—
843C2#5925412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C22×#389C2semidirect
4. C2×#2283C2semidirect
5. #16678C2semidirect
6. #16676C2semidirect
7. #15221C2semidirect
8. #15220C2semidirect
9. #14919C2semidirect
11. #14910C2semidirect
12. #14908C2semidirect
13. #14130C2semidirect
14. #14046C2semidirect
15. #14043C2semidirect
17. #13974C2semidirect
18. #13924C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C2×C4×#1232
C22×#3892
C2×#22832
#166782
#166762
#152212
#152202
#149192
#149122
#149102
#149082
#141302
#140462
#140432
#140192
#139742
#139242
#138722