Finite Group Databasebeta

← #705297

Subgroups — #705297

Order 512.

3340 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2513C211yesmaximal, characteristic, complemented
2C2×#2366C211yesmaximal, characteristic, complemented
3#16287C214yesmaximal, complemented
4#15423C214yesmaximal, complemented
5#15418C214yesmaximal, complemented
6#15244C211yesmaximal, characteristic, complemented
7#15142C211yesmaximal, characteristic
8#15140C211yesmaximal, characteristic, complemented
9#15127C211yesmaximal, characteristic, complemented
10#14795C214yesmaximal, complemented
11#14272C211yesmaximal, characteristic, complemented
12#14051C211yesmaximal, characteristic, complemented
13#14025C211yesmaximal, characteristic, complemented
14#14025C211yesmaximal, characteristic, complemented
15#14001C211yesmaximal, characteristic, complemented
16#14001C211yesmaximal, characteristic, complemented
17#13941C211yesmaximal, characteristic, complemented
18#13846C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C22×#127C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#127C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2212yes—
26#2513—28no—
27C2×#397C2212yes—
28C2×#397C2212yes—
29C2×#394C2214yes—
30C2×#394C2214yes—
31C2×#392C2214yes—
32C2×#392C2214yes—
33#2366—28no—
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2212yes—
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#388C2214yes—
52C2×#388C2214yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#386C2214yes—
56C2×#386C2214yes—
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×#376C2211yescharacteristic
65#1445C2212yes—
66#1443C2212yes—
67#1442C2212yes—
68#1442C2214yes—
69#1441C2212yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86#1434C2214yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C4×#95C2211yescharacteristic
90C4×#95C2211yescharacteristic
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2312yes—
98C23×D4C2314yes—
99C23×D4C2314yes—
100C24×C4C2312yes—
101C24×C4C2312yes—
102C2×#127—24no—
103C2×#127—24no—
104C2×#127—24no—
105C2×#127—24no—
106C2×#127—24no—
107C2×#127—24no—
108C2×#127—42no—
109C2×#127—42no—
110C2×#127—42no—
111C2×C4×D4—28no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—42no—
117C2×C4×D4—42no—
118C2×C4×D4—48no—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158#397—28no—
159#397—28no—
160#394—48no—
161#394—48no—
162#392—48no—
163#392—48no—
164#390—24no—
165#390—24no—
166#390—28no—
167#390—24no—
168#390—24no—
169#390—24no—
170#390—24no—
171#390—24no—
172#390—24no—
173#390—24no—
174#390—42no—
175#390—42no—
176#390—42no—
177#390—42no—
178#389—24no—
179#388—28no—
180#388—28no—
181#388—48no—
182#388—48no—
183#386—28no—
184#386—28no—
185#386—48no—
186#386—48no—
187#384—42no—
188#382—24no—
189#382—24no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—42no—
193C4×C4⋊C4D418yescomplemented
194#376—42no—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C25C2412yes—
219C25C2412yes—
220C25C2412yes—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—28no—
226C22×D4—28no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—24no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—28no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—28no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—28no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4#4114yes—
265C22×D4#4114yes—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292#127—232no—
293#127—416no—
294#127—416no—
295C4×D4—416no—
296C4×D4—416no—
297C4×D4—432no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
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—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4#4114yes—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
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×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—28no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—44no—
396C2×C42C2×D414yes—
397C2×C42C2×D414yes—
398C2×C42C2×D414yes—
399C2×C42#4114yes—
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—24no—
409#95—24no—
410#95—28no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95C2×D414yes—
422#95C2×D414yes—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—22no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—24no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24C2×#4114yes—
455C24C2×#4114yes—
456C24C2511yescharacteristic
457C2×D4—216no—
458C2×D4—216no—
459C2×D4—28no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—416no—
466C2×D4—416no—
467C2×D4—48no—
468C2×D4—416no—
469C2×D4—416no—
470C2×D4—416no—
471C2×D4—416no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—84no—
489C2×D4—84no—
490C2×D4—88no—
491C2×D4—88no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C2×D4—88no—
497C2×D4—88no—
498C2×D4—88no—
499C2×D4—88no—
500C2×D4—88no—
501C2×D4—88no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
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—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
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—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—88no—
581C22×C4—88no—
582C22×C4—88no—
583C22×C4—88no—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4H(5,𝔽2)14yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C4H(5,𝔽2)14yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)12yes—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—84no—
611C4⋊C4—88no—
612C22⋊C4—416no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—416no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C22⋊C4—88no—
631C22⋊C4—88no—
632C42—28no—
633C42—28no—
634C42—28no—
635C42—28no—
636C42—48no—
637C42—44no—
638C42—44no—
639C42—44no—
640C42—84no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23C23×D411yescharacteristic
711C23C22×#4111yescharacteristic
712C23C22×#4111yescharacteristic
713C23C22×#4111yescharacteristic
714C23C22×#4111yescharacteristic
715C23C2×H(5,𝔽2)12yes—
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)12yes—
719C23C2×H(5,𝔽2)12yes—
720C23#58512yes—
721D4—432no—
722D4—416no—
723D4—416no—
724D4—816no—
725D4—832no—
726D4—832no—
727D4—88no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—816no—
811C2×C4—816no—
812C2×C4#52514yes—
813C2×C4#52914yes—
814C2×C4#53514yes—
815C2×C4#53814yes—
816C2×C4#54614yes—
817C2×C4#55014yes—
818C2×C4#55114yes—
819C2×C4#55314yes—
820C22—48no—
821C22—48no—
822C22—44no—
823C22—44no—
824C22—48no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—48no—
830C22—84no—
831C22—84no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—84no—
839C22—82no—
840C22—82no—
841C22—84no—
842C22—84no—
843C22—84no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—84no—
853C22C2×#52511yescharacteristic
854C22C2×#52911yescharacteristic
855C22C2×#53511yescharacteristic
856C22#344911yescharacteristic
857C22C2×#53811yescharacteristic
858C22C2×#54611yescharacteristic
859C22C2×#55011yescharacteristic
860C22C2×#55111yescharacteristic
861C22C2×#55311yescharacteristic
862C22#349811yescharacteristic
863C22#349811yescharacteristic
864C22#350612yes—
865C22#350812yes—
866C22#351312yes—
867C22#351312yes—
868C22#351712yes—
869C22#351912yes—
870C22#351912yes—
871C22#351912yes—
872C22#354212yes—
873C22#354312yes—
874C22#354912yes—
875C22#355812yes—
876C4—24no—
877C4—44no—
878C4—42no—
879C4—42no—
880C4—44no—
881C4—44no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—44no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4#246718yes—
892C2—84no—
893C2—84no—
894C2—162no—
895C2C2×#246711yescharacteristic
896C2#3523311yescharacteristic
897C2#3553711yescharacteristic
898C2#3586512yes—
899C2#3808911yescharacteristic
900C2#3895311yescharacteristic
901C2#3973911yescharacteristic
902C2#3974511yescharacteristic
903C2#4253212yes—
904C2#4495912yes—
905C2#4503812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#15142C2
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×#2513C2semidirect
2. C2×#2366C2semidirect
3. #16287C2semidirect
4. #15423C2semidirect
5. #15418C2semidirect
6. #15244C2semidirect
8. #15140C2semidirect
9. #15127C2semidirect
10. #14795C2semidirect
11. #14272C2semidirect
12. #14051C2semidirect
13. #14025C2semidirect
14. #14025C2semidirect
15. #14001C2semidirect
16. #14001C2semidirect
17. #13941C2semidirect
18. #13846C2semidirect
19. #13785C2semidirect
193. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25132
C2×#23662
#162872
#154232
#154182
#152442
#151422
#151402
#151272
#147952
#142722
#140512
#140252
#140012
#139412
#138462
#137852