Finite Group Databasebeta

← #674770

Subgroups — #674770

Order 512.

3902 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2537C211yesmaximal, characteristic
3C2×#2427C212yesmaximal, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×#124C211yesmaximal, characteristic, complemented
6#15577C214yesmaximal, complemented
7#15302C214yesmaximal, complemented
8#15220C212yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#15132C212yesmaximal, complemented
11#15126C212yesmaximal, complemented
12#14712C211yesmaximal, characteristic, complemented
13#14137C212yesmaximal, complemented
14#13970C212yesmaximal, complemented
15#13926C211yesmaximal, characteristic, complemented
16#13907C212yesmaximal, complemented
17C4×#390C211yesmaximal, characteristic, complemented
18C22×#124C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×#121C2212yes—
21C22×#121C2212yes—
22C22×C4×Q8C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2212yes—
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2212yes—
27#2538—28no—
28#2537—28no—
29#2427—216no—
30C2×#397C2214yes—
31C2×#396C2214yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34D4×C4⋊C4—28no—
35C4×#124—28no—
36C2×#391C2211yescharacteristic
37C2×#391C2212yes—
38C2×#390C2211yescharacteristic
39C2×#390C2212yes—
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#386C2214yes—
50C2×#386C2214yes—
51C2×#385C2214yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2214yes—
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2212yes—
65C2×C43C2211yescharacteristic
66#1443C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1438C2214yes—
77#1437C2212yes—
78#1437C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C22⋊#95C2214yes—
88C23×Q8C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2314yes—
91C23×D4C2311yescharacteristic
92C24×C4C2312yes—
93C24×C4C2312yes—
94C24×C4C2314yes—
95C2×#124—24no—
96C2×#124—24no—
97C2×#124D418yescomplemented
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—44no—
101C2×#121—28no—
102C2×#121—28no—
103C2×#121—28no—
104C2×#121—28no—
105C2×#121—28no—
106C2×#121—44no—
107C2×C4×Q8—24no—
108C2×C4×Q8—24no—
109C2×C4×Q8—24no—
110C2×C4×D4—28no—
111C2×C4×D4—28no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—44no—
118C2×C4×D4D418yes—
119C22×C4⋊C4—28no—
120C22×C4⋊C4—28no—
121C22×C4⋊C4—44no—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#397—216no—
162#396—216no—
163#394—216no—
164#394—216no—
165#391—28no—
166#391—24no—
167#390—24no—
168#390—24no—
169#390—28no—
170#390—24no—
171#389—28no—
172#389—28no—
173#389—28no—
174#389—44no—
175#389—44no—
176#388—28no—
177#388—28no—
178#386—216no—
179#386—48no—
180#385—216no—
181#384—24no—
182#384D418yescomplemented
183#382—24no—
184#380—28no—
185#380—28no—
186#380—28no—
187#380—28no—
188#380—216no—
189C4×C4⋊C4—24no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4—44no—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C43—24no—
214C25C2412yes—
215C25C2412yes—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8C2×D414yes—
223C22×D4—28no—
224C22×D4—28no—
225C22×D4—28no—
226C22×D4—28no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4C2×D414yes—
241C22×D4C2×D414yes—
242C22×D4#4114yes—
243C22×D4#4114yes—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—28no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—28no—
259C23×C4—28no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—44no—
263C23×C4—44no—
264C23×C4C2×D418yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2414yes—
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2414yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280#124—232no—
281C22⋊Q8—432no—
282#121—432no—
283#121—432no—
284C4×Q8—416no—
285C4×D4—232no—
286C4×D4—432no—
287C4×D4—416no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—432no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C2×D418yes—
330C2×C4⋊C4C2×D418yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D418yes—
333C2×C4⋊C4#4114yes—
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—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
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—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4C2×D418yes—
377C2×C22⋊C4C2×D418yes—
378C2×C22⋊C4C2×D418yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—41no—
401C2×C42—41no—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42#4114yes—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—44no—
421#95—42no—
422#95—42no—
423#95—44no—
424#95—44no—
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—
449C24—22no—
450C24—22no—
451C24C22×D414yes—
452C24C22×D414yes—
453C24C2×#4114yes—
454C24C2×#4114yes—
455C24C2511yescharacteristic
456C2×Q8—28no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—416no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—416no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—88no—
481C2×D4—88no—
482C2×D4—88no—
483C2×D4#121116yes—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—216no—
537C22×C4—216no—
538C22×C4—216no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—416no—
568C22×C4—416no—
569C22×C4—416no—
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×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—88no—
582C22×C4—88no—
583C22×C4—88no—
584C22×C4—88no—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D418yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C2×#4114yes—
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×C4H(5,𝔽2)12yes—
607C22×C42−1+412yes—
608C22×C42−1+412yes—
609C22×C42−1+412yes—
610C4⋊C4—28no—
611C4⋊C4—216no—
612C4⋊C4—28no—
613C4⋊C4—216no—
614C4⋊C4—48no—
615C4⋊C4—416no—
616C4⋊C4—416no—
617C4⋊C4—44no—
618C4⋊C4—48no—
619C4⋊C4—44no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—84no—
624C4⋊C4—88no—
625C22⋊C4—216no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—416no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—416no—
636C22⋊C4—416no—
637C22⋊C4—416no—
638C22⋊C4—48no—
639C22⋊C4—88no—
640C42—28no—
641C42—44no—
642C42—44no—
643C42—48no—
644C42—44no—
645C42—48no—
646C42—44no—
647C42—44no—
648C42#121116yes—
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—24no—
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—
717C23—42no—
718C23C2×#12118yes—
719C23C23×D411yescharacteristic
720C23C23×D411yescharacteristic
721C23C23×D411yescharacteristic
722C23C22×#4111yescharacteristic
723C23C22×#4111yescharacteristic
724C23C22×#4111yescharacteristic
725C23C22×#4111yescharacteristic
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×H(5,𝔽2)11yescharacteristic
728C23C2×H(5,𝔽2)11yescharacteristic
729C23C2×2−1+411yescharacteristic
730C23C2×2−1+411yescharacteristic
731C23C2×2−1+411yescharacteristic
732C23#58511yescharacteristic
733C23#58511yescharacteristic
734Q8—416no—
735D4—232no—
736D4—416no—
737D4—832no—
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—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—41no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—432no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—832no—
830C2×C4—816no—
831C2×C4C2×#12114yes—
832C2×C4C2×#12114yes—
833C2×C4C2×#12114yes—
834C2×C4C2×#12114yes—
835C2×C4#52914yes—
836C2×C4#53714yes—
837C2×C4#54214yes—
838C2×C4D4214yes—
839C2×C4#54614yes—
840C2×C4#54614yes—
841C2×C4#54714yes—
842C2×C4#54714yes—
843C2×C4#54814yes—
844C2×C4#54814yes—
845C2×C4#55314yes—
846C22—28no—
847C22—28no—
848C22—28no—
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—44no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22C22×#12111yescharacteristic
877C22C22×#12111yescharacteristic
878C22C2×#52911yescharacteristic
879C22C2×#53711yescharacteristic
880C22C2×#54211yescharacteristic
881C22C2×D4211yescharacteristic
882C22C2×#54611yescharacteristic
883C22C2×#54611yescharacteristic
884C22C2×#54711yescharacteristic
885C22C2×#54711yescharacteristic
886C22C2×#54811yescharacteristic
887C22C2×#54811yescharacteristic
888C22D4×#4111yescharacteristic
889C22D4×#4111yescharacteristic
890C22C2×#55311yescharacteristic
891C22#348111yescharacteristic
892C22#348211yescharacteristic
893C22#348811yescharacteristic
894C22#348911yescharacteristic
895C22#349611yescharacteristic
896C22#349711yescharacteristic
897C22#349811yescharacteristic
898C22#349911yescharacteristic
899C22#351111yescharacteristic
900C22#351211yescharacteristic
901C22#351411yescharacteristic
902C22#351511yescharacteristic
903C22#351511yescharacteristic
904C22#351811yescharacteristic
905C22#351911yescharacteristic
906C22#352011yescharacteristic
907C22#354411yescharacteristic
908C22#354611yescharacteristic
909C22#354711yescharacteristic
910C22#355211yescharacteristic
911C4—24no—
912C4—42no—
913C4—48no—
914C4—44no—
915C4—44no—
916C4—44no—
917C4—42no—
918C4—42no—
919C4—42no—
920C4—82no—
921C4—82no—
922C4—84no—
923C4—82no—
924C4#241618yes—
925C4#242718yescomplemented
926C2—48no—
927C2—84no—
928C2C2×#241611yescharacteristic
929C2C2×#242711yescharacteristic
930C2#3556411yescharacteristic
931C2#3611411yescharacteristic
932C2#3625811yescharacteristic
933C2#3625911yescharacteristic
934C2#3645311yescharacteristic
935C2#3890811yescharacteristic
936C2#3892211yescharacteristic
937C2#3919311yescharacteristic
938C2#3937711yescharacteristic
939C2#5941211yescharacteristic
940C2#5942111yescharacteristic
941C2#5965411yescharacteristic
942C2#5966011yescharacteristic
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×#2538C2semidirect
3. C2×#2427C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. C2×C4×#124C2semidirect
6. #15577C2semidirect
7. #15302C2semidirect
8. #15220C2semidirect
9. #15179C2semidirect
10. #15132C2semidirect
11. #15126C2semidirect
12. #14712C2semidirect
13. #14137C2semidirect
14. #13970C2semidirect
15. #13926C2semidirect
16. #13907C2semidirect
17. C4×#390C2semidirect
97. C2×#124D4semidirect
182. #384D4semidirect
925. C4#2427semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#25372
C2×#24272
C2×D4×C4⋊C42
C2×C4×#1242
#155772
#153022
#152202
#151792
#151322
#151262
#147122
#141372
#139702
#139262
#139072
C4×#3902