Finite Group Databasebeta

← #687687

Subgroups — #687687

Order 512.

3406 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2566C211yesmaximal, characteristic, complemented
2C2×#2442C211yesmaximal, characteristic, complemented
3C2×#2339C211yesmaximal, characteristic
4C2×#2311C211yesmaximal, characteristic
5#16302C214yesmaximal, complemented
6#15958C214yesmaximal, complemented
7#15328C214yesmaximal, complemented
8#15240C211yesmaximal, characteristic, complemented
9#15238C211yesmaximal, characteristic, complemented
10#15237C211yesmaximal, characteristic, complemented
11#15237C211yesmaximal, characteristic, complemented
12#14767C214yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#13979C211yesmaximal, characteristic, complemented
15#13979C211yesmaximal, characteristic, complemented
16#13941C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic
18#13881C211yesmaximal, characteristic, complemented
19#13844C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2566—28no—
27#2442—28no—
28C2×#400C2212yes—
29C2×#398C2212yes—
30C2×#396C2214yes—
31#2339—28no—
32#2311—28no—
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2214yes—
48C2×#385C2214yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#381C2212yes—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2212yes—
59C2×#380C2214yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C22×#95C2212yes—
65#1445C2214yes—
66#1445C2214yes—
67#1444C2212yes—
68#1443C2214yes—
69#1443C2214yes—
70#1442C2212yes—
71#1442C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1439C2214yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41Q818yes—
102C23×Q8C2311yescharacteristic
103C23×D4C2312yes—
104C23×D4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2312yes—
109C24×C4C2312yes—
110C2×#125—24no—
111C2×#125—24no—
112C2×#125—42no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—42no—
118C2×C4×D4—42no—
119C2×#117—24no—
120C2×#117—24no—
121C2×#117—42no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#400—28no—
159#398—28no—
160#396—216no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—42no—
166#391—42no—
167#390—24no—
168#390—24no—
169#390—24no—
170#390D418yes—
171#389—24no—
172#389—24no—
173#386—216no—
174#386—28no—
175#386—28no—
176#385—216no—
177#385—28no—
178#384—24no—
179#382—24no—
180#382—24no—
181#382—42no—
182#382—42no—
183#381—28no—
184#380—24no—
185#380—24no—
186#380—216no—
187#380—28no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4—42no—
190C4×C22⋊C4—24no—
191C4×C22⋊C4D418yes—
192C2×#95—28no—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C25C2411yescharacteristic
224C25C2412yes—
225C2×#41—232no—
226C2×#41—232no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41—416no—
230C2×#41—416no—
231C2×#41—416no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8C2×Q814yes—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4C2×D414yes—
250C22×D4C2×Q818yes—
251C22×D4C2×Q814yes—
252C22×D4#4114yes—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4C2×D414yes—
279C23×C4C2×Q818yes—
280C23×C4C2×Q814yes—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299#125—416no—
300C4×D4—416no—
301C4×D4—416no—
302#117—416no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—416no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4C2×D414yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4C2×D414yes—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D4116yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42C2×D414yes—
395C2×C42C2×D414yes—
396C2×C42C2×D414yes—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—28no—
403#95—28no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—42no—
413#95—42no—
414#95—44no—
415#95—42no—
416#95—42no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—42no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95C2×D414yes—
426#95C2×D414yes—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—22no—
436C24—24no—
437C24—22no—
438C24—24no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24C22×D414yes—
444C24C22×D412yes—
445C24C22×Q812yes—
446C24C22×Q814yes—
447C24C2×#4112yes—
448C24C2×#4114yes—
449C24C2511yescharacteristic
450#41—4128no—
451C2×Q8—28no—
452C2×Q8—28no—
453C2×Q8—28no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×D4—216no—
459C2×D4—216no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4C22⋊Q8116yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—28no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—216no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—216no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
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—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—88no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—84no—
577C22×C4—88no—
578C22×C4—88no—
579C22×C4—88no—
580C22×C4—88no—
581C22×C4—88no—
582C22×C4C22⋊Q8116yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×Q814yes—
593C22×C4C22×Q812yes—
594C22×C4C22×Q812yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C4H(5,𝔽2)12yes—
600C4⋊C4—28no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—84no—
613C4⋊C4—88no—
614C4⋊C4—84no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—416no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—88no—
624C22⋊C4—88no—
625C22⋊C4—84no—
626C22⋊C4—88no—
627C42—28no—
628C42—28no—
629C42—28no—
630C42—44no—
631C42—44no—
632C42—44no—
633C23—22no—
634C23—24no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—24no—
647C23—28no—
648C23—24no—
649C23—22no—
650C23—28no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—28no—
655C23—28no—
656C23—24no—
657C23—28no—
658C23—28no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—44no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—44no—
671C23—44no—
672C23—42no—
673C23—42no—
674C23—44no—
675C23—44no—
676C23—42no—
677C23C2×C22⋊Q818yes—
678C23C2×C22⋊Q814yes—
679C23C23×D411yescharacteristic
680C23C23×D411yescharacteristic
681C23C23×Q811yescharacteristic
682C23C22×#4111yescharacteristic
683C23C22×#4111yescharacteristic
684C23C2×H(5,𝔽2)11yescharacteristic
685C23C2×H(5,𝔽2)11yescharacteristic
686C23#58512yes—
687C23#58512yes—
688C23#58512yes—
689C23#58512yes—
690Q8—416no—
691D4—232no—
692D4—432no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—232no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—28no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—432no—
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—44no—
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—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—816no—
787C2×C4—816no—
788C2×C4—816no—
789C2×C4C2×C22⋊Q814yes—
790C2×C4C2×C22⋊Q814yes—
791C2×C4C2×C22⋊Q814yes—
792C2×C4#54314yes—
793C2×C4D4214yes—
794C2×C4#54614yes—
795C2×C4#54614yes—
796C2×C4#55114yes—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—28no—
801C22—216no—
802C22—44no—
803C22—44no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—48no—
808C22—42no—
809C22—44no—
810C22—44no—
811C22—48no—
812C22—44no—
813C22—42no—
814C22—44no—
815C22—44no—
816C22—48no—
817C22—42no—
818C22—44no—
819C22C22×C22⋊Q811yescharacteristic
820C22C22×C22⋊Q811yescharacteristic
821C22#344911yescharacteristic
822C22#344911yescharacteristic
823C22C2×#54311yescharacteristic
824C22C2×D4211yescharacteristic
825C22C2×#54611yescharacteristic
826C22C2×#54611yescharacteristic
827C22C2×#55111yescharacteristic
828C22#348512yes—
829C22#349312yes—
830C22#350011yescharacteristic
831C22#350011yescharacteristic
832C22#350012yes—
833C22#350412yes—
834C22#350412yes—
835C22#351212yes—
836C22#352112yes—
837C22#352112yes—
838C22#353912yes—
839C22#355112yes—
840C22#356212yes—
841C22#356212yes—
842C4—24no—
843C4—42no—
844C4—44no—
845C4—42no—
846C4—44no—
847C4—44no—
848C4—42no—
849C4—42no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4#243718yes—
859C2—44no—
860C2—48no—
861C2C2×#243711yescharacteristic
862C2#3533311yescharacteristic
863C2#3562011yescharacteristic
864C2#3603112yes—
865C2#3768211yescharacteristic
866C2#3809211yescharacteristic
867C2#3894711yescharacteristic
868C2#3935711yescharacteristic
869C2#4295312yes—
870C2#4509212yes—
871C2#4512912yes—
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×#2566C2semidirect
2. C2×#2442C2semidirect
5. #16302C2semidirect
6. #15958C2semidirect
7. #15328C2semidirect
8. #15240C2semidirect
9. #15238C2semidirect
10. #15237C2semidirect
11. #15237C2semidirect
12. #14767C2semidirect
13. #14340C2semidirect
14. #13979C2semidirect
15. #13979C2semidirect
16. #13941C2semidirect
18. #13881C2semidirect
19. #13844C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25662
C2×#24422
C2×#23392
C2×#23112
#163022
#159582
#153282
#152402
#152382
#152372
#147672
#143402
#139792
#139412
#139372
#138812
#138442