Finite Group Databasebeta

← #719722

Subgroups — #719722

Order 512.

3380 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic
2C2×#2500C211yesmaximal, characteristic, complemented
3C2×#2501C211yesmaximal, characteristic, complemented
4C2×#2352C211yesmaximal, characteristic, complemented
5#16312C214yesmaximal, complemented
6#15432C214yesmaximal, complemented
7#15260C214yesmaximal, complemented
8#15233C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15195C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14761C214yesmaximal, complemented
13#14354C211yesmaximal, characteristic, complemented
14#13941C211yesmaximal, characteristic, complemented
15#13910C211yesmaximal, characteristic, complemented
16#13880C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18#13847C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C22×#123C2214yes—
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#121C2212yes—
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2537—28no—
29#2501—28no—
30#2500—28no—
31C2×#399C2214yes—
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#394C2214yes—
35C2×#394C2214yes—
36#2352—28no—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#389C2214yes—
42C2×#388C2212yes—
43C2×#388C2214yes—
44C2×#387C2212yes—
45C2×#386C2212yes—
46C2×#385C2214yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yes—
67C2×#376C2211yescharacteristic
68#1445C2212yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1443C2214yes—
74#1442C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2212yes—
84#1438C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2312yes—
103C2×#123—216no—
104C2×#123—48no—
105C2×#123—48no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#121—28no—
109C2×#121—24no—
110C2×#121—24no—
111C2×#121—48no—
112C2×#121—42no—
113C2×#121—42no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4D418yes—
120C2×#117—24no—
121C2×#117—24no—
122C2×#117—42no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—42no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167#399—216no—
168#394—216no—
169#394—28no—
170#394—28no—
171#394—48no—
172#390—24no—
173#390—24no—
174#390—24no—
175#390D418yescomplemented
176#389—48no—
177#388—28no—
178#388—216no—
179#387—28no—
180#386—28no—
181#385—48no—
182#384—24no—
183#384—24no—
184#384—24no—
185#384—24no—
186#384—42no—
187#382—24no—
188#382—24no—
189#382—42no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—24no—
194#380—28no—
195C4×C4⋊C4—24no—
196C4×C4⋊C4—24no—
197C4×C22⋊C4—28no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—24no—
202#376—24no—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C25C2411yescharacteristic
226C25C2412yes—
227C25C2411yescharacteristic
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—28no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—44no—
245C22×D4—42no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4C2×D414yes—
249C22×D4C2×D414yes—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—28no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—42no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290#123—464no—
291#121—416no—
292#121—416no—
293#121—432no—
294C4×D4—232no—
295C4×D4—416no—
296#117—416no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
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—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4C2×D414yes—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4C2×D414yes—
392C2×C22⋊C4C2×D414yes—
393C2×C22⋊C4C2×D4116yes—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—42no—
408C2×C42—44no—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411C2×C42#4114yes—
412C2×C42#4114yes—
413C2×C42#4114yes—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—28no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—28no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—21no—
442C24—22no—
443C24—21no—
444C24—22no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—22no—
455C24—21no—
456C24—24no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—22no—
461C24—21no—
462C24—22no—
463C24—24no—
464C24—22no—
465C24C22×D414yes—
466C24C22×D412yes—
467C24C22×D412yes—
468C24H(5,𝔽2)14yes—
469C24C2511yescharacteristic
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—44no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—416no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—88no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—88no—
491C2×D4—88no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
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—22no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
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—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—48no—
573C22×C4—416no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—88no—
587C22×C4—88no—
588C22×C4—84no—
589C22×C4—88no—
590C22×C4C22×D412yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C2×#4114yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4H(5,𝔽2)14yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C42−1+414yes—
609C22×C42−1+412yes—
610C4⋊C4—216no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—48no—
614C4⋊C4—416no—
615C4⋊C4—48no—
616C4⋊C4—416no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—84no—
624C4⋊C4—88no—
625C4⋊C4—88no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—416no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—416no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—416no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—88no—
643C22⋊C4—84no—
644C42—28no—
645C42—28no—
646C42—48no—
647C42—44no—
648C42—44no—
649C42—84no—
650C42#123116yescomplemented
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—28no—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—41no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—42no—
711C23—44no—
712C23—42no—
713C23—44no—
714C23—42no—
715C23—44no—
716C23—42no—
717C23—42no—
718C23—44no—
719C23#53514yes—
720C23C23×D411yescharacteristic
721C23C23×D411yescharacteristic
722C23C22×#4111yescharacteristic
723C23C22×#4111yescharacteristic
724C23C22×#4111yescharacteristic
725C23C2×H(5,𝔽2)12yes—
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×H(5,𝔽2)12yes—
728C23C2×2−1+411yescharacteristic
729C23C2×2−1+412yes—
730C23#58512yes—
731D4—416no—
732D4—416no—
733D4—816no—
734D4—816no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
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—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—416no—
791C2×C4—416no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
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—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—816no—
823C2×C4—816no—
824C2×C4C2×#12314yes—
825C2×C4C2×#12314yes—
826C2×C4C2×#12314yes—
827C2×C4#53214yes—
828C2×C4#54214yes—
829C2×C4D4214yes—
830C2×C4#54714yes—
831C2×C4#54714yes—
832C2×C4#55314yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—42no—
840C22—44no—
841C22—44no—
842C22—42no—
843C22—42no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—48no—
849C22—42no—
850C22—44no—
851C22—48no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—82no—
857C22—84no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—84no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22C22×#12311yescharacteristic
867C22C2×#53211yescharacteristic
868C22C2×#53511yescharacteristic
869C22#344911yescharacteristic
870C22C2×#54211yescharacteristic
871C22C2×D4211yescharacteristic
872C22C2×#54711yescharacteristic
873C22C2×#54711yescharacteristic
874C22C2×#55311yescharacteristic
875C22#348412yes—
876C22#348912yes—
877C22#349212yes—
878C22#349212yes—
879C22#349412yes—
880C22#349412yes—
881C22#349412yes—
882C22#349811yescharacteristic
883C22#349911yescharacteristic
884C22#351112yes—
885C22#354312yes—
886C22#354412yes—
887C22#354712yes—
888C22#355412yes—
889C4—24no—
890C4—24no—
891C4—44no—
892C4—44no—
893C4—44no—
894C4—42no—
895C4—42no—
896C4—44no—
897C4—44no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4#242218yes—
905C2—44no—
906C2—84no—
907C2—82no—
908C2C2×#242211yescharacteristic
909C2#3526211yescharacteristic
910C2#3553011yescharacteristic
911C2#3592312yes—
912C2#3767411yescharacteristic
913C2#3768011yescharacteristic
914C2#3786311yescharacteristic
915C2#3786911yescharacteristic
916C2#4251512yes—
917C2#4492812yes—
918C2#4497412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2537C2
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×#2500C2semidirect
3. C2×#2501C2semidirect
4. C2×#2352C2semidirect
5. #16312C2semidirect
6. #15432C2semidirect
7. #15260C2semidirect
8. #15233C2semidirect
9. #15219C2semidirect
10. #15195C2semidirect
11. #15130C2semidirect
12. #14761C2semidirect
13. #14354C2semidirect
14. #13941C2semidirect
15. #13910C2semidirect
16. #13880C2semidirect
17. #13879C2semidirect
18. #13847C2semidirect
19. #13785C2semidirect
175. #390D4semidirect
650. C42#123semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#25002
C2×#25012
C2×#23522
#163122
#154322
#152602
#152332
#152192
#151952
#151302
#147612
#143542
#139412
#139102
#138802
#138792
#138472
#137852