Finite Group Databasebeta

← #612928

Subgroups — #612928

Order 512.

2890 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2571C211yesmaximal, characteristic, complemented
2C22×C4×C4⋊C4C211yesmaximal, characteristic
3#15235C212yesmaximal, complemented
4#15221C212yesmaximal, complemented
5#14867C214yesmaximal, complemented
6#14767C214yesmaximal
7#14697C212yesmaximal
8#14686C211yesmaximal, characteristic
9#14682C212yesmaximal
10#14151C211yesmaximal, characteristic, complemented
11#14130C212yesmaximal
12#14030C212yesmaximal, complemented
13#13982C212yesmaximal, complemented
14#13911C211yesmaximal, characteristic, complemented
15#13911C211yesmaximal, characteristic, complemented
16#13881C212yesmaximal
17C4×#380C211yesmaximal, characteristic
18C23×C4⋊C4C2211yescharacteristic
19C23×C4⋊C4C2211yescharacteristic
20C23×C42C2212yes—
21C23×C42C2211yescharacteristic
22#2571—28no—
23C2×#400C2214yes—
24C2×#389C2212yes—
25C2×#389C2212yes—
26C2×#389C2212yes—
27C2×#389C2212yes—
28C2×#385C2214yes—
29C2×#384C2211yescharacteristic
30C2×#384C2211yescharacteristic
31C2×#382C2212yes—
32C2×#382C2212yes—
33C2×#382C2212yes—
34C2×#382C2212yes—
35C2×#380C2212yes—
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38C2×#380C2211yescharacteristic
39C2×#380C2212yes—
40C2×C4×C4⋊C4—28no—
41C2×C4×C4⋊C4C2212yes—
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2212yes—
50C22×#95C2212yes—
51#1445C2214yes—
52#1444C2214yes—
53#1443C2214yes—
54#1443C2214yes—
55#1442C2214yes—
56#1442C2214yes—
57#1442C2214yes—
58#1442C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1441C2214yes—
62#1436C2214yes—
63#1436C2214yes—
64C4⋊#95C2212yes—
65C4⋊#95C2212yes—
66C4⋊#95C2212yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2211yescharacteristic
77#1434C2212yes—
78#1434C2214yes—
79#1434C2214yes—
80C22⋊#95C2214yes—
81C22⋊#95C2214yes—
82C22⋊#95C2214yes—
83C22⋊#95C2212yes—
84C4×#95C2212yes—
85C24×C4C2312yes—
86C24×C4C2312yes—
87C24×C4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C22×C4⋊C4—24no—
91C22×C4⋊C4—24no—
92C22×C4⋊C4—24no—
93C22×C4⋊C4—24no—
94C22×C4⋊C4—24no—
95C22×C4⋊C4—24no—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2312yes—
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2314yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2314yes—
117C22×C42—24no—
118C22×C42—24no—
119C22×C42—28no—
120C22×C42—28no—
121C22×C42—44no—
122C22×C42Q818yes—
123C22×C42C2312yes—
124C22×C42C2312yes—
125C22×C42C2312yes—
126C22×C42C2312yes—
127C22×C42C2312yes—
128C22×C42C2312yes—
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2311yescharacteristic
133#400—216no—
134#389—28no—
135#389—28no—
136#389—28no—
137#389—44no—
138#385—48no—
139#384—24no—
140#384—24no—
141#382—28no—
142#382—28no—
143#382—28no—
144#382—44no—
145#380—28no—
146#380—24no—
147#380—28no—
148#380—24no—
149#380—44no—
150C4×C4⋊C4—24no—
151C4×C4⋊C4—24no—
152C4×C4⋊C4—24no—
153C4×C4⋊C4—28no—
154C4×C4⋊C4—24no—
155C4×C4⋊C4—24no—
156C4×C4⋊C4—28no—
157C4×C4⋊C4D418yes—
158C4×C22⋊C4—28no—
159C2×#95—28no—
160C2×#95C2312yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2312yes—
165C2×#95C2312yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2314yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C25C2411yescharacteristic
190C23×C4—22no—
191C23×C4—22no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—24no—
199C23×C4—24no—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4—24no—
203C23×C4—24no—
204C23×C4—22no—
205C23×C4—24no—
206C23×C4—24no—
207C23×C4—22no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—41no—
213C23×C4—41no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4C2×Q814yes—
219C23×C4C2×Q814yes—
220C23×C4C2×Q814yes—
221C23×C4#4114yes—
222C23×C4#4114yes—
223C23×C4#4114yes—
224C23×C4#4114yes—
225C23×C4C2412yes—
226C23×C4C2414yes—
227C23×C4C2414yes—
228C23×C4C2412yes—
229C23×C4C2412yes—
230C23×C4C2412yes—
231C23×C4C2412yes—
232C23×C4C2412yes—
233C23×C4C2411yescharacteristic
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2411yescharacteristic
237C23×C4C2411yescharacteristic
238C23×C4C2411yescharacteristic
239C23×C4C2411yescharacteristic
240C23×C4C2411yescharacteristic
241C2×C4⋊C4—232no—
242C2×C4⋊C4—232no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
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—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
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—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4—44no—
293C2×C4⋊C4C2×D414yes—
294C2×C4⋊C4C2×D414yes—
295C2×C4⋊C4#4114yes—
296C2×C4⋊C4#4114yes—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C42—22no—
307C2×C42—22no—
308C2×C42—22no—
309C2×C42—22no—
310C2×C42—22no—
311C2×C42—22no—
312C2×C42—24no—
313C2×C42—24no—
314C2×C42—232no—
315C2×C42—24no—
316C2×C42—24no—
317C2×C42—24no—
318C2×C42—24no—
319C2×C42—24no—
320C2×C42—24no—
321C2×C42—24no—
322C2×C42—24no—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—24no—
326C2×C42—24no—
327C2×C42—24no—
328C2×C42—432no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42C2×D418yes—
332C2×C42C2×D414yes—
333C2×C42C2×Q814yes—
334C2×C42C2×Q814yes—
335C2×C42C2×Q814yes—
336C2×C42C2×Q814yes—
337C2×C42#4114yes—
338#95—24no—
339#95—24no—
340#95—24no—
341#95—24no—
342#95—28no—
343#95—28no—
344#95—28no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—28no—
350#95—28no—
351#95—24no—
352#95—28no—
353#95—28no—
354#95—28no—
355#95—42no—
356#95—44no—
357#95—44no—
358#95—42no—
359#95—44no—
360#95—44no—
361#95—44no—
362#95—44no—
363#95—44no—
364#95—44no—
365#95—44no—
366#95C2×D418yes—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24C22×Q812yes—
376C24C2×#4112yes—
377C24C2×#4112yes—
378C24C2×#4112yes—
379C24C2×#4112yes—
380C24H(5,𝔽2)12yes—
381C242−1+412yes—
382C24C2511yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—28no—
396C22×C4—28no—
397C22×C4—28no—
398C22×C4—28no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—28no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—28no—
407C22×C4—216no—
408C22×C4—216no—
409C22×C4—28no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—28no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—44no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—44no—
487C22×C4—44no—
488C22×C4—44no—
489C22×C4—44no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4#125116yes—
501C22×C4#125116yes—
502C22×C4C22×D414yes—
503C22×C4C22×D414yes—
504C22×C4C22×D412yes—
505C22×C4C22×D412yes—
506C22×C4C22×D412yes—
507C22×C4C22×Q812yes—
508C22×C4C22×Q812yes—
509C22×C4C22×Q812yes—
510C22×C4C22×Q812yes—
511C22×C4C22×Q812yes—
512C22×C4C22×Q812yes—
513C22×C4C2×#4114yes—
514C22×C4C2×#4114yes—
515C22×C4C2×#4112yes—
516C22×C4C2×#4112yes—
517C22×C4C2×#4112yes—
518C22×C4C2×#4112yes—
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×C42−1+412yes—
530C4⋊C4—216no—
531C4⋊C4—216no—
532C4⋊C4—28no—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—28no—
536C4⋊C4—48no—
537C4⋊C4—48no—
538C4⋊C4—44no—
539C4⋊C4—44no—
540C4⋊C4—48no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—48no—
544C4⋊C4—84no—
545C4⋊C4—84no—
546C4⋊C4—88no—
547C4⋊C4—88no—
548C22⋊C4—48no—
549C22⋊C4—48no—
550C22⋊C4—416no—
551C42—28no—
552C42—28no—
553C42—28no—
554C42—216no—
555C42—48no—
556C42—48no—
557C42—48no—
558C42—48no—
559C42—48no—
560C42C22⋊Q8116yes—
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—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23C2×#12514yes—
590C23C2×#12514yes—
591C23#54414yes—
592C23#55514yes—
593C23#55614yes—
594C23#55614yes—
595C23#55914yes—
596C23C23×D411yescharacteristic
597C23C23×Q811yescharacteristic
598C23C22×#4111yescharacteristic
599C23C22×#4111yescharacteristic
600C23C22×#4111yescharacteristic
601C23C22×#4111yescharacteristic
602C23C22×#4111yescharacteristic
603C23C22×#4111yescharacteristic
604C23C22×#4111yescharacteristic
605C23C2×H(5,𝔽2)11yescharacteristic
606C23C2×H(5,𝔽2)11yescharacteristic
607C23C2×2−1+411yescharacteristic
608C23C2×2−1+411yescharacteristic
609C23#58511yescharacteristic
610C23#58511yescharacteristic
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—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—232no—
630C2×C4—232no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—416no—
647C2×C4—432no—
648C2×C4—432no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—44no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—44no—
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—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—44no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4C2×C22⋊Q814yes—
712C2×C4C2×C22⋊Q814yes—
713C2×C4C2×C22⋊Q814yes—
714C2×C4#52514yes—
715C2×C4#52514yes—
716C2×C4C2×#12514yes—
717C2×C4C2×#12514yes—
718C2×C4C2×#12514yes—
719C2×C4C2×#12514yes—
720C2×C4#52914yes—
721C2×C4#52914yes—
722C2×C4#53314yes—
723C2×C4#54414yes—
724C2×C4#54614yes—
725C2×C4#54814yes—
726C2×C4#55214yes—
727C2×C4#55314yes—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—24no—
741C22—24no—
742C22#257118yescomplemented
743C22C22×C22⋊Q811yescharacteristic
744C22C2×#52511yescharacteristic
745C22C2×#52511yescharacteristic
746C22C22×#12511yescharacteristic
747C22C22×#12511yescharacteristic
748C22C2×#52911yescharacteristic
749C22C2×#52911yescharacteristic
750C22C2×#53311yescharacteristic
751C22C2×#54411yescharacteristic
752C22C2×#54411yescharacteristic
753C22#345811yescharacteristic
754C22C2×#54611yescharacteristic
755C22C2×#54811yescharacteristic
756C22C2×#55211yescharacteristic
757C22C2×#55311yescharacteristic
758C22C2×#55511yescharacteristic
759C22C2×#55611yescharacteristic
760C22C2×#55611yescharacteristic
761C22#347511yescharacteristic
762C22#347511yescharacteristic
763C22C2×#55911yescharacteristic
764C22#348011yescharacteristic
765C22#348011yescharacteristic
766C22#348811yescharacteristic
767C22#348911yescharacteristic
768C22#349411yescharacteristic
769C22#349511yescharacteristic
770C22#350611yescharacteristic
771C22#350611yescharacteristic
772C22#350711yescharacteristic
773C22#350711yescharacteristic
774C22#351911yescharacteristic
775C22#352011yescharacteristic
776C22#352211yescharacteristic
777C22#352311yescharacteristic
778C4—24no—
779C4—24no—
780C4—24no—
781C4—44no—
782C4—44no—
783C4—44no—
784C4—44no—
785C4—42no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—84no—
790C4—82no—
791C4—84no—
792C4#244218yes—
793C4#285118yes—
794C2—28no—
795C2C2×#244211yescharacteristic
796C2C2×#257111yescharacteristic
797C2#3494811yescharacteristic
798C2#3518111yescharacteristic
799C2#3523911yescharacteristic
800C2#3525311yescharacteristic
801C2#3616011yescharacteristic
802C2#3616111yescharacteristic
803C2#3617611yescharacteristic
804C2#3617711yescharacteristic
805C2#3657911yescharacteristic
806C2#3658011yescharacteristic
807C2#3658611yescharacteristic
808C2#3658711yescharacteristic
809C2C2×#285111yescharacteristic
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×#2571C2semidirect
3. #15235C2semidirect
4. #15221C2semidirect
5. #14867C2semidirect
10. #14151C2semidirect
12. #14030C2semidirect
13. #13982C2semidirect
14. #13911C2semidirect
15. #13911C2semidirect
742. C22#2571semidirect

Maximal subgroups

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

subgroupindex
C2×#25712
C22×C4×C4⋊C42
#152352
#152212
#148672
#147672
#146972
#146862
#146822
#141512
#141302
#140302
#139822
#139112
#138812
C4×#3802