Finite Group Databasebeta

← #398476

Subgroups — #398476

Order 512.

1516 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2851C211yesmaximal, characteristic
2C2×#2059C211yesmaximal, characteristic, complemented
3C2×#1942C211yesmaximal, characteristic, complemented
4C2×#1941C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C8C211yesmaximal, characteristic
6#14697C211yesmaximal, characteristic
7#11385C211yesmaximal, characteristic, complemented
8#11325C211yesmaximal, characteristic, complemented
9#11208C211yesmaximal, characteristic, complemented
10#11096C211yesmaximal, characteristic
11#11096C211yesmaximal, characteristic
12#11095C211yesmaximal, characteristic
13#11095C211yesmaximal, characteristic
14#10880C211yesmaximal, characteristic, complemented
15#10880C211yesmaximal, characteristic, complemented
16C22×#125C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×C22⋊C8C2211yescharacteristic
23C22×C22⋊C8C2211yescharacteristic
24C22×C4×C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26#2851—24no—
27#2851—24no—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#387—21no—
33C2×#387—21no—
34C2×#385—21no—
35C2×#385—21no—
36C2×#385—21no—
37C2×#382C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42#2059—24no—
43#1942—24no—
44#1941—24no—
45C4×C22⋊C8—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1436—21no—
61#1436—21no—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2211yescharacteristic
64C22⋊#95—21no—
65C24×C4D411yescharacteristic
66C24×C4D411yescharacteristic
67C24×C4C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C23×C8C2311yescharacteristic
72C2×#125—22no—
73C2×#125—22no—
74C2×#125—22no—
75C2×#125—22no—
76C2×#125—41no—
77C2×#125—41no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4—21no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C22⋊C4—21no—
93C22×C22⋊C4—21no—
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C42—22no—
97C22×C42—22no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—41no—
101C22×C42—41no—
102C22×C42D411yescharacteristic
103C22×C42D411yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C2×#107—22no—
107C2×#107—22no—
108C2×#107—22no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107—41no—
112C2×#106—22no—
113C2×#106—22no—
114C2×#106—22no—
115C2×#106—22no—
116C2×#106—22no—
117C2×#106—41no—
118C2×C22⋊C8—22no—
119C2×C22⋊C8—22no—
120C2×C22⋊C8—22no—
121C2×C22⋊C8—22no—
122C2×C22⋊C8Q814yes—
123C2×C22⋊C8Q814yes—
124C2×C4×C8—22no—
125C2×C4×C8—22no—
126C2×C4×C8—22no—
127C2×C4×C8—22no—
128C2×C4×C8—41no—
129C2×C4×C8—41no—
130#389—22no—
131#389—22no—
132#389—22no—
133#389—22no—
134#389—22no—
135#389—22no—
136#389D414yes—
137#389D414yes—
138#387—28no—
139#387—28no—
140#385—28no—
141#385—28no—
142#385—44no—
143#382—22no—
144#382—22no—
145#380—22no—
146#380—22no—
147#380—22no—
148#380—22no—
149#380—22no—
150#380—22no—
151#380—41no—
152#380—41no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—41no—
178#340—41no—
179#336—22no—
180#336D414yes—
181C25C2×D411yescharacteristic
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—22no—
207C23×C4—22no—
208C23×C4—22no—
209C23×C4—22no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—41no—
213C23×C4—41no—
214C23×C4—41no—
215C23×C4—41no—
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2×D411yescharacteristic
221C23×C4C2×Q812yes—
222C23×C4C2×Q812yes—
223C23×C4C2411yescharacteristic
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8C2×D412yes—
245C22×C8C2×D412yes—
246C22×C8C2×Q812yes—
247C22×C8C2×Q812yes—
248C22×C8C2×Q812yes—
249C22×C8C2×Q812yes—
250C22×C8#4112yes—
251C22×C8#4112yes—
252#125—44no—
253#125—44no—
254#125—44no—
255#125—44no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4C2×D412yes—
317C2×C4⋊C4C2×D412yes—
318C2×C4⋊C4C2×D412yes—
319C2×C4⋊C4C2×D412yes—
320C2×C4⋊C4#4112yes—
321C2×C4⋊C4#4112yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—21no—
341C2×C42—21no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—44no—
347C2×C42—44no—
348C2×C42—44no—
349C2×C42—44no—
350C2×C42—41no—
351C2×C42—41no—
352C2×C42C2×D412yes—
353C2×C42C2×D412yes—
354C2×C42C2×D412yes—
355C2×C42#4112yes—
356#107—28no—
357#107—44no—
358#106—28no—
359#106—44no—
360C22⋊C8—28no—
361C22⋊C8—28no—
362C4×C8—44no—
363C4×C8—44no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—42no—
372#95—42no—
373#95—42no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24C4⋊Q812yes—
391C24#13512yes—
392C24#13512yes—
393C24C22×D411yescharacteristic
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—28no—
403C22×C4—28no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—44no—
441C22×C4—44no—
442C22×C4—44no—
443C22×C4—44no—
444C22×C4—44no—
445C22×C4—44no—
446C22×C4—44no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
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—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—44no—
467C22×C4—44no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4#12012yes—
519C22×C4#12012yes—
520C22×C4#12112yes—
521C22×C4#12112yes—
522C22×C4C4⋊Q812yes—
523C22×C4#13512yes—
524C22×C4#13512yes—
525C22×C4AGL(1,ℤ/8)12yes—
526C22×C4#13712yes—
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×Q811yescharacteristic
531C22×C4C22×Q811yescharacteristic
532C22×C4C2×#4111yescharacteristic
533C22×C4C2×#4111yescharacteristic
534C22×C4C2×#4111yescharacteristic
535C22×C4C2×#4111yescharacteristic
536C22×C4C2×#4111yescharacteristic
537C22×C4H(5,𝔽2)11yescharacteristic
538C22×C4H(5,𝔽2)11yescharacteristic
539C22×C42−1+411yescharacteristic
540C22×C42−1+411yescharacteristic
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C2×C8—41no—
563C2×C8—41no—
564C2×C8—41no—
565C2×C8—41no—
566C2×C8—41no—
567C2×C8C22⋊Q814yes—
568C2×C8C22⋊Q814yes—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—22no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—41no—
593C4⋊C4—41no—
594C4⋊C4—41no—
595C4⋊C4—48no—
596C4⋊C4—48no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—41no—
605C4⋊C4—84no—
606C4⋊C4—84no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—84no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—44no—
620C42—44no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23#49914yes—
656C23C2×#12011yescharacteristic
657C23C2×#12111yescharacteristic
658C23#52511yescharacteristic
659C23C2×C4⋊Q811yescharacteristic
660C23#53211yescharacteristic
661C23#53411yescharacteristic
662C23#53611yescharacteristic
663C23C2×#13511yescharacteristic
664C23C2×#13511yescharacteristic
665C23C2×#13511yescharacteristic
666C23C2×#13511yescharacteristic
667C23C2×AGL(1,ℤ/8)11yescharacteristic
668C23C2×#13711yescharacteristic
669C23#57511yescharacteristic
670C23#57511yescharacteristic
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—416no—
693C2×C4—416no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
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—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—81no—
757C2×C4—81no—
758C2×C4—81no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—81no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4#44914yes—
771C2×C4#45214yes—
772C2×C4C2×C22⋊Q811yescharacteristic
773C2×C4C2×C22⋊Q811yescharacteristic
774C2×C4#52511yescharacteristic
775C2×C4#52511yescharacteristic
776C2×C4#53211yescharacteristic
777C2×C4#53211yescharacteristic
778C2×C4#53311yescharacteristic
779C2×C4#53311yescharacteristic
780C2×C4#53911yescharacteristic
781C2×C4#53911yescharacteristic
782C2×C4#54211yescharacteristic
783C2×C4#54211yescharacteristic
784C2×C4D4211yescharacteristic
785C2×C4D4211yescharacteristic
786C2×C4#54611yescharacteristic
787C2×C4#54611yescharacteristic
788C2×C4#54711yescharacteristic
789C2×C4#54811yescharacteristic
790C2×C4D4×Q811yescharacteristic
791C2×C4D4×Q811yescharacteristic
792C2×C4D4×Q811yescharacteristic
793C2×C4D4×Q811yescharacteristic
794C2×C4#55211yescharacteristic
795C2×C4#55411yescharacteristic
796C2×C4#55411yescharacteristic
797C2×C4#55411yescharacteristic
798C2×C4#55411yescharacteristic
799C2×C4#55611yescharacteristic
800C8—24no—
801C8—24no—
802C8—42no—
803C8—42no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22#238811yescharacteristic
820C22#241011yescharacteristic
821C22#241511yescharacteristic
822C22#243411yescharacteristic
823C22#258311yescharacteristic
824C22#266311yescharacteristic
825C22#285711yescharacteristic
826C22C2×#44911yescharacteristic
827C22C2×#45211yescharacteristic
828C22#300211yescharacteristic
829C22#300211yescharacteristic
830C22#305011yescharacteristic
831C22#305011yescharacteristic
832C22#305511yescharacteristic
833C22#305611yescharacteristic
834C22#310211yescharacteristic
835C22#310211yescharacteristic
836C22#310511yescharacteristic
837C22#310811yescharacteristic
838C22C2×#49911yescharacteristic
839C22#316011yescharacteristic
840C22#316511yescharacteristic
841C22#316611yescharacteristic
842C22#316811yescharacteristic
843C22#316811yescharacteristic
844C22#317111yescharacteristic
845C22#317211yescharacteristic
846C22#318811yescharacteristic
847C22#319011yescharacteristic
848C22#319111yescharacteristic
849C22#319111yescharacteristic
850C22#322811yescharacteristic
851C22#323111yescharacteristic
852C22#323211yescharacteristic
853C22#323211yescharacteristic
854C4—24no—
855C4—24no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—161no—
866C4—161no—
867C4#244911yescharacteristic
868C4#244911yescharacteristic
869C4#245211yescharacteristic
870C4#245211yescharacteristic
871C4#246511yescharacteristic
872C4#246511yescharacteristic
873C4#255611yescharacteristic
874C4#255611yescharacteristic
875C2—44no—
876C2#1476311yescharacteristic
877C2#2356911yescharacteristic
878C2#2357211yescharacteristic
879C2#2438211yescharacteristic
880C2#2438311yescharacteristic
881C2#2470411yescharacteristic
882C2#2470511yescharacteristic
883C2#2581211yescharacteristic
884C2#2581511yescharacteristic
885C2#2929811yescharacteristic
886C2#2930011yescharacteristic
887C2#3036011yescharacteristic
888C2#3036111yescharacteristic
889C2#3320811yescharacteristic
890C2#3321811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2059C2semidirect
3. C2×#1942C2semidirect
4. C2×#1941C2semidirect
7. #11385C2semidirect
8. #11325C2semidirect
9. #11208C2semidirect
14. #10880C2semidirect
15. #10880C2semidirect

Maximal subgroups

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

subgroupindex
C2×#28512
C2×#20592
C2×#19422
C2×#19412
C2×C4×C22⋊C82
#146972
#113852
#113252
#112082
#110962
#110952
#108802