Finite Group Databasebeta

← #674188

Subgroups — #674188

Order 512.

3950 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C212yesmaximal, complemented
2C2×#2445C212yesmaximal
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×#127C211yesmaximal, characteristic
5#15300C214yesmaximal, complemented
6#15271C214yesmaximal, complemented
7#15138C212yesmaximal, complemented
8#15133C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#15129C212yesmaximal, complemented
11#14712C211yesmaximal, characteristic, complemented
12#13916C212yesmaximal, complemented
13#13906C211yesmaximal, characteristic, complemented
14#13906C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13872C212yesmaximal, complemented
17C4×#389C211yesmaximal, characteristic, complemented
18C22×#127C2211yescharacteristic
19C22×#123C2214yes—
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26#2486—216no—
27#2445—216no—
28C2×#398C2214yes—
29C2×#397C2214yes—
30C2×#394C2214yes—
31C2×#394C2214yes—
32D4×C4⋊C4—28no—
33C4×#127—28no—
34C2×#390C2211yescharacteristic
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#390C2212yes—
38C2×#390C2211yescharacteristic
39C2×#390C2212yes—
40C2×#390C2212yes—
41C2×#389C2211yescharacteristic
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#389C2212yes—
46C2×#389C2211yescharacteristic
47C2×#386C2214yes—
48C2×#385C2214yes—
49C2×#384C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#381C2214yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2212yes—
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C43C2211yescharacteristic
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1440C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1436C2212yes—
76#1436C2212yes—
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2212yes—
85C22⋊#95C2214yes—
86C4×#95C2212yes—
87C23×D4C2311yescharacteristic
88C23×D4C2312yes—
89C23×D4C2312yes—
90C23×D4C2311yescharacteristic
91C24×C4C2312yes—
92C24×C4C2312yes—
93C24×C4C2314yes—
94C2×#127—24no—
95C2×#127—24no—
96C2×#127D418yes—
97C2×#123—216no—
98C2×#123—216no—
99C2×#123—48no—
100C2×C4×D4—28no—
101C2×C4×D4—28no—
102C2×C4×D4—28no—
103C2×C4×D4—28no—
104C2×C4×D4—28no—
105C2×C4×D4—24no—
106C2×C4×D4—28no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—28no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—44no—
113C2×C4×D4—44no—
114C2×C4×D4D418yes—
115C22×C4⋊C4—28no—
116C22×C4⋊C4—28no—
117C22×C4⋊C4—44no—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158#398—216no—
159#397—216no—
160#394—216no—
161#394—216no—
162#390—24no—
163#390—28no—
164#390—28no—
165#390—28no—
166#390—24no—
167#390—28no—
168#390—28no—
169#389—28no—
170#389—28no—
171#389—28no—
172#389—24no—
173#389—44no—
174#389D418yescomplemented
175#386—216no—
176#385—216no—
177#384—24no—
178#384—24no—
179#384—24no—
180#381—216no—
181#380—28no—
182#380—28no—
183#380—28no—
184#380—28no—
185#380—44no—
186#380—44no—
187#380—44no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4—28no—
190C4×C4⋊C4—24no—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C43—24no—
210C25C2412yes—
211C25C2412yes—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—24no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—24no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4C2×D414yes—
235C22×D4C2×D418yes—
236C22×D4C2×D418yes—
237C22×D4C2×D414yes—
238C22×D4C2×D414yes—
239C22×D4#4114yes—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—28no—
247C23×C4—28no—
248C23×C4—28no—
249C23×C4—28no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4—44no—
260C23×C4C2×D418yes—
261C23×C4C2414yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276#127—232no—
277#123—464no—
278C4×D4—232no—
279C4×D4—432no—
280C4×D4—432no—
281C4×D4—432no—
282C4×D4—416no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—432no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4C2×D418yes—
337C2×C4⋊C4C2×D414yes—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
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—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—41no—
397C2×C42—41no—
398C2×C42C2×D414yes—
399C2×C42C2×D414yes—
400C2×C42C2×D414yes—
401C2×C42#4114yes—
402C2×C42#4114yes—
403C2×C42#4114yes—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—24no—
414#95—24no—
415#95—42no—
416#95—42no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95C2×D418yes—
422C24—22no—
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—
448C24C22×D414yes—
449C24C22×D414yes—
450C24C22×D414yes—
451C24C2×#4114yes—
452C24C2511yescharacteristic
453C2×D4—216no—
454C2×D4—216no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—216no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—216no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4#121116yes—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
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—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—216no—
524C22×C4—216no—
525C22×C4—216no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—416no—
562C22×C4—416no—
563C22×C4—416no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—416no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—88no—
577C22×C4—88no—
578C22×C4—88no—
579C22×C4C22×D412yes—
580C22×C4C22×D414yes—
581C22×C4C22×D414yes—
582C22×C4C22×D414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
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×C4H(5,𝔽2)12yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C42−1+412yes—
605C22×C42−1+412yes—
606C22×C42−1+412yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—216no—
611C4⋊C4—416no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—48no—
619C4⋊C4—416no—
620C4⋊C4—44no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—84no—
625C22⋊C4—216no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—416no—
631C22⋊C4—416no—
632C22⋊C4—416no—
633C22⋊C4—416no—
634C22⋊C4—48no—
635C22⋊C4—88no—
636C22⋊C4—88no—
637C22⋊C4—88no—
638C42—28no—
639C42—28no—
640C42—28no—
641C42—44no—
642C42—44no—
643C42—48no—
644C42—44no—
645C42—48no—
646C42#123116yescomplemented
647C23—24no—
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—42no—
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—
716C23C2×#12118yes—
717C23C23×D411yescharacteristic
718C23C23×D411yescharacteristic
719C23C23×D411yescharacteristic
720C23C22×#4111yescharacteristic
721C23C22×#4111yescharacteristic
722C23C22×#4111yescharacteristic
723C23C22×#4111yescharacteristic
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×2−1+411yescharacteristic
728C23C2×2−1+411yescharacteristic
729C23C2×2−1+411yescharacteristic
730C23#58511yescharacteristic
731C23#58511yescharacteristic
732D4—232no—
733D4—432no—
734D4—432no—
735D4—416no—
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—24no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—432no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4—832no—
826C2×C4—816no—
827C2×C4C2×#12114yes—
828C2×C4C2×#12314yes—
829C2×C4C2×#12314yes—
830C2×C4C2×#12314yes—
831C2×C4#53214yes—
832C2×C4#53614yes—
833C2×C4#54014yes—
834C2×C4D4214yes—
835C2×C4D4214yes—
836C2×C4#54614yes—
837C2×C4#54714yes—
838C2×C4#54714yes—
839C2×C4#54714yes—
840C2×C4#55014yes—
841C2×C4#55214yes—
842C2×C4#55214yes—
843C2×C4#55914yes—
844C22—28no—
845C22—28no—
846C22—28no—
847C22—44no—
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—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22C22×#12111yescharacteristic
875C22C22×#12311yescharacteristic
876C22C2×#53211yescharacteristic
877C22C2×#53611yescharacteristic
878C22C2×#54011yescharacteristic
879C22C2×D4211yescharacteristic
880C22C2×D4211yescharacteristic
881C22C2×#54611yescharacteristic
882C22C2×#54711yescharacteristic
883C22C2×#54711yescharacteristic
884C22C2×#54711yescharacteristic
885C22C2×#55011yescharacteristic
886C22D4×#4111yescharacteristic
887C22C2×#55211yescharacteristic
888C22C2×#55211yescharacteristic
889C22#347511yescharacteristic
890C22C2×#55911yescharacteristic
891C22#348811yescharacteristic
892C22#348911yescharacteristic
893C22#349611yescharacteristic
894C22#349611yescharacteristic
895C22#349711yescharacteristic
896C22#349911yescharacteristic
897C22#350611yescharacteristic
898C22#350711yescharacteristic
899C22#350711yescharacteristic
900C22#351111yescharacteristic
901C22#351111yescharacteristic
902C22#351211yescharacteristic
903C22#351911yescharacteristic
904C22#352011yescharacteristic
905C22#354711yescharacteristic
906C22#354711yescharacteristic
907C22#354811yescharacteristic
908C22#355011yescharacteristic
909C4—24no—
910C4—24no—
911C4—24no—
912C4—44no—
913C4—42no—
914C4—44no—
915C4—42no—
916C4—44no—
917C4—82no—
918C4—82no—
919C4—84no—
920C4—82no—
921C4—84no—
922C4#244518yescomplemented
923C4#248618yescomplemented
924C2—48no—
925C2—84no—
926C2C2×#244511yescharacteristic
927C2C2×#248611yescharacteristic
928C2#3551711yescharacteristic
929C2D4×#12111yescharacteristic
930C2#3612711yescharacteristic
931C2#3615311yescharacteristic
932C2#3627011yescharacteristic
933C2#3897511yescharacteristic
934C2#3934311yescharacteristic
935C2#3937811yescharacteristic
936C2#3947011yescharacteristic
937C2#5944211yescharacteristic
938C2#5944411yescharacteristic
939C2#5981511yescharacteristic
940C2#5982711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#127C22
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×#2486C2semidirect
3. C2×D4×C4⋊C4C2semidirect
5. #15300C2semidirect
6. #15271C2semidirect
7. #15138C2semidirect
8. #15133C2semidirect
9. #15129C2semidirect
10. #15129C2semidirect
11. #14712C2semidirect
12. #13916C2semidirect
13. #13906C2semidirect
14. #13906C2semidirect
15. #13906C2semidirect
16. #13872C2semidirect
17. C4×#389C2semidirect
174. #389D4semidirect
646. C42#123semidirect
922. C4#2445semidirect
923. C4#2486semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#24452
C2×D4×C4⋊C42
C2×C4×#1272
#153002
#152712
#151382
#151332
#151292
#147122
#139162
#139062
#138722
C4×#3892