Finite Group Databasebeta

← #947073

Subgroups — #947073

Order 512.

3126 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2494C211yesmaximal, characteristic, complemented
2C2×#2431C211yesmaximal, characteristic
3#17090C214yesmaximal, complemented
4#16382C214yesmaximal, complemented
5#16341C214yesmaximal, complemented
6#15372C214yesmaximal, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15226C211yesmaximal, characteristic, complemented
9#15222C211yesmaximal, characteristic, complemented
10#15219C211yesmaximal, characteristic, complemented
11#15140C211yesmaximal, characteristic, complemented
12#15130C211yesmaximal, characteristic, complemented
13#14272C211yesmaximal, characteristic, complemented
14#14261C211yesmaximal, characteristic, complemented
15#14153C211yesmaximal, characteristic, complemented
16#14001C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#121C2211yescharacteristic
24#2494—28no—
25#2431—28no—
26C2×#401C2212yes—
27C2×#397C2212yes—
28C2×#394C2214yes—
29C2×#394C2214yes—
30C2×#392C2212yes—
31C2×#392C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#388C2212yes—
49C2×#388C2214yes—
50C2×#387C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×#376C2211yescharacteristic
64#1445C2214yes—
65#1445C2214yes—
66#1443C2212yes—
67#1443C2214yes—
68#1442C2214yes—
69#1442C2212yes—
70#1440C2214yes—
71#1440C2212yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84#1438C2214yes—
85#1438C2214yes—
86#1437C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C22×#41—24no—
94C22×#41—24no—
95C22×#41—24no—
96C22×#41—42no—
97C22×#41—42no—
98C22×#41—42no—
99C22×#41—42no—
100C23×Q8C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C23×D4C2311yescharacteristic
103C23×D4C2312yes—
104C23×D4C2312yes—
105C23×D4C2312yes—
106C23×D4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C2×#127—24no—
110C2×#127—24no—
111C2×#127—42no—
112C2×#124—24no—
113C2×#124—24no—
114C2×#124—42no—
115C2×#121—24no—
116C2×#121—42no—
117C2×#121—42no—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153#401—28no—
154#397—28no—
155#394—48no—
156#394—48no—
157#392—28no—
158#392—28no—
159#391—24no—
160#391—24no—
161#391—42no—
162#391—42no—
163#391—42no—
164#390—24no—
165#390—24no—
166#390—42no—
167#390—42no—
168#390—42no—
169#390—42no—
170#390—42no—
171#390—42no—
172#390—42no—
173#389—24no—
174#389—24no—
175#388—28no—
176#388—48no—
177#387—28no—
178#386—28no—
179#386—28no—
180#384—42no—
181#382—24no—
182#382—42no—
183#380—24no—
184#380—24no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—42no—
187C4×C22⋊C4—42no—
188C4×C22⋊C4—42no—
189C4×C22⋊C4D418yes—
190#376—42no—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C25C2412yes—
219C25C2411yescharacteristic
220C25C2412yes—
221C2×#41—416no—
222C2×#41—416no—
223C2×#41—416no—
224C2×#41—416no—
225C2×#41—416no—
226C2×#41—416no—
227C2×#41—416no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8#4114yes—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—24no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4#4114yes—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4C2×D414yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301#127—416no—
302#124—416no—
303#121—416no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
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×C22⋊C4—44no—
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⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D414yes—
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×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—44no—
398C2×C42C2×D414yes—
399C2×C42C2×D414yes—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—44no—
420#95—44no—
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—24no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—24no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24C22×D412yes—
459C24C2×#4114yes—
460C24C2511yescharacteristic
461#41—4128no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—84no—
496C2×D4—84no—
497C2×D4—88no—
498C2×D4—88no—
499C2×D4—84no—
500C2×D4—84no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—88no—
504C2×D4—88no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
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—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4H(5,𝔽2)14yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C4H(5,𝔽2)12yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C4H(5,𝔽2)12yes—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—84no—
621C4⋊C4—88no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—416no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—88no—
634C22⋊C4—84no—
635C22⋊C4—88no—
636C22⋊C4—88no—
637C22⋊C4—88no—
638C22⋊C4—88no—
639C22⋊C4—88no—
640C22⋊C4—88no—
641C42—28no—
642C42—28no—
643C42—44no—
644C42—44no—
645C42—44no—
646C42—44no—
647C42—84no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—28no—
659C23—28no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—42no—
665C23—41no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—42no—
677C23—41no—
678C23—44no—
679C23—42no—
680C23—42no—
681C23—44no—
682C23—42no—
683C23—44no—
684C23—42no—
685C23—44no—
686C23—42no—
687C23—44no—
688C23—44no—
689C23—42no—
690C23—44no—
691C23—44no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23C23×D411yescharacteristic
718C23C22×#4111yescharacteristic
719C23C22×#4111yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)12yes—
725C23#58512yes—
726C23#58512yes—
727C23#58512yes—
728Q8—416no—
729D4—432no—
730D4—416no—
731D4—816no—
732D4—816no—
733D4—816no—
734D4—88no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—432no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—416no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4#53514yes—
825C2×C4#53814yes—
826C2×C4#53814yes—
827C2×C4#54614yes—
828C2×C4#54614yes—
829C2×C4#55114yes—
830C2×C4#56014yes—
831C22—44no—
832C22—42no—
833C22—48no—
834C22—44no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—44no—
841C22—42no—
842C22—48no—
843C22—82no—
844C22—84no—
845C22—82no—
846C22—82no—
847C22—84no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—84no—
855C22—84no—
856C22—82no—
857C22—84no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—84no—
864C22C2×#53511yescharacteristic
865C22#344911yescharacteristic
866C22#344911yescharacteristic
867C22C2×#53811yescharacteristic
868C22C2×#53811yescharacteristic
869C22C2×#54611yescharacteristic
870C22C2×#54611yescharacteristic
871C22C2×#55111yescharacteristic
872C22#349811yescharacteristic
873C22#350011yescharacteristic
874C22#351312yes—
875C22#351712yes—
876C22#352112yes—
877C22#352412yes—
878C22C2×#56011yescharacteristic
879C22#353912yes—
880C22#354012yes—
881C22#354212yes—
882C22#354612yes—
883C22#354612yes—
884C22#355812yes—
885C22#356212yes—
886C22#356212yes—
887C4—42no—
888C4—44no—
889C4—42no—
890C4—44no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4#268518yes—
903C2—84no—
904C2—82no—
905C2—162no—
906C2#3730511yescharacteristic
907C2#3754411yescharacteristic
908C2#3808911yescharacteristic
909C2#3809311yescharacteristic
910C2#3809411yescharacteristic
911C2#3894511yescharacteristic
912C2#4259812yes—
913C2#4290712yes—
914C2#4505312yes—
915C2C2×#268511yescharacteristic
916C2#5306012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2431C2
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×#2494C2semidirect
3. #17090C2semidirect
4. #16382C2semidirect
5. #16341C2semidirect
6. #15372C2semidirect
7. #15240C2semidirect
8. #15226C2semidirect
9. #15222C2semidirect
10. #15219C2semidirect
11. #15140C2semidirect
12. #15130C2semidirect
13. #14272C2semidirect
14. #14261C2semidirect
15. #14153C2semidirect
16. #14001C2semidirect
17. #13937C2semidirect
18. #13937C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24942
C2×#24312
#170902
#163822
#163412
#153722
#152402
#152262
#152222
#152192
#151402
#151302
#142722
#142612
#141532
#140012
#139372
#138422