Finite Group Databasebeta

← #875230

Subgroups — #875230

Order 512.

3258 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2494C211yesmaximal, characteristic, complemented
2C2×#2431C211yesmaximal, characteristic
3#16535C214yesmaximal, complemented
4#15634C214yesmaximal, complemented
5#15610C214yesmaximal, complemented
6#15244C211yesmaximal, characteristic, complemented
7#15237C211yesmaximal, characteristic, complemented
8#15226C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15140C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14708C211yesmaximal, characteristic, complemented
13#14700C211yesmaximal, characteristic, complemented
14#14523C214yesmaximal, complemented
15#14154C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#121C2211yescharacteristic
24#2494—28no—
25#2431—28no—
26C2×#401C2212yes—
27C2×#397C2212yes—
28C2×#394C2214yes—
29C2×#394C2214yes—
30C2×#392C2212yes—
31C2×#392C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2214yes—
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#388C2214yes—
52C2×#387C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C43C2211yescharacteristic
66#1443C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1440C2214yes—
70#1440C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1437C2214yes—
81#1437C2214yes—
82#1437C2214yes—
83#1437C2212yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88#1434C2212yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C22×#41—24no—
94C22×#41—24no—
95C22×#41—24no—
96C22×#41—42no—
97C22×#41—42no—
98C22×#41—42no—
99C22×#41—42no—
100C23×Q8C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C23×D4C2311yescharacteristic
103C23×D4C2312yes—
104C23×D4C2312yes—
105C23×D4C2312yes—
106C23×D4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C2×#127—24no—
110C2×#127—24no—
111C2×#127—42no—
112C2×#124—24no—
113C2×#124—24no—
114C2×#124—42no—
115C2×#121—24no—
116C2×#121—42no—
117C2×#121—42no—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155#401—28no—
156#397—28no—
157#394—216no—
158#394—48no—
159#392—28no—
160#392—28no—
161#391—24no—
162#391—24no—
163#391—42no—
164#391—42no—
165#391—42no—
166#390—24no—
167#390—24no—
168#390—42no—
169#390—42no—
170#390—42no—
171#390—42no—
172#390—42no—
173#390—42no—
174#390—42no—
175#390—48no—
176#389—24no—
177#389—24no—
178#388—28no—
179#388—28no—
180#388—48no—
181#387—28no—
182#386—28no—
183#386—28no—
184#384—42no—
185#382—24no—
186#382—42no—
187#380—24no—
188#380—24no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—42no—
191C4×C22⋊C4—42no—
192C4×C22⋊C4—42no—
193C4×C22⋊C4D418yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2312yes—
219C43—42no—
220C25C2412yes—
221C25C2411yescharacteristic
222C25C2412yes—
223C2×#41—416no—
224C2×#41—416no—
225C2×#41—416no—
226C2×#41—416no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41—416no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8#4114yes—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—24no—
250C22×D4—28no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4#4114yes—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4C2×D414yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303#127—416no—
304#124—416no—
305#121—416no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
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—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
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×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4C2×D414yes—
381C2×C22⋊C4C2×D414yes—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—24no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—44no—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—28no—
419#95—28no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95C2×D414yes—
431#95C2×D414yes—
432#95#4118yescomplemented
433C24—22no—
434C24—22no—
435C24—24no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—24no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—24no—
451C24—24no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—22no—
456C24—22no—
457C24—24no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—24no—
463C24—24no—
464C24C22×D412yes—
465C24C2×#4114yes—
466C24C2511yescharacteristic
467#41—4128no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—28no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—416no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—84no—
503C2×D4—88no—
504C2×D4—84no—
505C2×D4—88no—
506C2×D4—84no—
507C2×D4—84no—
508C2×D4—88no—
509C2×D4—88no—
510C2×D4—88no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
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—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4114yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4H(5,𝔽2)14yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C4H(5,𝔽2)12yes—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—84no—
627C4⋊C4—88no—
628C22⋊C4—28no—
629C22⋊C4—44no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—416no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—88no—
640C22⋊C4—88no—
641C22⋊C4—88no—
642C22⋊C4—88no—
643C22⋊C4—88no—
644C22⋊C4—84no—
645C22⋊C4—88no—
646C22⋊C4—88no—
647C42—28no—
648C42—28no—
649C42—48no—
650C42—48no—
651C42—44no—
652C42—44no—
653C42—44no—
654C42—44no—
655C42—84no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—28no—
665C23—22no—
666C23—22no—
667C23—28no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—41no—
676C23—42no—
677C23—44no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—44no—
683C23—44no—
684C23—42no—
685C23—44no—
686C23—44no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—41no—
694C23—44no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—44no—
699C23—42no—
700C23—44no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—42no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23C23×D411yescharacteristic
726C23C22×#4112yes—
727C23C22×#4111yescharacteristic
728C23C22×#4111yescharacteristic
729C23C2×H(5,𝔽2)11yescharacteristic
730C23C2×H(5,𝔽2)11yescharacteristic
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×H(5,𝔽2)11yescharacteristic
733C23C2×H(5,𝔽2)12yes—
734C23#58512yes—
735C23#58512yes—
736Q8—416no—
737D4—432no—
738D4—416no—
739D4—816no—
740D4—816no—
741D4—816no—
742D4—88no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—432no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
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—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—416no—
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—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4#53214yes—
832C2×C4#53514yes—
833C2×C4#53814yes—
834C2×C4#53814yes—
835C2×C4#54614yes—
836C2×C4#54614yes—
837C2×C4#55114yes—
838C2×C4#56014yes—
839C22—44no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—42no—
844C22—48no—
845C22—42no—
846C22—44no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—48no—
851C22—84no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—84no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—84no—
864C22—82no—
865C22—84no—
866C22—82no—
867C22—82no—
868C22—84no—
869C22—82no—
870C22—82no—
871C22—84no—
872C22C2×#53211yescharacteristic
873C22C2×#53511yescharacteristic
874C22#344911yescharacteristic
875C22C2×#53811yescharacteristic
876C22C2×#53811yescharacteristic
877C22C2×#54611yescharacteristic
878C22C2×#54611yescharacteristic
879C22C2×#55111yescharacteristic
880C22#348012yes—
881C22#348112yes—
882C22#349811yescharacteristic
883C22#350011yescharacteristic
884C22#350612yes—
885C22#351412yes—
886C22#351712yes—
887C22#351712yes—
888C22#351912yes—
889C22#352112yes—
890C22C2×#56011yescharacteristic
891C22#354212yes—
892C22#354612yes—
893C22#355112yes—
894C22#355812yes—
895C4—24no—
896C4—42no—
897C4—44no—
898C4—42no—
899C4—42no—
900C4—44no—
901C4—44no—
902C4—42no—
903C4—44no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4—82no—
908C4—82no—
909C4—82no—
910C4#268518yes—
911C2—84no—
912C2—82no—
913C2—162no—
914C2#3519111yescharacteristic
915C2#3636211yescharacteristic
916C2#3641911yescharacteristic
917C2#3730511yescharacteristic
918C2#3808911yescharacteristic
919C2#3894711yescharacteristic
920C2#3921812yes—
921C2#4014512yes—
922C2#4571612yes—
923C2C2×#268511yescharacteristic
924C2#5948312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2431C2
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×#2494C2semidirect
3. #16535C2semidirect
4. #15634C2semidirect
5. #15610C2semidirect
6. #15244C2semidirect
7. #15237C2semidirect
8. #15226C2semidirect
9. #15219C2semidirect
10. #15140C2semidirect
11. #15130C2semidirect
12. #14708C2semidirect
13. #14700C2semidirect
14. #14523C2semidirect
15. #14154C2semidirect
16. #14000C2semidirect
17. #13937C2semidirect
18. #13937C2semidirect
19. C4×#388C2semidirect
432. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#24942
C2×#24312
#165352
#156342
#156102
#152442
#152372
#152262
#152192
#151402
#151302
#147082
#147002
#145232
#141542
#140002
#139372
C4×#3882