Finite Group Databasebeta

← #398676

Subgroups — #398676

Order 512.

1496 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2085C211yesmaximal, characteristic, complemented
2C2×#1808C211yesmaximal, characteristic
3C2×#1807C211yesmaximal, characteristic
4C22×#336C211yesmaximal, characteristic
5#14697C211yesmaximal, characteristic
6#14682C211yesmaximal, characteristic
7#11358C211yesmaximal, characteristic, complemented
8#11325C211yesmaximal, characteristic, complemented
9#11257C211yesmaximal, characteristic, complemented
10#11256C211yesmaximal, characteristic, complemented
11#11220C211yesmaximal, characteristic, complemented
12#11219C211yesmaximal, characteristic, complemented
13#11208C211yesmaximal, characteristic, complemented
14#10721C211yesmaximal, characteristic
15#10721C211yesmaximal, characteristic
16C24×C8C2211yescharacteristic
17C24×C8C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C2×#389C2211yescharacteristic
24C2×#389C2211yescharacteristic
25C2×#385—21no—
26C2×#382C2211yescharacteristic
27C2×#382C2211yescharacteristic
28C2×#380C2211yescharacteristic
29C2×#380C2211yescharacteristic
30C2×#380C2211yescharacteristic
31C2×#380C2211yescharacteristic
32#2085—24no—
33#1808—24no—
34#1807—24no—
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×#336—24no—
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52#1436—21no—
53#1436—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58#1434—21no—
59#1434—21no—
60C22⋊#95—21no—
61C22⋊#95—21no—
62C22⋊#95—21no—
63C24×C4D411yescharacteristic
64C24×C4D411yescharacteristic
65C24×C4C2311yescharacteristic
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—22no—
69C23×C8—22no—
70C23×C8—22no—
71C23×C8—22no—
72C23×C8—22no—
73C23×C8—22no—
74C23×C8—41no—
75C23×C8—41no—
76C23×C8—41no—
77C23×C8—41no—
78C23×C8Q814yes—
79C23×C8Q814yes—
80C23×C8C2311yescharacteristic
81C23×C8C2311yescharacteristic
82C23×C8C2311yescharacteristic
83C23×C8C2311yescharacteristic
84C22×C4⋊C4—21no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C22⋊C4—21no—
95C22×C22⋊C4—21no—
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C42—22no—
99C22×C42—22no—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—41no—
103C22×C42—41no—
104C22×C42D411yescharacteristic
105C22×C42D411yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2311yescharacteristic
108C2×#107—22no—
109C2×#107—22no—
110C2×#107—22no—
111C2×#107—22no—
112C2×#107—41no—
113C2×#107—41no—
114C2×#106—22no—
115C2×#106—22no—
116C2×#106—22no—
117C2×#106—22no—
118C2×#106—41no—
119C2×#106—41no—
120#389—22no—
121#389—22no—
122#389—41no—
123#389—41no—
124#385—44no—
125#382—22no—
126#382—22no—
127#382—41no—
128#382—41no—
129#380—22no—
130#380—22no—
131#380—22no—
132#380—22no—
133#380—22no—
134#380—22no—
135#380—22no—
136#380D414yes—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—22no—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—41no—
164#340—41no—
165#340—41no—
166#340—41no—
167#336—22no—
168#336—22no—
169#336—22no—
170#336D414yes—
171C25C2×D411yescharacteristic
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×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—22no—
188C23×C4—22no—
189C23×C4—22no—
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—41no—
199C23×C4—41no—
200C23×C4—41no—
201C23×C4—41no—
202C23×C4C2×D411yescharacteristic
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D412yes—
208C23×C4C2×Q812yes—
209C23×C4C2×Q812yes—
210C23×C4#4112yes—
211C23×C4#4112yes—
212C23×C4#4112yes—
213C23×C4C2411yescharacteristic
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—28no—
223C22×C8—28no—
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—28no—
237C22×C8—28no—
238C22×C8—44no—
239C22×C8—44no—
240C22×C8—44no—
241C22×C8—44no—
242C22×C8—44no—
243C22×C8—44no—
244C22×C8—44no—
245C22×C8—44no—
246C22×C8—44no—
247C22×C8—44no—
248C22×C8C2×D412yes—
249C22×C8C2×D412yes—
250C22×C8C2×Q812yes—
251C22×C8C2×Q812yes—
252C22×C8C2×Q812yes—
253C22×C8C2×Q812yes—
254C22×C8#4112yes—
255C22×C8#4112yes—
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—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
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⋊C4C2×D412yes—
309C2×C4⋊C4C2×D412yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—44no—
337C2×C42—44no—
338C2×C42—44no—
339C2×C42—44no—
340C2×C42—41no—
341C2×C42—41no—
342C2×C42C2×D412yes—
343C2×C42#4112yes—
344#107—44no—
345#107—44no—
346#106—44no—
347#106—44no—
348#95—24no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—42no—
362#95—42no—
363#95—42no—
364#95—42no—
365#95—42no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24#12112yes—
375C24#12312yes—
376C24C4⋊Q812yes—
377C24#13512yes—
378C24#13512yes—
379C24AGL(1,ℤ/8)12yes—
380C24#13712yes—
381C24C22×D411yescharacteristic
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—28no—
411C22×C4—28no—
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—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—44no—
439C22×C4—44no—
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—41no—
467C22×C4—41no—
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#12112yes—
505C22×C4#12112yes—
506C22×C4#12112yes—
507C22×C4C22⋊Q814yes—
508C22×C4C22⋊Q814yes—
509C22×C4#12312yes—
510C22×C4#12514yes—
511C22×C4#12514yes—
512C22×C4C4⋊Q812yes—
513C22×C4#13512yes—
514C22×C4#13512yes—
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D411yescharacteristic
517C22×C4C22×Q811yescharacteristic
518C22×C4C22×Q811yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4C2×#4111yescharacteristic
521C22×C4C2×#4111yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4H(5,𝔽2)11yescharacteristic
526C22×C4H(5,𝔽2)11yescharacteristic
527C22×C4H(5,𝔽2)11yescharacteristic
528C22×C42−1+411yescharacteristic
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
540C2×C8—22no—
541C2×C8—22no—
542C2×C8—22no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—416no—
548C2×C8—416no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8C22⋊Q814yes—
558C2×C8C22⋊Q814yes—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
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—84no—
592C4⋊C4—84no—
593C22⋊C4—48no—
594C22⋊C4—84no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—44no—
602C42—44no—
603C42—41no—
604C42—41no—
605C42—41no—
606C42—41no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
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#39814yes—
636C23#46314yes—
637C23#46414yes—
638C23#48214yes—
639C23#48514yes—
640C23#49914yes—
641C23#50114yes—
642C23C2×#12111yescharacteristic
643C23C2×#12111yescharacteristic
644C23C2×#12311yescharacteristic
645C23C2×C4⋊Q811yescharacteristic
646C23#53211yescharacteristic
647C23#53411yescharacteristic
648C23#53711yescharacteristic
649C23C2×#13511yescharacteristic
650C23C2×#13511yescharacteristic
651C23C2×#13511yescharacteristic
652C23C2×#13511yescharacteristic
653C23C2×AGL(1,ℤ/8)11yescharacteristic
654C23C2×#13711yescharacteristic
655C23#57511yescharacteristic
656C23#57511yescharacteristic
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
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—416no—
684C2×C4—416no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
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#39814yes—
758C2×C4C2×C22⋊Q811yescharacteristic
759C2×C4C2×C22⋊Q811yescharacteristic
760C2×C4C2×C22⋊Q811yescharacteristic
761C2×C4C2×C22⋊Q811yescharacteristic
762C2×C4C2×#12511yescharacteristic
763C2×C4C2×#12511yescharacteristic
764C2×C4#53311yescharacteristic
765C2×C4#53311yescharacteristic
766C2×C4#54311yescharacteristic
767C2×C4#54311yescharacteristic
768C2×C4#54411yescharacteristic
769C2×C4#54411yescharacteristic
770C2×C4D4211yescharacteristic
771C2×C4#54611yescharacteristic
772C2×C4#54611yescharacteristic
773C2×C4#54611yescharacteristic
774C2×C4#54611yescharacteristic
775C2×C4#54711yescharacteristic
776C2×C4#54811yescharacteristic
777C2×C4#55111yescharacteristic
778C2×C4#55111yescharacteristic
779C2×C4#55111yescharacteristic
780C2×C4#55111yescharacteristic
781C2×C4#55211yescharacteristic
782C2×C4#55211yescharacteristic
783C2×C4#55311yescharacteristic
784C2×C4#55311yescharacteristic
785C2×C4#55311yescharacteristic
786C8—24no—
787C8—24no—
788C8—42no—
789C8—42no—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—24no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—24no—
804C22#208518yescomplemented
805C22C2×#39811yescharacteristic
806C22#241211yescharacteristic
807C22#241611yescharacteristic
808C22#249811yescharacteristic
809C22#254311yescharacteristic
810C22#265911yescharacteristic
811C22#285711yescharacteristic
812C22C2×#46311yescharacteristic
813C22C2×#46411yescharacteristic
814C22#303511yescharacteristic
815C22#303511yescharacteristic
816C22#305011yescharacteristic
817C22#305011yescharacteristic
818C22#305511yescharacteristic
819C22#305611yescharacteristic
820C22C2×#48211yescharacteristic
821C22C2×#48511yescharacteristic
822C22#309111yescharacteristic
823C22#309111yescharacteristic
824C22C2×#49911yescharacteristic
825C22#316011yescharacteristic
826C22C2×#50111yescharacteristic
827C22#316211yescharacteristic
828C22#316811yescharacteristic
829C22#316811yescharacteristic
830C22#318011yescharacteristic
831C22#318111yescharacteristic
832C22#318811yescharacteristic
833C22#319011yescharacteristic
834C22#319111yescharacteristic
835C22#319111yescharacteristic
836C22#324711yescharacteristic
837C22#324811yescharacteristic
838C22#325011yescharacteristic
839C22#325011yescharacteristic
840C4—24no—
841C4—42no—
842C4—42no—
843C4—42no—
844C4—42no—
845C4—82no—
846C4—82no—
847C4—161no—
848C4—161no—
849C4—161no—
850C4—161no—
851C4—161no—
852C4—161no—
853C4#243711yescharacteristic
854C4#243711yescharacteristic
855C4#243811yescharacteristic
856C4#243811yescharacteristic
857C4#244211yescharacteristic
858C4#244211yescharacteristic
859C4#256911yescharacteristic
860C4#256911yescharacteristic
861C2—28no—
862C2#1476611yescharacteristic
863C2C2×#208511yescharacteristic
864C2#2365611yescharacteristic
865C2#2455411yescharacteristic
866C2#2455511yescharacteristic
867C2#2475411yescharacteristic
868C2#2475511yescharacteristic
869C2#2785911yescharacteristic
870C2#2786011yescharacteristic
871C2#2857311yescharacteristic
872C2#2857611yescharacteristic
873C2#3029211yescharacteristic
874C2#3029411yescharacteristic
875C2#3320811yescharacteristic
876C2#3321711yescharacteristic
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
1. C2×#2085C2semidirect
7. #11358C2semidirect
8. #11325C2semidirect
9. #11257C2semidirect
10. #11256C2semidirect
11. #11220C2semidirect
12. #11219C2semidirect
13. #11208C2semidirect
804. C22#2085semidirect

Maximal subgroups

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

subgroupindex
C2×#20852
C2×#18082
C2×#18072
C22×#3362
#146972
#146822
#113582
#113252
#112572
#112562
#112202
#112192
#112082
#107212