Finite Group Databasebeta

← #649068

Subgroups — #649068

Order 512.

3734 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2500C211yesmaximal, characteristic, complemented
2C2×#2416C211yesmaximal, characteristic
3C2×#2352C211yesmaximal, characteristic, complemented
4C22×#384C211yesmaximal, characteristic, complemented
5#15643C214yesmaximal, complemented
6#15396C214yesmaximal, complemented
7#15244C211yesmaximal, characteristic, complemented
8#15231C211yesmaximal, characteristic, complemented
9#15195C211yesmaximal, characteristic, complemented
10#15130C211yesmaximal, characteristic, complemented
11#14719C214yesmaximal, complemented
12#14698C211yesmaximal, characteristic, complemented
13#14137C211yesmaximal, characteristic, complemented
14#14048C211yesmaximal, characteristic, complemented
15#14019C214yesmaximal, complemented
16#14001C211yesmaximal, characteristic, complemented
17#13881C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2214yes—
28C23×C42C2211yescharacteristic
29#2500—28no—
30#2416—28no—
31C2×#396C2212yes—
32C2×#394C2212yes—
33C2×#394C2214yes—
34C2×#394C2214yes—
35#2352—28no—
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#388C2212yes—
43C2×#388C2214yes—
44C2×#388C2214yes—
45C2×#387C2212yes—
46C2×#386C2212yes—
47C2×#386C2214yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2214yes—
51C2×#384—28no—
52C2×#384C2211yescharacteristic
53C2×#384C2214yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yes—
67C2×C4×C22⋊C4C2211yescharacteristic
68#1442C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1437C2212yes—
81#1437C2214yes—
82#1436C2214yes—
83#1436C2212yes—
84#1436C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×D4C2312yes—
96C23×D4C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102C24×C4C2312yes—
103C24×C4C2311yescharacteristic
104C2×#121—28no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—42no—
111C2×#121—48no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4D418yes—
115C2×#117—24no—
116C2×#117—24no—
117C2×#117—42no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—216no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4—48no—
126C22×C4⋊C4—48no—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C42—24no—
160C22×C42—24no—
161C22×C42—24no—
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170#396—28no—
171#394—216no—
172#394—28no—
173#394—48no—
174#390—24no—
175#390—24no—
176#390—24no—
177#390—24no—
178#390—42no—
179#389—24no—
180#388—216no—
181#388—28no—
182#388—48no—
183#387—28no—
184#386—28no—
185#386—28no—
186#386—216no—
187#386—28no—
188#386—48no—
189#384—24no—
190#384—24no—
191#384—216no—
192#384—24no—
193#384D418yescomplemented
194#382—24no—
195#382—24no—
196#382—42no—
197#380—24no—
198#380—24no—
199#380—24no—
200C4×C4⋊C4—24no—
201C4×C22⋊C4—24no—
202C4×C22⋊C4—28no—
203C4×C22⋊C4—24no—
204C4×C22⋊C4—24no—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C25C2412yes—
228C25C2411yescharacteristic
229C25C2411yescharacteristic
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—42no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4C2×D414yes—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—28no—
271C23×C4—28no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—44no—
275C23×C4—42no—
276C23×C4—44no—
277C23×C4—42no—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4#4118yes—
281C23×C4#4114yes—
282C23×C4#4114yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299#121—416no—
300#121—432no—
301#121—416no—
302C4×D4—232no—
303#117—416no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—416no—
336C2×C4⋊C4—416no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—464no—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2×D4116yes—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
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—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4C2×D414yes—
396C2×C22⋊C4C2×D414yes—
397C2×C42—232no—
398C2×C42—24no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—24no—
416C2×C42—42no—
417C2×C42—44no—
418C2×C42C2×D414yes—
419C2×C42C2×D414yes—
420C2×C42#4114yes—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—28no—
435#95—28no—
436#95—24no—
437#95—24no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—21no—
456C24—22no—
457C24—22no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—24no—
463C24—22no—
464C24—22no—
465C24—24no—
466C24—24no—
467C24—22no—
468C24—24no—
469C24—22no—
470C24C22×D412yes—
471C24C22×D412yes—
472C24C2×#4112yes—
473C24C2×#4112yes—
474C24C2×#4114yes—
475C24H(5,𝔽2)14yes—
476C24C2511yescharacteristic
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—88no—
497C2×D4—84no—
498C2×D4—88no—
499C22×C4—216no—
500C22×C4—216no—
501C22×C4—216no—
502C22×C4—216no—
503C22×C4—216no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—216no—
521C22×C4—28no—
522C22×C4—216no—
523C22×C4—28no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—416no—
591C22×C4—416no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—88no—
601C22×C4—88no—
602C22×C4#123116yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D414yes—
607C22×C4C22×D414yes—
608C22×C4C22×D412yes—
609C22×C4C22×D414yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4114yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4H(5,𝔽2)14yes—
621C22×C4H(5,𝔽2)12yes—
622C22×C42−1+414yes—
623C22×C42−1+412yes—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—416no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—416no—
631C4⋊C4—416no—
632C4⋊C4—416no—
633C4⋊C4—48no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—416no—
650C22⋊C4—48no—
651C22⋊C4—416no—
652C22⋊C4—88no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—88no—
656C42—216no—
657C42—28no—
658C42—28no—
659C42—28no—
660C42—48no—
661C42—44no—
662C42—44no—
663C42—84no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—41no—
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—44no—
713C23—42no—
714C23—44no—
715C23—44no—
716C23—42no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23C2×#12314yes—
729C23#53214yes—
730C23#53514yes—
731C23#55318yes—
732C23#55518yes—
733C23C23×D411yescharacteristic
734C23C23×D411yescharacteristic
735C23C22×#4111yescharacteristic
736C23C22×#4111yescharacteristic
737C23C22×#4111yescharacteristic
738C23C22×#4112yes—
739C23C2×H(5,𝔽2)12yes—
740C23C2×H(5,𝔽2)11yescharacteristic
741C23C2×H(5,𝔽2)12yes—
742C23C2×2−1+411yescharacteristic
743C23C2×2−1+412yes—
744D4—416no—
745D4—816no—
746D4—816no—
747D4—88no—
748C2×C4—264no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
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—232no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—28no—
778C2×C4—28no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—416no—
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—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
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—44no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—816no—
836C2×C4—816no—
837C2×C4C2×#12314yes—
838C2×C4C2×#12314yes—
839C2×C4#52514yes—
840C2×C4#53914yes—
841C2×C4D4214yes—
842C2×C4#54714yes—
843C2×C4#54818yes—
844C2×C4#54814yes—
845C2×C4#55318yes—
846C2×C4#55314yes—
847C22—24no—
848C22—24no—
849C22—28no—
850C22—24no—
851C22—24no—
852C22—28no—
853C22—24no—
854C22—28no—
855C22—24no—
856C22—28no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—84no—
871C22—82no—
872C22—82no—
873C22—84no—
874C22—82no—
875C22—84no—
876C22—82no—
877C22—82no—
878C22—84no—
879C22#250018yescomplemented
880C22C22×#12311yescharacteristic
881C22C2×#52511yescharacteristic
882C22C2×#53211yescharacteristic
883C22C2×#53511yescharacteristic
884C22C2×#53911yescharacteristic
885C22C2×D4211yescharacteristic
886C22C2×#54711yescharacteristic
887C22C2×#54812yes—
888C22C2×#54811yescharacteristic
889C22C2×#55312yes—
890C22C2×#55312yes—
891C22C2×#55311yescharacteristic
892C22C2×#55512yes—
893C22#348412yes—
894C22#349212yes—
895C22#349212yes—
896C22#349811yescharacteristic
897C22#349911yescharacteristic
898C22#351112yes—
899C22#351112yes—
900C22#351112yes—
901C22#354312yes—
902C22#354412yes—
903C4—24no—
904C4—28no—
905C4—28no—
906C4—44no—
907C4—44no—
908C4—42no—
909C4—42no—
910C4—42no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4—82no—
916C4—82no—
917C4—82no—
918C4#244318yes—
919C2—28no—
920C2—82no—
921C2—162no—
922C2C2×#244311yescharacteristic
923C2C2×#250011yescharacteristic
924C2#3553011yescharacteristic
925C2#3612211yescharacteristic
926C2#3618211yescharacteristic
927C2#3658112yes—
928C2#3767411yescharacteristic
929C2#3786311yescharacteristic
930C2#3973212yes—
931C2#5913512yes—
932C2#5930312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2500C2semidirect
3. C2×#2352C2semidirect
4. C22×#384C2semidirect
5. #15643C2semidirect
6. #15396C2semidirect
7. #15244C2semidirect
8. #15231C2semidirect
9. #15195C2semidirect
10. #15130C2semidirect
11. #14719C2semidirect
12. #14698C2semidirect
13. #14137C2semidirect
14. #14048C2semidirect
15. #14019C2semidirect
16. #14001C2semidirect
17. #13881C2semidirect
18. #13879C2semidirect
19. C4×#386C2semidirect
193. #384D4semidirect
879. C22#2500semidirect

Maximal subgroups

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

subgroupindex
C2×#25002
C2×#24162
C2×#23522
C22×#3842
#156432
#153962
#152442
#152312
#151952
#151302
#147192
#146982
#141372
#140482
#140192
#140012
#138812
#138792
C4×#3862