Finite Group Databasebeta

← #642229

Subgroups — #642229

Order 512.

3058 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2851C211yesmaximal, characteristic, complemented
2C2×#2297C211yesmaximal, characteristic
3#16893C214yesmaximal, complemented
4#16562C214yesmaximal, complemented
5#15246C214yesmaximal, complemented
6#15244C211yesmaximal, characteristic, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15238C211yesmaximal, characteristic, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15229C211yesmaximal, characteristic, complemented
11#15222C211yesmaximal, characteristic, complemented
12#15184C211yesmaximal, characteristic, complemented
13#15134C211yesmaximal, characteristic, complemented
14#14315C214yesmaximal, complemented
15#13937C211yesmaximal, characteristic
16#13937C211yesmaximal, characteristic
17#13879C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#380C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C42C2211yescharacteristic
24#2851—28no—
25C2×#396C2214yes—
26#2297—28no—
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#389C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#387C2212yes—
42C2×#387C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61#1445C2214yes—
62#1445C2214yes—
63#1443C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2212yes—
87#1434C2212yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C22×#41—24no—
94C22×#41—24no—
95C22×#41—42no—
96C22×#41—42no—
97C22×#41—42no—
98C22×#41—42no—
99C22×#41Q818yes—
100C23×Q8C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C23×D4C2312yes—
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C2×#125—24no—
108C2×#125—42no—
109C2×#125—42no—
110C2×#117—24no—
111C2×#117—42no—
112C2×#117—42no—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C42—42no—
141C22×C42—42no—
142C22×C42D418yes—
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#396—216no—
153#391—24no—
154#391—24no—
155#391—42no—
156#391—42no—
157#391—42no—
158#391—42no—
159#390—24no—
160#390—24no—
161#390—42no—
162#390—42no—
163#390—42no—
164#390—42no—
165#389—24no—
166#389—24no—
167#387—28no—
168#387—28no—
169#386—28no—
170#386—28no—
171#385—28no—
172#385—28no—
173#384—42no—
174#384—42no—
175#382—24no—
176#382—42no—
177#382—42no—
178#380—24no—
179#380—24no—
180#380—28no—
181C4×C4⋊C4—42no—
182C4×C4⋊C4—42no—
183C4×C22⋊C4—24no—
184C4×C22⋊C4—24no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—28no—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C2×#41—232no—
218C2×#41—416no—
219C2×#41—416no—
220C2×#41—416no—
221C2×#41—416no—
222C2×#41—416no—
223C2×#41—416no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8C2×Q814yes—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4C2×Q814yes—
244C22×D4C2×Q818yes—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—41no—
260C23×C4—41no—
261C23×C4—41no—
262C23×C4—41no—
263C23×C4C2×D414yes—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4C2×Q814yes—
267C23×C4C2×Q818yes—
268C23×C4#4114yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286#125—416no—
287#117—416no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4#4118yescomplemented
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—416no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—41no—
382C2×C42—41no—
383C2×C42—41no—
384C2×C42—41no—
385C2×C42C2×D414yes—
386C2×C42C2×D414yes—
387C2×C42C2×D414yes—
388C2×C42C2×D414yes—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—44no—
405#95—42no—
406#95—42no—
407#95—44no—
408#95—44no—
409#95—42no—
410#95—42no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24C22×D412yes—
436C24C22×Q814yes—
437C24C22×Q812yes—
438C24C2×#4112yes—
439C24C2511yescharacteristic
440#41—4128no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×D4—216no—
449C2×D4—28no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—44no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4—44no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—216no—
506C22×C4—28no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4C22⋊Q8116yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×Q814yes—
574C22×C4C22×Q812yes—
575C22×C4C22×Q812yes—
576C22×C4C2×#4114yes—
577C22×C4C2×#4114yes—
578C22×C4C2×#4112yes—
579C22×C4C2×#4114yes—
580C22×C4C2×#4112yes—
581C22×C4H(5,𝔽2)12yes—
582C22×C4H(5,𝔽2)12yes—
583C22×C4H(5,𝔽2)12yes—
584C22×C4H(5,𝔽2)12yes—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—48no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—48no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—88no—
598C4⋊C4—88no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—88no—
609C22⋊C4—88no—
610C22⋊C4—88no—
611C22⋊C4—88no—
612C42—28no—
613C42—28no—
614C42—44no—
615C42—44no—
616C42—48no—
617C42—44no—
618C42—44no—
619C42—44no—
620C42—44no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—28no—
639C23—28no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23C2×C22⋊Q814yes—
667C23C23×D411yescharacteristic
668C23C23×Q811yescharacteristic
669C23C22×#4111yescharacteristic
670C23C22×#4112yes—
671C23C2×H(5,𝔽2)11yescharacteristic
672C23C2×H(5,𝔽2)11yescharacteristic
673C23C2×H(5,𝔽2)11yescharacteristic
674C23C2×H(5,𝔽2)11yescharacteristic
675C23#58512yes—
676C23#58512yes—
677C23#58512yes—
678Q8—416no—
679D4—432no—
680D4—416no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—232no—
692C2×C4—24no—
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—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—416no—
711C2×C4—432no—
712C2×C4—416no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4C2×C22⋊Q814yes—
776C2×C4C2×C22⋊Q814yes—
777C2×C4#53214yes—
778C2×C4#53414yes—
779C2×C4#53514yes—
780C2×C4#53814yes—
781C2×C4#53814yes—
782C2×C4#54314yes—
783C2×C4#54314yes—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—44no—
796C22—48no—
797C22—48no—
798C22—44no—
799C22—44no—
800C22—84no—
801C22—84no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22C22×C22⋊Q811yescharacteristic
807C22C2×#53211yescharacteristic
808C22C2×#53411yescharacteristic
809C22C2×#53511yescharacteristic
810C22#344911yescharacteristic
811C22#344911yescharacteristic
812C22#344911yescharacteristic
813C22C2×#53811yescharacteristic
814C22C2×#53811yescharacteristic
815C22C2×#54311yescharacteristic
816C22C2×#54311yescharacteristic
817C22#347512yes—
818C22Q8×#4112yes—
819C22#350412yes—
820C22#350512yes—
821C22#350612yes—
822C22#351212yes—
823C22#351412yes—
824C22#351712yes—
825C22#353912yes—
826C22#354012yes—
827C22#356212yes—
828C22#356212yes—
829C4—24no—
830C4—24no—
831C4—44no—
832C4—44no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—44no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4#262618yes—
846C2—44no—
847C2—84no—
848C2C2×#262611yescharacteristic
849C2#3494711yescharacteristic
850C2#3503211yescharacteristic
851C2#3519111yescharacteristic
852C2#3533311yescharacteristic
853C2#3745511yescharacteristic
854C2#3754411yescharacteristic
855C2#3998412yes—
856C2#3998512yes—
857C2#4000812yes—
858C2#4000912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2851C2semidirect
3. #16893C2semidirect
4. #16562C2semidirect
5. #15246C2semidirect
6. #15244C2semidirect
7. #15240C2semidirect
8. #15238C2semidirect
9. #15237C2semidirect
10. #15229C2semidirect
11. #15222C2semidirect
12. #15184C2semidirect
13. #15134C2semidirect
14. #14315C2semidirect
17. #13879C2semidirect
18. #13879C2semidirect
19. C4×#380C2semidirect
327. C2×C4⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#28512
C2×#22972
#168932
#165622
#152462
#152442
#152402
#152382
#152372
#152292
#152222
#151842
#151342
#143152
#139372
#138792
C4×#3802