Finite Group Databasebeta

← #674762

Subgroups — #674762

Order 512.

3066 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2447C212yesmaximal
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3C2×C4×#124C211yesmaximal, characteristic
4#15915C214yesmaximal, complemented
5#15398C214yesmaximal, complemented
6#15221C212yesmaximal, complemented
7#15186C212yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#15132C212yesmaximal, complemented
10#14712C211yesmaximal, characteristic, complemented
11#14130C212yesmaximal, complemented
12#13926C211yesmaximal, characteristic, complemented
13#13926C211yesmaximal, characteristic, complemented
14#13916C212yesmaximal
15#13906C211yesmaximal, characteristic
16#13904C212yesmaximal, complemented
17C4×#389C211yesmaximal, characteristic, complemented
18C22×#124C2211yescharacteristic
19C22×C4×Q8C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23#2447—216no—
24C2×#397C2214yes—
25C2×#397C2214yes—
26D4×C4⋊C4—28no—
27C4×#124—28no—
28C2×#391C2211yescharacteristic
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#390C2212yes—
32C2×#390C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#385C2214yes—
42C2×#385C2214yes—
43C2×#384C2211yescharacteristic
44C2×#384C2211yescharacteristic
45C2×#382C2211yescharacteristic
46C2×#381C2214yes—
47C2×#381C2214yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C43C2211yescharacteristic
57#1445C2214yes—
58#1445C2214yes—
59#1444C2214yes—
60#1443C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1439C2214yes—
70#1436C2212yes—
71#1436C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C22⋊#95C2214yes—
85C4×#95C2212yes—
86C23×Q8C2311yescharacteristic
87C23×D4C2311yescharacteristic
88C24×C4C2312yes—
89C24×C4C2314yes—
90C2×#124—24no—
91C2×#124—24no—
92C2×#124D418yes—
93C2×C4×Q8—24no—
94C2×C4×Q8—24no—
95C2×C4×Q8—24no—
96C2×C4×D4—28no—
97C2×C4×D4—28no—
98C2×C4×D4—28no—
99C2×C4×D4—24no—
100C2×C4×D4—24no—
101C2×C4×D4D418yes—
102C22×C4⋊C4—28no—
103C22×C4⋊C4—28no—
104C22×C4⋊C4—44no—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C42C2312yes—
131C22×C42C2312yes—
132C22×C42C2311yescharacteristic
133C22×C42C2312yes—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140#397—216no—
141#397—216no—
142#391—28no—
143#391—28no—
144#391—24no—
145#390—28no—
146#390—24no—
147#389—28no—
148#389—24no—
149#389—24no—
150#389—28no—
151#389—44no—
152#389—44no—
153#388—28no—
154#388—28no—
155#385—216no—
156#385—216no—
157#384—24no—
158#384—24no—
159#382—24no—
160#381—216no—
161#381—48no—
162#380—28no—
163#380—28no—
164#380—44no—
165C4×C4⋊C4—24no—
166C4×C4⋊C4—28no—
167C4×C4⋊C4—24no—
168C4×C22⋊C4—28no—
169C4×C22⋊C4—28no—
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C43—24no—
197C25C2412yes—
198C22×Q8—22no—
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8—22no—
204C22×Q8C2×D414yes—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4C2×D414yes—
210C22×D4C2×D414yes—
211C22×D4#4114yes—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—28no—
219C23×C4—28no—
220C23×C4—28no—
221C23×C4—28no—
222C23×C4—44no—
223C23×C4—44no—
224C23×C4—44no—
225C23×C4C2×D418yes—
226C23×C4C2414yes—
227C23×C4C2412yes—
228C23×C4C2412yes—
229C23×C4C2412yes—
230C23×C4C2414yes—
231C23×C4C2411yescharacteristic
232C23×C4C2411yescharacteristic
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2411yescharacteristic
238C23×C4C2411yescharacteristic
239C23×C4C2411yescharacteristic
240C23×C4C2411yescharacteristic
241C23×C4C2411yescharacteristic
242#124—232no—
243C4×Q8—416no—
244C4×D4—232no—
245C4×D4—432no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—28no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—28no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—432no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4C2×D414yes—
296C2×C4⋊C4#4114yes—
297C2×C4⋊C4#4114yes—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—28no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4C2×D418yes—
320C2×C22⋊C4C2×D418yes—
321C2×C22⋊C4C2×D418yes—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—24no—
325C2×C42—24no—
326C2×C42—24no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—41no—
347C2×C42—41no—
348C2×C42C2×D414yes—
349C2×C42C2×D414yes—
350C2×C42#4114yes—
351C2×C42#4114yes—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—28no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—28no—
364#95—28no—
365#95—24no—
366#95—28no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—28no—
371#95—24no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378C24—22no—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24C22×D414yes—
391C24C22×D414yes—
392C24C2×#4114yes—
393C24C2511yescharacteristic
394C2×Q8—28no—
395C2×Q8—28no—
396C2×Q8—28no—
397C2×Q8—44no—
398C2×Q8—44no—
399C2×Q8—44no—
400C2×Q8—44no—
401C2×D4—28no—
402C2×D4—28no—
403C2×D4—28no—
404C2×D4—28no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4#121116yes—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—216no—
461C22×C4—216no—
462C22×C4—216no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—416no—
499C22×C4—416no—
500C22×C4—416no—
501C22×C4—48no—
502C22×C4—48no—
503C22×C4—48no—
504C22×C4—48no—
505C22×C4—416no—
506C22×C4—88no—
507C22×C4—88no—
508C22×C4—88no—
509C22×C4C22×D414yes—
510C22×C4C22×D412yes—
511C22×C4C22×D414yes—
512C22×C4C22×D412yes—
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C2×#4114yes—
518C22×C4C2×#4114yes—
519C22×C4C2×#4112yes—
520C22×C4C2×#4112yes—
521C22×C4C2×#4112yes—
522C22×C4C2×#4112yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4H(5,𝔽2)12yes—
529C22×C4H(5,𝔽2)12yes—
530C22×C42−1+412yes—
531C22×C42−1+412yes—
532C22×C42−1+412yes—
533C22×C42−1+412yes—
534C4⋊C4—28no—
535C4⋊C4—28no—
536C4⋊C4—28no—
537C4⋊C4—48no—
538C4⋊C4—48no—
539C4⋊C4—416no—
540C4⋊C4—48no—
541C4⋊C4—48no—
542C4⋊C4—48no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4—48no—
546C4⋊C4—44no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—84no—
550C4⋊C4—88no—
551C22⋊C4—216no—
552C22⋊C4—216no—
553C22⋊C4—216no—
554C22⋊C4—416no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—416no—
558C22⋊C4—88no—
559C42—28no—
560C42—44no—
561C42—44no—
562C42—48no—
563C42—48no—
564C42—44no—
565C42—44no—
566C42—44no—
567C42—48no—
568C42#123116yes—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23C2×#12118yes—
604C23C23×D411yescharacteristic
605C23C23×D411yescharacteristic
606C23C22×#4111yescharacteristic
607C23C22×#4111yescharacteristic
608C23C22×#4111yescharacteristic
609C23C22×#4111yescharacteristic
610C23C22×#4111yescharacteristic
611C23C2×H(5,𝔽2)11yescharacteristic
612C23C2×H(5,𝔽2)11yescharacteristic
613C23C2×2−1+411yescharacteristic
614C23C2×2−1+411yescharacteristic
615C23C2×2−1+411yescharacteristic
616C23C2×2−1+411yescharacteristic
617C23#58511yescharacteristic
618C23#58511yescharacteristic
619Q8—416no—
620D4—232no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—432no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
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—44no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—832no—
720C2×C4C2×#12114yes—
721C2×C4C2×#12314yes—
722C2×C4C2×#12314yes—
723C2×C4C2×#12314yes—
724C2×C4#52914yes—
725C2×C4#53614yes—
726C2×C4#54214yes—
727C2×C4#54614yes—
728C2×C4#54714yes—
729C2×C4#54714yes—
730C2×C4#54714yes—
731C2×C4#55214yes—
732C2×C4#55214yes—
733C2×C4#55614yes—
734C2×C4#55914yes—
735C22—28no—
736C22—28no—
737C22—28no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22C22×#12111yescharacteristic
751C22C22×#12311yescharacteristic
752C22C2×#52911yescharacteristic
753C22C2×#53611yescharacteristic
754C22C2×#54211yescharacteristic
755C22C2×#54611yescharacteristic
756C22C2×#54711yescharacteristic
757C22C2×#54711yescharacteristic
758C22C2×#54711yescharacteristic
759C22D4×#4111yescharacteristic
760C22D4×#4111yescharacteristic
761C22C2×#55211yescharacteristic
762C22C2×#55211yescharacteristic
763C22C2×#55611yescharacteristic
764C22C2×#55911yescharacteristic
765C22#348111yescharacteristic
766C22#348211yescharacteristic
767C22#348811yescharacteristic
768C22#348911yescharacteristic
769C22#349811yescharacteristic
770C22#349911yescharacteristic
771C22#350611yescharacteristic
772C22#350711yescharacteristic
773C22#351111yescharacteristic
774C22#351211yescharacteristic
775C22#351411yescharacteristic
776C22#351511yescharacteristic
777C22#351511yescharacteristic
778C22#351811yescharacteristic
779C22#352211yescharacteristic
780C22#352311yescharacteristic
781C22#354411yescharacteristic
782C22#355211yescharacteristic
783C22#355411yescharacteristic
784C22#355511yescharacteristic
785C4—24no—
786C4—42no—
787C4—44no—
788C4—44no—
789C4—42no—
790C4—44no—
791C4—42no—
792C4—44no—
793C4—42no—
794C4—84no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—84no—
799C4#244718yescomplemented
800C4#248618yes—
801C2—48no—
802C2C2×#244711yescharacteristic
803C2C2×#248611yescharacteristic
804C2#3551711yescharacteristic
805C2#3611411yescharacteristic
806C2#3625811yescharacteristic
807C2#3625911yescharacteristic
808C2#3629911yescharacteristic
809C2#3891111yescharacteristic
810C2#3892111yescharacteristic
811C2#3897711yescharacteristic
812C2#3937711yescharacteristic
813C2#5942811yescharacteristic
814C2#5943611yescharacteristic
815C2#5945011yescharacteristic
816C2#5964111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #15915C2semidirect
5. #15398C2semidirect
6. #15221C2semidirect
7. #15186C2semidirect
8. #15132C2semidirect
9. #15132C2semidirect
10. #14712C2semidirect
11. #14130C2semidirect
12. #13926C2semidirect
13. #13926C2semidirect
16. #13904C2semidirect
17. C4×#389C2semidirect
799. C4#2447semidirect

Maximal subgroups

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

subgroupindex
C2×#24472
C2×D4×C4⋊C42
C2×C4×#1242
#159152
#153982
#152212
#151862
#151322
#147122
#141302
#139262
#139162
#139062
#139042
C4×#3892