Finite Group Databasebeta

← #797453

Subgroups — #797453

Order 512.

4448 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2548C211yesmaximal, characteristic, complemented
2C2×#2431C212yesmaximal, complemented
3C2×#2448C212yesmaximal, complemented
4C2×#2341C211yesmaximal, characteristic, complemented
5#16810C212yesmaximal, complemented
6#15630C214yesmaximal, complemented
7#15493C214yesmaximal, complemented
8#15172C212yesmaximal, complemented
9#15148C211yesmaximal, characteristic, complemented
10#15142C211yesmaximal, characteristic, complemented
11#15124C211yesmaximal, characteristic, complemented
12#14977C212yesmaximal, complemented
13#14228C212yesmaximal, complemented
14#14154C212yesmaximal, complemented
15#13998C212yesmaximal, complemented
16C4×#399C211yesmaximal, characteristic, complemented
17#13817C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C22×#127C2212yes—
20C22×#127C2211yescharacteristic
21C22×#124C2212yes—
22C22×#121C2212yes—
23C22×C4×Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25#2548—28no—
26#2448—216no—
27#2431—216no—
28C2×#399C2211yescharacteristic
29C2×#399C2214yes—
30C2×#399C2212yes—
31C2×#397C2214yes—
32C2×#394C2214yes—
33C2×#392C2214yes—
34C2×#392C2214yes—
35C2×#392C2212yes—
36C2×#392C2212yes—
37C2×#392C2214yes—
38C2×#392C2212yes—
39C2×#392C2212yes—
40#2341—28no—
41C2×#391C2212yes—
42C2×#390C2212yes—
43C2×#390C2212yes—
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2212yes—
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2212yes—
52C2×#390C2214yes—
53C2×#390C2214yes—
54C2×#390C2214yes—
55C2×#389C2212yes—
56C2×#388C2214yes—
57C2×#388C2214yes—
58C2×#386C2214yes—
59C2×#386C2214yes—
60C2×#380C2212yes—
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2212yes—
64C2×C4×C4⋊C4C2212yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yes—
67C2×C4×C22⋊C4C2212yes—
68#1445C2211yescharacteristic
69#1445C2212yes—
70#1444C2211yescharacteristic
71#1439C2212yes—
72#1439C2214yes—
73#1439C2211yescharacteristic
74#1439C2212yes—
75#1439C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2212yes—
79#1438C2212yes—
80#1438C2214yes—
81#1437C2214yes—
82#1436C2214yes—
83C4⋊#95C2211yescharacteristic
84#1434C2212yes—
85C4×#95C2211yescharacteristic
86C4×#95C2212yes—
87C22×#41—24no—
88C22×#41—28no—
89C22×#41—24no—
90C22×#41—24no—
91C22×#41—44no—
92C23×Q8C2311yescharacteristic
93C23×D4C2312yes—
94C23×D4C2311yescharacteristic
95C23×D4C2312yes—
96C23×D4C2314yes—
97C23×D4C2312yes—
98C23×D4C2314yes—
99C23×D4C2314yes—
100C23×D4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×#127—28no—
104C2×#127—28no—
105C2×#127—24no—
106C2×#127—44no—
107C2×#127—44no—
108C2×#124—28no—
109C2×#124—28no—
110C2×#124—28no—
111C2×#121—28no—
112C2×#121—28no—
113C2×#121—44no—
114C2×C4×Q8—24no—
115C2×C4×Q8—28no—
116C2×C4×Q8—44no—
117C2×C4×Q8D418yescomplemented
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2314yes—
154C22×C42C2312yes—
155#399—216no—
156#399—24no—
157#399—44no—
158#397—216no—
159#394—216no—
160#392—216no—
161#392—216no—
162#392—28no—
163#392—48no—
164#392—44no—
165#392—44no—
166#392—44no—
167#391D4116yescomplemented
168#390—24no—
169#390—28no—
170#390—28no—
171#390—28no—
172#390—28no—
173#390—24no—
174#390—28no—
175#390—28no—
176#390—28no—
177#390—28no—
178#390—48no—
179#390—48no—
180#390—48no—
181#389—28no—
182#388—216no—
183#388—216no—
184#386—216no—
185#386—216no—
186#380—24no—
187#380—28no—
188C4×C4⋊C4—28no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—44no—
191C4×C22⋊C4—24no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4—28no—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2311yescharacteristic
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2311yescharacteristic
211C25C2414yes—
212C25C2411yescharacteristic
213C25C2412yes—
214C2×#41—232no—
215C2×#41—432no—
216C2×#41—432no—
217C2×#41—416no—
218C2×#41—416no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—24no—
222C22×Q8C2×D414yes—
223C22×Q8C2×D418yes—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—28no—
227C22×D4—28no—
228C22×D4—28no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—22no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—28no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—28no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—28no—
250C22×D4—24no—
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—42no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—42no—
270C22×D4—44no—
271C22×D4#4114yes—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—28no—
280C23×C4—44no—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2414yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296#127—432no—
297#127—416no—
298#124—432no—
299#121—432no—
300C4×Q8—416no—
301C4×Q8—416no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4C2×D414yes—
325C2×C4⋊C4C2×D418yes—
326C2×C4⋊C4C2×D418yes—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
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—28no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
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⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—28no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—28no—
395C2×C42—44no—
396C2×C42—44no—
397C2×C42—44no—
398C2×C42C2×D414yes—
399C2×C42C2×D418yes—
400C2×C42C2×D418yes—
401#95—22no—
402#95—22no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—28no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—44no—
414#95—42no—
415#95C2×D4116yes—
416#95C2×D4116yes—
417#95#4114yescomplemented
418C24—22no—
419C24—21no—
420C24—22no—
421C24—24no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—21no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—24no—
432C24—22no—
433C24—24no—
434C24—21no—
435C24—22no—
436C24—24no—
437C24—22no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24C2×#4114yes—
454C24C2×#4112yes—
455C24C2511yescharacteristic
456#41—4128no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—216no—
460C2×Q8—216no—
461C2×Q8#127116yes—
462C2×D4—216no—
463C2×D4—28no—
464C2×D4—216no—
465C2×D4—416no—
466C2×D4—416no—
467C2×D4—48no—
468C2×D4—416no—
469C2×D4—416no—
470C2×D4—416no—
471C2×D4—416no—
472C2×D4—416no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—416no—
477C2×D4—416no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—44no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—416no—
490C2×D4—48no—
491C2×D4—88no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C2×D4—88no—
497C2×D4—84no—
498C2×D4—88no—
499C2×D4—88no—
500C2×D4—84no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—88no—
504C2×D4—88no—
505C2×D4—88no—
506C2×D4—88no—
507C2×D4—88no—
508C2×D4—88no—
509C2×D4—88no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—216no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—28no—
549C22×C4—216no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—416no—
575C22×C4—416no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—48no—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D418yes—
584C22×C4C22×D414yes—
585C22×C4C22×D418yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D414yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C4H(5,𝔽2)14yes—
600C4⋊C4—28no—
601C4⋊C4—216no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—48no—
609C4⋊C4—88no—
610C22⋊C4—48no—
611C22⋊C4—44no—
612C22⋊C4—416no—
613C22⋊C4—416no—
614C22⋊C4—48no—
615C22⋊C4—416no—
616C22⋊C4—416no—
617C22⋊C4—48no—
618C22⋊C4—44no—
619C22⋊C4—48no—
620C22⋊C4—416no—
621C22⋊C4—88no—
622C22⋊C4—88no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C22⋊C4—88no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C22⋊C4—84no—
629C22⋊C4—88no—
630C42—28no—
631C42—216no—
632C42—48no—
633C42—48no—
634C42—44no—
635C42—48no—
636C42—88no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—28no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—28no—
646C23—24no—
647C23—42no—
648C23—41no—
649C23—42no—
650C23—41no—
651C23—44no—
652C23—42no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—44no—
657C23—42no—
658C23—41no—
659C23—42no—
660C23—44no—
661C23—41no—
662C23—42no—
663C23—42no—
664C23—41no—
665C23—44no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—44no—
670C23—42no—
671C23—44no—
672C23—42no—
673C23—42no—
674C23—44no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—44no—
679C23—44no—
680C23—42no—
681C23—42no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23C23×D411yescharacteristic
719C23C23×D412yes—
720C23C22×#4111yescharacteristic
721C23C22×#4111yescharacteristic
722C23C22×#4111yescharacteristic
723C23C2×H(5,𝔽2)12yes—
724C23C2×H(5,𝔽2)12yes—
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×H(5,𝔽2)11yescharacteristic
727C23#58511yescharacteristic
728C23#58512yes—
729Q8—232no—
730D4—432no—
731D4—416no—
732D4—832no—
733D4—816no—
734D4—832no—
735D4—832no—
736D4—816no—
737D4—816no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—432no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—416no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—44no—
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—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4#52514yes—
813C2×C4C2×#12718yes—
814C2×C4C2×#12714yes—
815C2×C4#53414yes—
816C2×C4#54618yes—
817C2×C4#54618yes—
818C2×C4#55018yes—
819C2×C4#55014yes—
820C22—44no—
821C22—42no—
822C22—42no—
823C22—44no—
824C22—42no—
825C22—44no—
826C22—44no—
827C22—48no—
828C22—44no—
829C22—48no—
830C22—84no—
831C22—82no—
832C22—84no—
833C22—81no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—81no—
838C22—81no—
839C22—82no—
840C22—81no—
841C22—82no—
842C22—84no—
843C22—84no—
844C22—84no—
845C22—84no—
846C22—84no—
847C22—84no—
848C22—84no—
849C22—84no—
850C22—84no—
851C22—84no—
852C22—84no—
853C22—84no—
854C22—84no—
855C22—84no—
856C22—84no—
857C22C2×#52511yescharacteristic
858C22C22×#12711yescharacteristic
859C22C2×#53411yescharacteristic
860C22C2×#54612yes—
861C22C2×#54612yes—
862C22C2×#55011yescharacteristic
863C22C2×#55012yes—
864C22#348011yescharacteristic
865C22#348111yescharacteristic
866C22#348711yescharacteristic
867C22#348712yes—
868C22#348811yescharacteristic
869C22#348812yes—
870C22#349811yescharacteristic
871C22#349812yes—
872C22#350612yes—
873C22#350811yescharacteristic
874C22#351312yes—
875C22#351411yescharacteristic
876C22#351412yes—
877C22#354312yes—
878C22#354612yes—
879C22#355812yes—
880C4—28no—
881C4—28no—
882C4—24no—
883C4—42no—
884C4—48no—
885C4—44no—
886C4—42no—
887C4—44no—
888C4—42no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—81no—
893C4#253918yes—
894C2—82no—
895C2—84no—
896C2—164no—
897C2C2×#253911yescharacteristic
898C2#3584411yescharacteristic
899C2#3606611yescharacteristic
900C2#3649311yescharacteristic
901C2#3659211yescharacteristic
902C2#3913511yescharacteristic
903C2#4296911yescharacteristic
904C2#4495712yes—
905C2#4501812yes—
906C2#5904612yes—
907C2#5904912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2548C2semidirect
2. C2×#2431C2semidirect
3. C2×#2448C2semidirect
4. C2×#2341C2semidirect
5. #16810C2semidirect
6. #15630C2semidirect
7. #15493C2semidirect
8. #15172C2semidirect
9. #15148C2semidirect
10. #15142C2semidirect
11. #15124C2semidirect
12. #14977C2semidirect
13. #14228C2semidirect
14. #14154C2semidirect
15. #13998C2semidirect
16. C4×#399C2semidirect
17. #13817C2semidirect
117. C2×C4×Q8D4semidirect
167. #391D4semidirect
417. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25482
C2×#24312
C2×#24482
C2×#23412
#168102
#156302
#154932
#151722
#151482
#151422
#151242
#149772
#142282
#141542
#139982
C4×#3992
#138172