Finite Group Databasebeta

← #2737469

Subgroups — #2737469

Order 512.

4286 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C212yesmaximal, complemented
2#17193C212yesmaximal, complemented
3#17094C214yesmaximal, complemented
4#17083C212yesmaximal, complemented
5#16255C214yesmaximal, complemented
6#16249C212yesmaximal, complemented
7#15195C211yesmaximal, characteristic, complemented
8#15181C212yesmaximal, complemented
9#15138C212yesmaximal, complemented
10#15130C212yesmaximal, complemented
11#15126C212yesmaximal, complemented
12#15123C212yesmaximal, complemented
13#14673C212yesmaximal, complemented
14#13902C211yesmaximal, characteristic, complemented
15C4×#392C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C22×#121C2212yes—
18C22×#121C2212yes—
19C22×#120C2214yes—
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic, complemented
22#2408—216no—
23C2×#397C2214yescomplemented
24C2×#394C2214yes—
25C2×#394C2214yescomplemented
26C2×#394C2214yescomplemented
27C2×#394C2214yescomplemented
28C2×#392C2211yescharacteristic
29C2×#392C2214yes—
30C2×#392C2214yescomplemented
31C2×#390C2212yes—
32C2×#390C2212yes—
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#389C2212yescomplemented
36C2×#384C2211yescharacteristic, complemented
37C2×#380C2212yes—
38C2×#380C2211yescharacteristic
39C2×#380C2212yescomplemented
40C2×#380C2212yescomplemented
41C2×#379C2212yes—
42C2×#379C2214yes—
43C2×#379C2212yes—
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2212yescomplemented
46#1444C2211yescharacteristic, complemented
47#1442C2214yescomplemented
48#1442C2212yescomplemented
49#1442C2212yescomplemented
50#1440C2214yescomplemented
51#1440C2214yescomplemented
52#1440C2214yescomplemented
53#1439C2211yescharacteristic
54#1439C2214yes—
55#1439C2212yes—
56#1439C2212yes—
57#1439C2214yescomplemented
58#1439C2214yescomplemented
59#1439C2214yescomplemented
60#1439C2214yescomplemented
61#1439C2212yescomplemented
62#1439C2214yescomplemented
63#1439C2214yescomplemented
64#1438C2212yes—
65#1438C2212yes—
66#1438C2214yes—
67#1438C2212yes—
68#1438C2214yescomplemented
69#1438C2214yescomplemented
70#1438C2214yescomplemented
71#1438C2211yescharacteristic, complemented
72C4⋊#95C2212yescomplemented
73C4⋊#95C2211yescharacteristic, complemented
74C4⋊#95C2212yescomplemented
75C4×#95C2211yescharacteristic, complemented
76C26C2312yes—
77C23×D4—44no—
78C23×D4—44no—
79C23×D4—42no—
80C23×D4—42no—
81C23×D4D418yescomplemented
82C23×D4C2312yes—
83C23×D4C2312yes—
84C23×D4C2311yescharacteristic
85C23×D4C2314yes—
86C23×D4C2314yes—
87C23×D4C2312yes—
88C24×C4C2312yes—
89C24×C4C2311yescharacteristic
90C2×#121—28no—
91C2×#121—28no—
92C2×#121—44no—
93C2×#121—44no—
94C2×#121—44no—
95C2×#121—44no—
96C2×#120—216no—
97C2×#120—48no—
98C2×#120—48no—
99C2×C4×D4—28no—
100C2×C4×D4—44no—
101C2×C4×D4—44no—
102C2×C4×D4—42no—
103C2×C4×D4—44no—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C22⋊C4C2312yes—
113C22×C22⋊C4C2314yes—
114C22×C22⋊C4C2314yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2311yescharacteristic
117C22×C22⋊C4C2312yes—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C42C2312yes—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136#397—48no—
137#394—216no—
138#394—48no—
139#394—48no—
140#394—48no—
141#392—216no—
142#392—24no—
143#392—48no—
144#390—28no—
145#390—28no—
146#390—44no—
147#390—44no—
148#389—44no—
149#384—42no—
150#380—28no—
151#380—42no—
152#380—44no—
153#380—44no—
154#379—216no—
155#379—28no—
156#379—44no—
157C4×C22⋊C4—42no—
158C4×C22⋊C4—44no—
159C2×#95C2314yes—
160C2×#95C2311yescharacteristic
161C2×#95C2312yes—
162C2×#95C2314yes—
163C2×#95C2312yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2311yescharacteristic
168C2×#95C2312yes—
169C2×#95C2311yescharacteristic
170C2×#95C2311yescharacteristic
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2312yes—
177C25—24no—
178C25—24no—
179C25—42no—
180C25—42no—
181C25—44no—
182C25—44no—
183C25—44no—
184C25—44no—
185C25—42no—
186C25—42no—
187C25C2×D418yes—
188C25C2414yes—
189C25C2412yes—
190C25C2411yescharacteristic
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—24no—
194C22×D4—24no—
195C22×D4—24no—
196C22×D4—28no—
197C22×D4—28no—
198C22×D4—28no—
199C22×D4—28no—
200C22×D4—22no—
201C22×D4—24no—
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—432no—
209C22×D4—416no—
210C22×D4—42no—
211C22×D4—42no—
212C22×D4—41no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4—42no—
216C22×D4—44no—
217C22×D4—44no—
218C22×D4—41no—
219C22×D4—44no—
220C22×D4—44no—
221C22×D4—44no—
222C22×D4—44no—
223C22×D4—44no—
224C22×D4—44no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—44no—
229C22×D4—416no—
230C22×D4—432no—
231C22×D4—416no—
232C22×D4C2×D418yes—
233C22×D4C2×D418yes—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4C2×D414yes—
246C23×C4C2414yes—
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2412yes—
250C23×C4C2414yes—
251C23×C4C2414yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258#121—432no—
259#121—432no—
260#120—464no—
261C4×D4—432no—
262C4×D4—416no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—41no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—44no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—44no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C22⋊C4—24no—
285C2×C22⋊C4—28no—
286C2×C22⋊C4—28no—
287C2×C22⋊C4—28no—
288C2×C22⋊C4—28no—
289C2×C22⋊C4—28no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—22no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—24no—
294C2×C22⋊C4—28no—
295C2×C22⋊C4—28no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—28no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—41no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—41no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4#4114yes—
347C2×C42—24no—
348C2×C42—24no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—24no—
354#95—28no—
355#95—22no—
356#95—24no—
357#95—28no—
358#95—24no—
359#95—42no—
360#95—41no—
361#95—41no—
362#95—41no—
363#95—42no—
364#95—42no—
365#95—42no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—21no—
380C24—22no—
381C24—24no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—22no—
389C24—24no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—24no—
395C24—24no—
396C24—24no—
397C24—22no—
398C24—22no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—22no—
404C24—22no—
405C24—24no—
406C24—24no—
407C24—22no—
408C24—216no—
409C24—416no—
410C24—48no—
411C24—416no—
412C24—48no—
413C24—48no—
414C24—416no—
415C24—48no—
416C24—84no—
417C24—84no—
418C24—88no—
419C24—88no—
420C24—84no—
421C24—88no—
422C24—88no—
423C24—84no—
424C24—88no—
425C24—84no—
426C24—88no—
427C24—88no—
428C24—88no—
429C24—88no—
430C24—84no—
431C24C22×D418yes—
432C24C22×D412yes—
433C24C2×#4112yes—
434C24H(5,𝔽2)14yes—
435C242−1+412yes—
436C24C2511yescharacteristic
437C2×D4—216no—
438C2×D4—216no—
439C2×D4—216no—
440C2×D4—216no—
441C2×D4—416no—
442C2×D4—48no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—44no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—44no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—44no—
453C2×D4—48no—
454C2×D4—416no—
455C2×D4—48no—
456C2×D4—4128no—
457C2×D4—48no—
458C2×D4—416no—
459C2×D4—416no—
460C2×D4—416no—
461C2×D4—416no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—88no—
467C2×D4—88no—
468C2×D4—88no—
469C2×D4—88no—
470C2×D4—88no—
471C2×D4—88no—
472C2×D4—88no—
473C2×D4—88no—
474C2×D4—88no—
475C2×D4—88no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—216no—
499C22×C4—28no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—44no—
541C22×C4—48no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4H(5,𝔽2)14yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C4H(5,𝔽2)14yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C4H(5,𝔽2)14yes—
559C22×C4H(5,𝔽2)12yes—
560C4⋊C4—48no—
561C4⋊C4—44no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—48no—
565C4⋊C4—84no—
566C4⋊C4—84no—
567C4⋊C4—88no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C22⋊C4—44no—
571C22⋊C4—48no—
572C22⋊C4—416no—
573C22⋊C4—416no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—416no—
577C22⋊C4—416no—
578C22⋊C4—416no—
579C22⋊C4—48no—
580C22⋊C4—88no—
581C22⋊C4—88no—
582C22⋊C4—88no—
583C22⋊C4—88no—
584C22⋊C4—88no—
585C22⋊C4—84no—
586C22⋊C4—88no—
587C22⋊C4—88no—
588C22⋊C4—88no—
589C42—48no—
590C42—44no—
591C42—44no—
592C23—24no—
593C23—22no—
594C23—24no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—28no—
605C23—28no—
606C23—28no—
607C23—28no—
608C23—28no—
609C23—28no—
610C23—24no—
611C23—28no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—41no—
619C23—42no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—42no—
628C23—432no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—44no—
637C23—42no—
638C23—44no—
639C23—42no—
640C23—44no—
641C23—44no—
642C23—42no—
643C23—42no—
644C23—44no—
645C23—44no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—42no—
653C23—44no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—42no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—42no—
668C23—44no—
669C23—44no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—42no—
674C23—44no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—42no—
679C23—42no—
680C23—44no—
681C23—44no—
682C23—42no—
683C23—42no—
684C23—44no—
685C23—832no—
686C23—816no—
687C23—832no—
688C23—816no—
689C23—816no—
690C23—816no—
691C23—816no—
692C23—832no—
693C23—832no—
694C23—816no—
695C23#54714yes—
696C23C23×D411yescharacteristic
697C23C22×#4111yescharacteristic
698C23C2×H(5,𝔽2)11yescharacteristic
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×H(5,𝔽2)12yes—
701C23C2×H(5,𝔽2)12yes—
702C23C2×H(5,𝔽2)12yes—
703C23C2×H(5,𝔽2)12yes—
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×2−1+411yescharacteristic
706C23#58511yescharacteristic
707D4—432no—
708D4—416no—
709D4—432no—
710D4—432no—
711D4—832no—
712D4—832no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—416no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—41no—
781C2×C4—816no—
782C2×C4#53418yes—
783C2×C4#53414yes—
784C2×C4#56014yes—
785C2×C4#56018yes—
786C2×C4H(3,𝔽4)14yes—
787C22—28no—
788C22—24no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—44no—
794C22—44no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22—48no—
800C22—48no—
801C22—48no—
802C22—48no—
803C22—44no—
804C22—44no—
805C22—44no—
806C22—48no—
807C22—48no—
808C22—44no—
809C22—48no—
810C22—44no—
811C22—44no—
812C22—864no—
813C22—82no—
814C22—84no—
815C22—82no—
816C22—82no—
817C22—84no—
818C22—82no—
819C22—82no—
820C22—84no—
821C22—82no—
822C22—84no—
823C22—84no—
824C22—82no—
825C22—82no—
826C22—84no—
827C22—84no—
828C22—84no—
829C22C2×#53412yes—
830C22C2×#53411yescharacteristic
831C22C2×#54711yescharacteristic
832C22#348412yes—
833C22#349611yescharacteristic
834C22#350511yescharacteristic
835C22#350811yescharacteristic
836C22#351912yes—
837C22#351912yes—
838C22C2×#56011yescharacteristic
839C22C2×#56012yes—
840C22C2×H(3,𝔽4)11yescharacteristic
841C22#353612yes—
842C22#353612yes—
843C22#353611yescharacteristic
844C22#353711yescharacteristic
845C22#353712yes—
846C22#354212yes—
847C22#354312yes—
848C22#354612yes—
849C22#354911yescharacteristic
850C22#354912yes—
851C22#356111yescharacteristic
852C4—42no—
853C4—44no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—81no—
858C4—82no—
859C4—84no—
860C4—82no—
861C4—84no—
862C4—84no—
863C4#281218yes—
864C2—44no—
865C2—84no—
866C2—88no—
867C2C2×#281211yescharacteristic
868C2#3891612yes—
869C2#3948611yescharacteristic
870C2#4242012yes—
871C2#4247511yescharacteristic
872C2#4564511yescharacteristic
873C2#4565512yes—
874C2#4633811yescharacteristic
875C2#5298112yes—
876C2#5298811yescharacteristic
877C2#5301511yescharacteristic
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×#2408C2semidirect
2. #17193C2semidirect
3. #17094C2semidirect
4. #17083C2semidirect
5. #16255C2semidirect
6. #16249C2semidirect
7. #15195C2semidirect
8. #15181C2semidirect
9. #15138C2semidirect
10. #15130C2semidirect
11. #15126C2semidirect
12. #15123C2semidirect
13. #14673C2semidirect
14. #13902C2semidirect
15. C4×#392C2semidirect
21. C22×C4×D4C22semidirect
23. C2×#397C22semidirect
25. C2×#394C22semidirect
26. C2×#394C22semidirect
27. C2×#394C22semidirect
30. C2×#392C22semidirect
35. C2×#389C22semidirect
36. C2×#384C22semidirect
39. C2×#380C22semidirect
40. C2×#380C22semidirect
45. C2×C4×C22⋊C4C22semidirect
46. #1444C22semidirect
47. #1442C22semidirect
48. #1442C22semidirect
49. #1442C22semidirect
50. #1440C22semidirect
51. #1440C22semidirect
52. #1440C22semidirect
57. #1439C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
61. #1439C22semidirect
62. #1439C22semidirect
63. #1439C22semidirect
68. #1438C22semidirect
69. #1438C22semidirect
70. #1438C22semidirect
71. #1438C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
75. C4×#95C22semidirect
81. C23×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
#171932
#170942
#170832
#162552
#162492
#151952
#151812
#151382
#151302
#151262
#151232
#146732
#139022
C4×#3922