Finite Group Databasebeta

← #612831

Subgroups — #612831

Order 512.

4050 conjugacy classes of subgroups.

The subgroup lattice has 943 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2854C212yesmaximal, complemented
2C2×#2537C211yesmaximal, characteristic
3C2×#2422C212yesmaximal, complemented
4C2×C42×D4C211yesmaximal, characteristic, complemented
5#15132C212yesmaximal, complemented
6#15126C212yesmaximal, complemented
7#14761C214yesmaximal, complemented
8#14741C214yesmaximal, complemented
9#14712C211yesmaximal, characteristic, complemented
10#14697C212yesmaximal, complemented
11#13974C212yesmaximal, complemented
12#13970C212yesmaximal, complemented
13#13910C211yesmaximal, characteristic, complemented
14#13906C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13876C212yesmaximal, complemented
17C4×#390C211yesmaximal, characteristic, complemented
18C22×#123C2214yes—
19C22×#121C2212yes—
20C22×#121C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C42C2212yes—
26#2854—216no—
27#2537—28no—
28#2422—216no—
29C2×#397C2214yes—
30C2×#394C2214yes—
31C2×#394C2214yes—
32C2×#390C2212yes—
33C2×#390C2211yescharacteristic
34C2×#390C2212yes—
35C2×#390C2211yescharacteristic
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#388C2214yes—
42C2×#388C2214yes—
43C2×#386C2214yes—
44C2×#385C2214yes—
45C2×#384C2212yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C42×D4—28no—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64C2×C43C2211yescharacteristic
65#1444C2214yes—
66#1443C2214yes—
67#1442C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1438C2214yes—
74#1437C2212yes—
75#1437C2212yes—
76#1436C2214yes—
77#1436C2214yes—
78C4⋊#95C2212yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2212yes—
86C22⋊#95C2214yes—
87C23×D4C2311yescharacteristic
88C23×D4C2314yes—
89C23×D4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2312yes—
92C24×C4C2312yes—
93C24×C4C2312yes—
94C2×#123—216no—
95C2×#123—216no—
96C2×#123—48no—
97C2×#121—28no—
98C2×#121—28no—
99C2×#121—28no—
100C2×#121—28no—
101C2×#121—28no—
102C2×#121—44no—
103C2×C4×D4—24no—
104C2×C4×D4—24no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4D418yes—
114C2×C4×D4D418yescomplemented
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
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×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C42—28no—
145C22×C42—28no—
146C22×C42—44no—
147C22×C42C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#397—216no—
159#394—216no—
160#394—216no—
161#390—28no—
162#390—28no—
163#390—24no—
164#390D418yescomplemented
165#389—28no—
166#389—28no—
167#389—28no—
168#389—44no—
169#389—44no—
170#388—216no—
171#388—216no—
172#386—216no—
173#385—216no—
174#384—28no—
175#384—24no—
176#384—24no—
177#380—28no—
178#380—28no—
179#380—28no—
180#380—28no—
181#380—28no—
182#380—28no—
183C4×C4⋊C4—24no—
184C4×C4⋊C4—24no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—24no—
187C4×C22⋊C4—28no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—28no—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C43—24no—
211C25C2412yes—
212C25C2412yes—
213C22×D4—28no—
214C22×D4—28no—
215C22×D4—28no—
216C22×D4—28no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4—44no—
230C22×D4C2×D414yes—
231C22×D4C2×D414yes—
232C22×D4C2×D414yes—
233C22×D4#4114yes—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4C2×D418yes—
261C23×C4C2×D418yes—
262C23×C4C2414yes—
263C23×C4C2412yes—
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277#123—464no—
278#121—432no—
279#121—432no—
280C4×D4—232no—
281C4×D4—232no—
282C4×D4—232no—
283C4×D4—416no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4C2×D414yes—
325C2×C4⋊C4C2×D414yes—
326C2×C4⋊C4C2×D414yes—
327C2×C4⋊C4#4114yes—
328C2×C4⋊C4#4114yes—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
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—24no—
359C2×C22⋊C4—24no—
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⋊C4C2×D418yes—
368C2×C22⋊C4C2×D418yes—
369C2×C22⋊C4C2×D418yes—
370C2×C22⋊C4C2×D418yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—432no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—41no—
398C2×C42—41no—
399C2×C42C2×D414yes—
400C2×C42C2×D414yes—
401C2×C42C2×D414yes—
402C2×C42#4114yes—
403C2×C42#4114yes—
404C2×C42#4114yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—28no—
420#95—28no—
421#95—44no—
422#95—44no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24C22×D414yes—
450C24C22×D414yes—
451C24C22×D414yes—
452C24C2×#4114yes—
453C24C2511yescharacteristic
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—416no—
464C2×D4—416no—
465C2×D4—416no—
466C2×D4—416no—
467C2×D4—44no—
468C2×D4—44no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—88no—
472C2×D4—88no—
473C2×D4—88no—
474C2×D4#121116yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—216no—
532C22×C4—216no—
533C22×C4—216no—
534C22×C4—216no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
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—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4C22×D412yes—
579C22×C4C22×D414yes—
580C22×C4C22×D414yes—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C42−1+412yes—
607C22×C42−1+412yes—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—416no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—416no—
621C4⋊C4—84no—
622C4⋊C4—88no—
623C22⋊C4—216no—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—416no—
631C22⋊C4—416no—
632C22⋊C4—416no—
633C22⋊C4—416no—
634C22⋊C4—416no—
635C22⋊C4—416no—
636C22⋊C4—48no—
637C42—28no—
638C42—28no—
639C42—28no—
640C42—44no—
641C42—44no—
642C42—48no—
643C42—48no—
644C42—48no—
645C42—48no—
646C42—44no—
647C42#123116yescomplemented
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
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—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23C2×#12118yes—
718C23C23×D411yescharacteristic
719C23C23×D411yescharacteristic
720C23C23×D411yescharacteristic
721C23C22×#4111yescharacteristic
722C23C22×#4111yescharacteristic
723C23C22×#4111yescharacteristic
724C23C22×#4111yescharacteristic
725C23C22×#4111yescharacteristic
726C23C22×#4111yescharacteristic
727C23C2×H(5,𝔽2)11yescharacteristic
728C23C2×H(5,𝔽2)11yescharacteristic
729C23C2×2−1+411yescharacteristic
730C23C2×2−1+411yescharacteristic
731C23#58511yescharacteristic
732C23#58511yescharacteristic
733D4—232no—
734D4—416no—
735D4—832no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
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—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—432no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—816no—
828C2×C4C2×#12114yes—
829C2×C4C2×#12314yes—
830C2×C4C2×#12314yes—
831C2×C4C2×#12314yes—
832C2×C4#52514yes—
833C2×C4#52914yes—
834C2×C4#52914yes—
835C2×C4#53214yes—
836C2×C4#53214yes—
837C2×C4#53214yes—
838C2×C4#54214yes—
839C2×C4D4214yes—
840C2×C4D4214yes—
841C2×C4#54714yes—
842C2×C4#54714yes—
843C2×C4#54714yes—
844C2×C4#55314yes—
845C22—28no—
846C22—28no—
847C22—28no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22C22×#12111yescharacteristic
876C22C22×#12311yescharacteristic
877C22C2×#52511yescharacteristic
878C22C2×#52911yescharacteristic
879C22C2×#52911yescharacteristic
880C22C2×#53211yescharacteristic
881C22C2×#53211yescharacteristic
882C22C2×#53211yescharacteristic
883C22C2×#54211yescharacteristic
884C22#346011yescharacteristic
885C22#346111yescharacteristic
886C22C2×D4211yescharacteristic
887C22C2×D4211yescharacteristic
888C22C2×#54711yescharacteristic
889C22C2×#54711yescharacteristic
890C22C2×#54711yescharacteristic
891C22D4×#4111yescharacteristic
892C22D4×#4111yescharacteristic
893C22D4×#4111yescharacteristic
894C22C2×#55311yescharacteristic
895C22#347511yescharacteristic
896C22#348211yescharacteristic
897C22#348311yescharacteristic
898C22#348811yescharacteristic
899C22#348911yescharacteristic
900C22#349611yescharacteristic
901C22#349911yescharacteristic
902C22#350611yescharacteristic
903C22#351111yescharacteristic
904C22#351111yescharacteristic
905C22#351211yescharacteristic
906C22#351511yescharacteristic
907C22#351811yescharacteristic
908C22#351911yescharacteristic
909C22#352011yescharacteristic
910C4—24no—
911C4—24no—
912C4—24no—
913C4—44no—
914C4—44no—
915C4—42no—
916C4—44no—
917C4—44no—
918C4—42no—
919C4—44no—
920C4—82no—
921C4—84no—
922C4—84no—
923C4#242218yescomplemented
924C4#285418yescomplemented
925C2—48no—
926C2—84no—
927C2C2×#242211yescharacteristic
928C2#3492511yescharacteristic
929C2#3493211yescharacteristic
930C2#3517011yescharacteristic
931C2#3520711yescharacteristic
932C2#3525511yescharacteristic
933C2D4×#12111yescharacteristic
934C2#3610011yescharacteristic
935C2#3611411yescharacteristic
936C2#3612711yescharacteristic
937C2#3625911yescharacteristic
938C2#3641111yescharacteristic
939C2#3646411yescharacteristic
940C2#3646811yescharacteristic
941C2C2×#285411yescharacteristic
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
1. C2×#2854C2semidirect
3. C2×#2422C2semidirect
4. C2×C42×D4C2semidirect
5. #15132C2semidirect
6. #15126C2semidirect
7. #14761C2semidirect
8. #14741C2semidirect
9. #14712C2semidirect
10. #14697C2semidirect
11. #13974C2semidirect
12. #13970C2semidirect
13. #13910C2semidirect
14. #13906C2semidirect
15. #13906C2semidirect
16. #13876C2semidirect
17. C4×#390C2semidirect
114. C2×C4×D4D4semidirect
164. #390D4semidirect
647. C42#123semidirect
923. C4#2422semidirect
924. C4#2854semidirect

Maximal subgroups

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

subgroupindex
C2×#28542
C2×#25372
C2×#24222
C2×C42×D42
#151322
#151262
#147612
#147412
#147122
#146972
#139742
#139702
#139102
#139062
#138762
C4×#3902