Finite Group Databasebeta

← #2736865

Subgroups — #2736865

Order 512.

3156 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic, complemented
2C2×#2422C211yesmaximal, characteristic, complemented
3#17146C214yesmaximal, complemented
4#17101C214yesmaximal, complemented
5#16986C212yesmaximal, complemented
6#16261C212yesmaximal, complemented
7#16250C212yesmaximal, complemented
8#15197C211yesmaximal, characteristic, complemented
9#15181C212yesmaximal, complemented
10#15135C211yesmaximal, characteristic, complemented
11#15131C212yesmaximal, complemented
12#15129C211yesmaximal, characteristic, complemented
13#15126C212yesmaximal, complemented
14#15123C212yesmaximal, complemented
15#14658C212yesmaximal, complemented
16#13920C211yesmaximal, characteristic, complemented
17C4×#392C211yesmaximal, characteristic, complemented
18C22×#123C2212yes—
19C22×#121C2211yescharacteristic
20C22×#121C2212yes—
21C22×#121C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2211yescharacteristic
25#2537—28no—
26#2422—28no—
27C2×#399C2212yes—
28C2×#397C2212yes—
29C2×#396C2214yes—
30C2×#394C2214yes—
31C2×#394C2212yes—
32C2×#394C2214yes—
33C2×#394C2212yes—
34C2×#392C2211yescharacteristic
35C2×#392C2214yes—
36C2×#390C2211yescharacteristic
37C2×#390C2212yes—
38C2×#389C2211yescharacteristic
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#385C2212yes—
42C2×#384C2211yescharacteristic
43C2×#384C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×C4×C22⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2212yes—
53#1445C2212yes—
54#1444C2212yes—
55#1444C2211yescharacteristic
56#1442C2214yes—
57#1442C2214yes—
58#1441C2212yes—
59#1441C2214yes—
60#1441C2214yes—
61#1441C2212yes—
62#1441C2212yes—
63#1440C2214yes—
64#1440C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2212yes—
69#1439C2211yescharacteristic
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1438C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1438C2211yescharacteristic
78#1438C2212yes—
79#1438C2214yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C4×#95C2211yescharacteristic
85C23×D4C2311yescharacteristic
86C23×D4C2311yescharacteristic
87C23×D4C2312yes—
88C23×D4C2312yes—
89C23×D4C2314yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2312yes—
93C2×#123—28no—
94C2×#123—28no—
95C2×#123—44no—
96C2×#121—24no—
97C2×#121—28no—
98C2×#121—28no—
99C2×#121—48no—
100C2×#121—44no—
101C2×#121—44no—
102C2×#121—44no—
103C2×C4×D4—24no—
104C2×C4×D4—44no—
105C2×C4×D4—44no—
106C2×C4×D4—44no—
107C2×C4×D4—44no—
108C2×C4×D4—44no—
109C2×C4×D4D418yescomplemented
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2311yescharacteristic
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C42C2312yes—
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146#399—44no—
147#397—28no—
148#396—48no—
149#394—28no—
150#394—216no—
151#394—44no—
152#394—48no—
153#392—24no—
154#392—48no—
155#390—24no—
156#390—44no—
157#389—24no—
158#389—44no—
159#389—44no—
160#385—28no—
161#384—24no—
162#384—24no—
163#380—28no—
164#380—24no—
165#380—28no—
166#380—44no—
167#380—44no—
168#380—44no—
169#380—44no—
170C4×C22⋊C4—24no—
171C4×C22⋊C4—44no—
172C2×#95C2311yescharacteristic
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2314yes—
176C2×#95C2311yescharacteristic
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2311yescharacteristic
180C2×#95C2311yescharacteristic
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C25C2412yes—
194C25C2411yescharacteristic
195C25C2412yes—
196C22×D4—24no—
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—28no—
200C22×D4—24no—
201C22×D4—24no—
202C22×D4—28no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4—24no—
206C22×D4—24no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—24no—
211C22×D4—42no—
212C22×D4—42no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4—42no—
216C22×D4—44no—
217C22×D4—44no—
218C22×D4—44no—
219C22×D4—44no—
220C22×D4—42no—
221C22×D4—44no—
222C22×D4—44no—
223C22×D4—44no—
224C22×D4C2×D414yes—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—22no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—44no—
240C23×C4—44no—
241C23×C4C2×D418yes—
242C23×C4C2414yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2411yescharacteristic
246C23×C4C2412yes—
247C23×C4C2414yes—
248C23×C4C2412yes—
249C23×C4C2411yescharacteristic
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256#123—432no—
257#121—432no—
258#121—416no—
259#121—432no—
260C4×D4—416no—
261C4×D4—416no—
262C4×D4—432no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4C2×D414yes—
300C2×C22⋊C4—22no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—28no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
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—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4C2×D418yes—
354C2×C22⋊C4#4114yes—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42C2×D414yes—
362#95—22no—
363#95—22no—
364#95—28no—
365#95—24no—
366#95—24no—
367#95—22no—
368#95—22no—
369#95—24no—
370#95—24no—
371#95—44no—
372#95—42no—
373#95—42no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—42no—
383C24—21no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—21no—
388C24—21no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24—24no—
401C24—24no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—24no—
407C24—24no—
408C24—22no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—22no—
417C24C22×D414yes—
418C24C2×#4112yes—
419C24H(5,𝔽2)14yes—
420C24C2511yescharacteristic
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—48no—
429C2×D4—44no—
430C2×D4—48no—
431C2×D4—48no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—416no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—416no—
439C2×D4—44no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4—84no—
443C2×D4—88no—
444C2×D4—88no—
445C2×D4—88no—
446C2×D4—88no—
447C2×D4—88no—
448C2×D4—88no—
449C2×D4—88no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—216no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—48no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—44no—
524C22×C4—48no—
525C22×C4—44no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—88no—
535C22×C4—88no—
536C22×C4C22×D412yes—
537C22×C4C22×D414yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4H(5,𝔽2)12yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)14yes—
545C22×C4H(5,𝔽2)14yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C42−1+414yes—
548C22×C42−1+412yes—
549C4⋊C4—28no—
550C4⋊C4—48no—
551C4⋊C4—44no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—48no—
556C4⋊C4—44no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—84no—
560C4⋊C4—84no—
561C4⋊C4—88no—
562C4⋊C4—88no—
563C22⋊C4—28no—
564C22⋊C4—48no—
565C22⋊C4—44no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—416no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—416no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—88no—
578C22⋊C4—88no—
579C22⋊C4—88no—
580C22⋊C4—88no—
581C22⋊C4—88no—
582C42—28no—
583C42—44no—
584C42—48no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—42no—
605C23—41no—
606C23—42no—
607C23—41no—
608C23—41no—
609C23—42no—
610C23—42no—
611C23—41no—
612C23—41no—
613C23—42no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—44no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—44no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—44no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—44no—
633C23—44no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—44no—
638C23—42no—
639C23—44no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—44no—
646C23—42no—
647C23—44no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—44no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—44no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23C23×D411yescharacteristic
667C23C22×#4111yescharacteristic
668C23C2×H(5,𝔽2)12yes—
669C23C2×H(5,𝔽2)12yes—
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×H(5,𝔽2)11yescharacteristic
672C23C2×H(5,𝔽2)12yes—
673C23C2×H(5,𝔽2)11yescharacteristic
674C23C2×2−1+411yescharacteristic
675C23C2×2−1+412yes—
676C23#58511yescharacteristic
677D4—416no—
678D4—432no—
679D4—416no—
680D4—832no—
681D4—816no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—816no—
759C2×C4—816no—
760C2×C4—88no—
761C2×C4#53414yes—
762C2×C4#53514yes—
763C2×C4#53714yes—
764C2×C4#54614yes—
765C2×C4#56018yes—
766C2×C4#56218yes—
767C22—44no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—42no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—42no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—82no—
790C22—82no—
791C22—84no—
792C22—84no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—84no—
797C22—82no—
798C22—81no—
799C22—81no—
800C22—82no—
801C22—82no—
802C22—84no—
803C22—81no—
804C22C2×#53411yescharacteristic
805C22C2×#53511yescharacteristic
806C22C2×#53711yescharacteristic
807C22C2×#54611yescharacteristic
808C22#348411yescharacteristic
809C22#348811yescharacteristic
810C22#349911yescharacteristic
811C22#350611yescharacteristic
812C22#351111yescharacteristic
813C22#351912yes—
814C22#352012yes—
815C22C2×#56012yes—
816C22C2×#56212yes—
817C22#353612yes—
818C22#353712yes—
819C22#353712yes—
820C22#354112yes—
821C22#354212yes—
822C22#354412yes—
823C22#354711yescharacteristic
824C22#354812yes—
825C22#354812yes—
826C22#354911yescharacteristic
827C4—24no—
828C4—42no—
829C4—44no—
830C4—42no—
831C4—42no—
832C4—44no—
833C4—81no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—84no—
838C4—84no—
839C4—82no—
840C4#281318yes—
841C2—84no—
842C2—82no—
843C2—84no—
844C2C2×#281311yescharacteristic
845C2#3890411yescharacteristic
846C2#3895111yescharacteristic
847C2#3946911yescharacteristic
848C2#4242811yescharacteristic
849C2#4248011yescharacteristic
850C2#4291611yescharacteristic
851C2#4564612yes—
852C2#4567612yes—
853C2#5295712yes—
854C2#5310112yes—
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×#2537C2semidirect
2. C2×#2422C2semidirect
3. #17146C2semidirect
4. #17101C2semidirect
5. #16986C2semidirect
6. #16261C2semidirect
7. #16250C2semidirect
8. #15197C2semidirect
9. #15181C2semidirect
10. #15135C2semidirect
11. #15131C2semidirect
12. #15129C2semidirect
13. #15126C2semidirect
14. #15123C2semidirect
15. #14658C2semidirect
16. #13920C2semidirect
17. C4×#392C2semidirect
109. C2×C4×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#24222
#171462
#171012
#169862
#162612
#162502
#151972
#151812
#151352
#151312
#151292
#151262
#151232
#146582
#139202
C4×#3922