Finite Group Databasebeta

← #674884

Subgroups — #674884

Order 512.

3090 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2442C212yesmaximal, complemented
2C2×D4×C4⋊C4C211yesmaximal, characteristic
3C2×C4×#125C211yesmaximal, characteristic, complemented
4#15787C214yesmaximal, complemented
5#15441C214yesmaximal, complemented
6#15220C212yesmaximal, complemented
7#15220C212yesmaximal, complemented
8#15156C212yesmaximal, complemented
9#15133C212yesmaximal, complemented
10#14712C211yesmaximal, characteristic, complemented
11#14018C212yesmaximal
12#13911C211yesmaximal, characteristic, complemented
13#13910C211yesmaximal, characteristic, complemented
14#13907C212yesmaximal, complemented
15#13906C212yesmaximal
16#13906C211yesmaximal, characteristic
17C4×#390C211yesmaximal, characteristic
18C22×#125C2211yescharacteristic
19C22×C4×D4C2212yes—
20C22×C4×D4C2211yescharacteristic
21C23×C4⋊C4C2212yes—
22#2442—216no—
23C2×#400C2214yes—
24C2×#398C2214yes—
25D4×C4⋊C4—28no—
26C4×#125—28no—
27C2×#390C2212yes—
28C2×#390C2211yescharacteristic
29C2×#390C2211yescharacteristic
30C2×#389C2212yes—
31C2×#389C2211yescharacteristic
32C2×#389C2212yes—
33C2×#389C2211yescharacteristic
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#387C2212yes—
39C2×#387C2212yes—
40C2×#385C2214yes—
41C2×#385C2214yes—
42C2×#384C2211yescharacteristic
43C2×#384C2211yescharacteristic
44C2×#384C2212yes—
45C2×#382C2212yes—
46C2×#382C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2214yes—
50C2×#380C2214yes—
51C2×#380C2212yes—
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C43C2211yescharacteristic
60#1444C2214yes—
61#1443C2214yes—
62#1443C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1437C2212yes—
74#1437C2212yes—
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C22⋊#95C2214yes—
86C23×D4C2311yescharacteristic
87C24×C4C2312yes—
88C24×C4C2314yes—
89C2×#125—24no—
90C2×#125—24no—
91C2×#125D418yescomplemented
92C2×C4×D4—28no—
93C2×C4×D4—24no—
94C2×C4×D4—28no—
95C2×C4×D4—24no—
96C2×C4×D4—44no—
97C2×C4×D4Q818yes—
98C22×C4⋊C4—28no—
99C22×C4⋊C4—28no—
100C22×C4⋊C4—28no—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C42C2311yescharacteristic
131C22×C42C2312yes—
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2312yes—
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2312yes—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140#400—216no—
141#398—216no—
142#390—24no—
143#390—24no—
144#390—28no—
145#389—24no—
146#389—24no—
147#389—28no—
148#389—28no—
149#389—28no—
150#389—44no—
151#389—44no—
152#389—44no—
153#387—28no—
154#387—28no—
155#385—216no—
156#385—216no—
157#384—24no—
158#384—24no—
159#384—44no—
160#382—24no—
161#382—28no—
162#380—28no—
163#380—216no—
164#380—28no—
165#380—48no—
166#380—44no—
167C4×C4⋊C4—28no—
168C4×C4⋊C4—28no—
169C4×C4⋊C4—24no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4D418yes—
172C4×C22⋊C4—28no—
173C4×C22⋊C4—44no—
174C2×#95C2312yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C43—24no—
198C25C2412yes—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4—22no—
203C22×D4C2×Q814yes—
204C22×D4#4114yes—
205C22×D4#4114yes—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—28no—
213C23×C4—28no—
214C23×C4—28no—
215C23×C4—28no—
216C23×C4—44no—
217C23×C4—44no—
218C23×C4—44no—
219C23×C4C2×Q818yes—
220C23×C4C2414yes—
221C23×C4C2412yes—
222C23×C4C2412yes—
223C23×C4C2412yes—
224C23×C4C2414yes—
225C23×C4C2411yescharacteristic
226C23×C4C2412yes—
227C23×C4C2412yes—
228C23×C4C2411yescharacteristic
229C23×C4C2412yes—
230C23×C4C2411yescharacteristic
231C23×C4C2411yescharacteristic
232C23×C4C2412yes—
233C23×C4C2411yescharacteristic
234C23×C4C2411yescharacteristic
235C23×C4C2411yescharacteristic
236#125—232no—
237C4×D4—232no—
238C4×D4—432no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—28no—
252C2×C4⋊C4—28no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—28no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—28no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—432no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4C2×D414yes—
296C2×C4⋊C4C2×D418yes—
297C2×C4⋊C4C2×D418yes—
298C2×C4⋊C4C2×D414yes—
299C2×C4⋊C4C2×D414yes—
300C2×C4⋊C4C2×D414yes—
301C2×C4⋊C4C2×Q814yes—
302C2×C4⋊C4#4114yes—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4C2×Q818yes—
327C2×C42—22no—
328C2×C42—24no—
329C2×C42—22no—
330C2×C42—24no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—24no—
342C2×C42—22no—
343C2×C42—24no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—41no—
351C2×C42—41no—
352C2×C42C2×D418yes—
353C2×C42C2×D414yes—
354C2×C42C2×D414yes—
355C2×C42C2×Q814yes—
356C2×C42#4114yes—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—28no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—24no—
371#95—28no—
372#95—44no—
373#95—42no—
374#95—42no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95C2×D418yes—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24C22×Q814yes—
393C24C2×#4114yes—
394C24C2×#4114yes—
395C24C2511yescharacteristic
396C2×D4—28no—
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—28no—
400C2×D4—28no—
401C2×D4—28no—
402C2×D4#125116yescomplemented
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—216no—
454C22×C4—216no—
455C22×C4—216no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—416no—
492C22×C4—416no—
493C22×C4—416no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—416no—
499C22×C4—88no—
500C22×C4—88no—
501C22×C4—88no—
502C22×C4C22×D412yes—
503C22×C4C22×D414yes—
504C22×C4C22×D414yes—
505C22×C4C22×D412yes—
506C22×C4C22×D414yes—
507C22×C4C22×D414yes—
508C22×C4C22×D412yes—
509C22×C4C22×D412yes—
510C22×C4C22×D412yes—
511C22×C4C22×D412yes—
512C22×C4C22×Q814yes—
513C22×C4C22×Q812yes—
514C22×C4C22×Q812yes—
515C22×C4C22×Q812yes—
516C22×C4C2×#4114yes—
517C22×C4C2×#4112yes—
518C22×C4C2×#4112yes—
519C22×C4C2×#4112yes—
520C22×C4C2×#4112yes—
521C22×C4C2×#4112yes—
522C22×C4C2×#4112yes—
523C22×C4H(5,𝔽2)12yes—
524C22×C4H(5,𝔽2)12yes—
525C22×C4H(5,𝔽2)12yes—
526C22×C42−1+412yes—
527C22×C42−1+412yes—
528C22×C42−1+412yes—
529C4⋊C4—216no—
530C4⋊C4—216no—
531C4⋊C4—28no—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—48no—
535C4⋊C4—48no—
536C4⋊C4—48no—
537C4⋊C4—416no—
538C4⋊C4—48no—
539C4⋊C4—44no—
540C4⋊C4—48no—
541C4⋊C4—48no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C4⋊C4—48no—
545C4⋊C4—84no—
546C4⋊C4—88no—
547C4⋊C4—88no—
548C4⋊C4—88no—
549C4⋊C4#121116yes—
550C22⋊C4—216no—
551C22⋊C4—48no—
552C22⋊C4—416no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—416no—
557C22⋊C4—88no—
558C42—28no—
559C42—216no—
560C42—44no—
561C42—44no—
562C42—44no—
563C42—44no—
564C42—44no—
565C42—48no—
566C42—48no—
567C42C22⋊Q8116yes—
568C23—24no—
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—42no—
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—
602C23C2×#12518yes—
603C23C23×D411yescharacteristic
604C23C23×D411yescharacteristic
605C23C23×Q811yescharacteristic
606C23C22×#4111yescharacteristic
607C23C22×#4111yescharacteristic
608C23C22×#4111yescharacteristic
609C23C22×#4111yescharacteristic
610C23C2×H(5,𝔽2)11yescharacteristic
611C23C2×H(5,𝔽2)11yescharacteristic
612C23C2×H(5,𝔽2)11yescharacteristic
613C23C2×2−1+411yescharacteristic
614C23C2×2−1+411yescharacteristic
615C23C2×2−1+411yescharacteristic
616C23#58511yescharacteristic
617C23#58511yescharacteristic
618D4—232no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—432no—
681C2×C4—44no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—44no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—832no—
717C2×C4C2×#12118yes—
718C2×C4C2×#12114yes—
719C2×C4C2×C22⋊Q814yes—
720C2×C4C2×C22⋊Q814yes—
721C2×C4C2×C22⋊Q814yes—
722C2×C4C2×#12514yes—
723C2×C4#53714yes—
724C2×C4#54414yes—
725C2×C4#54614yes—
726C2×C4#54814yes—
727C2×C4D4×Q814yes—
728C2×C4#55014yes—
729C2×C4#55214yes—
730C2×C4#55314yes—
731C2×C4#55414yes—
732C2×C4#55614yes—
733C22—28no—
734C22—28no—
735C22—28no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22C22×#12111yescharacteristic
749C22C22×C22⋊Q811yescharacteristic
750C22C22×#12511yescharacteristic
751C22C2×#53711yescharacteristic
752C22C2×#54411yescharacteristic
753C22C2×#54611yescharacteristic
754C22C2×#54811yescharacteristic
755C22C2×D4×Q811yescharacteristic
756C22C2×#55011yescharacteristic
757C22D4×#4111yescharacteristic
758C22D4×#4111yescharacteristic
759C22C2×#55211yescharacteristic
760C22C2×#55311yescharacteristic
761C22C2×#55411yescharacteristic
762C22C2×#55611yescharacteristic
763C22#348111yescharacteristic
764C22#348211yescharacteristic
765C22#348811yescharacteristic
766C22#348911yescharacteristic
767C22#349811yescharacteristic
768C22#349911yescharacteristic
769C22#350311yescharacteristic
770C22#350411yescharacteristic
771C22#350611yescharacteristic
772C22#350711yescharacteristic
773C22#351411yescharacteristic
774C22#351511yescharacteristic
775C22#351511yescharacteristic
776C22#351811yescharacteristic
777C22#351911yescharacteristic
778C22#352011yescharacteristic
779C22#354411yescharacteristic
780C22#354611yescharacteristic
781C22#354711yescharacteristic
782C22#355211yescharacteristic
783C4—28no—
784C4—24no—
785C4—42no—
786C4—44no—
787C4—44no—
788C4—42no—
789C4—42no—
790C4—44no—
791C4—42no—
792C4—82no—
793C4—84no—
794C4—82no—
795C4—84no—
796C4—82no—
797C4#244218yescomplemented
798C4#253818yes—
799C2—48no—
800C2C2×#244211yescharacteristic
801C2C2×#253811yescharacteristic
802C2#3551911yescharacteristic
803C2D4×#12511yescharacteristic
804C2#3625811yescharacteristic
805C2#3629011yescharacteristic
806C2#3644411yescharacteristic
807C2#3890811yescharacteristic
808C2#3896711yescharacteristic
809C2#3912611yescharacteristic
810C2#3936911yescharacteristic
811C2#5943611yescharacteristic
812C2#5943711yescharacteristic
813C2#5944411yescharacteristic
814C2#5968011yescharacteristic
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
1. C2×#2442C2semidirect
3. C2×C4×#125C2semidirect
4. #15787C2semidirect
5. #15441C2semidirect
6. #15220C2semidirect
7. #15220C2semidirect
8. #15156C2semidirect
9. #15133C2semidirect
10. #14712C2semidirect
12. #13911C2semidirect
13. #13910C2semidirect
14. #13907C2semidirect
91. C2×#125D4semidirect
402. C2×D4#125semidirect
797. C4#2442semidirect

Maximal subgroups

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

subgroupindex
C2×#24422
C2×D4×C4⋊C42
C2×C4×#1252
#157872
#154412
#152202
#151562
#151332
#147122
#140182
#139112
#139102
#139072
#139062
C4×#3902