Finite Group Databasebeta

← #669478

Subgroups — #669478

Order 512.

4176 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#552C211yesmaximal, characteristic
2C2×#2855C211yesmaximal, characteristic, complemented
3C2×C4×#123C211yesmaximal, characteristic
4C22×#389C211yesmaximal, characteristic, complemented
5#16104C214yesmaximal, complemented
6#16102C214yesmaximal, complemented
7#15218C212yesmaximal, complemented
8#15179C212yesmaximal, complemented
9#15069C212yesmaximal
10#14912C212yesmaximal
11#14139C211yesmaximal, characteristic, complemented
12#14129C212yesmaximal, complemented
13#14128C212yesmaximal, complemented
14#14017C212yesmaximal, complemented
15#13904C211yesmaximal, characteristic, complemented
16#13872C211yesmaximal, characteristic
17#13870C212yesmaximal, complemented
18C2×#552—28no—
19C2×#552—28no—
20C2×#552—28no—
21C22×#126C2212yes—
22C22×#125C2211yescharacteristic
23C22×#125C2212yes—
24C22×#123C2212yes—
25C22×#123C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C4⋊C4C2212yes—
34C23×C4⋊C4C2211yescharacteristic
35C23×C42C2211yescharacteristic
36#2855—28no—
37C4×#123—28no—
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#389—28no—
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2214yes—
45C2×#388C2212yes—
46C2×#387C2214yes—
47C2×#387C2212yes—
48C2×#386C2211yescharacteristic
49C2×#386C2212yes—
50C2×#385C2212yes—
51C2×#385C2211yescharacteristic
52C2×#381C2212yes—
53C2×#381C2211yescharacteristic
54C2×#381C2212yes—
55C2×#381C2212yes—
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C22×#95C2212yes—
62#1445C2214yes—
63#1444C2214yes—
64#1444C2214yes—
65#1444C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2212yes—
71#1441C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1439C2212yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1436C2214yes—
79#1436C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2212yes—
89C23×Q8C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97#552—2128no—
98C2×#126—28no—
99C2×#126—28no—
100C2×#126—28no—
101C2×#125—28no—
102C2×#125—28no—
103C2×#125—28no—
104C2×#125—24no—
105C2×#125—24no—
106C2×#125—24no—
107C2×#123—28no—
108C2×#123—24no—
109C2×#123—28no—
110C2×#123—24no—
111C2×#123—28no—
112C2×#123—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8D418yes—
119C2×C4×Q8—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×D4—24no—
123C2×C4×D4—24no—
124C2×C4×D4D418yes—
125C2×#117—24no—
126C2×#117—28no—
127C2×#117—24no—
128C2×#117—24no—
129C2×#117—28no—
130C2×#117—28no—
131C22×C4⋊C4—24no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—24no—
134C22×C4⋊C4—28no—
135C22×C4⋊C4—28no—
136C22×C4⋊C4—28no—
137C22×C4⋊C4—44no—
138C22×C4⋊C4D418yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2314yes—
168C22×C42—24no—
169C22×C42—24no—
170C22×C42—24no—
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2312yes—
175C22×C42C2312yes—
176C22×C42C2311yescharacteristic
177#391—28no—
178#391—28no—
179#389—28no—
180#389—28no—
181#389—28no—
182#389—216no—
183#388—28no—
184#387—216no—
185#387—28no—
186#386—24no—
187#386—44no—
188#385—28no—
189#385—24no—
190#381—28no—
191#381—24no—
192#381—28no—
193#381—44no—
194#380—24no—
195#380—28no—
196C4×C4⋊C4—28no—
197C4×C22⋊C4—28no—
198C4×C22⋊C4—24no—
199C2×#95—28no—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C25C2411yescharacteristic
223C25C2411yescharacteristic
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—24no—
227C22×Q8—24no—
228C22×Q8C2×D414yes—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4C2×D414yes—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—28no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—44no—
263C23×C4—42no—
264C23×C4C2×D418yes—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4C2×D414yes—
268C23×C4C2×D414yes—
269C23×C4#4114yes—
270C23×C4C2414yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2414yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285#126—264no—
286#125—264no—
287#125—232no—
288#123—232no—
289#123—264no—
290C22⋊Q8—232no—
291C22⋊Q8—232no—
292C4×Q8—232no—
293C4×D4—232no—
294#117—232no—
295#117—264no—
296C2×C4⋊C4—232no—
297C2×C4⋊C4—232no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—432no—
345C2×C4⋊C4C2×D414yes—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×D418yes—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2×D418yes—
351C2×C4⋊C4#4118yes—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4C2×D414yes—
382C2×C22⋊C4C2×D418yes—
383C2×C22⋊C4C2×D414yes—
384C2×C22⋊C4#4114yes—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—416no—
403C2×C42C2×D414yes—
404#95—28no—
405#95—28no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—22no—
440C24C22×D412yes—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C22×D412yes—
444C24C2×#4112yes—
445C24C2×#4112yes—
446C24H(5,𝔽2)12yes—
447C242−1+412yes—
448C24C2511yescharacteristic
449C2×Q8—28no—
450C2×Q8—216no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—48no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—216no—
466C22×C4—216no—
467C22×C4—216no—
468C22×C4—28no—
469C22×C4—216no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—216no—
473C22×C4—216no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—28no—
534C22×C4—216no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—416no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—416no—
553C22×C4—48no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—44no—
560C22×C4—48no—
561C22×C4—44no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4#120116yes—
569C22×C4C22×D412yes—
570C22×C4C22×D414yes—
571C22×C4C22×D412yes—
572C22×C4C22×D414yes—
573C22×C4C22×D414yes—
574C22×C4C22×D412yes—
575C22×C4C22×D414yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C2×#4114yes—
583C22×C4C2×#4118yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4114yes—
586C22×C42−1+414yes—
587C22×C42−1+414yes—
588C4⋊C4—216no—
589C4⋊C4—216no—
590C4⋊C4—216no—
591C4⋊C4—216no—
592C4⋊C4—216no—
593C4⋊C4—216no—
594C4⋊C4—28no—
595C4⋊C4—28no—
596C4⋊C4—216no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—216no—
600C4⋊C4—216no—
601C4⋊C4—48no—
602C4⋊C4—416no—
603C4⋊C4—416no—
604C4⋊C4—416no—
605C4⋊C4—48no—
606C22⋊C4—216no—
607C22⋊C4—216no—
608C22⋊C4—216no—
609C22⋊C4—28no—
610C22⋊C4—216no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—48no—
614C22⋊C4—44no—
615C22⋊C4—48no—
616C22⋊C4—88no—
617C42—216no—
618C42—216no—
619C42—28no—
620C42—48no—
621C42—48no—
622C42—48no—
623C23—22no—
624C23—22no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—42no—
652C23—42no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23C2×#12014yes—
663C23#52514yes—
664C23#53714yes—
665C23#54614yes—
666C23#54714yes—
667C23#54814yes—
668C23#55014yes—
669C23C23×D411yescharacteristic
670C23C23×D411yescharacteristic
671C23C23×D411yescharacteristic
672C23C22×#4111yescharacteristic
673C23C22×#4112yes—
674C23C22×#4111yescharacteristic
675C23C2×H(5,𝔽2)11yescharacteristic
676C23C2×2−1+412yes—
677C23C2×2−1+411yescharacteristic
678C23C2×2−1+412yes—
679C23#58512yes—
680Q8—416no—
681D4—416no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—232no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—28no—
706C2×C4—24no—
707C2×C4—28no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—24no—
716C2×C4—432no—
717C2×C4—416no—
718C2×C4—432no—
719C2×C4—416no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—416no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4C2×#12014yes—
776C2×C4C2×#12014yes—
777C2×C4#52514yes—
778C2×C4#53614yes—
779C2×C4#54718yes—
780C2×C4#54718yes—
781C22—24no—
782C22—28no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—28no—
788C22—28no—
789C22—24no—
790C22—28no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—44no—
795C22—42no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—82no—
801C22—82no—
802C22#240718yes—
803C22C22×#12011yescharacteristic
804C22C2×#52511yescharacteristic
805C22C2×#52511yescharacteristic
806C22C2×#53611yescharacteristic
807C22C2×#53711yescharacteristic
808C22C2×#54611yescharacteristic
809C22C2×#54711yescharacteristic
810C22C2×#54712yes—
811C22C2×#54712yes—
812C22C2×#54811yescharacteristic
813C22C2×#55011yescharacteristic
814C22#347512yes—
815C22#348212yes—
816C22#348611yescharacteristic
817C22#348711yescharacteristic
818C22#348912yes—
819C22#348912yes—
820C22#350912yes—
821C22#351312yes—
822C22#351512yes—
823C22#352312yes—
824C22#354412yes—
825C22#356312yes—
826C4—24no—
827C4—44no—
828C4—48no—
829C4—42no—
830C4—44no—
831C4—44no—
832C4—44no—
833C4—44no—
834C4—44no—
835C4—42no—
836C4—42no—
837C4—44no—
838C4—82no—
839C4—84no—
840C4#240618yes—
841C2—28no—
842C2—82no—
843C2C2×#240711yescharacteristic
844C2C2×#240611yescharacteristic
845C2#3565911yescharacteristic
846C2#3616211yescharacteristic
847C2#3637512yes—
848C2#3642311yescharacteristic
849C2#3804312yes—
850C2#3891911yescharacteristic
851C2#3946511yescharacteristic
852C2#5904712yes—
853C2#5911112yes—
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
2. C2×#2855C2semidirect
4. C22×#389C2semidirect
5. #16104C2semidirect
6. #16102C2semidirect
7. #15218C2semidirect
8. #15179C2semidirect
11. #14139C2semidirect
12. #14129C2semidirect
13. #14128C2semidirect
14. #14017C2semidirect
15. #13904C2semidirect
17. #13870C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5522
C2×#28552
C2×C4×#1232
C22×#3892
#161042
#161022
#152182
#151792
#150692
#149122
#141392
#141292
#141282
#140172
#139042
#138722
#138702