Finite Group Databasebeta

← #678304

Subgroups — #678304

Order 512.

2898 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2568C211yesmaximal, characteristic, complemented
3C2×#2365C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Q8C211yesmaximal, characteristic
5#15813C214yesmaximal, complemented
6#15796C214yesmaximal
7#15236C212yesmaximal
8#15225C212yesmaximal, complemented
9#15192C212yesmaximal, complemented
10#15179C212yesmaximal
11#14142C212yesmaximal, complemented
12#13969C212yesmaximal
13#13942C212yesmaximal, complemented
14#13926C211yesmaximal, characteristic, complemented
15#13911C211yesmaximal, characteristic, complemented
16#13875C212yesmaximal
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2212yes—
21C22×C4×Q8C2211yescharacteristic
22C22×C4×Q8C2212yes—
23C23×C42C2211yescharacteristic
24#2857—28no—
25#2568—28no—
26C2×#400C2214yes—
27#2365—28no—
28C4×C22⋊Q8—28no—
29C2×#391C2212yes—
30C2×#391C2211yescharacteristic
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#391C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2211yescharacteristic
40C2×#387C2214yes—
41C2×#387C2212yes—
42C2×#385C2212yes—
43C2×#384C2211yescharacteristic
44C2×#382C2212yes—
45C2×#382C2212yes—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58#1445C2214yes—
59#1443C2214yes—
60#1443C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1440C2214yes—
70#1440C2214yes—
71#1439C2214yes—
72#1437C2214yes—
73#1436C2214yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82#1434C2214yes—
83#1434C2214yes—
84#1434C2212yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2312yes—
88C23×Q8C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8—24no—
94C2×C4⋊Q8D418yes—
95C2×C22⋊Q8—24no—
96C2×C22⋊Q8—24no—
97C2×C22⋊Q8—28no—
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—24no—
100C2×C22⋊Q8—44no—
101C2×C4×Q8—28no—
102C2×C4×Q8—24no—
103C2×C4×Q8—28no—
104C2×C4×Q8—24no—
105C2×C4×Q8—24no—
106C2×C4×Q8—44no—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C42—24no—
130C22×C42—24no—
131C22×C42—24no—
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2312yes—
136C22×C42C2312yes—
137C22×C42C2312yes—
138C22×C42C2314yes—
139C22×C42C2312yes—
140C22×C42C2311yescharacteristic
141#400—216no—
142#391—28no—
143#391—28no—
144#391—28no—
145#391—28no—
146#391—28no—
147#391—24no—
148#391—28no—
149#389—28no—
150#389—28no—
151#389—28no—
152#389—24no—
153#387—216no—
154#387—28no—
155#385—28no—
156#384—24no—
157#382—28no—
158#382—44no—
159#380—24no—
160#380—28no—
161#380—28no—
162#380—24no—
163#380—24no—
164C4×C4⋊C4—28no—
165C4×C4⋊C4—24no—
166C4×C4⋊C4—24no—
167C4×C4⋊C4—28no—
168C4×C4⋊C4D418yes—
169C4×C22⋊C4—28no—
170C4×C22⋊C4—28no—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C25C2411yescharacteristic
201C22×Q8—22no—
202C22×Q8—24no—
203C22×Q8—22no—
204C22×Q8—22no—
205C22×Q8—24no—
206C22×Q8—22no—
207C22×Q8—24no—
208C22×Q8—24no—
209C22×Q8—24no—
210C22×Q8—22no—
211C22×Q8—22no—
212C22×Q8—24no—
213C22×Q8C2×D418yes—
214C22×Q8#4114yes—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—41no—
233C23×C4—41no—
234C23×C4#4114yes—
235C23×C4#4114yes—
236C23×C4C2414yes—
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2414yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2411yescharacteristic
247C23×C4C2411yescharacteristic
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252C4⋊Q8—232no—
253C22⋊Q8—232no—
254C22⋊Q8—432no—
255C4×Q8—432no—
256C4×Q8—416no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—28no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4C2×D414yes—
304C2×C4⋊C4C2×D418yes—
305C2×C4⋊C4C2×D418yes—
306C2×C4⋊C4C2×D414yes—
307C2×C4⋊C4#4114yes—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—44no—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—24no—
326C2×C42—28no—
327C2×C42—24no—
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—28no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—24no—
345C2×C42—44no—
346C2×C42—416no—
347C2×C42C2×D418yes—
348C2×C42C2×D414yes—
349C2×C42C2×D414yes—
350C2×C42#4114yes—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—24no—
356#95—28no—
357#95—24no—
358#95—28no—
359#95—28no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—28no—
364#95—28no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—28no—
370#95—28no—
371#95—24no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—42no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95C2×D418yes—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24C2×#4112yes—
393C24C2×#4112yes—
394C242−1+412yes—
395C24C2511yescharacteristic
396C2×Q8—216no—
397C2×Q8—28no—
398C2×Q8—216no—
399C2×Q8—216no—
400C2×Q8—28no—
401C2×Q8—28no—
402C2×Q8—44no—
403C2×Q8—48no—
404C2×Q8—44no—
405C2×Q8—48no—
406C2×Q8—48no—
407C2×Q8—48no—
408C2×Q8—44no—
409C2×Q8—44no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—28no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4C22×D418yes—
519C22×C4C22×D414yes—
520C22×C4C22×D414yes—
521C22×C4C22×D412yes—
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C2×#4114yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4C2×#4114yes—
531C22×C4C2×#4112yes—
532C22×C4C2×#4112yes—
533C22×C4C2×#4112yes—
534C22×C4C2×#4112yes—
535C22×C4C2×#4112yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4H(5,𝔽2)12yes—
539C22×C42−1+412yes—
540C22×C42−1+412yes—
541C22×C42−1+412yes—
542C22×C42−1+412yes—
543C4⋊C4—216no—
544C4⋊C4—216no—
545C4⋊C4—216no—
546C4⋊C4—28no—
547C4⋊C4—28no—
548C4⋊C4—28no—
549C4⋊C4—48no—
550C4⋊C4—416no—
551C4⋊C4—416no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—48no—
557C4⋊C4—44no—
558C4⋊C4—44no—
559C4⋊C4—48no—
560C22⋊C4—216no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—416no—
564C22⋊C4—48no—
565C42—216no—
566C42—416no—
567C42—44no—
568C42—44no—
569C42—44no—
570C42—48no—
571C42—48no—
572C42—48no—
573C42#121116yes—
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—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23#55614yes—
609C23C23×D411yescharacteristic
610C23C23×D411yescharacteristic
611C23C22×#4111yescharacteristic
612C23C22×#4111yescharacteristic
613C23C22×#4111yescharacteristic
614C23C22×#4111yescharacteristic
615C23C22×#4111yescharacteristic
616C23C2×H(5,𝔽2)11yescharacteristic
617C23C2×2−1+411yescharacteristic
618C23C2×2−1+411yescharacteristic
619C23C2×2−1+411yescharacteristic
620C23C2×2−1+411yescharacteristic
621C23C2×2−1+411yescharacteristic
622C23#58511yescharacteristic
623C23#58511yescharacteristic
624Q8—432no—
625Q8—416no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—28no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—28no—
642C2×C4—22no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—416no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—44no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—416no—
690C2×C4—416no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
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—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4C2×#12114yes—
727C2×C4C2×#12114yes—
728C2×C4C2×#12114yes—
729C2×C4#52514yes—
730C2×C4#52914yes—
731C2×C4#53614yes—
732C2×C4#54214yes—
733C2×C4#54614yes—
734C2×C4#54614yes—
735C2×C4#54714yes—
736C2×C4#54814yes—
737C2×C4#54814yes—
738C2×C4#54814yes—
739C2×C4#55214yes—
740C2×C4#55214yes—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22C22×#12111yescharacteristic
757C22C2×#52511yescharacteristic
758C22C2×#52911yescharacteristic
759C22C2×#53611yescharacteristic
760C22C2×#54211yescharacteristic
761C22C2×#54611yescharacteristic
762C22C2×#54611yescharacteristic
763C22C2×#54711yescharacteristic
764C22C2×#54811yescharacteristic
765C22C2×#54811yescharacteristic
766C22C2×#54811yescharacteristic
767C22C2×#55211yescharacteristic
768C22C2×#55211yescharacteristic
769C22C2×#55611yescharacteristic
770C22#347511yescharacteristic
771C22#348011yescharacteristic
772C22#348211yescharacteristic
773C22#348611yescharacteristic
774C22#348711yescharacteristic
775C22#348911yescharacteristic
776C22#348911yescharacteristic
777C22#349511yescharacteristic
778C22#349511yescharacteristic
779C22#350711yescharacteristic
780C22#350711yescharacteristic
781C22#350911yescharacteristic
782C22#351111yescharacteristic
783C22#351711yescharacteristic
784C22#351811yescharacteristic
785C22#352311yescharacteristic
786C22#352311yescharacteristic
787C22#355211yescharacteristic
788C22#355411yescharacteristic
789C22#355511yescharacteristic
790C22#355611yescharacteristic
791C4—24no—
792C4—44no—
793C4—44no—
794C4—42no—
795C4—42no—
796C4—44no—
797C4—42no—
798C4—48no—
799C4—44no—
800C4—82no—
801C4—82no—
802C4—84no—
803C4—82no—
804C4—82no—
805C4#242718yes—
806C4#253618yes—
807C2—44no—
808C2C2×#242711yescharacteristic
809C2C2×#253611yescharacteristic
810C2#3566111yescharacteristic
811C2#3617711yescharacteristic
812C2#3631411yescharacteristic
813C2#3640411yescharacteristic
814C2#3657911yescharacteristic
815C2#3891111yescharacteristic
816C2#3893311yescharacteristic
817C2#3947811yescharacteristic
818C2#3972411yescharacteristic
819C2#5906511yescharacteristic
820C2#5907111yescharacteristic
821C2#5907811yescharacteristic
822C2#5913411yescharacteristic
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
2. C2×#2568C2semidirect
3. C2×#2365C2semidirect
5. #15813C2semidirect
8. #15225C2semidirect
9. #15192C2semidirect
11. #14142C2semidirect
13. #13942C2semidirect
14. #13926C2semidirect
15. #13911C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25682
C2×#23652
C2×C4×C22⋊Q82
#158132
#157962
#152362
#152252
#151922
#151792
#141422
#139692
#139422
#139262
#139112
#138752
C4×#3802