Finite Group Databasebeta

← #875312

Subgroups — #875312

Order 512.

3316 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2562C211yesmaximal, characteristic, complemented
2C2×#2407C211yesmaximal, characteristic
3#16287C214yesmaximal, complemented
4#15660C214yesmaximal, complemented
5#15516C214yesmaximal, complemented
6#15238C211yesmaximal, characteristic, complemented
7#15229C211yesmaximal, characteristic, complemented
8#15195C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15150C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14698C211yesmaximal, characteristic, complemented
14#14571C214yesmaximal, complemented
15#14001C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2562—28no—
27#2407—28no—
28C2×#400C2212yes—
29C2×#397C2214yes—
30C2×#394C2214yes—
31C2×#394C2212yes—
32C2×#394C2212yes—
33C2×#392C2212yes—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#388C2214yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2212yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#1445C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1442C2214yes—
67#1441C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1438C2214yes—
75#1438C2214yes—
76#1437C2212yes—
77#1437C2214yes—
78#1436C2214yes—
79#1436C2214yes—
80#1436C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
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×D4C2312yes—
103C23×D4C2312yes—
104C23×D4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2312yes—
109C2×#125—24no—
110C2×#125—42no—
111C2×#125—42no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—42no—
118C2×C4×D4—42no—
119C2×C4×D4—42no—
120C2×C4×D4D418yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C42—42no—
152C22×C42—42no—
153C22×C42—42no—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161#400—28no—
162#397—48no—
163#394—28no—
164#394—28no—
165#394—216no—
166#392—28no—
167#391—24no—
168#391—24no—
169#391—42no—
170#391—42no—
171#391—42no—
172#390—24no—
173#390—24no—
174#390—42no—
175#390—42no—
176#390—42no—
177#388—28no—
178#388—28no—
179#388—48no—
180#386—28no—
181#386—28no—
182#386—48no—
183#385—28no—
184#384—42no—
185#384—42no—
186#380—24no—
187#380—24no—
188#380—24no—
189#380—24no—
190#380—24no—
191C4×C4⋊C4—24no—
192C4×C22⋊C4—42no—
193C4×C22⋊C4—42no—
194C4×C22⋊C4—42no—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C25C2411yescharacteristic
221C25C2412yes—
222C25C2411yescharacteristic
223C2×#41—416no—
224C2×#41—416no—
225C2×#41—416no—
226C2×#41—416no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41—416no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8#4114yes—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—28no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—41no—
251C22×D4—41no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—44no—
259C22×D4C2×D414yes—
260C22×D4#4114yes—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305#125—416no—
306C22⋊Q8—416no—
307#121—416no—
308C4×D4—416no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
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—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×D414yes—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
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—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4C2×D414yes—
390C2×C22⋊C4C2×D414yes—
391C2×C22⋊C4#4118yescomplemented
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
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—42no—
409C2×C42—42no—
410C2×C42—416no—
411C2×C42—44no—
412C2×C42C2×D414yes—
413#95—24no—
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—28no—
425#95—28no—
426#95—24no—
427#95—28no—
428#95—24no—
429#95—44no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—21no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—21no—
456C24—21no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—21no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—24no—
465C24—24no—
466C24—22no—
467C24C22×D412yes—
468C24C22×D412yes—
469C24C2×#4114yes—
470C24C2×#4114yes—
471C24C2511yescharacteristic
472#41—4128no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—416no—
497C2×D4—48no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—84no—
503C2×D4—88no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
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—21no—
523C22×C4—21no—
524C22×C4—21no—
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—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
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—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C2×#4114yes—
618C22×C4C2×#4114yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4H(5,𝔽2)14yes—
623C22×C4H(5,𝔽2)12yes—
624C22×C4H(5,𝔽2)12yes—
625C22×C4H(5,𝔽2)12yes—
626C22×C4H(5,𝔽2)12yes—
627C22×C42−1+414yes—
628C4⋊C4—44no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—88no—
639C4⋊C4—88no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—416no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—84no—
652C22⋊C4—88no—
653C22⋊C4—88no—
654C22⋊C4—88no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C42—28no—
659C42—48no—
660C42—44no—
661C42—44no—
662C42—44no—
663C42—44no—
664C42—84no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—28no—
686C23—22no—
687C23—22no—
688C23—28no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—41no—
704C23—41no—
705C23—42no—
706C23—41no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23—42no—
714C23—42no—
715C23—44no—
716C23—42no—
717C23—42no—
718C23—44no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—44no—
723C23—42no—
724C23—41no—
725C23—44no—
726C23—42no—
727C23—42no—
728C23—44no—
729C23—44no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23#53214yes—
734C23C23×D411yescharacteristic
735C23C22×#4112yes—
736C23C22×#4111yescharacteristic
737C23C22×#4111yescharacteristic
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×H(5,𝔽2)11yescharacteristic
741C23C2×H(5,𝔽2)11yescharacteristic
742C23C2×H(5,𝔽2)12yes—
743C23C2×2−1+412yes—
744C23#58512yes—
745Q8—416no—
746D4—416no—
747D4—432no—
748D4—416no—
749D4—816no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—432no—
778C2×C4—432no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
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—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—416no—
812C2×C4—416no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4#53414yes—
844C2×C4#53814yes—
845C2×C4#53814yes—
846C2×C4#54614yes—
847C2×C4#54614yes—
848C2×C4#55114yes—
849C2×C4H(3,𝔽4)14yes—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—44no—
854C22—44no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—42no—
863C22—42no—
864C22—44no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—44no—
869C22—42no—
870C22—48no—
871C22—42no—
872C22—48no—
873C22—82no—
874C22—84no—
875C22—82no—
876C22—82no—
877C22—84no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22C2×#53211yescharacteristic
884C22C2×#53411yescharacteristic
885C22#344911yescharacteristic
886C22C2×#53811yescharacteristic
887C22C2×#53811yescharacteristic
888C22C2×#54611yescharacteristic
889C22C2×#54611yescharacteristic
890C22C2×#55111yescharacteristic
891C22#348112yes—
892C22#348212yes—
893C22#349811yescharacteristic
894C22#349911yescharacteristic
895C22#350512yes—
896C22#350612yes—
897C22#351512yes—
898C22#351712yes—
899C22#351912yes—
900C22#352012yes—
901C22C2×H(3,𝔽4)11yescharacteristic
902C22#353612yes—
903C22#354112yes—
904C22#354212yes—
905C22#354812yes—
906C4—44no—
907C4—44no—
908C4—44no—
909C4—42no—
910C4—42no—
911C4—44no—
912C4—42no—
913C4—44no—
914C4—42no—
915C4—82no—
916C4—82no—
917C4—82no—
918C4—82no—
919C4—82no—
920C4—82no—
921C4#268418yes—
922C2—44no—
923C2—84no—
924C2—82no—
925C2#3503211yescharacteristic
926C2#3636211yescharacteristic
927C2#3637611yescharacteristic
928C2#3729611yescharacteristic
929C2#3808811yescharacteristic
930C2#3808911yescharacteristic
931C2#4014812yes—
932C2#4022112yes—
933C2#4560112yes—
934C2C2×#268411yescharacteristic
935C2#5937712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
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×#2562C2semidirect
3. #16287C2semidirect
4. #15660C2semidirect
5. #15516C2semidirect
6. #15238C2semidirect
7. #15229C2semidirect
8. #15195C2semidirect
9. #15182C2semidirect
10. #15150C2semidirect
11. #15130C2semidirect
12. #14702C2semidirect
13. #14698C2semidirect
14. #14571C2semidirect
15. #14001C2semidirect
16. #14000C2semidirect
17. #13937C2semidirect
18. #13937C2semidirect
19. C4×#386C2semidirect
391. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25622
C2×#24072
#162872
#156602
#155162
#152382
#152292
#151952
#151822
#151502
#151302
#147022
#146982
#145712
#140012
#140002
#139372
C4×#3862