Finite Group Databasebeta

← #410415

Subgroups — #410415

Order 512.

1102 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×#1923C211yesmaximal, characteristic
2C2×C4×#106C211yesmaximal, characteristic, complemented
3#13994C211yesmaximal, characteristic
4#13993C211yesmaximal, characteristic
5#11327C211yesmaximal, characteristic, complemented
6#11257C211yesmaximal, characteristic, complemented
7#11228C211yesmaximal, characteristic, complemented
8#11227C211yesmaximal, characteristic, complemented
9#11200C211yesmaximal, characteristic
10#11199C211yesmaximal, characteristic
11#11095C211yesmaximal, characteristic
12#11095C211yesmaximal, characteristic
13#10820C211yesmaximal, characteristic, complemented
14#10807C211yesmaximal, characteristic, complemented
15#10806C211yesmaximal, characteristic, complemented
16C22×#106C2211yescharacteristic
17C22×#106C2211yescharacteristic
18C22×C4⋊C8C2211yescharacteristic
19C22×C22⋊C8C2211yescharacteristic
20C22×C22⋊C8C2211yescharacteristic
21C22×C4×C8C2211yescharacteristic
22C2×#389C2211yescharacteristic
23C2×#389C2211yescharacteristic
24C2×#388—21no—
25C2×#380C2211yescharacteristic
26C2×#380C2211yescharacteristic
27C2×#380C2211yescharacteristic
28C2×#380C2211yescharacteristic
29C2×C4×C4⋊C4C2211yescharacteristic
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C22⋊C4C2211yescharacteristic
32#1923—24no—
33C4×#106—24no—
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1443—21no—
51#1442—21no—
52#1440—21no—
53#1439—21no—
54#1437—21no—
55#1436—21no—
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60#1434—21no—
61C24×C4C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C22×C4⋊C4—21no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4C2311yescharacteristic
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C22⋊C4—21no—
77C22×C22⋊C4—21no—
78C22×C22⋊C4—21no—
79C22×C22⋊C4—21no—
80C22×C22⋊C4D411yescharacteristic
81C22×C22⋊C4D411yescharacteristic
82C22×C42—21no—
83C22×C42—21no—
84C22×C42C2311yescharacteristic
85C22×C42C2311yescharacteristic
86C2×#106—22no—
87C2×#106—22no—
88C2×#106—22no—
89C2×#106—22no—
90C2×#106—22no—
91C2×#106—22no—
92C2×C4⋊C8—22no—
93C2×C4⋊C8—41no—
94C2×C4⋊C8—41no—
95C2×C22⋊C8—22no—
96C2×C22⋊C8—22no—
97C2×C22⋊C8—22no—
98C2×C22⋊C8—22no—
99C2×C22⋊C8—41no—
100C2×C22⋊C8—41no—
101C2×C4×C8—22no—
102C2×C4×C8—22no—
103C2×C4×C8D414yes—
104#389—22no—
105#389—22no—
106#389—41no—
107#389—41no—
108#388—44no—
109#380—22no—
110#380—22no—
111#380—22no—
112#380—22no—
113#380—22no—
114#380—22no—
115#380—41no—
116#380—41no—
117C4×C4⋊C4—22no—
118C4×C4⋊C4—22no—
119C4×C4⋊C4—22no—
120C4×C4⋊C4—22no—
121C4×C22⋊C4—22no—
122C4×C22⋊C4—22no—
123C2×#95—21no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—21no—
127C2×#95—21no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95D411yescharacteristic
140C2×#95D411yescharacteristic
141#340—22no—
142#340—22no—
143#340—22no—
144#340—22no—
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#336—22no—
156#336—22no—
157C25C2×D411yescharacteristic
158C23×C4—21no—
159C23×C4—21no—
160C23×C4—21no—
161C23×C4—21no—
162C23×C4—21no—
163C23×C4—21no—
164C23×C4—21no—
165C23×C4—21no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4—21no—
169C23×C4—21no—
170C23×C4—21no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2411yescharacteristic
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8C2×D412yes—
211C22×C8C2×D412yes—
212C22×C8#4112yes—
213C22×C8#4112yes—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—42no—
258C2×C4⋊C4—42no—
259C2×C4⋊C4—42no—
260C2×C4⋊C4—81no—
261C2×C4⋊C4—81no—
262C2×C4⋊C4#4112yes—
263C2×C4⋊C4#4112yes—
264C2×C4⋊C4#4112yes—
265C2×C4⋊C4#4112yes—
266C2×C4⋊C4#4112yes—
267C2×C4⋊C4#4112yes—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—22no—
274C2×C22⋊C4—22no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—42no—
277C2×C22⋊C4—42no—
278C2×C22⋊C4—42no—
279C2×C22⋊C4—42no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—81no—
283C2×C22⋊C4—81no—
284C2×C22⋊C4—81no—
285C2×C22⋊C4—81no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—21no—
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294C2×C42—21no—
295C2×C42—21no—
296C2×C42—42no—
297C2×C42—42no—
298C2×C42—42no—
299C2×C42—42no—
300C2×C42—81no—
301C2×C42—81no—
302C2×C42C2×D412yes—
303C2×C42#4112yes—
304#106—28no—
305#106—28no—
306C4⋊C8—44no—
307C22⋊C8—44no—
308C22⋊C8—44no—
309C4×C8—28no—
310#95—24no—
311#95—24no—
312#95—22no—
313#95—22no—
314#95—42no—
315#95—42no—
316#95—42no—
317#95—42no—
318#95—42no—
319#95—42no—
320#95—42no—
321#95—42no—
322#95—42no—
323#95—42no—
324#95—81no—
325#95—81no—
326#95—81no—
327#95—81no—
328C24—21no—
329C24—21no—
330C24—21no—
331C24—21no—
332C24—21no—
333C24—21no—
334C24—21no—
335C24—21no—
336C24—21no—
337C24—21no—
338C24—21no—
339C24—21no—
340C24—21no—
341C24—21no—
342C24#13512yes—
343C24C22×D411yescharacteristic
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4#12112yes—
459C22×C4#12112yes—
460C22×C4#13512yes—
461C22×C4AGL(1,ℤ/8)12yes—
462C22×C4#13712yes—
463C22×C4C22×D411yescharacteristic
464C22×C4C2×#4111yescharacteristic
465C22×C4C2×#4111yescharacteristic
466C22×C4C2×#4111yescharacteristic
467C22×C4C2×#4111yescharacteristic
468C22×C4C2×#4111yescharacteristic
469C22×C4C2×#4111yescharacteristic
470C22×C4C2×#4111yescharacteristic
471C22×C4C2×#4111yescharacteristic
472C22×C4C2×#4111yescharacteristic
473C22×C4H(5,𝔽2)11yescharacteristic
474C22×C4H(5,𝔽2)11yescharacteristic
475C22×C42−1+411yescharacteristic
476C22×C42−1+411yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8#12314yes—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4—41no—
525C4⋊C4—41no—
526C4⋊C4—41no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—84no—
538C4⋊C4—84no—
539C22⋊C4—28no—
540C22⋊C4—48no—
541C22⋊C4—44no—
542C22⋊C4—84no—
543C22⋊C4—84no—
544C22⋊C4—84no—
545C42—22no—
546C42—22no—
547C42—22no—
548C42—22no—
549C42—41no—
550C42—41no—
551C42—41no—
552C42—41no—
553C42—84no—
554C42—84no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
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—
590C23C2×#12111yescharacteristic
591C23#52511yescharacteristic
592C23#52511yescharacteristic
593C23#54611yescharacteristic
594C23#54611yescharacteristic
595C23#54711yescharacteristic
596C23#54711yescharacteristic
597C23C2×#13511yescharacteristic
598C23C2×#13511yescharacteristic
599C23C2×AGL(1,ℤ/8)11yescharacteristic
600C23C2×#13711yescharacteristic
601C23#57711yescharacteristic
602C23#57711yescharacteristic
603C23#57711yescharacteristic
604C23#57711yescharacteristic
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
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—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4#46814yes—
704C2×C4C2×#12311yescharacteristic
705C2×C4#52511yescharacteristic
706C2×C4#52511yescharacteristic
707C2×C4#52911yescharacteristic
708C2×C4#52911yescharacteristic
709C2×C4#52911yescharacteristic
710C2×C4#52911yescharacteristic
711C2×C4#52911yescharacteristic
712C2×C4#52911yescharacteristic
713C2×C4#53211yescharacteristic
714C2×C4#53511yescharacteristic
715C2×C4#53611yescharacteristic
716C2×C4#54211yescharacteristic
717C2×C4#54211yescharacteristic
718C2×C4#54211yescharacteristic
719C2×C4#54211yescharacteristic
720C2×C4#55211yescharacteristic
721C2×C4#55211yescharacteristic
722C2×C4#55211yescharacteristic
723C2×C4#55211yescharacteristic
724C2×C4#55311yescharacteristic
725C2×C4#55311yescharacteristic
726C2×C4#55311yescharacteristic
727C2×C4#55311yescharacteristic
728C2×C4#55511yescharacteristic
729C2×C4#55511yescharacteristic
730C2×C4#55611yescharacteristic
731C2×C4#55611yescharacteristic
732C8—24no—
733C8—42no—
734C8—81no—
735C8—81no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22#239211yescharacteristic
752C22#246811yescharacteristic
753C22#246811yescharacteristic
754C22#247411yescharacteristic
755C22#247411yescharacteristic
756C22#248611yescharacteristic
757C22#253511yescharacteristic
758C22#305011yescharacteristic
759C22C2×#46811yescharacteristic
760C22#305711yescharacteristic
761C22#306011yescharacteristic
762C22#310511yescharacteristic
763C22#310611yescharacteristic
764C22#310711yescharacteristic
765C22#310811yescharacteristic
766C22#312311yescharacteristic
767C22#312511yescharacteristic
768C22#312511yescharacteristic
769C22#312611yescharacteristic
770C22#329611yescharacteristic
771C22#329611yescharacteristic
772C22#330111yescharacteristic
773C22#330111yescharacteristic
774C22#332411yescharacteristic
775C22#332911yescharacteristic
776C22#333111yescharacteristic
777C22#333211yescharacteristic
778C22#333711yescharacteristic
779C22#333711yescharacteristic
780C22#334011yescharacteristic
781C22#334011yescharacteristic
782C22#334411yescharacteristic
783C22#334411yescharacteristic
784C22#334511yescharacteristic
785C22#334511yescharacteristic
786C4—24no—
787C4—42no—
788C4—42no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—81no—
794C4—82no—
795C4—81no—
796C4—82no—
797C4—161no—
798C4—161no—
799C4#250011yescharacteristic
800C4#252511yescharacteristic
801C4#252511yescharacteristic
802C4#252911yescharacteristic
803C4#252911yescharacteristic
804C4#260411yescharacteristic
805C4#263211yescharacteristic
806C4#285311yescharacteristic
807C2—82no—
808C2#1507811yescharacteristic
809C2#2370111yescharacteristic
810C2#2370711yescharacteristic
811C2#2709711yescharacteristic
812C2#2709911yescharacteristic
813C2#2710511yescharacteristic
814C2#2710711yescharacteristic
815C2#2732711yescharacteristic
816C2#2733311yescharacteristic
817C2#2733511yescharacteristic
818C2#2734111yescharacteristic
819C2#2765911yescharacteristic
820C2#2766311yescharacteristic
821C2#2814411yescharacteristic
822C2#2815011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×C4×#106C2semidirect
5. #11327C2semidirect
6. #11257C2semidirect
7. #11228C2semidirect
8. #11227C2semidirect
13. #10820C2semidirect
14. #10807C2semidirect
15. #10806C2semidirect

Maximal subgroups

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

subgroupindex
C2×#19232
C2×C4×#1062
#139942
#139932
#113272
#112572
#112282
#112272
#112002
#111992
#110952
#108202
#108072
#108062