Finite Group Databasebeta

← #759757

Subgroups — #759757

Order 512.

2922 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2551C211yesmaximal, characteristic, complemented
2C2×#2439C212yesmaximal
3C2×#2285C211yesmaximal, characteristic
4#16520C214yesmaximal
5#15230C212yesmaximal, complemented
6#15225C212yesmaximal, complemented
7#15131C212yesmaximal
8#15125C212yesmaximal
9#14800C214yesmaximal, complemented
10#14151C211yesmaximal, characteristic, complemented
11#14129C212yesmaximal
12#14053C212yesmaximal, complemented
13#14029C212yesmaximal, complemented
14#13911C211yesmaximal, characteristic, complemented
15#13910C211yesmaximal, characteristic, complemented
16C4×#380C211yesmaximal, characteristic
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2212yes—
19C22×C4⋊Q8C2212yes—
20C22×#117C2212yes—
21C23×C42C2211yescharacteristic
22#2551—28no—
23#2439—216no—
24C2×#396C2214yes—
25C2×#395C2214yes—
26C2×#393C2214yes—
27C2×#391C2214yes—
28C2×#389C2212yes—
29C2×#389C2212yes—
30C2×#389C2212yes—
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#387C2214yes—
35#2285—28no—
36C2×#384C2212yes—
37C2×#384C2211yescharacteristic
38C2×#384C2211yescharacteristic
39C2×#382C2212yes—
40C2×#382C2212yes—
41C2×#380C2211yescharacteristic
42C2×#380C2212yes—
43C2×#380C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55#1446C2214yes—
56#1446C2214yes—
57#1445C2214yes—
58#1444C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1436C2214yes—
69#1436C2214yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80#1434C2212yes—
81#1434C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C4×#95C2212yes—
85C4×#95C2212yes—
86C23×Q8C2314yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C2×C4⋊Q8—28no—
91C2×C4⋊Q8—28no—
92C2×C4⋊Q8—28no—
93C2×C4⋊Q8—28no—
94C2×C4⋊Q8—44no—
95C2×C4⋊Q8—44no—
96C2×#117—28no—
97C2×#117—28no—
98C2×#117—44no—
99C22×C4⋊C4C2312yes—
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C42—24no—
124C22×C42—24no—
125C22×C42Q818yescomplemented
126C22×C42C2312yes—
127C22×C42C2312yes—
128C22×C42C2312yes—
129C22×C42C2312yes—
130C22×C42C2314yes—
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135#396—216no—
136#395—216no—
137#393—216no—
138#391—216no—
139#389—28no—
140#389—28no—
141#389—28no—
142#389—28no—
143#389—44no—
144#389—44no—
145#387—216no—
146#384—28no—
147#384—24no—
148#384D418yes—
149#382—28no—
150#382—28no—
151#380—28no—
152#380—28no—
153#380—24no—
154#380—24no—
155#380D418yes—
156#380Q818yescomplemented
157C4×C4⋊C4—28no—
158C4×C4⋊C4—28no—
159C4×C4⋊C4—24no—
160C4×C4⋊C4—24no—
161C4×C4⋊C4—24no—
162C4×C4⋊C4—24no—
163C4×C22⋊C4—28no—
164C4×C22⋊C4—44no—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C25C2411yescharacteristic
194C22×Q8—28no—
195C22×Q8—28no—
196C22×Q8—28no—
197C22×Q8—44no—
198C22×Q8—44no—
199C22×Q8—44no—
200C22×Q8—44no—
201C23×C4—22no—
202C23×C4—22no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—41no—
214C23×C4—41no—
215C23×C4—41no—
216C23×C4—41no—
217C23×C4C2×D414yes—
218C23×C4C2×Q814yes—
219C23×C4C2×Q814yes—
220C23×C4C2×Q814yes—
221C23×C4C2×Q814yes—
222C23×C4C2414yes—
223C23×C4C2412yes—
224C23×C4C2412yes—
225C23×C4C2414yes—
226C23×C4C2412yes—
227C23×C4C2412yes—
228C23×C4C2412yes—
229C23×C4C2412yes—
230C23×C4C2411yescharacteristic
231C23×C4C2411yescharacteristic
232C23×C4C2412yes—
233C23×C4C2412yes—
234C23×C4C2411yescharacteristic
235C23×C4C2411yescharacteristic
236C23×C4C2411yescharacteristic
237C23×C4C2411yescharacteristic
238C4⋊Q8—432no—
239C4⋊Q8—432no—
240#117—432no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—28no—
260C2×C4⋊C4—28no—
261C2×C4⋊C4—28no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—28no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—28no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—44no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4C2×D418yes—
290C2×C4⋊C4C2×D414yes—
291C2×C4⋊C4C2×D418yes—
292C2×C4⋊C4C2×D414yes—
293C2×C4⋊C4C2×D418yes—
294C2×C4⋊C4C2×Q814yes—
295C2×C4⋊C4C2×Q814yes—
296C2×C4⋊C4#4114yes—
297C2×C4⋊C4#4114yes—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—44no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4C2×D418yes—
312C2×C22⋊C4C2×Q818yes—
313C2×C42—22no—
314C2×C42—22no—
315C2×C42—22no—
316C2×C42—22no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42—232no—
320C2×C42—28no—
321C2×C42—28no—
322C2×C42—24no—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—24no—
326C2×C42—24no—
327C2×C42—24no—
328C2×C42—24no—
329C2×C42—24no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—44no—
335C2×C42C2×D414yes—
336C2×C42C2×Q814yes—
337C2×C42C2×Q814yes—
338C2×C42C2×Q814yes—
339C2×C42C2×Q814yes—
340C2×C42#4114yes—
341#95—24no—
342#95—24no—
343#95—28no—
344#95—28no—
345#95—24no—
346#95—24no—
347#95—28no—
348#95—28no—
349#95—28no—
350#95—28no—
351#95—28no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—42no—
357#95—42no—
358#95—44no—
359#95—44no—
360#95—44no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—42no—
365#95—44no—
366#95—44no—
367#95C2×D418yes—
368#95C2×Q818yes—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24C22×D412yes—
382C24C22×Q812yes—
383C24C22×Q812yes—
384C24C2511yescharacteristic
385C2×Q8—416no—
386C2×Q8—416no—
387C2×Q8—416no—
388C2×Q8—88no—
389C2×Q8—88no—
390C2×Q8—88no—
391C2×Q8—88no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—28no—
401C22×C4—28no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—24no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—28no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—44no—
492C22×C4—44no—
493C22×C4—44no—
494C22×C4—44no—
495C22×C4C4⋊Q8116yescomplemented
496C22×C4C22×D414yes—
497C22×C4C22×D414yes—
498C22×C4C22×D418yes—
499C22×C4C22×D412yes—
500C22×C4C22×D412yes—
501C22×C4C22×D412yes—
502C22×C4C22×D412yes—
503C22×C4C22×D412yes—
504C22×C4C22×Q814yes—
505C22×C4C22×Q814yes—
506C22×C4C22×Q812yes—
507C22×C4C22×Q812yes—
508C22×C4C22×Q812yes—
509C22×C4C22×Q812yes—
510C22×C4C22×Q812yes—
511C22×C4C22×Q812yes—
512C22×C4C22×Q812yes—
513C22×C4C22×Q812yes—
514C22×C4C2×#4114yes—
515C22×C4C2×#4114yes—
516C22×C4C2×#4112yes—
517C22×C4C2×#4112yes—
518C22×C4C2×#4112yes—
519C22×C4C2×#4112yes—
520C22×C4C2×#4112yes—
521C22×C4H(5,𝔽2)12yes—
522C22×C4H(5,𝔽2)12yes—
523C22×C42−1+412yes—
524C22×C42−1+412yes—
525C4⋊C4—216no—
526C4⋊C4—28no—
527C4⋊C4—216no—
528C4⋊C4—28no—
529C4⋊C4—28no—
530C4⋊C4—28no—
531C4⋊C4—28no—
532C4⋊C4—28no—
533C4⋊C4—48no—
534C4⋊C4—416no—
535C4⋊C4—416no—
536C4⋊C4—416no—
537C4⋊C4—48no—
538C4⋊C4—48no—
539C4⋊C4—48no—
540C4⋊C4—44no—
541C4⋊C4—44no—
542C4⋊C4—88no—
543C4⋊C4—88no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C22⋊C4—48no—
548C22⋊C4—416no—
549C42—28no—
550C42—28no—
551C42—28no—
552C42—416no—
553C42—48no—
554C42—48no—
555C42—48no—
556C42—48no—
557C42C22⋊Q8116yes—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23C2×C4⋊Q814yes—
593C23C23×D411yescharacteristic
594C23C23×D411yescharacteristic
595C23C23×Q811yescharacteristic
596C23C23×Q811yescharacteristic
597C23C22×#4111yescharacteristic
598C23C22×#4111yescharacteristic
599C23C22×#4111yescharacteristic
600C23C2×H(5,𝔽2)11yescharacteristic
601C23C2×H(5,𝔽2)11yescharacteristic
602C23C2×2−1+411yescharacteristic
603C23C2×2−1+411yescharacteristic
604C23#58511yescharacteristic
605C23#58511yescharacteristic
606C23#58511yescharacteristic
607C23#58511yescharacteristic
608Q8—832no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—232no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—28no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—28no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—28no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—416no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—44no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—44no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—416no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4C2×C22⋊Q814yes—
709C2×C4C2×C22⋊Q814yes—
710C2×C4C2×C22⋊Q814yes—
711C2×C4C2×C4⋊Q814yes—
712C2×C4C2×C4⋊Q814yes—
713C2×C4#53314yes—
714C2×C4#54414yes—
715C2×C4#54414yes—
716C2×C4D4214yes—
717C2×C4#54614yes—
718C2×C4#54714yes—
719C2×C4#54814yes—
720C2×C4D4×Q814yes—
721C2×C4#55414yes—
722C2×C4#55514yes—
723C2×C4#55614yes—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22C22×C22⋊Q811yescharacteristic
740C22C22×C4⋊Q811yescharacteristic
741C22C2×#53311yescharacteristic
742C22C2×#54411yescharacteristic
743C22C2×#54411yescharacteristic
744C22#345811yescharacteristic
745C22#345811yescharacteristic
746C22C2×D4211yescharacteristic
747C22C2×#54611yescharacteristic
748C22C2×#54711yescharacteristic
749C22C2×#54811yescharacteristic
750C22C2×D4×Q811yescharacteristic
751C22D4×#4111yescharacteristic
752C22D4×#4111yescharacteristic
753C22C2×#55411yescharacteristic
754C22C2×#55511yescharacteristic
755C22C2×#55611yescharacteristic
756C22Q8×#4111yescharacteristic
757C22Q8×#4111yescharacteristic
758C22#348511yescharacteristic
759C22#348711yescharacteristic
760C22#349311yescharacteristic
761C22#349311yescharacteristic
762C22#349611yescharacteristic
763C22#349711yescharacteristic
764C22#350111yescharacteristic
765C22#350211yescharacteristic
766C22#351411yescharacteristic
767C22#351411yescharacteristic
768C22#351811yescharacteristic
769C22#351811yescharacteristic
770C22#354611yescharacteristic
771C22#354711yescharacteristic
772C22#355411yescharacteristic
773C22#355511yescharacteristic
774C4—24no—
775C4—24no—
776C4—42no—
777C4—44no—
778C4—44no—
779C4—42no—
780C4—48no—
781C4—44no—
782C4—44no—
783C4—44no—
784C4—44no—
785C4—82no—
786C4—82no—
787C4—84no—
788C4#243918yescomplemented
789C4#244018yes—
790C2—44no—
791C2C2×#244011yescharacteristic
792C2C2×#243911yescharacteristic
793C2#3493811yescharacteristic
794C2#3515111yescharacteristic
795C2#3516711yescharacteristic
796C2#3519211yescharacteristic
797C2#3762411yescharacteristic
798C2#5903511yescharacteristic
799C2#5903611yescharacteristic
800C2#5908011yescharacteristic
801C2#5908111yescharacteristic
802C2#5922911yescharacteristic
803C2#5923011yescharacteristic
804C2#5924411yescharacteristic
805C2#5924511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
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×#2551C2semidirect
5. #15230C2semidirect
6. #15225C2semidirect
9. #14800C2semidirect
10. #14151C2semidirect
12. #14053C2semidirect
13. #14029C2semidirect
14. #13911C2semidirect
15. #13910C2semidirect
125. C22×C42Q8semidirect
156. #380Q8semidirect
495. C22×C4C4⋊Q8semidirect
788. C4#2439semidirect

Maximal subgroups

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

subgroupindex
C2×#25512
C2×#24392
C2×#22852
#165202
#152302
#152252
#151312
#151252
#148002
#141512
#141292
#140532
#140292
#139112
#139102
C4×#3802