Finite Group Databasebeta

← #687689

Subgroups — #687689

Order 512.

3298 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic, complemented
2C2×#2442C211yesmaximal, characteristic, complemented
3C2×#2341C211yesmaximal, characteristic
4C2×#2311C211yesmaximal, characteristic
5#16304C214yesmaximal, complemented
6#15962C214yesmaximal, complemented
7#15326C214yesmaximal, complemented
8#15244C211yesmaximal, characteristic, complemented
9#15229C211yesmaximal, characteristic, complemented
10#15222C211yesmaximal, characteristic, complemented
11#15222C211yesmaximal, characteristic, complemented
12#14775C214yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#13978C211yesmaximal, characteristic, complemented
15#13978C211yesmaximal, characteristic, complemented
16#13942C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic
18#13881C211yesmaximal, characteristic, complemented
19#13844C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2565—28no—
27#2442—28no—
28C2×#400C2212yes—
29C2×#398C2214yes—
30C2×#398C2212yes—
31#2341—28no—
32#2311—28no—
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#390C2212yes—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2212yes—
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#387C2214yes—
48C2×#386C2214yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×#380C2212yes—
59C2×#380C2214yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65#1444C2212yes—
66#1442C2212yes—
67#1442C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1439C2214yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2214yes—
84#1436C2214yes—
85#1436C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90#1434C2214yes—
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×D4C2311yescharacteristic
104C23×D4C2312yes—
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C2×#125—24no—
109C2×#125—24no—
110C2×#125—42no—
111C2×C4×Q8—24no—
112C2×C4×Q8—24no—
113C2×C4×Q8—24no—
114C2×C4×Q8—24no—
115C2×C4×Q8—42no—
116C2×C4×Q8—42no—
117C2×#117—24no—
118C2×#117—24no—
119C2×#117—42no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#400—28no—
163#398—216no—
164#398—28no—
165#391—24no—
166#391—24no—
167#391—24no—
168#391D418yes—
169#390—24no—
170#390—28no—
171#390—28no—
172#390—24no—
173#390—24no—
174#390—24no—
175#390—42no—
176#390—42no—
177#389—24no—
178#389—24no—
179#387—216no—
180#386—216no—
181#385—28no—
182#384—24no—
183#382—24no—
184#382—24no—
185#382—42no—
186#382—42no—
187#380—24no—
188#380—24no—
189#380—28no—
190#380—216no—
191#380—28no—
192C4×C4⋊C4—24no—
193C4×C4⋊C4—42no—
194C4×C22⋊C4—24no—
195C4×C22⋊C4—28no—
196C4×C22⋊C4D418yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2311yescharacteristic
221C2×#95C2314yes—
222C2×#95C2311yescharacteristic
223C25C2412yes—
224C25C2411yescharacteristic
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×Q8C2×D414yes—
237C22×Q8C2×Q814yes—
238C22×Q8#4114yes—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—24no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4C2×Q814yes—
252C22×D4C2×Q818yes—
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—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4C2×D414yes—
269C23×C4C2×Q818yes—
270C23×C4C2×Q814yes—
271C23×C4#4114yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289#125—416no—
290C4×Q8—416no—
291C4×Q8—416no—
292#117—416no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—416no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—42no—
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—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4C2×D414yes—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
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⋊C4C2×D414yes—
376C2×C22⋊C4C2×D414yes—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42C2×D414yes—
399C2×C42C2×D414yes—
400C2×C42C2×D414yes—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—28no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—24no—
410#95—28no—
411#95—24no—
412#95—28no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—44no—
417#95—42no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—42no—
422#95—44no—
423#95—44no—
424#95C2×D414yes—
425#95C2×D414yes—
426#95C2×D4116yes—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24C22×D412yes—
446C24C22×Q814yes—
447C24C22×Q812yes—
448C24C2×#4112yes—
449C24C2511yescharacteristic
450#41—4128no—
451C2×Q8—28no—
452C2×Q8—28no—
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—28no—
457C2×Q8C22⋊Q8116yes—
458C2×D4—216no—
459C2×D4—216no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—216no—
513C22×C4—216no—
514C22×C4—22no—
515C22×C4—22no—
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—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—88no—
568C22×C4—84no—
569C22×C4—88no—
570C22×C4C22⋊Q8116yes—
571C22×C4C22×D412yes—
572C22×C4C22×D414yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D414yes—
576C22×C4C22×D412yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×Q812yes—
582C22×C4C22×Q814yes—
583C22×C4C22×Q812yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C4⋊C4—28no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—416no—
599C4⋊C4—48no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—84no—
606C4⋊C4—84no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—84no—
615C22⋊C4—84no—
616C22⋊C4—88no—
617C22⋊C4—88no—
618C22⋊C4—84no—
619C22⋊C4—88no—
620C22⋊C4—88no—
621C42—28no—
622C42—28no—
623C42—28no—
624C42—48no—
625C42—48no—
626C42—44no—
627C42—44no—
628C42—44no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—28no—
647C23—28no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—42no—
665C23—44no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23C2×C22⋊Q814yes—
675C23C23×D411yescharacteristic
676C23C23×D411yescharacteristic
677C23C23×Q811yescharacteristic
678C23C22×#4111yescharacteristic
679C23C22×#4111yescharacteristic
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23#58512yes—
683C23#58512yes—
684C23#58512yes—
685C23#58512yes—
686Q8—232no—
687D4—432no—
688D4—416no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—232no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—28no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—432no—
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—44no—
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—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—44no—
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—44no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—816no—
782C2×C4C2×C22⋊Q814yes—
783C2×C4C2×C22⋊Q818yes—
784C2×C4C2×C22⋊Q814yes—
785C2×C4C2×C22⋊Q814yes—
786C2×C4#54314yes—
787C2×C4D4214yes—
788C2×C4#54614yes—
789C2×C4#54614yes—
790C2×C4#55114yes—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—42no—
802C22—44no—
803C22—44no—
804C22—44no—
805C22—48no—
806C22—48no—
807C22—82no—
808C22—82no—
809C22—84no—
810C22—82no—
811C22—84no—
812C22—82no—
813C22C22×C22⋊Q811yescharacteristic
814C22C22×C22⋊Q811yescharacteristic
815C22#344911yescharacteristic
816C22#344911yescharacteristic
817C22C2×#54311yescharacteristic
818C22C2×D4211yescharacteristic
819C22C2×#54611yescharacteristic
820C22C2×#54611yescharacteristic
821C22C2×#55111yescharacteristic
822C22#348712yes—
823C22#349312yes—
824C22#350011yescharacteristic
825C22#350011yescharacteristic
826C22#350012yes—
827C22#350412yes—
828C22#350412yes—
829C22#351212yes—
830C22#352412yes—
831C22#352412yes—
832C22#353912yes—
833C22#355112yes—
834C22#356212yes—
835C22#356212yes—
836C4—24no—
837C4—28no—
838C4—42no—
839C4—42no—
840C4—44no—
841C4—42no—
842C4—44no—
843C4—42no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4#243718yes—
853C2—44no—
854C2—84no—
855C2C2×#243711yescharacteristic
856C2#3533311yescharacteristic
857C2#3562011yescharacteristic
858C2#3604012yes—
859C2#3768311yescharacteristic
860C2#3809311yescharacteristic
861C2#3894811yescharacteristic
862C2#3935711yescharacteristic
863C2#4295312yes—
864C2#4523612yes—
865C2#4526012yes—
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×#2565C2semidirect
2. C2×#2442C2semidirect
5. #16304C2semidirect
6. #15962C2semidirect
7. #15326C2semidirect
8. #15244C2semidirect
9. #15229C2semidirect
10. #15222C2semidirect
11. #15222C2semidirect
12. #14775C2semidirect
13. #14340C2semidirect
14. #13978C2semidirect
15. #13978C2semidirect
16. #13942C2semidirect
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×#25652
C2×#24422
C2×#23412
C2×#23112
#163042
#159622
#153262
#152442
#152292
#152222
#147752
#143402
#139782
#139422
#139372
#138812
#138442