Finite Group Databasebeta

← #649066

Subgroups — #649066

Order 512.

3352 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2417C211yesmaximal, characteristic
3C2×#2352C211yesmaximal, characteristic
4C22×#384C211yesmaximal, characteristic, complemented
5#15648C214yesmaximal, complemented
6#15388C214yesmaximal, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15231C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15150C211yesmaximal, characteristic, complemented
11#14776C214yesmaximal
12#14702C211yesmaximal, characteristic, complemented
13#14139C211yesmaximal, characteristic, complemented
14#14049C211yesmaximal, characteristic, complemented
15#14000C211yesmaximal, characteristic, complemented
16#13882C214yesmaximal, complemented
17#13881C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2214yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2499—28no—
29#2417—28no—
30C2×#398C2212yes—
31C2×#397C2214yes—
32C2×#397C2214yes—
33C2×#396C2212yes—
34#2352—28no—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#388C2212yes—
42C2×#387C2212yes—
43C2×#387C2214yes—
44C2×#387C2214yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#384—28no—
49C2×#384C2214yes—
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66#1445C2214yes—
67#1445C2214yes—
68#1445C2214yes—
69#1445C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1437C2212yes—
79#1436C2212yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2312yes—
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—42no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4D418yes—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—42no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—216no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—216no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4—48no—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42—24no—
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2312yes—
162#398—28no—
163#397—216no—
164#397—48no—
165#396—28no—
166#391—24no—
167#391—24no—
168#391—24no—
169#391—24no—
170#391—42no—
171#389—24no—
172#388—28no—
173#387—28no—
174#387—216no—
175#387—48no—
176#386—28no—
177#386—28no—
178#386—28no—
179#384—24no—
180#384—24no—
181#384—216no—
182#384—24no—
183#384D418yescomplemented
184#382—24no—
185#382—24no—
186#382—42no—
187#380—24no—
188#380—24no—
189#380—24no—
190#380—28no—
191C4×C4⋊C4—24no—
192C4×C22⋊C4—24no—
193C4×C22⋊C4—28no—
194C4×C22⋊C4—24no—
195C4×C22⋊C4—24no—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C25C2411yescharacteristic
225C25C2411yescharacteristic
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4C2×D414yes—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—28no—
257C23×C4—28no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4C2×D414yes—
265C23×C4C2×D414yes—
266C23×C4#4118yes—
267C23×C4#4114yes—
268C23×C4#4114yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C22⋊Q8—416no—
287C22⋊Q8—416no—
288C4×D4—232no—
289#117—416no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—28no—
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—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—416no—
332C2×C4⋊C4—464no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4C2×D414yes—
341C2×C4⋊C4C2×D4116yes—
342C2×C4⋊C4C2×D414yes—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
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—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4C2×D414yes—
372C2×C22⋊C4C2×D414yes—
373C2×C42—232no—
374C2×C42—24no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—24no—
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—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—42no—
393C2×C42—44no—
394C2×C42C2×D414yes—
395C2×C42C2×D414yes—
396C2×C42#4114yes—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—28no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—28no—
415#95—24no—
416#95—28no—
417#95—24no—
418#95—28no—
419#95—44no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C2×#4112yes—
444C24C2×#4112yes—
445C24C2×#4114yes—
446C242−1+414yes—
447C24C2511yescharacteristic
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—48no—
459C2×D4—48no—
460C22×C4—216no—
461C22×C4—216no—
462C22×C4—216no—
463C22×C4—216no—
464C22×C4—216no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—28no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—216no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—216no—
484C22×C4—28no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
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—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—416no—
559C22×C4—416no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—84no—
567C22×C4—84no—
568C22×C4—88no—
569C22×C4—88no—
570C22×C4#123116yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D412yes—
577C22×C4C22×D414yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4114yes—
583C22×C4C2×#4114yes—
584C22×C4C2×#4114yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)14yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C42−1+414yes—
591C22×C42−1+412yes—
592C4⋊C4—28no—
593C4⋊C4—28no—
594C4⋊C4—28no—
595C4⋊C4—232no—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—416no—
599C4⋊C4—416no—
600C4⋊C4—48no—
601C4⋊C4—44no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—416no—
607C4⋊C4—44no—
608C4⋊C4—84no—
609C22⋊C4—28no—
610C22⋊C4—28no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C42—216no—
621C42—28no—
622C42—28no—
623C42—28no—
624C42—48no—
625C42—44no—
626C42—44no—
627C42—84no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—24no—
632C23—22no—
633C23—22no—
634C23—24no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—41no—
654C23—41no—
655C23—42no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23C2×#12314yes—
670C23#53214yes—
671C23#53614yes—
672C23#55218yes—
673C23#55618yes—
674C23C23×D411yescharacteristic
675C23C23×D411yescharacteristic
676C23C22×#4111yescharacteristic
677C23C22×#4111yescharacteristic
678C23C22×#4111yescharacteristic
679C23C22×#4112yes—
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)12yes—
682C23C2×2−1+412yes—
683C23C2×2−1+411yescharacteristic
684C23C2×2−1+412yes—
685Q8—88no—
686D4—416no—
687C2×C4—264no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—232no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—416no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—816no—
782C2×C4—816no—
783C2×C4C2×#12314yes—
784C2×C4C2×#12314yes—
785C2×C4#52514yes—
786C2×C4#53914yes—
787C2×C4D4214yes—
788C2×C4#54618yes—
789C2×C4#54714yes—
790C2×C4#54814yes—
791C2×C4#55218yes—
792C2×C4#55314yes—
793C22—24no—
794C22—24no—
795C22—28no—
796C22—28no—
797C22—24no—
798C22—24no—
799C22—28no—
800C22—24no—
801C22—24no—
802C22—28no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22#249918yescomplemented
815C22C22×#12311yescharacteristic
816C22C2×#52511yescharacteristic
817C22C2×#53211yescharacteristic
818C22C2×#53611yescharacteristic
819C22C2×#53911yescharacteristic
820C22C2×D4211yescharacteristic
821C22C2×#54612yes—
822C22C2×#54711yescharacteristic
823C22C2×#54811yescharacteristic
824C22C2×#55212yes—
825C22C2×#55212yes—
826C22C2×#55311yescharacteristic
827C22C2×#55612yes—
828C22#348612yes—
829C22#349212yes—
830C22#349212yes—
831C22#349811yescharacteristic
832C22#349911yescharacteristic
833C22#350812yes—
834C22#350912yes—
835C22#351112yes—
836C22#355212yes—
837C22#355212yes—
838C4—28no—
839C4—28no—
840C4—24no—
841C4—44no—
842C4—44no—
843C4—42no—
844C4—42no—
845C4—42no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4#244318yes—
855C2—28no—
856C2—82no—
857C2C2×#244311yescharacteristic
858C2C2×#249911yescharacteristic
859C2#3553011yescharacteristic
860C2#3612111yescharacteristic
861C2#3616312yes—
862C2#3618111yescharacteristic
863C2#3767511yescharacteristic
864C2#3786211yescharacteristic
865C2#3947612yes—
866C2#5913412yes—
867C2#5930212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
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×#2499C2semidirect
4. C22×#384C2semidirect
5. #15648C2semidirect
6. #15388C2semidirect
7. #15240C2semidirect
8. #15231C2semidirect
9. #15182C2semidirect
10. #15150C2semidirect
12. #14702C2semidirect
13. #14139C2semidirect
14. #14049C2semidirect
15. #14000C2semidirect
16. #13882C2semidirect
17. #13881C2semidirect
18. #13879C2semidirect
183. #384D4semidirect
814. C22#2499semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#24172
C2×#23522
C22×#3842
#156482
#153882
#152402
#152312
#151822
#151502
#147762
#147022
#141392
#140492
#140002
#138822
#138812
#138792
C4×#3862